Cities and Regions as Self-organizing Systems: Models of Complexity (Environmental Problems & Social Dynamics Series, Vol 1)

Cities and Regions as Self-Organizing Systems

Environmental Problems and Social Dynamics

A series of books edited by Peter M.Allen, Cranfield University, Cranfield, UK and Sander E.Van der Leeuw, Université de Paris, Paris, France. Volume 1 Cities and Regions as Self-Organizing Systems: Models of Complexity Peter M.Allen In preparation: Volume 2 Environmental Management in European Companies: Case Studies and Evaluation Jobst Conrad This book is part of a series. The publisher will accept continuation orders which may be cancelled at any time and which provide for automatic billing and shipping of each title in the series upon publication. Please write for details.

Cities and Regions as SelfOrganizing Systems Models of Complexity Peter M.Allen Cranfield University, Cranfield, UK

LONDON AND NEW YORK

First Published 1996 by Gordon and Breach Science Publishers. This edition published in the Taylor & Francis e-Library, 2005. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/. Copyright © 1997 OPA (Overseas Publishers Association) Amsterdam B.V. Published in The Netherlands under license by Gordon and Breach Science Publishers. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, elec tronic or mechanical, including photocopying and recording, or by any information storage or retrieval system, without permission in writing from the publisher. British Library Cataloguing in Publication Data Allen, Peter M. (Peter Murray), 1944– Cities and regions as self-organizing systems.— (Environmental problems and social dynamics; v. 4) 1. Cities and towns 2. Regional planning 3. Community organization I. Title 307.7′6 ISBN 0-203-99001-3 Master e-book ISBN

ISBN 90-5699-071-3 (Print Edition)

TABLE OF CONTENTS

FOREWORD

viii

PREFACE

xii

ACKNOWLEDGEMENTS

xvi

1. Towards a Science of Complex Systems

1

INTER-URBAN EVOLUTION 2. Dynamic Models of Urban Growth

29

3. Urban Growth, Commuting and Regional Structure

52

4. Intervening in the System

81

CASE STUDIES AND FURTHER DEVELOPMENTS 5. Modelling the Long Term Structural Changes in the United States

107

6. The Spatial Evolution of Jobs and People in Belgium

133

7. The Sénégal Model

158

INTRA-URBAN EVOLUTION 8. A Simple Model of Intra-Urban Evolution

207

9. Towards Reality—Brussaville

224

10. A Town Like Brussels POLICY EXPLORATION AND DECISION SUPPORT FOR SUSTAINABLE DEVELOPMENT

234

11. An Integrated Framework for Exploring Sustainable Development

254

12. Self-Organizing Models in Urban and Regional Science

259

13. Conclusions

283

APPENDIXES

293

REFERENCES

297

INDEX

304

FOREWORD

Is the future given? Is nature ruled by deterministic laws? These questions have fascinated me for decades. It was often admitted that the human world was contingent while nature was not. This seemed to be the unavoidable consequence of the laws of nature as formulated by Newton and extended in the 20th century through quantum mechanics and relativity. As is well known, Newton’s laws are associated with determinism and time symmetry. Determinism means that if we know the present we could predict the future as well as calculate the past. Time reversibility means that present and future play the same role. There is no way to include ‘becoming’ into this picture of nature. The universe is, it does not become. Certainly this picture has a great appeal but there is a high price for it. Creativity and novelty become illusions. The preface I am writing at this very moment would have been preprogrammed at the moment of the big bang. Reason is identified to certainty and ignorance to probability. In spite of all the success of western science, this is a pessimistic view of the universe which leads to the cartesian dualism and therefore also to a dualism in human culture. In the 19th century a different concept of nature was proposed, a concept of nature based on the famous second law of thermodynamies, the law of increase of entropy. But what does this entropy mean? In a recent movie based on the highly popular book by Stephen Hawking, A Brief History of Time, a simple example is proposed. Suppose we take a cup of tea and throw it on the ground: it breaks. Instead of a single unit, the cup of tea, we have many pieces: this corresponds to the appearance of ‘disorder’. The essence of the second law would be precisely in that appearance of disorder, but can this be the whole story? It is true that we occasionally break some chinaware but surely we produce more cups than we break. Is then the production of cups an anti-entropic event? This would again be a deeply pessimistic view as the only predictable state of the universe would be the state of maximum disorder, the ‘heat death’. Fortunately we begin to overcome these pessimistic views. As early as in 1945 we have shown that there are ordering processes associated with non-equilibrium. In many situations irreversibility leads to order (think about a mixture in a vessel heated on one side and cooled on the other, one component is enriched at the cold side, the other at the hotter side), but at equilibrium, as well as close to equilibrium, there are optimization principles such as the minimum of free energy. As a result the system is stable, fluctuations are followed by a response which brings the system back to the minimum. It was therefore quite unexpected that this is no longer true in ‘far from equilibrium’

situations. Then there, is in general, no optimization principle and fluctuations can grow. There are bifurcation points at which new solutions the evolution equations may emerge. Which solution will emerge is determined by fluctuations and is not submitted to deterministic laws. We come to the concepts of ‘self organization’ of ‘dissipative structures’ and to ‘order through fluctuations’. Today one often speaks of the science of complexity to describe this field of science in which systems may take different structures according to the nature of the environment and especially to distance from equilibrium. Peter Allen came to Brussels in 1969 to study statistical mechanics but he was so fascinated by the new science of complexity that he changed his field of research. He was right. Indeed the importance of complex systems analysis for socio-economic and sociocultural systems can hardly be overstated. Such systems are indeed composed of multiple, interacting units, characterized by the emergence and evolution of nested hierarchical organization and structure, and complex spatio-temporal behaviour. Furthermore, in addition to the kind of complexity exhibited by non-linear dynamical systems with fixed microscopic interaction mechanisms, socio-economic and socio-cultural systems are composed of individual elements capable of internal adaptation and learning as a result of their experience. This adds an additional level of complexity to that of non-linear dynamics of traditional physical systems, but one which is shared with evolutionary biology and ecology. Contrary to molecules, the actors in a physico-chemical system, human beings develop individual projects and desires. Some of them stem from anticipations about how the future might reasonably look and from guesses concerning the desires of the other actors. The difference between desired and actual behaviour therefore acts as a constraint of a new type which together, with the environment, shapes the dynamics. Some early ideas in this direction were explored in my own work with Robert Herman on vehicular traffic flow, where the difference between desired and observed distribution behaviour was introduced into the models, in order to calculate traffic flows. Professor Allen’s book however, explores the application of the new paradigm to the much more general issue of the evolution and change of spatial organization in the patterns of human settlement and economic activities. Much of this work was carried out while the author was working at the University of Brussels, where a small interdisciplinary group was established. As a result of this collaboration, also involving Michele Sanglier, Francoise Boon, Guy Engelen, Isabelle Stengers and others, the ideas of ‘order by fluctuation’ that were becoming established in the physical sciences were shown to be important in the domain of spatial organization of human activities. Instead of the spatial structure of urban centres, and of regions being either ignored, or considered as fixed, these models demonstrated the importance of spatial organization, and showed that it was linked to technological progress (for example, of transportation) and energy costs to cultural factors and historical events, and also policy decisions of various kinds. So, instead of seeing the geographical patterns of economic activity and settlement as being fixed, the models and studies presented here demonstrate that these can be generated by non-linearities of the interactions between local actors together with their social and cultural preferences, and that they affect in their turn the functional organization and effectiveness of the economic system, and the opportunities and pressures that fashion people’s preferences. In other words, they show

that cities and regions are ‘self-organizing’ systems, where the interplay of system feedbacks and historical events shape the evolutionary process, and both the overall performance and the multiple local experiences that emerge. The book describes the successive stages of development of dynamic models relevant to regional and then urban structures, giving a clear methodological and philosophical introduction to complexity theory as applied to spatial self-organization. It contains a detailed series of case studies compiled over a number of years, which demonstrate the importance and potential usefulness of the work as the basis for policy exploration and decision support over a whole range of issues. In the final chapters of the book, Peter Allen discusses the many implications of this new perspective, where structures and processes are linked through a nested hierarchy of scales which link the microscopic level through successively larger scales to the biosphere itself. He also describes how the spatial models of human decision-making and economic activities, can be coupled to the natural resources of water, soils and vegetation to provide the basis of a truly integrated book for strategic policy exploration with regard to sustainable development. He also stresses the idea of modelling, not in order to make firm predictions, but instead as a systematic manner of learning about reality, by at least developing a model that can generate for itself the trajectory of the system in the past. In conclusion, this book brings together the application of complex systems theory to the spatial evolution of patterns of human settlement and economic activity. It explores the manner in which spatial variabilities and detail can generate structure and break symmetries, and is inherently multidisciplinary, stressing the richness of individual diversity, and the manner in which complexity builds on itself in a succession of symmetry breaking transformations. It also provides us with a real understanding of the ideas that underlie the ‘invisible hand’ of Adam Smith, but instead of this leading inevitably to an optimal solution in a free market, we see that there is, as in physics, no universal optimization principle for complex systems, that many futures are possible, and that they differ from each other qualitatively, so that any useful strategic policy exploration needs to be able to view these possible futures. This is the purpose of the methods that are set out here. Professor Allen’s book is most timely as, traditionally, western thought was dominated by the split into ‘two cultures’ to use the terminology of C.P.Snow. The recent progress associated with the science of complexity is overcoming this duality. Peter Allen’s work is an important contribution to the new dialogue between human sciences and concepts which originated in the natural sciences. I am convinced that Peter Allen’s book will be received with the attention it deserves. I.Prigogine, Nobel Laureate in Chemistry Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems, University of Texas, Austin, Texas et Instituts International de Physique et de Chimie, fondes par E.Solvay, U.L.B., Bruxelles, Belgique

PREFACE

This book is based on research work that began in 1976, at the Université Libre de Bruxelles, and which attempted to model the emergence and evolution of geographic structure, patterns of settlement and of economic activity that form urban and regional hierarchies. The research was based upon the concepts of ‘self-organizing’ systems that were developed particularly by Ilya Prigogine and his group at the Free University of Brussels. I was involved in the formation of a small interdisciplinary group with Michele Sanglier, Guy Engelen, Francoise Boon, Jean-Louis Deneubourg, Isabelle Stengers and Serge Pahaut, with the general aim of investigating the importance of the ideas of nonlinear dynamics and self-organizing systems in providing a new basis for understanding human systems. The work described here stems from this beginning. This was encouraged by the support given by David Kahn, Frank Hassler and then Bob Crosby from the US Department of Transportation, who saw the potential interest of such research, and what is rarer, were willing and able to support it. Their support, interest and encouragement was absolutely crucial to the initial development of the ideas, and Bob Crosby remained involved and helpful long after the election of Ronald Reagan put an end to official support, and indeed to much Agency sponsored research in the US. Another form of encouragement came from Denise Pumain and her group in Paris, who were interested in our approach and began to examine applications to French data, and also to make comparisons with other approaches. These studies were reported in several books and theses, and our collaboration has continued more recently as part of a large team under the European funded Archaeomedes Project, concerning desertification along the Mediterranean coast as a result of continuing urbanization and over-exploitation of natural resources. In the early 1970s the Brussels group had begun to show how the structural evolution of complex systems actually occurred as the result of a ‘dialogue’ between the average behaviour of a system, and the fluctuations around these average values. These ideas, the concept of systemic self-organization, gradually provided a new basis for understanding change and evolution. Of course, as often happens in science at about the same time a number of other groups were also working on the development of these exciting new ideas. Also coming from the direction of physics and chemistry were Herman Haken and the ‘Synergetics’ school starting originally from laser theory, and the application of the ideas to social systems was, and still is, being explored by Wolfgang Weidlich, Gunter Haag and colleagues. From biochemistry came important research by Manfred Eigen who

was concerned particularly with the origin of life, Benno Hess and Peter Schuster. From mathematics there was the work of René Thom on ‘Catastrophe Theory’, and on nonlinear dynamics, the work on chaos and complexity was also beginning, with Edward Lorentz, David Ruelle, and many others. Benoit Mandelbrot was laying the foundations of Fractal Theory, and from mathematical ecology Robert May was discussing complexity and chaos. In short it was an exciting time. Today, articles on subjects such as ‘chaos theory’ and ‘positive feedbacks in the economy’ are now featured in the popular press, and these are the fruits of the revolution that was brewed in the mid-seventies. The underlying issue is that of time and irreversible change, or conversely, the emergence and evolution of structure and organization. While this is not the main focus of this book, the ideas of Ilya Prigogine concerning change and emergence are the inspiration and scientific base from which the work discussed here springs. Despite the fascinating general questions that are raised however, this volume is restricted to issues of geographic, regional and urban change, and with the environmental systems in which these are embedded. Mathematical models are developed which attempt to simulate the evolution of towns and cities, and the complicated co-evolutionary interaction there is both between and within them. The aim of these models is to help policy analysis and decision making in urban and regional planning, energy policy, transport policy and the many other areas of service provision, infrastructure planning and investment that are necessary for a successful society. The models attempt to show how urban and regional structure evolves and changes as a result of the multiple decisions of the inhabitants, made according to individual goals and circumstances, yet each changing the circumstances and goals of others. Spatial self-organization based on human decisionmaking involving cultural, social, economic and environmental factors is the core of the models. This leads eventually to an integrated decision support framework, bringing together economics, demography, environmental and the sociocultural aspects, an integration that is indispensable for planning development and formulating investment policy, for assessing the impacts of proposed policy and regulations and for understanding the impacts of new technology. The first chapter reviews briefly the ideas in chemistry and physics that sparked the scientific research that follows. It concerns how the idea of ‘self-organization’ occurred in chemistry and physics, and explains in some detail the underlying microscopic processes that are involved. It underlines the fact that models based on the deduction of ‘differential equations’ or of System Dynamics, are in fact only approximations to reality. Underneath them is the richer, more difficult, microscopic reality of diversity and individual subjectivity, which in fact provides the basis for the adaptive responses of the system, and its creativity. As we see in this first chapter, moments of instability and structural change in a system are precisely when the macroscopic average description breaks down, and instability emerges from the individuals and local events within the system. In chapters 2 and 3 the structure of real settlement patterns is discussed, in order to establish what kind of results a successful self-organizing model should produce. Simple theoretical models of settlement pattern and economic activities are developed which attempt to capture the complex effects of interaction between the different actors of the system, and the transportation and service infrastructure, frontiers and political divisions,

and in chapter 4 we show how theoretically the integrated system can be used for policy analysis and decision support. In chapters 5 to 7, different case studies are presented. In the first, a simple model was developed of the changing populations of the States of the USA. This explored how a changing ‘base employment’ would induce realistic patterns of migration and selforganization of the rest of the economic activities. In the next example, a much more serious attempt is made to model the changes in the pattern of economic activities (in terms of standard sectors) and population in the different Provinces of Belgium. The model is shown to be reasonably successful in its attempt, but also to have some shortcomings. These are addressed in the next chapter which develops a model of Senegal which links economic activities, demography and migration, and environmental factors within a very ‘simple to use’ interactive framework. This model and framework were developed in collaboration with Guy Engelen who is now at the RIKS Institute in Maastricht. In chapters 8 and 9, ‘intra-urban’ models are developed which were designed to provide a basis upon which simulations could be carried out to explore the possible effects and consequences of planning concerning land-use, transportation, the location of Business Parks, sewage works etc. A model which is based on Brussels is described in chapter 10, and some examples are given of how the approach can be used to explore real policy issues of investment, transportation, the impacts of information technology and changing energy costs. In chapter 11 a general review is made, where the steps and lessons involved in the work are clarified. In particular, a description of the ‘decision modelling’ approach is given, together with a reflection on the multi-scalar, hierarchical nature of the emergent structures in such systems. A method for correctly aggregating decision models at successive scales is then made, showing how different scales of phenomena can be correctly nested in a model. A reflection is made concerning the ideas and concepts underlying the work, and of the new point of view to which it leads. Instead of seeing the world in clear and rational terms, where optimal decisions can be sought within a set of clear objectives and goals, we find that when the medium and longer term changes are considered, together with their inherent uncertainty, then any fixed set of goals and objectives are seen to be temporary, and strategies concerned with maintaining flexibility, the capacity to adapt and respond become much more important. Future energy prices, environmental considerations and indeed desired future lifestyles are not predictable phenomena, and therefore the use of decision support methods which make specific assumptions about future trends can be damaging and wasteful in the long term. The approach that this work represents, that of ‘complex systems’ dynamics, is one of using models to learn about the system, and explore possible futures. These models are not supposed to be predictive, but instead should encompass present wisdom about the mechanisms that operate and the values of people that underlie the behaviours exhibited within the system. They may tell us perhaps, where the system would evolve to if none of these change, or if they change in a specified way. An important use is that of estimating the ‘probability’ of different possible outcomes, and hence the potential ‘risk’ involved by the pursuit of a particular policy. Of course, these models can also be used as a basis for planning the development of a region or city towards some desired goal. But of course the models cannot tell us what these goals

should be. They can serve, however, to show us what might be possible, and how an end might be achieved and, perhaps more importantly, can show that there are internal contradictions in the system which will prevent the achievement of certain idealized goals. It is a useful role if this prompts people to discuss the choice between the real options open to them, and not imaginary, oversimplified and unattainable ends. Again, the ‘self-organizing’ ideas on which the modelling is based underline the concept of choice both in the present and the future, and one outcome of this kind of approach is therefore to focus attention more on the idea of keeping options open, and diversity in the system, than trying to attain collective, pre-defined goals reflecting ‘quality of life’. These models attempt to go beyond the purely mechanical view of traditional mathematical models. They see the system in terms of a constant co-evolution of the individual micro-actors with the structure, the non-linear dynamical system, that is born out of their collective interaction. The aim here is therefore to try to put back some of that creativity into the system so that our models contain the capacity to respond, as people do, to changes, opportunities and to regulation. It is a tool for imagining possible futures for the system.

ACKNOWLEDGEMENTS

I should like to thank many people who have contributed to the work described here. Firstly, my many friends and colleagues at Brussels; Ilya Prigogine, Gregoire Nicolis, Francoise Boon, Jean-Louis Deneubourg, Isabelle Stengers, Serge Pahaut and many others. In particular, of course thanks to Michelle Sanglier who worked with me from 1976 until 1990 in developing the urban and regional models, and also to Pierre Kinet who drew many of the figures in those days before easy PC graphics. Thanks also to the inspiration and financial support of the early years given by Dave Kahn, Frank Hassler and then by Bob Crosby at the US Department of Transportation. Thanks to Guy Engelen initially in Brussels and now with his group at RIKS in Maastricht. Also, I am most grateful for the continuing collaboration of Denise Pumain, Lena Sanders and the group at Paris. Their interest, support, knowledge and ideas have been and are an important factor in the continuation of the work. Thanks also to DGVIII at the European Commission for their support of the Sénégal project, and of DGXII for their support for the research into Integrated River Basin Models, and then of the Archaeomedes and Ermes Projects. In this context I would like to thank Sander Van der Leeuw and James McGlade for many interesting discussions and ideas. In 1987 I had the opportunity to join the International Ecotechnology Research Centre at Cranfield University, and to attempt to help develop a multi-disciplinary research centre whose aim was to provide policy and decision relevant research, advice and understanding for strategic planning and decision making in their ecological, economic, social and technological contexts. The ideas presented in this book provide some basis for this, linking ‘hard modelling’ to social enquiry, issues of technological and organizational change, and other areas of expertise within the Centre. Successful synergies seem to be occurring, and for this I should like to thank my colleagues at the IERC: in particular, Martyn Cordey-Hayes, Roger Seaton, Mark Lemon and Mark Strathern, for their help and contributions to the development of this work. Thanks also to Chico Perez-Trejo, Norman Clark and Mike Lesser for their collaboration and help, as well as to my students whose Ph.D. theses contributed to the work described here, Ana Saez and Fabienne Leloup. Finally, I should like to thank my parents for making it all possible, and most of all to thank my wife, Francine, who contributed through many discussions to the development of the ideas and models described here, and whose support and patience allowed me to

devote so much time to working, travelling, programming, attending conferences and meetings, discussing and even occasionally thinking.

1. TOWARDS A SCIENCE OF COMPLEX SYSTEMS 1.1 INTRODUCTION Since the great work of Newton, the mechanical vision of the world has been the basis of our understanding. Even though sub-atomic and atomic physics were revolutionized by quantum physics, the mechanical vision remained paramount in our comprehension of events at the level of our everyday experience. This means that we explain things on the basis of ‘causal mechanisms’, where components influence each other and form systems, in which the change seen in one part is explained by change in another, or in the external environment in which the system is embedded. These mechanisms could be written down as mathematical equations, as mathematical models expressing fundamental laws of nature, and then used to predict behaviour. The paths traced by the system from any given initial state were pre-determined by the equations and therefore it was believed that surprise could only come from the outside. However, although this might have seemed reasonable for mechanical systems before the recognition of deterministic chaos, in human systems it does seem at odds with everyday experience. For many people, the key choices of career or partner hinge upon events which are intrinsically extremely improbable, and as economists and politicians would agree, changes and trends in society are very difficult to anticipate correctly. Why are human systems different? To see why, let us imagine a very simple human situation, for example, of traffic moving along a highway or of pedestrians milling around a shopping centre. Clearly, movements cannot be predicted using Newton’s laws of motion because acceleration, change of direction, braking and stopping occur at the whim of each driver or pedestrian. Newton’s laws, the laws of physics, are obeyed at all times by each part of the system, but, despite this, they are not of help in predicting what will happen because the decision to coast, turn, accelerate or brake lies with the human being. Planets, billiard balls, and point particles are helpless slaves to the force fields in which they move, but people are not! People can switch sources of energy on or off and can respond, react, learn and change according to their individual experience and personality. This of course poses some fundamental questions: how can ‘choice’ and ‘freedom’ arise in living systems (assuming they do)? If they do not arise in ‘mechanical’ systems, does it mean that living systems are not mechanical? But, if they are not mechanical, then what are they? In this volume we explore how the new ideas emerging originally from the physics of open systems (ones which exchange energy and matter with their surroundings) begin to answer these questions, and of more practical interest, how they can be used to

Cities and regions as self-organizing systems

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understand the emergence and evolution of spatial pattern and structure in human systems. They offer a new understanding of the origins, and evolution of patterns of human settlement and land-use, as well as urban growth and structure. Our example of the highway traffic or pedestrian precinct shows us that there is a critical difference between asking whether a system obeys the laws of physics or whether its behaviour can be predicted from a knowledge of those laws. Only when the energy and momentum of the elements of a system obey a precise unvarying law is prediction possible. In the case of the human systems such as those above, clearly, the autonomy of the actors, and their ability to add and subtract energy to the system according to their own wishes is what makes prediction impossible unless we can find some fixed rules of behaviour, or some fixed ‘goal’ from which behaviour can be derived. This latter basis would suppose that the people concerned could correctly infer what behaviour they should have in order to attain their goals, and this of course is open to considerable doubt. Prediction would rely on such clarity of vision however, as well as there being no interaction between behaviours, and indeed between goals. Prediction concerning a car that has run out of fuel is much easier—it will slow down and eventually stop! But living systems with access to reserves of energy are not like this. People have choices and can make decisions. Even if an individual knows exactly what he would like to achieve, then if this involves other people, because he cannot know with certainty how everyone else will respond, he can never calculate exactly what he must do. He must make his decision, and see what happens, being ready to take corrective actions, if necessary. Since, in society, on the road and in the shopping centre we are all making these kinds of decisions, simultaneously, all the time, it is not surprising that occasionally there are accidents, or that such systems run in a ‘non-mechanical’ way. An important point to remember here is of course that human beings have evolved within such a system and therefore that the capacity to live with such permanent uncertainty is quite natural to us. It may even be what characterises the living. However, it also implies that much of what we do may be inexplicable in rational terms. In trying to bring the power of science to the understanding of human systems, understandably, these complexities were initially ignored. It was assumed that if someone knew what he wanted, then he could get enough information to make sure that his choice led to that goal. This course led directly to rational man and in the limit homo economicus where observed behaviour was supposed to be derived from the individual’s definition of his goals—his ‘utility’, usually expressed in monetary terms. By assuming a fixed form for this ‘utility’, the behaviour of the individual could be ‘predicted’ in changing circumstances, and the system could thus be made ‘deterministic’. In this way, mathematical models could be built describing similar individuals faced with a series of choices and predictions concerning, for example, residential or economic location choices, or shopping centre hinterlands. But these predictions used inferred ‘utilities’ which were based on observed structures, assuming tacitly therefore that everyone was fully satisfied, and the system was at equilibrium. This does not seem a promising basis for studying and understanding change, since this could not come from any pent up desire within the system, but only as a result of some external influence. This vision of equilibrium, and this machine-like image of individuals and organizations with clear and unique responses to events that are perceived with absolute clarity is, of course, not one that normal people would readily recognise as corresponding

Towards a science of complex systems

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to reality. People in real life seem much less clear about their choices, as well as seeming changeable according to their mood, and even when they are clear, the outcomes that ensue are often not what they expected. This ‘over rational’ approach has been softened but not fundamentally changed by statistical models of decision processes where the probability of making a particular choice is proportional to the expected utility derived. This gives rise to probabilistic behaviour for individuals and deterministic behaviour for sufficiently large populations. However, this simple approach ignores the fact that decisions made by individuals are not really independent of each other, and that there is an effect of the communication between individuals. Fashions, styles and risk minimising strategies affect collective behaviour considerably, and mean that it cannot be derived necessarily as the sum of independent, individual responses. Another problem is that we can only calibrate (put a value to) ‘utility functions’ by ensuring that they ‘reproduce’ observed behaviour, and without some independent determination of the ‘goals’ people have, then the modelling process is in danger of circularity approaching tautology. What is required if we are to ever understand human systems is some new approach which accepts that people interact and that their ‘utilities’ are linked in a complex, coevolutionary fashion. In addition we need to understand how we can ever write mathematical models which can capture such phenomena and in which structural changes can occur and new behaviours can emerge, going beyond the mechanical vision of classical science. 1.2 DETERMINISM, SELF-ORGANIZATION AND EVOLUTION In order to try to set up a conceptual framework within which these complexities can be considered let us step back and consider the process of ‘modelling’ itself. By considering this from first principles we can begin to see the assumptions involved in the mechanical representation of the world, and how we may hope to improve upon this with the new ideas of self-organizing and evolving systems. If we examine a region, and consider the remains of populations and artifacts that litter the landscape, then after dating and classifying them, an evolutionary tree of some kind emerges, possibly with discontinuities suggesting disaster and invasion, but nevertheless suggesting a changing set of activities and behaviours, that have occupied the site over time. Development concerns the introduction and growth of new activities, and the successful mutual adaptation of the landscape and the population to these changes, leading to their maintenance and continued development. In order to provide decision support for the planning and implementation of development policies we must have models that can capture the creative dialogue between new investments and infrastructure and the chain of responses of the populations and of the environment these. Development is about structural change on many scales, from the patterns of thought and habits of the inhabitants, to the patterns of intra and inter-regional and world trade and commerce. Models can be thought of in terms of a hierarchy, where increased ‘simplicity’ of understanding and predictive capability is obtained by making increasingly strong assumptions, which may be increasingly unbelievable. On the left of Figure 1.1 we have

Cities and regions as self-organizing systems

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Figure 1.1 Understanding results from bounding the domain of interest, classifying the contents and their interactions, and then making assumptions which can lead to deterministic, self-organizing or evolutionary models. ‘reality’. It makes no assumptions, and is drawn as a cloud, since we can say little about it other than that it includes all detail of everything, everywhere, as well as all perceptions and all points of view. However, from experience and intuition concerning the ‘problems’ that we want to address, we may construct an initial set of taxonomic rules concerning the differences and similarities of the objects, together with their dates, which leads to the construction of an ‘evolutionary tree’, showing that species, behaviours, forms, or artifacts emerged and evolved over time. The rules of classification that we use result from previous experience about such systems and what matters in them. Are there socio-economic ‘types’? Do firms of the same sector and size behave similarly? What is a sector? Is there as much variation within a group as between groups? Whatever the precise arguments advanced, in order to ‘understand’ a situation, and its possible outcomes, we do classify the system into components, and attempt to build mathematical models that capture the processes that are increasing or decreasing these different components. In order to build mathematical models, we identify the different objects or organisms that are present at a particular moment and attempt to write down the mechanisms describing the increase and decrease of each type. We apply the traditional approach of physics, which is to identify the components of a system, and the interactions operating

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on these, both to and from the outside world and between the different populations of the system. By considering the demographic, economic and environmental processes in play at a given time, a mathematical model can be produced which appears to offer deterministic predictions concerning the future, assuming different possible policies or exogenous events. However, as we see clearly from our broader picture of the ‘evolutionary tree’, the predictions that such a model gives can only be correct for as long as the qualitative structure of the system remains unchanged. Development concerns particularly the emergence of new spatial organization, new activities and behaviours, and the structural changes that these lead to. The mechanical model of deterministic equations, the System Dynamics, that we can construct at any given time has no way of producing ‘new’ types of objects, new variables, and so the ‘predictions’ that it generates will only be true until some moment, unpredictable within the model, when there is an adaptation or innovation, and new behaviour emerges. In recent research new models have been developed (Allen, 1992, 1993, 1994) which can generate a true structurally changing evolution, with new entities and activities appearing. However, the relationship between these ‘evolutionary’ models and the more conventional ones has not been made clear, and a clarification of this will be one of the aims of this first section. The conceptual framework of Figure 1.1 allows us to understand the relationship between different modelling techniques used to provide decision support, in terms of the assumptions that underlie them. We compare the assumptions made by different approaches to policy exploration and planning, such as static optimization models, evaluations based on short term cost/benefits, and the difficulties involved in long term, complex simulations. Clearly, the evolutionary tree reflects the changing structure of the system, with different variables, over the long term, as different types of actor emerge, flourish and then disappear or change. In the short term, however, we can identify the different objects or actors that are present, and write down some ‘system dynamics equations’ describing the mutual interaction of the different actors present. In other words, in describing the short term we can apply the traditional approach of physics (Prigogine and Stengers, 1987; Allen, 1988), which is to identify the components of a system, and the interactions operating on these, both to and from the outside world and between the different populations of the system. In ecology, this will consist of birth and death processes, where populations give birth at an average rate if there is enough food, and eat each other according to the average rates of encounter, capture and digestion. In economics, the macroscopic behaviour of the economy is assumed to result from the aggregate effects of producers attempting to maximise their profits, and of customers attempting to maximise their utility. Such a model expresses the behaviour or functioning of the system, given its structure, but does not ‘explain’ why this structure is there. In order to do this, we must try to understand and ‘model’ the evolutionary tree of successive structures. In order to do this, let us consider carefully the assumptions that have to be made in order to arrive at a description in terms of system dynamic equations. Such systems are characterized by dynamical equations of the type:

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(1.1)

where G, H, and J are functions which will in general have non-linear terms in them, leading to changes in x, y and z which are not simply proportional to their size. Also, these functions are made up of terms which involve variables x, y and z and also parameters expressing the functional dependence on these. These parameters reflect three fundamentally different factors in the working of the system: – the values of external factors, which are not modelled as variables in the system. These reflect the ‘environment’ of the system, and of course may be dependent on spatial coordinates. Temperature, climate, soils, world prices, interest rates are possible examples of such factors. – the effects of spatial arrangement, of juxtaposition, of the entities underlying the system. – the values corresponding to the ‘performance’ of the entities underlying x, y or z, due to their internal characteristics like technology, level of knowledge or strategies. These three entirely different aspects have not been separated out in much of the previous work concerning non-linear systems, and this has led to much confusion. Equations of the type shown above display a rich spectrum of possible behaviours in different regions of both parameter space and initial conditions. They range from a simple approach to a homogeneous steady state, characterized by a point attractor, through that of sustained oscillation of a cyclic attractor, to the well known chaotic behaviour characteristic of a strange attractor. These can either be homogeneous, but, much more importantly, they can involve spatial structure as well, and the phenomena of self-organization can be seen as the adaptive response of a system to changing external conditions, even if it is viewed as having fixed attributes for its microscopic entities. In other words, we shall see that self-organization is a collective, spatial response to changing conditions rather than an evolutionary response on the part of its constituent individuals. In order to see this let us first consider the assumptions that are made in deriving system dynamics equation such as in 1.1. In the complex systems that underlie something like the ‘economy’, there is a fundamental level which involves individuals and discrete events, like making a widget, buying a washing machine, driving to work etc. However, instead of attempting to ‘model’ all this detail, these are treated in an average way, and as has been shown elsewhere (Allen, 1990), in order to derive deterministic, mechanical equations to describe the dynamics of a system, two assumptions are required:

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– events occur at their average rate (Assumption 1) – all individuals of a given type, x say, are identical and of average type (Assumption 2) The errors introduced by the first assumption can be corrected by using a deeper, probabilistic dynamics, called the ‘Master Equation’ (Wiedlich and Haag, 1984) which while retaining assumption 2, assumes that events of different probabilities can and do occur. So, sequences of events which correspond to successive runs of good or bad ‘luck’ are included, with their relevant probabilities. As has been shown elsewhere (Allen, 1988) for systems with non-linear interactions between individuals, what this does is to destroy the idea of a trajectory, and gives to the system a collective adaptive capacity corresponding to the spontaneous spatial reorganization of its structure. Without going to the mathematical rigour of the Master Equation, its effects can be imitated to some degree by simply adding ‘noise’ to

Figure 1.2 The hierarchy of modelling. Deterministic and Selforganizing models assume that the underlying subsystems are ‘fixed’ in nature, while an evolutionary model attempts to deal with possible changes at that level as well. the variables of the system, so that the noise can search out different spatial arrangements which may be stable under the new conditions. In other words, self-organization can be

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seen as the adaptive response to changing external conditions, and may be greatly enhanced by adding noise to the deterministic equations of system dynamics. The fact is that unpredictable runs of good and bad luck, represented by ‘noise’, will occur, and this means that the precise trajectory of the system does not really exist in the future. Also, the fact of these deviations from the average rate of events, noise, means that a real system can ‘tunnel’ through what would be impassable barriers for the system without noise (the deterministic separatrices in state space), and can switch between attractor basins and explore the global space of the dynamical system in a way that the deterministic system dynamics would not itself predict. Let us now make the distinction between self-organization and evolution. Here, it is the assumption 2 that matters, namely that all individuals are identical and equal to the average type. The real world is characterized by system in which there is in fact microscopic diversity underlying the classification scheme of variables chosen at any particular time for the system model. The effects of this have been described elswhere (Allen and McGlade, 1987, 1989, Allen, 1988, 1990, 1992, 1994) and so we shall simply say that when microscopic diversity is taken into account, then it leads to a mathematical model of an evolutionary tree, where new behaviours emerge and an ecology of actors eventually fills any resource space. In Figure 1.3 we show an evolutionary model where a single

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Figure 1.3 An evolutionary model in which a single population evolves into a community of different population

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types, in some ‘character’ space. This model generates qualitatively changing variables and system dynamics through time. population gradual evolves into a community of population types, an ecology, over time, as microscopic diversity is continually produced and selected upon by the emerging dynamics. The full discussion of these issues would take us away from the primary aim of this book, which is to present spatially self-organizing models of urban and regional systems. However, we shall return to some of these issues in the final chapter. We can summarize the different levels of model from deterministic equations to full evolutionary models as shown in Figure 1.2. In reality, the interaction of the system within the larger one which is its environment will lead to a co-evolutionary dialogue involving the wider situation. This co-evolution of System and Environment means that, in reality, the changes in the environmental parameters will partially be related to the adaptations that occur within the system. Systems models in general describe the connected behaviour of sub-systems. If these are few, and each sub-system has a fixed internal structure, then a systems model can be a complete representation of the behaviour of the connected parts. A gear box, for example, can be modelled successfully as an assembly of gears, providing that none of the gear wheels gets stressed beyond breaking point. A complex system, however, is one where there are so many sub-systems connected together, that some reduced, aggregate description is necessary. In this case the behaviour will be defined in terms of aggregate ‘variables’, representing average types and average events. Obviously, all macroscopic systems are ‘complex’ systems, since they are ultimately composed of atoms and molecules. However, if, as in the case of the gearbox, there exist macroscopic components whose internal structure can be assumed to be fixed (or to obey known laws of deformation) during the system run, then a simple systems model will correctly describe the course of events, providing that the integrity of the components is not compromised. Clearly, for cases of breakage, a deeper description would be needed. For complex systems made up of microcomponents with fixed internal structure, their interactions can lead to self-organization. However, if the microcomponents have internal structure, and if in addition this can change through time, thus changing the behaviour of the individual elements, then evolution can take place as the emergent macrostructure affects the local circumstances experiences by individuals, and this in turn leads to a structured adaptive response which in turn changes the macrostructure generated. Complex systems modelling involving elements with internal structure that can change however, leads naturally to a hierarchy of linked levels of description. Stability, or at least metastability is achieved when the microstructures are compatible with the macrostructures they both create and inhabit. (Jantsch, 1980) Clearly, ‘dissipative structures’, which we shall briefly describe below, as discovered and investigated by the Brussels School (Nicolis and Prigogine, 1977, 1989, Prigogine and Stengers, 1987, Shieve and Allen, 1982) are all examples of self-organization rather than evolution, since the molecules underlying the chemical and biological reactions studied do not change their nature. These simple molecules do not ‘learn’. Complex spatio-temporal organization can form in such systems, as a result of the non-linearities

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of the interaction processes, and so they demonstrate the emergence of structure at a higher scale than that of the interacting entities. In the case of the Brusselator, for example, the molecules interact over distances of 10−8 cms, but the spiral waves and characteristic patterns are of the order of centimetres. 1.3 SELF-ORGANIZATION IN PHYSICS AND CHEMISTRY Molecules in interaction have none of the intelligence and complexity of human beings, and yet, as was understood about 20 years ago, they are capable of ‘self-organization’, of creating structure, form and functionality at a scale far larger than of single molecules. It results from the coherent behaviour of many billions of molecules, which succeed in being in the right places at the right times, to react and diffuse in such a way as to create and maintain various possible states of spatial organization. This should not be too much of a shock for us since, ultimately, molecules underlie whatever it is that we are. But, of course, in this volume concerning geography and changing urban systems, we are particularly interested in understanding how spatial structure emerges in systems and how it evolves. Because of the fundamental importance of these ideas, it seems necessary to spend just a short time on examining how this occurs in these simplest of possible examples from physics and chemistry. Physical systems contain innumerable numbers of atoms and molecules. Their behaviour, temperature, pressure rate of chemical reaction etc., are modelled by considering the effect of the statistical average of the molecular events. Temperature is related to the average energy of motion of the constituent molecules, and a chemical reaction proceeds at a rate that is calculated from the average numbers of collisions between the reactive molecules. All such systems when isolated from the outside world can be proved to move towards thermodynamic equilibrium, towards molecular disorder, which means that in such systems spatial structure, if it exists initially, can only erode. However, what is of great importance here is that systems that are open to exchanges of energy and matter with the external world can, under certain conditions, exhibit a quite different evolution, one corresponding to a decrease of its entropy, to a ‘selforganization’ (Glansdorff and Prigogine, 1971; Nicolis and Prigogine, 1977). Not surprisingly, a common feature of social and biological structures is that they occur in open systems and that their organization depends vitally on the exchange of matter and energy with the surrounding medium. However, the requirement of an open system is not a sufficient condition to ensure the appearance of such structure. This is only possible if there are, in addition, nonlinear mechanisms operating between the various elements of the system. A non-linear mechanism is one in which the change in a variable is not simply proportional to its size or local concentration. It therefore reflects some ‘collective’ behaviour of some kind which affects individual molecules, so that they react ‘faster’ or ‘slower’ than they would if they were alone. It is not surprising therefore that the consideration of non-linear affects leads to a profound revolution in our understanding of the collective properties of systems, and of societies. For example, the hydrodynamical equations describing the behaviour of a fluid subjected to temperature gradients provide just such a non-linearity. A most striking example of a dissipative structure is provided by a pan of liquid heated evenly from

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below. When the heating is gentle the liquid is in a regime of linear non-equilibrium and heat passes through the liquid by conduction. As the heating is intensified, however, at a certain well-defined temperature gradient convection cells suddenly appear spontaneously. As can be seen in Figure 1.4 the cells are very regular. This corresponds to a high degree of molecular organization when energy is transferred from thermal agitation to macroscopic convection currents.

Figure 1.4 Pattern of convection cells, viewed from above in a liquid heated from below. The theory of equilibrium systems of classical physics would assign almost zero probability to such an occurrence and is plainly incapable of describing a phenomenon of this type. The reason is of course that this is not an equilibrium system. Energy is flowing through it. So, what happens? We may imagine that there are always small convection currents appearing as fluctuations from the average state, but below a certain critical value of the temperature gradient these fluctuations are damped and disappear. On the contrary, above some critical value certain fluctuations are amplified and give rise to a macroscopic current. A flow pattern begins to emerge and stabilize when the up-flows and the down flows start to fit together. An organized pattern of hexagonal cells results

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with the up flows in the centre and the down flows at the edges. Contrary to equilibrium structures, this new type of structure involves the coherent behaviour of trillions of molecules. Beyond this first instability many possible states of organization can appear as the energy flows, relative densities and the viscosity all combine to ‘generate’ patterns of flow which fit together. Such phenomena are clearly ‘order out of chaos’ as the energy input to the system is ‘used’ by the non-linearities to build coherent organization and structure—without any plan or global consciousness. Structure and organization emerge and evolve spontaneously through successive spatial instabilities. If we turn now to chemical reactions we find an even richer spectrum of possible dissipative structures. Indeed it was the extraordinary behaviour of a particular chemical reaction, called the Belousov-Zhabotinsky reaction (Belousov, 1958; Zhabotinsky, 1964), which spurred much of the work in this field. This reaction concerns the oxidation of citric acid by potassium bromate and involves malonic acid and ceric sulphate. The important point is that two products of reaction

Figure 1.5 The growth of spiral waves as the initially homogeneous system becomes spatially unstable.

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happen to be red and blue, and as a result ‘interesting’, organized behaviour was observed. In a system that was stirred sufficiently to stop any spatial patterns emerging, instead regular oscillations of red and blue occurred, while in an unmixed system, the a large variety of spatial patterns could be generated, such as for example the spreading spiral waves of the kind shown in Figure 1.5. In attempting to understand how such a thing could possibly occur, Prigogine and colleagues at Brussels developed what became know as the ‘Brusselator’ reaction scheme, and spent many years exploring the remarkably rich patterns of behaviour of which it was capable. The proposed reaction scheme involved what is termed ‘crosscatalysis’, where a chemical X helped make Y, and Y in turn helped produce more X. The scheme was: (a) (b) (c) (d) where X and Y are now intermediate molecules in the overall reaction in which the species A and B become D and E. In this scheme, Y is produced from X, step (b), but at the same time the concentration of X increases because of collisions between X and Y, step (c). This scheme therefore corresponds to what we have termed cross-catalysis. The reader should note that the mathematics used to study the behaviour of the reaction is that of Chemical Kinetics, or Molecular Population Dynamics, and is in reality very similar to the population dynamics that is used in discussing the growth and decline of human populations, except that chemical reactions replace demographic processes. The point is of course, that if we can understand how the ‘Brusselator’ self-organizes its spatial structure, then perhaps we shall be able to see similar effects in human populations. If the reaction is driven from equilibrium by pumping in A and B and extracting D and E then all kinds of structure can evolve. The reaction scheme becomes: A→X

(a)

–

a molecule of A transforms itself into X

B+X→Y+D

(b)

–

when B collides with X they react to produce Y and D

2X+Y→3X

(c)

–

When 2 X meet a Y they transform it into an X

X→E

(d)

–

X decays into E

and the behaviour of these reactions can be represented by pair of simple equations for the average density of X and Y if the assumptions 1 and 2 of section 2 are made. That is, it is assumed that collisions and reactions occur at their average rate (i.e. that there are no fluctuations of density), and that all the molecules of X are identical, as are those of Y and the other reactants. With these assumptions, we find:

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These equations have a solution: x=A and y=B/A. However, this can become unstable, and in a well stirred system where spatial structure is impossible, the equations predict an oscillating solution with x and y moving through successive peaks of concentration. The system can go through successive frequencies, and also can oscillate chaotically for certain values of A, B, D and E. However, as spatial structure is what interests us here, let us imagine that the reaction occurs in two boxes side by side and with the diffusion of X and Y occurring between them. For box 1 we have the following kinetic equations:

and for box 2:

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Figure 1.6 The system dynamics model of this displays simple feedback loops.

Figure 1.7 In a well-stirred system the values of x and y exhibit oscillations. where the term DX(X2−X1) gives the quantity of X flowing into or our box 1 resulting from the difference in concentration between X1 and X2. One possible steady state solution (where X1, X2, Y1 and Y2 do not change in time) is, as easily verified: X1=X2=A; Y1=Y2=B/A However, in addition to this unstructured solution for certain parameter values this becomes unstable and the systems moves to a state where X1≠X2 and Y1≠Y2. This means that instead of a homogeneous situation, spontaneously the system moves to one in which either the left hand box is red and the right is blue, or vice versa. The important point is that the system itself breaks the initial symmetry and creates the notion and distinction between left and right. In a real system, instead of having two separate boxes spatial effects occur in three dimensions, and the concentrations can vary continu-

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Figure 1.8 For some values of A, B, D and E the homogeneous solution becomes unstable and the system breaks symmetry. ously throughout the system, rather than having simply two different values. This means that many more behaviours are possible and there is a whole cascade of possible spatial and temporal organizations that are possible, and the simple set of equations is shown to be capable of an immense range of behaviours, of different complexity, symmetry and beauty. A whole multiplicity of spatial structures, of moving bands of colour, of spiral waves and of oscillations can emerge. Simple molecules, with no such plan inside them, create complex patterns at a spatial scale completely different from that of themselves. For example, the typical pattern is about 100 million times bigger than the size of the molecules involved, and requires the coherent behaviour of billions of such molecules. Perhaps in a similar way, towns and cities are the undreamed of consequences of the interactions of individuals, at a scale beyond their imagination. The study of this chemical model, and of others, has enabled the mathematics describing the behaviour of dissipative structures to be developed and their properties explored. As the system is driven further away from equilibrium a single solution can branch into several possible solutions and each of these, in turn, may branch still further from equilibrium. This type of behaviour is described by the mathematics of ‘bifurcations’ or ‘catastrophes’ and has also been termed the ‘mathematics of chaos’ (Thom, 1972; Nicolis and Prigogine, 1977; Prigogine and Stengers 1984; Holden 1986; Lorentz, 1963; Prigogine, Allen and Herman 1977). These first examples from the early seventies have been the forerunners of many more. These concern the behaviour of lasers (Haken, 1977), striking patterns emerging in surface layers, turbulence in hydrodynamics, in electrical circuits, and a host of other areas.

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1.4 STABILITY, RESILIENCE AND SELF-ORGANIZATION In order to better understand the mechanism of self-organization we have to introduce the concepts of stability and resilience. A trivial example is provided by a triangular block resting on a table. If we put a flat side down as the base we have a stable state because if we rock the triangle slightly it returns to that original state. If, on the other hand, we attempt to balance the block on a point of the triangle, then although this is theoretically a possible equilibrium state, the smallest perturbation will cause the triangle to leave the initial state and move to a stable one, namely, resting on a flat side. But this simple example tells us about the behaviour of deterministic equations for which both assumptions 1 and 2 have been made. In the systems which are under discussion (chemical reactions, or towns and cities) there are a multitude of subunits (molecules or individuals) in interactions, and the kinetic equations assume that events take place only at their average rate. In reality there will be fluctuations that will lead to small, local perturbations, which will constantly probe the stability of a given state. In reality then, the average equations ‘sit’ within the nonaverage fluctuations, which shake them around spontaneously, and the persistence of any state therefore requires either that fluctuations be very small, or if this is not the case that the system be stable with respect to them. That is, the system must have ‘corrective’ forces which swing into action every time the system is pushed away from its stationary state. If there were a single, unique configuration that was stable to all possible fluctuations, then we would have a universal equilibrium. Nothing more could happen, and the state could be predicted successfully. But, with non-linear interactions, the dialogue between an existing configuration and local fluctuations may succeed in carrying the system off to some new spatial organization, which may in turn be stable for a while before changing once more. The ‘mechanism’ underlying self-organization is that of successive local instabilities, as fluctuations create new areas of growth and decline in the system, breaking symmetries, and creating structure and organization. But, fluctuations are real, and are just as much part of the system as the average behaviour which has been retained in the dynamic equations. They are what was left out of the model in order to get simple deterministic equations. The process of selforganization therefore cannot be understood from the set of kinetic equations, since it requires a knowledge of the actual non-average behaviour that may be present in the system. This is either achieved by solving the more correct ‘Master Equation’ formulation, or if this is too difficult, simply adding noise that seems ‘reasonable’. In this way the ‘modeller’ can create self-organization, and see the kind of things that might have occurred spontaneously. Such an evolution should be contrasted with that proposed by classical physics in which a system evolved towards equilibrium, a state characterized by maximum molecular disorder (maximum entropy). The erroneous transfer of this analogy to the human domain can lead us to expect the most banal response of a system to some policy or change, whereas in reality, we may find a very sophisticated and complex response which takes us by surprise. Self-organizing systems therefore have two modes of change. There is first the regime existing between instabilities, which is deterministic in the sense that equations such as those of chemical kinetics or population dynamics determine what happens to the

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variables of the system. Fluctuations, although present, are unable to de-stabilize the system. Stage two, however, involves chance as it concerns the behaviour of the system near instability. Here, fluctuations can drive the system away from its previous stable point. Which fluctuation actually succeeds in doing this depends on the chance of which occurs at the critical moment that the system becomes potentially unstable. Self-organization is therefore about the creative interplay of both chance and necessity. The explanation of the situation at any particular time involves both the external conditions being applied to the system, and also the detailed events that have occurred within it—its history. This approach already begins to throw light on the basic difference that was thought to exist between ‘science’ and ‘history’. In the former, explanation was believed to be traceable to the working of eternal, natural laws, while the latter provided explanation on the basis of ‘events’. Now, in this new perspective of selforganizing systems we see that both aspects are present, and that such systems are not described adequately by either ‘laws’ (kinetic equations) or ‘events’ (fluctuations) alone, but by their interplay. An additional characteristic that is important to the success of fluctuations in destabilizing the system, is their size. The smaller the scale of a fluctuation, the more frequently it is likely to occur, and the probability distribution is markedly different for small and for large (spatial scale) fluctuations. The non-linear reactions inside a small volume may tend to amplify a fluctuation, but for change to occur in the system as a whole it is necessary also to consider the effect of outside environment which will tend to damp any ‘unusual’ event that is occurring in a small region. This is a very general result. The smaller the spatial extent of the fluctuation, the more difficult it will be for it to spread into the environment, and because of the ‘surface to volume’ ratio, large scale fluctuations will find it much easier. This gives rise to a ‘threshold’ or ‘nucleation’ effect in the occurrence of instabilities whose origins can be traced back to the interplay of these antagonistic effects. Clearly, if we begin to think of intervening in a system and triggering an instability in order to create a coherent fluctuation, there will be an energetic (or economic) cost related to its size. Without such an intervention, the precise moment and path of an instability depends on the detail of the fluctuations that are occurring, which will be unpredictable in terms of the model equations. Having discussed instability, we now turn to the concept of ‘resilience’. This concerns the global rather than the local behaviour of the dynamical system of equations. As we have seen in the example of the Brusselator there are in parameter space many possible regimes of operation of the system. These correspond to different attractor basins for the system trajectory, possibly to static, oscillatory or chaotic patterns of organization. Resilience considers this more global vision of the possible behaviours of the system, and the different ‘basins’ of attraction that exist, and resilience refers to the ability of the system to stay within its basin of attraction and resist being kicked over into another basin, and another pattern of behaviour. It can be wobbling around within its present regime, and in that sense seem to be unstable, but this ‘elasticity’ may in fact play a role in its capacity to resist being pushed over the edge of that particular behaviour, that particular overall organization. The capacity to adapt and respond to external and internal variation, although requiring some ‘instability’, can be the origin of the system’s resilience. This is an example of the complexity of some these issues, in which adaptability may allow stasis in a broader sense, and rigidity may lead to collapse.

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Contrary to the traditional view in which average behaviour is paramount, and fluctuations are only a small ‘error’ factor, in the new view, the system is driven through successive instabilities by fluctuations, and so they play a major role in shaping the organization that emerges. Self-organization therefore leads to the view that both the structure and the fluctuations around that structure are the result of the evolutionary process, and that the adaptability and resilience that result are natural properties of complex systems. 1.5 KEY IDEAS Let us briefly survey the ideas discussed so far. Open systems, subject to exchanges of energy and matter with their environments, and with non-linear interactions between the

Figure 1.9 A bifurcation tree of possible solutions to the dynamic equations. micro-elements can give rise to macroscopic states of organization and behaviour that undergo bifurcation that is, for identical external conditions, various possible structures can exist, each of which is perfectly compatible with the microscopic interactions. The characteristic diagram describing such systems is the bifurcation ‘tree’ as shown in Figure 1.9. The development of the system is therefore this mixture of chance and necessity. On a branch the trajectory is fairly stable and its trajectory and response to external change may be deterministic. But when the system is near to a ‘branching’ or ‘bifurcation’ point it is relatively unstable, and hence small, chance disturbances, which are always present in the system, can be decisive in nudging it onto one branch rather than another. In this way, we find that history is made up of successive phases of relatively predictable development ‘along’ a particular branch, separated by moments of

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instability and real change during which the future of the system is laid down-by some rather indeterminate chance events which push it onto one or another branch. We now see the nature of an ‘historical accident’. And these new ideas suggest a new, weaker kind of ‘explanation’ for phenomena. The scientific explanation has long been associated with that of ‘mechanisms’, where A is the mechanical cause of B, and it is the churning of the connected parts which explains the overall behaviour. The only alternative was always thought to be simple ‘phenomenology’ where experimental relations between macro-variables were found to be true, for as long as they were true. However, self-organizing systems are collective structures which emerge from the interplay between average behaviour, and deviations around this which drive the system through successive instabilities. While a structure is stable, then it certainly can be ‘described’ by the churning of its connected parts. But, when instability occurs, it can change its structure spontaneously, and afterwards will be described by the churning of a new set of parts. The system is therefore both the ‘structure’ that is observed at some aggregate level, and the deviations around this which can change the structure observed. Instead of ‘reductionism’ we find a kind of ‘elevation’ of the material components of matter and to a realization that the ‘explanation’ behind a given macroscopic situation lies in the successive mutual consistency and inconsistency of two levels of description—the micro and macro levels. Another key point that this new description allows us to understand is that of innovation. The different branches of solution which the system can adopt differ qualitatively from one another, spanning different dimensions and offering novel features. Thus, when the system changes to a new branch, new features appear and the behaviour of the elements may now be influenced by these. Such a system can evolve from a relatively simple initial state of organization, through successive instabilities to a very complex pattern of structure and flows, which in earlier approaches were modelled ad hoc but which in ours are generated by the simple, basic interactions between the elements. The comparison between branches involves a ‘value judgement’ since they can span different dimensions, and the problems and pleasures characteristic of each branch will be perceived by the different parts of the system differently. This is why a decision that would have some kind of collective legitimacy must take into account the different voices in the system. The fundamental non-conservation of emergent properties involved in such an evolution is rather well illustrated by the example of origami, which is the subject of Figure 1.10. Origami consists in taking a flat sheet of paper and making folds in it in such a way as to produce a stable configuration which suggests to us some familiar object or creature. Consider, for example, some forms that can be made from a square sheet of paper (Kennaway, 1980). Figure 1.10 shows the number of folds necessary to create the various forms and also the moments when ‘bifurcation’ occurs and two objects become different (Allen, 1982). The various forms obtained by folding the paper are stable configurations in that the particular fold lines that have been impressed on it by the irreversible performance of work.

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Figure 1.10 Origami illustrates the emergence of form as a result of folding. It is a non-conservative evolution, in which the paper is conserved. They are self-consistent realizations of form and fold lines, otherwise the paper would either spring back or tear. Several important considerations emerge which are of great relevance to the understanding of evolutionary systems. Firstly, folding the paper generates new traits and new images, and the various branches differ qualitatively because of this. Initially, we start with a piece of paper that has few attributes. It is square and white. After the folding process many attributes can be assigned to the various forms. Wings, legs, petals, volume, shape, and elegance have emerged, and the problem of choosing the ‘best’ form, involves the comparison of objects spanning different dimensions, i.e. it is a ‘value judgement’ and in evolution depends on whether or not these various features are compatible with the environment. What is more, these traits emerge at certain moments in the folding process, and each object has a past in which it was not what it is now, and a future in which it would cease to be what it is now, if the folding were to continue. Modelling which is based on ‘what the system is now’, is merely descriptive, and does not contain the past or the future of the system. Generally, system dynamics models are of this kind. They describe, and are calibrated on, a set of data for a system that is changing in time. As a tool to explore the future, therefore, it must fail at some point. What we require in a model is that it should somehow generate the structure of today, from among other possibilities, and hence would be capable of examining the future without supposing that today’s structure would continue forever.

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Another important point arises when we open the paper and examine the pattern that the folds make. In some ways we may suppose that the pattern of folds represents the ‘DNA’ of the object—the irreducible essence of the ‘seagull’ or the ‘horse’. But, as is probably true for DNA, this is misleading. The creation of a ‘seagull’ or a ‘horse’ requires more than just the pattern of folds, it also requires that the folds be made in the correct context and order. In self-organizing systems, the timing of events, and of successive instabilities play a vital role in the evolution of the system and in the nature of the emergent structure. The same fluctuation at a different time, or context, will produce a different result. All that traditional, reductionist science would say about the evolutionary tree of Figure 1.10 is that all these objects weigh the same and are made of paper. Further tests would reveal with greater certainty that they were indeed made of paper, the type and quality of which could be identified. However, this is all quite beside the point. What is important are the attributes that are created during the folding process, and which we assign to an object distinguishing it from other objects, and these traits are not conserved. As noted in section 1.2 the first problem is that of classification—which variables are significant descriptors? Once a classification has been made, then in many ways building a model is relatively obvious. But, there is little guidance on how to take this critical initial step, and it is the difference between things that are vital, and they are the basis of language itself. A dictionary which necessarily defines words in terms of other words, is nevertheless useful because, when coupled with experience, it enables the communication of the essential differences between things. What our models of self-organization and evolution are telling us is that not only is classification an essential initial part of the problem of understanding, but, through time, the relevant classification will change, and the variables, and their attendant equations will also change in different phases of the development of the system. Another interesting idea arises if we imagine that these paper forms need to be renewed after a certain time. If paper is scarce, then they have to merit their renewal, and this could be accorded if each form possessed at least some unique quality, enabling them to ‘shelter’ from competition with the others. If however, there were more than one form with the same set of qualities, or traits, then a competition must ensue resulting in only one ‘survivor’. In this way the survival of a paper ‘duck’ depends on the fact that the other forms are not duck-like, and this means of selection will give rise to an ‘origami world’ of increasing diversity, populated by not-incompatible forms. Similarly, in the natural and the human world, if the ability to tap some resource is associated with the possession of some particular trait, quality or technology, then the same general picture of development would hold, and evolution in a given region would be characterized by a particular set of not-incompatible forms. From time to time, however, one could imagine that, as a result of gradual changes in particular species, or in the spectrum of available resources, the whole system might suffer a sudden re-organization. In some sense, then, the ‘unit of selection’ is the entire system, which will produce a set of ‘mutually compatible’ forms, inhabiting multiple dimensions of existence, and not expressing any particular global optimality. In this new view of ‘self-organization’, different solutions of the underlying microscopic dynamics, the macro-structure, have different symmetries, and hence we find this non-conservative evolution. We pass from homogeneity (at the macro level) through a series of broken symmetries, to structures and organizations, until ultimately, if

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this were to continue, we would return to the ‘chaos’ of so many broken symmetries that the average result was homogeneous again. As in work concerning information theory, we find this same paradoxical similarity between ‘zero’ and ‘total’ information. Life and organization are, it seems, situated somewhere between the two. 1.6 SELF-ORGANIZATION IN HUMAN SYSTEMS Since the start of the work described here, applications of these ideas have been made in fields as varied as geology, archaeology, ecology, oil exploration, social insects, economic markets, and the case we shall describe here, that of the developing spatial structure of regional and urban systems. Underneath this objective lies the paradox that in order to model change, we need to suppose some invariance underlying behaviour, or else we would simply be describing events as they occurred. Returning to our example of traffic or of people in the shopping centre, we may find this invariance if we can define what people are trying to do, and use that to calculate what they will therefore do in the changing circumstances. In modelling change and evolution of land-use and urban structure, the invariance or characteristic mechanisms which we suppose to be at the base of our model are the preferences of various types of actors in the system. These preferences are supposed to reflect their functional requirements, in both their professional and private capacities, conditioned by their perceived roles in society and by the available technologies, the means available to each of them to compete for locations, and also the current beliefs and myths as to what is considered desirable. It is through successive instabilities (spatial in this case) that complex behaviour emerges in the system, as actors interact with each other in both competitive and co-operative ways. Each actor, taken separately, may have very simple decision criteria and desires, but the dynamic ‘folding’ of the system can give rise to complex patterns and flows. This basis of the modelling in terms of the individual goals or preferences, and of course their diversity, should be contrasted with that involved in an ‘equilibrium’ approach to such problems. In the latter case, it is supposed that the collection of individuals within the system somehow make decisions in such a way as to drive the system to ‘equilibrium’, that is to some unchanging condition, which expresses some collective optimum. For example, the equilibrium state would correspond to a situation in which individuals, under the prevailing circumstances, had maximised their ‘utility’, or entrepreneurs had maximised their profits. For a very simple situation and unchanging circumstances the solution of a self-organizing simulation might coincide with such an equilibrium, but for situations that pertain to real life, this would not be so. The selforganizing dynamic approach would explore a particular trajectory of the system, and with the presence of fluctuations would for fixed circumstances eventually get ‘lockedin’ to a structure which might be one of many potentially possible. However, the particular choice made would depend on where it started from, and which fluctuations happened to occur and when. The symmetry of the solution could have changed, and indeed new properties could have emerged as a result. The equilibrium approach generally considers the stationary solution with the same symmetry as that of the initial condition, since it cannot anticipate structural changes.

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Even studies which discuss the possibility of multiple equilibria would tend to study those with the same symmetry as the initial condition. Even if other symmetries were envisaged, the stationary calculation would be unable to give any indication as to which solution among them was the most probable. These equilibrium models are also formally equivalent to those involving ‘entropy maximisation’ which were developed by Wilson and colleagues at Leeds. Once again, although valuable in giving a method for the inference of patterns of traffic flow from global data, the fact is that the real time evolution of the system is neglected, and the possibility of structural changes, particularly involving symmetry breaking, is specifically excluded. This may seem like a very technical point, but for example, it means that a circular city would be ‘doomed’ to always remain circular, even if decentralized sub-centres were to appear, they would appear evenly, and be of equal size. In reality, of course, the world is much more creative, and less restricted than that, so that cities can develop asymmetrically, and new foci can emerge. In the approach to urban and regional modelling derived from self-organizing systems in physics and chemistry, key events are the occurrence of spatial instabilities. During these, unpredictable events may play a vital role, nudging the system on to one or another branch of organization. From then on, the simple ‘generic’ preferences of each type of actor would have to be ‘expressed’ through the choices open within the particular urban structure that they inhabit. In this way, the same initial conditions, actors, and preferences can, following a different series of spatial instabilities, give rise to a variety of possible behaviours. Thus, even with actors whose spatial distribution is governed by a deterministic set of partial differential equations, ‘choice’ appears quite naturally because of the existence of many possible spatial structures that can emerge through bifurcations in the solutions to

Figure 1.11 In urban centres structural change occurs through successive instabilities when fluctuations can

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carry the system off to different possible futures. these equations. In any particular case, the interaction of the actors competing for space and co-operating in their functions gives rise to observed behaviour that is mutually consistent but different from that observed in other spatial structures. So, a single set of functional requirements, acted upon by ‘fairly rational’ actors, can be realized in many different ways because the choice made by each actor at a given moment depends on that already made by the others. Therefore, mutually consistent patterns emerge that nevertheless offer different ‘costs’ and ‘benefits’ to each type of actor. In this way, our approach goes beyond any particular case, since the equations of change can give rise to a whole range of different possible cities. The urban models that are used at present (see Wegener, 1994) could not generate ‘alternative’ cities that would have resulted from a different history. They are built by ‘calibratings’ them on observed behaviour for the city under study and, therefore constitute in reality only a ‘description’ of the existing state of affairs. The development of a ‘science of complex systems’ requires the formulation of generic models, not particular ones. In the next section, we attempt to test out the following idea. In physics and chemistry, non-linear interactions between molecules spontaneously produce spatial organization. Would the typical interactions operating between different kinds of people in cities and regions also spontaneously produce spatial structure, and if so, would it look anything like the spatial organization that is observed?

INTER-URBAN EVOLUTION

2. DYNAMIC MODELS OF URBAN GROWTH 2.1 THE URBAN SYSTEM In this section we first describe what real patterns of settlement and urban hierarchy are like, and then try to see whether a ‘self-organizing’ process based on reasonable interactions between people can possibly lead to such patterns. How do towns and cities grow and decline, structuring the landscape, the flows of people and goods and also shaping the lives of the inhabitants. Essentially, the story of increasing urbanisation is one of migration over a long period and of the spatial concentration of economic investments in particular areas. Clearly there is a relation between the two, since economic investment will go to places where there is a workforce, appropriate skills, and a market, and people will migrate to areas with job opportunities. It is this kind of ‘crosscatalytic’ effect that will generate the growing centres of urban concentration in our model, whilst the competition for space will set limits on how high urban densities can rise. Our models will try to show how the macroscopic pattern of settlement, the hierarchy of cities and towns, results from the aggregate effect of individual decisions, each of which is being made in pursuit of personal goals and with limited information. Let us first discuss the kind of patterns that emerge in systems of cities within a region. When urban centres interact the resulting evolution is, not surprisingly, rather complex. In some cases economic competition may result in the growth of a particular centre at the expense of those near to it. However, in other cases a centre’s growth can be a motor for the economic development of the region around it, with the appearance of flourishing industrial satellites and wealthy suburban dormitory towns. As the populations increase, as economic innovations invade the system, and as the transportation improves, hitherto independent towns and villages are gradually brought into interaction with each other causing some to grow and others to decline. Cities and towns of all sizes emerge, and the first question that we can ask is whether there is any regular pattern amongst these. In fact, it has long been noticed that there is a certain regularity in the relative sizes of those urban centres remaining in interaction within a region. This has been called the rank-size rule (Berry and Garrison, 1959; Berry and Pred, 1964). Considerable information has been amassed concerning this question and a rather complicated situation has been revealed. In particular, Berry (Berry and Horton, 1970) has studied the rank-size distributions of different countries, and as a result has made the

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Figure 2.1The distribution of city size and rank in the United States from 1790–1940. following classifications. Thirteen out of the 38 that he studied obey the simple rank-size rule, known as Zipf’s law (Zipf, 1949): Pn=P1/nb, (2.1) where Pn is the population of the nth city, and b is some power. Fifteen others had a ‘primate’ distribution, where the first, or first few ranked cities were disproportionally large. The others fell into intermediate classes, reflecting the play of historically different economic, social and technological forces in the different regions. Any model purporting to describe the evolution of a system containing several interacting urban centres must be able to take into account the effects of historical circumstances as well as the operation of ‘universal’ laws. Another important characteristic of urban settlement is the relation between the average separation of centres and their size. Broadly speaking, large centres are separated by large distances, while small centres are on average much closer to one another. The forces underlying such a distribution were clarified greatly by the work of Christaller (1954) who introduced the concept of central places, broadly synonymous with towns which serve as centres for regional communities by supplying them with their goods and

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services. Central places vary in importance, higher order centres offering a wider range of goods and services than lower order ones. In other words, the basic proposition of Christaller, which we shall adopt, is that the spatial and hierarchical relationships between urban centres reflect the play of economic forces, and that large centres are the seat of many economic functions, while small centres possess only a few. In Figure 2.2 we see the original area studied by Christaller, and several of the hierarchies that he suggested characterised the spatial pattern of towns and cities.

Figure 2.2 The original area studied by Christaller, which led him to the idea of ‘Central Places’. However, although these ideas concerning ‘Central Places’ were interesting, this view is characteristically one of an ‘equilibrium’ situation, when the region is filled and from such a description it is, of course, intrinsically impossible to know how the system will react to some change such as a modification of population density, or a transport

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Figure 2.3 Christaller central places for k=4, k=7. innovation. The extensions and developments of this type of theory (Central Place theory) by Losch (1939), Isard (1956) and others still reflect this basic shortcoming. The concept of ‘self-organisation’ which we have outlined in the introduction, permits us to initiate a new approach however, which, while based on the economic interactions of central place theory, describes dynamically the evolution of the system. This led to the idea of urban hierarchies of different types, characterised by different ‘k’ factors. These theoretical ideas concerning centrality, and the spatial structures that will develop as a result of the interaction of towns and cities, were based on the assumption of equilibrium, in the same manner as that of crystalline structure in physics. It supposed, without asking for the mechanism or the time sales of the processes involved, that such systems could arrive at a spatial organization which in some way expressed a global optimization. This has been typical of the ideas (mis)borrowed from physics by the ‘social’ sciences, which assumed that somehow, the disconnected actions of individuals, each pursuing his or her own goals, could drive the system to some equilibrium state that was characterized by some global optimality. Unfortunately, although a theoretical proof can be given in physics for such a result, this is certainly not the case in socio-economic systems. Such assumptions have the rather naïve implication that ‘whatever happens must be for the best’, and underlie the belief in the effectiveness of ‘free markets’. Since the aim of developing mathematical models is at least partially in order to make plans and explore the implications of policy options, with a view to interfering in the system clearly this is at odds with the basic assumptions of Central Place Theory. While these theories displayed a remarkable insight for the time, today we know that structures emerge and change as’ a result of the dis-equilibrium of the processes that

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Figure 2.4 The problem with Central Place Theory is that it cannot deal with change. underlie them. The assumption of equilibrium effectively rules out any successful modelling of changes, such as the emergence of new centres or the onset of decentralization or of new patterns of clustering. What is required is a dynamic theory of urban systems which will be suitable for use as a planning and policy exploration tool. 2.2 A SIMPLE THEORETICAL MODEL In this first, very simple model (Allen, 1978; Allen and Sanglier, 1978), the urbanization of a region is viewed as being due to the successive integration of economic functions introduced at random places and times into the system, together with an evolution of the means of transport and communication, as the different centres grow and compete with each other; and the population responds to the spatially inhomogeneous employment opportunities which result from this. Let us first consider the simple equation for population growth, that was first given by Verhulst, (dx/dt)=bx(P−x)−dx (2.2)

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for the population x. The constants b and d are related to the birth and death rates, respectively, while P measures in some sense the ‘natural richness’ of the environment. In Figure 2.5 we see the trajectory of the population for different initial conditions. If we wish to apply such an equation to the growth of a human population, then we must allow for the fact that the number of people located in a big city, far exceeds the normal ‘carrying capacity’ of that point. It is not the agricultural production of New York, London or Tokyo that ‘explains’ the populations. The carrying capacity of a particular locality can be enhanced by the presence of economic functions there. It is this possibility of an ‘agreement to exchange’ that is reached between people which adds new dimensions to evolution, involving the division of labour and urbanization. In order to model this mathematically, let us therefore represent our space by a lattice of points, each of which i has the equation for the change in its population, xi, (2.3)

Figure 2.5 Logistic growth curve for different initial conditions.

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Figure 2.6 Modified logistic equation as new economic functions appear at i. where b is related to the rate at which xi can grow due to births and immigration from other points, and m to the rate at which it can decrease due to natural mortality and emigration. The carrying capacity N, for self-sufficient families, is enhanced by a factor R(k) for each unit of production of type k at the point i: see Figure 2.6. This assumes that ‘migration’ flows respond to the distribution of job opportunities, so that the populations in each zone reflect the jobs located there. (Allen et al., 1979, 1980) Having written down a simple equation which describes how the population at a locality responds to the long-term employment potential capacity of the point, it is now necessary to develop an equation which governs the evolution of this employment capacity as economic innovations are introduced, as the different centres compete and as transport networks develop. In order to do this we write down an equation expressing the economic law governing the size of S(k), the number of units of production of k situated at i, as it adjusts to the demand for the good or service which it attracts. This must be zero when the function does not exist at the point, and grow at some rate to a ceiling which is determined by the available market, taking into account the competition coming from rival centres. We suppose the very simple form, (2.4) Let us consider each term in detail. First, the parameter α is a measure of the time-scale on which an entrepreneur reacts to possibilities of expansion, or to the necessity of contraction. This will be a function of the dynamism of local entrepreneurs, the availability of credit, the rewards in view, etc.

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The demand for the good k that will be attracted to i is written supposing that there exists some average reaction of the population relating the quantity that an individual buys Q to the price demanded relation has the form,

We have supposed in the simulations that this

Figure 2.7 Schematic law of demand as a function of price. (2.5) where e is some power reflecting the elasticity of demand. This inverse relation is particularly simple but others may be used without changing the form of the results. If we allow for the cost of transportation between the consumer at point j and the producer at i, a distance rj−ri, then the price will be: (2.6) where Φ(k) is some unit cost of transport for k. The quantity demanded by an individual situated at j is therefore, from equation (2.5). (2.7)

and the total demand coming from all the individuals situated at the different points jx; around i is, in the absence of competition, (2.8)

It is necessary, however, to take into account the possibility that the consumers at j may be drawn away from i to a rival centre. In order to do this, we must write a term which

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represents the relative attraction of the centre i for the function k exercised on the populaorder to deduce the form of such a function, we suppose, firstly, that the attraction of a tion xj at j, compared with the attraction of the other centres i′, which also produce k. In centre is all the greater if there are a number of other functions situated there. To some extent then, a single trip can satisfy several needs. Thus if n is the number of functions situated at i, we shall suppose an attraction proportional to 1+ρn, where ρ is some constant corresponding to this co-operativity. In addition we will suppose that the attraction is inversely proportional to the cost of buying the good there, giving a form:

In order to find the fraction of consumers drawn to centre i from all the possible centres i′, we have simply to write (2.9) where n′ is the number of functions situated at the point i′. The power I takes into account the sensitivity of the population to this relative attractivity—its discernment and its uniformity of response. It has the form of a factor of ‘intervening opportunities’ well known to urban geographers (Stouffer, 1940; Huff, 1963; Wilson, 1974). For a very large value of I the least difference in attractivity is translated by a 100 per cent response of the population at j, who all go to the most attractive centre. As I decreases, so the response becomes less clear cut, and we have a more realistic description where the choices of centre are distributed between the various possibilities, with probability proportional to the attractiveness of a particular centre. The theory of Christaller supposed real ‘frontiers’ corresponding to an administrative zone—this converts to I=∞, that is people have a total information on the relative merits of centres, and all react in exactly the same way to these. Our model can thus deal with the more realistic situation where the lack of information, and the diversity of individuals produces an intermediate response. Also, the factor ρn plays a role in displacing the lines of consumer indifference further away from a centre with many functions, corresponding to increased economies of scale that are being realized by a large unit of production then this is also reflected in its greater attractiveness over the surrounding clientele. The term γ(k)Si(k) in equation (2.4) fixes the market threshold of the unit of production. Thus when Si(k)=1, γ(k) is the figure which the economic demand for k at i must exceed if growth is to occur. It is supposed in our model that half of the turnover can be used for salaries, thus making R(k) of equation (2.3) equal to γ(k)/2. Clearly, one can change the capital/labour intensity in time, simply by changing the value of the fraction. The system structures under the action of several simple non-linear mechanisms. The installation of an exporting activity in a zone will result in an increase in the domestic

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Figure 2.8 The urban multiplier. sector of the town’s economy as the population there increases. This augmentation in the demand for local goods and services results in an increased employment capacity in the domestic sector, which in turn causes a further increase in the local population, and so on increasing local demand and local population until a new steady state is attained, marked by a total increase in population which is considerably greater than that initially introduced directly by the implantation of the export activity. This amplifying mechanism is called the ‘urban multiplier’, and it appears quite naturally in play between the equation for the population (1) and those for the domestic sector and for an export activity. The second basic process which is present in our model is that, as the system develops and populations grow as a result of the implantation of various functions, so new market thresholds are exceeded at these points, with the result that still more activities may appear at points where several are already concentrated. Let us now describe the simulations. 2.3 RUNNING THE MODEL The initial situation is supposed to be that of ‘self-sufficient’ villages, spread homogeneously across the flat even plain. We suppose that there is an first level of activity present which corresponds to subsistence farming. The simulation concerns the appearance in the system of a ‘new’ activity, which has a market threshold greater than the population at a single point, and which is characterized by a coefficient of transport permitting exportation of this good or service to other points. The computer program proceeds to parachute the ‘innovation’ onto random points of the system, at random moments. The values of the parameters used are such that when the function lands on the first point, it becomes established and starts to grow. At the point where this occurs, the implantation of this export activity causes the population increase and through the effect

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of this on S(1) for the ‘urban multiplier’ to operate on the number of residents at this point. In these series of Figures 2.9–2.12 we show a typical sequence of events. After the first successful implantation of the activity, the economic innovation appears at other random points at random moments, as other entrepreneurs imitate the first. Thus the lattice is gradually filled with centres providing the function 2, and the effect of competition between rivals begins to be felt. In these simulations every point is tried as a centre for this function, but only those that manage to obtain sufficient territory survive. The second level function was chosen with characteristic parameters such that it corresponds to that of a Christaller K=4 lattice. Comparing our result with that of Christaller, however, we conclude that the fact that entrepreneurs are parachuted in at random times and places means that the beautiful symmetry of the Christaller pattern will almost never occur. It is only one of a great many possible stable final distributions of centres of function 2, and normally could only occur as a result of planning. Function 2 appears first on point 39 (Figure 2.9) and immediately the population at this point starts to increase. Thus the domestic sector expands also, and the exportation ‘hinterland’ of this initial point is the entire surface of the lattice. However, very quickly, function 2 appears on point 42, and the lattice is now shared between these two points. At a later time, t=0.15, there have been six attempts to imitate point 39. Five of these have come off, but the imitation on point 1 fails very rapidly because of the competition from points 11 and 4. As time goes on more centres appear, and at the moment t=0.5 we

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Figure 2.9 Distribution of centres at t=.02. Function 2 appears first at point 39.

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Figure 2.10 The distribution at t=.5. have the maximum number of centres that will simultaneously exist in the system of 50 points—nine in all. After this, there is a certain weeding out and the number of centres drops to six, by the time t=1. The point that first received the innovation, point 39, is still the largest, having had the longest continuous period of population growth. However, its hinterland has been cut down from the whole lattice initially, to some eight surrounding points. As function 2 becomes fully integrated into the system, and population growth ceases the number of inhabitants at a particular point reflects the size of the hinterland that it happens to possess at the end of the simulation. For example, by time t=5, the initial point 39 is only the third largest centre having been overtaken by points 4 and 34. From this first simulation we see that, in the long run, only six centres stay the course and remain at the end. Since all 50 points were tried at first sight, it seems that 44 centres failed. This is not entirely true. In fact, six centres appeared, grew and later were eliminated through competition, while the remaining 38 never exceeded the market

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threshold, and never had any real existence. In some ways they correspond to a ‘thought experiment’ on the part of an entrepreneur, who seeing that the conditions for the subsistence of a unit of production are not met at this point, dismisses the idea of starting his enterprise there. Of course, even if he should persist in his attempt, the result will be the same.

Figure 2.11 The distribution at t=1.

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Figure 2.12 The final distribution at t=5. Coming back to Figure 2.12, we see that, overall, 12 centres have existed at different times, six of which remain, the rest being eliminated, and this kind of figure for the success and failure rate of the urbanization history of a region is not at all in disagreement with results obtained by Berry (1967). Neither is the evolution of the number of centres, which, early on, passes through a maximum and then as the centres interact declines to some lower level. In Figures 2.13 and 2.14 we see the final distribution resulting from simulations of the implantation of function 2 which has exactly the same values of the characteristic parameters and of the initial conditions, but where the random choice of the moments and points of implantation are different, that is to say, the ‘history’ is different for each simulation. Because of this the final distribution of centres is different in each case although the number of centres is roughly the same.

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Having explored the effects of launching a first wave of ‘blacksmiths’ onto our uncomplaining population, we now need to show how cities and towns emerge under the continuous rain of a series of further functional innovations. In the next series of figures this is what is shown. We take part of the lattice (30 of the 50 points above) and in this way study the ‘evolution’ of an urban hierarchy as the new activities are integrated into the system. In Figure 2.15 we show the state of the system when function 2 has been introduced, where only seven centres remain in a stable configuration. To this is added a third function, which has a large market threshold and in consequence establishes itself at only one point in the system. This point is one at which function 2 is already established, because firstly, there is a heavy concentration of population and hence of demand for 3,

Figure 2.13 Final distribution of centres after a different sequence of fluctuations, that is, a different ‘history’.

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Figure 2.14 Final distribution of centres for another sequence of fluctuations. but also because of the ‘cooperativity’ that exists between functions. This effect can be viewed either as the result of customers being able to fulfil two purposes in a single trip in the case of distributive activities, or that the transport facilities that have been developed for function 2 can be used by activity 3 at very little extra cost. Thus, in equation (2.9), the attraction of demand to a point having both functions 2 and 3 is greater than the sum of the attractions to two points, one with 2 and the other with 3. This point is allowed for when ρ≠0. When function 3 is introduced the result is as shown in Figure 2.16. Centres having only function 2 that are too near to the ‘capital’, at point 18, are suppressed, while those that remain grow further. Thus the system structures into three levels, and the addition of a third function causes the difference between levels to increase. For Figure 2.16 we have calculated the rank-size rule for this simple three-level hierarchy. That is to say, we have supposed the law,

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P2=P1/2b, P3=P1/3b, where P1, P2, and P3 are the populations of the first, second and third levels of centre, respectively. In this case, the ‘capital’ has a population 261, and the second level centres offering function 2 have populations 103, 100 and 99. These slight differences are purely the result of the random events leading to the capture of slightly different territories.

Figure 2.15 Distribution of centres having function 2. We have therefore,

and

The fact that the value of b is almost constant shows that Zipf’s law holds, although in the terms of Berry the distribution is slightly ‘primate’. This means that compared to the

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urban hierarchy which would give rise to a constant value of b, here the ‘capital’ is a little too important. In Figures 2.17 and 2.18 we have the final distributions of two similar simulations on a lattice of 30 points. Again the introduction of the third function causes the region to structure into three levels of centre. Again we may calculate the value of b relating to the rank-size rule for the region and for Figure 2.17 we find P1=265, P2=110, 109, 102 and P3=66.6 which gives b12=1.27 and b13=1.26 We conclude that Zipf’s law is a good approximation for the hierarchy. For Figure 2.18 we have P1=327, P2=136, 113, P3=66.6 and the values of b are: b12=1.39 and b13=1.45 Again the values of b are almost the same, showing that the relation Pn=P1/nb is consistent although a slightly different choice of parameters has led to a considerably higher level of urban population than in the preceding cases.

Figure 2.16 Distribution of centres after the launching of function 3.

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Figure 2.17 Final distribution of functions 2 and 3 for a different sequence of events. In the following example, Figure 2.19, on a lattice of 50 points we find a rather complex structure. In this case, the values of b corresponding to the different levels are: b12=0.94, b13=0.89 and b14=1.04

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Figure 2.18 Alternative final distribution.

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Figure 2.19 Final distribution of three economic functions on a lattice of 50 points. This rather uneven value reflects the difference in the spatial organization of the upper and lower halves of our diagram. In the lower half there is no centre having both functions 2 and 3, and we may regard this as being an instance of the ‘chance’ vanquishing the ‘laws’ arising from the interactions. The non-linear action of the cooperativity between functions 2 and 3 were not sufficient to overcome the entirely haphazard implantation of these functions. An interesting remark is that if we compare the ‘urban populations’ resulting directly from the implantation of both functions on the point, with that resulting from the implantation on neighbouring points, we find: (a) urban population due to 2 and 3=217; (b) that due to 2 and 3 on neighbouring points =162.

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This is obtained by studying points 15, 35 and 36 of Figure 2.19. The difference between 217 and 162 represents the difference in the effectiveness of the action of the urban multiplier on the same point, or when the urban growth is split between two neighbouring points. In a certain sense the structure in the upper half is economically more effective than in the lower. All the simulations that we have presented have supposed that the ease of transportation is uniform throughout the system. The values chosen for F(k) were in all cases: F(1)=1 and F(2)=F(3)=F(4)=0.1. This corresponds to the reasonable supposition that the exported goods or services cost roughly 10 per cent of their production costs to transport between neighbouring points. 2.4 DISCUSSION Having run our simple theoretical model of an emergent urban hierarchy, we can decide how to make it resemble a real urban system. First let us see what worked well. Firstly, the general form of the urban distributions resulting form our simulations are entirely reasonable, both in their spatial aspects as well as in their hierarchical size relations. This suggests that the basic form of our equations is correct, although further refinements can certainly be made. The eventual aim of this work is to set up a method suitable for modelling the dynamic evolution of the urban centres of large regions, based on the concepts of ‘self-organizing systems’, and this first step seems to succeed quite well. The models displays the reality of structural ‘lock-in’, where a sub-optimal structure, once it is initiated due to the chance initial events, cannot be easily transformed into the optimal structure. More recently, the importance of this result in economics has been emphasised by Arthur (1988, 1994). However, there are some problems. Several important mechanisms were missing. Most importantly, it assumed that the place of work was the same as the place of residence. While this may be alright during the early stages of urbanization, certainly, at a later time, a differentiated pattern of urban structure emerges, as part of the selforganization, with some neighbourhoods attracting concentrations of economic activities, and others of private residences. In other words, commuting will emerge and this will need to be added into the model. Another process that has not been treated properly is that of migration. In the simulation, people simply moved around according to the employment opportunities, which assumes firstly that they have perfect information concerning these, and secondly that this is all that motivates people to migrate. Other factors might be that of the transportation network. In the model, so far, the distances between centres are simply ‘as the crow flies’, and of course, in reality these distances would reflect the transport network, and the time of travel would reflect the type of road and the traffic encountered. In the next chapter, an improved version will include some of these missing mechanisms.

3. URBAN GROWTH, COMMUTING AND REGIONAL STRUCTURE In Chapter 2 a preliminary model was developed which simply explored the kind of settlement pattern that would arise from the interplay of processes of positive and negative feedback that exist between jobs and people. Jobs attract jobs and people, and people attract some jobs. The system showed that reasonable urban hierarchies were the outcome of reasonable assumptions about the processes, and that many different outcomes were potentially possible. The system showed ‘lock-in’ of sub-optimal structures. An important point was that it was not necessary to assume that the distribution of people or of jobs was at equilibrium at each instant. Not only was it not necessary, but it would have destroyed much of the usefullness of the model, since even common sense tells us that the real outcome of a given situation will in fact depend critically on the actual path that it follows and the strains and stresses that are encountered ‘on the way’ to equilibrium. Furthermore, just a little bit more common sense will tell us that the system may never ‘go’ to equilibrium, since all the time there are changes in technology, in patterns of demand, in peoples desires and expectations, and in the economic and social structure that underpins the whole aggregate description used in the model. Since these models were already published in 1978, it is illuminating (with regard to the manner in which science interacts with government) to note that even today (1996) the models that are actually used by decision makers make the assumption of spatial equilibrium in modelling the ‘changing’ spatial pattern. Having pointed out these fundamental aspects of the preliminary model of chapter 2, let us now turn to improvements aimed at making it more realistic. The first improvement that we shall make is to allow the possibility that the population commute to work from a neighbouring zone as the density of occupation of the urban centres increases. This will lead to the development of structure within the emergent urban centres, as a spatial pattern of land price develops reflecting the dual effects of peoples and employers desires and their financial possibilities. In response business and economic activities may tend to cluster in the centre, and residential suburbs spread out around them. The driving force which leads to such structure, however, is complex. Because people and jobs want to be at the centre of town, land prices tend to increase there, and at the same time, the physical conditions of noise, congestion, and pollution encountered there decrease its ‘attractivity’ to potential residents. These effects lead to ‘crowding’ effects, which tend to affect residential choice, and lead to the development of suburban areas away from the centre. After a certain time, this in turn allows retail and service activities to migrate to the periphery, and to offer jobs outside the ‘centre’, thus leading to the further spatial extension of the town as it grows. With this modification the model leads to a more realistic description of the urbanization of a region, giving rise to successive phases of central growth, urban sprawl, central core decay and to counter urbanization.

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3.1 AN IMPROVED MODEL Instead of explicitly ‘launching’ the economic functions, we have chosen population thresholds above which economic functions appear spontaneously in a neighbourhood, and in addition have fluctuated the values of the populations by a small percentage around the values at each point that result from the equations of evolution. In this way we allow for the necessary uncertainty in the exact value of the population at a point, supposing some 5 per cent variation for a small village, and decreasing to 3 per cent for more densely occupied points. As a result of this, when several points are approaching the necessary threshold value to receive some new level economic activity, these fluctuations will result in them attaining the threshold in a random manner, giving rise to a ‘stochastic launching’ of economic functions similar to our previous method. The economic activity, once launched, will either find a sufficient market and grow and prosper, or will be eliminated by its competitors. The advantage of this new method is that it retains at all times the possibility of the system adapting to new circumstances, functions appearing where it was impossible before, owing perhaps to changes in transport technology, or in the population of the region following changes in the natural demography, or in the relative attractivity of the region to migrants. (Allen, 1980; Allen and Sanglier, 1979; 1981) The basic variables of our model are the number of residents xi, and the number of jobs offered in each sector k, at each point of the system i. The ‘actors’ of the system are individuals who tend to migrate under the ‘pressure’ of the distribution of potential employment and entrepreneurs who offer or suppress employment, depending on the market they perceive for their particular good or service. The scheme of interaction is shown in Figure 3.1 and is very similar to that of the previous chapter, with positive feedback coming from the urban multiplier, with the concentration of employment creating ‘externalities’ and ‘agglomeration economies’. However, we have now added the loop of negative feedback corresponding to the competition for space among the potential occupiers of a particular location. These basic mechanisms are expressed by two very simple equations, describing respectively the change of the residential population xi, at each point i, and the number of jobs offered there, (3.1)

This equation is similar to that of Chapter 2 except that is now simply the number of jobs in sector k in the zone i. The coefficients b and m take into account approximately both the demographic change (the birth and death rates) and the mobility of the popula-

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Figure 3.1 Local population and the demand for economic activities constitute the ‘urban multiplier’. tion as it relocates residences under ‘pressure’ form the available employment. The parameter Ni corresponds to the ‘basic’ or ‘natural’ carrying capacity of point i. The term that has been added to the equation of Chapter 2 is an expression that corresponds to the loop of negative feedback shown in Figure 2.1.

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This supposes that the crowding at a point grows as the square of the local density, and that people who work at point i choose to reside at point j, at a distance dij, to an extent depending on Φ, reflecting the ease or difficulty of commuting between i and j. Clearly, Φ will change with the quality of the transport system. The second equation describes the evolution of the distribution of employment in the system as decision makers change the production of a good or service k, at point i: (3.2) where α is a measure of the rate at which entrepreneurs react to changes in the market for their goods. and

is the employment that could be derived from the production of k at i,

Figure 3.2 The behaviour of the attractivity for activity K at i, as felt by the population xj as the size of centre i grows. is given by the number of jobs required per unit of production multiplied by the potential market

that can be commanded by the centre i. (3.3)

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where pk is the number of jobs per unit of demand and εk the quantity of goods or services is the price practised by k at i, dij is of type k desired by an individual at unit price. the distance between i and j, and Φk is the cost per unit distance of transporting k. The parameter β depends on the elasticity of demand of k. is the attractivity of the centre i, for function k, as viewed by potential clients xj at j The new form used is: (3.4)

which is a slightly more subtle function than our previous one. The denominator, however, is the same as before, expressing simply the desire on the part of consumers for the cheapest source of k, all other things being equal. The numerator expresses the extra attraction of a large centre, offering more choice, better infrastructure, and the possibility of obtaining several goods with a single trip. Before this attractivity simply increased by a given amount each time a level was added to a centre, but now the attractivity grows as the centre obtains the function k, and the activity becomes firmly established there and xi increases. Above a certain intensity, however, it ceases to increase the attractivity for that function, particularly for the lower-level functions. The attractivity exerted by a given centre for a particular good saturates at some upper value. Thus, for example, the addition of further insurance companies to the city of London does not result in the people of Scotland being tempted to buy their bread from this augmented metropolis.

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Figure 3.3 The numbering of the Points on our Simulation Lattice. The influence of the differences of attractivity on the fraction of the population attracted depends further on the parameter I, which reflects two basic effects. First, a large value of I corresponds to a virtually unanimous response on the part of the xj to the differences of attractivity of the competing centres around them. Thus it would apply only to the case where the population was very homogeneous, having almost identical values, and also to the availability of correct information concerning the ‘real’ attraction of each centre.

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Clearly, a small value of I corresponds to a rather inhomogeneous, uninformed population. The technique used in modelling the urbanization process is basically similar to that used in the previous model. However, instead of explicitly ‘launching’ the economic activities, we have chosen population thresholds, xthk, above which the activity k appears spontaneously at a point, and we have fluctuated the populations by a small percentage around the values dictated by the equations of evolution. In this way we allow for the real uncertainty in the exact value of the population resident at each point, supposing some 5 percent variation for a small village, and decreasing to about 2 percent for more densely occupied points. 3.2 SIMULATIONS OF THE URBAN SYSTEMS Once again the simulation concerns the emergence of urban centres in a region which, initially, has none. The central place system that emerges results from the successive appearance and differential growth of three levels of economic activity, corresponding to goods and services with successively greater spatial range. These economic functions at the low levels are ubiquitous, short range functions of goods and services required very frequently by consumers, and at the high level are long range, rare activities that are only required infrequently by consumers. The higher the function the greater the market area or hinterland that is required to support it, and hence the higher the probability that it will be located in large urban centres with large hinterlands. In our model, however, we hope that these features will emerge spontaneously themselves as economic functions of successively greater range appear in the system. The same lattice is used as in the previous chapter, numbered as in Figure 3.3. In these simulations, we shall not attempt to introduce a transportation network. We shall suppose for this particular set of studies that travel costs are isotropic and that the natural carrying capacity of each point, Ni, is the same. The values chosen for the various parameters are given in the Appendix. The simulation begins with 66 units of population on each of the 50 points of the lattice. They are, however, subject to fluctuations on the order of 5 percent, and when a point exceeds 68 it receives the first export function and begins to grow if there is sufficient market. In Figure 3.4 we see the simulation after 4 units of time. Five points have received the second-level function and have grown to a population greater than 75. These are ‘nuclei’ of future cities, and they lay down a basic form for the urban structure that may emerge. In Figure 3.5 the situation after 12 units of time is shown. The structure that was only ‘embryonic’ has ‘solidified’, and we see that five large centres are growing. Already many of the futures that ‘could have been’ have receded to an extreme improbability, and this will be accentuated further as time goes on. The system is now evolving in a restricted area of freedom and is exploring states that are characterized by the position of these five main centres. Two points have received all three export functions, while three others have two export functions. Furthermore, a careful examination at a and around point 15 reveals that the ‘crowding’ of this centre is leading to the growth of residential

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Key to Figures 3.4 to 3.16: Centre having only function 1; Centre with functions 1 and 2; Centre with functions 1, 2, and 3; Large Centre having functions 1, 2, 3, and 4.

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Figure 3.4 At time t=0 the population of each point was 67. This is the pattern at t=4.

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Figure 3.5 The distribution of Population at t=12 units. The structure is beginning to ‘solidify’ around five main centres. ‘suburbs’ on the surrounding points, which have coefficients of employment less than unity. This, the largest urban centre, is undergoing residential decentralization at this period. Also of interest is the ‘chance’ formation of a ‘twin-city’ on points 38 and 40, due simply to the particular sequence of fluctuations that has occurred for this simulation. In the next period, between 12 and 20 units of time, the central core of the largest centre continues to grow, but it reaches a peak at about this time. Meanwhile a decentralization of economic functions is occurring, as the short- and medium-range activities find a sufficient market in the suburbs. In Figure 3.6 we can also discern the beginning of similar tendencies for the other centres.

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After another 14 units of time have elapsed, the distribution of population and of economic activity is as shown in Figure 3.7. The largest centre has undergone both residential and economic decentralization, which has led to a decline in the central core density. Also of note is the fact that the ‘balance of power’ of the twin cores has swung in favour of point 38, which is, geographically speaking, in a more favourable situation. This development continues to the final stage of this particular simulation, Figure 3.8, which corresponds to time t=46. By analysing carefully the spatial distribution of the growth and declines that occur during different periods, we discover four distinct phases in the patterns. First, the growth is heavily concentrated in the five centres that are at the origin of the urban structure of the region. We have a period of ‘central urbanization’. In the next stage, while the central cores continue to grow strongly, the ‘growth plateaux’ are much broader, showing the effects of suburban growth. After this, an entirely different growth pattern is observed.

Figure 3.6 At t=20 the central core density of the largest centre is peaking (152) and there is marked ‘urban sprawl’.

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Figure 3.7 At t=34 the basic structure is stable. Two centres have undergone ‘central core decay’.

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Figure 3.8 Between t=34 and 46 the basic pattern is stable, except for the centre of the ‘twin city’.

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Figure 3.9 The time evolution of points A, B, and C shows spatial intraurban dynamic. The central cores of the largest centres decline strongly, and the others begin to stagnate, while the ‘above average growth’ is nearly all concentrated in the interurban zone, marking a period of ‘counter-urbanization’. In the final period of our simulation, it is clear that the interurban growth of the preceding one heralds the beginning of real competition between the various centres of the urban structure, and the growth becomes polarized into two areas in the upper and lower halves of the lattice, respectively. The results of our simulation indicate that equations (3.1) and (3.2) give rise to a much more realistic evolution pattern than those of the previous chapter. In Figure 3.9 we see the evolution of the points A, B and C which are indicated in Figure 3.7. Point A is the central core of the largest urban centre, while points B and C are in its first and second surrounding rings, respectively. We see that the internal dynamics of the centre are also reasonably well represented in the context of a model describing the growth of several cities interacting with one another within the confines of a large region.

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3.3 REGIONAL STRUCTURE—CHANCE AND NECESSITY In this section we want to show that the equations of our model are like some elastic framework which can be pulled around and made to adopt different forms depending on the ‘scenario’ of policies, technology changes and events that occur over time. Furthermore, we want to show that ‘timing’ is itself a critical issue in history, and that the nature and personality of a city, and the quality of life of its different inhabitants are all dependent on the dialogue between the processes captured in the model equations and the scenarios of policy, and of microevents that actually occur. In such a view timing matters, and the dis-equilibrium trajectory of the system is important in determining its future. This is illustrated by a sequence of scenarios. (Allen and Sanglier, 1981; Allen, 1980) Starting from a uniform distribution as for the series Figures 3.3 to 3.8, the structure A evolves. Then we explore how this situation would evolve under different ‘scenarios’ of transportation costs. Also, in the simulation B to L and K we study the effect of a small ‘new town’ added into the structure at a particular point. The simulation that we have described above is typical of others performed with the same parametric values. Of course the exact details of the structure that evolves within a region depends on its precise ‘history’—on the particular sequence of events that actually occurred—but the broad lines of the structure engendered are always similar to those described above. For example, the number and separation of the large centres that appear are always roughly the same, as are the four characteristic phases of growth. The interactions of the system provide a ‘memory’ of the sequence of events; a ‘memory’ fossilized in the spatial structure of the system. (Berry, 1976) In a second series of simulations, we have started from the same initial condition, but we go on to explore the different possible evolutions of the system resulting from different ‘scenarios’ of transportation costs, in this case much reduced transport costs, and of particular investment. The sequence of events is shown in Figure 3.10. We begin to study questions like—what are the ‘generic’ effects on urban systems of increased/decreased transportation costs? After a time of 31 units, the distribution is shown in Figure 3.11. It is indeed quite different from the previous series. We can now explore the effect on the structure of either simply continuing the evolution under the same conditions as before, or of the transportation costs being reduced substantially. In Figure 3.12 the structure that would have evolved for unchanged conditions is shown. Several centres have been eliminated and we have changes as indicated below each point in the figure. We may compare this with the structure shown in Figure 3.13, which is that obtained with a reduction in transportation costs given by the values Φk* compared to that of Φk. The real effects of a decision or a technological change that reduces transportation costs are complex and not intuitively obvious. We can calculate the ‘relative spatial efficiency’ of the different structures by considering the quantity generated by the potential demand for the goods k, at each centre i. If we sum these terms over the whole

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Figure 3.10 Sequence of Simulations described in the text.

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Figure 3.11 Structure A. Starting from an initially uniform situation, this is the structure after 31 units of time.

Urban growth, commuting and regional structure

Figure 3.12 Structure B. If the simulation is continued without change, then this is the structure at t=44.

69

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Figure 3.13 Structure D. If at time t=31 the cost per unit distance is reduced, then structure A will evolve to this at t=44. system, for all the centres producing k, then we have a measure of the total demand for function k that characterizes the particular spatial structure. This takes into account the fact that the larger the average distance that must be travelled for consumers, the less will be this total demand. Thus, the term

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provides an index of the average efficiency of a structure for a function k. The continued evolution of structures B and D of Figures 3.12 and 3.13 until time t=53 gives the stable structures C and E, which are shown in Figures 3.14 and 3.15. In Table I we calculate the index µ for the different levels of these two structures. We see that they are indeed of quite different efficiencies, particularly at levels 3 and 4. It turns out that this is quite different from the structure of the previous series, owing to the different historical accidents that characterized it. Another point of interest is that we find that the ‘natural evolution’ of the system does not necessarily change this efficiency in a positive sense. In order to see this we must simply calculate µk for structures B, C and E, and this is shown in Table II. We see that in both cases the average distance that consumers must travel for the various goods actually increased in the time interval t=44 to t=53, as a result of the structural evolution of the system. This begins to reveal how naïve it is to simply suppose that ‘free markets’ lead to ‘optimal’ economic structures. Clearly, the efficiency of the structure is a complex function

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Figure 3.14 Structure C evolves from B (t=44) at time 53, if there is no change in the parameters.

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Figure 3.15 Structure E. At t=53 structure D evolves to this. Transport costs remain reduced. Table I Index of Efficiency of the two spatial structures C and E. Level 2

Level 3

Level 4

Total

Structure C

0.09525

0.018

0.0043

0.1174

Structure E

0.097

0.025

0.0093

0.1412

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Table II Index of Efficiency for B, C, D, and E Level 2

Level 3

Level 4

Total

Structure B

0.0966

0.0185

0.00745

0.1224

Structure C

0.0952

0.018

0.0043

0.1174

Structure D

0.1081

0.0316

0.0096

0.1494

Structure E

0.097

0.025

0.0093

0.1412

B and D are at t=44, while C and F are at t=53.

of the changing spatial structure, and this evolves in a complex way which economic equilibria cannot represent. Another interesting experiment we can perform is to examine the effect on the evolution if, after enjoying a period of reduced transportation costs (sequence A−C)—on to E at t=53, the transportation costs increase at t=44, and return to their previous high value. In Figure 3.16 we see structure F, and we may compare its efficiency with that which would otherwise have been attained, E (Table III).

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Figure 3.16 Structure F. At t=53, this is what evolves if for structure B at t=44 the transport costs are returned to their normal value. Table III Index of Efficiency of Structures E and F Level 2

Level 3

Level 4

Total

Structure E

0.097

0.025

0.0093

0.1412

Structure F

0.0974

0.027

0.0075

0.143

From this we again see how the precise ‘trajectory’ of the system matters. Even though E and F have the same transport costs and started originally from the same initial condition,

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the fact that F had higher costs for part of the time led to a different (more efficient) spatail structure which shows up later when transport costs are reduced again. From this we see that the evolution of the system leads to at least a partially counter intuitive result; the effect of increasing the cost per unit distance of transporting functions 2 and 3 has nevertheless given rise to a structure such that more is consumed, meaning that on the average the costs of obtaining these are less than for the simulation with cheaper transportation, E. Although costs per unit distance may increase, the resulting evolution of the system may involve a structural evolution such that distances are more than proportionally shorter, giving rise to this ‘surprising’ result in the long run. Returning to the situation at time t=44, structure B, we wish to try to ‘modify’ the structure and help the backward rural area that has formed between the main concentrations. In order to do this, we make a specific ‘investment’ of 21 units of population and employment at the point 33. After running the simulation twice, we see from Figures 3.17 and 3.18 two quite different possible results at time t=53, owing to the different series of random fluctuations that have occurred in each simulation. In K the ‘new town’ has managed to establish itself, and to modify the structure that would have evolved—C. In the other case L, however, the ‘investment’ has wasted away and the structure is very comparable to that of C. The relative efficiencies are given in Table IV. From this we see that K is considerably more efficient at delivering levels 3 and 4 than either C or L. This result shows that there is a threshold size which a perturbation requires, if it is to modify the evolution of the structure. In the case shown here, this threshold is around 21 extra units on point 33. A larger investment would almost certainly succeed in changing the structure, whereas an injection of less than 21 units at this point will almost certainly waste away to nothing. Once again an ‘equilibrium’ based model can say nothing about critical thresholds and necessary levels of intervention. What is important to a ‘planner’, who is attempting to intervene in the evolution of the system in order to attain some kind of greater social welfare than would otherwise have been the case, is the stability of the evolving structure with which he is faced. If it is very stable, then this means that there is a very high threshold which must be exceeded in order to modify it, and perhaps it is beyond the means of the planner in question, or perhaps the results do not justify such a large intervention. What is clear, however, is that the whole question of successful planning and intervention within urban systems must depend on a knowledge of the stability of the structure that is evolving without this knowledge many well-intentioned projects will prove abortive, as the system ‘unexpectedly fights back’.

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Figure 3.17 (left) Structure K. Here we see the urban structure that has evolved at t=53, when 21 units of population were added to point 33 at time t=44. In this case the ‘investment’ has grown from 90 to 95, and it has also succeeded in increasing the population on the surrounding points—we may say that it has ‘succeeded’ in its intention of stopping the relative decline of this locality.

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Figure 3.18 (right) Structure L. An identical simulation as that of Figure 3.16 starting from the structure B (Figure 3.12 with 21 units added to point 33, leads in this case at t=53 to this result. The different history of small fluctuations around the values dictated by the equations had led to the ‘failure’ of the investment. The population of point 33 has declined from 90 to 77. These two qualitatively different central place structures

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(Figures 3.16 and 3.17) are possible from the same ‘scenario’ because the investment only produces a situation of marginal stability, and so small fluctuations can cause it to evolve to either stable structure. There is a threshold for the size of investment that can ensure ‘success’. Table IV The Efficiency Index of Structures C, L and K Level 2

Level 3

Level 4

Total

Structure C

0.0952

0.018

0.0043

0.1174

Structure L

0.106

0.0176

0.0049

0.1286

Structure K

0.102

0.0225

0.0066

0.1314

3.4 DISCUSSION The model we have developed, although still very simple, enables us to examine the long term effects on the whole system, either of changes in parameters concerning transportation costs or, non-linearities in the cost functions depending on technology or secondly, those of specific changes imposed on the spatial structure. The dual aspects of chance and determinism appear clearly. As we see from the two series of simulations when we start from an initial situation empty of any urban structure, there are many possible paths of evolution open to the system. However, as the structures begin to form, following a particular sequence of events, many of these paths become virtually impossible, and the evolution proceeds with a restricted ‘branch’ of the whole tree of evolution. The ‘planner’ can then discuss the relative merits of different possible attainable paths (for energy costs, social justice, etc.) and decide how to induce the system to change branches, or to ‘choose’ the desired branch at a point of bifurcation. These ‘self-organizing’ models of urban form offer us a kind of ‘operationalized’ lateral thinking device, which can explore many different possible configurations of urban processes, including many that we would not be able to imagine. In this way, real alternatives to any existing configuration can be examined as a possible candidate for the future, as a goal for policy or planning to attain. The new perspective of our model views the evolution of a system of urban centres as a’dynamic’ interaction of ‘supply’ and ‘demand’ in the two spatial dimensions of the chosen region. Instead of this interaction leading inevitably to a ‘unique’ equilibrium structure, characterized by an ‘optimal’ distribution of population and economic activity, we find a multitude of possible stable stationary states, of differing character and ‘optimality’, which can be attained through different dynamic evolutions.

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In undertaking intervention in the evolution of a complex system, it must be recognized that the various branches differ from one another qualitatively, being perhaps of different character and optimizing different factors. It is therefore necessary to define a combination of criteria in order to decide which branch seems more desirable, and in fact this multi-criteria analysis can only be correctly framed when considered in conjunction with a dynamic model of the type described here; only then can the ‘trade-offs’ between the values of the various factors be explored for different possible evolutions. The solutions open to the system only permit certain simultaneous values of factors such as energy costs, maximum densities, haulage distances, commuting distances, variances of these, accessibility of parks; therefore decisions made to attain some policy objectives, in ignorance of the dynamic evolution of the system, are more likely to simply displace a problem, if indeed they succeed in doing that. Even such a simple, highly artificial computer simulation as that presented here already yields a multitude of very complex paths of spatial organization. This shows that there is indeed an important role for local, regional, and national planners. However, they will only be able to influence events in the manner in which they intend if they have access to some model of the kind described here, which can permit them to explore the probable consequences of a given policy or action.

4. INTERVENING IN THE SYSTEM Here we extend the work described in Chapter 3 and consider more fully the effects of interventions in the system described by the model. In particular, we will consider the rather important example of the effects of lifting trade barriers. This problem of course bears some resemblance to the question of reducing transportation costs dramatically, or building a bridge or tunnel to link two previously separate regions. The point is that two previously stable urban hierarchies of centres are suddenly brought into contact with each other, and the resulting changes are clearly difficult to anticipate. 4.1 LIFTING TRADE BARRIERS The presence of long range functions in both hierarchies ensures that the effects of lifting the frontier are not only felt at the border but right across the whole domain. Naturally, short range functions interact locally at the border, but also they are affected right in the interior of each territory through the action of the urban multiplier, as the long range functions interact. Although it is generally assumed that it is beneficial to establish free trade agreements, and to lift frontiers whenever possible, there really has been no quantitative mathematical model which has been developed that shows what the long term effects of such actions really are. It seems therefore that political decisions of this kind are based on economic ‘ideology’ whereby it is believed that an unfettered market evolves to a ‘better’ situation than otherwise. The work presented here offers the possibility of testing these assumptions, since it simulates the path of spatial socio-economic development resulting from the lifting of some trade barrier at different possible stages of the development of the urban hierarchies. What emerges from the study is that lifting frontiers changes the evolution of the system, but what is considered to be ‘better’ or ‘worse’ depends both on who and where one is in the system, and what is being sought from life. The models attempt to capture some of the complexity of the real world, and clearly, the adoption of simple ‘ideologies’, whilst understandable, is no substitute for evaluating the complicated compromises that really are generated when decisions are taken. And evaluation needs ‘values’. The exploration of the consequences of using different values sets to weigh choices is itself an important issue that this work raises. Here, we shall examine the evolution of two central place systems, when the frontier between them is lifted at different moments, as well as considering this for different possible situations of transportation technology and demographic change. The equations which we shall use have been explained in our previous article, and we shall simply write them down here. The rate of change of population xi at i is:

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(4.1)

and for the employment at

in activity K, at i, (4.2)

We shall again use a similar ‘lattice’ of simulation as before, but this time it will be of 40 points only. As in the previous chapter, there are four levels of economic activities of successively greater range and higher market threshold. As the basis for our study here, we have taken as our initial distribution of population and of economic functions, the situation attained in one of our earlier simulations at time t=20, (with a central band of 10 points removed) and is shown in Figure 4.1, with a frontier drawn between the 20 upper and 20 lower points. Our dynamic equations (4.1) and (4.2) allow us to study the evolution of the system with different scenarios for the lifting of the frontier, the demography of the population and the transportation costs. As We shall see, the urban structure is marked permanently by these different scenarios, and evolves to different, but stable (to small fluctuations), structures. From our equations however, we can deduce much more information than the simple fact that they are different. For example, the term (4.3)

is the fraction of xj that are clients of centre i for the function K. We can now improve on the structural indicator of the last chapter by noting that: (4.4)

is the quantity of ‘goods’, K, flowing per unit time, between the point i and j. These quantities can of course be printed during the simulation, and therefore we know the commercial traffic flowing between the points of our system at all times. We may also characterize the particular structure by calculating the total traffic flow (i.e. ton-miles) necessary in the system by summing these flows over all links and, furthermore, we can then calculate the mean haul distance per function K by dividing the total ton-miles by the total tons shipped.

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HK=Total haulage of K in the system =

Figure 4.1 The intial distribution of residents and of economic functions for our regions, A and B. • Level 1; Level 2; Level 3; Level 4. and mean haul distance per function:

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Let us now turn to our simulations, where hopefully, all these points will become clear. The values of the parameters used are given in Appendix 1. 4.2 POSSIBLE HISTORIES—4 EXPERIMENTS Experiment 1 In our first ‘experiment’, we have allowed the two regions A and B to evolve separately. A ‘customs barrier’ eliminates trade between the two regions for 21 units of time. The total population of each region is held constant, although each urban structure continues to evolve to A′ and B′, Figure 4.2 respectively. (For the sequence of events see Table I).

Table I The sequence of simulations concerning the lifting of the frontier between A and B Time

Good Transport

Poor transport

t=0

AB

AB

t=21

A1′ (AB)′1 B1

A′2 (AB)2 B′2

t=42

A′ (A′B′)1 B′

(A′B′)′2

t=63

A*1 B*1

t=84

(A*B*)1

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Figure 4.2 The situation at t=21, for the separate evolution of the two regions, with constant population and the values of Φ corresponding to ‘good’ transportation. The next part of the experiment is to lift the frontier between the two regions, and allow the two urban hierarchies to interact and for a new trading pattern to be established which at time t=42, is shown in Figure 4.3 (A′B′)1. Experiment 2 The second experiment concerns the structure which would emerge if the two urban systems are joined immediately, at t=0. We shall then compare this final structure (A′B′)1, obtained by uniting two ‘mature’ hierarchies A′ and B′ with that which would have been obtained if the two ‘young’ hierarchies A and B had been united at the beginning of the

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experiment. In that case, the urban structure would have been as shown in Figure 4.4 (AB)1.

Figure 4.3 The urban structure at t=42, when the frontier between A′ and B′ was removed at t=21. We have constant total population and ‘good’ transportation. The structure (AB)1, has attained its stationary state at t=21, and hence we may compare it with (A′B′)1, at time t=42. The first remark is that the structure (A′B′)1 is clearly different from that of (AB)1, the latter being much more ‘centralized’ than the former which has two ‘capitals’ having all four functions. Thus we find that, for the same equations, with the same parameters, the same demographic scenario, we obtain two different stable structures simply because of the different moments at which the frontier was lifted. Once again it is important to point out that equilibrium models could not

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obtain this kind of result. In Table 2 we give the complete details of the variables Hk and dk for all the simulations. We may characterize these differences by examining the ‘quality’ of the two structures. For example, both (A′B′)1 and (AB)1 have the same population, but demand a different number of ‘ton-miles’ and hence a different consumption of goods and services due to the ‘losses’ involved in greater transport costs. For (A′B′)1 we have 3178 (tonmiles), while for (AB) we have 3364, a difference of 6 per cent, and, as concerns function (4), we have a difference of 20 per cent in the transport ‘costs’ of the two structures. And yet both are stable to small fluctuations around the values given. In fact the difference of ‘transportation efficiency’ in the two structures is reflected in the figures for the total consumption at each level, and in the different ‘mean haul’ distances associated with these. (A′B′)1 Consumption of 4=131 mean haul distance—10 units, (AB)1 Consumption of 4=123 mean haul distance—12 units.

Figure 4.4 The stable state attained at t=21, when the two regions A and B are united at t=0. The population is

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constant, and we have ‘good’ transportation. Table II HK total transport generated (nonmiles)

Consumption of function K

d

4 2

Mean haul distance

2

3

4

2

3

3

4

A′1

133

81

66

355

379

545 2.7

4.6

8.2

A″1

222

111

81

222

417

682 1

3.7

8.4

A*1

147

96

68

315

337

557 3.1

3.5

8.2

B′1

123

87

64

370

356

675 3

4

10.6

B″1

223

103

77

206

445

888 0.92

4.3

10.8

B*1

136

86

64

337

362

684 2.5

4.2

10.8

AB1

268

171

123

687

734

1560 2.5

4.3

12.6

A′B′1 273

162

131

698

785

1306 2.6

4.8

10

AB*1 273

162

131

687

713

1307 2.5

4

10

A′2

142

66

34

252

319

241 1.8

4.8

7.1

B′2

141

71

30

249

306

270 1.8

4.2

9

AB2

272

140

65

533

622

505 2

4.4

7.8

AB′2 286

128

65

489

642

495 1.7

5

7.6

Our dynamic equations furnish us therefore with a great deal of information, for example, about the energy consumption involved in the ‘functioning’ of a given structure. Thus, the total transportation generated in the system is related to the energy consumption of the system, but the efficiency of its spatial structure is related to the total transportation generated (or required) per head of the population, and this is precisely the ‘mean haul distance’. The shorter this is, the more ‘efficient’ the structure is for the distribution of this particular good or service. Similarly we may print out the ‘passenger-miles’ generated by commuter traffic throughout the system. We have not only the average consumption of the system but also its distribution and hence the extremes associated perhaps with very poorly served communities. Presumably, any policy designed to promote some socially desirable structure, must take into account not just the average value for the whole region, but also the variance around this. Experiment 3 Let us continue our simulation experiment by returning to the moment t=21, just as A1 and B1 were united, to give (A′B′)1 and let us suppose that instead of being united the customs barrier remains in place, and A1 and B1 continue to evolve separately. During the next interval, however, we shall suppose a period of demographic growth during which

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the population at each point increases proportionally to its size until, at t=42, A′1 reaches A″1 with population 1823 and B′1 with population 1819. In Figure 4.5 we see the two structures, which have reduced some ‘mean haul’ distances. For example, compared with A′1 and B′1, we find the results shown in Table III. Thus this increased population density has served to improve the service of ‘shorter range’ functions, but the increased centralization of the long-range function 4 has in fact worsened the average service. The question we can now examine concerns the effect of changing a parameter, the natural growth rate, letting the simulation run, and then changing the parameter again in

Figure 4.5 Instead of uniting the regions A′1 and B′1 at t=21, we leave them separate until t=42. We obtain a population for A″ of 1823 and for B″ of 1819.

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Table III Here we see the complexity of the effects. The mean haul distances for the short range function 2 are shortened considerably, but the increased centralization has lengthened the mean haul distances of the function 4 Mean Haul Distances Structure

Function 2

Function 3

Function 4

A′

2.7

4.6

8.2

A″

1

3.7

8.4

B′

3

4

10.6

B″

0.92

4.3

10.8

such a way as to return the population at t=63, to the level it had at t=21. We see that the resulting structures A+ and B+, Figure 4.6, are not the same as A′1 and B′1 The structure attained after an increase and then decrease of population, does not come back to its initial conformation, as it has been irreversibly, marked by the event. As can be seen from the table, A*1 and B*1 is a more efficient structure than A′1 and B′1, with shorter meanhaul distances for nearly all the functions. If we now unite the two regions, we obtain (AB)*1 (Figure 4.7), which, with the same population as (A′B′)1, is more efficient, particularly for the function 3, which involves 10 per cent less ton-miles and has a meanhaul distance 20 per cent shorter. The results obtained show us how important the role of history is in determining the structure of urban systems. In fact, it clearly demonstrates that there can be no equilib-

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Figure 4.6 From t=42 to 63, we keep the frontier and reverse the population trends. At t=63, population A1=1523 and B1=1519.

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Figure 4.7 If we lift the frontier at t=63, then at t=84 we find the structure above. rium theory relating the urban structure observed in a system to the boundary conditions applied to the system. Experiment 4 Another important factor in determining the structures and traffic flow patterns of a region is not only the timing of the lifting of a frontier with respect to the degree of maturity of the urban system, but also the quality of the transport system at that time. In this experiment, we examine the evolution of the two regions A and B from the same initial condition as before, but where the coefficients of transport costs (given in the Appendix I) are considerably higher than in the first series. Thus, we compare the evolution if they remain separated for a time t=21, A→A′2 and B→B′2 (Figure 4.8), and then are united to form (A′B′)2 which is shown in Figure 4.9. We can compare this with

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Figure 4.10, showing (AB)2, the structure obtained when the two regions are united at t=0. They are very similar, except for one centre, situated on the frontier of B with A, on the left-hand side. In the note, comparing the different results (AB)1, (A′B′)1, (AB)*1, (AB)2 and (A′B′)2, that for a particular region certain historical sequences can lead to structural changes which are not intuitively obvious. Apart from this, however, the structures obtained from the early and late unification of two regions with high transport costs, are much more alike than those obtained for low transport costs.

Figure 4.8 A and B as shown in Figure 4.1, but this time transportation costs in time or money are greater than in the preceding studies.

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Figure 4.9 If at t=21 we unite the two regions, then after another two units of time, at t=42, we obtain the above structure.

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Figure 4.10 This distribution of population and economic activities is obtained for the same high transportation costs as above, but for unification of A and B at t=0. We may summarize the tendencies indicated by our various simulations by saying that the urban structure observed in a region depends on the sequence of ‘internal’ historical accidents, which was dealt with in the previous chapter, and also on the relative timing of demographic changes, of the lifting or imposing of economic barriers and on the range of interaction of the centres, which depends on the transportation technology at a given time. The interplay of all these factors influences the evolution of the system.

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4.3 INTERVENINGIN REGIONAL DEVELOPMENT In this section we explore the outcomes of attempts to influence the evolution of the theoretical simulations described above. This allows us to demonstrate the potential of our methods in the examination of the effects of different decisions, where either local or global changes can be imposed on the system, and where we begin to see the possibility of studying quantitatively the most basic issues of government: who should a decision favour and how much, and at the expense of whom? And what hierarchy of decisional power will lead to which local strategies, and what will be the impact of the latter on the evolution of the whole? The importance of these results is not in their detailed resemblance to reality. It is rather in the principle which is demonstrated that in a complex system of interdependent entities the decisions made by individuals, or by collective entities representing certain localities, lead to the emergence of large scale structure, which is not anticipated in their thinking, and which later will in fact determine the choices which are open to them. This is the ‘collective’ aspect of individual actions which characterizes society. The models here can help to make explicit the longer term, structural effects that may emerge ‘surprisingly’ from the adoption of certain policies and decisions. By providing information about these longer term implications, hopefully the actors of the system can weigh their decisions in the knowledge of these collective effects, instead of simply discovering that the ‘system’ is sweeping the various actors in a quite unexpected and undesirable direction. Let us return to the simulation at t=34 with an urbanization pattern as shown in Figure 4.11. We shall investigate the effects of three different decisions and afterwards the question of a decisional strategy. First, let us suppose that the population of the region as a whole is fixed over the next period, and explore its relative growth and decline from the time t=34 to the time t=50, First of all, if there is no intervention, no decision, and all the parameters are unchanged then the ‘growth and decline’ zones are those shown in Figure 4.4. We note that the system undergoes a certain ‘polarization’, and that in particular, the area across the centre of our region, which has no urban development continues to decline, and in terms of percentage change is most marked.

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Figure 4.11 The spatial distribution of jobs and population at time t=34 of our earlier simulation.

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Figure 4.12 Urban centres compete among themselves leading to a polarization of the growth. This basic pattern of change is independent of the particular pattern of fluctuations the occurs Now let us examine the effects on the growth/decline patterns of system, of some governmental ‘road building’ program, or of some new technology. which has the effect

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of halving transportation costs (that is the values of Φ(2), Φ(3), Φ(4) relevant up to t=34 are now halved). This is in fact a strategy that has been proposed various countries in order to help arrest the decline of different regions. In the case our simulation (and as is perhaps the case for those countries) the improved transport efficiency has the effect of accelerating the decline of the rural areas between centres, and of favouring most the largest centre, as in Figure 4.13. The third strategy which we shall examine concerns the possibility of directly interfering in h urban structure by the placing of a specific investment at a particular point This corresponds to the idea of a ‘New Town’ or of the sustaming economic growth in the otherwise declining zone. The most important remark that must be made is that in all our simulations there are presen fluctuations of population and employment which test the stability of the basic structure, and could if this is not assured lead to the amplifications of a particular fluctuation and the adoption of a new spatial pattern. However, we may see from the

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Figure 4.13 If transportation costs are halved at t=34 the system evolves as follows until t=50. earlier figures of this chapter that the basic structure becomes stable to these small fluctuations by about t=16. Thus, we know already that if we wish to modify the pattern, and in particular to move to a structure without the ‘declining rural backwater’ in the middle, then a perturbation of some larger size is required. In fact, in a series of computer

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simulations it was possible to ascertain that for almost certain self sustaining growth at the chosen point 26, it is necessary to invest 19 units at time t=34. If less than this is inserted then the chances are that it will simply waste away since the basic structure is stable. But the question then arises as to who is favoured and who is penalized by an action, and who is making the decisions, and what are the decision criteria used, and to whom is he or she responsible? Let us consider the difficulties that still arise in a ‘democratic’ situation. In Figure 4.14, we see the growth/decline pattern for a simulation where 19 units of population and employment were added to point 26. The investment flourishes, producing a remarkable increase of population and jobs at and around the point. Of course this is at the expense of other points which would otherwise have grown, but it can be shown that the final structure resulting at time t=50 following the perturbation, is, considering only the transportation costs, more ‘efficient’ than otherwise, since there is less transportation required for the same total consumption as before, which means that the ‘mean

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Figure 4.14 If 19 units of population are added at t=34, then this is the evolution to t=50. haul distances’ are shorter and variations in the consumptions of goods between urban and rural areas is less marked.

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However, before drawing any hasty conclusions about which strategy should be adopted, let us briefly examine the manner in which the administrative division of a region may affect which decisions are adopted. Consider the case where the lattice is divided into two separately governed districts: the upper and the lower halves. Let us briefly discuss the consequences for each half of each of the three strategies. First, if there is no change, Figure 4.12, then between t=34 and t=50 the relative growth of the two regions is: upper half +11, lower half −11. (This is the relative growth of population, and let us suppose that for some reason this growth is considered desirable for the region.) Let us compare the second strategy to this, in which transportation costs have been halved (Figure 4.13). The particular history of the fluctuations that occurred leads to quite different structures. For the second strategy, greatest growth occurs in the largest centre (point 15), but this growth is in some way achieved at the expense of the district itself, since for the period t= 34 to t=50 we find, upper half −6, lower half +6, a reversal in the relative tendency. The third strategy consists in placing 19 units of population on the point 26, which is in the lower half. Not surprisingly, when the investment pays off we find that the lower half gains greatly: upper half −41, lower half +41. From this we see that it would pay the lower half to invest the 19 units of population itself, rather than doing nothing, since it gains 41–19+11=33. However, we must realize that this result is dependent on the fact that the upper half does not ‘riposte’ in this simulation. Our model begins to show us the real complexity of decision making, where the reaction of the other actors of the system to changing circumstances must be taken into account if it is desired to attain at least some partial objective. In the case of our particular example, the ‘strategy’ played by the lower half is to invest in a centre on its frontier with the upper, which causes a growth at the expense of the upper half. This basic idea of strategy corresponds clearly to many problems such as the conflict of two political parties where effort must go into attracting supporters from the middle ground, and similarly for competing firms with different ranges of products. 4.4 MULTIPLE POSSIBLE FUTURES The new perspective behind our model views the evolution of a system of urban centres as a ‘dynamic’ interaction of ‘supply’ and ‘demand’ in the two spatial dimensions of the chosen region. Instead of the ‘interaction’ leading inevitably to a ‘unique’ equilibrium structure characterized by centres of production and flows of goods and services, which are supposedly an ‘optimal’ or at any rate a ‘neutral’ translation of the ‘demand’, we find a multitude of possible stable stationary states, of differing character and ‘optimality’, which can be attained through different dynamic evolutions.

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This clearly must bring into question any ‘equilibrium’ theory which may claim to explain spatial structure or ‘predict’ the effects of some action or policy. Our experiments show that structure is not determined uniquely by the ‘parameter values’ of its environment and its processes, but in fact also depends on its history, so that the size and relationship between centres, the efficiency of the structure etc. really depend precisely on the timing and sequence of events or actions, factors lost to equilibrium based models. This changes profoundly the nature of ‘explanation’ in such systems compared to that of classical science. Instead of being able to relate structure to the values of the parameters of the environment and the mechanisms, explanation also includes the initial condition, and the detailed history! We see that the structure of our system results from a mixture of historical necessity and historical accident, because the non-linear interactions provide a rich ‘media’ which events mark irreversibly. This richness poses real problems at attempting comparisons between structures resulting from different scenarios. There are several possible bases of comparison, and it is not entirely clear which are more fundamental. For example, one could compare spatial structures at fixed time intervals under different scenarios, which would express a real confidence in the absolute values of the time constants of the dynamic equation. Or, one could compare the spatial efficiency of different structures that evolve at moments when they have identical populations. This may correspond to quite different times, since the ‘demographic potential’ of a region is affected by its economic attractiveness (net migration) and hence we can have very different rates at which a given population is attained according to the scenario. The comparisons we have used in this paper are a compromise. We have chosen a time interval of 21 units which is sufficient to assure that for each ‘slice’ of evolution the system virtually attains its stationary state. Thus, our comparison is one of possible stationary states and not really a continuously dynamic evolution. In any real problem care would need to be exercised in order to synchronize demographic and economic changes with other factors of the scenario, and it must be said that the comparison of the relative merits of different branches of such an open evolution is a delicate matter. The potential usefulness of this kind of model can be estimated by considering the importance of a decision such as that of lifting the internal frontiers within Europe. Naturally, it will mark irreversibly the evolutionary path of European cities and regions, influencing patterns flow of goods and services and of migrants. Patterns of investment, and of consequent economic growth and decline will all be affected, and it is believed that this will be, on the whole, for the greater good of the Community as a whole. However, this has never been shown clearly by any realistic calculation or simulation. But, even if we accept that it is better to lift frontiers than not to, we would still like to know what the patterns of growth and decline will be, and what measures and policies should be put in place to best deal with them. Our approach can possibly help with this. If we lift the frontiers in Europe, then as it is an area comparable to the USA, with a comparable transportation technology and a similar consumer society, should we expect that, when the ‘frontiers’ are lifted, the rather short ‘mean haul’ distances will evolve, through the elimination of competing centres, towards the type of ‘flow structure’ observed for the USA (Hassler, 1977)? But, our analysis tells us something different. It tells us that the joining of ‘mature’ urban systems does not give rise to the same ‘centralized’ structure characterized by long mean-haul

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distances, as the joining of two ‘young’ regions. It tells us that what happened in America, will not necessarily happen in Europe, because the historical circumstances are entirely different. It tells us furthermore, that whatever flow patterns we see, for a given region, they are not necessarily the ‘best’ ones. Indeed it falls upon us to define criteria to decide which structures would be desirable, and then, knowing the dynamic equations, how, and at what cost, they could be achieved. The importance of this section should therefore be judged, not on the details of the particular example used, since clearly our simulation model is outrageously simple compared to reality. However, the real point is that it seems to capture in a simple way the essential dilemmas that lie at the heart of social systems, and questions of the legitimacy of institutions, and of government and their relationship to the individual. Our models show that even if individuals pursue their own goals selfishly, there is a collective structure which emerges which is not part of any individual’s plans. An urban hierarchy, and within that cities with internal structures emerge, offering differential access to employment and amenities and characterized by different global characteristics. These collective structures arise from the interaction of individual decisions, but of course, then constrain the choices and options open to the individuals within them. In other words, the ‘urban hierarchy’ and the ‘city structures’ that emerge, arise from a permanent dialogue between the individuals, their goals and aspirations, and the macro-structure that they have allowed to emerge. It is only with the appearance of computer based simulation models such as the simple one proposed here, that a conscious exploration of the consequences of individual and collective decisions can be explored. This is really the justification for spending time describing these extremely simple models. This is the basic aim of the methods that we have described here, by choosing the various parameters so that they correspond to a particular urban hierarchy, it is possible to simulate not only the long term repercussions of a given strategy for the immediate locality involved, but also the consequence of that strategy for the region in which it is embedded.

CASE STUDIES AND FURTHER DEVELOPMENTS

5. MODELLING THE LONG TERM STRUCTURAL CHANGES IN THE UNITED STATES 5.1 INTRODUCTION In the preceding sections ‘interurban’ models were developed which generated the linked spatial evolution of population and economic activities over long times. While the theoretical ideas seem rather seductive, the question of their usefulness and successful application remains to be proven. Here we shall describe a simple application of the ideas that was made to try to model the changing patterns of population and economic activities in the United States, from 1950–1980. (Allen and Engelen, 1985) The chapter describes a limited attempt (owing to limited funding) to understand the migration flows between the different States of the USA, and to explore how they might continue until the year 2000. The problem is a very interesting one, and at least would link the economic, demographic and migration issues together, instead of treating them separately, as is still the case in the calculations used by the US government today. However, the work described here resulted from a 6 month study, with the consequence that it is inevitably rather superficial. However, the results seem informative and interesting and represent a useful application of the models. 5.2 STRUCTURAL CHANGE IN THE USA Changes in the economic and settlement patterns that have occurred in the United States over the past decades were studied by a number of authors, and as a result a view began to emerge from the discussions of geographers and economists which provided a global interpretation of these patterns of change as the growth and development of a large, interacting spatial system. Here we refer particularly to the work of Berry and Kasarda whose interpretation of the changing patterns is truly historical and long term, and which we shall briefly sketch first. Then, more particularly, we focus on the identification of mechanisms of change which seem particularly relevant to the situation in the 60’s and 70’s, and rely largely on the work of Yeates. Having identified the historical framework of the spatial evolution, and identified specific mechanisms at work which are producing today’s changes we show how the dynamic models that we have developed capture the richness of these effects in a causal, though not necessarily deterministic, model.

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The land settlement pattern of the US reflected initially the fact that immigrants landed on the east coast, and after succeeding in the initial problem of surviving, were gradually attracted by the distribution of the important resources for that particular economy—good farm land. Towns and cities began to grow up around the trade with Europe, and also as central places within this agricultural community. Then, as the industrial revolution spread from England, factors other than agricultural land became important resources, and because coal and iron were discovered in vast quantities to the interior of the previously populated regions of the coast, investment and jobs sprang up in Pennsylvania, New York, West Virginia and Ohio, pulling the population westwards. Population growth over the next decades reflected largely this new distribution of resources. The subsequent discovery of more good agricultural land, together with the diversification of industry later redefined once more the resources demanded by the national economy, and broadened still further the spatial extent of investment, employment and of settlement. All sorts of metallic and non-metallic minerals became valuable and were mined, drilled for, shipped by rail, road, sea, air and pipeline back to the manufacturing centres of the North East. The relationship between the very large centres of population of the North-East, and the smaller, more scattered communities of the South and West became that of the heartland-hinterland, reflecting a functional and organizational structure somewhat like an empire. The North East had the large centres of population, and the economic control of the manufacturing and service industries. The other regions—the hinterland—existed to send raw materials to the factories and consumers of the heartland, buying back expensive manufactured goods, working for low wages in highly specialized and dependent communities whose livelihood could disappear following some change in taste, or of the cost of production factors in the North East. However, gradually, the population of the hinterland began to diversify their economy base, and to attain sizes which enabled tertiary and service industries to install themselves, so providing new, local competition to the established centres of the heartland. As this occurred, so the NE gradually lost some of its more distant clientele, and in consequence some of the resulting employment. These jobs, transferred to the new emerging centres of the south and west, served to further fuel the growth that was occurring due to the shifting pattern of the manufacturing industries. The long term historical trend underlying the very great changes of recent decades is therefore the demise of an empire. Instead, we see emerging a collection of semiautonomous, but economically integrated, interacting regions. The economic bases of these regions still reflect the comparative advantages offered by the region for a particular type of activity, but this has become diversified and much less dependent on the North East as economic and demographic growth in the south and west continue to transfer power to these regions. This very broad view of the spatial evolution of the settlement pattern of the United States is an interesting backcloth to the analysis of Yeates in ‘North American Urban Patterns’, in which he clarifies the processes underlying these changes, and identifies four specific mechanisms. The first one is that of Economic Convergence. From an examination of the data concerning the recent evolution of the urban and economic spatial pattern, Yeates finds that there has been a strong decrease in the differences between the economic structure of different regions. In a sense regions have all become

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‘more average’, as tertiary and service activities developed strongly in regions where hitherto it had been notably absent. This may be due to many factors such as the much greater circulation of information concerning the possibilities of employment and wages rates elsewhere. So, areas having very low wages lost migrants to areas of high wages, but the fact of low wages attracted more industry into a zone, increasing the demand for labour to some extent, and therefore also tending to increase the wages offered in low wage areas. Also, national chains were established, and government services extended, all of which tended to increase the uniformity of standards of pay expected by both workers, and employers. This decrease in the disparity of income is tabulated below. The second important element identified by Yeates as being important in the changes that have occurred in the regions of the United States is what he terms the ‘staples’ hypothesis. This recognizes the fact that the different regions of a nation will tend to develop a ‘base’ economy consisting of certain staple products or commodities which reflect the natural advantages that the region possesses. Furthermore, the size to which the regional economy, and population grows will depend on the size of this basic sector. Because of this, the demand from the national economy for the particular staple of a region will therefore tend to dictate the growth or decline of the region. The third mechanism identified by Yeates as being of importance in the changes taking place in the US economy, is that of economic divergence, a process that already been hypothesised by earlier authors. This mechanism is one by which some relatively small change corresponding for example to the location of a new manufacturing plant in an area sets off a chain of events leading to a further increase in the location of firms and services according to the interaction scheme shown below. The impact of a new plant on the local economy is amplified by two interrelated processes. The first relates to the direct increase in local job opportunities which leads to some population increase and the creation of a wider variety of skills in the local labour force. This provides a greater attraction for other industries to enter the area, and also creates an additional demand for more local services which, because of the population increase can now be provided at lower per unit costs. This leads to a better level of local service provision which can well prove attractive to other plants that might be considering locating in the area.

Table I Regional Distribution of per capita incomes as a percentage of the U.S., from 1930–1970, from Yeates REGION

1930

1950

1970

New England

129

106

108

Middle Atlantic

140

116

113

East North Central

111

112

105

West North Central

82

94

95

South Atlantic

56

74

86

East South Central

48

63

74

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West South Central

61

81

85

Mountain

83

96

90

130

121

110

Pacific

Figure 5.1 Circular and cumilative causation model with respect to the implantation of a new manufacturing firm in an urban area. The second interrelated process concerns the indirect impact on industrial activity and population growth due to the forward and backward linkages that may well be created by the input and output requirements of the newly established plant. The size of these multiplier effects will depend in general on the size of the urban area in question, and will be greater the larger the urban area. In fact it is through processes of this kind that a region arrives at its ‘specialization’ in staple products, and obviously, this development does not expand indefinitely. Initially, there are increasing returns to scale as a manufacturing ‘complex’ develops in a region, but later, there are decreasing returns to scale, the gradual exhaustion of the local natural resources and the problems which arise in exceedingly large cities, which lead eventually to a saturation of growth, and to economic stagnation. Another important feature concerning the changes that have occurred in the spatial structure of the US economy, is that of the effects of decline. In general, it seems that the multiplier effects attached to growth and to decline are not entirely symmetrical. The social and psychological investment in a community, together with the existence of welfare, mean that people who lose their employment do not immediately migrate to

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areas of supposedly greater opportunity. Also, very often, they are skilled only in the ‘staple’ sector of their region, and it is precisely this specialization that is in oversupply, and has given rise to the unemployment. The pattern of events, in a region which undergoes a long period of decline is that the young grow up with the idea that they should leave the area in search of employment, and this is indeed what seems to occur. So, any model which we attempt to construct to describe the flows of migrants from one region to another must take into account this basic asymmetry whereby population responds to positive opportunities by migratory flows, but economic decline does not lead to the exodus of the local population to the same degree. The fourth process, is that of economic control. This takes into account the fact that if we wish to understand the decisions made concerning the patterns of investment of companies, then it is necessary to understand who has the control of such decisions, and what his motivations may be in arriving at his decisions. In fact the pattern of investment reflect the desire of those who control and finance large companies to maintain and if possible enhance their own roles, and power, and do not necessarily reflect an objective, nationwide assessment of the comparative advantages of different locations for new capacity. Clearly, part of the changes which we are witnessing in the pattern of economic development reflects the changing structure of the organisations which control investment. Instead of powerful concentrated structures with strong family ties, or identification with some city or region, we see more anonymous, multinational, multisectorial conglomerate corporations interested in making safe investments in areas without problems. Having discussed the historical reasons for the changing structure of economic activity, we must now turn to a discussion of the link between that and migration flows. So we are examining the various components that make up our Figure 5.1, so that it may serve as a basis for the development of a dynamic model. 5.3 MODELLING MIGRATION FLOWS In the past it has generally been the view that economic development and decline was the motor of migration ‘push’ and ‘pull’ and that models simply need take into account the relative unemployment and wage and salary rates to ‘explain’ the flow patterns observed. However, since 1970, other factors have often been cited as being of growing importance and for a model that attempts to generate endogenously the ‘reasons for migrating’ as well as the migration patterns, it is clearly of great interest to see to what extent these reasons have diversified. A study entitled ‘Reasons for Interstate Migration: jobs, retirement, climate and other influences’ was published by the bureau of census in order to report on just these questions. In Table II, taken from this report we see a summary of the study results, based on the first reason people gave for migration. Undoubtedly, however, people have mixed reasons, and even if job transfer or new job is the first reason, then the choice or

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Table II Reasons for moving given by household heads in the 12 months preceding the 1974, 75 and 76 Annual housing surveys EMPLOYMENT Job transfer

% HOUSEHOLDS

FAMILY

% HOUSEHOLDS

23.8 House size

.6

Military

4.8 Widowed

.7

Retirement

3.4 Separated

1.2

23.6 Divorced

1

New job/search Commuting reasons

1 Moved to relatives

7.5

For school

5.4 Newly married

Other

2.4 Family increased

.1

Family decreased

.1

Form household

1.2

Other

2.7

OTHER

Natural disaster

5.1

Change of climate

5.5

Other

5.6

1.6

acceptance may well be conditioned by considerations of climate or natural beauty and indeed anticipation of this may well condition the investments which create employment also. (Smith and Slater, 1981) One question that the model may well illuminate is indeed how much these other factors really count, whatever people may give as reasons for their decisions. Another very important point is that of the different behaviour of the various age groups, which migrate to a greater or lesser extent. In general, it is young adults (18–24 years) that make up the greater part of migration flows, 40%–50%, mature adults (aged 35–55) 20%–30% next and then retired people. Also, babies and children (1–17 years) form a large part of migrating flows (20%–30%), and if we take them together with young adults then they form an extremely large fraction of migratory exchanges (60%– 80%) and hence, any large net flows will have a strong influence on the demographic potential of a state, so that here we see clearly a mechanism of delayed interaction between economics and population, one which makes the analysis of any one set of census data, for one time, extremely misleading. Specific age groups tend to have different reasons for their choice of destination, and when we realize that the age pyramids of the States differ considerably and that in addition, economic conditions are evolving inhomogeneously, we begin to perceive the real complexity of the problem. The question which we shall attempt to address is whether a simple dynamic model can be developed which will succeed in generating the changes in the US over recent

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decades, and could be used with some assurance to explore various possible scenarios for the coming decades. In the Figures 5.2, 5.3 and 5.4 we see the evolution of the United States over the years 1950–1970, in terms of population, of basic and tertiary employment, and this shows the

Figure 5.2 The relative change in population by State, 1950–1970.

Figure 5.3 The relative change in ‘carrying-capacity’, 1950–1970.

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Figure 5.4 The relative change in tertiary employment, 1950–1970. type of evolution which we wish to model, taking into account the effects of demographic, economic and migration change in each state of the system. The equations of our earlier work discussed only the population of ‘active’ residents, at each point in the system and clearly from the above discussion, the importance of young adults and of their children in the migration flows indicates that we must study the population of both active and non active individuals in each state. (Keyfitz, 1980; Ledent, 1978) Our method consists however in writing dynamic equations which are based on the idea that in the long term the population of a state must adjust itself to the employment potential there, which is related to its resources, its comparative advantages for industry, for distribution and manufacture, and the possibilities for tertiary employment there, within the national hierarchy of cities. It is an ‘ecological model’ in some sense, and the migratory flows are generated by the adjustment process. In many models, the variable ‘employment’ of a state is given by the number of actives, but in our model we are going to consider the active population xi, the jobs Ji available both filled and as yet vacancies on offer, and the ‘potential employment’ that could exist at a point, Mi. It is for us, precisely the differences between these that drives the system, and only at equilibrium with full employment will they be equal. The space in which our study will be made consists of 42 points corresponding roughly to the continental United States but some small states such as New Hampshire, Vermont, Rhode Island, Delaware and Connecticut have been aggregated with populous neighbours like Massachusetts, New York and Washington DC, Virginia and Maryland. We are going to use as variables for each state i, the active, employed population xi, the non-active and unemployed population ni, the available jobs both filled and vacant Ji and the potential jobs Mi. The total population Pi=xi+ni We suppose the equations:

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which says that active population xi changes at a rate ε time the number of non-actives multiplied by the number of jobs vacant, or for decline, the number of jobs that have become redundant.

The non-actives grow because of the rate of natural increase λi, and change because of the non-actives in i′ that get jobs, or lose them, and also through in and out migration and Such a choice of equations is based on the idea that non-actives migrate in response to the need for employment, in that either a ‘new job’ or a ‘job transfer’ requires a ‘vacancy’ to be created in another state, but may or may not leave a vacancy in turn in the state from which the immigrant comes. The calculation of natural increase is done using an average rate only, but clearly it could be relatively simple and desirable at a later stage to take into account the evolution of the age pyramids of each state, and their resulting greater or lesser propensity to generate migrants, who in turn will modify the age pyramids. The parameter ε reflects the efficiency of the flow of information within the state i concerning the job vacancies available to the ni and also the degree of matching of these vacancies with the qualifications of the job hunters. and are calculated according to the number of The migration flows non-actives at each point ni, who are susceptible to migrate (which depends on the population increase and the rate at which local vacancies can absorb these individuals) as well as on the perceived attractivity of possible destinations which reflects the numbers of vacancies which are available there.

where ξ reflects the ‘ease’ of migration flow per non active for a given stimulus—that is the natural mobility of the population, the costs of moving, the rate of construction of new housing, the costs of buying and selling houses etc… The attractivity Vij is supposed simply to be a function of the advantages and disadvantages of i as viewed by the nonactives at j, and we have supposed that there is only a dependence on the ‘job availability’ at i and perhaps the distance between i and j.

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Thus if Ji is greater than xi, then i will be viewed as being attractive by the nj proportionally to its size Pi and depending on the clarity with which this is perceived ‘α’. If α is zero, then there is no information about the different job opportunities, if α is infinite there is ‘total information’ and unanimous behaviour, in that all the migrants from i go to the same state, that state which is temporarily the most attractive. Now, in addition to these equations we must give an equation which will generate the jobs available at each point i, Ji, and also the ‘potential’ jobs Mi. Once again let us stress that the actives xi, the available jobs Ji and the potential Mi will only be equal at a full employment equilibrium. Otherwise, xi will be different from Ji and Ji from Mi. We shall suppose that entrepreneurs and employers generally perceive potential employment and therefore adjust their jobs offers, or redundancies to match the actual employment with the perceived level:

where k is a constant reflecting the dynamism of employers and the speed with which they react to the possibilities. Ji is divided into two parts.

the carrying-capacity or basic sectors, of agriculture, mines and manufacturers and the tertiary sector. In attempting to reconstruct the past we must now describe the way in which potential employment Mi changed, and this can only be inferred from the way in which xi actually changed. For example, we know that between 1950 and 1970, the number of people (50) to actually employed in the basic sector of state i changed from therefore that there was an average rate of change during the 20 years of

(70) and

We will assume that the ‘potential market’ Mi for these goods changed by an amount proportional to this:

and η is a constant.

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Then, η and k must be such that during a simulation representing this period 1950– 1970, the

generated

that led to the actual values of the change in basic

employment For the tertiary activity, we have a similar hypothesis, but in addition here, since we do not hope to describe correctly the spatial competition between tertiary centres of the urban hierarchy, then we shall make a simple hypothesis concerning the induction rate of tertiary employment per inhabitant. In particular, we shall make the very simple assumption that, starting from the initial tertiary structure, the induction rate per inhabitant of each state changes uniformly with the average rate for the US. For example, during the period 1950–1970, the tertiary employment per head rose by 20.4%, and so in consequence we have supposed that each state increases its rate of tertiary induction—the potential tertiary employment per head—by roughly 1% per year. Clearly, this will create vacancies according to the population of each state at each moment and this will in turn depend on its demography, and on the migration flows which will, in turn, depend on the job vacancies in the state compared to others. The evolution of the induction rate βi of state is given by the average US rate of increase acting on the initial value of βi. (12)

and (13) based on the observed national change, which gives us the equation for potential employment (14) which closes our model, and permits us to start simulating the spatial evolution of the US, and from this to find the values of ε, ξ, α, k, η which best fit reality. In summary, our model will generate the migration between states, and predict from the initial condition in 1950 say, the population and tertiary employment of each state. The ‘prediction’ can then be compared to the real values observed for 1970, and in this way the best values of the five parameters can be found. The information input to the model is, for the initial time (1950 say), for each state: a) the population b) the basic employment c) tertiary employment In addition we use:

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d) the basic employment of each state at the final time e) the average growth of tertiary for the US f) a demographic hypothesis for the period of study. Our model can then tell us how population and employment of each state will evolve, and this on the basis of five parameters, which are all independent of the state i. It corresponds to an assumption of ‘uniform human responses’ over the whole United States. We attempt to generate all the complexities of migration, investment, population growth and tertiary structure, of different cultural, social and climatic conditions using only 5 parameters. The first question is whether or not such a model can succeed in generating an important fraction of the real changes observed. 5.4 SIMULATIONS 1950–80 In this first step we have used the data for 1950 and 1970, and have run the model from the initial condition of 1950 for a period of 20 years. The parameter of natural increase (λi) of the changing carrying capacities γi and the rate of growth of tertiary employment per head are used to generate the observed ‘global’ figures for the USA, and by choosing values of ε, ξ, α, k and η we explore the way in which the population and tertiary employment predicted for 1970 by the model differ from the values observed in reality. The map shown in Figure 5.6 shows these % discrepancies of the populations. Obviously, for the whole set of possible values of the parameters there exists such a map, but with in general a much greater average error. Our map shows us one of the ‘best fitting’ results for values of the parameters: ε=4.25.10−6 ξ=0.2175/yr α=7.7 k=1.4/yr η=2.112 where the average error is 5%. We have the fairly satisfying result that after 20 years in which some states more than doubled while others were halved, the model generates some 95% for the structure of 1970, on the basis of migration parameters of ‘push’ and ‘pull’ which are homogeneous throughout the US without supposing an ‘attractivity per point’ other than that generated by the model equations, and the changes observed in the basic sector. In order to judge the significance of this result, let us compare it to the discrepancies that would have resulted from a model based only on the ‘natural increase’ observed in each state, without the redistribution of population between 1950 and 1970 caused by migration flows. In the map shown in Figure 5.6 we see that the average error is of 25% with those for particular states being as high as −54% (Florida) and +45% (West Virginia). This shows us that our ‘economic redistribution’ of the population is very much in the right direction. However, if the small average discrepancies of Figure 5.5 are encouraging, it is also true that the residual differences themselves are interesting, since they are not distributed randomly throughout the nation, but are clearly spatially organised. This reveals the existence of spatial mechanisms not included in our simple model.

Modelling the long term structural changes in the United States

Figure 5.5 The percentage difference between populations observed in 1970 and those predicted by the model run forward from 1950 using only global migration parameters.

Figure 5.6 The percentage difference between the populations observed per state in 1970 and those that would

119

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120

have resulted from simply projecting the rates of natural increase. We can imagine several possibilities for these missing mechanisms: a) Structural changes in the tertiary hierarchy b) Evolution of the distribution of income in the USA c) Effects of changing age pyramids in the different states d) Anticipation on the part of actors e) Stored growth in the system at the initial moment f) Cultural differences between regions Here we shall not discuss all of these possibilities which will be the object of further more detailed studies. However, it is important to reflect on at least two of those possibilities which are particularly important for our model. The first one concerns the structural changes of the tertiary hierarchy which in our present simulation are not modelled at all. Because we impose the national average ‘growth’ of tertiary per head, then clearly this corresponds to an assumption that the structure does not change its character. Our models are of course quite capable of treating such an evolution. In order to do so, however, we must have more information than at present in order to describe the spatial competition between tertiary centres. A second important mechanism concerns that of the ‘stored’ growth that may exist in such a system, where delayed effects may still be occurring years after the events which triggered them. In order to examine this question we can perform the following experiment. At the end of our simulation 1950– 1970 during which US population grew from 150 to 202 million, and the tertiary activities grew 60% we can see how much delayed change is still ‘hidden’ in the system by arresting the natural population increase and the changes in basic employment per state, and tertiary activity per head, but letting the model run on for another 40 years. In this way we isolate the changes generated by ‘exogenous’ forces of natural increase and economic change, and reveal those due purely to the differences between ‘potential’ and ‘real’ employment in the various States in 1970. These differences can and do continue to produce migration flows, and these flows lead to the induction of new tertiary potentials, leading in turn to further migrations, as the ‘non-equilibrium’ of 1970 works its way out of the system. Only at equilibrium, when the ratio of potential Mi to actives xi are equal in each state, will net migration cease and the initial movement be dissipated. In Figure 5.7 we see the population changes (as %) that are still stored in the equations after the period 1950–1970. This ‘experiment’ is performed by freezing population, industrial investment and tertiary growth, and just running the equations on for 1970– 1990. In Figure 5.8, if we continue the experiment 1990–2010, the addition changes become almost negligible. We conclude that our equations express mechanisms which have a ‘time-delay’ of some 20 years, because the ‘stored’ evolution seems to be mostly dissipated by 1990. Thus the values of the parameters which we have found to fit ‘best’ the changes from 1950–1970 seem to be characterized by a delay of some 20 years. Such a delay seems to be in agreement with the ideas that geographers have expressed concerning the full operation of the multipliers following a particular investment in some locality as new housing, retail and services grow in the vicinity.

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Figure 5.7 The percentage changes still stored in the system disequilibrium at the end of the simulation 1950–1970. Of course, in reality, between 1970 and 1990 we shall not see the changes shown in Figure 5.7, because these will be superimposed and mixed with that generated by economic and demographic changes taking place after 1970, and in 1990 there will in fact be another 20 years change ‘hidden’ in the potentials of the system. But of course, if that is true of the future, it was true of the past and in particular of 1950, when perhaps there were many phenomena stored in the system as a result of changes which occurred between 1930 and 1950. We find that we have an ‘initial condition’ problem which is a profound one, suggesting that in order to ‘fix’ the 1950 values of Ji and Mi we must perform the simulation 1930–1950, and for 1930 we require that of 1910–1930 and so on. This results from the fact that in a dynamic model we must always discuss some ‘unobservable’ variables, whose values are inferred from subsequent system behaviour. In our model, we use the observations of 1950 and 1970 to suppose how Ji and Mi changed over time, and the parameters k, ε and ξ translate potential employment into job vacancies and finally into jobs, the parameters we find which ‘fit best’ the observed changes are therefore the result of the assumption made about how Mi changed. If we suppose that there was ‘very high potential’, then we will find that in order to ‘fit’ observed changes we must have very ‘slow’ kinetics which convert potential into real. If on the other hand the potential was small then it will require ‘fast’ kinetics (k, ε, ξ) to convert it into the necessary changes. Here we discover a basic ambiguity in such modelling however. For these two extremes will give quite different amounts of ‘stored change’ for the future, so that if at that moment exogenous changes of population and technology were to stop, in one case change will continue for decades, in the other it would stop rapidly.

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Figure 5.8 The remaining stored disequilibrium 1990–2010, after fixing zero natural increase, no change in basic employment or tertiary per head, per State, in 1970. The only way in which such ambiguity can be resolved is to ‘calibrate’ the model over several past periods exceeding the largest values of the ‘delays’ that seem probable. Not only must we calibrate the values of the variables xi, Pi etc., but we must also know their rates of change at past times. This information should then permit some confidence in the model calibration. Returning to our particular model, we have supposed that changed as two linear functions of time, one proportional to the observed change in basic employment and the other to the change in tertiary employment induced by the actual value of the population and the linearly changing induction rate per head. With this supposition, together with the initial value of Ji and Mi corresponding to a xi plus a year’s change in potential, then we can generate our maps and our reasonable ‘delay time’ of 20 years. However, in order to use the model we must modify it further since, although a result with an average error of 5% is very satisfactory for a model based on global mechanisms, we still are faced with particular instances of large errors (−23% for Florida, −17% for Arizona) and this would mean that we would begin any simulation of the future (i.e. after 1970) with initial conditions which already were seriously erroneous. However, to simply ‘put in’ the real values observed for 1970 and continue forward would also be false, because the ‘potentials’ would still correspond to our final state, and for example Florida and Arizona would immediately start to decrease, and others overestimated to increase. In order to get around this problem, it is necessary to recognize first of all that our model is extremely simple and many mechanisms are missing including those listed in the above. In that case, although 95% of the observed situation in

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1970 is good, what we must do is to find what the ‘attractivities’ of States really were in order to explain 100% of what occurred. Thus, we can multiply each attractivity, by a factor fi. Such a procedure is often called ‘calibration’ in social science, but natural scientists would tend to refer to the ‘f’ as ‘fudge factors’. In other words they compensate for what the model fails to describe properly. The relative success of the model therefore depends on how large a part of the pattern of flows the model succeeds in describing without the fi.

Φ=0 for our simulations, and fi are centred on 1, and are adjusted per state until the observed flows are generated. The interconnected nature of these effects leads after a trial and error search to fairly precise map of the values necessary for each state, and for the period 1950–1970 we find the results shown in Figure 5.9. For these values we generate the 1970 situation to within 1/2%, permitting us to continue our simulation forwards. We also have examined the evolution from 1970–1980, first without these additional factors. Here we find that despite a prolonged search our global mechanisms still lead to an average error of some 5% for the 10 years period compared to that of Figure 5.6 which was for a 20 year period. This already suggests that the rational behaviour of economic ‘push and pull’ is less effective in describing migration patterns than it was over the earlier period. The map of the ‘best result’ is shown in Figure 5.10. It is interesting to note that the values of the parameters which generate the ‘best fit’ are considerably different from the preceding period demonstrating a considerable increase in information flows and in mobility. This would seem also to agree with observations. Once again, we can find the ‘distortion factors’ which generate the real flows and these are shown in Figure 5.11.

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Figure 5.9 The difference between the populations per state in 1980 and those predicted by the model, using global migration parameters.

Figure 5.10 The adjustment factors fi necessary for each State in order to reproduce exactly (.5%) the changes observed in the population from 1950– 1970.

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Figure 5.11 The adjustment factors fi necessary per State to reproduce exactly (.5%) the population changes 1970–1980. These additional factors seem to display considerable stability in their spatial distribution, reflecting the persistent presence of factors outside those considered in our simple model. The interpretation of these values is again complex however since there can be two possible ‘reasons’ for either a ‘high’ or a ‘low’ score. For example, a ‘higher attractivity’ than ‘expected’ can result either from growth driven by forces other than the strict economic rationality of our model (e.g. Florida) or from a rapid collapse of employment which has not yet led to out migration of the ‘expected’ magnitude (e.g. West Virginia). Again, a low score may come from employment growth leading to the growth of population (e.g. Texas 1970–1980) or from people leaving a state faster even than economics would dictate (e.g. New York 1970–1980). Of course, a further stage of research would involve the identification of the underlying reasons, such as for example in New York in the seventies the urban crisis which led to falling standards of services, high crime rates, increased taxes and city bankruptcy which certainly affected the image of the city. While this type of statement is often made to ‘explain’ whatever has occurred, we should stress that our model already takes out the ‘normal’ changes due to economic growth or decline and spotlights the residual effects. One interesting remark is the relative stability of the adjustment factors, with only some states changing sign. This implies some systematic effects underlying these enhanced or diminished attractivities and clearly their spatial grouping in a model which does not use a distance matrix is also significant. 5.5 EXPLORING POSSIBLE FUTURES Having calibrated our model for 1970–1980, so that it takes into account the non-linear interactions of basic employment, population growth, and the tertiary multipliers, and found the additional adjustment factors which characterized the evolution of each state, we can now continue our simulations to explore the possible future of the United States. Of course, necessarily, we must make a series of assumptions about what will continue to be true in the future concerning the spatial distribution of investments in the basic sector, the growth of tertiary activity and demographic increase. As a first example, we have supposed that in the period 1980–2000 the increase or decrease in the basic sector of each state continues at the same rate as in the period 1970–1980. Also, the rate of tertiary increase per head is taken as following the trend of the earlier period, and the rates of natural increase of population also reflect those observed for 1970–1980. The result is shown in Figure 5.18. It shows that the growth league would be headed by: Texas

49.1%

Colorado

48.3%

Cities and regions as self-organizing systems

Arizona

46.7%

Nevada

46.4%

Wyoming

44.3%

Florida

41.5%

126

and the states exhibiting long term stagnation would be: Michigan

7.4%

New Jersey

6.9%

Ohio

6.6%

Pennsylvania

5.4%

Of course, many questions spring to mind when attempting to imagine the unfolding of such an evolution: could the water supply in Texas take another 7 million inhabitants? Where could another 12 million Californians live? Is the South Atlantic’s rather ‘average’ performance correct, since the bureau of census projections estimate this as the highest growth area? These questions are obviously extremely important because they may in fact help us to decide at what future time the ‘adjustment factors’ may change in a new way reflecting some effects such as, for example, the increasing cost, crowding and difficulties for new inhabitants in California. Perhaps the trend noticed in the change from positive adjustment (good image perhaps) in 1950–1970, to negative one from 1970 to 1980, may well continue to be accentuated as the ecosystem of the west coast is strained further. Similarly, problems of water availability could possibly limit the growth of Texas, but these are all questions which can be examined in greater detail once these growth dynamics have been suggested, and real estimates made. In other words, the model should be used to better ‘imagine’ and anticipate future trends and problems, which may in fact alter and invalidate its actual predictions, rather than supposing that the equations are a deterministic model of what must occur, and that the evolution is a firm prediction.

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Figure 5.12 Population changes generated under the assumption that demography and the changes in employment follow the pattern of 1970–1980, and that tertiary per head increases at 2.2% annually.

Figure 5.13 Bureau of Census population increase projections by region for 2000. It is interesting also to compare the ‘predictions’ of our model with that of the bureau of census projections of 1970. This is shown in Figure 5.12 and we see that it predicts much

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smaller changes than our model, and a more homogeneous pattern of regional variation. It is interesting to note that between 1970 and 1980 the Bureau of Census projections are already 5% in error on average, and the states which are particularly underestimated are those which show such strong growth in our model. If we continue with other possible future scenarios, then we find other, slightly different patterns, but one of the most striking features of the five scenarios explored here is the remarkable stability of the projections. They all show growth of over 40% in the states such as Texas, Colorado, Arizona, Nevada and Florida, and stagnation in States such as Michigan, Ohio and Pennsylvania. These results are presented in Figure 5.13 to 5.15. Our model can now be used to explore the future growth or decline of the various regions of the United States, under various scenarios of investment decisions. This will generate a pattern of future growth and decline, providing some knowledge of future needs for the planning of infrastructural investments, as well as of areas where strong pressure on natural resources can be anticipated. 5.6 POSSIBLE FUTURES, NOT PREDICTIONS Here is a good place to stress the point of view that is being advanced here concerning the use of these models, and the meaning of the simulations into the future. As has been stressed in the general remarks concerning ‘self-organization’, living systems are not

Figure 5.14 Changes predicted in the population 1980–2000 supposing that demography follows the pattern 1970– 1980, basic employment continues to

Modelling the long term structural changes in the United States

change, and tertiary employment per head increases at 2.6% annually.

Figure 5.15 Changes 1980–2000 supposing that demography and changes in basic employment follow 1970–1980 pattern. Tertiary employment per head increases by 3% annually.

Figure 5.16 Predicted changes in population 1980–2000 with demographic growth as 1970–1980,

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tertiary increase 2.2% per year. Specific assumptions per state in the basic sector: NY −2000, PA −15000, OH −10000, MI −5000, MN 9000, IL 2000 reflecting prospects for the steel industry. mechanical, and so any set of deterministic equations that appear to describe the situation at a given time, will at some point fail to describe the future. This is because, evolutionary processes are at work which will introduce new limiting factors, new kinds of economic activity with different locational criteria, new patterns of external and internal trade, and possibly new ‘ideals’ about the ‘quality of life’ that people seek, and hence new trends in migration. So, when the future simulations show a growth of 50% in Texas or in Nevada, this is based on the factors that were at work in the period 1950–1980, but does not mean that this will necessarily be continued until 2000. For example, the pattern of industrial investment may well switch away from the previous pattern, and in order to assess the likelihood of this, detailed studies would be required to see what the basis for the investment growth was from 1950–1980. In Texas it was largely the oil industry that was the motor of the economy, and so with the decline of the industry during the 80’s the pattern certainly changed. Clearly, environmental factors are limiting the further growth of California too, where water supply and air quality are major concerns. In Figure 5.17 we can show the actual growth/decline of populations between 1980 and 1990. These are considerably different from the projections of the simulations based on the 1970–1980 patterns. If we map the differences in growth between the real and the projected values of Figure 5.18 then we see that there are significant differences across the

Modelling the long term structural changes in the United States

Figure 5.17 Population changes 1980– 1990

Figure 5.18 The difference between the growth actually observed from 1980–1990 and that predicted by the model.

Figure 5.19 The growth decline in carrying capacity from 1980–1990.

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nation. Firstly, population growth decreased on average, and the Central States were overestimated, while the West, together with Florida and Georgia were underestimated. This suggests that there was a change in the underlying pattern of investment in the carrying capacity, and that the distribution of growth and decline related to this was clearly part of the explanation of the differences between the real and projected growth. Clearly, the differences between the actual growth and decline of the different States is largely explained by the pattern of growth and decline in the carrying capacity. The whole area of the Central States, agricultural and manufacturing employment fell, thus modifying the predicted evolution. The important point is that the changes in the pattern of growth would have been evident already by about 1983, and the whole picture could have been revised under different, more relevant assumptions. Our simple model would have provided an integrated framework with which to explore the projected evolutions as information concerning the shift in industrial and agricultural employment became evident. What the results show is that by reading in changes in the base employment, which is only a small part of the total, inter-state migration could be generated as well as the remaining 70% of employment. The discrepancy between the projections to 2000 and the real outcomes show us that in fact the pattern of investment in the base employment has changed considerably. The ‘self-organization’ part of the model generates the migration responses, the pattern of population distribution and the dynamic development of the tertiary employment, as a complex dynamical process of delay and inertia. In addition to this, however, it is clearly necessary to put more effort into examining the probable future pattern of investment in the employment base. Also, it might help a State Planner to better anticipate the probable overall consequences of an investment in industrial infrastructure. Will it attract sufficient subsequent growth to be worth the effort? The simulations are really a simple aid to the imagination. It provides a basis for the State planner to begin to imagine whether the ‘predicted’ growth or decline is a realistic possibility. If it is, then plans should be put in hand to accommodate the changes. If the planner feels that it is not realistic, then he should explain why he believes this. There may be some clear limiting factor, such as water supply, which cannot support the higher population. But, in this case, the model will help imagine the year in which the problems will become sufficiently severe to arrest migration. Planning for this crisis will also be useful. Also, if it is felt that it would be preferable to attempt to overcome the limiting factor, so that the potential growth can be realized, then plans could be put into effect to invest in the necessary infrastructure to cope with the in-flux of population. (Engelen and Allen, 1986) In other words, the model provides some ‘measure’ of the projected populations resulting from current ‘wisdom’, and so when the actual changes are observed to deviate from the ‘predictions’ of the model, then the causes can be sought, and the model modified accordingly. In this way, it can be the ‘compact, coherent expression’ of present knowledge about the working of the processes involved.

6. THE SPATIAL EVOLUTION OF JOBS AND PEOPLE IN BELGIUM 6.1 INTRODUCTION Following the development of the simple US model of population and employment change, it seemed interesting to attempt to improve the representation of the system to describe the changes in employment in terms of the scheme of standard industrial indexes, with which economists and political administrations are familiar. Instead of crudely splitting economic activity into base and tertiary sectors, we want to deal with more familiar categories such as manufacturing industry, finance etc. In addition, instead of simply driving the model by reading values for the base employment, we want to allow the decision making processes within the model to drive the system as much as possible. This ‘causal mechanism’ approach, linked to the functional requirements of actors, should be contrasted with the alternative modelling philosophy based on the calibration of flows from data. In this chapter we develop a model of the changing pattern of economic activity and residential populations in the 9 Belgian Provinces. (Sanglier and Allen, 1989) Our model is based on the dynamic spatial interaction of the different urban actors governing the locations and numbers of jobs and residents. Each variable represents the spatial behaviour of a typical actor of that category as a function of his locational preferences. As the model is based on the behaviour of the actors, it can be applied to several levels of the ‘urban structure’. In this application the spatial unit is the Province. The following scheme (Figure 6.1) shows the interactions and the flows between each province and the others, which lead to the migration of economic activities and people between provinces, and thus induce long-term structural changes. There are four basic mechanisms in our dynamic equations, related to two different time scales of flow. 1. Short term flows which are functional flows: (a) The residential location for a given distribution of employment, taking into account the transportation networks, available housing, and the different qualities of services and environment. It may be seen in the daily traffic to and from work. (b) The pattern of demand of goods and services coming both from the population and from the producers of inputs to a particular activity and from them to other producers and to the final consumers. It concerns the logistics of supply and of distribution, for production, consumption, import and export.

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2. Long-term flows which are evolutionary adjustments: (a) Demographic changes and the perception of the pattern of employment and housing opportunities, which generate migrational flows of population. (b) The perception of the pattern of economic opportunities and the distribution of investments. Capital flows of investment—sectorial and geographic. The originality of the approach is that the underlying driving force of the system is the difference between the present value of each variable and its potential value. An earlier use of this notion of ‘potential’ in the social system was that of Prigogine and Herman in 1971 in their models of traffic flows in which they introduced a ‘desired velocity distribution’ for traffic. In our problem, at each moment we calculate the ‘desired’ spatial distribution which leads to a certain ‘potential’ for the different types of actor at each point of the system. It may differ from the actual distribution observed. This may be either because they have never been equal or because, even though they were equal at some time, changes that have since occurred have upset the equilibrium. Whatever the reason, the differences between present and potential values create a pattern of opportunities and dissatisfactions, which if they are perceived, will drive the long-term mechanisms to produce spatial shifts of investment and migration patterns. With each change however, the potential pattern will have changed as well as the real one, and so a complex chain of successive readjustments is set in motion. More precisely in Figure 6.1, the driving force behind the model is the difference between the number of residents and the potential number of residents, which takes into account the pattern of employment in the Province itself and in the other Provinces. The numbers of people working in a zone wishing to reside at a particular location are calculated by weighting the attractiveness of each zone according to factors such as distance, the infrastructure, the quality of the environment, the cost of land,… We have considered that the migration of residents results from the difference between the number who would like to live in a zone and the number who actually do. The employment sector is modelled in a very similar way. At each moment, the change in the number of jobs of a given sector is caused by the difference between the existing and the potential number of jobs. The latter are calculated from the economic demand by taking into account the relative competitiveness of economic activities. The competitiveness of a given point for a given sector depends mainly on input costs, which reflect the availability and price of raw material, services, and goods, and distribution costs to customers, and so the competitiveness reflects the economic links between the sectors, the infrastructure, the transportation network, and the spatial requirements of the activity. 6.2 THE VARIABLES OF THE MODEL In Belgium we have data on employment by place of work which are published by INS (Institut National de Statistique) every ten years, but as the sectorial categories were dif-

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Figure 6.1 Interaction scheme of the EMUS (evolutionary models of urban systems) model. ferent before 1970, we have compatible data only for 1970 and 1981. Because we need intermediate data to calibrate the dynamics of the system, we have chosen the social security data which are published each year and which are a combination of data from two sources: ONSS (Office National de Sécuritè Sociale) and INASTI (Institut National d’Assurances Sociales pour Travailleurs Indépendants). We have considered nine different economic sectors following the NACE (Nomenclature des Activités des Communautés Européennes) code: (1) agriculture and fisheries (Sl)

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(2) energy industry (S2), that is, industries related to the production of energy (coal, oil, gas, water, and electricity), (3) basic industry (S3) which contains metal-working industry, ceramics, glass, and the chemical industry, (4) manufacturing industry (S4), food, textiles, wood, leather, tobacco, and the paper industry, (5) building (S5),

Figure 6.2 Economic flows between the different variables of our model based on the input-output table of the Belgian economy. (6) commerce (S6), hotels, restaurants, cafés, (7) transport (S7), by rail, road, sea, and air, (8) finance and insurance (S8) (9) public and private services (S9).

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The final variable is the total population, which we shall model by zone, and which will be divided into active and non-active parts. 6.3 MODELLING EMPLOYMENT The evolution of employment,

in sector L at point j is given by (6.1)

where parameter πL is related to the adjustment rate of investments for economic sector L, and the term

is the potential market of sector L at point j.

This potential market

expresses the amount of production/employment L that it

would be desirable to have at point j. It is the sum of the real economic demand, coming from all the points of the system, the external demand, demand, point.

and the potential

All these demands are weighted by the relative attractiveness, A, of the

The expression for the potential market

is (6.2)

expresses the demand for sector L from all the other The real economic demand, economic sectors and from the population. The calculation of the parameter βLL′ (see Figure 6.2), the percentage of demand for sector L from sector L′, is based on the inputoutput table of the Belgian economy (INS, 1983); (6.3)

where and are the total employment in sectors L and L′ in Belgium. Figure 6.3 is a map of the Belgian provinces. In order to understand more clearly how our model works, let us consider a particular case, for example, the change in employment in manufacturing industry in Brabant, S24 in 1970 (at the beginning of the simulation). In Figure 6.2, we can see the values of β4,L at the national level. 37% of the production of manufacturing industry goes to the export market, 36% (β4,10) is consumed by the population, and 8% (β4,4) goes to firms within the same sector. Other connections are too weak to be shown on this figure, but they are considered in the calculation. On the

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other hand, manufacturing industry buys 58% of agricultural products (β1,4) and induced 7% of the jobs in the transport sector (β7,4). Thus, we can calculate the total demand for this sector, and also the demand generated by this sector in any particular province. The real economic demand for manufacturing goods coming from residents and activities in the Province of Brabant is shown in Figure 6.4. We can see that jobs and residents

Figure 6.3 Map of the Belgian provinces (with the abbreviations used in the rest of the paper).

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Figure 6.4 Real economic demand for manufacturing industry generated by the population and the economic sectors in Brabant in 1970. of this province generate 84361 jobs in the manufacturing industry sector, but only some of them (28,622) are captured by the Province itself, the rest being customers of firms outside the Province. However, in compensation for this loss, Brabant attracts some of the demand generated in the other provinces and also some of the export market. The relative attractiveness can be thought of as a sort of ‘utility function’ which contains within it the various factors that may influence the decisions of actors in making their locational choice. It is made up of four terms, (6.4) are the geographical characteristics of the region j which influence the where location of sector L, is the distance between producer j and clients j′, is infrastructure, available services…at point j for sector L; (6.5)

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where αLL′ is the intensity of the link between sector L and sector L′, and ΦLL′ is inversely related to its range,

is the relative land cost of region J for sector L, (6.6)

γL′ is the average floor space required per job in sector L′, is the sensitivity of sector L to the cost of land (inversely related to the value added per unit area), θj is total land use in zone j The parameter gives the relative importance of these terms. This rather complicated expression of the attractiveness has the advantage that it allows all the effects to be potentially present, and perhaps for new decisional factors to play a role. The importance of each term is a function of the size of the activity and also a function of the level of the spatial description. To clarify this let us analyze the pattern of the potential market (coming from the real demand) of manufacturing industry in the different provinces. Figure 6.5 represents the calculation of the term

This is the potential market captured by each province, derived by considering its competitiveness among the other provinces and the manner in which it may therefore succeed or fail in attracting customers from other places, despite the existence of competitors situated perhaps closer to them. In order to do this we calculated the relative attractiveness of firms—for example, for Brabant—for potential customers in each province, including Brabant itself. This will reflect the natural advantages of Brabant, for example. It is an important road, rail, air, and sea communication centre, with a large skilled labour force available, with financial expertise, and already a wide spectrum of manufacturing firms producing the intermediate components and supplies required in manufacturing. The price and the availability of industrial land and premises will also play a role. We have summarised these kinds of terms as ‘infrastructure’, which is really a measure of the availability of the necessary inputs of production. Also, the distance to potential clients will play a role by introducing distribution costs, which will naturally depend on

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Figure 6.5 Distribution of clients from all the Provinces for the manufacturing industry sector in Brabant (for abbreviations see Figure 6.3). the spatial distribution of clients, that is, the spatial distribution of industry and population, as well as of access to external markets. It is in this way that externalities enter into the calculation, and give rise to self-reinforcing processes which generate forces of spatial concentration of manufacturing employment, forming a dynamic spatial structure of industrial poles and complexes. When the competitiveness of each province has been calculated we can estimate the potential market for those goods attracted there, and hence the potential employment that

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could exist there. We can compare this with the existing actual distribution of manufacturing jobs in each province (Figure 6.6) and compare it with the real value (Figure 6.7). Hence we see that not enough demand was attracted to Brabant, and we may imagine that stock and inventories were too high, and prices had to be cut in order to maintain production. This led to lower profits and eventually to a decrease in capacity. In contrast to this, in Limburg in 1970, potential was higher than the actual value, and there was

Figure 6.6 Distribution of clients for the manufacturing industry sector in sector in the different provinces (dots represent the provincial centres).

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Figure 6.7 Comparison between the and the potential market, real value, for manufacturing industry. therefore competition among customers for available stocks, higher profits, and growth in the sector. In a similar way the model calculates the changes that will occur in each of the different sectors of employment. When this has been done for the different activities in each spatial zone, the changes calculated for that time step are made, and the computer moves on to consider the increase or decrease in residential population at each point.

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6.4 MODELLING THE POPULATION The population is modelled in a very similar manner. The equation describing the evolution of the active population, Xj at point j is (6.7)

The first term concerns the conversion of ‘inactive’ to ‘active’ at a rate εj, the second term represents the internal Belgian migration due mainly to job opportunities, where ξ is the rate of migration of the active population, and (6.8)

(6.9) the evolution of the total population, Pj is given by (6.10) ξ′ is the rate of migration of the total population, and mext is the balance sheet of external migration. The first term represents the natural growth at rate λj, the second the internal migration between the different zones of the system, and the third represents the external migrations. An important part of these equations is therefore the ‘residential location submodel’ which allows us to calculate at each moment the potential or desired residential population of a zone, and to drive the system by the difference between this and the actual population. The potential number of residents, Uj is given by (6.11)

The potential market or residents, Mj is calculated in a similar fashion to the potential market for jobs, by taking into account the demand for labour at and around point j and the relative attractiveness of zone j as a place of residence. In this case, increased employment in a particular zone may not necessarily lead to more residents in that zone, but it will enter as a factor in the locational decision of more households, and will in general reflect the attractiveness of the different zones as viewed by those working at that point. The relative residential attractiveness of zones depends on the availability and type of housing, the quality of local services, the price of land and housing, and the quality of the environment and character of the population already there. The model calculates a potential number of residents and compares it with the actual one, and the difference drives the migration term. The distribution of population responds

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to that of employment, and this in turn responds both to itself and to the distribution of population. Changes in either will have repercussions along these channels of response, which reflect sectorial complementarity and spatial proximity. 6.5 CALIBRATION OF THE MODEL The model was calibrated for the period 1970–84, and generates the spatial distribution of the nine sectors of activities and of the population in each Belgian province. This evolution has been compared with the real one, the simulation has reproduced the evolution shown by the data with an average error of less than 2% (see Table I and Figure 6.8). We have reproduced the distribution of the variables not only for 1984, but also for four intermediate years 1975, 1977, 1980, and 1982, and this has allowed us to find a set parameters which are self-consistent. The evolutions of the national values of the different economic sectors were calibrated through two parameters, πL and DpotL. Parameter πL represents the adjustment rate of the employment L to the dynamic of investments. The role of DpotL, the potential demand, is very important. From the first calibrations of the model we observed that we could not reproduce the national evolution of each sector using only the real internal and external demand. We must add a factor which takes into

Table I Average error for each sector at different times during the simulation EL

1975

1977

1980

1982

2

0.40

0.38

0.43

0.32

3

0.93

1.36

0.89

0.78

4

0.55

0.43

0.51

0.36

5

2.56

1.86

1.52

2.07

6

0.62

0.77

0.55

0.87

7

0.85

0.96

0.72

0.52

8

0.30

0.36

0.57

0.62

9

S

0.59

0.37

0.37

0.30

S10

0.28

0.24

0.26

0.39

S

S S S S S S

SjsimL

is the value of the simulation of sector L at point j

SjismL

is the real value, and

Stot

L

is total employment in sector L

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Figure 6.8 Spatial distribution of the fit between simulation and experimental data for manufacturing industry. The figures in the top left corners are the average errors (see Table I). account the perspective of investment in sector L. This factor can be positive or negative, as a function of the expansion or decline of the sector considered. Also, it is through the parameters DpotL and DextL that we can include international trade. These parameters are very important and take into account the position of Belgium within the common market and the rest of the world. In the future, we shall attempt to see whether parameter DpotL can be connected to some financial and sectorial index related to the balance of the export market and to the political situation.

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In order to make simulations which explore the future, these two parameters allow us to generate the national changes in the sectors for a given scenario. So the national evolution of each sector is not a constraint of the model, but is generated by the two parameters, πL and DpotL. As we have mentioned previously, the parameters βLL′ and DextL are calculated from the input-output table for the Belgian economy (INS, 1977). Clearly the economic demand between the different variables will change over time as the economy and technology evolve, but as no other data are available we are at present limited to that first approximation of the connections between the inputs and outputs of the different types of employment. For the parameters which are used to construct the relative attractiveness, the values of γL′ (the average floor space of a job in sector L′) and θj (the total land use of the zone j) were taken from data, whereas the others were calibrated for the whole period and kept constant. 6.6 RESULTS Figures 6.9 and 6.10 show the map of Belgium with the absolute and relative changes in the total employment and in the total population, for the different provinces, that have occurred during the period of the calibration. We can see the deep decline of Hainaut and Liege. These provinces specialised in basic industry which has suffered greatly during the past fifteen years, and this effect has induced the decline of other economic sectors linked to basic industry and led to an emigration of the population. The growth of the tertiary sector, principally services and finance has not compensated for the loss of industrial employment. On the other hand, we observe the growth of Flandre Occidentale and Limburg where the evolution of all the economic sectors has been better than the national average. At present we have tested a national and sectorial scenario for 1990. Compared with the values of 1985 the scenario used is: Agriculture: Energy industry:

−7% −9.8%

Basic industry:

−6.97%

Building:

−1.69%

Commerce:

1.52%

Finance:

15.27%

Services:

5.37%

Total Employment:

0.25%

If we analyze in more detail the sectorial evolution we note that Belgium underwent strong sectorial and structural changes during the past fifteen years. This can be seen more precisely in Figures 6.11, which show the evolution of the different provinces for each sector of employment. For example, at the spatial level, we can see the

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decentralisation of the finance and the service sectors (Figures 6.13 and 6.14) which have begun to be saturated in Brabant and there is a wave of growth to the surrounding provinces. The population scenario is based on the population predictions published by the INS (1985). The scenario implies no change in the present political situation, and very few modifications to the external commercial balance. The simulation can now be used to explore possible future paths of the system.

Figure 6.9 a) the observed absolute and b) relative changes in total employment 1970–1984.

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Figure 6.10 The observed a) absolute and b) relative changes in total population 1970–1984.

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Figure 6.11 The evolution of sectors 1–5 for the different Provinces.

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Figure 6.12 The evolution of sectors 6–9 for each Province.

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Figure 6.13 a) The evolution of total employment in each Province and b) the evolution of each economic sector for Belgium. 6.7 DISCUSSION The real use of this research is not to predict the future, but to furnish an integrating frame-work, which offers a better understanding of the complex mechanisms generating the socioeconomic structure. This type of model therefore helps us to learn about the system, and how it operates, and from this to better explore and imagine different possible futures. The most important points are: a) The interdisciplinary aspect: this type of model links the economic, demographic, social, geographic, and technological aspects of the system.

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b) The spatial and dynamic aspects: change in the behaviour of an actor in one zone induce changes in the distribution of the other actors and in the other zones.

Figure 6.14 Changes in the Financial Sector 1970–85 a) as observed; b) 1985–1990 from the simulation.

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Figure 6.15 Changes in the Service Sector a) observed, 1970–85 b) simulated 1985–1990.

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Figure 6.16 a) Absolute and b) relative changes in total employment for the period 1984–1990 as shown by the simulation.

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c) The need for a potential demand shows that the motor of the evolution is not visible in the existing situation but may be seen in the perception of the potentialities of the system by the actors. Information about these opportunities must diffuse inside the system in order to generate growth. This important parameter, which is the potential demand, shows that the system under consideration must be situated in its international context and underline the importance of the flows and influences between the country analyzed and others. What is not in this model, but which is always in our mind, is the appearance and impact of innovations and new technologies. However, the model developed here does not generate innovations endogenously, but can be used to examine the possible chains of consequences and impacts that might occur if specific innovations are introduced. Clearly, the model can investigate such things as the impacts of increasing productivity in different sectors, of changing costs of transport or of energy, of telecommunications innovations and new services, and it can show how the immediate responses will cascade down through the system possibly resulting in new settlement patterns, in the emergence of new centres and of changed patterns of commuting. These changed patterns can be used in turn to imagine better the possible changes in demand for different types of product, and the changing patterns of need for different services. Inclusion of a consideration of demographic cohorts would also allow the exploration of the changing patterns of demand for educational, health and social services. In this way the model could be of considerable use in exploring possible futures in an integrated fashion. However an important missing factor is that of the endogenous processes of adaptation and change, as well as the generation of innovation and technical change, which really underlie the capacity of the Belgian Provinces to sustain their economic activities through time. Clearly, a more detailed model of intracompany processes would be necessary for this, and so here at the level of Provinces we simply assume an aggregate effect according to some scenario. Since this is one of the major factors that is driving the evolution of the socio-economic system it would be desirable to link the co-evolving models at different scales in order to generate their combined evolution. Clearly, there is also a need to develop the kind of model described here within a ‘nested hierarchical’ structure. That is, we should imagine that the Provincial model of Belgium should sit within a larger model in which Belgium is itself a single point, whose behaviour is generated by the sum of the Provincial Model. Similarly, within each Province, there are Arrondissements and Communes, and the behaviour of the Province could be disaggregated into the sum of the behaviours of these separate parts. Such a model would allow the linkage down to the level of detail of a Geographical Information System, and would be able to interact with data at that very detailed level. However, what would be unique would be that the patterns of population and activities present in different locations over time, would be generated by a causal, integrated model of the kind described above. We shall return to this point at in the third section, and demonstrate how this might be achieved. Summarizing the work presented in this chapter, we can see the differences between this model and that of Chapter 5. In Chapter 5 we ‘drove’ the model by imposing changes over time in the base employment of each State of the US. This did lead to a successful description of the migration and economic flows which ‘followed’, but transferred the

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problem of prediction to that of predicting the future pattern of investment in the base employment. Given that many factors may influence this, including ones relating to the rest of the system, that is the population and the other economic activities, then we see a weakness in that model. It is not sufficiently ‘self-organizing’. In this Chapter, however, our model of Belgium does not use imposed changes per Province to drive the changing distributions of population and employment. Instead, it requires some overall scenarios for the changes per sector that are to be supposed, and then it generates the spatial distribution of the employment of each sector, and of the populations, for each Province. This therefore marks a significant step forward in developing a ‘self-organizing’ urban model, but of course still uses a scenario on the overall changes per sector, when in fact these should result from the ‘sum’ of the competitivity and experiences of each Province. This would really necessitate the formulation of the hierarchical model mentioned above, in which Belgium would be one zone, and its competitivity in each sector would be calculated from that of its component Provinces, as would the competitivity of the other competing nations. Another weakness of this model is that it does not really formulate the supply process properly, simply describing the level of activity and employment, and not considering the environmental effects or the real supply of raw materials and input factors to the system. This will be dealt with better in the following Chapter.

7. THE SÉNÉGAL MODEL 7.1 INTRODUCTION In this chapter we present a much more sophisticated and ‘user friendly’ development of the Belgian Model, which was designed to be used by policy makers and planners in Sénégal. It is an integrated modelling framework which is based on the ideas developed earlier, but including environmental effects. It was financed by the Directorate General VIII of the European Commission, as a tool for decision support for development policies and projects in developing countries, both for use by the Commission and also for use within the countries themselves. It is seen as an alternative to macroeconomic and project based evaluations for development initiatives presently used by international funding agencies. The framework allows the evaluation of the longer term, broad consequences and changes brought about by a decision or policy. While estimates of economic cost and benefit can be adequate for certain problems of restricted scope, they can provide quite incorrect guidelines for the long term. Improved information systems, and higher technology have combined to exacerbate rather than improve the problem, since narrow economic ‘optimization’ can be carried out more thoroughly. And this merely serves to push many of the costs into ‘externalities’, as economists refer to them. And, ‘externalities’ are everything that is outside the restricted set of factors actually included in the assessment, so that the natural and social environment, technological change and the future of the whole system itself, are simply excluded from the calculation. The aim of the system was to allow decision makers, planners and policy analysts to test out their ideas and the proposed plan of implementation on the computer, and in this way to avoid the painful and destructive practice of learning what not to do, by doing it. The model is slightly more ambitious than our previous examples in that it attempts to link the not only the demographic and economic variables of the system, but also some environmental and ecological aspects such as water demand and supply, soil qualities and productivity. This was necessary because in the previous example of Belgium, the whole system was ‘demand driven’, meaning that the economic system responded to final and intermediate demand, and there was no question that this demand might not be fulfilled. But, in Sénégal, when there is a drought, there is not enough food for people, and so they may have to flee the area, or starve. Similarly, in the groundnut basin, if the soil becomes exhausted then productivity and yield drop, so that incomes decline, and farmers must move elsewhere, give up and go to Dakar, or accept a reduced standard of living. Supply and demand are both real, and the environment is intimately connected with the maintenance of crop production and also of important ‘non-economic’ activities like cooking, where the wood burning stoves of the inhabitants exact a heavy price on local

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trees and bushes. In order to deal correctly with this more complex situation, the equations of our model have had to be considerably revised. However, the aim remains the same. Can we build a dynamic, spatial model which will re-generate the historical changes observed in Sénégal over recent decades? If we can, then we can use it to explore how this structure may evolve over time under different policy options. In order to evaluate a policy, it is necessary to examine how the system would evolve with and without that policy. Similarly, in order to choose between several possibilities, the consequences of each must be considered and compared. There are therefore two basic requirements for policy evaluation: – a model which can make explicit the effects of that policy on the many different aspects of the system. – a system of values in order to ‘weigh’ the relative importance of the different factors, and to decide which of the outcomes, and hence policies, is the most desirable overall. Our concern is with the first of these objectives. We wish first and foremost to provide better information concerning the probable consequences of an action or policy, in order to best ‘inform’ the decision process. Our model also has a policy evaluation utility, however, so that outcomes can be compared with the goals set by the decision maker. Our system is aimed at exploring the longer term gains and losses that different policies may involve through changes induced in the natural and the human system in which economic activities are embedded. It is vital to be able to see beyond the short term profit and loss that characterizes cost/benefit analyses. Sustainable development is about maintaining the adaptability and resilience of a system, which ultimately requires the maintenance of ecological and human diversity, both in the flora and fauna of the system, and in the activities and geographical locations which are populated. Our system must link: the natural resources, such as the soils and their nutrients, river and marine fish stocks, and water quality and quantity, to the economic activities, the choice of crops grown, the cost and availability of inputs, wastes discharged, the market for the activity from other sectors and from the population, the price mechanism and rewards of production, and the changing population, age cohorts, disposable income, education and skills, unemployment. The model links all of these factors together through the spatial patterns of choice and flow related to comparative advantages and to the transport network. It then generates the changes in these over time as conditions and competitivities grow and decline. By linking the demography, the input and output requirements for human activities and the environment, in terms of water requirements, soil quality and the transport of pollution of different kinds, the model can be really useful in exploring the real consequences of proposed economic developments. For example, the addition of large areas of paddy fields in St. Louis would allow farmers there to increase their output, since the value added by a double harvest of rice each year is very large. Of course, input requirements are also increased, because rice requires large quantities of water, nitrates and pesticide. However, there are also other less obvious effects of such developments. For example, the fertility of the river valley is not in general maintained by the richness of the silt that is washed down the river. Instead, it is partly maintained by the passage of cattle belonging to pastoralists who graze cattle in the adjoining plain of the Ferlo. These populations are largely self-

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sufficient, but of course, if they are unable to bring their cattle to the valley as usual, because of the presence of large areas of paddy field, then this could severely affect their way of life. Such people could find their lives threatened by the developments, and either end up migrating to the shanty towns around Dakar, or to waging war on the valley farmers. In addition, large quantities of water are needed for rice growing, and this might well prove difficult to supply when the other water requirements of electricity generation, navigation in the river and water supplies to Dakar are considered. Adding large quantities of nitrates and pesticides will also affect the quality of the water down stream from the new rice fields, and so the effects of these on the very active artisanal river and lake fishing of St. Louis need to be considered. It is not impossible that many of the gains made in food production through the extra growth of rice could be counterbalanced by the loss of protein supply that the fishery undoubtably represents. Such a pessimistic view is not necessarily correct, but it is important in planning developments of this kind, in Sénégal or anywhere else, to take such possibilities into consideration. The failure of many development projects can be attributed to myopic planning and decision making, where only the narrowest of economic measures have been considered, and the multiple and inevitable side-effects have been entirely left to be discovered afterwards. Each of the major factors: population, economic activities and natural resources will be considered in turn below, showing how they can be represented in the model, how data can be obtained to estimate the parameters, and how the mechanisms linking the different factors can be represented and captured in the model. First, we shall describe the situation in Sénégal, and the trends and linkages between these different factors. After this, we shall describe in detail how these can be successfully modelled. Following the development of the model, the ‘user-friendly’ software that has been developed will be presented. This has been explicitly designed so that it might be used by decision makers and planners themselves, and enable them to explore their own beliefs and assumptions about the system, as well as the possible consequences of policies or actions that they may take. The different screen presentations, interventions and ways of storing information are described, and then a number of policy explorations are carried out and illustrated. There is a discussion of anthropogenic environmental change, and the aim of sustainable development, and the way in which the model can be used to help in these aims. Although scientific analysis of such things as erosion, soil chemistry, hydrology, flora and fauna etc. are important, it seems that most degradation is being caused by human decision making which is driving land-use patterns and sacrificing future biological potential and carrying capacity for short term gains. This decision support system is aimed at providing information to illuminate such trade-offs. Let us first provide a brief picture of Sénégal as a backcloth to obviously greatly simplified picture that any computer model must represent. (F.Leloup, 1992) 7.2 THE LAND The background upon which development policy and planning, and our decision support system, must operate is the situation that exists in Sénégal, together with the processes of

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Figure 7.1 The basic soil types of Sénégal. change that are on-going there. In this chapter therefore we provide a brief survey of the important features and trends that are occurring in Sénégal. Clearly, these basic features are the physical geography and natural resources of the regions, as well as the skills and activities of the different ethnic populations that make up its varied population. Sénégal is a fairly flat country, in which the only region of any altitude is in the far south east, where a plateau rises just above 200 metres. It has two basic kinds of soil: brown, red and ferruginous soils in the centre, and secondly, hydromorphic soils and vertisoils in the plains and the valleys. The first kind of soil is easy to farm, but not very deep, while the other is more difficult to crop, but there is more of it. In addition to this there are some saline areas located in the Sénégal and Casamance deltas. The climate of the country has three major components: the maritime winds, the Harmattan, and the Mousson (see Figure 7.3). The interplay of these winds is governed by the strength and exact positions of the anticyclones of the north and south Atlantic, and therefore the potential for agricultural production, and hence for population in Sénégal, depends dramatically on the regular occurrence of a favourable pattern of rain bearing winds.

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The maritimes are associated with the North Atlantic anticyclone centred on the Azores. They blow from the north or north west, and are fresh and damp. The Harmattan is a hot dry wind from the edge of the Sahara. It blows from the east, and gives very hot days, cold nights and no rain. The Mousson is a warm wet wind associated with the South Atlantic anticyclone centred on St. Helena. Its long passage across the sea makes it particularly humid, and coming in from the south west it the parts of Senegal that it reaches an abundant rainfall. The line where the Mousson meets the Harmattan is called the inter-tropical front, and it marks the edge of the region receiving rain. This front moves north west from March to August, and back from August to February. Clearly, it is the combination of this rainfall with the existence of fertile soils which gives to Sénégal its life supporting capacity. It would be very important for Sénégal to know how the predicted climate changes resulting from increased CO2 might affect its seemingly precarious patterns of rainfall. It would only take a small change in the spatial patterns of the North and South Atlantic anticyclones to give rise to a spectacular increase or decrease in the agricultural potential of the country. The climate divides into two seasons: the dry season from October until March, and the rainy season from March until October. The pattern of rainfall is very variable both in time and space. The map of Figure 7.2 shows the pattern of median rainfall. The temperatures are high and increase as one moves inland. This is important, and for crop growth not only are the mean values important, but also the extremes. In Figure 7.3 we show the characteristics of the basic 7 climatic regions of the country. The disaggregation is made on the basis of the temperatures, rainfalls, length of the rainy season etc. Another basic factor in the environment, which shapes the ecological communities and human activities that have developed there is the hydrology. Two major rivers flow through Sénégal: the Sénégal and the Gambia rivers. In addition, the Casamance and the Kayana shape the land in the southern areas. Some seasonal rivers flow across the Sine, the Saloum and the Ferlo regions. The Sénégal River used to flood from July to September, and after this period, the level would fall and sea water would come up the river estuary as far as Dagana. Now, however, since the construction of the Diama dam, the sea water is kept out of the lower valley, and rice and other intensive crops can be cultivated there. Also, the construction of the Manantali dam means that the annual floods can be controlled and permanently

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Figure 7.2 Median rainfall from 1968– 1983 in millimetres/year.

Figure 7.3 The climatic regions of Sénégal.

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irrigated crops can be grown all along the river. The problems that must be solved in the execution of this vast development project are one of the main uses for the decision support system that is the subject of this project. The Lac de Guiers is a freshwater lake fed by the river, and from which much of the water supply for Dakar is taken through two pipelines. It is a shallow lake, providing good fishing, and it is proposed to build a canal from the lake down to Dakar to increase its supply of freshwater. Much water use relies on groundwater, and there are several regions where this is already becoming a serious problem. Firstly the resources of Cap-Vert cannot be extended at all, and so water supply is already a serious problem. Other areas where insufficiencies are showing up are in eastern Sénégal, in the Fatick-Kaolack regions and also in the areas of Louga and Diourbel. The primary sector of the economy supports over 70% of the population, and so the ecological conditions, and the trends in these, are of vital importance. There are problems of overexploitation of the soils and of the forests, and Figure 7.4 shows the distribution of ecological risks due to wind and water erosion, as well as of salinization and alkalinization. As can be seen, there are considerable problems of ecological risk. Wind erosion occurs mostly in the North and the Centre, while rain erosion occurs in the South. This phenomenon is made worse by overgrazing, deforestation, drought and the drilling of wells. Salt destroys soil fertility, and also, wherever rice is grown acidification occurs and gradually prevents future farming. Plans for development need to consider these effects if they are to be of lasting benefit to the population. The development of the Sénégal Valley for example, must take into account many issues such as the use and leaching of large quantities of nitrates and pesticides in intensive rice growing areas, and their transport

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Figure 7.4 Map showing the distribution of ecological risk in Senegal. down the river basin, the use of vegetation as fuel for cooking stoves, the difficulties of switching from a flood based agriculture with a single harvest, to a double harvest, permanently irrigated pattern of life. There are many protected areas of forest, sylvo-pastoral woodlands and National Parks in Sénégal. These have been set up with the intention of conserving plant and animal species, and also of attracting tourists and visitors. Over the last hundred years, much of the economic success of Sénégal has rested upon the development of groundnut cultivation. Moving eastwards from the coast since the

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early 1900s, the traditional agriculture has gradually been replaced by groundnuts, and this was for a long period the most important component of Sénégalese exports. However, with the gradual exhaustion of the soils, the return on this crop has been declining, so that the people who migrated to the growing areas over the past decades are now moving on to Dakar and other urban centres. The decline in revenue from groundnuts has led to a deficit in the balance of payments, and this has led to a growth in the exportation of fish. While in economic terms this is a perfectly valid substitution, for the population it poses some large problems. For much of the population, the stable diet and main source of protein was fish, and so the fact that so much is now exported means a very real decrease in the quality of life for many Sénégalese. Maintaining the size and viability of fish stocks both in the sea and in the rivers is an important task. In particular, development projects such as that on the River Sénégal should consider the possible implications for fishing activities there. The problems of nitrates, and pesticides and the impact on the food chain in the region needs to be included in the development project studies. 7.3 THE POPULATION The population of Senegal today is more than 6,928,000 inhabitants (1988). Since 1980 the average rate of growth has been around 2.65%, with a birth rate of 4.6% and a death rate of 1.9%. This average growth rate, however, actually hides a great disparity between the regions, especially between Cap-Vert, the region of Dakar, and the other regions. In fact the different regions have very different population densities, from 2728 inhabitants/km2 for Cap-Vert, through 141 for Diourbel and 142 for Thies, to 15 in the region of Fleuve and 6 inhabitants/km2 in Senegal Oriental. Overall some 35% of the population now live in urban areas, which is a high proportion by African standards, and some 22% of the total population live in the Dakar Region. Growth is more or less similar everywhere except Cap-Vert which has a notably faster growth rate. Indeed, the average rate of increase is some 5% as opposed to 2.65 for the national average. Another important issue in understanding the future growth in the different regions of Sénégal is the age distribution of the population. The population of Senegal is predominantly young, with the majority of the population between 1 and 25. In the computer model of population change which we have developed, we have disaggregated the population into three age cohorts: 0 to 10, 10 to 60 and over 60. Clearly, the 10 to 60 age group provide both the fecundity of the population, and the labour force needed to sustain it. This age pyramid has of course important implications for development and the scale of future needs, as well as on the structure of employment, the burden of educational services and on the pattern of consumption. Today, there is a striking overpopulation of schools and also of the labour market, particularly in the capital. The growing level of urbanization of the population of Sénégal is also another important evolutionary factor. The flow of population from decentralized, rural locations puts stress on the infrastructure necessary for their support. Water supplies to the capital, for example, pose a growing problem, as does waste disposal. Migration seems to be related more to the idea that there is a possibility of success in the city, while there is little or none in the villages from where they come. This is not necessarily a rational, well

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founded belief, since conditions in the city may well be worse than those in villages. Because of this, simple ‘economic’ explanations of such movements, as unemployed people migrating to job vacancies thus equilibrating the labour market, are found to be incorrect and over-simplistic. Dakar continues to grow despite the many difficulties that residents face, and the level of urbanization of Sénégal continues to increase. This seems to be linked to the spread in the population of the idea that urban life is ‘modern’, and more desirable, which people are perfectly at liberty to believe. The concern of the work presented here is simply that good information should be provided to decision makers concerning the problems that may arise, and the best policies and development strategies for handling them. One of the basic requirements for any development policy is clearly the estimation of future population growth, and its possible distribution in the different regions. Clearly, this will in reality depend on the policies which are pursued, and on their success or failure. The model which we are developing will certainly be able to help in the formulation of scenarios for this, but until it is available the Sénégalese government has worked out a number of possibilities, based on different planning policies. These can be examined using our model, and an estimate can be made concerning their probability. However, more importantly, the consequences of any one of them, for all the other economic and environmental variables of the system, can be explored. The National Plan of 1982 was based on 4 development scenarios, which were used to estimate the populations of the different regions until 2005. The 4 scenarios were: – the continuation of present trends (actually those of the early eighties) – a slightly greater population growth rate as a result of economic development. – constraints on economic development slowing population growth. – an active policy in the agricultural and rural development. In addition to these hypotheses for economic growth there were different possible scenarios for demographic change. These were essentially linked to the mortality and fecundity rates. The three outcomes which were thought to be the most probable were: – slow economic growth with slowly decreasing rates of mortality and fecundity. – moderate economic growth with a decreasing mortality rate and only a very slight decline in the birth rate. – strong economic growth with lower mortality and a rapid decrease in the birth rate. In fact, the first hypothesis seems to have occurred, as economic growth has fallen below expectations, and the overall rate of natural increase has declined a little. But, whichever perspective turns out to be true, the population will still rise above 10 million by 2006 (10,899,000; 11,376,000; 10,150,000). These overall scenarios are certainly useful for planning and development policy, but within them, the evolution of Senegal will in fact be conditioned by detailed economic factors, social conditions, regional development and cultural change in the populations. This brings out the utility of our approach, which does not aim at ‘prediction’, but offers instead a means of exploring possible futures, and allowing a better understanding of the interlinked facets of natural resources, economics, demography and socio-cultural change, and hence a better grasp of what may or may not actually happen.

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In Figure 7.5 we show the interregional migration for the years 1960 to 1988. There are large movements of population, but still over the period, these have actually intensified. Some regions are centres of permanent out-migration while others persistently attract population. Cap Vert (Dakar) is essentially a region of strong immigration, attracting migrants from all the other regions. During the 80s, the groundnut basin of Sine-Saloum, Thies and Diourbel also attracted migrants, but in recent years this has stopped. Migration towards Dakar has continued unabated, even though economic conditions there have deteriorated

Figure 7.5 The inter-regional migration pattern of Sénégal. over recent years. In the seventies and early eighties the hope of getting a job in the government was an attraction to the Capital, but since recruitment has been frozen for a number of years this is no longer the case. Nevertheless, the idea of opportunity and potential exists in the city, while it may be completely absent in the rural villages from which migrants come, and it is the search for new opportunities that draws people to Dakar, where they can often get started by finding something to do in the informal sector of the economy, while lodging with relatives who have already made the transition. These are the kind of phenomena that must be successfully modelled if we are to capture correctly the changing pattern of demographic potential, population pressure, and of economic activities that follow people. In the project described here, many different factors are being linked in a dynamic, spatial model which generates migratory movements as part of the whole Senegalese economic, demographic and socio-cultural system. In order to calibrate the different parts of this combined approach, we can use past data for certain variables and let the model determine others. In this way, we have used past data concerning employment,

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demography and population in each region, in order to test out different possible mechanisms for the ‘push’ and ‘pull’ of migrants between the regions. Our spatial analysis attempts to ‘generate’ the inter-regional flows by reconstituting the perception and reasoning of the population that underlies them. In order to do this, we must consider the behaviour of potential migrants, and allow the model itself to generate its dynamic. 7.4 ECONOMIC ACTIVITIES The basis of the Sénégalese economy is agriculture. Together with fishing and forestry it accounts for over 70% of the employment, and for about 20% of GDP. Until recently, groundnut oil was the largest single export item, but with soil degradation leading to decreasing yields, and with a falling world market, its place as the principal earner of foreign currencies has been taken by fish. Let us briefly consider the different sectors in turn. Two basic kinds of agriculture exist: intensive, industrial exploitations and subsistence farming. As well as groundnuts, important amounts of cotton, sugar cane and tomatoes are grown as cash crops. Groundnuts became important towards the end of the 19th century in the regions of Cayor and Baol. The area where it was grown, however, expanded steadily into Sine Saloum, and then on towards Tambacounda. From a production of only 25,000 tons in 1885, it progressed to 500,000 tons by 1930 and reached around one million tons in the 60’s. Since then, the yields have decreased, and the international markets have declined. The farming of groundnuts grew because of the high rates of return that could be obtained, and the fact that cultivation methods were similar to the traditional ones used in the region. However, traditional crops were replaced by groundnuts and with some bad years of drought, and also with increasing soil exhaustion the carrying capacity of the land has been considerably reduced. In order to diversify agriculture, cotton was introduced, and this has been fairly successful in supplying domestic needs and also some exports, even just 5 years after its introduction. Because cotton has very high water requirements, production is limited to the southern part of Sénégal. Sugar cane plantations have also been set up successfully at Richard-Toll in the north, together with industrial tomato production. Cereals form the main part of the subsistence agriculture, particularly through crops of millet, sorghum and rice. Other crops are niebe, manioc and market garden produce. Millet and sorghum growing has declined over recent years and has partly been replaced by wheat. Rice is grown in Casamance where traditional cultivation methods have been replaced by Asiatic ones, and rice is also produced on the estuary and the lower reaches of the River Sénégal. Market garden produce is developing along the Great Coast and near suburban areas, but they depend very strongly on the availability of water supplies. Because of its central role in the whole economy of Sénégal, agriculture is of great concern to the government. It has many aims, some of which may in fact be conflicting with each other: food self-sufficiency, to increase the rural standard of living and ensure better agricultural earnings, to promote the participation in national life of the rural

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communities, to protect the natural environment and to reduce the deficit in external trade. It is clear that the protection of the natural environment, and the development of such activities as ‘eco-tourism’ may often lead to conflicts with greater development of the agricultural sector. This is one of the reasons why a ‘Dynamic, Geographic Information System’ such as we have developed can be of great use in exploring and resolving, or at least minimizing, some of these conflicts of interest. Another basic activity is cattle raising. This is either done by nomadic pastoralists who traditionally move around with their cattle, and also throughout Sénégal as an additional activity of sedentary peoples. The major area for the nomadic pastoralists is the Ferlo, where the Peul people live. Some aspects of modernization have affected them, for example with respect to the drilling of wells. While this has some favourable effects, particularly during times of drought, it also lead to the clustering of peoples around the wells and to ecological destruction of these vicinities. Livestock includes cattle, sheep and pigs. Sheep and pigs have been less affected by problems of drought, and also there has been a gradual increase in poultry production, both in traditional and industrial units of production. Fisheries are also of vital importance to Sénégal since they provide an important contribution to the protein consumption of the population, and also the largest single item of export. Fishing is still carried out largely by artisanal methods. The industrial fishing sector after some growth has reached a limit and coastal fisheries probably cannot be increased further without risking irreversible reduction of stocks, particularly in the case of sardines, tuna and prawns. Inland fisheries are also of considerable importance. Although they constitute only some 15% of the total landings, they provide a valuable source of protein for the peoples who live along the river valleys, and this question must not be ignored in considering developments such as the implantation of paddy fields along the River Sénégal. The introduction of nitrates and pesticides into the river could well have an important impact on these fisheries. Forestry is another important part of the primary sector. It is mainly situated in the Northern Sahel region, the Soudanian and the Guinean regions. Its contribution to the national economy has decreased considerably as a result of droughts and over exploitation. It is required for two principal needs: charcoal for fuel stoves and industrial uses. The former creates a considerable pressure on forest resources and potentials. In Dakar, Thies, Diourbel overuse has led to a serious deforestation and depletion of tree cover. In St. Louis, Louga and Siné Saloum an overexploitation has also led to problems of fires, overgrazing and drought. The secondary sector is made up of four basic components: food production, mining manufacturing and energy. It accounts for around 30% of GDP and is of course strongly linked to world markets and prices, and to levels of agricultural production and government policies. Phosphates are the major mining output and also very important exports. Different Sénégalese companies exploit the mines at Taiba, Matam and Pallo. Two kinds of phosphates are produced. One involving calcium phosphate is used for producing fertilizer by the Sénégalese chemical industry and for export. The aluminium phosphate mine is unique of its kind in the world. Phosphate output in 1989 was 390,000 tons

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(3.2bnCFA) up on the 1988 figure of 371,000 tons, but still below the peak of 427,000 tons of 1986. There are plans to develop considerably the mining operation, with plans to open a mine at Tobene, and also another for previously unexploited deposits at Semmé, near Matam. Sea salt is mined at Kaolac and 80% of this production is exported to other African countries. In the region of Niayes, peat reserves are exploited. Some other possibilities exist for copper, lead, zinc, iron and gold. There has been some prospecting for oil, but this has proved unsuccessful. Oil and gas prospecting continue with the national company Petrosen. Several possible fields have been found, the best one being the Dome Flore field which is about 60 kms and is estimated to contain 2–8 mn tons of light crude oil. Other small on-shore fields exist and are producing small quantities of oil and gas. Food industries can be disaggregated into two major activities: processing of goods for export, and the outputs developed as substitutes for imports. The former products are largely concerned with oilseed and fish processing. The oilmills are located at Dakar, Kaolac, Ziguinchor and Diourbel and are strongly affected by the success of the harvests. Food canneries expand and diversify their products to more luxury goods and frozen foods. Brewing, flour milling, soft drinks and milk, confectionary tobacco production are the main manufactured outputs used as import substitutes. Two large public companies situated at Richard-Toll are concerned with processing sugar and tomatoes. The food industry is limited not only by the harvests of any particular year, and hence by drought and soil degradation, but also by conditions in the world market. Most of these industries are situated at Dakar and the Cap Vert region, but there are some processing plants where the crops grow, in the Sénégal River valley, at Diourbel, Kaolack and Ziguinchor. The industrial sector includes the production of textiles, chemicals and metal working. The textile industry uses the cotton that is grown in the south of the country. The chemical industry was set up fairly recently (1984) and produces sulphuric and phosphoric acids and fertilizer at Darou, using imported sulphur and Sénégalese phosphates. Other plants provide pharmaceuticals, paints, and soap and others are concerned with plastics. The sector has grown slightly over recent years. Activities are nearly all in Dakar, Kaolac, Ziguinchor and Saint-Louis. The domestic and industrial energy requirements of Sénégal are met by several different energy sources. Charcoal and wood are the traditional sources, and remain dominant in the rural areas, where cooking is done on charcoal or wood burning stoves. Today, however, in urban areas small gas burning stoves are becoming popular. Electricity is used in urban areas, but is not available in many of the rural regions. Oil and petroleum products are imported and this is a serious drain on the economy, as it requires hard currency which must be earned by the export of such products as fish, groundnut oil and phosphates. The dam that has been built at Manantali will allow the generation of electricity, and this will be fed to Dakar through a power line. This should enable a reduction in the quantity of oil that has to be imported. There are also some peat reserves which may be developed, as well as experimentation concerning the use of solar cells, biomass and wind energy.

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The tertiary sector includes employment in the fields of: administration, finance, trade, commerce, handicrafts, transport and communication and tourism. Most of the employment in this sector is in Dakar. The tertiary sector makes up over 50% of GDP. Due to the role of Dakar as the administrative centre of French West Africa, it achieved a predominant place in the independent Sénégal. Government institutions and bureaucracy are an important source of employment in the capital and provide a significant part of local revenue. The financial sector is controlled largely by the government. A dozen commercial banks, four credit institutions two development banks, an agricultural credit institution and a bank for housing financial credit make up the national banking network. Some foreign banks, especially french, have branches in Dakar. As a member of the West African Monetary Union, Sénégal does not have its own central bank but the headquarters of the AMU are at Dakar. Handicrafts are a traditional economic activity and are widely spread throughout the country. These consist of various kinds of simple repair shops, the making of small tools and utensils, art crafts and products based on the by-products of industry. Handicrafts can be increased as a result of better marketing and credit facilities. Dakar plays a dominant role in trade relations, while Kaolack, Diourbel, Thies and Ziguinchor have kept the economic role of staging posts that were created during the colonial period. International trade is mainly located at Dakar, while wholesale and retail is spread throughout the towns and villages of the whole country. For some years the tourist industry in Sénégal grew steadily. However, in more recent times it has not developed as anticipated. It is composed of business tourism, especially in Dakar, leisure tourism attracted by the climate, the fauna and the exotism, and a tourism based on cruises and their stop-off points on the River Sénégal, in Siné Saloum and in Casamance. This sector could be a source of future growth, particularly because of its multiplier effects on banking, trade and arts and crafts. Tourist centres are mainly along the coats at Dakar, Casamance and on the river Sénégal, but there are also some destinations in Eastern Sénégal and in Casamance mostly connected with the National Parks and the richness of the natural flora and fauna. There are important facilities such as holiday villages and luxury hotels. There is also a kind of integrated tourism linked to traditional and natural ways of life and this and various forms of ‘eco-tourism’ are important for the future. Conflicts of interest exist between these developments and the more usual development of agriculture. There is a considerable network of road, rail, river and air connections throughout Sénégal. In our model, this can be accessed by selecting ‘NETWORK’, and one of the important uses that the model has is to explore the complex effects of improvements in the transportation network. It is important for the development of domestic trade, external exchanges and the transport of travellers. Even if the road system is the best in Western Africa, it remains highly centralized around Dakar and the region of Siné Saloum. Air transport operates between about a dozen airports, the most important of which is Dakar. Air freight has more than doubled in ten years. The railway system has two main lines: one from Dakar to Bamako and the other from Dakar to St. Louis. The network is rather old and improvements are required to meet the needs of goods and passenger transport that are

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envisaged. Dakar is an important port, the second in West Africa after Abidjan. It is mainly used for the transport of goods, fishing fleets, as a dockyard and a military port. The quaternary sector involves housing, environmental and urban policies health and social services, education and culture and research and information. There is in fact no statistical data concerning traditional housing and so all the figures that we have refer to the modern housing sector. Because of this Dakar has a very large proportion of the stock, although Thies, Diourbel and Casamance also have some minor housing plans. Public policy is concerned with the building of low cost social housing. The main difficulties are that there is not an effective banking service, and that raw materials are very costly. The degree of urbanization of the different regions show that Dakar is almost completely urbanized, and that the degree of the other regions is growing steadily. In addition to the ecological investments aimed at reducing desertification and overgrazing, environmental policies concern pollution control, the improvement of the quality of urban life, and training and research. The problem of the pollution of the Baie de Hann has been studied, as well as methods to control and plan the shanty towns adjacent to Dakar. The health of the population is related to four main indicators: level of nutritional inadequacy, the sanitary environment, the amount of sickness and disease and the mortality rate. For these factors the urban regions are significantly better than the rural. Dakar is the privileged area while the regions of Casamance, Fleuve and Sénégal Oriental are worst. Health services in rural areas are provided by small clinics and in each Department there is a hospital. Medical infrastructure is growing with the population and with the higher sanitary standards that are desired. Dakar has a higher level of service than other places both for hospital beds available, and for the numbers of doctors and dentists. Louga, Tambacounda, Diourbel and Siné Saloum are the most under-privileged, and this may well influence decisions concerning migration, where some perception of ‘quality of life’ may be related to the presence of such services. There are three levels of schooling: primary, secondary and higher education. Despite a general increase in the fraction of the child population that attends schools, there is a very strong regional disparity. For example, while Dakar has over 72% of children attending schools, Louga has only some 20%. Literacy remains quite limited at around 30% of adult males and only 14% of adult females (1980). The difficulties facing the future development of Sénégal can be understood from the above summary. The people depend largely on the land, and this is in some cases becoming exhausted, owing to the overexploitation of the soils. There is therefore considerable danger that the increasing pressure of population, together with this partial soil exhaustion and the overuse of water resources will lead to a serious ecological degradation, and to declining standard of living. The age pyramid of Sénégal is excessively biased towards the young, and so clearly the burden on the land, the sea and rivers to provide food, energy and raw materials will continue to increase for the foreseeable future. It is for these reasons that development policy and plans must be assessed as carefully as possible before being implemented, since the apparent economic benefits that may exist in the short term may well lead to an irreversible destruction of biological potential in the long. Although issues such as climate change, and the unpredictable onset of droughts may be important, the main

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dangers of desertification—soil exhaustion, overgrazing, river pollution, destruction of fish stocks—come from man. And this is how the decision support system described here can be useful. By providing a tool which can allow the complex impacts on all the other sectors of increased or changed activities in one, then damaging ‘side-effects’, unanticipated consequences and surprising results can be factored into the original decision process, and negative implications perhaps minimised. 7.5 THE DYNAMIC SPATIAL MODEL The dynamics of the population has been modelled for each region of Sénégal, and fertility and death rates vary somewhat between regions. The number of regions is 10 that is: – Dakar, Diourbel, Fatick, Koalack, Kolda, Louga, St. Louis, Tambacounda, Thies, Ziguinchor Not only are the population sizes different for these regions, but the age pyramids are different, and the birth, fertility and death rates are also different. This means of course that the rates of natural increase of each population will differ, and that in addition to this, we shall need to consider the cumulative effects of migration which will transfer population form one zone to another. The first disaggregation has been that into children (0–10 years), active adults (10–59) and the elderly (60+). The equations for the rate of change of the numbers of each age class in a given region i are therefore simply given by the usual kind of equations of population dynamics. The equation for the changing size of the child population in a region takes into account the following mechanisms: – the increase due to births and in-migration – the decrease due to death, out migration and the successful passage of a child to the next age cohort. The number of births depends on the number of adults and the fertility rate for the region. We have assumed at this stage that because of the extended family structure, migration of children is not significant. In addition we have taken into account the probability of survival from 0 to age 10, which reduces the flow to the next age group from 1/10 to .069. dXchildi/dt=bi*Xadulti−mi*Xchildi−0.069*Xchildi (7.1) where: Xchildi=population of age 0→10 in region i. d/dt=rate of change of (expressed as an annual rate) bi=annual birth rate per adult Xadulti=population of age 10→60 in region i. mi=annual mortality rate per head

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The birth rates are known from the census data, and therefore the annual rate of increase of the population of children in a region can be calculated. Similarly, the survival rate is also known, and therefore the mortality rate of the age group 0 to 10 gives us the net change in number due to birth and death. From this we can also calculate the rate at which successful survivors pass from the child to the adult cohort, and this is what gives rise to the value .069. In a similar manner, we can consider the terms which govern the changing numbers of adults that inhabit each region. The first term corresponds to the passage of children reaching 11 years old from the child to the adult population. Having successfully survived their childhood. The individual mortality rate for this age group can be found by examining the demographic data, and clearly this diminishes the number that survive through to become 60 years old and pass into the elderly population. Another very important term concerns that of adult migration. This is represented by a term which takes into account both the ‘readiness’ of the local population to migrate and the choice of destination that they may make when they actually decide to leave. This intrinsic mobility may be linked to the ethnic origin of the individuals, the length of residence at the place in question, the level of unemployment or modern amenities there, or the perception of opportunities accessible there as opposed to those elsewhere. Similarly, the choice of destination may be affected by the distance involved, the level of amenities at each destination, the level of economic opportunity or wages that are perceived. The model introduces an ‘attractivity’, Rij, which reflects the perceptions of the population at i of the attractions of the region j. dXadulti/dt=0.069*Xchindi−m*Xadulti+ Mob*{∑i≠jXadultj*Rij/∑i′Ri′j−Xadulti′Rij/∑i′Rji′}−0.0025*Xadluti (7.2) This equation describes how the adult population moves between the regions of Sénégal in response to the perceived difficulties and opportunities. This redistributes the demographic potential spatially, and therefore by modifying the distribution of population over the long term has a major effect patterns of demand for raw materials (fuel wood, water etc.) and for goods and services. At first it might simply be assumed that migration flows would simply operate in such a way as to lead to an ‘equilibrium’ distribution of opportunity or scarcity, with a final state of zero flows representing the fact that no further advantage can be obtained by an individual moving to another zone. However, this is certainly not the case in reality, and as we shall see, it is the coupling of these population equations with other equations describing the change in the pattern of economic opportunities that can continue to feed migration on a permanent, or even an accelerating path. Dis-equilibrium does not drive migration and establish a new equilibrium, but instead it can drive an increase in the disequilibrium. The equation for the change in numbers of elderly people Xoldi at i, is given by the number of adults surviving to their 60th birthday. dXoldi/dt=0.0025*Xadulti−mold*Xoldi (7.3) This completes the equation for the change in spatial distribution of the population. Although very simple, it nevertheless generates a very complicated pattern of growth and

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decline as the natural growth and the pressures of migration react to and generate pull and push factors for the population. 7.6 MODELLING MIGRATION FLOWS Clearly, many factors and government policies can affect this spatial and temporal pattern of growth, decline and migration. Better health facilities, family planning clinics, educational opportunities, nutritional levels and hygiene all affect the rates of birth, survival and death. A careful study of migration processes in Senegal was carried out by Fabienne Leloup and described in her Ph.D. thesis (1990). Migration, however, which is a major factor in the longer term spatial pattern of growth and decline, is much more related to differences in the level of perceived opportunities between origins and destinations of potential migrants. In turn, these differences are related to flows of information concerning the existence of high wage jobs in the modern sector, of the chance (however small) of a secure job with the government, of a flexible informal sector which can allow migrants to survive while waiting for good opportunities, and of course, the decline of wages in rural regions as water supplies, or soil begin to be exhausted. All these factors together act on the regional populations and affect the pattern of flows. The migration flows are represented in the model by the terms: Mob*{∑i≠jXadultj*Rij/∑i′Ri′j−Xadulti′Rji′/∑i′Rji′} (7.4) where the terms Rij represent the ‘attractivity’ of the region i as a migration destination for the potential migrants from region j. This is given the form of an exponential function: (7.5) where ri is the homogeneity of response; Avwage the average wage at i, and Amen the level of Amenities at i. For any region j, therefore, the fraction of total migrants that

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Figure 7.6 Migration flows between j and i determined by the number of potential migrants, and their choice of i as a destination among others. chooses i as a destination can be expressed by dividing Rij by the sum of this for all possible destinations i, Σi Rij. Migration is a very important factor in the long term evolution of Sénégal, and the ecological and environmental stresses that will be produced. Throughout the seventies and eighties the main focus of migration has been Dakar, with the result that there are very difficult problems of water supply and waste disposal that have built up, together with those of anarchic urban development and shanty towns. On of the major issues for development policy in Sénégal is therefore the issue of successful rural development, and measures which may succeed in changing the patterns of migration so that other the interior of the country, particularly the Sénégal river valley, and the Eastern regions will cease their decline. The policy tool that is presented here can help to plan such measures. 7.7 ECONOMIC DEMAND Having dealt with the question of demographic and migratory change, the population also plays an active role in the system by making choices concerning consumption. Here, instead of making the rather unreasonable assumptions of ‘rational choice’, based on perfect information, either of consumers maximizing utility or producers maximizing profits, we have a simpler, more realistic approach.

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Populations, whether they be consumers or producers or both, are not considered to be made up of identical individuals, nor to have perfect information. Instead, they have a distributed response around an average, as a result of individual differences of preference, and also of information. To capture this effect we use terms of ‘attractivity’, similar to those of a logit choice model, which correspond to the fraction of a population attracted to choice i among n. Let us start by considering any sector L and any geographic zone j, and ask the question—what factors will influence the final consumption behaviour of consumers in; with respect to purchases of L from all other zones i=1, 2, 3,…I,…, n? In order to answer this question we introduce the notion of ‘attractivity’ and define ALij=exp(−ρint(PLi+ts1dij) (7.6) where ρint represents a response rationality parameter. PLi=price of L in zone i. tsldij=transport costs for a unit of L between i and j. In order to find the relative attractivity of zone i viewed from zone j we must now sum over all the potential sources of L from j, including the outside world: ALj =ΣiAij+exp−ρext(WorldP1+ts1dwj) (7.7) where WorldP1=world price for sector L, including customs duties tsldwj=transport costs from j to the world market The relative attractivity of i viewed from j is therefore: RALij=ALij/ALj The fraction of demand situated at j that is likely to be satisfied by a supply from i is RALij, and the ALj are all positive numbers expressing the attractivity of the different choices. Instead of 100% of the population choosing the ‘best’, there is a spread in the response, from the ‘best’ to the ‘worst’. The strength and homogeneity of the response are important features of the behaviour, and need to be calibrated on real data. When ρint is large, then the response is very homogeneous, and nearly all the population will make the

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Figure 7.7 The choice of consumers at j that falls on i depends on Aij. same choice. However, when ρint is small, demand from the population will be distributed fairly evenly between all the possible choices of supply. As an example, consider 2 choices, at price 5 and 8 with a transport cost of 1 between them: If ρint=1 then the relative attractivity RA12=A1/(A1+A2) and RA12=exp−1*(5+1)/(exp−1*(5+1)+exp−1*(8)) =.00248/(.00248+.000335)=.8808 So, 88% of consumer demand at 2 goes to 1. Similarly, RA21=.000123/(.000123+.00674)=.018 Only 1.8% of consumers at 1 choose to go to 2. But if ρint=.1 then, we have a much greater spread of consumer preferences. RA12=.549/(.549+.449)=.549 or 54.9% RA21=.406/(.406+.606)=.401 or 40.1% In this way we see that depending on the value of ρint the reaction to differences in costs for the consumer can lead to very weak or very strong differences in the pattern of consumer choices. If βL is the fraction of total income that is directed to sector L from points within the system, Final consumption demand from within Senegal=ΣβLjY.RALij (7.8)

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A similar calculation may be carried out to estimate intersectorial demand, IDLi, which sums over the demands from economic activities which implicitly also contains the investment demand, and we are now in a position to compute the total overall demand falling on any zone i. The intersectorial demand can be obtained from the input/output coefficients between the different sectors of the economy, and these can be used to calculate how a unit of production in one sector requires the output of another, and this in turn from others, and so on. From this information, the linked economic effects of changes induced in any particular sector can be shown, and by combining these with the choices of supply and of consumer choice, the spatial and sectorial linkages can be represented in the model. This is equal to disposable income partitioned by a set of sectorial parameters βL+ intersectorial demands+external demand from the rest of the world (exports). Disposable income is made up of wages+rents received. (7.9) where DW=external demand for L This allows us to calculate the value of goods that are demanded from a sector L in region i, and also the amount that they import and export from the outside world. Clearly, this can be affected by the customs duties, or exchange controls that are imposed. It also reflects the transport costs between the regions of the system and also to the world markets. In the model demand is expressed in millions of CFAs, and for the whole of Sénégal corresponds approximately to the total number of jobs multiplied by the average wages, multiplied by βL for the sector L. By choosing to look at Sénégal as a whole, the macroeconomic indicators can be examined. Similarly, national values of population, of children, adults and old people can be obtained from this, as well as sectorial employment, the imports and exports of each sector and the GDP, and the balance of trade. 7.8 MODELLING EMPLOYMENT CHANGE Having developed expressions which calculate how much of the different goods and services the population would like, we need to make them interact with the potential supply. Supply, however, will only respond to demand if it is profitable to do so. In other words if revenue from sales does not cover the costs of production, then supply will decline. Price, however, in the absence of government intervention will be affected by the balance between supply and demand within any region. If demand is greater than supply in a given region, then prices will rise, and if the opposite is true then prices will fall. If production is profitable, because the quantity and price of goods sold generates profit over and above the costs of production, then the sector will expand, and if the opposite is true it will contract. The cost of production is due to the costs of inputs such as land, machinery, fertilizer, tools, seeds, etc. and of course wages. But wages provide the income for the population and hence are the source

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of the demand for goods and services from within Sénégal. As the model shows, what is important is the productivity of labour that is important for development, since it is the only way in which consumption and production can move beyond simply responding to basic needs.

Figure 7.8 The chain of causality surrounding supply and demand for a sector L. From the previous section, we are now in a position to compare total economic demand falling on i (in sector L) with supply of L in i. The supply is given by: SLi=ELi*PLi*PryLi (7.10) where ELi=employment in sector L in region i PryLi=productivity of labour in sector L at i It is now simple to model the change in economic activity which will result from any disequilibrium between supply and demand in terms of a rate of desired expansion and a rate of price change: (7.11)

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But, the price that is asked per unit will affect the profitability of the production of L at i. If the price is greater than the cost, then the profitability will drive an increase in supply, while if the inverse is true, then supply will contract and there will be less job opportunities. (7.12) where QLi=desired output by sector L in region i CLi=costs per unit of production of L in i V=the rate of response to opportunity RI=Parameter reflecting homogeneity within the sector If desired and real output are equal, then clearly, there is no change in the level of employment in the sector L in the region i, but if the desired output less than or greater than the level actually in place then there will either be an expansion or a contraction of employment. An expansion is only achieved if job vacancies appear in the region, and these are filled by available people. The rate at which they are filled will therefore depend on the availability of labour, and the rate at which the information concerning vacancies is transmitted to those looking for work. If there is a skill requirement for the job, then clearly expansion will depend on the numbers of job seekers with the appropriate skill, with information about the vacancy. If an increase is required, then the desired output, and hence desired employment level is achieved if as vacancies become jobs: dJLi/dt=sig·(OLi−JLi)·(xadulti−Total employmenti) (7.13) where sig is a measure of the effectiveness of the information flow in the labour market. If a decrease in employment is required, then the JLi is simply decreased towards OLi, and unemployment at i increases. The model therefore contains a mathematical representation not only of the disequilibrium between supply and demand of goods and services, which changes prices, profitability and therefore the spatial pattern of desired output and investment, but also the dynamics of the labour market as demographic processes and migration change the number of adults looking for work in each region. The disequilibrium between the supply and demand of labour leads to the growth and decline of wages in the different sectors and regions, which in turn decreases and increases the final consumption of each region, and its attractivity as a destination for migrants. 7.9 PRODUCTIVITY, NATURAL RESOURCES AND THE ENVIRONMENT In the equations for economic activity, a key term is the productivity of labour. The prosperity of each region depends on the population being able to produce goods and services which it can consume, and which it can trade in order to bring in the goods and services which it is not well able to produce itself. The model has all the mechanisms

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which gradually shape regional economies and allow them to play a specialized role in the national system. For example, if a region is well suited to produce a particular crop, then the production per person, and per hectare will be considerable. However, if there is no way to transport the harvest to reach a broader market, then the limited local demand will cause the price to fall, and thus reduce the reward of cultivating this crop. However, if transportation allows the harvest to reach enough demand, and maintain its competitivity, then the price will be maintained, or increase, and production will be reinforced. In this way, the presence of a transportation network will move the regions towards economic specialization, and the concentration of production at the places where costs are least. However, part of the costs of production are due to the need for various inputs, such as water, soil nutrients, tools and machines, and other materials coming from other sectors

Figure 7.9 and economic activities. This will tend to give an advantage in costs to activities which can be carried out near to a variety of others, and so there is a self-reinforcing spatial effect tending to focus growth on areas which already have a concentration of other activities. In theory, this could lead to the gradual emergence of a single urban centre, there are also other factors which balance such an effect. For example, as demand for labour, and for land and buildings on the transportation network, grows, then the cost of these inputs

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will increase as the imbalance of demand and supply puts their price up. The spatial evolution of growth will therefore be shaped by two main factors: – the changing pattern of comparative advantage due to the costs of inputs, and the accessibility of markets. – the changing pattern of productivity due to the availability and quality of the natural resources, such as water and soil nutrients, that are required for production. The economic equations that have been described above express the operation in the different regions of the first factor. However, the importance of the second must also be considered and given an explicit mathematical representation. Water is a vital input for almost all activities. Agriculture and industry are perhaps the heaviest users per job, but tourism and the domestic supply are also very important. The limited supply of any input to an economic activity can show up in two different places. First, if it is an economic input, it can affect costs of production, and therefore the competitivity of the sector in that region. However, it can also affect productivity itself, even if there is no price involved. For example, the lack of water will severely reduce production in a region, although it may be a ‘free’ commodity when available, and similarly, the failure to maintain natural soil fertility will inevitably lead to reduced production. In the latter example, it may be that the soil nutrients were maintained perhaps by the grazing of cattle for some periods in the year, but that a project aimed at intensifying agricultural output may well interfere with this, and therefore with soil fertility. In our system of equations, there is an equation for productivity, and its changing value as a result of different factors. The first factor is simply the area of suitable land available for the activity or crop in question. If the existing capacity, that is number of jobs, already effectively uses up the best land so that an increase will involve more marginal land, then productivity will fall. Secondly, if there is a certain quantity of water which is available for the crop or sector in that region, then a shortfall in this will also result in reduced productivity. Policy makers can intervene in these terms by creating more suitable land area in the region, and extending the area supplied with water. The expression for productivity is: PryLi=Pry0Li·(1+techim·t)·(1−AreaLi/TareaLi)·(1−Wri/Twri) (7.14) where: PryLi=Productivity of sector L in region i. Pry0Li=Basic Productivity, related to soil fertility or the technology available. techim=rate of technological improvement AreaLi=Area used by sector L in region i TareaLi=Total area available for sector L at i Wri=Water required by sector L in region i Twri=Total water available for L at i The different factors such as suitable area available and the provision of a water supply can be modified by investment decisions either on the part of the government, or by private investors. In addition, we have assumed that half of the profits are put back into an activity in order to maintain and improve its productivity. Once again we see a

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process which leads to self-reinforcement of success activities. Profits are used to invest in the maintenance of machinery and also in the acquisition of higher technology. This, in turn, increases productivity, decreases costs, and improves competitivity from which flow more profits. This is the virtuous circle that we hope development can lead to. The important question however concerns the use of natural resources. The amount of water, and soil nutrient available in a region at a given time depends on what has been happening in the system over the previous period. They are not fixed quantities. For example, the rainfall history, and the releases that have been made over past years will determine the volumes of water available in the different reservoirs, but the allocation available for any single usage, such as for rice fields in Fleuve for example, will depend on this and also on the competing demands from other users. So, the productivity that may really characterize the rice fields will depend on the priority that it is accorded, and on the availability. Similarly, providing that there is sufficient water, rice growing is highly productive, it uses very high levels of soil nutrients, and also requires the use of considerable quantities of pesticide. Consequently, rice requires the heavy use of fertilizers to supply these nutrients, and also affects the downstream water quality very negatively. In order to model the supply and demand of water, we have examined the ‘state of the art’ software that is available. These are not satisfactory, however, being based on linear programming algorithms, which do not deal correctly with the historical dependence of events. In order to correct this, and to allow a correct modelling of reservoir levels, and of the changing situation over several years, we have developed our own simulation model, and over the next 6 months this will be connected into our present software package, so that real changes in water supply, and in productivities can be studied together. 7.10 SENSIM—THE SOFTWARE This very complicated spatial, dynamic model which links the demographic, economic and environmental variables of the 10 regions of Sénégal has been made ‘user friendly’ through the work of Guy Engelen and his group at the RIKS Institute of Maastricht. The software has an extensive help system available in French or English, and also a full and interactive presentation of the equations, and of all the variables, parameters and underlying hypotheses. The model comes on a single high density diskette. Clearly, the idea of ‘capturing’ the multiple facets of all that is going on in Sénégal on a single disk, and being able to make plans and explore policy, has to be treated with great caution. Such a reduced view of the real complexity must be used correctly if it is to help decision makers. The model can address certain questions concerning the probable impacts of investments in infrastructure or production capacity, or of droughts or soil exhaustion. Macroeconomic variables can be examined, and from these some conclusions might be drawn concerning the advantages and disadvantages of different possible policies. The real use of the model is as a learning tool with which to ascertain whether the processes and parameters in the model still seem to be describing what is taking place. Running the model is largely self-explanatory, and this has been one of our primary aims. Data sets can be saved and recalled automatically, and preferences for graphical displays can be stored as well.

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Part of the software program consists in an explanation of how to run a simulation, and how to intervene in it with a particular policy or decision. Also, time series charts can be made, printed and stored and so there is little point in writing about these aspects at length here. Instead, let us show the sequence of screens that appear as the model is used, and how the barrier represented by the underlying complexity of the mathematical equations is successfully overcome. In the section following this we shall show how the software can be used to study the effects of different interventions or events. Policies of improvement of transportation infrastructure for example, or of developing the area of rice paddy fields in the Region of St. Louis are important issues, as are the effects of drought, or of climate change can also be explored using the software. Similarly, we can explore the effects of different rural development policies on the preservation of flora and fauna, by simulating the real pressures of population and agricultural development that will be experienced. The continued existence of conservation areas, of forests and reserves, and the possible development of ecotourism are also issues that need examination because of the conflicts of interest that arise between the different kinds of possible exploitation. After typing ‘Sensim’, this is the screen which appears first, with several icons which can be selected for more information about IERC and RIKS, or about the software, or in order to continue with the simulation. By selecting the menu ‘SENSIM’ a complete explanation of the software can be accessed, with explanations of how simulations are carried out, and what features are available.

Figure 7.10 The opening screen of the Sénégal Program.

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Figure 7.11 Each line in the ‘Table des Matières’ is explained.

Figure 7.12 The interactive ‘HELP’ manual that is available. There is an interactive Table of Contents which enables any particular topic to be studied directly. This also forms the basis of a ‘help’ file which can be accessed at any time during the simulation. The selection ‘Expert du Modèle’ provides a complete presentation of the equations that have been used and of the parameters required to run it. This is also interactive and the ‘mouse’ can be used to select the terms for which an explanation, and the equations are required.

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Simulations can be run by selecting ‘Fichier’, and choosing the appropriate data file. The default file is ‘data.mod’ and so it is important not to call any subsequent files by this name. Having chosen a simulation, then the type of presentation required can be chosen by selecting the menu ‘Presentation’ which offers the choice of a map with histograms, numerical data, time series plots, or the fluxes of goods, services and people between the regions. The user can either select a previous presentation through the menu option ‘Preferences’, or alternatively can develop his own, and save it for future use. The presentation can either take the form of a map of Sénégal with histograms show the relative size of different variables, of one can choose to view numerical data. In any of these modes of presentation, the choice of variables can be modified by pushing the ‘Legend’ button, and using the mouse to select the variables, their colours, and the scale of representation. As well as the presentations shown above, time series graphs can be produced showing the changes in the chosen variables over the period simulated. These enable comparisons to be made concerning the real effects, both direct and indirect, of any given policy or decision.

Figure 7.13 The details of the model, the equations and parameters are all available.

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Figure 7.14 The user can select the term for which an explanation is required.

Figure 7.15 The map display shows the changing values and a summary of the numerical data.

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Figure 7.16 Another presentation choice is numerical data. 7.11 POLICIES, INTERVENTIONS AND EVENTS An intervention can be made during the simulation by selecting the appropriate menu, and the kind of policy or intervention can be selected from the screen below. A whole range of policy options can be explored by using this, and they include interventions and investments in infrastructure, and different policies on prices, family planning, health care, water management etc. If, for example, an intervention concerning the transportation network is envisaged, then this is selected, and another screen appears, as below, in which the effect of the new road or transport link on different parameters can be inserted. A screen which allows the impact to be inserted for each economic sector and for the population then appears, and either a strong or weak positive or negative effect can be inserted. If an investment is envisaged in the transportation infrastructure, for example a new road link is to be built, or an existing one improved, then this can be implemented on the transportation network of Sénégal by selecting the choice ‘Network’ which is under the menu item ‘Autres’. i) Changing the Road Transportation Network For many developing countries investments in better transportation infrastructure are a high priority. It is believed that it will allow harvests and artisanal craft products to be

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Figure 7.17 Different types of intervention can be selected.

Figure 7.18 The factors which are directly affected are chosen.

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Figure 7.19 The parameters affected by the intervention can be modified.

Figure 7.20 The transportation network of Sénégal. brought from the interior of the country to the markets of the coast, or even for export. The increased transportation is supposed to bring services within easier reach of the more distant communities, and through this to perhaps reduce the desire of young people to migrate.

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An entire sub-model concerning transportation then appears on the screen, with the possibility of operating buttons to add link, or to modify an existing one. By selecting ‘Zoom’, the user can select the locality where he wishes to change the network. Then, using the mouse, a new road can be added between any two nodes, and it can be assigned a ‘distance’ reflecting both its real distance and its quality and capacity. The software allows the user to modify the transportation network using the mouse. The area that will be affected can be made magnified using ‘zoom’, and then the two end points of a new link can be selected. A window opens up then which allows the user to specify the ‘length’ of the link, which may be considerably longer than the ‘straight line’ distance. Once the modification to the network is made, the computer recalculates the distance matrix that shows the distances between the different regions, and then uses it in the simulations. This enables the overall impact of improved transportation infrastructure to be estimated, as the changed economic competition between producers leads to a change in the cones of demand, and the relative sizes of activities in the different regions. In this way, the real gains of improving the transportation infrastructure can be examined by performing simulations with and without the improvements and comparing them. This is a complex matter, because although better roads may open up a large urban

Figure 7.21 The ‘zoom’ facility allows the selection of an area in which the road network can be changed.

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Figure 7.22 The network can be modified by selecting two points.

Figure 7.23 The length of the new link can be adjusted to take into account the precise route and quality of the road.

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Figure 7.24 This demonstrates the possibility of mounting a full GIS underneath our dynamic model and of fully connecting the two. market to goods produced in the rural areas, the improved transport works both directions. Goods produced in the urban centres may outcompete those produced in the rural areas by local artisans, and so the resulting evolution is a complex mix of increased opportunity and increased competition. Better transport can also increase migration flows as the ‘cities’ become that much closer and more familiar. In this application, there is also place for a Geographic Information System. At present it only contains the names and details of the towns and cities corresponding to the different nodes, but this can clearly be extended to give all kinds of details of soil, flora, fauna, microclimate, economic activities, population, etc. In a fully developed version that we hope to develop, these would then be linked by the main model that is running under ‘SenSim’, achieving the goal of a fully dynamic and spatial decision support system. ii) Developing the Senegal Valley In this small experiment, we can test out the effect of attempting to develop the Sénégal River valley by providing irrigated paddy fields, and organizing increased rice production. This is a major aim of the Sénégalese government who seek food security and import replacement from these major projects. The initial situation that we start from corresponds to the spatial distribution of people and jobs in 1981, resulting from an extensive study of the data. The parameters expressing the demographic, economic and ecological mechanisms in operation have been carefully adjusted and tested so that they successfully regenerate the events from 1980 until 1988. The patterns of migration, and the changing distribution of economic

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activities link the developments in St. Louis to changes that occur in the rest of the country. Depending on the annual increase in hectares of paddy fields, the employment opportunities differ, and farmers can stay and grow rice, providing that it is profitable. This is so, provided that there are tariff-barriers to Thai rice. The model then calculates who buys this rice, and how this affects the interregional flows of trade, and these consequences flow through the system changing it as a whole, and allowing a global assessment to be made of the consequences of particular actions in St. Louis. When interventions are made, or an event such as a drought occurs, the model shows the changes that will probably occur in the system as a whole, and not just in the sector directly concerned. The model begins with the situation in 1981, for which Figure 7.25 shows the population, jobs and other variables for St. Louis. If there is no policy of investment in paddy fields then the situation that is arrived at in St. Louis is shown in Figure 7.26. By 2001 the total population has grown to 990 thousand, with 297 thousand jobs in all, but an unemployment of 160 thousand. This compares to a population of 794 thousand, and total employment of 337 thousand and unemployment of only 123 thousand with the investment in paddy fields and the consequent development of the Senegal Valley. Clearly, the development of St. Louis has led to the creation of jobs in the intensive agriculture sector, and with a greater retention of population in the region. The population of nearly all the other Provinces is less than it would have been without the investment, and in particular Dakar has some 3 thousand less inhabitants to deal with. To study the differences, we can use the ‘COMPARE’ utility in SENSIM.

Figure 7.25 The situation in St. Louis in 1981.

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Figure 7.26 The situation in St. Louis in 2001 without any investment in paddy fields.

Figure 7.27 This is the situation in St. Louis in 2001 if 5000 hectares of paddy are created per year.

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Figure 7.28 The COMPARE utility allows the differences between policy runs to be compared. Using this, we may call up the two states, one without the investment and the other with 5000 hectares/yr added in St. Louis, and display the disparities. This Comparison Utility allows us to see the differences in population for each Province that arise as a result of the investment in St. Louis. It shows us the accumulated

Figure 7.29 The difference in the population of St. Louis with the investment compared to without.

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Figure 7.30 The corresponding difference to the population of Dakar.

Figure 7.31 The increase in jobs in St. Louis in the intensive agriculture sector as a result of the rice policy.

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Figure 7.32 Increased jobs in commerce in St. Louis because of the greater local employment. The multiplier is weak because the population is only 4000 greater, it is the unemployment that has decreased. effect of a changed migration pattern, in particular reducing the flow to Dakar, but also reducing that to other destinations as well. This in turn produces an effect on the demand for goods and services both in St. Louis and in the various destinations for the migrant population. We can examine the difference that the policy leads to in the jobs created in intensive agriculture in St. Louis, as well as in the multiplier of services and commerce. This demonstrates how the SENSIM software can allow policy explorations which show the overall effects of policies or actions. The number of jobs in Dakar in 2001 are reduced as one might expect by the investment in St. Louis, and the modified pattern of employment and of population can be explored using the Compare utility. In the particular case considered, we see how the provision of extra rice fields leads to increased production as the activity is taken up by local farmers. This increased rice can provide a substitute for imports, and the whole economy gains as a result. However, this depends on the precise level of costs, the productivity per hectare, and the policy as regards price controls. Many different aspects of policy and intervention can be explored in this way, whether it concerns questions of price guarantees, import controls, wage levels, education and health, industrial development and so on. In addition, the evolution of Sénégal can be explored under the effects of events such as droughts, or a change in the world markets. As part of this work a full manual has been written describing how the software is to be used, and the ways in which policies, events, interventions and scenarios can be

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constructed. In this section, therefore, we shall simply describe the operation of the system, and present some simple cases which show its potential. 7.12 FURTHER IMPROVEMENTS The model was studied then extended by Yuejin Tan, a visiting professor from China, who saw that the investment dynamics needed some additional terms. He introduced the capital accumulation factor, and developed an equation describing the pattern of investment across Sénégal, considering separately investment made on a national basis (foreign aid for example) and investment in regions that are self-generated. The attraction of an investment in sector l of zone i is:

where the first term in the exponential considers the proportion of available land for sector l in region i, and the second the relative unit profit for sector l in region i. µ1 and µ2 are parameters representing the relative importance of profit and land in the decision process. From this attractivity, the flow of investment into a particular sector l of region i can be calculated according to:

where I is the total available national investment for all sector and regions, and Ii the total available regional investment for all the sectors in the region. The capital accumulation is then given by:

where the accumulated capital in sector l of zone i is Cai1, Ii1 is the investment rate, and Dei1 is the depreciation rate in sector l of zone i. By using these equations different investment strategies can be investigated. The equation for the creation of vacancies was also modified to take into account the costs per vacancy that pertain to a given sector. It is hoped that a model of the kind described here will be developed in China, in order to provide a new basis for exploring the consequences of different development policies in what is now an extremely dynamic situation.

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7.13 ENVIRONMENT, ECOLOGY AND DEVELOPMENT POLICY At first sight the integrated decision support system that has been developed seems much closer to dealing with economic and political problems than that of the environment. But this is misleading. Today, it is recognized increasingly widely that changes in the natural patrimony of a nation are not driven by natural events but are of anthropogenic origin. Throughout his existence man’s activities have modified the flora, fauna and the landscapes that he has inhabited. However, over the very long periods of time that characterize pre-history, pastoral and agricultural practices evolved which were compatible, and even a necessary part of, the natural cycles of materials. Ecosystems developed in which man played a role, and which were sustainable over the long term, even with the occurrence of extreme events such as droughts, floods and plagues of different kinds. The traditional agriculture and grazing systems were not necessarily efficient in the short term, but were such as to give a resilience to the whole system so that it could survive over the long term. The western scientific vision that underlies modern technology and economic development views ecological and human systems as if they were mechanical systems, and hence encourages the idea that they can be ‘optimised’ for a particular ‘goal’, such as profitability. But, we now know that any such optimization process will automatically reduce diversity and redundancy in the system, and leave it vulnerable and less capable of an adaptive response to extreme conditions or the effect of some pests. Short term profit and long term sustainability are in reality to some extent mutually exclusive, and we need the kind of tool that we have developed here in order try to reflect on the evolution of the system as a whole, and to give us some wisdom in our decision making. In Sénégal, as elsewhere, there is an understandable desire to develop as other nations have, and to increase the wealth and quality of life of its citizens. As elsewhere too, the growth of the urban population is the indicator of these changes, as people leave the land and seek their livelihood in the cities. Intensive agriculture increases in the rural areas they leave, and industrial and commercial activities intensify in the cities, becoming both a motor of this migration, and a necessity in employing the migrants. In this way the system concentrates consumption of all kinds of resources such as water, food, raw materials, chemicals and energy into small areas such as Dakar, as well as producing large quantities of waste and of pollution. Similarly in the rural areas, the use of fertilizer and pesticide grows and (particularly for example, in the increased acreage of paddy fields), leaches into the river systems and groundwater supplies, often causing modifications in the ecosystem as it is concentrated in food chains, or leading to contamination and problems of water quality. This switch from a rural to an urban dominated society, and the accompanying loss of wisdom concerning sustainable practices of land use has been assisted and encouraged by ‘development projects’. Pressure has been exerted on the local populations in developing nations to increase their productivity, by switching their farming to monocultures of cash crops, often totally unsuited to the soil type and water resources, and this has already led to considerable levels of soil degradation and erosion. But erosion of soils spells the irreversible destruction of biological potential and life sustaining capacity in a region, and therefore constitutes perhaps the most serious crime possible against a people.

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The goal of sustainable development therefore requires different policies, actions and choices from that of short term profit optimization. In order to achieve this change in behaviour therefore, a system such as the one that we have developed here is required in order to consider as a whole the ecological and environmental effects of possible economic development. In this way, the kind of ‘development’ that leads to the overexploitation of soils, water resources, forests, fish stocks and indeed of humans can be displayed, and either rejected, or modified so as to reduce or reverse some of the adverse effects. That is one of the aims of this project. By showing the effects of the linkages between the different factors of the system, then it enables decisions to be made with knowledge concerning the complex consequences that may ensue. Within the loops of the complex system that is Sénégal there are real conflicts of interest and possible symbioses between different kinds of agriculture, industry, tourism (particularly eco-tourism), and the needs of the population. Industry may be necessary to manufacture tools and implements, but it certainly will not attract tourists to those areas. Similarly, the growth of agriculture may be at the expense of the natural vegetation and landscape, and hence be directly opposed to the needs of ecotourism, while a local increase in population may lead to deforestation as a result of the need for firewood. Desertification, although due in part to large scale climatic shifts, can be considerably accelerated or arrested according to the decisions and actions of the local population. The planting of unsuitable and unsustainable crops for a rapid but short-lived profit, the over cutting of forest, or the over grazing of soils all play a large part in the creation of situations leading to irreversible erosion. While Geographical Information Systems can provide information concerning the possible location of ‘high risk zones’, the view they have is both static and based on purely physical data. The model which we have developed can consider the dynamic stability of the patterns of land-use, and also the human decision making that drives these changing patterns. One of the great difficulties that faces attempts to establish policies which may aim for a sustainable development is the problem of bridging the gap between the political and administrative agents on the one hand, and scientists on the other. The perceptions and motivations of the two groups are quite different, and it is very important that scientific advice should be made understandable and clear for decision makers. But for the latter to really appreciate and weigh correctly the advice that they are getting, it is necessary that they should be able to interact with the science in a very simple, transparent way. And not only that, the advice coming from the different areas of expertise—economics, agronomy, ecology, social science etc. should fit into an integrated picture which enables the composite, integrated effects to be clearly pictured by the decision makers. This is the use of the system that we have developed. With it, the opinions and knowledge of each kind of expert can be used to adjust the parameters and assumptions of each part of the model, and then it can be run forward to show how the separate domains affect each other, and what the outcome might really be. Not only that, but the user, or panel of users representing the interested parties in the development of a region, might interrogate the system and decide whether they agree with the assumptions and mechanisms that the model is built upon. They may decide how these should be modified, or whether there are important mechanisms missing.

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Through this process of exploration and testing, users will both improve the model, and improve their understanding of both the real system, and the model that is supposed to represent it. This learning process may perhaps be the most valuable part of the whole enterprise, since it can genuinely build mutual understanding and consensus between the actors. However, it may also point out and make clear some of the conflicts of interest that are present in the system, but which had remained hidden. Equally well, however, it may show areas of potential mutual opportunity, where a combined action on the part of several different actors in the region may be able to produce a far greater result than their separate evaluations would have supposed. An example of this might be the need to link projected economic development with simultaneous improvements of transportation, supplies of utilities, training for the local population, and tertiary services to the population. The framework developed here would not only serve to show where this would be appropriate, but could also serve as a basis on which real plans and schedules could be prepared. Ultimately, our system will serve as a step towards a geographical information system which serves as the input and output interface for a dynamic spatial model such as ours. Such a system would allow information to be retrieved and used concerning the spatial locations and distributions of different factors. However, it would then be possible to run the system forward into the future and explore the changes in these patterns that may occur. Instead of invoking relatively simple methods of ‘overlays’ of different factors, we would have the very complex and sophisticated spatial, dynamical models that we have described here. These provide an understanding of the reasons underlying the patterns of vegetation, crops, urban development etc. and therefore contain the reasons why these may lead to a change in these patterns. For example, it would be able to show the geographic locations in which critical thresholds, involving multiple factors, might be exceeded. Not only that, but the spatial ‘knock-on’ effects would then appear. In summary then, we believe that this integrated system provides a useful basis for exploring the probable impacts of different aspects of policy and planning. It links the economic development of each region to that of the others, to the natural system, raw materials and the environment, as well as to the social and demographic factors of the human population. It offers a conceptual framework for both understanding and reflecting upon the goals and values that are appropriate and relevant for Sénégal. In addition, and perhaps most importantly, the framework developed is completely generic, and can be transferred to a considerable extent to describe many other region or nation. The values of the parameters may differ, and the variables may require different disaggregations, but the integrity of the interaction scheme linking the different factors remains. These are based on the fundamental processes of biological growth, of human effort producing some valued output, and of the processes of exchange of the fruits of production. This, coupled with the dynamics of the natural system, the use of information by people to adapt and change their behaviour as they pursue their particular goals produces the integrated system described above. The very simple and easy to use interface allows decision makers to anticipate how such a system may respond to a possible action or policy. Instead of ‘learning by doing’, and more usually ‘learning what not to do’ by doing, we have a chance to ‘learn’ by simulation, and to improve our simulations through our learning.

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The linkage between development economics and these new ideas has been explored by Norman Clark in a series of books and papers over recent years. Firstly, together with Calestous Juma the whole question of how economics looks at the long term was addressed in ‘Long Run Economics’. They pointed out the inadequacies of the traditional economic approach, and pointed the way to evolutionary thinking. This has been further developed and described in various recent publications. (Allen, Clark and Perez, 1993; and Clark, Perez and Allen, 1995).

INTRA-URBAN EVOLUTION

8. A SIMPLE MODEL OF INTRA-URBAN EVOLUTION In this chapter, we look at the problem of modelling changes in the patterns of employment and residence at the scale below that of the previous chapters—that of within cities and towns. We also begin to discuss the issue of modelling more explicitly the decision making process of the individuals within a system. Instead of simply adopting an ‘ecological’ description such as that of Chapters 2 to 4, with a ‘crowding’ term acting on a population within a zone, we develop an ‘intra-urban’ version of the actors decision making models used in the model of Belgium. Again, in the terms laid out in Chapter 1 the models concern self-organization rather than evolution because the model generates the changing spatial patterns of employment and residents of different kinds, but the classification itself does not change over time. The model generates changing spatial structure, but not changing structures of variables, nor the possibility that actors involved may change their goals and preferences. The initial aim is not to describe a completely realistic model in microscopic detail, but rather to set out the basic framework, a matchstick drawing as it were, of the ‘workings’ of a city, in the hope of being able to explore the long-term evolution, involving structural changes. In other words, the aim is to be able to build a model which, at least, can predict the sort of structure that may evolve under a certain scenario, with the accent on the qualitative features of that structure, rather than on quantitative accuracy. We shall deal later with the need to couple this rather macro-scale model to a hierarchy, in which the very local details relevant to planning and architecture can be embedded correctly, and within which the external conditions of the region or nation can be applied. As demonstrated in our previous models, the first step in the building of an intraurban model is to identify the significant actors of the system, whose decisions, and their repercussions, will underlie the changes in spatial structure of the system. This choice is related to the problems that which to be examined using the model, and so if the main focus of interest is in the interaction between urban form and transportation and communication flows, then we may choose perhaps not to disaggregate populations into detailed age cohorts, for example, but instead to choose to represent different types of economic activity and their associated flows, as well as different types of household, as it reflects on car ownership, and type of neighbourhood sought. Clearly, in these models once the choice of variables is made, then structure can only be analysed in these terms, although, clearly, the values and patterns of many ‘dependent’ variables may be inferred from these. No new variables can emerge, only new configurations of existing ones. That is the difference between self-organizing and evolutionary models. Also, the ‘perceptions’ of the decision makers that are modelled cannot change qualitatively the

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attributes which affect their choices. In this way, learning of a significant kind is not present in the model, but nevertheless, as the spatial structure changes, new spatial behaviours can emerge, as the existing preferences of actors respond to new patterns of opportunity or threat. Another important point which we have not yet considered is that of ‘reflexivity’ (Soros, 1984). In an evolving system, the ‘pay-offs’ that characterize each choice will change in time, and this evolution will be predicted by the decision-maker according to the ‘system model’ they are using. It is somewhat disquieting to realize that the model we are going to build will contain the behaviour of actors, which will depend in turn on the models available to them, which may include this one. That is why the aim of these models is not that of predicting the future. It is to help understand the past and the present and the mechanisms that underlie them, and to explore possible futures so that they can be discussed, and evaluated more clearly. The initial use of such models would be to help set the agendas of the different actors: what would be a good or bad thing, and for whom? From that, strategic evaluations might be made, and eventually precise plans could be formulated. The real assumption with any model is that the behaviour of the components can be parametrized under all conditions likely to occur during the running of the model. This implies some degree of ‘rationality’ on the part of actors responding to their perceived local circumstances. However, we should not underestimate or forget the fact that most people do not really know what might happen, and as a consequence tend to follow what others do, or to speculate on what they might do. The models that we shall build will allow for the exploration of such effects. This may well be important in noting the difference between equilibrium models that assume that ‘the system’ gets somehow to the equilibrium distribution without asking about its path. Once imitation or speculation are accepted as being part of the behaviour of actors, then the path becomes most important, and as we know from real life, the situation and spatial patterns that emerge can be significantly marked by ‘irrational’ speculations and fashions along the way. This will discussed more in the final section of the book. Let us next consider a simple urban model, where we want to model the structural changes that will occur as it grows from an initial small town. 8.1 A SIMPLE URBAN MODEL Now let us turn to the construction of a simple dynamic model of urban evolution. In agreement with much previous work, particularly, for example, the philosophy of a Lowry-type model, we first include the basic sector of employment for the city, and, in particular, two radically different components of this; the industrial base and the business and financial employment. Then we consider the demand for services, and therefore the service employment, generated by the population of the city and by the basic sectors. We shall suppose that there are two levels: frequently required, short-range services and more specialized, rarer long-range set. The residents of the city, depending on their type of employment, will exhibit a range of socio-economic behaviour, and for this we have supposed two populations corresponding essentially to ‘blue’ and ‘white’ collar workers. The next phase of the modelling is to attempt to construct the interaction mechanisms of these variables, which in essence requires a knowledge of the values and preferences

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of the different types of actors represented by the variables, and, of course, how these values conflict and reinforce each other as the system evolves. (Allen, 1983a) In Figure 8.1 we see the basic interaction scheme for the six types of population which we have supposed are most important in the evolution of the city. From this, using the assumption that the probability per unit time of an individual actor making a particular choice is proportional to

From this, we can construct our kinetic equations based on the fractions of each population that will make a particular choice. So, the number of people of socioeconomic group k, working in sectors m at j, that would like to reside at i is given by:

and hence an equation of change of the residential population at i, xi,

which expresses how the number of residents of socio-economic group k, at the point i, xik, change in time by the residential decisions of the sum of all those employed in the different possible sectors m, whose jobs are located at j. Thus, Aijk is the attractivity of residence at i as viewed by someone of socio-economic group k, employed in sector m at the point j. The equation describes the growth of xi up to the level at which the fraction of people attracted there is exactly equal to its fractional or relative attractivity. Of course, Aijk is a term which reflects the values of the population of type k, perhaps concerning travel cost in time and money, the quality of the neighbourhood and its composition, as well as the price of land and housing, and the availability of housing there. In fact, the simple functional form we have supposed for this attractivity, considers basically three dimensions of values, for different possible locational choices. Firstly, we have the effect of distance from the place of employment, which can be further broken down to allow the consideration of different factors such as time of travel, cost, comfort, etc. In the initial simulations of this chapter, however, we have simply assumed an expression of the type e−bdij The second factor we have allowed for is the effect of crowding, which, of course, may be analyzed in terms of price, of the type of building of noise, etc., and whose effect will vary depending on the particular mix of residents and commercial activities present, since some uses require greater areas than others, and some actors are less sensitive than others to high prices. The functional form used here is

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Figure 8.1 The interaction scheme of our simple city system. Finally, we have also allowed for the attractivity of a particular point to depend on its natural beauty, and also on the character of the residential population already present. This would allow for the possibility that, for example, people from the upper socioeconomic group prefer to live in an area where their own group is already present. (It is the mathematical expression of ‘a nice area’.) Putting all these factors together, we find the expression

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which we have supposed to express the value structure of the different types of resident, k, and also how this system of values ‘reacts’ to changing possibilities. We have written down similar equations for the other actors, which in brief express, for example, the need for industrial employment to be located at a point with good access to the outside, and for a very large area per job, as well as some 85 percent of their workforce being taken to be in the lower socio-economic group. We have also added the fact that the interdependence of many industrial activities leads to a preference for locations adjacent to established industrial locations. This term also covers many subtle effects of the infrastructure that grows around existing situations. The main effects are all noted in the interaction scheme of Figure 8.1, and the full equations are given in the appendix II, and so here we shall simply proceed to discuss the evolution of our simple city system. 8.2 SOME SIMULATION RESULTS In this section we shall briefly describe some of the simulations that we have made using our simple model. In the first case, we have looked at the evolution of a centre which initially is only a small town, but throughout the simulation, due to population growth and expanding external demand from the industrial and financial sectors the town grows, spreading and sprawling in space as it does, and also developing an internal structure. The initial condition of the simulation is shown in Figure 8.2, and the particular values of the parameters which we have used as given in Appendix II. After ten units of time, the situation has evolved to that shown in Figure 8.3, where already, an internal structure has appeared. Industry, commercial and financial employment are all still located at the centre, but now we observe residential decentralization, particularly on the part of the upper socioeconomic group. The centre is very densely occupied and is strongly ‘blue collar’. In Figure 8.3, after 10 units of time, residential decentralization is already well developed, particularly for white collar workers who display an exponentially decreasing density distribution, with a crater at the centre. Blue collar residents have a shorter range exponential, reflecting lower mobility. In terms of employment, the structure is still basically centralized. As the simulation proceeds, however, at around fifteen units of time, this urban structure becomes unstable. It is not a question of simply growing or shrinking: what is at issue is the qualitative nature of the structure. For, at this point in time, the very dense occupation of the centre is beginning to make industrial managers think about some new behaviour. For some of them the cost of continuing to operate in the centre, is making them contemplate the abandonment of the infrastructure and mutual dependencies that have grown up with time. At this point, as for a dissipative structure, it is the fluctuations which are going to be vital in deciding how the structure will evolve. At some point there is an initiative when some brave individual decides to take his chance and try to relocate at some point in the periphery. Where, exactly, will depend on his particular perceived need and opportunities. However, what is important is that whereas before this time such an initiative would have been ‘punished’ by being less competitive, now around t=15, the opposite is true. Once the nucleus is started, and of course, its own infrastructure begins

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to be installed, so almost all the industrial activities decentralize, and establish themselves in this new position in the periphery. In order to show the effects of chance, we had present on several points the ‘seeds’ of an industrial initiative. By passing through the instability several times with different simulations, it was found that minute differences in the relative sizes of the ‘seeds’ led to the reorganization of industry at different points. However, owing to the attractivity of the points lying along the communications axis, it was much more difficult to provoke growth of an industrial centre away from the axis. Summarizing the effect then, at around t=15, the hitherto circular symmetry of the urban system becomes unstable. At this

Figure 8.2 The initial urban structure condition. A small town, unstructured

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as yet, and lying on a line of communication, begins to grow. point, many different initiatives could succeed in carrying the system off to different new states of organization and different possible futures. However, those which succeed with the least effort are the industrial nuclei in the periphery, lying along the communication axis. In Figure 8.4 at t=20, we see the new structure. From this point on, however, the locational decisions of the ‘blue collar’ workers are particularly affected by the fact that their value systems are now based on the fact that their value systems are now based on the fact that industrial employment has relocated in the southwestern corner of the city. Thus, the spatial distribution of blue collar residents in the city starts to change, having in a sense, a new focus. This in turn, acts on the locational choices of the white collar workers, who find space easily in the regions of the city less

Figure 8.3 The urban structure after ten units of time.

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Figure 8.4 The urban structure after twenty units of time. Industrial employment is leaving the centre and relocating on the communications axis In the southwest periphery. favoured by the blue collars, and whose spatial distribution adjusts accordingly. Changes in the distribution of local service employment also then occur, and the whole structure evolves to the pattern shown in Figure 8.4 by time t=40. Here, we see that we have actually displaced the centre of gravity of the urban centre, and have an urban structure which resembles two overlapping urban centres of different character. In the southwest we have a predominantly working class, industrial satellite, while, the original city centre is a CBD and important shopping and commercial district, with predominantly white collar suburbs stretching away from it on three sides. In this part of the city, it is the second ring that has attracted the local shopping centres, while in the industrial satellite, it is the heavily populated, industrial district itself that has become an important shopping centre. During the simulation we can calculate a great deal of interesting information concerning the urban structure, and its ‘running costs’. For example, we can calculate the

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total number of jobs available in each sector and the total travel generated by commuting workers. This can be calculated separately for ‘blue’ and ‘white’ collar workers, and if necessary, can be calculated for each residential location. Similarly, from the location and size of shopping centres, together with the distribution of residences, we can calculate the total travel involved in consumer shopping trips. Clearly, the energy consumption of the urban centre is related to the sum of the total travel of commuters and shoppers, and this can therefore be calculated. What is particularly interesting here, is that the usual procedure is to simply divide the total distance travelled in the city by the population and discuss the

Figure 8.5 After forty units of time, the urban structure has changed qualitatively having developed a second focus. It has structured functionally.

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Figure 8.6 Changing trend of average commuting distances with structural reorganization. average distance travelled per inhabitant. When we look, for example, at the average distance commuting to work of ‘blue collar’ workers, we find that the trend changes when the city restructures at around t=15, as it does also for ‘white collar’ workers. This shows us the dangers involved in global modelling, for on that scale what we see is an apparently inexplicable change in behaviour, in which the distance travelled per person, and the average energy consumption per person stops rising, and even decreases. Only a model which can describe the internal restructuring of the city could have predicted such a change, and linear systems theory, and input-output flow models would have to be re-calibrated at this point. This also highlights another aspect of modelling method which is sometimes used incorrectly. The important point about say, the energy consumption of urban travel is that it results from all the travel that is taking place in the city, and hence, is an ‘observable’ which has the value it does, because the city has the distribution of residences, jobs and shops that it does. It would be quite incorrect to use this total urban travel in order to model the system, or as part of a global model, because as we have seen, changes in say, total urban population can lead, through the type of average trave requirements. In other words, relationships between global variables of complex systems are nearly always non-linear and a systems analysis which assumes linearity will only be reasonable in the short term, or in a neighbourhood of the calibration. As a final example here, let us briefly describe a series of simulations which were performed in order to investigate the impact of rising travel costs in a city. In this case we started from the same initial condition as for the previous simulation, but with a slight change in the value of parameter lp′ (a systematic examination of the effects of the various parameters is given in Allen et al (1980). At t=20, the situation is that shown in Figure 8.7; characterized by circular symmetry, with a CBD, industry and main commercial and shopping concentration in the centre, and with a ‘white collar’ residential suburbs surrounding it. At this time, we have performed two simulations starting from

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this particular state. In one case, we allowed transport costs per unit distance (costs being in time or money) to fall, and the other to rise. The first case corresponds to a policy of heavy investment in order to continue decreasing these costs in a still growing city, while in the other case, there was perhaps little investment and travel costs were allowed to rise.

Figure 8.7 Structure after twenty units of time. Possibly also, the first case corresponds to a heavy subsidy on rising fuel costs, and the second to simply passing this on to the consumer. After running the simulations for a further twenty units of time, the structures which evolved were examined. They are shown in Figures 8.8 and 8.9. We see that they differ qualitatively, in that the simulation performed under falling transport costs still retains its circular symmetry, while that performed under the scenario of rising costs has become asymmetrical, as industrial activity has decentralized and nucleated in the periphery. The transportation and energy requirements of the two urban structures are quite different. The total travel generated in the ‘low-cost’ city is approximately twice that of the ‘highcost’ city, and the average commuting distances of ‘blue collar’ workers is doubled. In other words, the reduction in travel cost per unit distance of the scenario causes a quite

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different urban structure to evolve, and this is such that blue collar workers on average must travel much further to work than in the other case. This means that although the cost per unit distance decreases, it is more than compensated by the increase in travel distance that the urban structure requires. It is interesting to note that the ‘GNP’ of the city requiring or generating greater total travel would probably be higher than that of the second city, although the actual consumption of goods and services is smaller. Again this points out the dangers of using such global indicators for complex systems, where structure and function are inextricably mixed, and where evolution and changing conditions can lead to internal reorganizations. Various other problems can be examined, such as, for example, the effects of regulation of industrial and commercial location, or of changing patterns of external access for

Figure 8.8 Evolution of structure with low transport costs after forty units of time.

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Figure 8.9 The evolution of the structure with high cost transportation.

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Figure 8.10 The evolution of the urban system as modified by the construction of a metro line. goods and raw materials, changing productivity in industrial or office employment. Similarly, a study can be made of the effect on the urban structure of the sets-up in the long-term involving modified land prices, and changing commercial and residential attractivities. Our final simulation (Figure 8.10) shows one of our preliminary simulations of the problem, where we see that apart from distorting the urban space by causing greater residential densities along its path, we can discern the beginning of two new commercial centres which are forming at each end, and by becoming employment centres themselves, they lead to further modifications of the residential location pattern. Thus, the simple decision concerning the building of a metro line sets off a whole series of events, leading to the formation of sub-centres, and a change to a polynuclear structure, although intuitively, the effect of a metro line running to the centre of town would be to reinforce and preserve the status of the latter.

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8.3 DISCUSSION The simulations which we have briefly described illustrate the self-organization of our simple urban system. They show how policy decisions concerning transportation, housing regulations, industrial location, etc., can modify the evolution of the system qualitatively, leading to new spatial patterns and to changes in the trends of macro-variables related to the whole city. An important general point that arises from such models is that a structural reorganization of the urban space leads to a corresponding reorganization of the mental maps and values of the various actors. Essentially the symmetry breaking properties of self-organization lead to a corresponding expansion of the dimensions of the actors’ value space. For example, in the example given above, while initially under circular symmetry, the variables and parameters of decisional criteria can all be expressed in terms of the scalar distance from the centre, once the symmetry is broken, the value space expands to include all the angle-dependent possibilities. Similarly, for example, when all cars were black, the question or value attached to colour was of no importance. Once the symmetry had been broken however, and cars of other colours appeared, then the new dimension is created in the value space of buyers, and finally it can become an important factor in sales. Complexity feeds on itself because it creates new situations and dimensions, which widen the experience of people and create new tastes and qualities, leading to new behaviours and to further complexity. The important point is that fluctuations around ‘normal’ behaviour in the real world, and fluctuations in the mental models of actors, both explore situations which are ‘richer’ than the reduced description of the world which is given by our model. These explorations can be amplified by the non-linearities in the system and lead to a structural evolution of the system. But, what are these non-linearities exactly? Firstly, there exist purely physical non-linearities in the workings of objects, related ultimately to energy and matter flows but also to such effects as, for example, surface area to volume ration. These lead to ‘optimal sizes’ for elements, and give rise to economies and dis-economies of scale, to division of labour, to aggregation and cooperation, pooling of resources, etc. Let us try to imagine a ‘city’ of say a million inhabitants, which has no internal structure. Each small locality contains small units of each type of industry, of all types of shops and services. In such a city there are no ‘head offices’ or central depots because such things already arise because of the spatial selforganization processes of the type I am attempting to imagine absent. Amid all this, we find at each point the same mix of blue collar and white collar residences. Clearly, such a vision is impossible n reality, because there exist real advantages in the functioning of certain size units of each type (due to analogous questions of internal organization), which means that they obey non-linear laws, Thus, any small fluctuations away from total uniformity will be amplified by the advantages perceived by at least some of the actors. Herein lies the other very strong source of non-linearity in human systems. It is the functional form of the ‘attractivities’ derived from a model of preferences which leads to dramatic non-linearities, because the different factors which appear are connected to each other through the mechanisms of the system. In the simplest case, for example, people attract shops, since the market available depends on local population, but shops

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attract people because local services are part of the amenity level of the neighbourhood. The changing patterns of population and of different kinds of economic activities interact with each other through the different terms in the preferences of the different types of actor. If information is readily available, I is large and even a small change in the advantage offered by a particular choice i can result perhaps in a large change in the population’s behaviour. Thus, it is the human capacity to ‘treat’ information and to choose his behaviour which is at the root of much strong non-linearity. However, even in a system with rather poor information concerning the ‘true’ advantages and disadvantages of different behaviour, which I believe is our situation, people’s behaviour is largely determined by repeating previous actions which were not calamitous, and when a change is thought desirable, by imitating others. This imitation introduces a strong element of non-linearity into the problem. Equally true, of course, is the fact that it is the perceived situations that affects what happens, and therefore the manipulation or misinterpretation of information can lead to a different evolution of the system. Inherent to any such system is for example the existence of speculation since one simple rule for behaviour when not sure of the future, is to simply follow the trend and do what others do. But this can have a significant effect on the evolution, and can result in a considerable impact on the allocation of investment. However, in the mutual interdependence of the decisions of different actors, this is fairly normal. We do not have some kind of fixed, objective ‘comparative advantages’ which mean that the choices derived from the preferences of the different actors can only lead to a single unique spatial configuration. Instead, these preferences are interdependent, and indeed when linked to possible functional advantages, may not be very clear to the individuals concerned. What we must face is that almost all of our everyday actions are not the expression of an absolute rationality, but result from the dynamic dialogue between ‘system’ and ‘values’, between ‘supply’ and ‘demand’, during which particular bifurcations have occurred. Their ‘rationality’ is simply conferred on them by the society in which they are thought normal, where they evolved, and they can, and will, change. The problem of policy-making in a world with changing values is indeed a fundamental one. Summarizing the main points made above, then, a preliminary urban model has been developed which shows how the different types of actor in the system interact in a continual dialogue in time and space to generate structure and form. There are business districts, shopping areas, rich and poor districts and industrial satellites. The degree to which the structure responds to the needs of the different actors varies, and offers different overall and individual levels of satisfaction. Our model begins to show us the real difficulties of living in an interdependent society. The evolution of any neighbourhood town or city can never be disassociated from that of the surrounding regions or the included elements, and the decisions policies and plans executed in any sub-unit of the whole will influence the evolution of all the other parts of the system. What liberty should therefore be accorded to the individual, the local community, the region or the nation? At what level should policy decisions be evaluated, and whose money should be used to implement those decisions? Such questions lie at the root of much political debate, but of course there are not necessarily clear cut answers to these questions. But, after all, why should there be? Complex systems structure over time as a

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result of the dialogue between the macrostructure and the individual explorations around this, based on subjective, personal goals and information, and probably neither able nor willing to consider the ‘overall’ good. As in the regional and national models of the previous chapters this one is characterized by a self-surpassing evolution resulting from this dialogue between that individual diversity and average behaviour. It concerns a ‘dynamic interplay’ between three levels of the system: the properties of matter and the physical resources of the system, the entities of organization and their roles (which constitutes the type of actors making up the system), and finally, the perceptions, beliefs and values of these actors as they reflect and act on the changing world around them. Most importantly, we see that this throws some light on the extraordinary idea that ‘free markets’ will operate as if there was an ‘invisible hand’ guiding the evolution towards the optimal, equilibrium state. This notion, if true, would limit the need for ‘planners’ or ‘governments’ to that of alleviating marginal areas of socially unacceptable hardship, while events moved inevitably towards the ‘best’ (in the circumstances) solution. We see that this apparently ‘free system’ can evolve to many different possible structures, and that each of them will offer different cocktails of good and bad attributes. In turn these attributes will be perceived by the city’s inhabitants according to their own individual locations and experiences, thus making the idea of ‘optimal’ itself extremely difficult to define. But this is a tenacious idea. Even if many of us disavow such a view consciously, nevertheless we often feel that the ‘survival of the fittest’ at each local level of the system must lead to a super-fit system, but this is a very strong assumption. The fact is that although individuals may have some idea of the short term implications of their actions, as these models show they do not in general understand the longer term, collective aspects, indeed that is the whole point of these models. Because of this, it is simply naïve to suppose that whatever happens will be optimal, or more often would have been optimal but for the ‘inefficiencies’ in the system. Our new perspective tells us that there really is a choice of futures, and that these possible futures are of different ‘optimalities’, some being more efficient from certain points of view than others. Once we understand and accept this, then clearly, we realize that we need some kind of tool, such as our model, in order to identify the real choices open to us, some discussion concerning the relative advantages of different possible future paths, and if one is thought more desirable than the others the means to guide the system in that direction.

9. TOWARDS REALITY—BRUSSAVILLE 9.1 AN IMPROVED MODEL In this chapter the preliminary urban model is developed further. In particular, industry is divided into two different sectors: a heavy exporting sector as before, and also a local industry which served both local residents and also the heavy industry. The model is not really different in nature from the earlier version, but it is now inspired by data coming from Brussels, and so comes much closer to really describing reality. The characteristic feature of human systems is of course that of the complex interaction of human actors with their environment and with each other. An important point of our approach is that we attempt to represent the decision process of the interacting actors, taking into account

Figure 9.1 The scheme of interaction for an intraurban evolution.

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their limited perceptions, and particular value systems of each type. To do this we construct the ‘value space’ for each type of actor from the various dimensions which they can discern of the attributes of the various choices. The dimensions retained by various types of actor are of course ‘role dependent’, and are the result of how they have been led to believe people in their positions should act. The essential first step is to decide how many types of urban actor it is necessary to consider, and this depends in turn on the types of question which it is hoped to address, and on the intuition of the modeller as to the ‘important’ variables of the system. The model presented here deals with the spatial interaction of seven types of actor. The interaction scheme is shown in Figure 9.1. (Allen, 1983b) There are five types of employer: industrial, financial, two levels of tertiary activity, and local industry. Each of these has its own locational criteria involving land and their infrastructural requirements, as well as differing types of access to road, rail, canal or to air communication. They also have differing labour requirements both in terms of the number of jobs created per square metre and in the socio-economic group of employees. Thus, heavy industry requires overwhelmingly blue-collar labour, whereas the financial and business firms of the central business district employ almost entirely white-collar citizens. We have therefore chosen to distinguish between these two types of resident, and these together with the five types of employer form our ‘mechanics’ of seven mutually interacting variables. Details of the types of intraurban structure that can evolve have been given already and so here we shall simply present a typical evolution but also present some results concerning the spatial structure of the tertiary functions, the shopping centres, and their evolution within the urban tissue. In Figure 9.2 we see the initial condition used for the simulations. It is already the result of an earlier simulation from a smaller centre. We have: (a) Industrial employment lies along a transportation axis suitable for heavy goods; (b) employment in local industry is located near heavy industry and also near the residential population; (c) financial and business employment are all concentrated in the centre of the city, we have a central business district (CBD); (d) low-level tertiary employment is simply a reflection of the population distribution; (e) high-level tertiary employment is also concentrated in the city centre; we have a single shopping district located in the centre; (f) blue-collar residents are mainly concentrated in the centre of the city; (g) white-collar residents, whose employment is located in the CBD and the tertiary activities are spread throughout the city. The situation at t=900 is shown in Figure 9.3. Employment in Industry, (a)(b) heavy and local industry concentrates in a single massive complex; (c) finance and business remain concentrated in the central business district (CBD) (d) low-level tertiary employment has spatial structure and reflects both the total population distribution and competition for land with, that same population; (e) high-level tertiary employment located at and around the centre (f) blue-collar residents are concentrated largely along the transportation axis, but now the highest density is neither at the city centre, nor at the pole of industrial employment, but is in between. (g) White-collar residents are still much more evenly spread through the city with a ‘crater’ around the industrial area, and peak density off centre. This structure arises through several spatial instabilities, leading to the

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creation of a functional structure where certain activities are concentrated in certain areas, and where residential segregation has also developed.

Figure 9.2 These are the initial conditions for the simulations. Clearly, such a model enables us to study the effects of introducing some new transportation link, or the effects of changing energy or fuel costs on the urban structure as the decisions of employers and of residents concerning their locational choices interact with each other, causing complex, cumulative changes to occur which go beyond the intuition of any single actor. To look closer at this equation of ‘anticipation’ or ‘intuition’ and its interaction with ‘rationality’ let us look at the tertiary sector in a city which is still growing, and see the effects of different strategies of investment in this sector. First of all, we have an evolution of the spatial distribution of tertiary activity if the only fluctuations in density of population and in number of tertiary jobs are very small. Thus, in terms of a pure ‘rationality’, calculated using a simple extrapolation of the observed profits being made

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at each moment, the place to invest in, for the tertiary activity is the centre of the city. The mechanics of our system tells us this, because the growth of tertiary activity occurs there, and this is therefore the ‘most attractive’ investment. Other points of potential investment do not grow ‘naturally’. This is shown in Figure 9.4.

Figure 9.3 The situation after 900 time units. A complex spatial structure has emerged.

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9.2 INTERVENING IN DEVELOPMENT However, there are two ways in which more exciting things can happen. Either we put less rationality in the system by increasing the size of ‘random fluctuations’ of investment and population, or we could imagine an actor, not described by the ‘mechanics’ of the model, who can perhaps anticipate, imagine intuitively, some different structure for the system and place his investment so as to produce this new state. This is shown for example in Figure 9.5(a) where four simultaneous investments are made in ‘shopping

Figure 9.4 In the absence of any intervention this is the type of highlevel tertiary structure that evolves (a) t=0, (b) t=500, (c) t=900. centres’ out in the ‘second ring’ of the city. Subsequent events show, in Figures 9.5(b) and 9.5(c), that this investment was very shrewd, because the centres attract more and more business, even killing off the original shopping centre at the centre of the city. Of course, if it had failed, the actor would have been considered ‘stupid’, and people would have felt a certain satisfaction in seeing that someone behaving abnormally, not

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Figure 9.5 If we intervene in the tertiary sector at the initial time with four suburban centres, we find an evolution of the type shown here (a) t=0, (b) t=500, (c) t=900. to say irrationally, was punished for his sins. However, in the case that we took, the investment succeeded, the actor was therefore ‘clever’ in guessing the threshold required, and in any case the urban structure is irreversibly marked by this action, which is nevertheless a small one compared with the scale of its consequences. However, if we study the effect of attempting to introduce the four centres successively, instead of simultaneously, then, as Figure 9.6 shows us, after the successful launching of the first suburban centre, the attempt to launch the second suburban centre fails and the investment that sufficed before is unable to survive. However, launching the second centre appears to modify the distribution of tertiary employment, even though the second centre itself fails. The urban evolution is quite different depending on whether the initiative is taken simultaneously, or successively. The fact that launching four suburban centres, early or late, gave rise to a structure in which all four survived still leaves some question as to the ‘spontaneous’ formation of a hierarchy of shopping centres. To examine the question of whether there is some ‘natural separation’ of shopping centres, we can perform the following experiment.

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Figure 9.6 Launching 4 centres at the same locations as for 9.5, but at successively and not simultaneously, lead to a totally different result. Suppose that at the initial moment all twelve locations of the second ring are given a dose of tertiary investment. What will happen? The resulting evolution is shown in Figure 9.7, where as we see, small differences in initial height and of accessibility on the transportation network, lead to the breakup of the ring of shopping centres into five large centres spaced out approximately every other point on the second suburban ring. Thus five centres are roughly all that this ring can support, and it ‘explains’ why when we launched four simultaneously they all survived. If we tried six or seven then probably some would be eliminated. However, as one of our experiments showed, if we launch our investments successively then an asymmetrical structure can develop which is stable except to very large interventions. This suggests that in reality, since in general investments will not be simultaneous, that development and growth may very often be inherently asymmetrical. It may well require considerable ingenuity on the part of modellers in order to find the ‘correct’ level of aggregation in order to succeed in finding simple forms. Another point

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is that the spatial mechanisms of clustering that characterise different types of economic activity and residential neighbourhoods, are of differing spatial scales. This means that ‘asymmetricalities’ of many different spatial scales will occur naturally as a result of the non-synchronous behaviour of individual actors. Apparent simplicity of pattern in the spatial data will then require appropriate aggregations to be made, and we begin to see the non-linear causal mechanisms that may underlie the kind of fractal patterns that are demonstrated in urban data by Batty and Longley (1995). Clearly, we are a long way from the elegant discussion of ‘urban economics’ of a few years ago, when for example, radial utility functions of actors which were independent of angle, in this way inadvertently excluding ‘angle dependent’ solutions that might maximise ‘utility’. Not only was a polycentric city excluded, but so was a city with wedges of characteristic structure. Similarly, calculations which are made using the maximization of ‘entropy’ as a methodological pillar, will also tend always to produce and discuss the most symmetrical structures and traffic flows under the circumstances, and will not explore possible asymmetries that might emerge over time.

Figure 9.7 All 12 points of the inner ring are seeded with shopping centres, but only 5 survive. 9.3 DISCUSSION Summarizing the points raised by this chapter we see that on the whole the ideas expressed here recognize still further limits on our ‘predicting’ and ‘controlling’ the world we live in. First, there is the unpredictability related to bifurcation phenomena, and second, there is the need to take into account the internal structures ‘accumulated’ in a system by its previous history. The system is partly a memory of its past, just as in our origami example the ‘essence’ of a bird or a horse lies both in the nature and in the order of the folds.

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At the heart of all these interesting phenomena lies the fact of nonlinearity and of aggregation. The different levels of description corresponding to the aggregation of individuals within a zone, for example, mean that fluctuations are inevitable, and unpredictable. Their existence, combined with the nonlinearities in the mechanisms of interaction lead through bifurcations, spatial instabilities, to the formation of structure, and the breaking of previous symmetries. The particular scale of the zones chosen for the model will select the kind of spatial organization that will be observable at that scale, so that for example the ubiquitous retail space may be simply proportional to the population/ income of a zone in our model above, but manufacturing and financial activities may be very much clustered in one single zone. However, ubiquitous retailing although fairly uniform (per head of the population) between zones, will in fact be clustered in shopping centres of various sizes within each zone. If a smaller scale of zone had been chosen, then the spatial organization of ubiquitous retail would have been evident. Similarly, our model of Belgium in terms of Provinces shows considerable similarities in the employment per head in different sectors, but nevertheless reveals some pattern of specialization in the agricultural, industrial and financial sectors. So, our choice of spatial disaggregation ‘decides’ which clustering mechanisms the model will be able to ‘understand’. Because of this, it will be important in the next chapter to discuss the coupling of multi-scale models in a hierarchy, so that the different scales of structure can be correctly dealt with. In modelling such systems as stressed in the first chapter, the classification scheme used to choose the variables is a very important consideration. When the spatial structure changes qualitatively, when a bifurcation occurs, there may well be emergent attributes that make the original classification scheme inadequate, and in turn invalidate the existing variables as successful descriptors of system behaviour. Here we find a link with cognition and language itself. If something has been given a name, then enough of its characteristic structure must be known to differentiate it from other objects. However, objects within which bifurcation can occur, have a hidden, inner space which allows a further differentiation in the future. Thus, the difficulty of modelling is to be able to anticipate such an instability and to be prepared for it to occur. In the urban and regional models discussed here we study the occurrence of spatial instabilities, and show how these may affect the behaviour and response of the whole system. This is considerably better than the alternative, more usual method, which is to ‘recalibrate’ a global model (which ignores spatial structure) when it is found to be necessary. However, we have to admit that as well as spatial structure, and its attributes, there will be other dimensions of behaviour and attributes of the system which could change, since cultural and social innovations can occur just as much as technological ones. In the models presented here we cannot anticipate such changes and would also have to ‘re-calibrate’ our parameters after the event. This brings us to another fundamental point concerning the fact that the occurrence of spatial instabilities in our models constitutes an adaptive response to growth or changing external parameters. It results from the dialogue between ‘fluctuations’—non-average behaviours, and the existing average spatial structure. In the model this may be represented by a stochastic process, using the computer’s random number generator for example. But, in reality, fluctuations may result from the diversity of individuals present, each with differing views and understanding of the possible consequences of their

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actions. Obviously, real change will only occur in situations which turn out to be unstable to a particular fluctuation, and so the system structure acts like a ‘selection mechanism’, responding to certain fluctuations but not others. The question then arises as to the intentionality and intelligence of such a system. Clearly, a system with microdiversity of individuals will have more potentially de-stabilizing fluctuations occurring at any time, and so will adapt and change more rapidly. In this way, intelligence would reside in the diversity of individuals, each of which may be relatively ignorant of the real consequences that might follow his actions. However, another possibility is that an actor might understand the system well enough to anticipate a potential instability of the structure, and anticipate another state of the system, in which what is presently ‘abnormal’ will be considered ‘normal’. The possibility of ‘imagining’ another branch of solution—an origami ‘horse’ instead of a ‘bird’—would require the actor to have a cognitive model something like our ‘self-organizing’ models, but once again, the imagination required to see a new structure would still require fluctuations in the mental model. One way or another, it seems, the source of creative intelligence is ‘noise’, which enables a system to break out of a pre-existing ‘logic’ and find a new one. In practical terms this work was actually applied to several French cities by Pumain, Sanders and Saint-Julien (1989). They used data from Rouen, Bordeaux, Nantes and Strasbourg, and explored the problem of the calibration of a model of this kind. The careful study showed that the model was able to reproduce much of what had actually occured, and that the parameters leading to a good fit were completely understandable and coherent. Their work substaniated the fundamental hypothesis that the qualitative evolution of urban centres can be understood on the basis of very general mechanisms. However, their work showed the need to embed any such urban model within a spatial hierarchy, so that on the one hand, macro decisions and the comparative advantages of the site could be better understood, and on the other, that the effects of the particularities of the terrain, and of individual neighbourhoods and local history could be incorporated. As a result, since this study their work has been focussed on the development of hierarchical models of city systems (Sanders, 1984, 1990; Pumain, 1991; Sanders, 1992).

10. A TOWN LIKE BRUSSELS 10.1 FURTHER IMPROVEMENTS In this chapter, the intra-urban model developed in the previous chapters is made more like the case of Brussels. In particular, all the perceived ‘distances’ and decisions concerning residential location, shopping destinations etc. are all made along transportation networks, which were based on those that are present in Brussels. What we were trying to achieve was to see whether the qualitative evolution of Brussels could be understood and ‘recaptured’ by our model. If this was possible, then it implied that the model contained the ‘reasons’ why the structure of Brussels was as it was, and therefore perhaps the limits to the stability of this structure. In which case it would also contain an idea of alternative future structures that might evolve under different possible policies, investment decisions and changing scenarios of in and out migration. The point here is of course, that whatever the shortcomings of our application, nevertheless, the other ‘operational’ methods used for decision making concerning transportation, land-use planning etc. simply do not address the real dynamic impacts at all. It seems better to explore the effects of causal linkages on the medium and long term evolution of the system even if this is done in a fairly simple way, than to use methods which ignore the whole issue completely, but give an appearance of great precision as a result of their high degree of ‘disaggregation’. In other words, the traffic models used in transportation decisions today still give no indication at all as to the effects that they will have on locational decisions and hence on urban structure, nor the effects that this will have in turn on the generation of traffic. This is the reason, for example, for the failure to anticipate the effect of building the M25 around London. As explained before our basic set of urban mechanisms is represented by a set of nonlinear differential equations each of which describes the time evolution of the number of jobs or residents of a particular type at a given point. In a homogeneous space one possible solution of these equations would be to have an equal distribution of all variables on all points. Such a non-city, although theoretically possible, corresponds to an unstable solution, and any fluctuations by actors around this solution will result in a higher payoff, and this will drive the system to some structural distribution of actors, with varying amounts of concentration and decentralization. However, in reality, there are two reasons for the structure of the system: the first is due to the nonlinear interaction mechanisms which give rise to instabilities as mentioned above. The second is due to the spatial heterogeneity of the terrain and of the transportation networks.

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10.2 TRANSPORTATION NETWORKS The model presented in the previous chapter, with interaction scheme Figure 9.1 is now modified by the addition of transportation networks. In particular, we have supposed that linking the different zones will be private and public networks. One is a road network for private transportation taking into account three different qualities of road and the other is a set of four public transport networks, corresponding to the networks of the train, bus, metro and tram. Each link of each network depends on the relative sensitivity of an actor to these. We have therefore a dynamic land use-transportation model which permits the multiple repercussions involved in the various decisions concerning land use or transportation to be explored as the effects are propagated, damped or amplified around our interaction scheme.

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Figure 10.1 The Private and Public transportation networks of the city. 10.3 THE EVOLUTION OF CITY STRUCTURE The interaction scheme of Figure 9.1 is now run forward from a simple, ‘pre-present day’ situation, with most things at the centre of the city. Then a period of growth is imposed

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on the system globally, and the interactions allowed to structure the spatial patterns of different kinds of employment and of residences. (Allen, 1985; Allen et al., 1984) The simulations described here have been based broadly on the evolution of a city resembling Brussels. The global characteristics of employment and population are shown in Table I and the transport networks in Figure 10.1. The spatial evolution of urban structure is shown in Figures 10.2–10.5 for successive times of the simulation. The simulation times of 0, 10, 20 and 30 are of course somewhat unreal but they are supposed to describe changes of urban structure which could occur over some 40 to 50 years. The initial condition of our simulation, which of course affects the structure which evolves is in fact taken from figures resulting from a previous simulation made earlier without a transportation network. Industry grows rapidly in the north and the south-west of the city, along the transportation axis. Light industry, after some ‘spatial indecision’ locates at around t=7 near the airport in the north-east of Brussaville. The administrative and tertiary functions, characterized by office employment after growing intensely in the very centre of the city face a potential instability at around t=7. If at that moment a seed of investment or planning had been planted in the periphery, then it would have grown rapidly. However, in fact, without any such intervention, it is the neighbourhood directly to the east of the centre that attracts these exporting tertiary jobs. This corresponds to the immense concentration of office jobs in insurance, banking, and administration that in fact are packed along the Rue de la Loi, down towards to European Commission building to the east. Shopping centres and commercial properties, grow initially in the centre of the city. However, as land prices soar, a peripheral shopping centre springs up in the north of the city, and this is rapidly followed by others, except in the south-east, where the presence of the Bois de la Cambre and the Foret de Soignes reduce residential densities. Blue collar residents concentrate in the north, the centre and the south west, while white collar residents live mainly in the east and south. As the time continues through t=20,

Table I Global Figures Generated by Model Simulation for Three Time Periods VARIABLE

t=10

t=20

t=30

Total employment

729,600

669,500

674,300

Total number of active residents

462,670

411,560

414,200

Coefficient of Employment

1.58

1.63

1.63

—Industry

25%

22%

22%

—Tertiary

75%

78%

78%

40%

33%

33%

Employment Structure:

Structure of Commuter Flows from Outside the Urban Centre —Blue Collar

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33%

238

44%

Figure 10.2 The initial spatial distributions of variables. Time=0. total industrial employment in Brussaville decreases and this jobloss falls mainly on the southern industrial pole. The asymmetric spatial distribution of shopping centres has not evolved from the previous situation. The structure does not reflect very well the

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distribution of population, but appears to be stable along this trajectory of the deterministic equations. It will be an interesting question to examine how large a scale of action will be necessary to modify this and launch a new retail centre into the ‘gap’ in the south east. We see that our urban system evolves to a complex interlocked structure of mutually dependent concentrations. We have two poles of heavy industry, and a distribution of blue collar residents reflecting this. Light industry, after remaining diffuse for some time

Figure 10.3 After 10 units of time this complex spatial structure of different economic activities and residential areas has emerged.

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concentrates in one place in the north east. Financial and business employment in the city centre, at round t=6 begins to spread through the urban space. Then, it exceeds a threshold at a point adjacent to the centre and grows dramatically there, causing the decentralized locations throughout the city to decrease. The white collar and blue collar residents spread out, many live outside the system, according to the accessibilities of the networks, and a spatial hierarchy of shopping centres appears, serving the suburban population and encouraging further urban sprawl. (Allen, Engelen and Sanglier, 1984)

Figure 10.4 Between t=10 and t=20, there has been a decline in industrial employment, and more people are commuting from outside the area.

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This completes our description of the evolution of our system according to the purely deterministic equations of our model, and starting from the particular initial conditions that we have used. In the next section we shall discuss further the problems that still make such a simulation an insufficient basis for decision making and city planning. The reality that the model is supposed to be ‘imitating’ will contain all kinds of individual and local inhomogeneities and particularities, and therefore our simulation should not run its course undisturbed by external and internal disturbances. This is the point that we shall examine in the next section.

Figure 10.5 The situation at t=30 shows us that the previous structure was stable. Total employment within

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the city has grown slightly, but the structure is unchanged. 10.4 POLICY AND DECISION EXPLORATION The ideas sketched out in our first section tell us that the deterministic equations governing the average behaviour of the elements of a complex system are in fact insufficient to determine precisely the state of the system and even its qualitative character. This is because of the existence of many possible branches of possible solution. Only the effects of factors and events not included in the differential equations break this ambiguity and decide which branch precisely the system will really be on! In this way an event of historical significance is one which is not contained in the average behaviour of the elements. Just as the events which are important in Origami are not the mechanical properties of the paper, but rather the intervention of human hands which decide, at times and places when it is possible, where and when to fold the paper. This tells us that choice really exists and that planning, policy and intervention need not be empty words used by well-meaning (hopefully) people attempting to stem inevitable tides of change. However, in order that planning and policy should be meaningful, it is necessary to have a good idea of the consequences of a plan, a policy or an intervention, as well as those of other plans, policies and interventions. We must always compare the evolution following an action with that following other actions or indeed that following inaction, and we must make the comparison in as many dimensions as possible, identifying the effects as they will be experienced subjectively by the different actors of the system. Such comparisons are possible using our approach, but of course the actual decision concerning which action or policy should be pursued is a value judgment which must be made by political decision makers on behalf of the community. The weighting accorded to different social groups, to the long or the short term, and to the degree of disparity between groups that is reasonable, are matters of political judgment. However, in the absence of a successful model, this judgment can be exercised on entirely fictitious future perspectives. Developers may depict the desperate need for some particular development, with future demand soaring, job creation, local economic revival and increasing local property values, and all this with apparently no harm, indeed positive good, for the environment. Objectors however, will paint an image of the same development in terms of increased noise and traffic and decreased residential values, the destruction of natural beauty or of an area of historical and architectural interest, or threatened ecological collapse, of future over-capacity in the area offering, therefore, only slight short term economic benefits which certainly would not offset the serious reduction in property values that must be expected. Since in a democracy political success seems to depend on not offending the side commanding the greatest number of voters, then there is a tendency for unpleasant facilities necessary for dense urban centres to be either thrust on sparse rural communities, or simply not to be installed. Of course, this is sometimes offset by the possible financial power of other interests, who may be able to offer future campaign funds etc., and therefore be very persuasive in the political game. Whatever the precise

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details of such mechanisms however, this is clearly a very poor way for society to plan and make policy. Without for a moment suggesting that disagreement and discord could ever be entirely banished from the domain of human affairs, a most unwelcome prospect, the existence of better, more successful and firmer based models could at least change the nature of the debate. Instead of presenting different, perhaps equally fictitious, views of the consequences of some development or policy, the use of the model as a focus for discussion could at least demand a better justification for particular beliefs, and could provide a means of comparing the probable outcomes of different possible actions. Our models, hopefully, may provide a step towards such a situation, enabling the consequences of policy to be explored, not just in its narrow context, but also in its wider systemic one, in which the action may set off a chain of events and repercussions throughout the system. Most disagreements concerning decisions are not about the immediate short term effects and the narrow context of construction costs, floor area, kilowatts required, immediate traffic changes etc., but instead concern the long term and wider implications of the decision. Our model is aimed at exploring these kind of ‘follow on’ effects in the wider system. Here we shall briefly illustrate different types of urban decisions which can be explored in an evolutionary context of possibly changing spatial organization and travel patterns. In the first example, we show in Figure 10.6 several possible outcomes of the creation of a new shopping centre in our theoretical city, Brussaville. In the first example, our model shows us that if we launch a new centre at the location indicated, of size 40 units, implying a total involvement of some 4000 jobs, at time t=10, then it will grow and stabilize the retail structure, preventing similar initiatives nearby from succeeding afterwards. We have assumed that prices are the same as those elsewhere, but if the developer were prepared to accept lower profits during the start up period, then the centre could be

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Figure 10.6 Impacts at t=30 of a new shopping centre launched at t=10 with an total investment in some 4000 jobs. launched with a smaller initial size. This question can of course be explored using our model. However, we see from the second part of Figure 10.6 that if the same investment of 40 units is made at the same place but at a later time, t=20, then it does not succeed, regressing to zero as a total loss. Clearly, it could be maintained at some level by lowering prices and profits, but intrinsically we see that time t=20 is less propitious than

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t=10. In the event, at t=20, an investment of 50 units (3rd part of (10.6) does in fact succeed at this point, but our model shows us that if only 40 units are available, and normal profits necessary, then it could succeed if the location of the proposed shopping centre were shifted to the point shown in the fourth part of Figure 10.6. In the second example, Figure 10.7, we show the long term impact of adding a new Metro line across the city. Blue collar workers tend to increase in the neighbourhoods at each end of the line, and white collar residents return to the central core indicating some gentrification occurrences. The model could be used to make a cost-benefit analysis of

Figure 10.7 Impacts of a New Metro Line at Time 30. On the left we see the situation without the line, and on right the situation with it.

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Figure 10.8 Impacts of improved and telecommunications and information systems between time=10 and time=30.

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different possible routes, frequencies and speeds, in order to weigh the possible long term consequences and arrive at a decision before embarking on such a major upheaval of the urban issue that such a project implies. The next example shows that if the increasing use of computer and telecommunication systems leads to a decrease in the need for business, finance and administration employment to aggregate and form the CBD, then our city could undergo a major structural revolution. In Figure 10.8 we see that a certain critical value the CBD disappears and office jobs are dispersed through and outside the city. Clearly, traffic flow patterns, residences and retail distribution will be vitally affected by this and we see some possible outcomes. Another type of effect which it is interesting to observe is that of ‘happenstance’ or natural accident. Our model could be used to explore the effect of various types of disaster on the functioning of the city, of pieces removed from the transportation system of neighbourhoods devastated by earthquake or floods, and also of course the effects of some manmade catastrophes such as the closure of some large industry on which the city depends, or of war and bombardment. One particular example of less dramatic ‘happenstance’ is shown in Figure 10.9 where an urban centre grows form exactly the same initial conditions as before, with identical locational criteria of the actors and parameter values, except that instead of the city developing with a canal-river-railway crossing it as before, we have in its place a line of hills. The only effect of this on the model is that the accessibility of these points, for the functioning of heavy industry, instead of being privileged is reduced. We see that the city that evolves, Figure 10.9, is quite a bit different form that of our reference simulation shown in Figures 10.4–10.7. Industry is dispersed throughout the

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Figure 10.9 If instead of a river, the urban space had been marked by a line of hills, this would be the outcome at t=10. urban area and with it the blue collar residents and local industry. White collar residents, instead of locating in the south-east, aggregate along the line of hills which have replaced the canal. The distances travelled to work are not the same as before, nor are the

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costs of shopping trips or the distribution of retail centres. Furthermore, not only are the spatial distributions of the variables different, but also the global quantities of industrial and tertiary activity and of blue and white collar residents are modified. In fact differences in these totals has been true for all our exploratory simulations, but here it is perhaps more striking because none of the parameters are different, only the terrain has changed. In this case the absence of an axis of good accessibility for industry lowers the attractivity of the whole city for this type of investment, and our model takes into account this change in its global performance. This underlines the fact that global quantities are not constraints on an evolution, but on the contrary are observables which are generated by the processes going on in the system. Our approach is generic in the sense that it should be contrasted with one based on the observed behaviour of a particular system. For example, a model based on this city of Figure 10.9 would suppose as part of the utility function of white collar residents that they wish to live on the hills. This means that in exploratory simulations of the future, this factor would play a role in attracting these residents. But, as we can see from our model, this is not in the preferences of the white collar population. The interaction of the locational criteria of the actors (Industrial location is sensitive to the terrain, and white collar to the presence of industrial activity) of our system can produce white collar neighbourhoods along the line of hills without any such factor appearing explicitly in the preferences for location.

Figure 10.10 Urban Origami: Different Distributions of Blue Collar Workers.

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Figure 10.11 Urban Origami: Different Distributions of Retail Employment Our simple interacting locational criteria can generate many different cities, and in this way offer us the mechanics of our system on which the circumstances and history of each city will act, generating as evolutionary tree of possibilities of qualitatively different urban structures. This is briefly illustrated in Figures 10.10 and 10.11. (Allen, 1985) These models have recently been adapted for a PL environment and further developed by Thomas Buchendorfer (1995). Hopefully this will lead on to a more systemmatic examination of their properties, and to the development of improved versions. 10.5 DISCUSSION In our models of human systems based on the concepts emerging from the study of dissipative structures in physics and chemistry, we adopt a new approach to the question of anticipating the future, and evaluating policies. We recognize the fact that evolution results from the dialogue between the deterministic equations of change expressing the average behaviour of actors, and a whole series of perturbations from outside the model, or from outside this level of description. Instead of stoehastic effects being simply minor irritations for the modeller, producing a deviation from the mean of his prediction, we see that in fact they drive the system from one state of organization to another; they are the vital force of evolutionary change. It is under the effect of stochastic fluctuations, arising in human systems from limited information, from non-rational behaviour, from unusual local circumstances, or simply

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from a desire to be different, that structural instabilities occur and new average behaviours arise. Such changes can also be precipitated by a fluctuating environment, in which case they represent system adaptation to the uncertainty and extreme possibilities of its environment. Other vital factors which a modeller may represent as a stochastic or random element in his simulations are the probabilities of external intervention in the system, by macro-actors not included in the equations of the model which describe micro-decisions. Instead of viewing a model as closed and capable of predicting the future course of events, merely reflecting a scenario of exogenous changes in a mechanical fashion, we are led to another view. Our model provides a set of dynamic relationships which can be used to explore many possible futures and alternative structures which could evolve as a result of various perturbations and shocks which it may experience. This new view of the importance of stochasticity, uncertainty and adaptation in the evolutionary process suggests that in a very broad range of contexts, long term survival may be related to the presence of stochasticity in a system. Just as in biological evolution, the existence and even the rate of genetic mutation may be itself a result of the evolution, so in social and cultural systems long term survival may depend on the presence of ‘a rational’, chaotic and original members of the social group probing the efficacity of possible other behaviour. Such a viewpoint stresses the dangers of short term, narrow optimization procedures often used to make decisions in the economic, social and political spheres. These methods, often of great apparent (computer aided) sophistication, threaten society with a programme for its own fossilization at best, or more probably with collapse. The adaptive possibilities of societies allow them to survive and to compete in the real world, and these adaptive possibilities are related to the presence of original thought and this must ultimately be based on mental models which are also capable of structural reorganization. Perhaps, in stochasticity, we see the source of man’s creative intelligence.

POLICY EXPLORATION AND DECISION SUPPORT FOR SUSTAINABLE DEVELOPMENT

11. AN INTEGRATED FRAMEWORK FOR EXPLORING SUSTAINABLE DEVELOPMENT 11.1 LINKING PHYSICAL, ECOLOGICAL AND HUMAN VARIABLES With ‘sustainability’ a fashionable word, there is a general understanding of the need to consider the long term consequences of our present urban ‘lifestyle’. This is a good thing, although it comes somewhat late in the day. The problem is though, that there is no clear view as to the meaning of ‘sustainability’, nor the manner in which it can be attained. In the UK, government interest has focussed on ‘economic’ sustainability, which is translated into attempts to encourage commercial ventures with new, cleaner technology products, and to promote energy savings, waste recycling and charging full economic costs for things. While in themselves such initiatives are probably beneficial, as regards long term sustainability of our system, it rather misses the point that it might be the market system itself that is the greatest threat, in that it forces a decision making perspective on human activities which is characterized by a priority for short term high economic returns. If we think seriously about ‘sustainability’, then it should concern the preservation of the options for future productive activities, and should involve a whole range of measures reflecting our ‘quality of life’. In other words, in order to evaluate the contribution a policy, technology or action might make to ‘sustainability’, we would require an integrated framework that could explore its overall, long term effects. For technologies, for example, it would include the implications of the production, use and disposal phases, of the products, and also the overall effects of the chain of effects such as spatial re-organization, which would be involved. The kinds of model described above clearly offer a possible basis for such an integrated framework, but in the examples described, environmental variables are only taken into account in a very simple manner, and the ‘sustainability’ in environmental terms is not addressed very clearly. In some recent research (Phaeocystis Report, 1993), however, the Belgium model of Chapter 6 was used as the socio-economic part of an integrated model that examined the whole Escaut/Scheldt river basin. The changing pattern of inputs to the river system and the groundwater was generated from the changing pattern of population, employment and land-use of an extended Belgian model which included the relevant part of Northern France. These human activities and impacts were then connected to an ecological, biochemical and physical model developed by G.Billen (1992) of the river basin, which allowed the calculation of such variables as the

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concentrations of oxygen, phosphates, nitrates, phyto and zooplankton, bacterial and organic wastes in each branch of the river as the water descended to the estuary. So, the water quality in the different branches, the eutrophication of the lower reaches, the output of phosphates and nitrates to the North Sea, and much else, could be simulated by the integrated model. In this way, possible environmental policies and regulations could be tested on the system as a whole, showing their complex consequences. For example, improved water treatment of urban outflows to the river, led to greater discharges of nitrate and phosphate to the sea, and to eutrophication, because the lower bacteria concentrations in the river were not able to de-nitrify as much of the nitrates as before. The model also allows an evaluation of the most effective actions/locations for a given investment, and explores the chain of effects that really accompany any particular environmental measure. A similar integrated model is being developed for the Rhone Basin, which is much larger geographically, and provides a good example of a natural modelling spatial hierarchy, as the system can be viewed as a single basin with average properties of its tributaries, as 11 connected sub-basins with average properties of the tributaries in each, or as 221 connected sub-basins with average properties of the tributaries within these. Such a model should therefore link the interactions of hydrology, soils, vegetation, agriculture,

Figure 11.1 The Integrated Rhone River Basin Model that links a socioeconomic spatial model with an ecological, biochemical and hydrological river model for environmental policy exploration.

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and the activities of urban and rural populations and the wastes, extractions, emissions and depositions that they produce. This should provide a basis for the long term planning of residential, commercial and industrial development, so that the water demand and supply, and the waste disposal can be considered within the framework, and long term consequences of different plans thought through. (Cecoseom EU Report, 1996) 11.2 THE ARGOLID EXAMPLE Another example of an integrated model that allows an examination of sustainable landuses, and links environmental and socio-economic variables is that of a model of agriculture in the Argolid plain of Greece (Archaeomedes Report, 1994). The on-going process of urbanization is running fast in the Mediterranean, and the coastal areas are all the scene of increasing urban populations, and of the intensification of agriculture. In an attempt to obtain rates of return on capital that are comparable with those of ‘urban’ activities, traditional farming practices are being replaced by more ‘modern’ ones, with more lucrative crops, requiring increased use of water resources through irrigation. In the case of the Argolid, the increased exploitation of the coastal aquifers has led to the salinization of the aquifers and of the land, and in recent research a dynamic model has

Figure 11.2 The Argolid Plain. Modern agriculture based on irrigation has grown, but incursion of the sea into the depleted aquifer has led to salination of the land.

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been built which successfully generates this self-destructive process which farmers have engaged upon. It is of interest because it shows how well intentioned policies at one level of the system can have a quite negative effect at another level. In the case of the Argolid, farming has gradually switched from the production of olives and cereals to the irrigated production of citrus fruits. The efforts of the European Commission’s policy to avoid the decline of rural areas was crystallised into price support policies, and it is the action of these for citrus fruits that have led the farmers to increase production. The model considers 7 spatial zones and 3 layers: the surface, the subsurface layer that may be permeable or not, and the aquifer. The flows of water through the area of study was then modelled by considering the 3-D movements of water onto and off the surface, through the subsurface layer if it is permeable, and in and out of the aquifer. The main human impact has been the decision to grow irrigated crops, and the resulting need to pump water up from wells, boreholes and from canals to maintain growth during the hot, dry summer. Otherwise, for geological times, the winter rainfall has fed the aquifers and springs, and given rise to a net positive hydrostatic pressure throughout the zone. Our model considers the chain of effects of the pumping of underground water as the area of irrigated crops has increased. The dynamic model that has been developed considers that crop choice decisions are made annually, and that this sets out the agricultural requirements for water for the next 12 months. The amount of irrigation that will be required then depends on the profile of crop needs throughout the succeeding weeks of the year, and the rainfall and the evapotranspiration that actually occurs. The model therefore uses a short time step of 3 days (one tenth of a month) to describe the movement of water and salt over and through the different zones and sections of the model. It simply uses balance equations based on water and salt accounts of each sections. Without discussing the detail of these calculations, we can simply summarize the model by saying that it allows us to model the farmers response to his circumstances: market prices and uncertainties, crop choice, and water requirements. This then allows us to model the change in surface and aquifer water, and the salt concentrations in both as sea water is drawn into the aquifers. This in turn produces a pattern of salinization, the demand from farmers for fresh water to be supplied to them by canal, from somewhere else, and finally the need to increase production and water consumption to make up for falling yields. The medium which transports the salt around the system is water. Initially, before large scale irrigation occurred, there was a gentle, positive hydraulic head throughout the system, which meant that the aquifers were pure, and that there were some marshy areas of land. There was a steady transfer of the catchment water to the sea. However, as the hectares of irrigated land were increased, the overall water balance of the ground water changed, and at around 1960, it became negative. The coastal zone irrigation rapidly led to the incursion of sea water into the ground water, with a consequent transfer of salt. The continued irrigation pumping transferred the salty water from the aquifer onto the surface, where, gradually the productivity of the soil was eroded. (Lemon, Seaton and Park, 1994) In response to this, a first, small canal was built which brought spring water from the western corner of the Argolid, and this water was used for irrigation along the coastal

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strip. While this allowed intensive fruit tree growing to continue, the farmers further back from the coast continued to expand the area of irrigated crops and hence the amount of water pumped from the aquifer. The lowered hydraulic pressures led water to feed back from the coastal aquifers, thus transporting sea salt underground some 20 kms inland. Gradually then, the salt problem has increased as a result, so that a large canal project was put in place to deliver spring water over a wide area of the plain. In addition, the lowered water level of the aquifer has meant that farmers in the periphery have found it increasingly difficult to get water at all, and so there is a demand for water to be delivered from the large canal both because of salinization, and because of water demand. The problem is that fresh water is something with a limited supply, and the sources used have also been growing more salty, and so ever greater technological interventions may be called upon to maintain the production of citrus fruits, in an increasingly artificial landscape, totally reliant on costly infrastructure. When we realize that many of the oranges produced are in fact not consumed but buried, to maintain market prices, it seems clear that there is some need to review policy in an integrated fashion. What is also important is that this situation in the Argolid is being repeated in many other locations, and is in reality, part of the unsustainable hidden reality of urbanization. As populations have shifted to the cities, so the decision makers are increasingly divorced from the reality of the natural system that really supports the cities. Cities not only ‘selforganize’ themselves, but also their own and distant landscapes. The dubious power of economic exchange ensures that cities continue to maintain their supplies, if necessary with more intensive exploitation at greater distances, essentially ‘strip-mining’ the world’s agricultural land. There is clearly a need for an integrated framework which will allow an appreciation of the net change in real ‘wealth’, meaning not just the temporary flows of money captured in GNP, but the value of biological potential, the stocks of fertile soil, fresh water and other natural resources, which support the urban as well as the rural population.

12. SELF-ORGANIZING MODELS IN URBAN AND REGIONAL SCIENCE 12.1 THE BASIS: MODELLING ACTORS DECISION MAKING Fundamentally, whatever the fascination of complex mathematical behaviour, the real interest of all the models and equations that have been presented and discussed concerns their usefulness in helping people deal with real problems, and real decisions. But this in turn depends on how well the perceptions and responses of the different actors involved in the system are represented. This is because we now see that in reality, any model describing the connected behaviour of its different components, is based on the supposition that the separate behaviours of each of them taken alone has been successfully represented for all the situations that may be encountered during a simulation. It is therefore worth spending some time reflecting on how this is done, and what problems and questions remain to be resolved, since clearly, models fail when the conditions encountered during a ‘run’ go beyond those within the expected range. This implies that the modeller has successfully parametrized all the relevant attributes which matter to the actor, and also excludes the possibility of individuals learning from their own experiences, during the run, and changing their responses as a result. Whilst noting these issues, let us continue to see what is the most consistent framework within which to develop our decision making models. Firstly then, the modelling of any particular actor is reduced to that of relating the ‘response’ of an actor, or average actor of that type, to the different factors affecting their behaviour. If, in a geographical model it concerns location, then one considers the many different criteria that will enter the evaluation of the attractivity of a particular location. For a company thinking of locating in an area, this might involve the accessibility of the location to the necessary input materials, to the potential customers, to suitable staff, and also it will be affected by the cost of land, the going rents and the availability of suitable buildings. For residentś looking for a home, this would be affected by the price, but also by the quality of the neighbourhood, the existence of good quality schools, shops and health services. Of course, each individual or family would have its own additional, particular requirements, but nevertheless, most would have a positive response to these more general attributes. An urban or regional model is based on the mathematical representation of the responses of people to the characteristics of the different locations open to them. How should this be done?

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Figure 12.1 4 possible choices in the space of relevant attributes for an actor. The basic assumption, about which almost all multi-criteria analysts agree, is that each actor can, when faced with a choice, at least list his main criteria of decision; price, facility, prestige, time involved, etc. Let us assume that these factors define the ‘rationality’ of that particular actor, without asking whether or not there is an objective definition of rationality. The second step in attempting to characterize the preference for one or another choice is to assign some appropriate ‘weighting’ to the various criteria already retained so that in some way their relative importance can be taken into account. Let us stress here that we are discussing the preferences of a single actor. Figure 12.1 shows four possible choices with three dimensions of preferences. Clearly, if the three criteria are strictly quantitative, and can be represented by numbers, then it is possible to simply ‘add’ their weighted values for each choice and identify the ‘best’ choice. This is the basis of most econometric modelling, and is also the basis of the decision models used in the examples given in the different chapters here. In econometrics, however, usually it is the ‘monetary’ value of the different criteria are considered. So, in such a view, it would be necessary for actors being modelled to attribute ‘prices’ to environmental factors, for example, or to any of the qualitative attributes that they may in fact consider in their decisions. For example, the ‘quality’ of a neighbourhood, the attraction of ‘old’ buildings, of architectural heritage, of the landscape, or of the ‘community’. This is one of the key points of disagreement between economists and their critics. However, in the models that we have developed the problem is not evident. This is because in our models, we consider the ‘utilities’ of actors, including whatever qualitative attributes are appropriate, and then we consider the exponential of this. In other words, the response of a population to the perceived

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differences between two choices, say, is captured by an exponential in which the exponent is the difference in utilities. The probability of an individual choosing 1, is therefore: Probability (1)=eu1/(eu1+eu2) (12.1) where u1=αa1+βb1+γc1K K α, β, γ are the weights (relative importance) attached by the individual to the attributes a, b and c of the choice, which have values a1, b1, and c1 for choice 1 and a1, b2 and c2 for choice 2. The important point here is that what appears in an exponent must be dimensionless, and therefore, whatever units are chosen for the attributes a, b and c the weights α, β, γ must have the inverse dimensions. So, if a is the cost of choice 1, then α must have dimensions 1/money, so that the multiple has no dimensions. But because of this, it means that each term can really refer to whatever is appropriate: quality of the landscape, ethical factors or whatever, since it will always be multiplied by a ‘response’ factor with inverse dimensions. This comes down to realizing that the equation (12.1) is really only interested in considering the corresponding change in probability of making choice 1 for a change in the attribute values. In this way our models are perfectly free to include qualitative factors, for as long as we have information eoncerning the response of people to these attributes. As we shall see in this section, we can add in terms which say for example that in general people do not like to live very close to a heavy industrial plant, or like a green and wooded environment, or like the view. In other words qualitative information concerning for example the environment can be put into the exponent, provided that there is some data available to calibrate their responses. An important point is that this traditional way of modelling decision making neglects the fact that in reality individuals will differ from each other, and that this may well translate into sensitivity to different sets of attributes. This brings us back to the initial classification problem mentioned in Chapter 1, where we classify individuals as belonging to the same population if they are sensitive to the same set of attributes, and have similar response weights. But, of course, this does not allow for the possibility that there might be other factors about which individuals differ, but which were absent in our ‘calibration’ data. Because we are developing self-organizing models, situations can arise during a simulation in which zones do display new attributes as a result of a spatial reorganization. In this case, our model of actor behaviour may be inadequate as new attributes emerge, and a hitherto homogeneous population reveals inner differences. Questions of ‘evolution’ in which such changes must be considered will be left to the final section of the book. Returning to our modelling problem, from the ‘utilities’ of types of individual, we can construct the probability of individuals making choices 1 or 2, and from that the different fractions of population making choice 1 or 2. This then attaches the ‘attractivities’ and the ‘Relative attractivities’ of our previous models to more conventional econometric type modelling. The number of people choosing 1 is:

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P(1)=Total Population. eu1/(eu1+eu2) (12.2) It is through these expressions that we calculate the potential markets for activities at different points, as well as for residential populations. And the dynamics is generated by the difference between those who would wish to make a choice 1 say, and those that have actually already made that choice. As wishes are turned into real decisions, so the system and the attributes that characterize each choice change, modifying in turn the number of people wishing to make that and other choices. In other words, the dynamics is generated by the ‘dialogue with delay’ between the perceived advantages and disadvantages of different courses of action, and the changes that occur in these as a result of people actually carrying out their decisions. The modelling of decision making processes is a vast area with a considerable literature, and we shall therefore limit ourselves here to describing the simple, rather intuitive methods that we have used in order to develop our self-organizing models. The interested reader should certainly refer to the relevant literature. Let us illustrate the methods used here by thinking about an actor selecting one of four choices. A particularly clear way of visualizing the problem of choice is to imagine that each actor is at the ‘origin’ of a set of axes, each of which represents a criterion involved in the evaluation of the decision. The origin represents the ‘ideal’ choice for the actor with the maximum imaginable pay-off in all directions, and, of course, has nothing necessarily to do with what that actor actually does, since the real choices presented to him will be somewhere out in the space defined by the dimensions of his value system, a ‘mental map’ of imperfect offer he draws with the information he has received. In such a space, the ‘distances’ of each choice along any particular axis will be ‘stretched’ or ‘squeezed’ to a degree which depends on the weighting the actor accords to that criterion. In such a representation then, the four possible choices of our previous example viewed by an actor who puts equal weight on each criterion will look as shown in Figure 12.2a, and the same four choices, viewed by an actor who puts a much greater weight on the third factor, would appear quite different, as we see in Figure 12.2b. Thus, we may view the problem of choice under multiple criteria as the ‘distance’ from the origin, in an n-dimensional space, of the various possible choice. Of course, the position of each point is uncertain to a degree, depending on the uncertainties involved in the estimation of the ‘pay-offs’ associated with each choice, and also depending on the degree of precision one can give to the weightings assigned to each axis. Each possible choice is therefore associated with a ‘cloud’ rather than a point, and the problem of decision reduces to that of estimating which choice gives rise to a ‘cloud’ which is nearest to the origin. This corresponds to supposing that the ‘attractivity’ of a given choice decreases as its distance from the origin increases.

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Figure 12.2 In a) the 4 choices are viewed by an actor with equal weighting on each axis. b) Here the actor with strong concern about axis 3 sees a different picture. Thus, for a single actor at a particular moment, we may suppose that the choice i will be selected with probability (12.4)

where I gives a measure of the informational precision of the distances. Thus, when I→∞ then the probability of choice is simply 1 for that nearest to the origin, and 0 for the others. In the opposite case, of extreme uncertainty, I→0 and we simply have equal probabilities for all choices. Clearly, most decisions fall somewhere in between these two extremes. In this formulation the expressions for utility can vary from minus infinity to plus infinity, so that the exponential of this changes from 0 to infinity. This ensures that expression (12.4) is always between 0 and 1, which makes it appropriate as a probability that an individual make a certain choice. This probability becomes a deterministic fraction providing that we have sufficiently large populations under study. This imposes a significant restriction on the scale of the phenomena that can be studied using the models of the type developed in the earlier chapters. Spatial zones that would consider populations of less than 100. If we look now at the behaviour of populations then, assuming that we may define the probability of each individual making a particular choice in an interval is given by equation (12.4), then we can construct kinetic equations for the behaviour of the system. If all the decisions made in the system are independent of one another then we have an essentially trivial problem, but, if as is the case in any human system, the decisions of actors impinge upon each other, then we have a much

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more interesting situation. Actions that have been taken, changes in the ‘real’ system, are reflected in the ‘mental maps’ or internal psychological value spaces of the actors, causing them to modify their behaviour. If we consider, for example, the very simple problem of a homogeneous population, which is growing in size, locating around a centre of employment, then initially location occurs close to the centre, but later as the density increases, the choice shifts to more distant locations. In the value space of the population the choice of the central location, while remaining attractive in the dimension of spatial convenience, receded from the origin in dimensions associated with crowding, and led to the adoption of the other more distant locations which seemed more attractive in comparison. Of course, with a single population, and such a simple problem, the evolution is trivial, but if we think of the interplay of decisions that are made by the many different types of actor present in the city, say, we see that we have a highly non-trivial relation between the decisions that have been made and those that are going to be made, because the dynamic interplay of the system evolution with the value space of the actors is very dependent on the precise timing of events. However, these kind of ‘choice’ models leave an important question unanswered: When we observe a system, to what extent does the behaviour of individuals correspond to their desired choice? Now, clearly, in a situation in which all the factors affecting choice were fixed, then after some sufficient time, the pattern of choices observed in reality would correspond to that of the ‘formula’ above. Indeed, the problem could be reversed, and peoples desires and preferences could be correctly inferred from their behaviour. But, in reality, the factors that influence choice are not fixed, and indeed often change as the number of people making a particular choice changes! So, in reality, we must expect that the preferences revealed by observation and statistics may well differ from the underlying, latent, preferences that people have. It may even be the case that people do not really know what they want without trying it, and so the ‘adjustment’ process is really a learning experience which could lead to fairly complex responses. From this discussion, however, the important point that emerges is that the models the dynamic, self-organizing models that have been presented in the preceding chapters use the mathematical models of choice above to calculate an ‘ideal’, latent potential for a given choice. The dynamics of the system is driven by the difference between the observed, revealed, patterns of choice at a given time, and the value of the ideal. In this way, the dynamics is driven by this potential difference between desired and real behaviour, and as the real behaviour changes, so factors within the ‘utility functions’ change, and in turn change the potential difference driving the system. In other words, the dynamics results from movement towards a moving target. This is a key difference between this approach and others which assume, or are calibrated, so that revealed behaviour defines preferences, and change is simply modelled as a quasi-equilibrium process of instantaneous adjustments to exogenous changes in some parameters. 12.2 NESTED COMPLEXITY—MULTISCALAR ORGANIZATION

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Having decided how decisions can be modelled, if we are to use this base to explore possible future scenarios, we then need to consider how these interact to form an urban or regional system, in order to understand how its many different parts are connected together, and what the functional structures are within it. We will also need to know how to evaluate different outcomes. What would we mean by success? There are no simple goals, because when we look at a city, or region, or any group of humans, we find that their total behaviour is the result of an intricate web of influence and effects that links all the many different scales of process and organization. Behaviours and processes sit within each other, and their effects penetrate to the parts within them, as well as to their surroundings, and the connections is in both directions. It is this linking across the spatial and temporal scales that is really why the understanding of human systems requires a ‘complex systems’ approach. Let us first consider the traditional systems modelling perspective in which a series of variables are defined as being significant for the phenomenon in question, and the changes in the values of these variables are governed by the mechanisms that are identified as causing the increase or decrease in numbers. Typically, in our urban models these would be mechanisms of birth, death and migration for the population, and of the growth, decline and creation of ecónomic activities in a given zone. These mechanisms will depend on the values of the variables of the system, as well as on three types of parameter: i) parameters reflecting the external environment of the system. ii) parameters reflecting the ‘spatial configuration’ of the variables. iii) parameters expressing the internal behavioural characteristics of the individual elements aggregated in the variables in question. A model involves 3 levels of description, the micro, meso (system) and the macro (global) levels, and traditionally, they are connected in the following manner.

In this way, the variables of the ‘meso’, or system, level are changed according to mechanisms which are affected by both the external environmental conditions and the internal nature of the elements involved. Models therefore always calculate ‘change’ on the basis of the aggregated behaviour of micro-elements whose responses to their situation are assumed fixed, and known. Variation is calculated through invariance. So for example, a traffic model will suppose that the vehicles and drivers involved do not modify their performance parameters as a result of their particular experiences. Similarly, the cost of fuel per litre will be fixed, or changed exogenously, as will the pattern of origins and destinations of the trips, and these will not depend on the pattern of traffic flow. These simple models are characterized by ‘one way’ causality, in which changes in the variables are driven by ‘fixed’ equations. The parameters within them are either unchanging, or are changed from the outside as an external action. For example, what happens to traffic flows if we double the cost of fuel?

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But, this is an over-simplification. In reality, we have a co-evolution of the environment with the populations that live in it, and a process of learning and adaptation in the microscopic elements and individuals that inhabit the system. Instead of a clear causality from fixed parameters to the variables, we find a web of interaction that links the levels to each other.

In order to illustrate these ideas of complexity, let us consider again the simple problem of traffic flows that occur on the road network of a city. In this case, the micro level is that of the individual car and drivers, different makes, different driving styles, and also the details of the road, the precise occurrence of traffic signals etc. All of these details would need to be considered if we were building a ‘model’ of a particular trip to work, but if our aim is to understand the pattern of traffic flow then the details of the micro level will be aggregated and represented through average values: the average family car; the average truck; the average driver; average street of type 1, 2 etc. So, different links of the network will be characterized by an average cost and time of travel, and this will reflect the kinds of obstacles typically encountered, and the average kind of driving. These parameters will appear in the decision making models of drivers concerning their routes, and this in turn will determine the traffic flow patterns. However, in addition there is also the macro level that will influence the flows. This will correspond to fuel costs for example, as well as the distributions of the homes of car owners, and of the jobs which they will attempt to reach in their cars. These patterns of ‘origin and destination’, as they are called, will in fact set the boundary conditions of the meso problem. For the model of traffic flow that we are examining, the distribution of origins and destinations will be considered as fixed, affecting the generation of flow, but not being affected by it. These micro and macro parameters are then used in calculating the meso level—which will be the average daily flows of traffic on each link. Obviously, the size of the flows on one link affects those on another, and the ‘experience’ of congestion or of easy driving will be considered as being transmitted in some way through the population so that the steady pattern reflects some implicit learning process leading to a relatively homogeneous spread of congestion levels. In this way equations are written down, once again based on the principles of accountancy, in which the different flows on the branches affect each other, and they are affected by the pattern of origins, destinations and of relative costs in time and money experienced on the different links. If we move down the scale from a traffic flow model to that of the individual vehicle, we can construct a 3-level model once again, but in that case the inner details might be the moving pistons, the gears, the accelerator pedal and the driver’s reactions, and the fixed external circumstances would be the road network and the traffic and particular obstacles that it poses. A model of a car trip could then be developed in which the variables of acceleration and velocity were calculated from the detailed timing of external events, and the averaged performance of the internal parts of the car and driver. Moving up the scale from the traffic flow model, we come to the level of the models presented in the previous sections of this monograph. They are not aimed at calculating

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the traffic flow patterns, but instead the changes that occur one scale longer than these: that of the changing patterns of origin and destination, as homes and jobs grow and decline in different areas of the city or region. In these, the ‘traffic flow’ pattern is considered to be a microscopic internal detail, represented by parameters reflecting average costs in time and money and affecting, over the longer term, the meso level distribution of ‘origins’ and ‘destinations’, as the population moves house, increases or decreases and as the location of jobs of different kinds changes. In addition, the changing values of the variables, population and jobs of particular types located in a zone, are governed by the macroscopic parameters that come from the environment of the city or region. These affect the choices made in the housing market, as people search for quiet, charming tree lined suburbs, within easy reach of their workplace, and simultaneously, factories and offices seek locations which fit their particular needs, and which are sufficiently accessible for their workforce. Values concerning lifestyle and possible real estate gains combine to shape the choices that are made. Similarly, factors such as demographic coefficients reflect wider cultural and economic conditions, as do levels of health and education that are current in the region. It is these fixed factors which we attempt to use to explain the changes in the distribution of jobs and of residents in the urban centres. These parameters are considered as fixed in the models, but can be changed by the model user from the ‘outside’ in order to explore the possible effects. In reality, of course, all these parameters will change as a result of people’s experiences in the particular history that unfolds. So, the experiences that occur in suburban living may drive a new generation to try something different, and new tastes and patterns may emerge, just as the pressures exerted on the transportation system may lead to new initiatives in public transport, or to road pricing, the banning of cars from urban centres, or a number of radical responses. This hierarchy of convoluted causality is represented in Figure 12.3 and this shows us the essence of complexity as being the kinds of system that are about the co-evolution of a hierarchy of structures, with loops of positive and nega-

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Figure 12.3 The web of interactions traversing the spatial and temporal scales of a real system. The separation of micro, meso and macro levels is invalid. tive causalities linking the different scales as an integral whole. Here we see that changes at the scale of minutes and hours sit within processes with the timescale of a day, and these within slower processes whose change takes several years. These too, sit within a longer term evolution of culture, technology and world trade which may take one or several generations to change significantly. Eventually, we arrive at the seemingly eternal questions which concern human values and ethics, and which underlie all societies. In complex systems, we must realize that instead of ‘causality’ always being considered as operating neatly ‘one way’ from the macro to the meso, or from the average micro to the meso, we see that what is a parameter and what a variable is a ‘subjective’ matter that our choice of scale decides. Our so-called ‘parameters’ will in fact co-evolve with the ‘variables’ of the system. We find a complex web of interactions where the long term and the short term communicate, and affect each other. This is the essence of a complex system, since it really includes the reality of ‘learning’ and ‘adaptation’ inside systems, as a kind of selection process operates on the individual differences of response and experience. The experiences of people driving into the city affect their choices of route, and the effectiveness of their allocation to the available network results in a greater or smaller satisfaction and therefore affects the pressure and needs to re-locate. This affects building, and land prices, which of course affects the traffic flows and the demands on the road network, in turn leading to a

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changing pattern of residential and business locations and flows. The overall effectiveness of the system, and the kind of quality of life that it offers affects its competitiveness with respect to other cities as a location for further investment and activity. The opportunities will attract migrants who will bring their culture and demographic potential with them, which in the long run will affect the population and the age pyramid, thus changing the need for services and amenities and the character of the city. It will also have modified the nature of the typical individuals that inhabit the different neighbourhoods, and so throughout the urban tissue, a complex process of coevolutionary change is taking place. 12.3 MULTISCALAR MODELLING The models developed in the preceding chapters allow us to explore how two particular levels of description are linked by the interactive mechanisms resulting from the decisions and behaviours of their inhabitants. The levels are those the system as a whole (Brussels for example), and that of the 40 zones chosen to describe its spatial structure. Each zone is characterized by rather aggregate measures of accessibility and housing and land availability, and is populated by inhabitants with behaviour that is distributed around an average. The ‘attractivity’ of a zone is given on average, and therefore fails to represent explicitly the possible existence of different sub-localities with perhaps very different characteristics. The model as it stands would therefore fail to entirely capture the real behaviour of firms and residents locating there, who may well find localities within it which are highly attractive and others which are quite unsuitable. In order to improve our representation therefore, we need to examine the lower level of description, and to build up the parameters which characterize a zone as the result of a more detailed calculation carried out at the microscopic level. This could be done in a variety of possible ways, and one simple one would be to examine the sub-locations in terms of their attractivity, using the criteria developed in the urban model above. Inside each zone therefore, we may trace the patterns of accessibility to the external zones, as well as of the suitability of land, the type of housing and the qualities of the different neighbourhoods. From this, at any given time the different types of firms, and inhabitants could be distributed through the zone according to the suitability of each parcel within the zone. This is illustrated in Figure 12.4. The key point here is that we need to write the Attractivity of a zone as the sum of the attractivities of each unit area within it. So, in the case where a zone i is made up of some z sub-units, we must write: Attractivityi=Σz Attractivityz In this way we can correctly link different scales of description and describe the aggregate level attractivity as: Attractivityi=Areai·(Average Attractivity of each sub-zone) and this links back to the expressions used in earlier work, where the attractivity of a shopping centre was taken to be for example: Attractivity of Shopping Centre=Retail Area/(Cost of travel)e

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Now we can see that the form that we now have enables a complete generalization of this, through as many spatial scales as are necessary.

Figure 12.4 The microdistribution of employment and of residencies can be modelled using the attractivities expressing actors preferences, and the very local circumstances. So from equation (12.4) the attractivity of a zone z, with sub-units ω is: Attractivityz=Σω Attractivityω The lowest level of description for which data is available is then treated as the average value as shown in Figure 12.4. It is also at this point that these models link up to several other pieces of research that are on-going. Firstly, this urban model can be seen as sitting within an evolving urban hierarchy, and the work of Pumain (1991, 1992) and Sanders (1992) has developed and applied such models. At present a generic simulation framework is being developed to look at this (Buza et al., 1995). This also links to the work of White and Engelen (1993), who have developed cellular automata rules which generate the locational and colocational features that characterise a particular city locally. More microscopic approaches have been developed with ‘Multi-Agent’ systems, where rule based computer simulations have been built which generate aggregate behaviour as the result of individual interactions and decision making. The most ambitious example of this appears

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to be the Transims traffic model of Albuquerque, developed by Chris Barrett and his team at Los Alamos, where the interaction of several million automobiles on the road network can be simulated (Barrett et al., 1993, 4, 5). This is clearly a much more disaggregate representation than that of the kind of models presented in this volume, and makes use of massive computational power that is available. However, while this is a most interesting piece of research, it is also true that the exploration of many strategic issues of importance may not require such detailed representation. One of the important goals of modelling must be to establish what level of disaggregation is appropriate in order to explore a certain question. The self-organizing models described here bear an interesting relationship to the work on ‘spatial syntax’ of Hillier and Hanson (1984), Hillier and Penn (1992, 1993). This interesting approach examines the properties of the urban space itself, and the manner in which these influence flows of people. Their spatial analysis is able to obtain better agreements with observation for the patterns of pedestrian and traffic flows than the conventional models based on the distance, time or cost of travel. However, while there analysis of spatial patterns arising within the built form are remarkably successful, the strategic issues arising from the longer term evolution of the built form, and of the circumstances driving it, are absent from their considerations. Because of this, it would be an interesting piece of research to put the spatial syntax analysis within the context of a longer term, self-organizing urban model. Another interesting link is to the work of Batty and Longley (1994), which looks at the fractal nature of the spatial patterns both of the boundaries of cities and also of manner in which jobs and residences fill the space. Inside our self-organizing macromodel of large zones, the constraints and pressures for the growth or decline of different types of inhabitant or employment can be enacted in detail using the micro-model, and from this a more precise and sensitive response will be generated within the localities, giving rise to more accurate representation of the ‘average’ parameters characterising the zone. This in turn will affect the macrodynamics, and through this the micro-repercussions in the other zones. We can represent the attractivity of a zone as resulting from that of its constituent micro-zones, which may reflect the existence of ‘functionally efficient’ clusterings. Clearly, however, a microzone can only contribute to the ‘attractivity’ of the zone of which it is part, if it is connected through the different transport and communication networks to the outside of the zone. So, if there were only a single road, for example, traversing a zone, then only those microzones lying along the road could contribute to the attractivity of the zone. The ‘fractal filling’ factor observed by Batty and Longley would be 1. Conversely, if such a dense network existed that every microzone of the zone was connected to the outside world, then the fractal filling factor would be 2, total two dimensional filling is possible. However, depending on the scale, the figure would normally be somewhere between these two limits. This leads to the correct way in which we can include the dynamics of the built form, both of housing and of commercial property. For this, the attractivity as we have developed it above would normally reflect the costs of renting/buying appropriate space in a zone. This would in turn reflect the pressure on existing space, indicated by the level of occupancy. In this way we can develop a dynamics of the commercial and domestic rents, which in turn can be used to drive the building of new space.

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For the commercial sector for example: Rent=Σ Commercial Employment. space needed/Σ Commercial Space The pay-off expected from building new capacity will depend on the expected rents, and the costs will depend on the expected rates of interest. In this way we can write a dynamic equation which will describe the building of additional capacity:

In this way we can adjust the space available and the pattern of rents that will result. This in turn will feed into the Attractivities in terms of available space, and rent levels, as well as the accessibility of each zone and sub-zone along the available transportation links. 12.4 A LINK TO SYSTEM-DYNAMICS Having discussed the modelling of actors behaviour, and the methods of aggregation of these into successive levels of description, we now should make some comments about the aggregate models that result, and the relation between the self-organizing models discussed here, and the earlier ‘System Dynamics’ models of Forrester. There are two main differences: first, the System Dynamics models are deterministic and fluctuations do not play an important role, and second, the structure of the different zones is set down before hand. So, for example, the zones used for the model are the City Centre and the suburbs. Each of these have their own type of occupancy and parameter sets, which are pre-set by the existing structure. In contrast to this, the accent of the SelfOrganizing models is very much to explore the functional differences that arise from different possible configurations of the system. The Centre and suburbs might only emerge during the simulation, or even if the centre was present initially, it is quite possible that under some conditions the city might de-centralize and form new, more important centres in the ‘periphery’! Of course Systems Dynamics models may not have fluctuations present, but it may well use sensitivity analysis to examine the possible trajectories of the system that might possibly occur. This is of course a good idea, and indeed comes down to using non-linear, deterministic equations as a ‘test-bed’ to try to see the kind of situations that may occur, and what the possible attractors of the system are. This is an excellent procedure, but of course, in the urban and regional problems that we have been considering the most important feature has been the different possible spatial configurations that might emerge, and the possible properties of these. The Forrester model did not really address spatial structure at all seriously, and obviously with two zones, the centre and the suburbs, can scarcely find many different configurations. The point is that the Forrester model had quite different intentions from the models presented here, and did not arise from the desire to provide a ‘decision support system’ for the strategic planning of transportation and social, cultural and economic implications of different types of urban development. Its aim was to consider/demonstrate the fact of overall urban dynamics, by calibrating the different variables according to observations, without considering the possibilities of internal structural changes that might occur in urban form and transport flows, and the corresponding consequences that these might have.

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In other words, the Forrester models correspond to a given set of mechanical equations, calibrated at the initial time, which are run to reveal the dynamic trajectory, assuming that parameters, relationships and mechanisms are not modified as a result of underlying changes in the behaviour of individuals, organizations and structure, which means also that learning as a result of the ‘experience’ is excluded. What we must remember is that the multiple facets of reality, the particular products consumed, transport generated, quality of life, etc. are all linked through the detailed existence of individuals living their daily lives. When we run macroscopic, statistical equations, we are assuming that despite the changes that our equations are revealing, everything else, and everything implicitly underlying the variables and parameters is not changing. In other words believing the trajectory of the equations implies an assumption of massive Ceteris Paribus. Our ‘self-organizing’ models also require this, but go one stage further than Forrester in that they do consider the possibility of underlying change in spatial organization at the zonal scale chosen for the model. Otherwise they too require that for example, technology, demographics, desired lifestyles etc. remain constant. However, both Forrester and the models described here do consider the interaction of quite a considerable number of factors, and this issue of Ceteris Paribus is one that cannot be overemphasized, since the urban system is constantly manipulated by ‘single issue’ agencies, considering for example, transport, or pollution, or education etc. and if they are allowed to implement policies designed to deal with their own particular issues, will certainly cause all kinds of other effects and impacts on the other aspects of the system. What is required is an integrated approach, a systems approach, through which the many different aspects of reality are linked, and which can allow an exploration of the integrated development of the whole thing. 12.5 DECISION SUPPORT—INFORMATION AND EVALUATION In order to help decision makers and politicians to make better decisions we need to be able to assist them in two ways. First, they need to have as good an idea as possible of the consequences of their possible actions. Second, they would like to know how these future situations will be perceived by the different constituencies and actors of the system, so that they may evaluate the possible outcomes. Let us consider the first requirement—to know something of the consequences of possible actions or policies. But on what timescale, and in what dimensions? As discussed in the section above, the kind of model used for decision support will depend on the answer to these questions. For example, if I consider the building of a light rail system from a popular suburb to the centre of town, then am I interested in knowing how many people use it in the first month, the first year or over a decade or more? Also, am I interested in the effects on usage of other public transport, and of cars or am I also interested on the effects on land values, on accessibilities, on commercial locations for retail outlets, and on the changes induced by this on the rest of the city? Is this part of a strategic plan for transportation in the city, integrated with future plans for land-use and for residential and commercial development? Clearly, if the vision is simply short term, and aims merely to remedy a particular problem of traffic congestion and no more, then a ‘traffic model’ will be quite sufficient

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to achieve this. It will take the present demand for travel from the suburb to the town centre, and will calculate how the present distribution of trips by the various possible means: bus, car, metro and train etc. will be affected by the new opportunity of light rail. However, despite the apparent sufficiency of the short term model for a short term analysis of a short term problem, nevertheless there will always be longer term consequences of such actions, and therefore all that is happening is that entirely unforseen long term consequences are being generated as the cost of only taking a short term view. If, however, the light rail project is seen as part of a larger plan to attempt to deal with the transport problem of the whole city, and its projected growth into the future, then a longer term, broader understanding would be necessary. This would require an attempt to understand the directions of growth or decline in the city as well as the possible effects that policies or actions might have on accessibilities, property prices, and on residential and commercial locations. These will all affect the actual numbers of people requiring travel to or from destinations in the city, and the costs and congestion generated in the transportation network will be part of the pressures generating change in the future. This longer term view is clearly that which the models that have been described in the previous chapters hope to provide. This is because the evolution of a system which only uses successive short term ‘corrections’ as it evolves will be quite different from one in which long term, broad strategic planning can occur. The problem of ensuring the long term development of a city therefore depends on the organizational structure and whether or not this allows decision makers to take a longer term view. If careers and promotion depend on the perceived ‘problem solving’, judged in the short term, then clearly, this will not be conducive to strategic thinking and planning. Similarly, if there is no level of policy or decision making that has responsibility for the overall integrated city or region as a whole, then the unforeseen effects of one sector and location on another will play a large part in the evolution. Decisions will tend to be in immediate response to a problem, resulting from change elsewhere perhaps, and by using narrow criteria will lead in turn to unforseen consequences elsewhere. Concerning the question of evaluation then, although it is not the scientist or modellers job to provide the criteria on which possible system trajectories will be judged, it nevertheless is true, that the broader, longer terms implications of a decision could only be included in the evaluation if the models, or the simulation, was able to explore these wider consequences. In this way, the modeller nevertheless plays a role in the evaluation process, by providing an indication of the possible outcomes, and importantly, the extent to which these are uncertain. This introduces two aspects into strategic planning: first, the development of long term goals and a plan of action to achieve these; second, the recognition of the limits to prediction, an idea of the different kinds of evolution that could occur, and the need for flexibility and adaptive capacity to be built into the system. The approach described in the preceding sections suggests that both of these are important, since it implies that the right decisions and policies could lead the system to a desirable structure, but also that there are other structures that could emerge and that the evolution is not deterministic. But what precisely is the present situation?

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12.6 URBAN MODELS—STATE OF THE ART In a recent paper Michael Wegener (1994) summarizes the situation that has developed since most of the work described here was completed (1982). Despite the premature obituary of Lee (Requiem for Large Scale Models) he documents 12 large scale urban models that are currently in use and which have been developed linking transportation and land-use in an integrated fashion. He produces a most helpful table describing the properties of these different models, and pointing out which factors are treated best in which models etc. This table is reproduced below. The important point is that these models are operational, and treat very detailed data, requiring a lot of computing power and represent an enormous investment in time and money on the part of many, highly skilled and motivated researchers. This work therefore represents, as Wegener suggests, the ‘state of the art’ in urban modelling, and some obviously useful tools for decision support. Why therefore is there still any need for a book such as this, which puts forward relatively crude models (in terms of the spatial zoning used) and seemingly ignores all this work? The answer is that despite the complication of these other models, and the sophistication of their software, they do not capture the phenomenon of structural change. This underlying reason for this is that they do not consider the difference between revealed and latent preferences, and thus do have a representation of any real endogenous dynamics, since the utility functions, or locational preferences, are calibrated from observed data. The models are therefore ‘descriptive’ rather than ‘causal’, since they are not based on actors underlying goals, which lead to their observed choices, but simply on the observed choices. The patterns of trips is projected forwards to incorporate the effects of whatever decision is considered (changed transportation links, costs, etc,) and even though the feedback between transportation and land-use is contained within the model, they do not allow for new centres to emerge, or for any fundamental shift in the trip patterns (that is the functional structure of the city) to be anticipated. In reality then, the problem of real change, of possible spatial re-organization, is simply not captured in these models. By using various assumptions of equilibria in the locational distributions, or by projecting forwards past trip distributions with minimal change, the possibility of an instability in the spatial distributions is suppressed, and therefore none can be anticipated. So, although these other, operational models have much to commend them, they really only serve to anticipate the short term. In the medium or long term however, structural changes will occur, but they will not be correctly anticipated by the computer simulation model. The 12 Urban Models are: POLIS, Projective Optimization Land-Use Information System (Prastacos, 1986); CUFM, the California Urban Futures Model, (Landis, 1992, 1993); BOYCE, Compbined model of location and travel choice, (Boyce, 1983, 1985, 1986, 1992); KIM, Non-Linear version of an Urban Equilibrium Model, (Kim, 1989; Rho and Kim, 1989); ITLUP, Integrated Transportation and Land-Use Package. (Putman, 1983, 1991); HUDS, Harvard Urban Development Simulation, (Kain and Apgar, 1985); TRANUS, Transport and Land-Use Model, (de la Barra et al., 1984, 1989); 5-LUT, 5 Stage Land-Use Transport Model, (Martinez, 1991, 1992a, 1992b); MEPLAN, Integrated

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Modelling Package, (Echenique et al., 1990, Hunt and Simmonds, 1993); LILT, Leeds Integrated Land-Use/Transportation Model, (Mackett, 1983, 1990, 1991a, 1991b); IRPUD, Model of the Dortmund Region (Wegener, 1985, 1991); RURBAN, the Random Utility Urban Model, (Miyamoto et al., 1986, Miyamoto and Kitazume, 1989). As was pointed out in a series of papers by Wilson and Clarke, as parameters change it is possible that several spatial equilibria are possible, and in this work they focussed on the possible stationary states that the system could evolve to. However, by only studying the equilibria two important factors are lost: – we cannot see which possible equilibrium the system will most probably evolve towards. – by assuming maximum entropy or maximum utility patterns we lose the dissatisfaction that really characterizes the situation and which in fact drives the dynamics. If dissatisfactions exceed some threshold, maybe some new behaviours may be triggered, such as ‘rioting’, which may turn out to be the crucial factor in the unfolding history of the city. In the models that have been described in this book the non-equilibrium character of the systems is what makes it dynamic. The non-equilibrium is generated at each instant by Model

Subsystems modeled Model theory

Policies modeled

POLIS composite

employment population housing land use travel

random utility location surplus

land-use regulations transportation improvements

CUFM composite

population land use

location rule

land-use regulations environmental policies public facilities transportation improvements

BOYCE unified

employment population networks travel

random utility general equilibrium

transportation improvements

KIM unified employment population networks goods transport travel

random utility bid-rent general equilibrium input-output

transportation improvements

ITLUP composite

employment population land use networks travel

random utility network equilibrium

land-use regulations transportation improvements

HUDS composite

employment population housing

bid-rent

housing programs

TRANUS composite

all subsystems

random utility bid-rent network equilibrium land-use equilibrium

land-use regulations transportation improvements transportation-cost changes

5-LUT unified

population networks housing

random utility bid-rent general equilibrium

transportation improvements

LILT

all subsystems except

random utility network

land-use regulations

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composite

goods transport

equilibrium land-use equilibrium

transportation improvements travel-cost changes

MEPLAN composite

all subsystems

random utility network equilibrium land-use equilibrium

land-use regulationss transportation improvements transportation-cost changess

IRPUD composite

all subsystems except goods transport

random utility network equilibrium land-use equilibrium

land-use regulations housing programs transportation improvements travel-cost changes

Model

Subsystems modeled

Model theory

Policies modeled

RURBAN unified

employment population housing land use

random utility bid-rent general equilibrium

land-use regulations transportation improvements

Table of Urban Models.

the difference between what individuals are doing (where they are living and working, shopping etc.) and what they would like to do, but have not as yet put into execution. In other words, our models of a dynamic driven by stored decisions reflecting the changing situation, but with a characteristic average time of realisation. The models not only accept the difference between ‘stated’ and ‘revealed’ preferences, changes are actually driven by them. Of course, the external parameters may also change (energy costs, the economic situation, technology etc.) and these feed change into the urban system, but the response of the inhabitants is not instantaneous, and they therefore respond to the new opportunities or pressures only slowly. Social pressure can build up if the rate of change imposed on a neighbourhood exceeds that rate of response of the inhabitants for too long. Then their frustrations and ‘dis-utilities’ build up and can lead to catastrophic instabilities if they are ignored. In the review by Michael Wegener concerning the 12 operational models, states, ‘All of them have been (or could have been) estimated from observed data, using readily available computer programs and following well established methods and standards. In particular, maximum likelihood estimation of the ubiquitous logit model has become a routine activity’. But this estimation assumes stationarity, so that in reality all these models describe dynamics as a series of stationary states. While ‘ease of calibration’ can be presented as a sign of a good model, it also reveals that underlying ‘positivist’ tradition, which does not separate what people do from what they desire. Our models, statistically crude as they may be, attempt to look at change as a process driven from ‘within’, by people. In the models above the idea was to ‘infer’ the stored, latent demand using the rates of change observed, but a much more satisfactory method is to relate it to social enquiry, and indeed to evolutionary theory, since it is underlying value systems, and the reasons for these, that drive the system and characterize the populations. In other words, if you don’t know the underlying agendas of actors, then you won’t get their response to change right. Ultimately, then this means that urban modelling should be linked either to the elicitation of peoples’ agendas, or more profoundly, to an evolutionary theory which shows how their goals arise from their social and cultural

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history, where fundamental needs of survival and success have led to the spectrum of agendas observed (or not observed). It is this genuine, non-linear dynamics that allows structural change, and apart from the models presented here, Wilson and Clarke also showed the existence of multiple equilibria in the distribution of retail space, and raised the issue of different possible futures. However, as the list of operational models shows, development has favoured the more descriptive models that are incapable of exploring the qualitative changes that may occur. Whilst these have been quite successful perhaps in matters of traffic planning, they do not provide the basis of a decision support tool with which long term, strategic planning and policy making can be addressed. It is therefore with regard to broad, strategic exploration that the kind of model that is described here comes into its own. It is precisely aimed at exploring possible future structures of cities and regions, and in offering some estimate of what these may be like. In reality, then, we should see the role of the ‘self-organising’ models described here as being to complement detailed studies concerning precise traffic flows and zonal occupations. They offer broad visions of the longer term futures that may occur under various scenarios of action. Our models therefore represent a ‘first stage’ of qualitative analysis that aims at exploring the long term, strategic aspects of urban and regional development, which allows the broad outlines of policies to be decided. The more detailed, more correct, spatial interaction models that are used today would then still be useful as a ‘second stage’ in accomplishing the actual, detailed policies and decisions that need to be made in any case. If decision makers only have the ‘short term’ models to explore their decisions then we would expect to find a cascade of successive changes that would in reality affect the larger scale, long term evolution. And this is almost certainly the present case. While obviously there is some merit in solving a short term problem, what are the consequences of ignoring the long? Does the action tend to reinforce centralizing or decentralizing forces for example. If it leads to a re-population of the centre of the city, or to a continued expansion of the suburbs, then this would have implications for the need for schools, health care, transportation, retail and commercial development and indeed for the whole ‘character’ that the city projects. The essential differences between the evolution of a city or region that is being ‘run’ according to the short term or the long term mode, is that the former has a much more limited scope of futures than the latter. In the former, events trigger responses, and these entrain further responses and so on. The particular trajectory of the system is virtually defined by a ‘marginal’ search at a given moment for ‘pain reduction’ in the most politically pressing factor. There is no ‘vision’ at all. The longer term approach, which would require the kind of models developed here, attempts to explore not only the short term, but the longer term implications of the ‘solution’ to the short term issue. It attempts to reveal the kind of situations that may emerge, and the kind of structural shifts that are either accelerated or impeded by a particular action. It also provides a basis upon which policies in different domains and locations can be correlated and made to reinforce some overall aim rather than to cancel each other out. While the reality of long term change is not part of the short term approach, short term reality is part of the long term view, which attempts to generate successive short term realities, and to examine them from the point of view of the different participants

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involved. These significantly different approaches arise out of the whole scientific enterprise itself as traditionally applied to human systems. It somehow became accepted that scientifically, it was better to try to say something completely correct about an unrealistically simple and static system than to say something incomplete about complex reality. This has partly been due to disciplinarity, and to the fact that credibility has tended to be conferred within disciplines, and therefore that career opportunities in academia have reflected these narrow considerations rather than the broader ones such as ‘usefulness’ for example. The aim of the ‘self-organizing’ models presented here is to link together knowledge concerning demography, economics, migration, natural resources, environmental factors and whatever seems to be necessary to endogenously generate the spatial structures observed, and hence to understand a situation in a more fundamental way than simply describing it. The longer term evolution that is considered is generated by equations and from mathematical models, but the outcomes are not only quantitative but also qualitative. Many important questions for regions concern the issues of structural change, and the way in which current decisions, concerning apparently immediate and short term issues, may influence, or be influenced by, the strategic changes that are occurring. For example, changes in residential patterns, in lifestyles, in the economic structure of the region, or in the demographic parameters may all be driven, and drive, problems of traffic congestion, of urban decay or of increasing crime. Our models must therefore span the short and the longer term if they are to really inform decision makers. Another important issue in the ‘evaluation’ of different possible futures is that the kind of models that have been developed lend themselves remarkably well to assessing the possible views and perceptions of different actors and constituencies. Firstly, the whole basis for the modelling are mechanisms which reflect the perceived utilities and local circumstances of different types of actor, according to their location. This therefore offers an obvious basis on which the likely responses of different actors and constituencies could be assessed, since the degree of satisfaction or dissatisfaction of each type of actor, spatially aggregated as required, can be displayed throughout a simulation. For a decision maker, these could be considered with whatever weightings were thought appropriate, so that the evaluation could be made taking into account the priorities accorded to the different constituencies, and these would therefore be visible, and explicit if required. In the Senegal model, there is an explicit software utility called ‘Evaluation’ that allows the weightings of the goal functions for different types of actor, and locations to be

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Figure 12.5 The difference between short term, narrow evaluations and the longer term, broader ones at the centre of the models here. set. The outcome of a simulation is then compared with a policy objective and in this way different policy options can be compared in their ability to achieve their objectives. In the next section we shall briefly examine why the traditional scientific modelling approach is inadequate when dealing with complex, evolved systems such as cities or regions. Because of the complex linking of levels of description over the long term, the whole concept of models as being ‘predictive’ has to be modified since the adaptive, learning processes within the system can in reality take the system off to many different possible futures, and these cannot necessarily be captured from existing data. For example, changes in desired ‘lifestyle’, in ‘family size’, the attraction of the city or the country, of the sunbelt or the snowbelt, all these things are socio-cultural and can only be deduced either by conducting surveys at regular intervals, or from the statistics after the event. In other words, although trends can be found and extrapolated, the evolution of the system will always depend on the continuation of these trends. If people’s ideas change, then in fact the predictions will be wrong. This is one argument for trying to connect subjective views, arrived at through interviews, to the observed macro-behaviour. This comes down to trying to find ‘lower level’ invariants upon which to base the behaviour represented in the model.

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Another way of approaching the problem is to consider the cultural aspect, and attempt to see whether this exhibits any long term stability on which ‘explanation’ can be based. For example, over a long time span, and a broad spatial scale, the ‘latin’ tradition that the city was the centre of civilization, and that everything worth anything happened there, has been giving ground to the Anglo-Saxon idea that cities are fine, but living in a semi-rural environment is better. From the clash and confrontation of two such different ideas flows a long term trend for cities either to develop suburbs, and for these to extend outwards like tentacles, leaving inner cities as desolate areas at night, or for the Centre to contain ultra-expensive neighbourhoods, cultural and social activities, and for the suburbs to be bleak and desolate at night. The point is that any such basic cultural force shapes the self-organization processes as feedbacks amplify its effects, and the effects change the experience and beliefs of the population. This means that the evolution of urban and regional systems is only partly conditioned by the values of parameters representing external factors such as energy costs, economic development within the region or nation, or by cultural changes driven by external influences for example. In addition, seemingly small initial differences of detail can build up through accumulative effects on linked variables, and so situations which are initially similar can in fact evolve in quite different directions. As a result therefore, we see that seemingly minor decisions, or unimportant differences, could lead potentially to quite different futures for the whole system, as the feedback amplifies the tendencies. Once again we are faced with the limits to prediction, since two seemingly identical situations may evolve differently. In addition, of course, our initial information concerning the two situations will always be imperfect and incomplete, since we do not know what would be necessary to complete it. Only after a difference has become manifest might one trace back the small difference that was critical. We must simply admit the fact that however good our models there will be some developments that they will fail to anticipate, and as a result there is a need to leave adaptability in the system to deal with future unknowns. But, if this is the case, then what is the purpose of building models? 12.7 MODELLING AS A LEARNING PROCESS The purpose of the models that have been described in this text is to help us to understand the mechanisms and processes that underlie the working of the city or region in question. They integrate in a single framework demographic, economic, social and environmental aspects of the system, and from this complex interaction allow us to study and understand the processes that led to the present situation. That understanding will always be incomplete and imperfect, but, nevertheless will be the best basis that we have on which to explore possible futures. The purpose of our models is not to predict the future, since as we have seen feedback mechanisms can amplify even very small events, through an instability, and lead eventually to a re-structuring of the system. However, by exploring the stability of the system to all kinds of noise, the possible instabilities can be explored considerably, and in this way possible futures can be ‘tried out’ to some extent. Instead of thinking that a failure to predict is a negative result, we should instead understand that it

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is the very fact that the future is not determined that offers us the possibility of intervening, and of affecting the outcome. A model allows an exploration of the consequences of the interacting mechanisms that have been put forward to explain events. If the comparison with history shows that they succeed in doing this, then the model may be considered satisfactory for the present. If it is unable to generate the structural changes that have occurred, then the different path traced by the model and by the real system force us to change our model. Either some external events intervened, or there are some missing mechanisms that must be sought. Either way, fresh questions emerge, requiring more research and study. When fresh agreement can be obtained between the model and the real history of the system, then it can be considered satisfactory until it is shown to be inadequate at some later time, or for some new aspect of the situation.

Figure 12.6 The development of a model implies an iterative process of model conception, calibration, comparison with reality and reconceptualization. Without a model to provide the measure of what we believe to be true, we cannot know that our beliefs are inadequate, and hence will not seek to correct them. The model is therefore both a stimulus to learning and the embodiment of present knowledge.

13. CONCLUSIONS 13.1 COMPLEX SYSTEMS AND MICRODIVERSITY Despite the difficulties presented by modelling, and the uncertainty and possible ambiguity of the outcomes that can be generated, we must face up to our responsibilities and try to improve our decision making. We cannot simply decide that it is all too complicated and so there is no point doing anything. And we must give answers to certain questions to the best of our ability, even though there can be no ‘objective’ justification for the particular answers we arrive at. Who should play a role in the decision making, and who should be considered in a decision? How much weight should the opinion of each type of actor carry? How does the present system’s hierarchy of structure and function depend on the rules and behaviours of individuals in the system? The problem is that individuals matter in the performance of firms and of organizations, and these play a role within towns and the rules, values and structures of towns, and of firms affects individuals. Each town and city plays a role within the larger region, and is in turn affected by the larger region. So, which decisions should be regional, which should be local and which should be left to firms and to individuals? This is the essence of the issue of ‘subsidiarity’, and if we take it seriously, then we must admit that, probably, we know very little about the real ‘causal relations’ that underlie the particular functional characteristics of a social system. In fact for the many different actors involved in a system, each will have his own set of values. These are multidimensional, with different importance to different dimensions. In order to evaluate possible actions, the different probability of outcomes should be multiplied by the different ‘scores’ assigned by each type of actor. Then, according to the weights attached to each actor, the ‘consensus’ can be arrived at. But there is as yet no organizational recipe to ensure that a ‘fair’ process of evaluation and planning is in fact achieved, or that this will lead to the adoption of ‘successful’ solutions. And, of course, one has to admit that there is no reason why there should be. We can only do the best we can, and this will always be considered imperfect, or unfair by some of the constituencies involved. What matters perhaps is that each participant in the decision making process should be able to say what he or she thinks of the problem, and be able to say why certain interests should be overruled in favour of others. However, once we admit this very imperfect vision and process for decision making it becomes more obvious why in the long term it would be good to keep as many options open as possible. In general, then ‘small and diverse’ will allow for adaptation and change better than the ‘large and monumental’. Just as central planning failed because of its rigidity in a changing world, so large monolithic organizations and plans will tend to

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be unsustainable. The lesson seems to be that plans which encourage variety and diversity in the inhabitants of a region, in their activities, their means of transportation and in the landscape, tend to lead to creative and adaptive systems capable of generating their own development and in responding to the challenges of the economic, natural and social environment. Policies which tend to reinforce particular specializations, will in the long run lead to disaster, as the external situation evolves. But, while rigid, central planning has been shown to be unsuccessful, we should not conclude from that, that the opposite— the adoption of a unplanned, free market system will necessarily produce success. As our models show, there are different possible structures that might merge, and they can have qualitatively different atttributes. It is important therefore to understand what kind of structures are possible, and to have some idea of their relative merits, and what actions or policies might lead to which type of situation. This is the real meaning of ‘strategic’ thinking about systems. 13.2 EQUILIBRIUM, DYNAMICS AND CHANGE A key point about the models described her is that they are about ‘non-equilibrium’ situations. They model change as the result of two different forces: – due to changes in the parameters involved in the interaction, that is exogenous factors such as external trade, or internal ones such as technology change for example. – due to endogenous factors which exist in the difference between the ‘potential’ and ‘actual’ behaviour of people. That is, the difference between latent and revealed preferences, and the dynamics of the latency. This second type of change is one that is crucial to the development of decision support tools, since it can explore the responses of actors to some new policy or action, going beyond the previously observed behaviour. It also presents us with the point at which social enquiry and techniques of elicitation of actors preferences and goals, meet mathematical modelling that is often simply calibrated on existing, statistical data. In our models, social enquiry is used whenever possible to estimate the preferences and utility functions of different types of actor, so that the model can examine the effects of the differences between their existing, observed behaviours, and those which they may well express later. Even today, the ‘operational’ urban models mentioned in the section 12.7, although successful in the sense that they are being used, do not contain dynamics driven by the difference between latent and revealed preferences. Instead, they are coupled ‘equilibrium’ models which do not really have intrinsic time-scales. The argument advanced is that when a policy or action is taken, always an exogenous event such as for example the construction of the M25, by the ideas of rational expectations actors move the system to the ‘new’ equilibrium in some unspecified, but rapid time. In the case of MEPLAN for example, this is chosen to be 5 years, since 1 year would be unbelievable, and 10 would not be interesting for the planners. In reality, such models have no time scale, but have the ingratiating property of presenting an ‘equilibrium before the action’, and an ‘equilib-rium after’. This allows neat calculation of a ‘cost/benefit of the policy or

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action, and so fits neatly the political agenda. This is partly the reason for the success of such models. In reality, of course, the system was not at equilibrium initially, since latent and revealed preferences were certainly in the process of driving changes. The policy, or action on the system provides additional changes to the parameters that figure in the different actors preferences, and this can lead possibly to new behaviours, or perhaps more usually to a continuing dynamic due to new opportunities or threats that the changes have created for the actors. Consider for example the building of the M25 Ring Road around London. In reality, the relocation of employment as a result will be a very long timescale process, since mostly firms re-locate as they grow and change. This means that jobs will shift slowly, and residents will therefore respond, also with some delay, to this changing spatial pattern of employment. In its turn, the shift in the residential pattern of active population will lead services, both to employment and to residents to change also, again with some delay. All this will, in turn change the patterns of traffic flow and of congestion, calling for new policies and interventions, which will all set off their own cascade of complex effects. And all of this will only be the outer, visible signs of what can be observed. The underlying motivation, tastes and goals of people will also be changing with their experiences so that the differences between latent and revealed preferences may still be large, even after much change. In other words, cities and regions do not go ‘to equilibrium’, but continue along paths of non-equilibrium. The discussion of sustainability, and the decision support tools that we build should reflect this better. We probably should not look for a sustainable equilibrium, but for a sustainable trajectory, and possibly a more realistic task would be to look for advance warnings of unsustainable trajectories. 13.3 LAISSER FAIRE AS A POLICY The models described above essentially show us the behaviour of ‘free market’ systems, as they structure in space and time, although obviously, the effects of interventions, planning regulations and other factors can be studied. It shows us that it is ‘simplistic’ to say that the evolution of the systems underlying these models is necessarily ‘progress’ towards the optimal solution. As we have shown, many qualitatively different solutions may be possible, and they will be characterized by different compromises. Because of the insight afforded by these models, therefore, some reflection on the ‘performance’ of market systems might be excused. The multiple linkages of conflicting and complementary interests, together with the creativity that underlies progress of any kind, has meant that attempts to plan and centrally plan societies are not generally considered to have been a success. This is because, they fail to take into account the essentially evolutionary character of development. Except in a theocratic state, a government cannot really consider that it knows already what people should want, and simply schedule the production of these goods. Over recent decades it has become increasingly obvious that economic growth and development is much more concerned with the discovery of new areas of consumption, new products and new technologies. This has been driven very much by the pursuit of profits within market systems, with the development of products for mass consumption,

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and has involved not just the successful production of useful and practical goods, but perhaps more characteristically has led to a remarkable development of relatively frivolous and luxury goods. The consumer society that has resulted is dedicated to a considerable degree to leisure and entertainment, and this is a natural result of the very high levels of productivity that have been attained in agriculture and manufacturing. This result was a natural one for market economies where profits are usually to be found in supplying goods to the wealthy rather than to the poor. Problems of poverty and social deprivation certainly persist in the ‘successful’ western economies, but clearly however, central planning although it may set out with the laudable intention of providing an adequate supply of the necessary goods for basic consumption, it fails to deal with the creative needs of people, and therefore does not lead to a healthy pattern of innovation and change. For this reason, it has been rejected very widely in favour of market based systems. Despite the advantages of such market based systems, however, they do not in themselves solve all the problems, and indeed are the cause of many new ones. For example, it is not clear how ‘objective’ knowledge can be made available for decision making on the part of consumers, and indeed of suppliers, in a system where government abandons all to the market. This promotes the piecemeal nature of investment decisions, which therefore address mainly the short term issues of bottom line shareholder value. Without objective knowledge and proper studies, risk avoidance becomes important, because the investors that make up the market know that they don’t really know what might happen. Sometimes, the ‘risk avoidance’ strategy consists of imitating what others are doing and joining in a speculative boom that is in reality very risky. This leads to the paradox of caution leading to crowd following behaviour, and thence to prodigious failure. The London Docklands scheme with, in particular, the vast office spaces of Canary Wharf is an example of the kind of error that can occur during a boom in office building. It serves to illustrate that the market does not always ‘know’. And not only doesn’t the market always know, in fact nobody does, and even with a model of the kind that we have described above, outcomes are uncertain. However, if a model of the kind described here had been developed, then it would have been possible to estimate the risks much better. How much was the estimate of expected demand for office space? Where was it supposed to be coming from? On what were these estimates based?, For the residential part of the development, who would locate there, and how would this fit into the general development of London ? All these questions would have been thought through in the ‘model building process’. It would have forced the developers to ask themselves all the real questions, and to estimate the uncertainty in their answers. And Canary Wharf is not by any means the only such disaster. There have been a multitude of investments like this, sometimes in office space, sometimes in hotel rooms, booms and slumps that have affected many major cities. They are no different from the phenomena of the ‘pork belly’ cycle that is well known in commodity trading. Speculation and positive feedback are an inherent problem in a ‘free market’ economy. Returning to Canary Wharf in London for a moment, it has to be said that this ‘mistake’ was not just a minor problem for a few investors. Fundamentally, it sucked an enormous amount of investment capital away from other possible ventures, including real business investments in manufacturing and commerce. It resulted in the mistaken building of the largest building in Europe. It offers us though a monument to the fact that markets do not

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always allocate capital successfully or even reasonably. Markets are driven by people, generally wealthy and powerful people, and therefore markets are as blind and as greedy as their participants. They may allocate resources efficiently in the case of very short term goods, with fully foreseeable consequences, this is not the case for large capital expenditures where structural change and multiple responses are encountered. Then, the outcomes and the consequences are not obvious, and only a complex systems model can explore some of the possibilities. To build a model such as those in our previous chapters is relatively inexpensive for the amount of the capital at risk. And by undertaking such initiatives it would increase the knowledge about the risks involved, and about the complex interactions between landuse, transportation and the changing range of employment activities and desired lifestyles. However, in general instead of attempting to build a model and to understand the situation, and estimating the risks involved, what happens instead is that speculators simply imitate each other, and move into rising markets, which then become falling markets. Speculation and speculative cycles are a natural result of decision makers not using ‘fundamentals’ to decide what action to take, but instead using the ‘market’ as an indicator of what to do. But of course if everyone believes that ‘the market knows’, then the question becomes, who is the market, and what do they know? In the absence of an opinion based on an analysis of the problem, and a willingness to take the risk of backing it, it is easier to simply jump into a market that is rising, and be an imitator. In this way, if office development is being pursued by others so that the price of property is rising, then the temptation is to simply join the crowd, and use the expected increase in value of property or office space to justify acquiring or building. The folly of this cannot be observed directly, because of the delay involved in the extra supply coming onto the market. For a time, the rush to provide extra capacity increases the value of the assets involved in its production, but when finally the oversupply becomes clear, then there is a crash in values that can wipe out even the largest companies. Not only does the market not ‘know’, but it almost forces this ignorance on whoever is in the game. It is very difficult for a longer term player to resist the criticism that would occur if he did not play this short term game, since he may be being judged on monthly or yearly performance. Briefly then, this section merely points out some of the limitations on market systems when used as a major force for economic development in cities and regions. What it tells us is that there are simply no simple answers. Neither central planning, nor free markets offer satisfactory solutions to the problems of urban and regional development, because of the multiple constituencies, the complex linkages between factors and the difficulty of defining satisfactory goals for a broad enough section of the community. Simplistic ideologies are flawed, and what is left is the attempt to formulate suitable regulations within which markets can function, and integrated systems to help decision makers better imagine possible outcomes. 13.4 URB ANIZATION AND WORLD TRADE Having spent these many pages describing a dynamic approach to understanding the changing structure of cities, regions and nations, we must now begin to reflect on the

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ultimate meaning of this evolution, and attempt to think through our overall policies and concerns. All the models presented in the previous chapters were about the structuring of space by largely economic interactions. In some ways our models retrace the history of the urbanization process, starting from some simple, self-sufficient farming society, and adding successive waves of economic function, seeing towns and cities form, structure the land around them, and drive the patterns of settlement and of demographic potential. In other words trade and exchange was the great structuring factor of humanity, and in the early models was not concerned with comparative advantages, like mineral resources or good agricultural land, but was about the growth of urban structure and concentration as a result of the formation of synergistic complexes, essentially of complementary activities and ‘know-how’. In these models comparative advantages that are important for agriculture and industry are seen more as additional factors which play a role in the urban structuring process, but which do not necessarily dominate it. What therefore is the effect of linking one society to another as a result of cheaper transportation technology and costs, or of free trade? The classic calculation of economics concerns the advantages of free trade which results from the ability of each to specialize in what it does best—cheapest, and focuses on ‘comparative advantage’. But as we have shown, urban hierarchies can form independently of physical comparative advantage, simply through the clustering processes of cooperation. It is the level of economic activity that dominates the structuring. This is about the concentration or comparative advantage of ‘know how’. If we join two hierarchies of different maturity or development then the result is that the one with the higher levels of function dominates the other. The key issue to understand here is that whereas all the lower levels of activity are in spatial competition with each other, the upper levels are not. Only one side has them, and therefore they reach across the entire system and through the multipliers that they provide, offer advantages to all levels of function in their own system. In other words, the more developed hierarchy incorporates the less developed one, and on the whole outcompetes it. Only the particular activities with real physical comparative advantages can successfully survive the unification of the two systems. This in turn implies that the less developed hierarchy becomes a ‘supplier’ of particular commodities to the more developed one, probably competing with other potential suppliers of the central system. The ‘terms of trade’ decline for the less developed zones, and only migration from there to the growing, dominant urban centres allows them to benefit from the unequal opportunities. In just this way, large dominant cities have always drawn in the people from the surrounding rural areas, and then, with cheaper transport and reduced tariff barriers, their domain of domination has extended outwards to encompass eventually the whole world. But, whereas within nations migration flows could redistribute population and re-define the nation, internationally this has its limits. Although the growth of the United States was very largely built on migratory flows from Europe, today the idea of unlimited migration is unsustainable, since factors concerning the quality of life outweigh those of simple economic costs of production. For developing countries the picture is one in which economic development is driven from without, and the process is not necessarily serving the local people but instead is serving those that dominate it. In essence, the ‘free market’ will always respond best to those who have the money to express their needs as economic demand. It can not respond

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to those who have needs, but no money to express them. Because of this, consumption and demand on the world market is naturally heavily biased towards the needs of the rich developed nations, and therefore the unification of the trading patterns of the world tend to bring the resources of the less developed nations into the game to serve the needs of the richer ones. Fertile land will tend therefore to be used to grow ‘cash crops’ for export, rather than to feed the local population. Fish stocks that have always been exploited locally (and sustainably) will be exported to provide hard currency, and mineral wealth will be stripped out in competition with other suppliers, thus forcing down the prices obtained. Suppliers cartels are considered to infringe the rules of ‘free trade’ and exchange controls are frowned upon. But if the system is unfair, why do developing countries choose to sell off their natural resources and their natural endowments? The answer is that the decision makers, and perhaps the people, seek what they see as ‘modern living’. The information flows that impinge upon the inhabitants of ‘less’ developed lands tell them that they are not living successfully. They rapidly come to believe that they, like us, need radios, televisions, air conditioners, running shoes, Mercedes, and a modern lifestyle. It is this ‘cultural’ change that drives the economic and ecological processes of development that follow. And herein lies the problem. Traditional lifestyles have evolved over centuries to be (at least roughly) in tune with their natural resources, climate and the environmental conditions of the region. Under apparent economic inefficiencies they often hide clever adaptations to the environment and particularly to the statistical distribution of extreme circumstances of various kinds. They have proved to be sustainable over many years. Modern economies, on the other hand, have abandoned traditional subsistence farming, as urbanization has continued its course. Instead, we have adopted a highly successful version of ‘slash and burn’, moving ever outwards to exploit further and further afield. The spread of urbanisation therefore corresponds at present to allowing the short term criteria to replace the long in the human activities of a region. In this way, sustainable development has often been a clear contradiction in terms, and indeed, the whole idea of bringing the free market forces of world trade onto developing countries seems equally likely to produce, the growth of non-sustainable activities based on the ‘mining’ of natural resources. If sustainability is the measure, then who is less developed? Modern economies are essentially identified with the urban lifestyle, and with a process of urbanization which has continually transferred power from rural areas to urban ones, and to decision makers who are increasingly remote from the natural world. The growing urban centres have been becoming more and more dependent on the nonsustainable exploitation of natural resources, a process that is presented as economic development. While there may be problems associated with restrictions on free trade, we should not ignore the other set of problems that come with its acceptance. For example, it will prove to be extremely difficult to maintain environmental and humane social legislation in a competitive world in which tariff barriers are not allowed. The ability and indeed the encouragement of capital to flow across international borders means that it will flow where it is most advantageous and therefore that attempts at enforcing any long term policies, at the expense of short term profits, will generally lead simply to the money flowing elsewhere.

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Just as the complexity of urban development within a region is not necessarily best served by any simple recipe such as for example unrestrained free enterprise, so, on the international scale the same is true. We need to attempt to understand how the atmospheres, the oceans, the great river basins and the land-use patterns all fit together as a complex, evolved system, and how it might evolve under different scenarios of development. 13.5 CONCLUSIONS Some of the work that has been presented here dates from over 10 years ago. However, it seems that despite this, it still remains ‘pioneering’ in that it attempts to deal with the problem of structural change in complex systems. These models should be seen as strategic tools for reflection concerning the medium and longer term outcomes of decision or indecision. They provide a qualitative exploration of the kinds of structures that might emerge, and which it would perhaps be possible to attain. They are not necessarily in conflict with the operational models that are in use today, models which may seem to be much more detailed and much better calibrated than these. However, these operational models only extrapolate present structure and existing trends, and therefore give a false sense of detailed prediction. In reality they may well turn out to be qualitatively wrong if structural changes occur. In reality, the kinds of models described here should be used to make an exploration of the strategic possibilities potentially open to the system, and then, perhaps the detailed, operational models could be used in planning the actual actions that need to be taken, having already established the kind of outcome that is needed in the longer term. We find then a complementary role for the different models that have been developed, one strategic and the other for detailed tactical planning. The difficult point, however, that we will have to accept one day, is that it is probably impossible to correctly anticipate the nature and the consequences of structural changes that may occur in a system. In the long run, they will occur. It is no good the Minister, the bureaucrat or the business man insisting that he must know what will happen and turning to scientists and modellers who promise they can predict. It is similar to a prediction that a coin will fall down ‘heads’, because it did before, while a prediction that it will fall down either ‘heads’ or ‘tails’ is actually more useful and correct. We cannot really predict, but we can explore possible futures, and can help to imagine some of the properties of these. We can possibly assign some level of probability to different paths into the future, but nevertheless we must also admit that new situations may well open new dimensions of behaviour and experience, so that we can never obtain a complete picture of a particular path (thank heavens!). We can only get some idea, and we can only do our best to choose the best path, but in reality, we can never vanquish uncertainty about the future (but how awful if we could!). Because we recognize this, we therefore must urge that policies should reflect this uncertainty and always allow diversity, and redundancy in the system to allow for future adaptations to the emerging reality. Maintaining diverse knowledge, multiple technologies and making plans which are seemingly sub-optimal in a strict economic sense are therefore part of the message that comes out of this work.

Conclusions

291

This discussion of self-organization in complex systems hopefully teaches us humility. Science has revealed its own limitations, and this too is an achievement. Knowing that we cannot know is an important step on the road to wisdom, and today we are far from the earlier promises of prediction and objectivity that science was thought to bring. Since we must nevertheless make decisions and take action, then the kind of models developed above can help us, since they take into account some of the linkages in the system, and help us to avoid some of the errors, and evolutionary ‘dead-ends’ that otherwise we might not. However, the overriding lesson that we may take from this work is that diversity, flexibility and pluralism are in general to be encouraged, and that plans which might seriously reduce these, should be examined and tested very thoroughly before being adopted. Survival is more valuable than efficiency, and more general since it does not pose the question ‘efficient at doing what’, and the ideas concerning self-organization certainly help to understand better the evolutionary process. The work presented here is therefore a step towards a better understanding of ‘sustainability’, and perhaps marks a preliminary foray into a new and exciting area of scientific research, which will lead eventually to greater wisdom and long term success in dealing with the human predicament.

APPENDIX

APPENDIX I The equations

The values of the parameters

Coefficient of transport per unit distance Φ: For series 1, ‘good transportation’: Φ(1)=1, Φ(2)=0.15, Φ(3)=0.1, Φ(4)=0.01 For series 2, ‘bad transportation’: Φ(1)=1, Φ(2)=0.2, Φ(3)=0.15, Φ(4)=0.1

Appendix

294

APPENDIX II Equations Describing the Evoluation of the System The different types of equations expressing the evolution of these variables in each point of the system are a)

with

this equation describes the evolution of the employment linked to an external demand which we call the ‘industry’ (S1) and the ‘finance’ sectors (S2), L=1, 2 respectively. b)

with

this equation describes the evolution of the employment related to a local demand which we call the ‘ubiquitous’ (S3) and ‘specialized’ services (S4), L=3, 4 respectively. c)

with

this equation describes the evolution of the two types of population considered, which we have called ‘blue collar’ residents (x1) and ‘white collar’ residents (x2). APPENDIX III

Appendix

295

Definition of Parameters The meaning of the ‘parameters in these equations is given as follows: The εL, εu and ηk characterize the dynamic response of employment L and the population k to external environment. AJL and AJJ′L, represent the attractivity of the economic function at the point J. DL is the external demand for the function L that in the following simulations we have kept constant. ρL measures the cooperativity between the different functions. nµL is the production cost which contains the input cost for the industrial sector. 0L is the transportation cost which can be a combination of time and money. The αJ parameter represents the access of the point J to the communication axes and in the following simulation it is more especially the access to the canal/railway which is very important for heavy industry. The

parameter measures the intensity of the crowding supported by the function L,

the crowding of a point J takes into account the population employments

and all the

at the point J.

is the quantity of function L demanded per individual at unit price. eL is the elasticity of the service L. The parameter sector L′.

is related to the percentage of people of the type k working in the

is the residential attractivity of the point J viewed by someone who is employed at the point J′. It contains the parameters σk which expresses the affinity between members of a population of the same type. vk represent the sensitivity to the crowding perceived by the population k. The parameter bk is related to the ease with which an individual of the type k may commute daily the distance work at the point J.

which is the distance between his residence located at J′ and his

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INDEX

active population, 87 actors, 22 adaptability, 17 agglomeration economies, 42 aquifers, 221 Argolid, 221 attractivities, 227 attractivity, 44 attractor basins, 17 attributes, 20 average errors, 117 basic employment, 88 Belousov-Zhabotinsky reaction, 11 bifurcation, 17, 19, 56 bifurcation tree, 18 bifurcations, 15, 22, 198 blue collar, 180 breaking symmetries, 16 broken symmetries, 21 Brusselator, 9, 12, 13 Brussels, 191, 201 calibration, 199 carrying capacity, 30, 43 carrying-capacity, 86 catastrophes, 15 CBD, 182, 192, 211 cellular automota, 235 central core decay, 42 central place, 45 central place systems, 60 Central Place theory, 28, 29 Central Places, 27, 81 central urbanization, 48 Ceteris Paribus, 237 chance, 16

Index Chemical Kinetics, 13, 16 chemical reactions, 11 citrus fruits, 223 classical physics, 16 classification, 20, 227 coherent behaviour, 15 commuter traffic, 66 comparative advantages, 81, 84 Complex systems, 9, 17 convection cells, 10 cost functions, 56 cost of transport, 32 costs\ and \benefits, 22 counter urbanization, 42 creative intelligence, 199 cross-catalysis, 12 cultural changes, 245 cyclic attractor, 6 Dakar, 135 decentralization, 179 decision making, 227 deforestation, 135 Desertification, 171 Developers, 208 Diamadam, 134 disaster, 211 disposable income, 148 dissipative structure, 10 dissipative structures, 9 distribution of city size, 27 diversity, 255 DNA, 20 economic control, 83 Economic Convergence, 81 economic divergence, 82 economic functions, 30 economies of scale, 33 eco-tourism, 142, 170 elasticity of demand, 31, 44 emergence, 70 emergent properties, 18 energy consumption, 65 entropy, 197 entropy maximisation, 22 equilibrium, 16, 21, 249 erosion, 171 events, 16 evolution, 9 evolutionary process, 17

305

Index explanation, 18 externalities, 42 firewood, 171 fluctuations, 16, 179, 194 fluctuations of density, 13 folding process, 20 fractal filling, 236 free market, 250 free markets, 29 free trade, 60, 252 fudge factors, 94 functionalflows, 106 Geographic Information System, 163 global optimization, 29 groundnuts, 136 growth/decline patterns, 72 Harmattan, 133 heartland-hinterland, 81 heavy industry, 192 hierarchy, 9, 232 high-level tertiary, 192 hinterland, 35 historical accident, 18 homo economicus, 2 hydrodynamical equations, 10 hydrology, 134 induction rate, 89 industrial satellite, 182 infrastructure, 179 innovation, 34 innovations, 127 input-output table, 118 intersectorial demand, 148 intervention, 56 invariance, 21 invisible hand, 188 irrigated production, 222 Lac de Guiers, 135 Laisser Faire, 250 land-use planning, 201 latent and revealed preferences, 249 lateral thinking, 56 learning, 233 local industry, 192 local instabilities, 16

306

Index lock-in, 40 Logistic growth, 30 logistics, 107 long range, 45 low-level tertiary, 192 Manantali dam, 134 Master Equation, 6, 16 mathematics of chaos, 15 maximum entropy, 16 mean haul distance, 61 mental map, 228 metastability, 9 Metro, 210 microscopic diversity, 7 migration, 115, 138, 145 migration flows, 80 mobility, 145, 179 Modified logistic equation, 31 molecular disorder, 10 Mousson, 133 multi-criteria analysis, 57 multiple equilibria, 21 multiplier effects, 83 myths, 21 natural advantages, 82 natural increase, 87, 90 natural laws, 16 negative feedback, 42 new attributes, 227 Newton, 1 nitrate, 220 nitrates, 132, 135 noise, 199 non-actives, 87 nonlinear interaction, 201 non-linear mechanism, 10 nucleation, 16 of “intervening opportunities, 33 open systems, 10, 17 optimization, 215 options, 219 order out of chaos, 11 Origami, 18, 198, 208 over grazing, 171 overgrazing, 135 parameters, 6

307

Index passenger-miles, 66 pesticides, 132 phenomenology, 18 phosphate, 220 point attractor, 6 population dynamics, 16 potential clients, 44 potential demand, 110, 127 potential employment, 89 potential market, 110 preferences, 21, 22 rain erosion, 135 rank-size rule, 27, 38 rationality, 194 reductionism, 18 reflexivity, 176 relative attractivity, 32 residential suburbs, 41 Resilience, 15, 17 retail structure, 209 Rhone Basin, 220 risk, 251 salinization, 222 Salt, 135 scientific explanation, 18 self-organization, 9, 15, 16, 103, 187 self-organizing, 56 settlement pattern, 81 settlement patterns, 26 shopping centre, 182 short range functions, 45 social welfare, 56 soils, 133 spatial instabilities, 11 spatial organization, 10 spatial syntax, 235 speculation, 188, 251 spiral waves, 15 Stability, 15 Stability, 9 staples, 82 statistical average, 10 strange attractor, 6 subjective views, 245 sub-optimal structure, 40 subsidiarity, 248 suburban growth, 48 sustainability, 219 Sustainable development, 131, 170

308

Index symmetry breaking, 22, 187 system, 1 System Dynamics, 5, 237 tertiary activity, 89 tertiary employment per head, 90 the “urban multiplier, 33 the lines of consumer indifference, 33 the transportation network, 59 thermodynamic equilibrium, 10 threshold, 16 trade barriers, 60 trade-offs, 57 traffic flow patterns, 211, 232 traits, 20 Transims traffic model, 235 transportation, 158 transportation costs, 50 Transportation Network, 160 transportation networks, 202 unit of selection, 20 United States, 80 urban hierarchies, 29, 60 urban hierarchy, 26, 76 urban multiplier, 34, 40, 42 urban sprawl, 42 urbanization, 254 utility, 21 utility function, 111 utility functions, 230 value judgement, 18 water supply, 152 water treatment, 220 white collar, 180 Wind erosion, 135 Zipf’s law, 27, 38

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