Bioassays with Arthropods,

 

2331_C000.fm  Page i  Thursday, May 10, 2007  11:19 AM

Bioassays with Arthropods Second Edition

 

2331_C000.fm  Page ii  Thursday, May 10, 2007  11:19 AM

 

2331_C000.fm  Page iii  Thursday, May 10, 2007  11:19 AM

Bioassays with Arthropods Second Edition Jacqueline L. Robertson Robert M. Russell Haiganoush K. Preisler N.E. Savin

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

 

2331_C000.fm  Page iv  Thursday, May 10, 2007  11:19 AM

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-0-8493-2331-7 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Bioassays with arthropods / Jacqueline L. Robertson ... [et al.]. -- 2nd ed. p. cm. Rev. ed. of: Pesticide bioassays with arthropods / Jacqueline L. Robertson and Haiganoush K. Preisler. Includes bibliographical references and index. ISBN-13: 978-0-8493-2331-7 (hardcover : alk. paper) ISBN-10: 0-8493-2331-2 (hardcover : alk. paper) 1. Pesticides--Environmental aspects--Measurement. 2. Arthropoda--Effect of pesticides on. 3. Biological assay. I. Robertson, Jacqueline L. II. Robertson, Jacqueline L. Pesticide bioassays with arthropods. III. Title. QH545.P4R478 2007 571.9’515--dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

2007013142

  

 

2331_C000.fm  Page v  Thursday, May 10, 2007  11:19 AM

Dedication Dedication for the second edition: This edition is dedicated to David J. Finney of the University of Edinburgh, whose work is  the basis of all that we  have done.

Dedication from the first edition: To Lucille Boelter (1921–1988), my technician and friend: she did so much of my work that I had time to think, and to Johnnie Nicholas (1915–2000), whose moral support meant so much to me. —Jacqueline L. Robertson

 

2331_C000.fm  Page vi  Thursday, May 10, 2007  11:19 AM

 

2331_C000.fm  Page vii  Thursday, May 10, 2007  11:19 AM

Table of Contents Preface to the Second Edition........................................................................... xiii Authors..................................................................................................................xxi Chapter 1 Introduction ......................................................................................1 References.................................................................................................................8 Chapter 2 Quantal Response Bioassays....................................................... 11 I. Types of Quantal Response Bioassays...........................................................12 II. Experimental Design of Bioassays ................................................................13 A. Randomization ........................................................................................14 B. Treatments ................................................................................................14 C. Controls ....................................................................................................15 D. Replication ...............................................................................................16 E. Order of Treatments within a Replication ..........................................17 III. Computer Programs.......................................................................................18 References...............................................................................................................18 Chapter 3 Binary Quantal Response with One Explanatory Variable ..........................................................................................................21 I. Terminology and General Statistical Model .................................................22 II. Statistical Methods...........................................................................................23 A. Probit or Logit Regression ....................................................................23 1. Goodness of Fit ...........................................................................24 2. Lethal Dose Ratios ......................................................................26 B. Hypotheses Tests .....................................................................................28 1. Regression Lines..........................................................................28 2. Point estimates ............................................................................29 3. Groups of Lines with Equal Response....................................31 C. Alternatives to Probit and Logit Analysis ..........................................31 References...............................................................................................................32 Chapter 4 Binary Quantal Response: Data Analyses................................35 I. PoloPlus ...............................................................................................................35 A. Data...........................................................................................................36 B. Choice Screens and Program Options .................................................38 vii

 

2331_C000.fm  Page viii  Thursday, May 10, 2007  11:19 AM

viii

Table of Contents

C. Display Results........................................................................................39 1. Options .........................................................................................39 2. Parameters....................................................................................40 3. Individual Regressions...............................................................40 4. Hypotheses Tests.........................................................................44 5. Lethal Dose Ratios ......................................................................44 D. Display Summary (summary.txt screen) ............................................45 E. Plot ............................................................................................................46 F. Conclusions...............................................................................................51 II. SAS .....................................................................................................................51 III. R and S-PLUS..................................................................................................52 References...............................................................................................................54 Chapter 5 Binary Quantal Response: Dose Number, Dose Selection, and Sample Size........................................................................55 I. PoloDose ...............................................................................................................57 II. Basic Binary Bioassays ....................................................................................58 III. Specialized Binary Bioassays........................................................................62 IV. Practical Considerations ................................................................................66 A. Basic Bioassays........................................................................................66 B. Specialized Bioassays..............................................................................67 V. Reality Checklist for Bioassays ......................................................................67 References...............................................................................................................68 Chapter 6 Natural Variation in Response....................................................71 I. Definition ............................................................................................................72 II. Statistical Boundaries of Natural Variation.................................................72 III. Levels of Variation..........................................................................................72 A. Sibling Groups ........................................................................................72 B. Cohorts within a Single Generation.....................................................73 C. Developmental Stage..............................................................................74 References...............................................................................................................75 Chapter 7 Quarantine Statistics .....................................................................77 I. Tolerance Distributions in Quarantine Security...........................................78 A. Laboratory Bioassays to Estimate the Q9 in a Confirmatory Test ...........................................................................79 1. Differences in Estimates Depending on Tolerance Distribution .....................................................79 2. General Formula for Selection of Dose in a Confirmatory Test Based on Laboratory Bioassays .............................80 3. Dose Placement and Sample Size Requirements for Estimation of a Q9 in Bioassays .....................................80 4. Varietal Differences.....................................................................81 B. Confirmatory Tests..................................................................................83 II. Ecological Approaches to Quarantine Security: Risk ................................84

 

2331_C000.fm  Page ix  Thursday, May 10, 2007  11:19 AM

Table of Contents

ix

A. The Alternative Efficacy Approach for Species on Poor Hosts ......84 B. Risk for Preferred Hosts and Heavy Infestations: Systems Approach...........................................................................85 III. Conclusions .....................................................................................................85 References...............................................................................................................86 Chapter 8 Statistical Analyses of Data from Bioassays with Microbial Products.......................................................................................89 I. Biological Units and Standards.......................................................................90 II. A Revised Definition of Relative Potency ...................................................90 III. Effects of Natural Variation on Product Quality ......................................91 IV. Conclusions......................................................................................................96 References...............................................................................................................96 Chapter 9 Pesticide Resistance.......................................................................99 I. Resistance Defined ..........................................................................................100 II. Natural Variation versus Resistance...........................................................101 III. Use of Bioassays to Separate Populations and Strains ..........................101 A. Population Bioassays ...........................................................................101 B. Response Ratios.....................................................................................102 C. Selection of a Discriminating Dose....................................................102 IV. Statistical Models of Modes of Resistance Inheritance ..........................103 A. Standard Method of Analysis with Bioassay Data .........................103 1. Degree of Dominance...............................................................104 2. Hypothesis Testing ...................................................................104 B. Inferences Using the Standard Method.............................................105 1. Mode of Inheritance .................................................................105 2. Binomial Distribution...............................................................106 3. Both Mode of Inheritance and Binomial Distribution........106 4. Other Causes for Bad Fit .........................................................107 C. Examples ................................................................................................108 1. Dose-Response Bioassays ........................................................108 2. Dose-Mortality Lines ................................................................108 3. Estimation of Overdispersion .................................................109 4. Mode of Inheritance of Cyhexatin Resistance ..................... 110 5. Mode of Inheritance of Propargite Resistance ..................... 112 V. Host-Insect Interaction and the Expression of Resistance ...................... 112 References............................................................................................................. 112 Chapter 10 Mixtures ....................................................................................... 117 I. Independent, Uncorrelated Joint Action of Pesticide Mixtures .............. 118 A. A Statistical Model ............................................................................... 119 B. A Test of Hypothesis of Independent Joint Action ......................... 119 C. PoloMix....................................................................................................120 1. Data Input Files.........................................................................120 2. Running PoloMix .......................................................................121

 

2331_C000.fm  Page x  Thursday, May 10, 2007  11:19 AM

x

Table of Contents

3. Program Output ........................................................................121 II. Similar (Additive) Joint Action....................................................................122 III. Other Theoretical Hypotheses of Joint Action of Pesticides .................123 IV. Synergists .......................................................................................................124 V. Conclusions .....................................................................................................125 References.............................................................................................................126 Chapter 11 Time as a Variable......................................................................129 I. Purposes of Studies Involving Time ............................................................129 II. Sampling Designs ..........................................................................................130 A. Alternatives............................................................................................130 B. General Statistical Models ...................................................................130 III. Analysis of Independent Time-Mortality Data........................................131 A. Experimental Design............................................................................131 B. Limitations and Constraints ................................................................132 IV. Analysis of Serial Time-Mortality Data.....................................................133 A. Experimental Design............................................................................133 B. Statistical Methods ................................................................................134 C. Estimation ..............................................................................................135 1. Estimation of Response Probabilities ....................................135 2. Estimation of Lethal Doses over Time ..................................136 3. Example ......................................................................................137 V. Conclusions .....................................................................................................144 References.............................................................................................................144 Chapter 12 Binary Quantal Response with Multiple Explanatory Variables ...............................................................................147 I. Early Examples and Inefficient Alternatives ..............................................147 II. A General Statistical Model .........................................................................148 III. Types of Variables in Multiple Regression Models ................................149 IV. Computer Programs .....................................................................................149 V. Multiple Probit Analysis: An Example from PoloEncore .........................150 A. A Statistical Model ...............................................................................151 B. Hypothesis Tests....................................................................................151 C. Data Analysis with PoloEncore ............................................................152 VI. Multiple Logit Analysis: Sample of Analysis with GLIM.....................155 A. Statistical Model....................................................................................156 B. Hypothesis Tests....................................................................................157 C. Search for the Best-Fitting Dose-Mortality Model ..........................157 D. An Example: Acephate ........................................................................158 1. Significance of Average Body Weight....................................158 2. Parallelism of the Logit Lines .................................................158 3. Best-Fitting Logit Line..............................................................158 VII. Conclusions ..................................................................................................161 References.............................................................................................................161

 

2331_C000.fm  Page xi  Thursday, May 10, 2007  11:19 AM

Table of Contents

xi

Chapter 13 Multiple Explanatory Variables: Body Weight....................163 I. Effects of Erroneous Assumptions about Body Weight............................164 II. Testing the Hypothesis of Proportional Response ...................................166 III. When Body Weight Is a Significant Independent Variable ...................169 IV. Standardized Bioassay Techniques Involving Weight............................175 V. Conclusions .....................................................................................................176 References.............................................................................................................176 Chapter 14 Polytomous (Multinomial) Quantal Response....................179 I. Example ............................................................................................................180 II. The Multinomial Logit Model .....................................................................181 A. Statistical Model....................................................................................182 B. Estimation of Parameters.....................................................................182 C. Data Analysis.........................................................................................183 III. Conclusions ...................................................................................................185 References.............................................................................................................186 Chapter 15 Improving Prediction Based on Dose-Response Bioassays ......................................................................................................187 References.............................................................................................................190 Index .....................................................................................................................193

 

2331_C000.fm  Page xii  Thursday, May 10, 2007  11:19 AM

 

2331_C000.fm  Page xiii  Thursday, May 10, 2007  11:19 AM

Preface to the Second Edition Jacqueline L. Robertson Compared with the first edition, this second edition has been much easier to write because I actually resurrected the original version of the first edition. As we finished that draft, Haiganoush K. Preisler and I had become so used to our cast of characters that we were laughing constantly—and about statistics, no less! Our editor then threatened not to publish the book at all unless we took out the escapades of Dr. Paula Maven and her pals because a statistical reviewer objected to their less-than-serious nature. This was, after all, science! And it must be presented as such, so out went most of the characters (although I was able to sneak in a few zingers). Robertson’s First Law states that scientific writing need not be dry, dull, and dreary. In journal publications, stylistic requirements always force us to write in the same way lest our papers be rejected. In a textbook, however, anything that enhances readability should keep readers interested in the subject and we hope that, as a result, they will learn more. So, in this edition, each chapter begins with our characters involved in some silly situation. Within what you will discover to be a readable framework are statistical equations with clear explanations of their meanings. One of my favorite authors, Rex Stout, once said, “If I’m not having fun writing a book no one’s going to have fun reading it.”1 We hope that you, the reader, will get a few chuckles as our heroine, Dr. Maven, becomes an expert in the subject of quantal response bioassays. Any resemblance between Dr. Maven and Dr. Paula Levin Mitchell (Winthrop University, Rock Hill, South Carolina) is absolutely intentional. After all, it is Paula’s fault that I even know the definition of the word maven. This book should have been called (Pesticide) Bioassays with Arthropods even in its first iteration. Twelve years ago, many quantal response (doseresponse) experiments with arthropods involved pesticides, so the word snuck into the original title. However, other types of chemicals besides toxicants, and many physical factors, can be tested in the same types of doseresponse experiments. Now, the word pesticide will probably mean that many readers who can use the information in this volume for their experiments with pharmaceuticals, botanicals, and physical processes might not read it. Regardless of one’s specialty, here is a universal warning: Be advised, Gentle xiii

 

2331_C000.fm  Page xiv  Thursday, May 10, 2007  11:19 AM

xiv

Preface to the Second Edition

Reader, that this is not Miss Manner’s Guide to Excruciatingly Correct Statistics.2 We do not present definitions of common statistical terms and methods such as standard error, standard deviation, normal distribution or linear regression (to name just a few). For such definitions, we recommend any standard statistical textbook such as Elementary Statistics by Wonnacott and Wonnacott,3 or Essential Statistics by Rees.4 Statistics and Experimental Design for Toxicologists, by Gad,5 provides many useful statistical definitions in the context of vertebrate toxicology. Our intended audience consists of biologists who have had an introductory course in statistics and some course work in environmental science, toxicology, or integrated pest management. I have now spent more than 30 years exploring the details of experimental design of dose-response bioassays and requisite statistical methods for data analyses, especially probit analysis. Much of my research has concerned pesticides. How ironic! I first became interested in the effects of pesticides when I had no intention of becoming an entomologist, let alone an entomologist whose research involved pesticide testing. When I was in high school, Silent Spring6 affected me so deeply that I was convinced that the people who tested pesticides willfully killed fish, birds, wildlife, and all the other organisms that author Rachel Carson described. In my mind, these scientists were villains and stupid ones at that. Surely, pesticide testing was so simple that they could have prevented environmental disaster. The last paragraph of Silent Spring made me want to do anything besides being an applied entomologist: “The ‘control of nature‘ is a phrase conceived in arrogance, born of the Neanderthal age of biology and philosophy, when it was supposed that nature exists for the convenience of man. The concepts and practices of applied entomology for most part date from the Stone Age of science. It is our alarming misfortune that so primitive a science has armed itself with the most modern and terrible weapons, and that in turning them against the insects it has also turned them against the earth.” Despite my graduate training as an insect neuroendocrinologist, I took a permanent job as an applied entomologist with the USDA Forest Service. I was now one of them.7 I quickly learned that pesticide testing was not as simple as I had once thought. Yes, the methods themselves seemed standard: all I had to do was find the procedure in one of the classic references, do the experiment, and publish the results in the Journal of Economic Entomology. This approach could easily have become a mindless (and endless) exercise in data collection, I decided, unless I tried to make a contribution to science rather than simply to publish a long list of papers in a very short time. In my own niche in the laboratory, I pursued a personal mission to protect conifers from the ravages of defoliators such as western spruce budworm (Choristoneura occidentialis Freeman) and Douglas fir tussock moth (Orgyia pseudotsugata [McDunnough]) with chemicals safer than DDT. Toxicity compared with DDT was one issue, but Robert van den Bosch was my hero: if a pesticide were to be used, it had to be more selective against the target species compared with other organisms in the forest ecosystem.8 My

 

 

2331_C000.fm  Page xv  Thursday, May 10, 2007  11:19 AM

Preface to the Second Edition

xv

experiments became increasingly sophisticated, but my data analyses remained ridiculously primitive. For the next few years, I simply plotted results on strange-looking paper called probit paper. A few computer programs9,10 were available when journal editors began to demand “real“ statistical analyses, but I never cared what the program did as long as it produced an LD50 and confidence limits. Somewhere along the way, I began to read about probit analysis and statistics in general so that I would have a vague idea about what the numbers meant and whether the computer program was producing numbers that made sense. David J. Finney’s Probit Analysis11 was my guide, even though the details were far beyond my comprehension. Eventually I produced two huge data sets that needed special statistical methods to determine whether dose-responses of species and populations were significantly (not just numerically) different. I asked William O’Regan, then head of our research station’s statistics group, for help. Bill had a graduate student, N. E. (Gene) Savin, come to talk with me. Gene bounced ideas off of walls, furniture, and me until he finally understood that I was asking a key question: How do you test whether two or more lines are significantly different from one another? We decided that two hypotheses had to be tested—the hypothesis of equal slopes (in which case the lines would be parallel), and the hypothesis of equal slopes plus equal intercepts (in which case the lines would be statistically the same). Gene and I thought that we should begin with a detailed examination of the inner machinations of the available computer programs for probit analysis, compared with our “bible according to Finney.11” We asked Robert Russell for help. Thus began one of the funniest and most successful collaborations to ever occur without administrative approval. The framework of federal research tends to be rigid, and the three of us had absolutely no idea how long our work would take. My solution was quite simple: say nothing until we were finished. For the next two summers, Gene spewed out the statistics, Robert programmed like crazy after Gene left the room, and I interpreted our results biologically. My other responsibility was camouflage; I was totally and purposefully vague in any discussions of probit analysis with my supervisor. Meanwhile, the noise level from Robert’s office drove everyone crazy. When Gene and I moved to my laboratory, my faithful technician Lucille Boelter threatened to banish us to the alley outside the autoclave room. (Or perhaps she wanted to throw us into the autoclave with the rest of the hot air.) Finally, we finished. The result was POLO,12 a probit- or logit- (you could choose the model) analysis program that ran on a UNIVAC 1108 mainframe computer that was like something out of the film Desk Set.13 Every detail of the probit program, down to the last digit, matched the output of David Finney’s program BLISS.14 However, we included automatic tests of the hypotheses of parallelism and equality, and the program itself reflected the latest developments in both statistics and computer sciences.15 POLO led to POLO-PC,16 which was specifically designed for personal computers. We recently released the

 

2331_C000.fm  Page xvi  Thursday, May 10, 2007  11:19 AM

xvi

Preface to the Second Edition

Microsoft Windows–compatible version, PoloPlus.17 In PoloPlus, we have omitted portions of the original output which provided extraneous and often confusing details. We have also added new features specifically developed for use in toxicology and pharmacology. Gene, Robert, and I next tackled the question of the significance of body weight as a variable in my bioassays. As usual, I had carloads of data with no means to analyze whether an explanatory variable besides dose was significant. These data dated back to the first bioassay I ever performed; I had been told to adjust dose in proportion to body weight, and that is exactly what I continued to do for years. When I began to get a sinking feeling that I had made an assumption that might be very wrong, I asked Gene and Robert for help. As with POLO, Gene decided what we needed to do statistically and Robert dissected the available computer programs. And just as before, none of the available computer programs suited our needs. When Gene returned from Cambridge University for yet another summer, we developed POLO2.18 We have recently released PoloEncore,19 a vastly improved Windows version of the original DOS multivariate probit/logit program. As useful as multivariate probit analysis is, I have noticed that few entomologists have ever examined their assumptions about body weight or other explanatory variables besides dose. We hope that PoloEncore19 will help remedy this situation because it is user friendly. Meanwhile, back in the lab, data from new experiments with different types of variables began to accumulate. Lucille, Richard (Not-the-Fugitive20) Kimball and I tested juvenile hormone analogues and chitin synthesis inhibitors. Each experiment included multiple explanatory variables such as dose and sex, and multiple response variables that appeared at various stages after the insects were exposed to the chemical. Robert had retired that fall, but Gene returned for one final summer to introduce me to a new polytomous logit program21 for use with the insect growth regulator data. The cult of the polytomous logits was born that year when my pal and coeditor of the Journal of Economic Entomology, Paula Levin Mitchell, and I were discussing the moniker of my newfound statistical miracle method. Gene left for the University of Iowa, and our formal collaboration ended—until the preparation of this new edition. During the preparation of the first edition, members of my research project—Haiganoush K. Preisler, as well as Ann Christensen, Lula Greene, Perlina Magno, and Margaret Walker—carried an extra burden while I wrote. They all knew what they had to do for our project, they did their work without bothering me with unnecessary questions, and they helped save my time by assuming extra work that I would ordinarily have done. I am still grateful to each of them. Friends in New Zealand forced me to organize my thoughts about much of the subject matter in this book for the first time when they invited me to their wonderful country to present a series of workshops about bioassays. David R. Penman and D. M. (Max) Suckling have my special thanks for that invitation. Another dear friend, Susan P. Worner (Lincoln University, Canterbury, New Zealand), got me to think

 

2331_C000.fm  Page xvii  Thursday, May 10, 2007  11:19 AM

Preface to the Second Edition

xvii

about many things including the use of ecological methods to make pesticide bioassays more predictive. This new direction may, I think, result in attainment of a goal that Rachel Carson (and Rosemary F. Strout, my biology teacher at Lansdowne-Aldan High School in Lansdowne, Pennsylvania) instilled in my mind long ago. Laughing hysterically all the while, Sue Worner and I simulated bioassays with water pistols, but only after Graeme J. Worner had confiscated the necessary implements from his students at Christ’s College in Christchurch, New Zealand. Those well-used water pistols passed undetected through airport security at Auckland, Christchurch, and Los Angeles several times in the days before September 11, 2001. I had an explanation ready just in case, but who would have believed it? For the use of the water pistols and for their enduring friendship, Sue and G. J. have my thanks. Two wonderful friends, my coeditor of the Journal of Economic Entomology, Paula Levin Mitchell, and Carl W. Schaefer (coeditor of the Annals of the Entomological Society of America) made the trauma of writing the first edition tolerable with their encouragement and reassurances that I would survive. Carl probably suggested that “She who must be obeyed”22 (namely, me) prepare a second edition of this book in a conversation with John Sulzyki, our present editor at CRC Press. As the first edition progressed, several friends provided me with invaluable comments and suggestions. Once again, I thank Kate Kelly, former managing editor at the Entomological Society of America (ESA); Elizabeth A. Mitchell, copyeditor at the ESA; Paula Levin Mitchell; Carl Schaefer; and Sue Worner for taking the time to read, review, and suggest changes in several drafts. Beth, Paula, Carl, and Sue have taken their valuable time once again to review parts of this second edition. All of my life, my best friend and most valued critic was my younger sister, Marilyn Larson, who died of ovarian cancer on October 24, 2001. No one will ever surpass her acid wit and critical view of the uses and misuses of the English language, especially in scientific writing, but I enlisted our youngest sister Carolyn Troiano as a reviewer for this edition. Every author needs a good editor, and who better to ask for a review than James E. Throne (USDA, ARS)? Jim upheld the statistical requirements for manuscripts concerning quantal response bioassays in the Journal of Economic Entomology. These standards were the first of their kind in any biological journal and were instituted during my 15-yearlong tenure as editor and coeditor. I deeply appreciate his efforts to maintain the quality of the journal that Paula and I worked so very hard to change. Robert Miller (USDA, ARS) also reviewed portions of this manuscript and provided many thoughtful suggestions. Now a word about my coauthors. Haiganoush joined my research group in 1985, and we have worked together since. Over the years she has become accustomed to my lapses into horse-show vernacular when we are writing. I have worked with Robert and Gene for a very, very long time—in fact, for more years than any of us can believe. Robert quietly develops perfect computer programs with the user always in mind. He also has the grace to

  

2331_C000.fm  Page xviii  Thursday, May 10, 2007  11:19 AM

xviii

Preface to the Second Edition

laugh at my stupid mishaps, such as frying the hard drive of my PC without backing anything up. Overall, working with Gene is an experience driven by his infectious enthusiasm and maniacal energy. He listened to me every time I screamed for help early in my Forest Service career; he also forced me to learn basic statistics whether I wanted to or not because otherwise I could not keep up with him. Gene, Robert, and I work on our separate parts of our computer programs and the accompanying verbiage until we achieve the desired (user-friendly) product. We have included new chapters in this edition that reflect our involvement with valuable collaborators who shared both their knowledge and raw data with us. I am particularly grateful to the late Patrick V. Vail (USDA, ARS) for giving me a key role in the debate about varietal testing of horticultural exports. Pat, James Leesch, Victoria Yokoyama, and J. Larry Zettler (USDA, ARS) provided invaluable advice about how best to implement alternatives to one of my pet peeves, the probit 9. In New Zealand, E. Ruth Frampton has also been a great friend and collaborator in our work in quarantine statistics. Ruth’s explanations of the minimum threshold concept were cogent; she provided many logical explanations for extremely complex issues. Our development of statistical methods for modes of inheritance of pesticide resistance would not have been possible without the contributions of Elizabeth Grafton-Cardwell (University of California–Davis), Marjorie A. Hoy (University of Florida), and Richard T. Roush (Cornell University). I dedicated the first edition to two people whose presence I miss to this day. Eleen  “Johnnie” Nicholas, a dear friend and neighbor, gave me a lot of encouragement and moral support when I needed it. When Johnnie was murdered, I could not continue to work on the first edition for quite a while. Knowing what her attitude would have been, though, I finally got on with the job. Lucille M. Boelter was my technician for 18 years until her retirement in 1987; she died six months later. Every mad scientist should work with a person as competent, able, sensible, hard working, and full of fun as Lucille; few, I think, are that fortunate. For a high school graduate from Ripon, Wisconsin, she did some wonderful science based on just plain common sense. I may have had something to do with it, but I will always wonder how much. Perhaps it was synergism. This second edition is dedicated to the statistician who is responsible (I am tempted to say, to blame) for my fixation on probit analysis. Everything I have done with probit analysis since I first realized that statistics was a necessary evil in quantal response bioassays has been based on the foundation that David J. Finney built. In 1986, Haiganoush and I finally met with David when he passed through Berkeley on his way back to Scotland from the Philippines. David gave POLO and the rest of our work his stamp of approval; he told us to carry on because there would not be another edition of his Probit Analysis.11 Robert, Gene, and I had long suspected that David was our primary anonymous reviewer for the very first publication describing POLO, because his comments had given his identity away; David confirmed our suspicions. We had a lively discussion about why we thought

 

2331_C000.fm  Page xix  Thursday, May 10, 2007  11:19 AM

Preface to the Second Edition

xix

biologists needed to know whether lines were significantly different. To actually talk with the very person who wrote the book I had used every day for so many years was absolutely wonderful. We have continued to move forward; each time our probit programs have been recast into a more modern format or a contemporary operating system, we use Probit Analysis11 as our standard for comparison. So, this volume is dedicated to David J. Finney as my way of saying thank you for providing the basis of our work with probit analysis.

References 1. Baring-Gould, W. S., Nero Wolfe of West Thirty-fifth Street, Penguin Books, New York, 1982, p. vii. 2. Apologies to Judith Martin, the one and only “Miss Manners” and author of (among other gems) Miss Manner’s Guide to Excruciatingly Correct Behavior, Antheneum, New York, 1982. 3. Wonnacott, P. H. and Wonnacott, R. J., Introductory Statistics, John Wiley & Sons, New York, 1990. 4. Rees, D. G., Essential Statistics, 4th ed., Chapman & Hall/CRC Press, Boca Raton, FL, 2001. 5. Gad, S. G., Statistics and Experimental Design for Toxicologists, CRC Press, Boca Raton, FL, 1998. 6. Carson, R., Silent Spring, Houghton Mifflin, Boston, 1962. 7. Not to be confused with Them!, the 1954 movie about giant ants running amuck (or was it in muck?) in the sewers of Los Angeles. 8. van den Bosch, R., The Pesticide Conspiracy, Doubleday, Garden City, NY, 1976. 9. Daum, R. J., A revision of two computer programs for probit analysis, Bull. Entomol. Soc. Am. 16(1), 10–15, 1970. 10. Daum, R. J. and Killcreas, W., Two computer programs for probit analysis, Bull. Entomol. Soc. Am. 12(4), 365–369, 1966. 11. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 12. Robertson, J. L., Russell, R. M., and Savin, N. E., POLO: a user’s guide to Probit Or LOgit analysis, USDA Forest Service Gen. Tech. Rep., PSW-38, 1980. 13. In this 1958 MGM movie starring Katherine Hepburn and Spencer Tracy, a huge computer named EMARAK (designed by Spencer Tracy) computes (among other things) the total acreage defoliated by spruce budworm more quickly than do the research librarians (led by Katherine Hepburn). Several short circuits later, the computer blows up. Our UNIVAC 1108 was considerably more advanced, but about the same size. 14. Finney, D. J., BLISS, Department of Statistics, University of Edinburgh, Edinburgh, Scotland, 1971. 15. Russell, R. M. and Robertson, J. L., Programming probit analysis, Bull. Entomol. Soc. Am. 25(3), 191–192, 1979. 16. LeOra Software, POLO-PC, A user’s guide to probit or logit analysis, 1997. 17. LeOra Software, PoloPlus, POLO for Windows, LeOra Software, 1007 B St., Petaluma, CA 94952. See http://www.LeOraSoftware.com.

2331_C000.fm  Page xx  Thursday, May 10, 2007  11:19 AM

xx

Preface to the Second Edition 18. Russell, R. M., Savin, N. E., and Robertson, J. L., POLO2: a user’s guide to multiple probit or logit analysis, USDA Forest Service Gen. Tech. Rep., PSW-55, 1981. 19. LeOra Software, PoloEncore, LeOraSoftware, 1007 B St., Petaluma, CA 94952, 2007. See http://www.LeOra Software.com. 20. David Janssen was the first actor to play Richard Kimball, a doctor from Chicago, in the television series The Fugitive (1963–1966). Harrison Ford played Dr. Kimball in the 1993 movie of the same name. Our Richard Kimball (from Folsom, CA) was not running from the authorities. 21. Hughes, G. A., Robertson, J. L., and Savin, N. E., Comparison of chemical effectiveness by the multinomial logit technique, J. Econ. Entomol. 80, 18, 1987. 22. The beloved English barrister, Horace Rumpole, refers to his wife Hilda as “She Who Must Be Obeyed.” See, for example, Mortimer, J., Rumpole on Trial, Viking, New York, 1992.

2331_C000.fm  Page xxi  Thursday, May 10, 2007  11:19 AM

Authors Jacqueline (Jackie) L. Robertson received both her B.A. (1969, zoology) and Ph.D. (1973, entomology) from the University of California–Berkeley. She joined the USDA Forest Service as a temporary employee in 1966, became a research scientist at the Pacific Southwest Research Station in 1972, and left as a senior scientist in 1996. She is responsible for biological interpretation of statistical results for LeOra Software. Dr. Robertson is the author of more than 150 technical publications. She is a member of the Entomological Society of America (for which she served as an editor of the Journal of Economic Entomology from 1981 through 1996) and the Entomological Society of Canada. Her current research interests concern forensic veterinary entomology and statistical models of insect population responses to toxins in their environment. Robert M. Russell is founder of LeOra Software Company. He received a Bachelor of Science in Mathematics from the University of Michigan (1956). While a graduate student in mathematics at the University of California–Berkeley, he worked on computer research problems at the UC Computer Center and became a computer software engineer while the field was still in its infancy. He went on to participate in research programs at the Pacific Southwest Forest and Range Experiment Station in Berkeley, specializing in computational statistics, database design, and computer mapping. In the late 1980s he entered private industry developing library and telecommunication systems. He has maintained a lively interest in social and political issues and has kept abreast of progress in all of the sciences, especially biology. Haiganoush K. Preisler received her B.S. (1970) and M.S. (1972) from the Department of Mathematics of American University in Beirut, Lebanon. She received a Ph.D. in Statistics from the University of California–Berkeley in 1977. She is a member of the American Statistical Society and the Biometrical Society. Dr. Preisler is a statistician with the USDA Forest Service’s Pacific Southwest Research Station. Her research interests concern statistical studies of environmental factors that threaten forest lands.

xxi

2331_C000.fm  Page xxii  Thursday, May 10, 2007  11:19 AM

xxii

Authors

N. E. (Gene) Savin received a B.A. in economics (1956), an M.S. in statistics (1960), and a Ph.D. in statistics (1969) from the University of California–Berkeley. He has been a statistician for the USDA Forest Service and a fellow of Trinity College (Cambridge, England). He currently holds a Sandler Fellowship at the Tippie College of Business at the University of Iowa. Dr. Savin is a fellow of the Econometric Society and the American Statistical Association. His current teaching interests are econometrics and the history of economic thought.

2331_C001.fm Page 1 Wednesday, May 9, 2007 5:42 AM

chapter one

Introduction –

–

Ma´ven, ma´vin, n. [Yiddish, from late Hebrew meven]. An expert or connoisseur, often a self-proclaimed one. —Webster’s Unabridged Dictionary Consider the tribulations of our novice, Dr. Paula L. Maven. She wants to test an insect growth regulator (IGR) as a possible chemical to reduce populations of some very large and dangerous Lepidoptera (Ascalapha giganticus Ubetterduck). A. giganticus is a newly discovered agent of bioterrorism that resulted from insertion of DNA from tomato hornworms, Manduca qunquemaculata (Haworth), into black witch, Ascalapha odorata L. (Although absolute proof is lacking, a disgruntled scientist with a temporary appointment is suspected of doing this insidious bit of genetic engineering in an attempt to blackmail his employer into making his job permanent.) The resulting new species, first discovered in Marin County, California, was given the common name wicked witch of the west. After its release into the ecosystem, the new species spread through California’s Central Valley and swiftly chewed its way into the southern United States. Clearly, wicked witches must be controlled. At stake is the part of the national economy (e.g., salsa and pizza) that depends on tomato, bell pepper, olive, onion, and garlic production. Paula Maven is an ecologist with no previous experience in pest management, but she has accepted a research appointment at the local university in Schaeferville. Her assignment is to establish an integrated pest management program for tomatoes. The crown jewel of the University of Schaeferville is its International Research Center, a renowned institution that recruits high school students for their skills in competitive insect pinning, quick taxonomy, and precision sweep netting. The purpose of Dr. Maven’s first experiment is deceptively simple. She wants to find a dose of the IGR that will control the population or at least kill about 90% of the varmints. The first problem is practical: How is she to keep the behemoths alive in the laboratory long enough to find her answer?

1

2331_C001.fm Page 2 Wednesday, May 9, 2007 5:42 AM

2

Bioassays with arthropods, second edition

They are huge and horrible; the adults are dangerous. So, after a very time-consuming collection that yields a total of 37 mature caterpillars, Dr. Maven discovers that the caterpillars eat tomato plants and each other. That leaves 30 test subjects, each of which must be housed in a separate 25-cm diameter Petri dish. Dr. Maven begins the experiment by diluting the IGR to the concentration that the manufacturer recommends for mosquito control (i.e., at least 90% mortality of the larvae). A second major problem arises: Should the IGR be applied directly to the caterpillar, to the tomato leaves, or to the filter paper lining the Petri dish? Dr. Maven chooses direct application to the larvae. After all, the IGR contacts mosquitoes and all other targets listed on the label. If it is effective by contacting the other pest species, she reasons that it should be effective on wicked witches in the same way. Next, how many caterpillars should she test? Dr. Maven decides to use 20 of the 30 survivors (the other 10 will be used to start a laboratory colony). Now, how should the chemical be applied? She chooses microapplication (a process by which a small, measured drop of the pesticide is put on each insect’s body) because published literature suggests that many other researchers use that method. Should the IGR be applied in proportion to the weight of each larva? Certainly; that is how physicians prescribe medication, so it seems reasonable to apply the chemical to each caterpillar in the same way. With only 20 caterpillars, Dr. Maven next wonders how many dilutions to make from the stock solution. Given her intention to construct a dose-response relationship for the IGR, Dr. Maven decides to dilute the stock solution three times, in ten-fold increments, with water. Use of water seems reasonable because mosquitoes are exposed to the chemical in that medium. As each caterpillar is weighed, Dr. Maven assigns it to a concentration so that the first five will be treated with the first concentration, the second five with the second concentration, and so on. Treatment begins with the highest concentration and progresses to the lowest. Dr. Maven next places a carefully measured drop of the IGR solution on each caterpillar’s back. Never mind that it rolls off; perhaps enough got through the cuticle to do the trick. She waits for something to happen. Will the response of each caterpillar be an all-or-nothing event? The literature suggests that it may not be. The caterpillar might curl up and die, it might molt to the pupal stage and be malformed, or it might grow. Nevertheless, Dr. Maven selects death as the criterion for effectiveness because that would be the intent of using the IGR to protect tomato plants. To make the data fit the dead versus alive classification, she reduces the effects that she observes into one or the other category. Seven days later, all of the caterpillars are “dead.” What has Dr. Maven accomplished? Unfortunately, nothing. Can a dose-response relationship be estimated from her data? Certainly not. Among the obvious deficiencies in Dr. Maven’s experiment are lack of replication, use of a stock concentration appropriate for species in a totally unrelated insect family, lack of a control (treated with water only), and use of an untested assumption that the response will be in proportion to body weight. The main problem, however,

2331_C001.fm Page 3 Wednesday, May 9, 2007 5:42 AM

Chapter one: Introduction

3

is that a dose-response relationship could not have been established with 20 test subjects even if she had done everything else perfectly. Clearly, Paula Maven needs help! Dr. Maven has attempted to do a bioassay—that is, an experiment in which a living organism is used as a test subject. When a stimulus is applied, the organism responds; a bioassay provides a means to quantify the response or responses. A quantal response is one that varies in relation to a measurable characteristic of the stimulus. Quantal response bioassays are done to estimate the relationship between the response (or responses) and the quantity or intensity of a stimulus. These bioassays can differ in terms of the response variables and the explanatory variables (independent variables) involved. Explanatory variables are the measurable characteristics of a stimulus or stimuli that cause a response or responses to vary. Response variables (the dependent variables) are the random outcomes of the experiment; they vary in relation to the stimulus (i.e., in relation to the independent variables). Statistical models are used to estimate the mathematical relationships between and among variables. Quantal response bioassays are often done with pest species. Pest has no scientific definition; instead, this designation is solely a product of human activities and needs and so is totally anthropocentric. Most pests are members of the invertebrate phylum Arthropoda; within this phylum, most arthropod pests belong to the classes Insecta or Arachnida. Some pests interfere with our production of food, fuel, or fiber. Others spread disease or parasites to humans, domestic or wild animals, or plants. Still others are parasites of humans and domestic animals. Nuisance pests include cockroaches and gnats. Others, such as wasps, yellowjackets, mosquitoes, and some spiders, can cause severe allergic reactions in humans and other mammals.1 The most subjectively defined group of pests includes those that are aesthetically offensive. A single arthropod is never the culprit. Instead, a pest population (an interbreeding group of individuals of the same species2) is responsible for damage, disease transmission, terror (for those allergic to bee stings), or petty annoyance. When reduction of numbers of pests in a population is the goal, bioassays are done to estimate the probability that the pest population will respond in the desired manner—they will, for example, die, become sterile, or, at the very least, suffer horribly—and so be made innocuous. Although most quantal response bioassays have been done to estimate the activity of pesticides (natural or synthetic substances that harm a pest), principles of valid bioassay also apply to any physical factor that can be manipulated to affect numbers of pests. Radiation,3 microclimate,4 and temperature5 have been used in some situations to minimize the use of or completely replace synthetic organic chemicals. Many procedures for organic gardening are also based on bioassays; these include estimating the amounts of active ingredients necessary for baits, attractants, and repellents.6 Beneficial microorganisms such as bacteria (Bacillus thuringiensis),7 insect viruses (nuclear polyhedrosis [NPV]8 and granulosis [GV]), nematodes,9 and proto-

2331_C001.fm Page 4 Wednesday, May 9, 2007 5:42 AM

4

Bioassays with arthropods, second edition

zoa ( Nosema spp.) 10 also used in organic gardening are tested in dose-response bioassays before they are developed commercially. Van den Bosch’s11 principles of safety and selectivity in the environment mean that all organisms, not just pests, must be considered when any control method is used. Quantal response bioassays can and should be used to estimate risk to nontarget species, such as parasites, predators, and other organisms in the environment. Beyond the arthropods and in the general framework of environmental health and safety, the methods and principles described in this book are applicable to any tests where an agent or treatment is tested on any living thing. For example, research in one of the major topics of this book, experimental design in dose-response bioassays, began with a “simple” question from statisticians in the U.S. Fish and Wildlife Service: How many grizzly bears would have to be tested to prove that chemical X is harmless to this endangered species? Because a supply of Ursus horribilis was not available, we used computer simulation to find an answer.12 Results are as applicable to grizzly bears and bald eagles as they are to insects. Our primary emphasis is the design of valid quantal response bioassays and use of appropriate statistical models to analyze resultant data. The information and suggestions presented here should help even a novice like Paula Maven to avoid mistakes that can invalidate an experiment. Without good experimental design, data from a bioassay will be meaningless at worst and suspect at best. In any quantal response bioassay, experiments must be carefully designed so that maximum biological information can be extracted from statistically valid data. Design includes considerations such as identification of response variables and explanatory variables, numbers of replications, where to place doses in a simple dose-response bioassay to achieve greatest precision, and the number of subjects that must be tested. These topics were treated previously in statistical texts by Finney,13,14 but they have never been interpreted specifically for a biological scientist whose research includes quantal response bioassays. Models in quantal response bioassays range from very simple to extremely complex. The simplest model is a binary model (e.g., dead, alive) with one explanatory variable (e.g., dose). A more complex model is a binary model with multiple explanatory variables; the most complex model is a multinomial (or polytomous) model in which multiple responses are related to multiple explanatory variables. Will Paula Maven wear out calculators solving complex equations? Not if we can help it! We realize the importance of computationally correct and user-friendly computer programs. Most biologists lack the programming skills necessary to use experimental statistical programs. So, for the sake of statistical mavens everywhere, we primarily illustrate data analyses with the programs that we wrote to be both useful and comprehensible. In cases where we illustrate use of an experimental statistical program, we first provide the commands for the program, followed by the analysis itself. If that particular program is not available, we advise the reader to find and use the same type of analysis (e.g., analysis of deviance) if available in their computer package. Many commercial computer programs are written to do

2331_C001.fm Page 5 Wednesday, May 9, 2007 5:42 AM

Chapter one: Introduction

5

analyses of quantal response data. Dr. Maven is familiar with only one such program; can she use it to analyze data from all of her experiments? Certainly not, unless she intends to use the same experimental design repeatedly. Each analysis must be appropriate for each experiment. Dr. Maven must resist the tendency of many biologists to force data through the same computer program just because they know how to use that program. In summary, familiarity with one particular program does not guarantee valid analysis. Mindless experimental design that results in data subjected to equally mindless analyses is a waste of time and resources. Dr. Maven is aware that extrapolation must be avoided in any regression analysis, but she learns that she must also pay careful attention to where doses are placed and how many test subjects she uses, even in basic bioassays such as routine screening experiments. Specialized bioassays require far larger sample sizes per dose as well as more doses. Entomologists have had a history of making blithe recommendations about the lethal dose levels that must be estimated for specific purposes such as exclusion of exotic organisms or resistance testing to separate different genotypes. Although these recommendations were intended to answer very practical problems, the sample sizes that would be necessary to provide valid results are impractical because of the realities of insect rearing or collection from wild populations. The lesson here is that even a well-planned and perfectly executed bioassay with a very simple statistical model cannot answer an impossible question. In commodity treatment for pest exclusion, for example, bioassays have been used in attempts to estimate a response level (99.9968% mortality) that defies statistical reality.15 An off-the-cuff remark made over 65 years ago16 as an educated guess was codified as the criterion for effective commodity treatment. Pity poor Paula Maven as she tries to estimate a probit 9 with confidence limits that do not stretch from minus infinity to plus infinity so that tomatoes can be exported from Schaeferville to its sister city (Hokitika, New Zealand). We present alternatives to the probit 9 and discuss more statistically reasonable approaches to problems in quarantine entomology. When the probability of death is the only criterion used to estimate the future establishment of a pest population, Q915 is a general term that can replace automatic use of the probit model. Natural variation has been the most frequently ignored factor in quantal response bioassays. Paula Maven is not alone when she panics because the results of repeated bioassays with the same chemicals tested on her laboratory population are not exactly the same. We show the equations necessary for estimation of the boundaries of natural variation in response based on large sample theory. Variation within a population occurs at various levels, including sibling groups, cohorts within a population, and developmental stage. A more ecological approach to the description of population response based on the variability within a population may be possible if, for example, contour plots of mortality17 in a population over time are integrated with ecologically based methods based on life tables and demographic toxicology.18

2331_C001.fm Page 6 Wednesday, May 9, 2007 5:42 AM

6

Bioassays with arthropods, second edition

In bioassays of microbial pesticides, dose (given in arbitrary units) is conventionally defined by comparison of the activity of an unknown preparation with that of a standard. This comparison is exactly the same as relative toxicity of chemicals, and any assumptions that binary responses must be parallel are erroneous. Use of the terms potency and relative potency in the literature stems from an early statistical method13 that was used to compare dose-response regressions. This method has been replaced by methods that we describe in detail here. Because of natural variation, the estimated potency of production lots of Bacillus thuringiensis varies even within the same laboratory over time. Dr. Maven also notices that responses of her wicked witch colony differ each time that a bioassay is repeated with toxicants. When wild insects are brought into the laboratory for testing, they are collected from multiple locations where various chemicals have been applied. Does variation among the field-collected groups indicate resistance, variation that is related to the host, or natural variation? Artificial or semi-artificial diets are often used to raise the insects used for testing on a year-round basis.19 The only way for Dr. Maven to continue her research with wicked witches when she could not obtain tomato plants was to find or develop a suitable diet. Do the insects that spend most of their life cycle on plants respond in the same way as they do when they are reared on artificial diet? Suppose different varieties (cultivars) of tomato are involved? When A. giganticus larvae eat ‘Redneck’ foliage or fruit, is their response the same as when they feed on the leaves or fruit of other tomato cultivars such as ‘Julia Sugarbaker’ or ‘Golden Girl’? For Paula Maven to separate the significance of these effects, she must be able to estimate the limits of natural variation in response. The evolutionary consequence of pesticide use (and overuse) has been the development of pesticide resistance by numerous important pest species.20 The most reliable criterion for a diagnosis that resistance has developed is failure of a chemical to manage arthropod populations in the field.21 Quantal response bioassays provide basic information for studies of pesticide resistance. Estimated responses of parental susceptible and resistant strains and their F1 progeny are often used to test hypotheses about modes of inheritance.22 Paula Maven needs a clear explanation of statistical methods to test hypotheses about the genetic mechanisms of resistance based on quantal response bioassays.23 Given natural variation in response, she also needs guidance in the design of experiments to monitor resistance in populations collected from the field. How can bioassays be designed for this purpose? Bioassays with mixtures (pesticide + pesticide, pesticide + microbial agent, or any other combination) have become more frequent as pesticide costs have increased and as new ways to decrease environmental pollution have been sought. Although we describe experimental designs for bioassays with mixtures, a problem frequently encountered with mixture bioassays occurs not at the level of experimental design, but once the data have been collected. How will Dr. Maven know whether the components are acting

2331_C001.fm Page 7 Wednesday, May 9, 2007 5:42 AM

Chapter one: Introduction

7

independently, synergistically, or antagonistically? What is a synergist? What is an antagonist? Do categories such as “true, actuated, offset, pseudosynergistic and similar”24 make any biological sense? We discuss methods to test hypotheses about various kinds of chemical interaction so that they are biologically logical rather than exercises in statistical theory. Bioassays of response over time require special experimental designs. At the request of Schaeferville’s tomato barons (and the university’s largest benefactors), Paula Maven must estimate how quickly chemicals will control another pest, tomato stem cleaver ants, because a valuable crop of ‘Redneck’ tomatoes become detached from their stems before the fruit can ripen. How does she design experiments to estimate rates of mortality? Can she save the ‘Rednecks’? We explain appropriate designs to use in bioassays that concern time and how to avoid common mistakes in data analyses when time is a variable. Probit or logit techniques may or may not be appropriate. What is a serial experimental design? What is an independent design? What other models might be used to analyze time data? We discuss the use of alternatives such as the complementary log-log model.25 Suppose that Dr. Maven has assumed that a variable has no significant role in response when, in fact, it is crucial. What happens if the appropriate model is not binary but includes two or more explanatory variables? An untested assumption can invalidate an otherwise perfectly designed bioassay. For example, does response to a pesticide or another factor always vary in proportion to body weight? Experimental evidence suggests that sometimes it does, that sometimes it does not, and that no general assumption should be made.26,27 When Dr. Maven constructs her models, they should include all of the relevant explanatory variables. A difficult model to consider, but one that is especially relevant to analyses of the effects of insect growth regulators, involves multiple explanatory variables and multiple responses. When Paula Maven bumbled through her first bioassay with the IGR on A. giganticus, she simplistically used death as the criterion for effectiveness. In fact, she observed several different effects; she then reduced them to two categories. She should have used a polytomous quantal response model in such bioassays. We explain how to use these models and how to analyze such data. In the future, they will be important in the transition from bioassays with laboratory populations to toxicology at the levels of populations, communities, and the ecosystem. Statistical models and ecological models are not the same, as Paula Maven has quickly come to realize. Statistical models use experimental data (the more, the better) to describe mathematical relationships between and among variables. Ecological models, in contrast, are conceptual maps about components of a particular ecosystem.28 Such models tend to include simplified descriptions of the various components, along with weighting factors for their importance. Ecotoxicology has been defined as the science of predicting the effects of toxicants on ecosystems and on nontarget species;29 the effects of toxicants at the individual, population, and ecosystem level are of concern.30 How can quantal response data for arthropods be used in predic-

2331_C001.fm Page 8 Wednesday, May 9, 2007 5:42 AM

Bioassays with arthropods, second edition

8

tive, conceptual models? In the final chapter of this book, we suggest some possible steps to identify all significant explanatory variables and multiple response variables that should be included in a comprehensive multinomial approach to ecotoxicology. A major improvement necessary to make quantal response bioassays more predictive is the use of response variables other than simply “dead versus alive,”31 and to use statistical methods especially for prediction. Stark and Wennergren32 and Stark and Banks33 described modifications to the demographic approach to toxicology, but only one life table parameter was considered. Dr. Maven has clearly learned a very important lesson in her transition from novitiate to maven: data reduction means a loss of information.

References 1. Goddard, J., Physicians Guide to Arthropods of Medical Importance, 4th ed., CRC Press, Boca Raton, FL, 2003. 2. Mayr, E., Principles of Systematic Zoology, McGraw-Hill, New York, 1969. 3. For example, Lester, P. J. and Barrington, A. M., Gamma irradiation for post-harvest disinfestation of Ctenopseustis obliquana (Walker) (Lepidoptera, Tortricidae), J. Appl. Entomol. 121, 107, 1997. 4. Shipp, J. L. and Zhang, Y., Using greenhouse microclimate to improve the efficacy of insecticide application for Frankliniella occidentalis (Thysanoptera: Thripidae), J. Econ. Entomol. 92, 201, 1999. 5. Jang, E. B., Nagata, J. T., Chan, H. T., Jr., and Laidlaw, W. G., Thermal death kinetics in eggs and larvae of Bactrocera latifrons (Diptera: Tephritidae) and comparative thermotolerance to other tephritid fruit fly species in Hawaii, J. Econ. Entomol. 92, 654, 1999. 6. For example, see Roberts, T., 100% Organic Pest Control for Home & Garden, Book Publishing Company, Summertown, TN, 1998, and Ellis, B. W. and Bradley, F. M., eds., The Organic Gardener’s Handbook of Natural Insect and Disease Control, Rodale Press, Emmaus, PA, 1996. 7. Beegle, C. C. and Yamamoto, T., Invitation paper (C. P. Alexander Fund): history of Bacillus thuringiensis research and development, Can. Entomol. 124, 587, 1992. 8. Shapiro, M. and Robertson, J. L., Natural variability of three geographic isolates of gypsy moth (Lepidoptera: Lymantriidae) nuclear polyhedrosis virus, J. Econ. Entomol. 84, 71, 1991. 9. Anderson, T. E., Hajek, A. E., Roberts, D. W., Preisler, H. K., and Robertson, J. L., Colorado potato beetle (Coleoptera: Chrysomelidae): effects of combinations of Beauveria bassiana with insecticides, J. Econ. Entomol. 82, 83, 1989. 10. For example, Burges, H. D., Microbial Control of Pests and Plant Diseases, 1970-1980, Academic Press, London, 1981. 11. van den Bosch, R., The Pesticide Conspiracy, Doubleday, Garden City, NY, 1976. 12. Robertson, J. L., Smith, K. C., Savin, N. E., and Lavigne, R. J., Effects of dose selection and sample size on the precision of lethal dose estimates in dose-mortality regression, J. Econ. Entomol. 77, 833, 1984. 13. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 14. Finney, D. J., Statistical Method in Biological Assay, Griffin, London, 1964.

2331_C001.fm Page 9 Wednesday, May 9, 2007 5:42 AM

Chapter one: Introduction

9

15. Robertson, J. L., Preisler, H. K., and Frampton, E. R., Statistical concept and minimum threshold concept, in Paull, R. E. and Armstrong, J. W., eds., Insect Pests and Fresh Horticultural Products: treatments and Responses, CAB International, Wallingford, England, 1994, pp. 47–65. 16. Baker, A. G., The basis for treatment of products where fruit flies are involved as condition for entry into the United States, USDA Circular 551, Washington, DC, 1939. 17. Robertson, J. L., Richmond, C. E., and Preisler, H. K., Lethal and sublethal effects of avermectin B1 on the western spruce budworm (Lepidoptera: Tortricidae), J. Econ. Entomol. 78, 1129, 1985. 18. Stark, J. D. and Banks, J. E., Population-level effects of pesticides and other toxicants on arthropods, Ann. Rev. Entomol. 48, 505, 2003. 19. For example, see Singh, P. and Moore, R. F., Handbook of Insect Rearing, Vols. I and II, Elsevier, Amsterdam, 1985. 20. Roush, R. T. and Tabashnik, B. E., eds., Pesticide Resistance in Arthropods, Chapman & Hall, London, 1990. 21. Ball, H. J., Insecticide resistance: a practical assessment, Bull. Entomol. Soc. Amer. 27, 261, 1981. 22. For example, Hoy, M. A., Conley, J., and Robinson, W., Cyhexatin and fenbutin-oxide resistance in Pacific spider mite (Acari: Tetranychidae): stability and mode of inheritance, J. Econ. Entomol. 82, 11, 1988. 23. Preisler, H. P., Hoy, M. A., and Robertson, J. L., Statistical analysis of modes of inheritance for pesticide resistance, J. Econ. Entomol. 83, 1649, 1990. 24. Sakai, S., Joint action of insecticides, Bull. Daito Bunko Univ. 1, 1, 1969. 25. Preisler, H. K. and Robertson, J. L., Analysis of time-dose-mortality data, J. Econ. Entomol. 82, 1534, 1989. 26. Robertson, J. L., Savin, N. E., and Russell, R. M., Weight as a variable in the response of western spruce budworm to insecticides, J. Econ. Entomol. 74(5), 643, 1981. 27. Savin, N. E., Robertson, J. L., and Russell, R. M., The effect of body weight on lethal dose estimates for the western spruce budworm, J. Econ. Entomol. 75(3), 538, 1982. 28. Jorgensen, S. E. and Bendoricchio, G., Fundamentals of Ecological Modelling, Elsevier, Amsterdam, 2001. 29. Hoffman, D. J., Rattner, B. A., Burton, G. A. Jr., and Cairns, J. Jr., Introduction, in Handbook of Ecotoxicology, Lewis Publishers, Boca Raton, FL, 2003. 30. Kammenga, J. and Laskowski, R., Demographic approaches in ecotoxicology: state of the art, in Kammegna, J. and Laskowski, R., eds., Demography in Ecotoxicology, John Wiley & Sons, New York, 2000. 31. Robertson, J. L. and Worner, S. P., Population toxicology: suggestions for laboratory bioassays to predict pesticide efficacy, J. Econ. Entomol. 83, 8, 1990. 32. Stark, J. D. and Wennergren, U., Can population effects of pesticides be predicted from demographic toxicological studies?, J. Econ. Entomol. 88, 1089, 1995. 33. Stark, J. D. and Banks, J. E., Population-level effects of pesticides and other toxicants on arthropods, Annu. Rev. Entomol. 48, 505, 2003.

2331_C001.fm Page 10 Wednesday, May 9, 2007 5:42 AM

2331_C002.fm Page 11 Wednesday, May 9, 2007 5:42 AM

chapter two

Quantal response bioassays Dr. Maven is well aware that her first attempt at doing a bioassay was a disaster. Obviously, she reasons, I need some help. And so, she decides to audit a one-day workshop in the Schaeferville University Department of Entomology. Given her status as a faculty member who does not want to reveal her ignorance (let alone her identity), a disguise seems in order. Her husband, Carl Maven, suggests that Dame Edna1 glasses and the San Francisco Skyline Hat from Beach Blanket Babylon2 might just do the trick. Paula suspects that a dress would probably do just as well. The air is warm and still as nine students set off for bioassay lessons. Their instructor is Dr. Garland Tarleton, a kindly, middle-aged, portly fellow with an Albert Einstein coiffure and a lively sense of humor. After he divides his nine students into groups of three, Dr. Tarleton gives each group the choice of a .44 magnum water pistol and a bucket of water or a precision paintball gun with a supply of red paintballs. Dr. Tarleton warns the groups to choose their weapon carefully because he cannot allow them to change midexperiment. Group 1 selects the paintball gun; groups 2 and 3 each choose a water pistol. The target for each group differs. Group 1’s target is a molded plastic Gary Larsonesque coreid (leaf-footed bug3) with electronic sensors; when paint contacts any part of the bug’s body, a synthesized voice screams “Call me Shane!”4 Group 2’s target is a very small circle with eight legs (possibly a grossly magnified spider mite) drawn on a sheet of acetate. Group 3 also has an acetate target, but the drawing is a large outline of a caterpillar’s head; the lines have been drawn with a broad-tipped felt pen. Dr. Tarleton gives each group the same instructions: In a replicated experiment, estimate the distance for which the probability of hitting the target is 50%. How do the students begin? Clearly, their first task is to locate the distance beyond which the target is out of range. Their second step is to find the distance at which it is virtually impossible to miss. Everyone agrees that these limits need not be defined with utmost precision, and that the real experiment (within these boundaries) should be the focus of most effort. But a major problem arises when groups 2 and 3 try to define a hit. (Group 1 is

11

2331_C002.fm Page 12 Wednesday, May 9, 2007 5:42 AM

12

Bioassays with arthropods, second edition

not concerned with this problem because of the screaming coreid’s signals; groups 2 and 3, however, must define a hit more arbitrarily). Group 2 decides to consider any contact of water with the body or legs of the spider mite as a hit. The members of group 3 decide that they can hit their caterpillar in two ways, on the lines and within the lines. Groups 2 and 3 decide to move away from group 1 because they find the screaming distracting, so they move into a convenient canyon where the wind is blowing in intermittent gusts. As they begin their experiment, it becomes clear that the wind affects their accuracy. One member of each group, for reasons known only to himself, happens to have a pocket anemometer with him. Both groups record both distance from the target and wind speed for each shot. They also beg to switch to the paintball method because water is so hard to see on the targets. Dr. Tarleton’s answer is an absolute no. The next problem concerns definition of a replication. Should one person do all the shooting? If not, in what order should group members take their turns? Group 1 assigns the order in which members shoot the paintball gun at random, and everyone takes one shot before any one person shoots again. Group 2 independently does the same. In group 3, however, one person does all the shooting, another person serves as the target observer, and yet another records wind speed when each shot is taken. As the experiments proceed, no one has any idea how many shots are necessary to estimate the distance from the target where the probability of hitting the target is 50%. Certainly, each group may be able to give a rough estimate, but how reliable will it be? Are they sure that they will obtain the same 50% distance if they repeated the experiment under exactly the same conditions? Is there an absolute, true answer to this problem? Furthermore, how can they estimate a probability with these kinds of data? Will group 1 ever get the paint out of their clothes? Will groups 2 and 3 ever get dry? Paula Maven’s notes from the bioassay course provide a good introduction to the general subject of bioassays. After the shooting is over (and all of the students are either red or soaked), Dr. Tarleton provides the following general information and critique.

I. Types of quantal response bioassays These experiments illustrate quantal response bioassays. Each target represents the test subject. The paintball gun or the water pistol applies the treatment. Data collected by the three groups differ in terms of the response variables and the explanatory variables involved. Group 1 did the simplest type of quantal response experiment: it dealt with only one explanatory variable (distance from the target) to estimate an all-or-nothing result (“Call me Shane,” or no sound). This kind of test is a binary quantal response

2331_C002.fm Page 13 Wednesday, May 9, 2007 5:42 AM

Chapter two: Quantal response bioassays

13

experiment with one explanatory variable. Group 2 measured two explanatory variables (distance from the target and wind speed), but its members also recorded an all-or-nothing result. This type of test illustrates a binary quantal response experiment with multiple explanatory variables. Group 3 attempted to do the most complex type of experiment: it measured two explanatory variables (distance from the target and wind speed) and two response variables (hits on the lines and hits within the lines). This was a multinomial (polytomous) experiment. The frequency with which these different types of experiments have been used in biological experiments seems to vary as a direct function of the complexity of the data analyses involved. Because it is the simplest, the binary quantal response experiment with one explanatory variable (dose-response or concentration-response) is done most frequently. The multiple quantal response (multivariate) experiment is not done very often, perhaps because it is more time-consuming and because the statistical methods used to analyze the data are complex.5,6 The polytomous quantal response experiment is extremely time-consuming to complete; until recently,7–9 reliable computer programs were not available except for analyses of very small data sets.

II. Experimental design of bioassays The way a bioassay is done is its experimental design. The design must be considered in terms of the experimental unit—the entity actually receiving the treatment.10 In the water pistol experiments, groups 2 and 3 had to define their units because of the way the targets were drawn. Examples of experimental units are single insects,11 or cages containing plants or fruit.12,13 Treatments frequently involve use of groups, rather than individuals, exposed to each treatment level. For some species, a standard procedure is to select individuals from a laboratory colony, place them in groups of 10 into a Petri dish or other container, and treat each insect with a measured drop.14 In this instance, the individual insect is the experimental unit. Suppose that the entire group is sprayed simultaneously or presented with treated diet. In this situation, the group (not each insect) is the experimental unit.15 In a quantal response bioassay, nothing except the treatment level or intensity can distinguish one group from another: the experimental unit must be a constant. Occasionally, an unforeseen event (such as cannibalism or a simple mistake in counting) can occur without affecting the integrity of the bioassay. In experiments to select arthropods for resistance to a treatment, a preplanned minor modification of the initial experimental unit (for example, from use of two insects in each container) to another unit (for example, use of one insect in solitary confinement) may also be necessary as the insects grow and develop.14

2331_C002.fm Page 14 Wednesday, May 9, 2007 5:42 AM

14

Bioassays with arthropods, second edition

A. Randomization The process of assigning experimental units to treatments and controls at random is known as randomization. Use of this process is one way to avoid bias so that results represent responses of the units. A formal randomization procedure (such as the use of a random number table) is best to use even if more record keeping is required and the experiment is more expensive to undertake. If randomization is not formalized, for example, large insects might be selected preferentially, as might larvae that move most slowly. Results of the data analysis would then pertain to subsets of the population (large or sluggish caterpillars) and not to the population as a whole. Logistical convenience can result in bioassays with invalid designs.10 In the laboratory, for example, insects are often held in stacks of Petri dishes or rearing containers placed on shelves where gradients in light intensity and temperature might significantly affect response. A sample consisting only of insects selected from the top dishes at the front of shelves is not a random sample of the population. Instead, containers from which individuals are removed should be randomly selected to account for location on shelves and position within stacks. When wild populations are tested, individualized randomization procedures suited to each population are usually necessary. For example, natural units such as leaves, branches, or cones might be numbered, and insects on each unit can then be selected at random for testing. If the arthropod remains in or on the natural unit during testing, then these numbered units can be randomly assigned to treatment levels. In the laboratory or greenhouse, light intensity and temperature gradients must be considered in the randomization process for these units.

B. Treatments Dr. Tarleton may be vehement about the importance of randomization in experimental design, but he is an absolute fanatic about treatment methods remaining constant during a statistically valid bioassay. In a quantal response bioassay with a single explanatory variable, only the intensity of treatment can be subject to change. Thus, group 1 could change the distance to the target, but not the fact that they were shooting paintballs; groups 2 and 3 were stuck with using their water pistols. When multiple explanatory variables are investigated, the identity of variables also cannot be changed in the midst of the bioassay. Group 2 could change the distance to the target and continue their measurements of wind speed, but not change the fact that they were shooting water at the target. Finally, the treatments in a quantal response bioassay with multiple explanatory variables and multiple response variables cannot be changed midway through the experiment: group 3 could not change the variables it measured or the effects it recorded. When an investigator changes the exposure method (that is, the treatment) midway through an experiment with one explanatory variable, the two (or more) exposure methods become additional explanatory variables.

2331_C002.fm Page 15 Wednesday, May 9, 2007 5:42 AM

Chapter two: Quantal response bioassays

15

Paula Maven remembers Dr. Tarleton’s warning: “In the end, you have destroyed your experiment. Remember that!” Suppose an investigator also changes the time(s) at which an effect (such as mortality) is assessed midway through the experiment. Without knowing the relationship between time and mortality, versus exposure method, Dr. Tarleton describes the subsequent bioassay as a fruitcake: “A mixture of apples, oranges, walnuts, those strange candied fruits, and flour; who knows what you have? Try to add the results back together into a publishable form: I dare you!” Unfortunately, results of seemingly invalid bioassays occasionally appear in the published literature.16

C. Controls A control group should be exposed to everything except the treatment, and must be included in each replication of a bioassay. Dr. Tarleton explains that he cannot foresee a circumstance in which the inclusion of controls is similar to a clinical trial of a cancer drug with human subjects (and therefore inclusion of controls might be inhumane). The rationale for control groups is simple: without them, it will be difficult to attribute an observed effect or response to the treatment with any certainty. Suppose that test subjects are exposed to a chemical in water. In this case, the control group should be treated only with water. Excess test subjects (that is, the dregs of those available) should not be used in control groups that are assembled after selection of treatment units. Instead, the controls must represent a randomly selected treatment unit. Use of a common control group for several treatments in a quantal response bioassay is not desirable even if the same solvent is used. Each treatment tested in a quantal response bioassay must have its own control. To illustrate what might happen if a common control is used, suppose a control group is treated first, followed by groups treated with several levels of treatment A, several levels of treatment B, and several levels of treatment C. None of the controls respond, the test subjects treated with treatment A respond in relation to the dose applied, and all test subjects treated with treatments B and C respond regardless of dose. What does this bioassay reveal about the effects of treatments B and C? The answer is, unfortunately, not very much. Possibly, these two treatments are very effective, and lower rates should be tested. Equally possible is contamination of the application device with the highest level of treatment A and resultant contamination of treatment B, followed by contamination of treatment C with treatment B. Given the choice of testing more treatments at the expense of testing a control with each one, the wisest option is to test fewer treatments. Is an “untreated” control a real control? The answer is no, unless the experiment is done with the treatment in its pure form (without a carrier or solvent) or unless the fumigation activity of a chemical is being tested. In tests with fumigants, air is the carrier and an untreated control is appropriate. However, when a treatment is applied as an emulsion in water, the appro-

2331_C002.fm Page 16 Wednesday, May 9, 2007 5:42 AM

16

Bioassays with arthropods, second edition

priate control is water containing all of the emulsifying agents in the undiluted formulation, then diluted to the same concentrations present in the aliquots actually tested.

D. Replication Garland Tarleton next discusses a common tendency among scientists never to replicate a successful experiment (defined as one in which the results are exactly as expected the first time). Reports of unreplicated bioassays occasionally appear in the published literature.16 Without exception, all experiments must be replicated. A replication is repetition of a bioassay at a different time, but under the same conditions (as much as possible) as the first test. One purpose of replication is to randomize effects related to uncontrollable procedures and conditions. These include effects caused by workers or by time. Another reason for replication is to detect errors in formulation (that is, in the preparation of the solutions actually tested); for this reason, the best way to ensure true replication is to prepare a fresh series of doses diluted from a new stock solution. Some investigators refer to subsets within a replication as replications. For example, 20 insects might be treated in groups of 10 with concentrations of 0 (the control), 1, 2, 5, 7, and 10 mg/ml of chemical X. Unless each group of 10 treated with any concentration was treated with a fresh formulation and (to be absolutely sure) at a different time, it is not a separate replicate. For this example, each group of 20 treated with the same concentration is a replicate and each of the groups of 10 treated with that concentration is a subset of that replicate. When the subset is called a replicate, the investigator has done pseudoreplication. Pseudoreplication is not unique to quantal response bioassays, but it occurs with alarming frequency. Ideally, replications should be done on different days within a relatively short period of time (for example, a week). This recommendation assumes that day-to-day variability is not in itself a source of error in the experiment. However, time constraints related to the condition of test subjects, use of the application equipment, or varying personnel may require modifications of the ideal method. Decisions about the minimum time that should pass between replications must be made by investigators based on their common sense. Just as no specific guidelines are available to define the lower time limit for replication, none are available to identify the maximum time that can pass after which a treatment becomes an altogether different experiment. Certainly, the same bioassay done with the same species, but in different years, cannot be considered a replication in the usual sense. Because of these problems, administration of a series of fresh solutions or treatment levels is more specific than time as a criterion for true replication. Suppose, for example, that chemical A is to be tested on a group of arthropods collected from the field, and a shipment of another group from a different site will arrive the next day. Time available to do the bioassay is obviously limited. One set of treatment solutions is prepared, but three

2331_C002.fm Page 17 Wednesday, May 9, 2007 5:42 AM

Chapter two: Quantal response bioassays

17

different groups will be tested one hour apart. Is this true replication? The answer is no, not because only an hour separates the experiments, but because a possible error in preparation of the test solutions cannot be detected. If the experiments were done with fresh solutions, the biosassay would be truly replicated. Now suppose that fresh solutions are used. In the first replication, the concentrations that are applied kill between 5% and 95% of the insects. In the second, all of the controls live, but all of the insects treated with the chemical die regardless of concentration applied. Although these results may be valid, a procedural error may have occurred; but in which replicate? Results of the third and fourth replications might suggest that a formulation error occurred in one of the first two replicates. Results from a replicate can be disregarded if (and only if) an error is known to have occurred in that replicate. Data must never be discarded without extremely strong justification, such as a known procedural error or an outlier that is detected as part of the data analysis (see 3.II.A.1, “Goodness of Fit”). If an error does not seem likely (for example, if the results of the third replication are like those of the first, but results of the fourth replication are like those of the second), all data should be used for statistical analyses. Inconsistency from replication to replication may be the result of extrabinomial variability or outliers (see 3.II) and various other reasons.

E. Order of treatments within a replication On both practical and theoretical grounds, Dr. Tarleton suggests that the order in which treatment rates are applied in a quantal response bioassay should be from lowest to the highest, never vice versa. If the treatment is highest to lowest in a bioassay with a chemical, for example, results can be spurious because the test subjects may actually be exposed to a higher rate than intended. The impracticality of cleaning an application device and letting it dry completely between applications of different concentrations is obvious. But such cleanings are necessary even if concentrations are applied in random order. (Equally impractical is the use of differently calibrated syringes or spray reservoirs for each concentration.) Theoretically, some residual solvent will remain in the application device after cleaning without subsequent drying. If the solvent is pure (as would be the case if cleaning had just occurred), the concentration of the chemical tested next will be diluted more than if solvent plus a lower concentration of chemical remains in the needle, syringe, spray reservoir, or nozzle. In the treatment sequence of lowest to highest rate, the application device need not be cleaned. When more than one treatment is tested as part of each replication, the order in which the treatments are applied should be randomized among replications. Suppose that, unknown to the investigator, small amounts of chemical A interact with chemical B to cause a greater effect than would be expected if the joint effects of the two chemicals were independent and

2331_C002.fm Page 18 Wednesday, May 9, 2007 5:42 AM

18

Bioassays with arthropods, second edition

additive. Each time chemical B was tested, observed effects will not just be due to B if it is always tested after A. Randomization of the treatment sequence of chemicals helps minimize the possible experimental bias and error that may occur.

III. Computer programs Computer programs are not only crucial for analyses of bioassay data, but their manuals and documentation often provide a useful guide to the statistical literature. According to Dr. Tarleton, before the availability of personal computers and access to large statistical packages that once ran only on mainframe computers, analyses of bioassay data were a horrendous chore. Programs developed by individual scientists for specific methods were occasionally developed for programmable calculators,17 but their documentation tended to be vague. FORTRAN code for special procedures18 was published by some authors, but was rarely, if ever, used by other investigators; these programs and routines were usually used exclusively by the people who developed them. Large commercial statistical packages sometimes do not automatically provide enough information to prevent the user from doing the wrong test on the wrong type of data and then reaching the wrong conclusions.19 Whatever program is used, it must be capable of producing all of the necessary test statistics so that maximum information can be extracted from the bioassay data, and all hypotheses of interest can be tested. Dr. Tarleton concludes the bioassay workshop with sample data sets from binary quantal response bioassays with one or more explanatory variables,20,21 along with their analyses with two user-friendly computer programs. These programs were designed specifically to provide biologists bumbling their way through bioassays from going too far astray. In addition, they are computationally correct and well documented. As a contrast, he also provides command lines for analyses of selected data sets with the statistical-computing environment R.22 (The same command lines are used for the commercial product S-PLUS.23) He recommends that a user-friendly program should be used if available. If not, a well-documented statistical package9,23 can be used with proper guidance.

References 1. Refer to www.dame-edna.com for a look at true designer eye wear. 2. For a picture of this particular headdress, refer to www.beachblanketbabylon and go to the Hat Gallery page. 3. Mitchell, P. L., Leaf-footed bugs (Coreidae), in Schaefer, C.W. and Panizzi, A. R., eds., Heteroptera of Economic Importance, CRC Press, Boca Raton, FL, 2000, pp. 337–403.

2331_C002.fm Page 19 Wednesday, May 9, 2007 5:42 AM

Chapter two: Quantal response bioassays

19

4. Schaefer, J., Shane, Houghton Mifflin, Boston, 1949. Jack Schaefer's book, one of the best novels about the American West that has ever been written, is dedicated “To CARL: for my first son, my first book.” Carl W. Schaefer is a specialist in coreid systematics and evolutionary biology of the Heteroptera who may be distantly related to Dr. Cotton Mather Schaefer, the founder of the University of Schaeferville. 5. McCullagh, P. and Nelder, J. A., Generalized Linear Models, CRC Press, Boca Raton, FL, 1999. 6. Colin, D., Models for teratological data, in Krewski, D. and Franklin, C., eds., Statistics in Toxicology, Gordon and Breach Science Publishers, New York, 1991, pp. 335-347. 7. Hines, R. J. O. and Hines, W. G. S., The analysis of grouped longitudinal mortality data allowing for natural mortality, in Morgan, B. J. T., eds., Statistics in Toxicology, Oxford University Press, Oxford, England, 1996, pp. 101-126. 8. Hughes, G. R. and Guilfoyle, A., MLPACK: user's Guide, Cambridge University, Cambridge, England, 1984. 9. Stata Corporation, Stata 9 software, 4905 Lakeway Dr., College Station, TX, 77845. 10. Krewski, D. and Bickis, M., Statistical issues in toxicological research, in Krewski, D. and Franklin, C., eds., Statistics in Toxicology, Gordon and Breach Science Publishers, New York, 1991, pp. 11-41. 11. For example, Li, S. Y. and Otvos, I. S., Comparison of the activity enhancement of a baculovirus by optical brighteners against laboratory and field strains of Choristoneura occidentalis (Lepidoptera: Tortricidae), J. Econ. Entomol. 92, 534, 1999. 12. Stark, J. D. and Wennergren, U., Can population effects of pesticides be predicted from demographic toxicological studies?, J. Econ. Entomol. 88, 1089, 1995. 13. Bergh, J. C., Rugg, D., Jansson, R. K., McCoy, C. W., and Robertson, J. L., Monitoring the susceptibility of citrus rust mite (Acari: Eriophyidae) populations to abamectin, J. Econ. Entomol. 92, 781, 1999. 14. For example, Robertson, J. L. and Kimball, R. A., Toxicities of topically applied insecticides to western spruce budworm, 1979, Insecticide Acaricide Tests 5, 203, 1980. 15. For example, Robertson, J. L. and Boelter, L. M., Toxicity of insecticides to Douglas-fir tussock moth, Orgyia pseudotsugata (Lepidoptera: Lymantriidae) I. Contact and feeding toxicity, Can. Entomol. 111, 1145, 1979. 16. See Table 1 in Bolin, P. C., Hutchison, W. D., and Andow, D. A., Long-term selection for resistance to Bacillus thuringiensis Cry1Ac endotoxin in a Minnesota population of European corn borer (Lepidoptera: Crambidae), J. Econ. Entomol. 92, 1021, 1999. 17. For example, Toth, S. J. Jr. and Sparks, T. C., Effect of temperature on toxicity and knockdown activity of cis-permethrin, esfenvalerate, and λ-cyhalothrin in the cabbage looper (Lepidoptera: Noctuidae), J. Econ. Entomol. 83, 342, 1990. 18. For example, Robertson, J. L. and Smith, K. C., MIX: a computer program to evaluate interaction between chemicals, USDA Forest Service Gen. Tech. Rep., PSW-112, 1989. 19. Gad, S. G., Statistics and Experimental Design for Toxicologists, CRC Press, Boca Raton, FL, 1998.

2331_C002.fm Page 20 Wednesday, May 9, 2007 5:42 AM

20

Bioassays with arthropods, second edition 20. LeOra Software, PoloPlus, LeOra Software, 1007 B St., Petaluma, CA 94952, 2003. See http://www.LeOraSoftware.com. 21. LeOra Software, PoloEncore: multiple probit or logit analysis for Windows, LeOra Software, 1007 B St., Petaluma, CA 94952, 2007. See http://

www.LeOraSoftware.com. 22. See http://www.r-project.org. R version 1.9.1 was released on June 21, 2004. 23. See http://www.insightful.com/products/splus.

2331_C003.fm Page 21 Wednesday, May 9, 2007 5:43 AM

chapter three

Binary quantal response with one explanatory variable As a graduate student in insect ecology, Paula Maven often referred to entomologists who studied pesticides as “nozzleheads.” She went so far as to refer to the Journal of Economic Entomology as Nozzlehead News. Her graduate research concerned development of a computer model to predict outbreaks of the black witch on broom (Cytisus scoparius L.). She concluded that peak population levels occur on October 31 of each calendar year; moth flights begin at dusk and continue until midnight on that night in particular. Because of the close systematic relationship between the black witch and the wicked witch of the west, Paula originally thinks that the new species can be studied easily. She is so very wrong. First, the wings of adult A. giganticus are covered with pointed scales that explode with the force of microamounts of C-4 explosive about two hours after contact with human or animal skin. Severity of the injury depends on the number of scales contacted (another quantal response that a pathologist will need to study later). Second, the saliva of larvae contains an exotic, ghastly, and unidentified chemical that renders fruit and other plant material totally inedible. On contact with mammalian saliva, the nasty chemical foams and tastes like soap. Third, tomatoes sent to processing plants explode at random and wreck expensive machinery. Finally, larvae preferentially chew near xylem, which spreads the chemical throughout the plant tissue very rapidly. Laboratory rearing might prove to be a bit complicated. Before anything else can be done, Paula Maven’s technician, Blanche St. James, requisitions Kevlar coats and gloves for everyone in the lab. Then, based on simple logic, common sense, and familiarity with every insect diet ever developed,1,2 Blanche develops a new one specifically for this beast. After combining tomato paste, garlic, and onions in a large blender, she suspends the mixture in autoclaved, molten agar (liquefied at slow exhaust, then cooled to 75°C). She next pours the cooling tomato-agar mixture onto 21

2331_C003.fm Page 22 Wednesday, May 9, 2007 5:43 AM

22

Bioassays with arthropods, second edition

a thin crust that has been pre-baked inside a large aluminum tray. The crust is made from unbleached wheat flour combined with a suspension of 2 packages of quick-rise yeast in scalded milk; the dough rises twice and Blanche punches it down each time before pressing it into each tray. The complete diet can be removed in slices from the tray as needed. The diet preparation room might smell like a pizza parlor, but the insects eat the diet hungrily and the laboratory population soon flourishes. Larvae reach about 6 cm in length when mature. Only 35 days pass from the egg to the adult stage. Now the bioassays can begin. The simplest quantal response bioassay is a binary quantal response experiment with one explanatory variable. This is the kind of bioassay that Dr. Maven has Blanche do first with the laboratory colony of A. giganticus. The bioassays are done for three reasons. First, Paula needs to estimate the relationship between dose and response and compare the regression lines for individual chemicals. For each generation of laboratory rearing, Paula uses three chemicals—DDT, pyrethrins, and mexacarbate—as standards to monitor changes in response across generations. Second, she must compare the doses that cause the same levels of mortality. For these experiments, Blanche tests 10–15 toxicants to estimate their toxicities relative to responses to the three standard chemicals tested in the same generation. Third, Blanche tests several geographically separate strains of NPV on the wicked witches. For these experiments, Dr. Maven will identify the groups of strains with equal response. Thus, three types of comparisons—among lines, among points on lines, and among groups of lines—are necessary. As will be described in Chapter 12, “Binary Quantal Response with Multiple Explanatory Variables,” Dr. Maven could do bioassays with more than one explanatory variable. But their design, statistical basis, and data analysis are very different from the situation with a single explanatory variable. One of the greatest causes of problems in quantal response bioassays is, in fact, the assumption that a particular variable or another (e.g., insect body weight) is not a significant factor in response and therefore, that the experiment includes only one explanatory variable (e.g., dose). So, just to be sure, Dr. Maven carefully examines each of her binary quantal response experiments for any hidden assumptions before she actually starts the experiment.

I. Terminology and general statistical model Any binary response bioassay typically involves the selection of several doses, administration of each dose to a number of test subjects, and, after a specified time, designation of each subject's response as either yes (e.g., dead, knocked down) or no (e.g., alive, not knocked down). In arthropod toxicology, the definition of dose has become unnecessarily complicated.3,4 The most sensible definition is that of Finney as “an intensity specified in units of concentration, weight, time, or other appropriate measure. . . .”5 Similarly,

2331_C003.fm Page 23 Wednesday, May 9, 2007 5:43 AM

Chapter three: Binary quantal response with one explanatory variable

23

Hamilton6 has defined dose as a generic term for the level of exposure. We will use Finney’s5 definition here. The statistical statement of the binary quantal response with a single explanatory variable is shown in Equation 3.1: Pi = F(α + β xi )

(3.1)

where Pi is the probability of response, xi is the ith dose or a function of that dose, and F is a distribution function, and α + βxi is the regression line. In a quantal response bioassay, the points along the regression line are such that, for a given dose or concentration on the X axis, there is a corresponding probability level of response. The dose that corresponds with a specific probability level is the LD (lethal dose) for that level. Depending on the definition of dose, other terms in the scientific literature are LC (lethal concentration), ED (effective dose), ID (inhibitory dose or dose necessary for x% inhibition), and LT (lethal time necessary for x% mortality). Because Dr. Maven is using a statistical model to obtain this dose, estimation is the correct terminology; she neither measures nor determines lethal dose.

II. Statistical methods A. Probit or logit regression Of the numerous types available,7 the two distribution functions most commonly used in Equation 3.1 are the normal and the logistic. The normal distribution is assumed in probit analysis, so that the model specified by Equation 3.1 is pi = Φ (α + β xi ) where Φ is the standard normal distribution function. For the logit model

Pi =

1 − α +β x 1 + e ( i)

=

e α +β x i 1 + e α +β x i

where e ≅ 2.71828 . The ‘linear predictor’ α + βx is called the probit or logit line depending on whether the normal or the logistic model is used. The parameters α and β are the intercept and the slope of the probit or logit line. Entomologists have tended to use the probit model. Although a debate about use of one model versus the other has continued among statisticians,7,8 no biological evidence has ever shown that bioassay data are always distributed as either a normal or logistic function. Does the use of one model or the other matter? This question is impossible to answer because similar results are obtained with either one except at the extreme ends of the probability distribution. For example, Savin et al.9 have showed that, for mexacarbate applied to laboratory-reared (nondiapausing) western spruce bud-

2331_C003.fm Page 24 Wednesday, May 9, 2007 5:43 AM

24

Bioassays with arthropods, second edition

worm, estimates of LD50s for probit and logit models varied by 1.4% and LD90s varied by 0.48%. At the LD99, however, logit values were consistently higher (25%). Results from probit and logit analysis of the same data sets are shown in Table 3.1. Clearly, estimates at 50% and 90% levels of mortality are very close, regardless of the model used. Parameters of each model can be estimated by maximizing a loss function. Two popular loss functions are (1) minus the logarithm of the likelihood function (maximum likelihood [ML] procedure), and (2) the chi-square function (minimum χ2 method).10,11 A third function is the deviance,12 which is a standardized log-likelihood function.

1. Goodness of fit The measure of how well data fit the assumptions of the model (whether probit, logit, or some other related model; whether error is binomial) is called goodness of fit. The usual way to test fit is with a χ2 test. In this test, values (responses) predicted by the model are compared with values actually observed in the bioassay. If the values differ significantly at P = 0.05, the model is assumed not fit to the data and a more appropriate model should be sought. However, alternatives to the probit or logit models are not easy to use. (The need for further research and development in this aspect of pesticide bioassay techniques is further discussed later in this chapter.) Some scientists abandon the probit or logit model and examine response at each dose level separately. Others (Williams,13 SAS14) multiply the variances by a heterogeneity factor (χ2/(k–2), where k is the number of doses) to account for extra variation that causes poor fit. However, neither of these alternatives provides any clue about why the data do not fit the model. A more meaningful approach is to examine possible causes of lack of fit by means of residual plots (Preisler15). A residual is the difference between the observed value and the expected value. Because binomial responses do not have a constant variance over the Table 3.1 Comparison of Results of Probit (P) and Logit (L) Analyses of Dose-Response Data for Mexacarbate Applied to Western Spruce Budworm LD50

LD90

Generation

N

P

L

P

L

F11 F13 F11 F19 F20

290 494 180 484 364

0.83 0.72 0.86 0.95 0.64

0.83 0.73 0.89 0.94 0.64

3.32 2.95 2.46 3.14 1.84

3.21 2.90 2.49 3.15 1.79

Note: Part of these results were reported in Savin, N. E., Robertson, J. L., and Russell, R. M., Bull. Entomol. Soc. Am. 23(4), 257–266, 1977.

2331_C003.fm Page 25 Wednesday, May 9, 2007 5:43 AM

Chapter three: Binary quantal response with one explanatory variable

25

range of responses tested, they must be standardized by division by their standard errors, np(1 − p). The variable n is the number of subjects tested at the specific dose and p is probability. For good fit, residuals plotted against predicted values usually lie within a horizontal band around zero (mostly between –2 and 2). Preisler15 identified five causes of significant departure from the probit binomial model that produce large χ2 values. First, outliers that do not fit the model might be the cause of lack of fit, especially if they occur at a response level near 0 or 100%. An outlier should be discarded from the data set only if strong evidence suggests that a recording error has occurred. Otherwise, the outlier may indicate interaction with or the existence of an important independent variable. The second cause may be omission of a significant explanatory variable from the model (for example, when a multiple probit or logit model is appropriate but a univariate model is used). Third, the statistical model might not fit the data. For example, a probit regression line with a plateau is characteristic of genetically heterogeneous populations and is often observed in groups that contain resistant and susceptible individuals.16 Responses related to some factor in the model may cause correlation between test subjects. As a result, error terms are not independent. Thus, insects from the same generation might be more alike in their response to a pesticide than they are compared with insects in another generation. A large data set for experiments in which three pesticides—mexacarbate, pyrethrins, and DDT—were tested on more than 40 generations of a laboratory colony of nondiapausing western spruce budworm17 shows this type of lack of fit. In Figure 3.1, clustering of residuals within each experiment is apparent. Therefore, a simple binomial model is not appropriate because use of such a model assumes that observations are independently distributed.

Standardized residuals

4 2 0 -2 -4 0

2

4

6

8

10

Experiment number

Figure 3.1 Data in Which Residuals Are Clustered.

12

14

16

2331_C003.fm Page 26 Wednesday, May 9, 2007 5:43 AM

26

Bioassays with arthropods, second edition

Finally, Preisler15 has identified a situation in which error terms are not binomial. The data set18 that she used was collected in tests with an acaricide, propargite, on spider mites. Even when residuals were standardized, many of their absolute values were still >2 (see Figure 3.2). The extrabinomial variability in these data could not be explained by an experiment or generation effect. Likewise, sampling from a genetically heterogeneous population did not appear to be responsible. For lack of fit caused by lack of independence of error terms (as in the data set for western spruce budworm) and extrabinomial variability (as in the data set for spider mites), Preisler15 has described a method to obtain maximum likelihood estimates for parameters in a compound binomial probit model so that hypotheses of parallelism and equality can still be tested. This method is based on addition of a random effect factor to the probit line at the dose (or concentration) level. Inclusion of this procedure in available probit or logit statistical packages would improve the reliability of standard errors for lethal dose estimates and the reliability of the results of tests of parallelism and equality.

2. Lethal dose ratios Ratios at a specific response level such as LD50 or LD90 are often used to determine the relative toxicity of a number of chemicals compared with a standard chemical19 to determine relative susceptibility of populations,20 and to study the extent,21,22 and genetic bases,23 for pesticide resistance. A lethal dose ratio is more general than the alternative statistic, relative potency,5 which assumes that the regression lines being compared are parallel. If there were some rationale by which parallelism could always be assumed to occur, relative potency could be used rather than a lethal dose ratio. However,

Standardized residuals

4 2 0 -2 -4 0

1

2

3

4

5

Experiment number

Figure 3.2 Data in Which the Absolute Value of More than 5% of Standardized Residuals Are >2.

2331_C003.fm Page 27 Wednesday, May 9, 2007 5:43 AM

Chapter three: Binary quantal response with one explanatory variable

27

regression lines are rarely parallel, particularly in bioassays of several pesticides with different modes of action or among populations in the process of becoming resistant to a pesticide. Given the fact that a simple ratio of one lethal dose to another does not provide any estimate of the error involved in the calculation, the most practical and least restrictive alternative is to estimate 95% confidence intervals for each ratio. Based on estimates for the intercepts (αi) and the slopes (βi, i = 1,2) of two probit (or logit) lines and estimates of their variance-covariance matrixes, the 95% confidence interval for the ratio is calculated by the following steps: 1. Calculate x − αˆ i θˆi = π βˆ i for i = 1,2 where xπ is the π−th percentile point of the probit (or logit) distribution curve. Values of xπ for levels of response that are most often of interest are: π

10

25

50

75

80

90

95

97.5

99

xπ

-1.28

-0.67

0

0.67

0.84

1.28

1.65

1.96

2.33

For example, if π = 90, then x90 = 1.28. 2. Calculate ˆ θˆi ) = var(

1 ⎡ ˆ αˆ i ) + 2θˆi cov( ˆ αˆ i , βˆ i ) + θˆi 2 var( ˆ βˆ i )⎤ var( ⎦ 2 ⎣ ˆ θi

for i = 1,2. 3. Calculate a = θˆ1 − θˆ2 and ˆ θˆ1 ) + var( ˆ θˆ2 ) σ = var(

2331_C003.fm Page 28 Wednesday, May 9, 2007 5:43 AM

28

Bioassays with arthropods, second edition 4. Estimates of the ratio of two lethal doses and the approximate 95% confidence boundaries are given by: ratio = 10a lower boundary = 10a-2 σ upper boundary = 10a+2 σ

Relative potency between two toxicants is always the same regardless of dose level, while ratios of lethal doses can be very different at, for instance, LD 50 and LD 90 , because two lines are not parallel. Especially when dose-response regressions are used as evidence for resistance to pesticides, reporting of ratios at two response levels such as 50 and 90% is probably most informative.

B. Hypotheses tests An essential aspect of the analyses of bioassay data is statistical hypotheses testing. As Dr. Tarleton so wisely stressed during his course, a difference in results is not a difference unless it is significant. Identification of significant differences is the interface between biology and statistics. The specific nature of hypotheses that can be tested with binary response data depends on whether Dr. Maven is interested in regression lines, point estimates (i.e., LD’s) on different lines, or groups of regression lines.

1. Regression lines Hypothesis tests can be done to compare the slopes and intercepts of different probit or logit lines. Three hypotheses are usually of interest: (1) the lines are parallel but not equal; (2) the lines are equal; or (3) the lines are neither parallel nor equal. When two (or more) lines are parallel but not equal, their slopes are not significantly different (see Figure 3.3a) even though their intercepts differ significantly. Biologically, the slope of a probit or logit regression estimates the change in activity per unit change in dose or concentration. Pharmacological evidence described by Hardman et al.24 and Kuperman et al.25 suggests that the slope of a probit or logit regression also reflects the quality of enzymes involved in detoxification. Thus, parallel lines may indicate that organisms have qualitatively identical, but quantitatively different, levels of detoxification enzymes.26 However, direct biochemical evidence of this interpretation is lacking. In conjunction with biochemical studies of relevant detoxification mechanisms, bioassays may provide further information about this interpretation. A definitive biochemical definition of slope would be particularly useful in studies of resistance and environmental toxicology. Theoretically, the intercept of a probit or logit regression should correspond with the response threshold (i.e., the response that occurs with no

2331_C003.fm Page 29 Wednesday, May 9, 2007 5:43 AM

Chapter three: Binary quantal response with one explanatory variable

29

treatment). Natural response is a statistical estimate of this response threshold; this value is provided by the response of controls in a bioassay. At the response threshold, at least one organism in the population responds to the treatment. If regressions are equal (a second possible outcome of hypothesis testing), they do not differ significantly in either slope or intercept (see Figure 3.3b). Equality may mean that detoxification enzymes in the organisms with equal responses are qualitatively and quantitatively the same. However, this interpretation has not yet been examined biochemically in arthropods. Finally, when lines are neither equal nor parallel (see Figure 3.3c), neither their slopes nor their intercepts are equal. This outcome may mean that detoxification enzymes differ qualitatively or that totally different enzymes occur in the organisms. Physical processes such as absorption through the cuticle or gut, target site sensitivity, or excretion may also be relevant in inequality, parallelism, and equality. In summary, the biochemical bases and physiological processes in the arthropod that result in parallelism and equality would be useful areas for future toxicological and biochemical research. Hypotheses tests of parallelism and equality of lines can be tested by likelihood ratio (LR) tests. The degrees of freedom in the LR test is the number of parameters in each line (= 2 for slope and intercept), multiplied by the total number of individual lines, minus the number of parameters in the composite line (= 2). In the LR test of parallelism, slopes of individual lines from different experiments are assumed to be the same; each line is then compared with the composite line. In this test, the degrees of freedom is the number of individual lines minus 1. As will be illustrated in Chapter 4, “Binary Quantal Response: Data Analyses,” LR tests of equality and parallelism are done automatically by the PoloPlus software program.27

2. Point estimates Suppose that Blanche has completed a large study of the responses of wicked witches to geographic isolates of a virus. Dr. Maven is interested in whether the LDx of one isolate differs significantly from the LDx of another, and which isolates merit full-scale production. In the past, the usual way to compare lethal doses or other point estimates was to examine their 95% confidence limits.28 If the limits overlapped, then the lethal doses were not considered to be significantly different except under unusual circumstances. Based on the evidence provided by Wheeler et al.,29 we recommend that this test not be used because it lacks statistical power. By using Monte Carlo simulation, these authors29 provide valuable evidence that the ratio test is far preferable to the overlap test based on statistical power of the test and better type I error rates. The ratio test, for which significance can be set at P = 0.05 or any other probability level of choice, is done as follows. Calculate the ratio of the LDs; then calculate the 95% confidence interval for this ratio as shown above (3.II.A.2, “Lethal Dose Ratios”). If the 95% confidence interval includes 1, then the LDs are not significantly different.

2331_C003.fm Page 30 Wednesday, May 9, 2007 5:43 AM

30

Bioassays with arthropods, second edition 6 a Parallel lines

4 2 0 -2 -5

-3

-1

1

3

5

log (dose)

6 b Equal lines

4 2 0 -2 -5

-3

-1

1

3

5

log (dose)

8 6

c Lines not equal

4 2 0 -2 -5

-3

-1

1

3

5

log (dose)

Figure 3.3 The Three Possible Results of Tests of the Hypothesis of Parallelism and the Hypothesis of Equality.

2331_C003.fm Page 31 Wednesday, May 9, 2007 5:43 AM

Chapter three: Binary quantal response with one explanatory variable

31

3. Groups of lines with equal response LR tests of equality and parallelism are perhaps the most efficient means to compare probit or logit regressions, assuming, of course, that the data fit the probit or logit model. An alternative method is use of a weighted analysis of variance. One example of the use of this method is separation of response lines of Indianmeal moth, Plodia interpunctella (Hübner) to the microbial pesticide Bacillus thuringiensis Berliner.30 However, analysis of variance ignores information such as the fact that dose-response curves are monotonically increasing, S-shaped curves. Weighted analysis of variance is also computationally less efficient than maximum likelihood estimation. Tabashnik et al.31 have argued that analysis of variance is preferable for studies of pesticide resistance because, among other reasons, it avoids some of the problems that occur when probit analysis is used for detecting and monitoring resistance. These problems are described by Roush and Miller.32 One of the assertions made by Tabashnik et al.31 is that analysis of variance provides a direct, overall test of the hypothesis that populations differ in their response. Separation of probit or logit regressions into groups has merit, especially when the results concern insecticide resistance or other areas of research in which genetic shifts in populations of a target organism or genetic differences in a microbial pesticide affect the responses estimated by probit or logit regression. Examples of useful information to be gained by grouping dose-response lines are (1) detection of significant shifts in a species’ response in a particular geographic area in relation to continued selection pressure; (2) comparison of activities of isolates of a particular strain of virus or bacterium on a target organism (see, e.g., Shapiro et al.33); and (3) detection of geographic variation in a species' response to a pesticide. No statistical tests analogous to multiple range tests have been developed for use with probit or logit regressions. The only procedure available consists of a sequence of tests of the hypothesis of equality (e.g., Robertson and Stock,34 Shapiro et al.33). Each test must be done at a level of probability lower than P = 0.05 so that the overall P = 0.05.

C. Alternatives to probit and logit analysis Both probit and logit analyses are based on two-parameter, symmetric tolerance distributions described by Finney5 and Cox.35 Copenhaver and Mielke36 have described another method, quantit analysis, that is based on a three-parameter family of symmetric tolerance distributions. The Ω distribution includes both the normal distribution used in probit analysis and the logistic distribution used in logit analysis. Thus, the normal and logistic distributions are subsets of the Ω distribution. Possibly because the computer program available for quantit analysis was written in FORTRAN for IBM mainframe computers and the output is fairly difficult to interpret, quantit analysis has not been used widely for analysis of bioassay data.

2331_C003.fm Page 32 Wednesday, May 9, 2007 5:43 AM

32

Bioassays with arthropods, second edition

Because the Ω distribution is symmetric, LD50 values estimated by probit, logit, or quantit analyses do not differ appreciably. However, differences at LD99 are large. As shown by Copenhaver and Mielke,36 the Ω model represents a more generalized symmetric tolerance distribution that may give better fit in the extreme tails of response, such as below the LD5 and above the LD95. However, many of the data sets used as examples include too few test subjects to be considered well-designed even with perfect dose placement. Furthermore, quantit analysis is, like probit and logit analysis, inflexible in the sense that it is based on symmetric distribution functions. As will be described in Chapter 11, “Time as a Variable,” the two-parameter complimentary log-log (CLL) model37 may offer even greater flexibility than does the Ω model, because it includes asymmetric tolerance distributions but can give approximations of symmetric distributions such as the normal, logistic and Ω models. Future research in statistical analyses of binary quantal response data should be directed at the development of more flexible methods, such as CLL analysis, for practical use by biologists. Finally, Hubert38 describes numerous nonparametric models; these may merit further consideration for use in the analysis of data from univariate quantal response bioassays.

References 1. Singh, P. and Moore, R. F., Handbook of Insect Rearing, Vols. I and II, Elsevier, Amsterdam, 1985. 2. Cohen, A. C., Insect Diets: Science and Technology, CRC Press, Boca Raton, FL, 2004. 3. Robertson, J. L. and Preisler, H. K., Pesticide Bioassays with Arthropods, 1st ed., CRC Press, Boca Raton, FL, 1992. 4. Stark, J. D. and Banks, J. E., Population-level effects of pesticides and other toxicants on arthropods, Annu. Rev. Entomol. 48, 505, 2003. 5. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 6. Hamilton, M. A., Estimation of the typical lethal dose in acute toxicity studies, in Krewski, D. and Franklin, C., Statistics in Toxicology, Gordon and Breach Science Publishers, New York, 1991, pp. 61–68. 7. Hastings, N. A. J. and Peacock, J. B., Statistical Distributions, A Handbook for Students and Practioners, Butterworths, London, 1974. 8. Berkson, J., Why I prefer logits to probits, Biometrics 7, 327, 1951. 9. Savin, N. E., Robertson, J. L., and Russell, R. M., A critical evaluation of bioassay in insecticide research: likelihood ratio tests of dose-mortality regression, Bull. Entomol. Soc. Am. 23, 257–266, 1977. 10. Berkson, J., Maximum likelihood and minimum χ2 estimates of the logistic function, J. Amer. Stat. Assoc. 50, 130, 1955. 11. Smith, K. C., Savin, N. E., and Robertson, J. L., A Monte Carlo comparison of maximum likelihood and minimum chi square sampling distributions in logit analysis, Biometrics 40, 471, 1984. 12. Fox, J., Applied Regression Analysis, Linear Models, and Related Methods, Sage, Thousand Oaks, CA, 1997.

2331_C003.fm Page 33 Wednesday, May 9, 2007 5:43 AM

Chapter three: Binary quantal response with one explanatory variable

33

13. Williams, D. A., Extra-binomial variation in logistic linear models, Appl. Statistics 31, 144, 1982. 14. SAS Institute, http://www.sas.com/technologies/analytics/statistics/stat. 15. Preisler, H. K., Assessing insecticide bioassay data with extra-binomial variation, J. Econ. Entomol. 81, 759, 1988. 16. Tsukomoto, M., The log-dosage probit mortality curve in genetic researches of insect resistance to insecticides, Botyu-Kagaku 28, 91, 1963. 17. Savin, N. E., Robertson, J. L., and Russell, R. M., A critical evaluation of bioassay in insecticide research: likelihood ratio tests of dose-mortality regression, Bull. Entomol. Soc. Am. 23, 257, 1977. 18. Grafton-Cardwell, E. E., Granett, J., and Leigh, T. F., Spider mite species (Acari: Tetranychidae) response to propargite; the basis for a resistance management program, J. Econ. Entomol. 80, 579, 1987. 19. Kontsedalov, S., Weintraub, P. G., Horowitz, A. R., and Isaaya, I., Effects of insecticides on immature and adult western flower thrips (Thysanoptera: Thripidae) in Israel, J. Econ. Entomol. 91, 1067, 1998. 20. Luttrell, R. G., Wan, L., and Knighten, K., Variation in susceptibility of Noctuid (Lepidoptera) larvae attacking cotton and soybean to purified endotoxin proteins and commercial formulations of Bacillus thuringiensis, J. Econ. Entomol. 92, 21, 1999. 21. Scharf, M. E., Meinke, L. J., Siegfried, B. D., Wright, R. J., and Chandler, L. D., Carbaryl susceptibility, diagnostic concentration determination, and synergism of U.S. populations of western corn rootworm (Coleoptera: Chrysomelidae), J. Econ. Entomol. 92, 33, 1999. 22. Prabhaker, N., Toscano, N. C., and Henneberry, T. J., Evaluation of insecticide rotations and mixtures as resistance management strategies for Bemisia argentifolii (Homoptera: Aleyrodidae), J. Econ. Entomol. 91, 820, 1998. 23. Bengston, M., Collins, P. J., Daglish, G. J., Hallman, V. L., Kopittke, R., and Pavic, H., Inheritance of phosphine resistance in Tribolium casteneum (Coleoptera: Tenebrionidae), J. Econ. Entomol. 92, 17, 1999. 24. Hardman, H. F., Moore, J. I., and Lum, B. K. B., A method for analyzing the effect of pH and ionization of drugs upon cardiac tissue with special reference to pentabarbitol, J. Pharmacol. Exp. Therap. 126, 136, 1959. 25. Kuperman, A. S., Gill, E. W., and Riker, W. F., The relationship between cholinesterase inhibition and drug-induced facilitation of mammalian neuromuscular transmission, J. Pharmacol. Exp. Therap. 132, 65, 1961. 26. Robertson, J. L. and Rappaport, N. G., Direct, indirect and residual toxicities of insecticide sprays to western spruce budworm, Choristoneura occidentalis (Lepidoptera: Tortricidae), Can. Entomol. 111, 1219, 1979. 27. LeOra Software, PoloPlus, POLO for Windows, LeOra Software, 1007 B St., Petaluma, CA 94952. See http://www.LeOraSoftware.com. 28. Payton, M. E., Greenstone, M. H., and Schenker, N., Overlapping confidence intervals or standard error intervals: what do they mean in terms of statistical significance? http://www/insectscience.org/3.34. 29. Wheeler, M. W., Park, R. M., and Bailey, A. J., Comparing median lethal concentration values using confidence interval overlap or ratio tests, Environ. Toxic. Chem. 25, 1441, 2006. 30. McGaughey, W. H., Insect resistance to the biological insecticide Bacillus thuringiensis, Science 229, 193, 1985.

2331_C003.fm Page 34 Wednesday, May 9, 2007 5:43 AM

34

Bioassays with arthropods, second edition 31. Tabashnik, B. E., Cushing, N. L., and Johnson, M. W., Diamondback moth (Lepidoptera: Plutellidae) resistance to insecticides in Hawaii: intra-island variation and cross-resistance, J. Econ. Entomol. 80, 1091, 1987. 32. Roush, R. T. and Miller, G. L., Considerations for design of insecticide resistance monitoring programs, J. Econ. Entomol. 79, 293, 1986. 33. Robertson, J. L. and Stock, M. W., Toxicological and electrophoretic population characteristics of western spruce budworm, Choristoneura occidentalis (Lepidoptera: Tortricidae), Can. Entomol. 117, 57, 1985. 34. Shapiro, M., Robertson, J. L., Injac, M. G., Katagin, K., and Bell, R. A., Comparative infectivities of gypsy moth (Lepidoptera: Lymantriidae) nucleopolyhedrosis virus isolates from North America, Europe, and Asia, J. Econ. Entomol. 77, 153, 1984. 35. Cox, D. R., Analysis of Binary Data, Methuen, London, 1970. 36. Copenhaver, T. W. and Mielke, P. W., Quantit analysis: a quantal assay refinement, Biometrics 33, 175, 1977. 37. Preisler, H. K. and Robertson, J. L., Analysis of time-dose-mortality data, J. Econ. Entomol. 82, 1534, 1989. 38. Hubert, J. J., Bioassay, Kendall/Hunt, Dubuque, IA, 1984.

2331_C004.fm Page 35 Thursday, May 10, 2007 5:20 AM

chapter four

Binary quantal response: data analyses Paula and Blanche have just completed an important series of bioassays in order to determine which strain or strains of the wicked witch they will raise continuously in the laboratory. This laboratory colony will serve as their standard for population comparisons in all future experiments. Insects from two geographically separate populations in California—Fairfax (Marin County) and Pixley (Kern County)—were sent to Schaeferville in special quarantine shipping containers. Larvae and adults from tomato plants in and around Schaeferville were collected during a sweep-net competition in the university’s entomology department. All of the insects were transferred to artificial diet and first instars were randomly selected for testing. Although Blanche carefully recorded the average weight of each group of 10 first instars in a single Petri dish, she applied a uniform volume of 2µL of solution to each larva. Dose is expressed in units of mg (AI) per ml of acetone. Mortality of the larvae in each Petri dish was tallied after 7 days. These data are typical of binary quantal response experiments and provide Paula and Blanche with an opportunity to become familiar with the use, terminology, and statistical parameters of PoloPlus1 and the experimental statistical package R.2 Because Paula has used SAS in the past and it is still on her laptop, she also does probit analysis with SAS Proc-Probit.3

I. PoloPlus The POLO4 software program was written to do the computations described in Finney’s Probit Analysis,5 but with two unique additions. First, logit analysis was an option. Second, and of most practical importance to biologists, likelihood ratio tests of equality and parallelism were included. POLO-PC6 produced an identical output. PoloPlus1 is computationally identical to its predecessors. However, when the program was redone for Microsoft Windows, new features were added and unnecessary details were eliminated 35

2331_C004.fm Page 36 Thursday, May 10, 2007 5:20 AM

36

Bioassays with arthropods, second edition

from the output. Among the new features are automatic computation of resistance ratios and plots of the fitted response curves. Two ways of displaying goodness-of-fit tables of standardized residuals, and their plots, were added to identify sources of poor fit to the probit or logit model. The last new feature, calculation of the probit 9, will be described in Chapter 7, “Quarantine Statistics.” Of the commercially available probit or logit programs, PoloPlus is one of the very few to be easily used and understood by users who are not statisticians. Statistical terminology in the program is adapted from that used by Finney.5 Unfortunately, some terms cannot be explained in words and must be described by equations that will be described here.

A. Data Many text processing programs can be used to create a data file, so Blanche decides to enter their data in a Microsoft Excel file saved to text format. On the opening screen (see Figure 4.1), Blanche clicks on “Open a Data File.” The next screen (see Figure 4.2) is blank until Blanche clicks on “Open”; at this command, all of the files within the “Data” folder are listed. When “WickedWitch.txt” is selected, the data file for the experiment is listed on the screen (see Figure 4.3). In this file, each data set consists of a title line designated by an equal (=) sign, followed by sets of preparation (*) lines that separate the actual data. In the preparation line, only the first eight characters

Figure 4.1 PoloPlus Startup Screen.

2331_C004.fm Page 37 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

Figure 4.2 PoloPlus Ready to Open a Data File.

Figure 4.3 PoloPlus Displaying Data File.

37

2331_C004.fm Page 38 Thursday, May 10, 2007 5:20 AM

38

Bioassays with arthropods, second edition

are shown. Fairfax is a unique location where only one collection was done, but what if Blanche had managed to make separate collections around Schaeferville? In this case, a unique designation would be entered somewhere in the eight spaces after the * symbol. Under a given title, any number of data sets can be analyzed. In each data line, only one line per dose can be used. Each data line contains three fields in specific order. The first is dose (x), the second is the number (n) of test subjects, and the third is the number that respond (r). The results of each bioassay can be summarized manually but should entered separately. Entry of the separate data points without manual summarization minimizes the introduction of errors in addition and provides the correct degrees of freedom for the analysis.

B. Choice screens and program options Four possible options appear on the main screen that appears after the data file appears (see Figure 4.4). The first choice is the mathematical model (probit or logit). Next, is natural response a parameter? In the very unusual case where controls were not included, the box would remain unchecked. Next, the lethal doses, or LDs (up to 12), of interest are entered. If the probit or logit 9 (99.9968% mortality) is to be estimated, the P9 or L9 box is checked. (This option is explained in Chapter 7, “Quarantine Statistics.”) Default

Figure 4.4 PoloPlus Showing Choose Options Window.

2331_C004.fm Page 39 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

39

values in the choice options dialog box are probit model; doses converted to logarithms; LDs 10, 50, and 90. PoloPlus then returns to the “Open a Data File” screen. Blanche clicks on “Check Data” to see whether the data are entered correctly. If so, the program screen says “No errors were found in the data file” (see Figure 4.5). If something is wrong, however, a message on an orange screen will appear to explain the mistake. Among the possibilities are that the data entries are in the wrong order, a preparation line is missing, or that a header line is missing. Once she clicks on “OK” in the small “no error” window, the “Open a Data File” screen reappears but with the “OK” ready to be clicked on. Blanche clicks “OK,” and the opening screen appears again; she now clicks on “Calculate.” As the calculations are done, the word “Crunching” appears on the screen. The opening screen reappears, with five choices available (see Figure 4.6): “Display Results,” “Display Summary,” “Plot,” “Do Another Data File,” or “Quit.”

C. Display results 1. Options Choosing “Display Results” produces on the screen the listing shown in Figure 4.7. Besides reading the display off the computer screen, Paula and

Figure 4.5 PoloPlus Reporting No Errors in Data File.

2331_C004.fm Page 40 Thursday, May 10, 2007 5:20 AM

40

Bioassays with arthropods, second edition

Figure 4.6 PoloPlus Ready to Present Output.

Blanche have the choice of “Print” or “Save As. . . .” The “Save As . . .” option permits flexibility in naming, storing, and using the program output in programs such as Microsoft Word or PowerPoint.

2. Parameters The first section lists the parameters for the analysis of the data file designated in line 4. In this example, Paula and Blanche chose the probit model; natural response is a parameter; doses are converted to logarithms; the number of preparations is 3; the total number of dose groups is 14; 3 LDs will be estimated, and these LDs are at the 10%, 50%, and 90% levels (lines 5–10). Natural response is estimated when control mortality occurs in the bioassay. When no mortality is observed among the controls, natural response is assumed to be zero.

3. Individual regressions Results from the experiment with the header designation “Wicked witch of the west first instars. Average weight of 10 insects” are shown next (line 13). Parameters of the individual regressions for Fairfax (lines 16–45), Pixley (lines 48–79) and Schaefer (lines 82–111) follow. For each of these regressions, intercepts and slopes are always unknown (lines 16, 48, and 82). Unconstrained means that the values are unknown parmameters of the individual

2331_C004.fm Page 41 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

41

Figure 4.7 PoloPlus Display of Results.

lines to be estimated from the data. (Constrained slopes and intercepts are used only for the hypotheses tests to be described below.) If natural response has been observed, the second line will state “Estimating natural response”

2331_C004.fm Page 42 Thursday, May 10, 2007 5:20 AM

42

Bioassays with arthropods, second edition

Figure 4.7 (continued)

(Pixley, line 49). If not, line 2 will state “Not estimating natural response” (Fairfax, line 17; Schaefer, line 83). The next subsection for each preparation’s output gives the values, standard errors, and t-ratio (column headings given in lines 19, 51, and 85) for the intercept (row labeled with the preparation name), natural response if

2331_C004.fm Page 43 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

43

Figure 4.7 (continued)

present (line 53, Pixley), and slope (lines 21 and 92, Fairfax and Schaefer; line 60, Pixley). CAUTION: IF THE T-RATIO OF ANY SLOPE IS < 1.96, THE REGRESSION IS NOT SIGNIFICANT AND THE TREATMENT HAS NO EFFECT, AND THE DATA SET MUST BE EXCLUDED FROM FURTHER ANALYSIS. The variance-covariance matrix follows (lines 23–26, Fairfax; lines 56–60, Pixley; lines 89–92, Schaefer). These numbers are used to estimate the 95% confidence intervals for ratios and to identify significant differences between the first and subsequent preparations. The goodness-of-fit test subsection (lines 28–34, Fairfax; lines 62–68, Pixley; lines 94–100, Schaefer) shows the chi-square test and values of the standardized residuals. A residual is the difference between the observed value and the expected value (for example, line 29, r column versus expected column). The standardized residuals (last column) should be plotted for further examination of lack of fit. Because binomial responses do not have a constant variance over the range of responses tested, they must be standardized by division by their standard errors, np(1 − p). The variable n is the number of subjects tested at the specific dose (for example, lines 30–34, column labeled “n”) and p is probability (for example, lines 30–34, column labeled “probab”). For good fit, standardized residuals plotted against predicted values usually lie within a horizontal band around zero (with approximately 95% of them between –2 and 2).

2331_C004.fm Page 44 Thursday, May 10, 2007 5:20 AM

44

Bioassays with arthropods, second edition

Values of chi-square, degrees of freedom, and the heterogeneity factor (which equals the chi-square divided by degrees of freedom) follow (line 36, Fairfax; line 70, Pixley; line 102, Schaefer). When the heterogeneity factor is > 1.0, a plot of the data should be examined because the data do not fit the model. Such a plot may reveal systematic departure from linear regression, in which case a function other than logarithm of dose may be more appropriate. Plots of the residuals should also be examined to identify an outlier or other possible causes of lack of fit. Both types of plots can be done with PoloPlus. Estimated lethal doses with upper and lower confidence limits at 90% and 95% (and 99% if they can be calculated) are listed in the last subsection of the output for individual preparations (lines 38–45, Fairfax; lines 72–79, Pixley; lines 104–111, Schaefer). In these examples, the third column (“dose”) gives estimates of the LD10, LD50, and LD90. The upper and lower limits at 0.90 and 0.95, and 0.99 (columns 5–7) are the upper and lower 90%, 95%, and 99% confidence limits for the three lethal doses. If the statistic g (Finney5) is > 0.5 at 0.90, 0.95, or 0.99, that confidence limit will not be printed. For example, none of the 99% limits for the LDs can be printed for these populations.

4. Hypotheses tests The likelihood ratio (LR) test of equality tests whether slopes and intercepts of the regression lines are the same (line 115). If so, the lines (i.e., treatment or population effects) are not significantly different. If the hypothesis is rejected, the lines are significantly different as in this example. The statistics used in the test are the LR, degrees of freedom, and the tail probability (line 116). The LR test of parallelism tests whether slopes of the lines are the same; results are given in the same format as the test of equality (lines 120–21). In this test, slopes of each line are constrained to be the same. Each line is then compared with a composite line. For these three populations, the hypothesis of parallelism is not rejected and the lines have slopes that are not significantly different. Blanche and Paula conclude that the relative response rates of their populations appear to be the same. If these were different chemicals in the example rather than populations, the relative potency of the chemicals would be considered to be the same.

5. Lethal dose ratios This final section of the analysis (lines 127–46) shows the lethal dose ratios (relative toxicity ratios) with their upper and lower 95% confidence limits calculated in comparison with the first population. These calculations were described in Chapter 3, “Binary Quantal Response with One Explanatory Variable” (3.II.B.2). Ratios are calculated for the same LDs estimated for the individual preparations. In this example, the LD10, LD50, and LD90 for Pixley are significantly different from the LD10, LD50, and LD90 for Fairfax, whereas the values for Schaefer are not.

2331_C004.fm Page 45 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

45

Figure 4.8 PoloPlus Display of Summary.

D. Display summary (summary.txt screen) When “Display Summary” is chosen on the main screen, a listing of the summary (Figure 4.8) appears. It can be read from the computer screen, printed, or saved to a file. The first section (lines 1–10) lists the parameters of the analysis. The second section (lines 14–31) presents the summaries for each regression. The first line (lines 14, 20, and 26) gives the preparation title, number of test subjects, and number of controls. The second and third lines (lines 15–16, 21–22, and 27–28) list slope ± standard error, natural response ± standard error, and heterogeneity factor of the regression. The LDs and their 95% confidence limits are given next (lines 17–19, 23–25, and 29–31). The third section (lines 32–33) shows the results of the

2331_C004.fm Page 46 Thursday, May 10, 2007 5:20 AM

46

Bioassays with arthropods, second edition

Figure 4.9 PoloPlus Plot of Fairfax Regression Line.

LR tests of equality and parallelism. Lethal dose ratios in comparison with the first preparation are given last (lines 34–43).

E. Plot The plot button becomes available on the main screen after PoloPlus does the computations. Each fitted curve or a plot of the residuals, plotted on a linear or logarithmic scale, can be obtained by clicking in the appropriate places. Blanche and Paula use the Print menu to print a copy of each plot. They can also use the “Save As . . .” menu to save the plot as a graphics file in bitmap format, ready for export to PowerPoint (among other options). When Next is clicked repeatedly (with Fitted Curve marked), plots of the individual curves (see Figures 4.9–4.11) , the data used to estimate the composite line for the hypothesis of equality (collinear; see Figure 4.12), and the lines for the test of parallelism (see Figure 4.13) are shown. When “Next” is clicked on in sequence with Residuals marked, the standardized residuals for individual data sets are shown (see Figures 4.14–4.16), followed by the standardized residuals for the tests of equality (see Figure 4.17) and parallelism (see Figure 4.18).

2331_C004.fm Page 47 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

Figure 4.10 PoloPlus Plot of Pixley Regression Line.

Figure 4.11 PoloPlus Plot of Schaefer Regression Line.

47

2331_C004.fm Page 48 Thursday, May 10, 2007 5:20 AM

48

Bioassays with arthropods, second edition

Figure 4.12 PoloPlus Plot of Collinear Case Regression Line.

Figure 4.13 PoloPlus Plot of Parallel Case Regression Line.

2331_C004.fm Page 49 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

Figure 4.14 PoloPlus Plot of Fairfax Residuals.

Figure 4.15 PoloPlus Plot of Pixley Residuals.

49

2331_C004.fm Page 50 Thursday, May 10, 2007 5:20 AM

50

Bioassays with arthropods, second edition

Figure 4.16 PoloPlus Plot of Schaefer Residuals.

Figure 4.17 PoloPlus Plot of Collinear Case Residuals.

2331_C004.fm Page 51 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

51

Figure 4.18 PoloPlus Plot of Parallel Case Residuals.

F. Conclusions PoloPlus produces essential information needed to analyze binary response data with accuracy and ease of interpretation. In the Windows format, the output of the original POLO and POLO-PC programs has been streamlined to include new features such as toxicity ratios and standardized residuals, thus eliminating the need for hand calculations. The carefully condensed results eliminate the intermediate calculations that tend to clutter other programs and confuse users.

II. SAS The output for the probit procedure in SAS3 exemplifies a computational scheme for rectangular data sets (defined by Fox7 as those were originally punched on cards). Listings of results are long, detailed, and unwieldy and will not be shown here. The first part of the analysis consists of computation of the mean percent mortality at each dose. Next, a logistic estimation of the mean (µ) and the standard deviation (σ) for the normal distribution is done for each preparation. Goodness of fit by a chi-square test is followed by a listing of first log10(dose) and dose with their confidence limits. Parameter estimates for calculations of toxicity ratios and their standard errors are not presented;6 test statistics for hypotheses tests of parallelism or equality of

2331_C004.fm Page 52 Thursday, May 10, 2007 5:20 AM

52

Bioassays with arthropods, second edition

regressions are not clearly labeled. Despite these problems, this program continues to be widely used despite the availability of other alternative programs.

III. R and S-PLUS Blanche and Paula have downloaded R2 from the Internet, and have rounded up very helpful references.7–9 R10 is a state-of-the-art, flexible software environment that can be used for all of the quantal response calculations; S-PLUS is a similar commercial package.11 Writing the lines of code are beyond our intrepid team’s capabilities, so Paula asks Dr. Tarleton to write the command lines for her to use. With R, data must be entered in a slightly different format. In this example, results for the wicked witch bioassays (WickedWitch.txt) have been entered in a file called “Data” (see Figure 4.19). The R probit analysis, including tests of equality and parallelism, is as follows:

2331_C004.fm Page 53 Thursday, May 10, 2007 5:20 AM

Chapter four: Binary quantal response: data analyses

Figure 4.19 The R Probit Analysis Including Tests of Equality and Parallelism.

53

2331_C004.fm Page 54 Thursday, May 10, 2007 5:20 AM

54

Bioassays with arthropods, second edition

Figure 4.19 (continued)

References 1. LeOra Software, Polo-Plus, POLO for Windows, LeOra Software, 1007 B St., Petaluma, CA 94952. See http://www.LeOraSoftware.com. 2. http://www.r-project.org. R version 1.9.1 was released on June 21, 2004. 3. See http://www.sas.com/technologies/analytics/statistics/stat. 4. Russell, R. M., Robertson, J. L., and Savin, N. E., POLO: a new computer program for probit analysis, Bull. Entomol. Soc. Am. 23(3), 209–213, 1977. 5. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 6. LeOra Software, POLO-PC, LeOra Software, 1007 B St., Petaluma, CA 94952. 7. Fox, J., An R and S-PLUS Companion to Applied Regression, Sage Publications, Thousand Oaks, CA, 2002, Preface. 8. Dalgaard, P., Introductory Statistics with R, Springer-Verlag Inc., New York, 2002. 9. Venables, W. N., Smith, D. M., R Core Development Team, An Introduction to R, Network Theory LTD., Bristol, England, 2004. 10. R Core Development Team, R Reference Manual Base Package Vols. I–II, Network Theory LTD., Bristol, England, 2004. 11. See http://www.insightful.com/products/splus.

2331_C005.fm Page 55 Wednesday, May 9, 2007 5:44 AM

chapter five

Binary quantal response: dose number, dose selection, and sample size One of the many qualities that Dr. Maven values about Blanche is her logical approach to problems. So, when Blanche suggests that advance planning might improve the quality of the bioassays that they have planned for the future, Paula Maven listens attentively. They have already started several types of bioassays, among them continuous monitoring of the responses of their laboratory population; comparisons among more field populations when they can be collected; tests with chemicals, microbials, and, perhaps, physical factors; and periodic comparisons of the laboratory population, with its source populations collected from the field. In the future, surveys to determine patterns of resistance might even be necessary. Blanche explains her position quite firmly: in her opinion, they were just plain lucky in their first tests with the Fairfax, Pixley, and Schaeferville populations. In two of the experiments, she tested five doses, but only had enough time to test four doses with the population from Pixley. The overall sample size for the Schaeferville experiments was almost twice that of the other two bioassays, but the number of doses was the same. The number of insects in the treatment groups was simply not consistent. Blanche needs a guide for dose selection and sample size because without it she could waste time, effort, and valuable insects and still not achieve the results that seem deceptively simple to obtain. Paula begins with an extensive literature review. Although she finds that both dose placement and sample size affect the precision of estimation,1 she quickly discovers that practical and complete guidelines have never been established for use in what she considers to be the two primary types of binary response bioassays. The two types can be identified by both their purpose and the lethal doses (LDs) of interest. In basic binary bioassays, comparisons are made at the LD50 because this is the most stable point for

55

2331_C005.fm Page 56 Wednesday, May 9, 2007 5:44 AM

56

Bioassays with arthropods, second edition

comparison,2 and it is more easily estimated. The LD90 may be included in the presentation of results to show the effect of slope on response (e.g., Robertson3). Examples of basic binary bioassays are those made with the same preparations tested over time or generations (e.g., Robertson et al.4), one or more preparations tested among populations (e.g., Robertson et al.5), responses of the same species among preparations (Robertson and Rappaport6) and comparative responses among phylogenetically related groups (e.g., Robertson et al.7). In specialized binary bioassays, more extreme LDs, such as the LD95 or even LD99, are estimated for comparative purposes. An experiment to estimate a discriminating dose that will distinguish between resistant and susceptible genotypes (e.g., Bergh et al.8) is such a specialized bioassay. The most extreme type of a specialized bioassay is one to estimate a probit or logit 9 (LD99.9968); problems associated with these bioassays will be discussed in Chapter 7, “Quarantine Statistics.” In a limited investigation of the problems of dose number, selection, and sample size, Smith and Robertson9 used a DOS program to examine the precision of estimates from several designs by using the criterion of width of 95% limits around the LD50 or the LD90, assuming the logit model. They examined the effects of sample size and dose placement for three to eight doses and total sample sizes of 120 to 720. Before their limited examination of the problem, the guidelines for experimental design of dose-response bioassays described by Finney2 were used routinely by many investigators, without their realizing that these recommendations for dose selection pertain to the LD50 and not necessarily to other LDs. Likewise, methods described by Brown10 and Freeman11 also are applicable to the 50% response level or to responses in that vicinity. Tsutakawa12 presented an approach to the problem of dose selection for efficient estimation of an arbitrary lethal dose, but his method was not general and its computational difficulty prevented routine use by a biologist. Müller and Schmidtt13 addressed the problem of how to select the number of doses to provide the best estimate of the LD50 based on the criterion of optimizing the asymptotic variance. They concluded that as many doses as possible should be tested in a bioassay and that use of only three doses cannot be recommended. Because estimates with confidence limits occurred occasionally even with a sample size of 120, Robertson et al.1 concluded that at least 240 test subjects should be used to estimate a dose-response relationship with minimally acceptable precision. These results may indicate minimum requirements for a basic bioassay, but further investigations are clearly necessary to explore other possible combinations of sample size and dose placement applicable to other LDs in either basic and specialized binary bioassays. Paula Maven can think of only one solution: place crank calls to LeOra Software.

2331_C005.fm Page 57 Wednesday, May 9, 2007 5:44 AM

Chapter five: Binary quantal response

57

I. PoloDose After constant calls, nagging, and harassment from Dr. Maven, the senior software engineer at LeOra Software develops a new program specifically for the study of dose placement and sample size for any dose that would cause >0% and <100% mortality. PoloDose14 calculates the length of the confidence interval (L) for µ0, the dose level that produces a certain probability of response P0, where 0 < P0 < 1. In this program, P0 is estimated to 35 digits, thus permitting examination of doses necessary to estimate the probit and logit 9. The equations used in PoloDose are based on those given by Smith and Robertson,9 but with the following substitutions: L* was replaced with L, v* with v, g* with g, and wt* with wt. There are T dose levels, and at the tth dose level xt is the dose and nt is the number of subjects. The probability of response is Pt = F ( β1 + β 2 xt ) where β1 and β 2 are unknown parameters, and P0 is the probability of response associated with the LD of interest. F • is a CDF with density f • and inverse F −1 (•) . The Normal (Gaussian) CDF is

()

()

1

F ( x) =

2π

∫

x

e

− 1 z2 2

dz

−∞

The Logistic CDF is

(

()

F x = 1 / 1 + e− x

)

2

( ( )) / P ( 1 − P )

w t = f F −1 Pt

t

t

Covariances of β1 and β2 are

⎡ ν11 ⎢ ⎣ ν12

⎡ ν12 ⎤ ⎢ ⎥= ν22 ⎦ ⎢ ⎢⎣

∑n w ∑ n w F (P ) ⎤⎥ ⎥ ∑ n w F (P ) ∑ n w ⎡⎣ F (P )⎦⎤ ⎥⎦ −1

t

t

t

−1

t

t

t

2

−1

t

t

t

−1

t

t

z is the abscissa of the Normal probability distribution corresponding to the significance level, which is 5% in PoloDose. g = z2 ν22

2331_C005.fm Page 58 Wednesday, May 9, 2007 5:44 AM

58

Bioassays with arthropods, second edition The measure of precision is

L=

2 2z ν11 + 2 F −1 P0 ν12 + ⎡⎣ F −1 P0 ⎤⎦ ν22 − g ν11 − ν12 2 / ν22 1− g

( )

( )

(

)

II. Basic binary bioassays Dr. Maven uses values of the probit L* to assess the quality of each bioassay design. The estimated 95% confidence intervals for both the probit and logit models with cell sizes of 25, 50, 100, 200, and 400 with 4–10 doses clearly show that estimates become more precise as total sample size increases (see Table 5.1). Likewise, precision increases as the numbers of doses increases. Smith and Robertson9 previously concluded that minimally acceptable precision is achieved with 240 test subjects, which had a logit L* (Robertson and Preisler15) of 0.58. This value corresponds with a probit L* of ca. 0.34. Suspecting that minimally acceptable might be a euphemism for marginal precision, Dr. Maven decides that a probit L* value ≤ 0.30 should indicate fully acceptable precision. She does not want to base future decisions about either research or management of wicked witches populations on results that could have been more precise if more insects or doses were tested. In an ideal basic bioassay for comparisons at LD50, Paula concludes that Blanche should test 4 or 5 doses with at least 100 insects per dose; with 6–10 doses, she should test at least 50 insects per dose. Bioassays to estimate the LD90 require more test subjects. For 4 or 5 doses, at least 200 insects per dose are needed; for 6–10 doses, tests with at least 100 insects per dose are necessary. For estimation of an LD50, a minimum sample size of 300–500 is required. At LD90, a minimum sample size of 600–1,000 is necessary for the fully acceptable precision that Dr. Maven requires in her experiments. For simultaneous estimation of both the LD50 and the LD90, neither estimate can ever be based on extrapolation. Thus, the designs for estimation of the LD50 shown in Table 5.1 cannot also be used to estimate an LD90. One approach to the problem of simultaneous estimation of the LD50 and LD90 is to combine the full range of doses shown in Table 5.1 so that at least one dose causes « 10% mortality and the rest cause 50% to 95% mortality. For example, results in Table 5.2 show probit L* values for various designs derived from the results from designs shown in Table 5.1. With 5 doses, the design with 500 test subjects (100/cell) provides marginal precision, and ≥ 750 test subjects assures acceptable precision. For the 6 dose shown, 600 test subjects (100/cell) appears to provide fully acceptable precision. When 7–12 doses are tested, most estimates of LD50 are precise regardless of dose placement or sample size, but the LD90 is less precise unless large sample sizes are used. The practical problems associated with simultaneous precise estimation will be discussed in section IV, “Practical Considerations,” below.

2331_C005.fm Page 59 Wednesday, May 9, 2007 5:44 AM

Chapter five: Binary quantal response

59

Table 5.1 Comparison of Designs for Estimation of an LD50 and LD90 DOSES CELL SAMPLE LD50 4

a 0

P

L*b L*b PROBIT LOGIT

25 50 100 200 400

100 0.25, 0.35, 0.65, 0.75 200 400 800 1600

0.591 0.390 0.267 0.186 0.131

0.990 0.650 0.444 0.309 0.217

5

25 50 100 200 400

125 0.25, 0.30, 0.50, 0.70, 0.75 250 500 1000 2000

0.515 0.344 0.237 0.166 0.116

0.859 0.572 0.394 0.275 0.193

6

25 50 100 200 400

150 0.25, 0.30, 0.35, 0.65, 0.70, 0.75 300 600 1200 2400

0.460 0.312 0.216 0.151 0.106

0.768 0.518 0.358 0.251 0.176

7

25 50 100 200 400

175 0.25, 0.30, 0.35, 0.55, 0.65, 0.70, 0.75 350 700 1400 2800

0.423 0.286 0.198 0.139 0.098

0.701 0.473 0.327 0.229 0.161

8

25 50 100 200 400

200 0.25, 0.30, 0.35, 0.40, 0.60, 0.65, 0.70, 0.75 400 800 1600 3200

0.392 0.266 0.185 0.129 0.091

0.647 0.439 0.304 0.213 0.150

9

25

225 0.25, 0.30, 0.35, 0.40, 0.45, 0.60, 0.65, 0.70, 0.75 450 900 1800 3600

0.368

0.606

0.250 0.173 0.121 0.085

0.410 0.284 0.199 0.140

0.347

0.570

0.236 0.164 0.115 0.081

0.386 0.268 0.188 0.132

50 100 200 400 10

25 50 100 200 400

250 0.25, 0.30, 0.35, 0.40, 0.45, 0.55, 0.60, 0.65, 0.70, 0.75 5000 1000 2000 4000

2331_C005.fm Page 60 Wednesday, May 9, 2007 5:44 AM

60

Bioassays with arthropods, second edition

Table 5.1 Comparison of Designs for Estimation of an LD50 and LD90 (continued) DOSES CELL SAMPLE LD90 4

a 0

P

L*b L*b PROBIT LOGIT

25 50 100 200 400

100 0.05, 0.80, 0.90, 0.95 200 400 800 1600

0.847 0.579 0.403 0.283 0.199

1.688 1.134 0.783 0.547 0.385

5

25 50 100 200 400

125 0.10, 0.80, 0.85, 0.90, 0.95 250 500 1000 2000

0.729 0.500 0.348 0.244 0.172

1.426 0.966 0.670 0.469 0.330

6

25 50 100 200 400

150 0.10, 0.75, 0.80, 0.85, 0.90, 0.95 300 600 1200 2400

0.668 0.457 0.318 0.223 0.157

1.298 0.877 0.607 0.425 0.299

7

25 50 100 200 400

175 0.05, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95 350 700 1400 2800

0.633 0.432 0.300 0.210 0.148

1.259 0.842 0.580 0.405 0.284

8

25 50 100 200 400

200 0.05, 0.10, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95 400 800 1600 3200

0.602 0.417 0.292 0.205 0.145

1.148 0.788 0.550 0.386 0.272

9

25

225 0.05, 0.10, 0.15, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95 450 900 1800 3600

0.595

1.121

0.414 0.290 0.205 0.144

0.776 0.543 0.382 0.269

0.569

1.070

0.396 0.278 0.196 0.138

0.740 0.518 0.364 0.257

50 100 200 400 10

25 50 100 200 400

250 0.05, 0.10, 0.15, 0.65, 0.70, 0.80, 0.85, 0.90, 0.95 500 1000 2000 4000

Notes: a P0 is the probability of response; b L* is the measurement of precision.

2331_C005.fm Page 61 Wednesday, May 9, 2007 5:44 AM

Chapter five: Binary quantal response

61

Table 5.2 Designs for Simultaneous Estimation of the LD50 and LD90 Assuming the Probit Model ND

PL (RANGE)

P0

NC

NS

5

0.01–0.80

0.90, 0.95, 0.975, 0.99

100 150 175 200 300 400 500 600 700 800 900 1000

500 750 875 1000 1500 2000 2500 3000 3500 4000 4500 5000

0.456–0.480 0.370–0.377 0.342–0.346 0.319–0.321 0.257–0.260 0.221–0.225 0.197–0.201 0.179–0.183 0.165–0.170 0.154–0.159 0.145–0.149 0.138–0.142

6

0.90, 0.925, 0.95, 0.975, 0.99

100 175 185 200 300 400 500 600 700 800 900 1000

600 1050 1110 1200 1800 2400 3000 3600 4200 4800 5400 6000

0.395–0.436 0.295–0.314 0.288–0.304 0.276–0.292 0.225–0.234 0.195–0.201 0.174–0.179 0.159–0.163 0.147–0.150 0.137–0.140 0.129–0.132 0.123–0.125

7

0.90, 0.925, 0.95, 0.975, 0.98, 0.99

100 150 175 200 300 400 500 600 700 800 900 1000

700 1050 1225 1440 2100 2800 3500 4200 4900 5600 6300 7000

0.368–0.380 0.299–0.302 0.276–0.277 0.257–0.258 0.208–0.210 0.179–0.182 0.159–0.162 0.145–0.148 0.134–0.137 0.125–0.128 0.118–0.121 0.112–0.115

8

0.90, 0.925, 0.95, 0.96, 0.975, 0.98, 0.99

100 125 150 175 200 300

800 1000 1200 1400 1600 2400

0.337–0.346 0.301–0.305 0.274–0.276 0.253–0.254 0.236–0.237 0.190–0.194

L*

2331_C005.fm Page 62 Wednesday, May 9, 2007 5:44 AM

62

Bioassays with arthropods, second edition

Table 5.2 Designs for Simultaneous Estimation of the LD50 and LD90 Assuming the Probit Model (continued) ND

PL (RANGE)

P0

9

0.90, 0.925, 0.93, 0.95, 0.96, 0.975, 0.98, 0.99

10

0.90, 0.915, 0.925, 0.93, 0.95, 0.96, 0.975, 0.98, 0.99

NC

NS

L*

400 500 600 700 800 900 1000

3200 4000 4800 5600 6400 7200 8000

0.164–0.167 0.146–0.150 0.133–0.137 0.123–0.127 0.115–0.118 0.108–0.112 0.103–0.106

85 100 200 300 400 500 600 700 800 900 1000

765 900 1800 2700 3600 4500 5400 6300 7200 8100 9000

0.338–0.358 0.310–0.325 0.218–0.222 0.178–0.179 0.154–0.155 0.137–0.138 0.125–0.126 0.116–0.117 0.108–0.109 0.102–0.103 0.096–0.097

85

850

0.316–0.343

100 200 300 400 500 600 700 800 900 1000

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0.289–0.312 0.203–0.212 0.165–0.171 0.143–0.148 0.128–0.131 0.117–0.120 0.108–0.111 0.101–0.103 0.095–0.099 0.090–0.092

Notes: Column headings are number of doses (ND); probabilities in the lower range of response (PL); P0 is the probability of response; number of cells (NC); total number in the sample (NS); L* is the measurement of precision.

III. Specialized binary bioassays Estimation of extreme levels such as the LD95 (Table 5.3) and the LD99 (Table 5.4) require more doses and larger sample sizes than a basic bioassay. For estimation of the LD95, sample sizes ≥ 1000 will provide fully acceptable precision with 5–10 doses. For these optimal designs, one dose causes ≤ 80% mortality and the remainder cause mortality from 90% to 99% mortality. A specialized bioassay to estimate an LD95 might be useful in studies of resis-

2331_C005.fm Page 63 Wednesday, May 9, 2007 5:44 AM

Chapter five: Binary quantal response

63

Table 5.3 Optimal Designs for Precise Estimation of the LD95 ND

PL (RANGE)

5

0.01–0.80

NC

NS

0.90, 0.95, 0.975, 0.99

P0

100 150 175 200 300 400 500 600 700 800 900 1000

500 750 875 1000 1500 2000 2500 3000 3500 4000 4500 5000

0.456–0.480 0.370–0.377 0.342–0.346 0.319–0.321 0.257–0.260 0.221–0.225 0.197–0.201 0.179–0.183 0.165–0.170 0.154–0.159 0.145–0.149 0.138–0.142

L*

6

0.90, 0.925, 0.95, 0.975, 0.99

100 175 185 200 300 400 500 600 700 800 900 1000

600 1050 1110 1200 1800 2400 3000 3600 4200 4800 5400 6000

0.395–0.436 0.295–0.314 0.288–0.304 0.276–0.292 0.225–0.234 0.195–0.201 0.174–0.179 0.159–0.163 0.147–0.150 0.137–0.140 0.129–0.132 0.123–0.125

7

0.90, 0.925, 0.95, 0.975, 0.98, 0.99

100 150 175 200 300 400 500 600 700 800 900 1000

700 1050 1225 1440 2100 2800 3500 4200 4900 5600 6300 7000

0.368–0.380 0.299–0.302 0.276–0.277 0.257–0.258 0.208–0.210 0.179–0.182 0.159–0.162 0.145–0.148 0.134–0.137 0.125–0.128 0.118–0.121 0.112–0.115

8

0.90, 0.925, 0.95, 0.96, 0.975, 0.98, 0.99

100 125 150 175 200 300 400

800 1000 1200 1400 1600 2400 3200

0.337–0.346 0.301–0.305 0.274–0.276 0.253–0.254 0.236–0.237 0.190–0.194 0.164–0.167

2331_C005.fm Page 64 Wednesday, May 9, 2007 5:44 AM

64

Bioassays with arthropods, second edition

Table 5.3 Optimal Designs for Precise Estimation of the LD95 (continued) ND

9

10

PL (RANGE)

P0

0.90, 0.925, 0.93, 0.95, 0.96, 0.975, 0.98, 0.99

0.90, 0.915, 0.925, 0.93, 0.95, 0.96, 0.975, 0.98, 0.99

NC

NS

500 600 700 800 900 1000

4000 4800 5600 6400 7200 8000

0.146–0.150 0.133–0.137 0.123–0.127 0.115–0.118 0.108–0.112 0.103–0.106

L*

85

765

0.338–0.358

100 200 300 400 500 600 700 800 900 1000

900 1800 2700 3600 4500 5400 6300 7200 8100 9000

0.310–0.325 0.218–0.222 0.178–0.179 0.154–0.155 0.137–0.138 0.125–0.126 0.116–0.117 0.108–0.109 0.102–0.103 0.096–0.097

85

850

0.316–0.343

100 200 300 400 500 600 700 800 900 1000

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0.289–0.312 0.203–0.212 0.165–0.171 0.143–0.148 0.128–0.131 0.117–0.120 0.108–0.111 0.101–0.103 0.095–0.099 0.090–0.092

Notes: Column headings are number of doses (ND); probabilities in the lower range of response (PL); P0 is the probability of response; number of cells (NC); total number in the sample (NS); L* is the measurement of precision.

tance such as genetic patterns, inheritance, and surveys of occurrence (see 9.III). For precise estimation of the LD99, none of the designs with 4–6 doses is acceptable. Use of at least 7 doses is necessary, but total sample sizes are 3,000–3,600 based on doses expressed as base 10 percentages. One dose must cause ≤ 0.80% mortality. The rest caused between 97% and 99.99995% mortality. At this extreme dose, finding the exact dose that causes the upper level of mortality in the series will require that 99,995 of 100,000 test subjects die. Thus, a sample size of 100,000 will be necessary just to identify the upper

2331_C005.fm Page 65 Wednesday, May 9, 2007 5:44 AM

Chapter five: Binary quantal response

65

Table 5.4 Optimal Designs for Precise Estimation of the LD99 ND

PL

P0

NC

NS

L*

7

0.01–0.80

0.97, 0.98, 0.99, 0.995, 0.9995, 0.99995

300 400 500 600 700 800 900 1000

2100 2800 3500 4200 4900 5600 6300 7000

0.372–0.421 0.327–0.362 0.293–0.323 0.267–0.294 0.247–0.271 0.231–0.253 0.218–0.239 0.206–0.226

8

0.97, 0.98, 0.99, 0.9925, 0.995, 0.9995, 0.99995

200 300 400 500 600 700 800 900 1000

1600 2400 3200 4000 4800 5600 6400 7200 8000

0.430–0.471 0.350–0.380 0.303–0.327 0.271–0.292 0.247–0.265 0.224–0.245 0.214–0.229 0.201–0.216 0.191–0.205

9

0.97, 0.975, 0.98, 0.99, 0.9925, 0.995, 0.9995, 0.99995

100

900

0.545–0.627

200 300 400 500 600 700 800 900 1000

1800 2700 3600 4500 5400 6300 7200 8100 9000

0.382–0.428 0.311–0.346 0.269–0.298 0.240–0.266 0.219–0.242 0.203–0.224 0.190–0.209 0.179–0.197 0.170–0.187

100

1000

0.505–0.577

200 2000 300 3000 400 4000 500 5000 600 6000 700 7000 800 8000 900 9000 1000 10000 1500 15000 2000 20000

0.354–0.395 0.288–0.319 0.249–0.275 0.223–0.245 0.203–0.224 0.188–0.207 0.176–0.193 0.166–0.193 0.157–0.172 0.128–0.141 0.111–0.122

10

0.97, 0.975, 0.98, 0.985, 0.99, 0.9925, 0.995, 0.9995, 0.99995

Notes: Column headings are number of doses (ND); probabilities in the lower range of response (PL); P0 is the probability of response; number of cells (NC); total number in the sample (NS); L* is the measurement of precision.

2331_C005.fm Page 66 Wednesday, May 9, 2007 5:44 AM

66

Bioassays with arthropods, second edition

Table 5.5 Precision of Bioassays with Sample Sizes of 250–500 N 250

NC D

50 42 31 25 21 300 60 50 38 30 25 400 80 67 50 40 33 500 100 83 63 50 42

5 6 8 10 12 5 6 8 10 12 5 6 8 10 12 5 6 8 10 12

P0 .05, .05, .10, .05, .05, .05, .05, .10, .05, .05, .05, .05, .10, .05, .05, .05, .05, .10, .05, .05,

.80, .35, .25, .10, .25, .80, .35, .25, .10, .25, .80, .35, .25, .10, .25, .80, .35, .25, .25, .25,

.85, .80, .35, .25, .30, .85, .80, .30, .25, .30, .85, .80, .35, .25, .30, .85, .80, .35, .30, .30,

.90, .85, .75, .30, .35, .90, .85, .75, .30, .35, .90, .85, .75, .35, .35, .90, .85, .75, .65, .35,

.95 .90, .80, .70, .65, .95 .90, .80, .70, .65, .95 .90, .80, .70, .65, .95 .90, .80, .70, .65,

.95 .85, .90, .95, . .80, .85, .90, .95 .70, .75, .80, .85, .90, .95, .99 .95 .85, .90, .95 .75, .80, .85, .90, .95 .70, .75, .80, .85, .90, .95, .99 .95 .85, .90, .95 .80, .85, .90, .95 .70, .75, .80, .85, .90, .95, .99 .95 .85, .90, .95 .75, .80, .85, .90, .95 .70, .75, .80, .85, .90, .95, .99

L50*

L90*

0.558 0.452 0.404 0.396 0.407 0.506 0.412 0.362 0.360 0.372 0.435 0.354 0.315 0.311 0.322 0.388 0.317 0.280 0.286 0.284

0.497 0.538 0.582 0.597 0.615 0.452 0.490 0.522 0.542 0.560 0.389 0.421 0.452 0.466 0.483 0.346 0.377 0.352 0.409 0.426

Notes: Column headings are number of test subjects (N), number in each cell of cells (NC), and number of doses (D); P0 is the ideal probability of response at each dose; L* is the measurement of precision at the 50% or 90% response levels.

dose in the series of dilutions tested. The total sample size required for the replicated experiment is completely impractical under most circumstances for most species.

IV. Practical considerations A. Basic bioassays Despite all of her reading, Paula Maven has never found a detailed discussion of the practical aspects of doing a typical bioassay such as one that is done when a new insect species is first received in a laboratory, or when a new chemical or biological or physical treatment is to be tested on a species for which bioassays have been done before. Often, the number of test subjects available for the bioassay is the primary limiting factor for how many doses can be tested. As with Dr. Maven’s initial shipments of wicked witches from field populations, less than 500 insects may constitute the entire sample. Table 5.5 shows the precision of designs for total sample sizes of 250, 300, 400, and 500 test subjects. These results indicate that, if possible, a total

2331_C005.fm Page 67 Wednesday, May 9, 2007 5:44 AM

Chapter five: Binary quantal response

67

sample size of 500 test subjects with eight doses (63 insects/dose) should be tested. Blanche finally has her guidelines! Besides limits on available test subjects, a standardized test such as a population assessment or a screening experiment is usually done under severe time constraints. (Blanche says that it is like running a vermin assembly line.) To minimize the time involved, a standard procedure based on preliminary data can be used to select the doses for the first replication of the bioassay. This part of the experiment, the dose-fixing phase, consists of using a broad series of logarithmic dilutions to test about 10 insects per dose. Results of dose-fixing can identify the narrower range of effective doses based on mortality that occurs a short time after treatment. A series of dilutions between the doses that very crudely estimate 1–99% mortality can also be identified from these preliminary results by analyzing that data with the PoloPlus program using the “Graphics” option. Once the effective dose ranges are identified for each population, five doses can be selected and tested in the first actual replication. After the first replication is completed, the doses can be adjusted further in the second and third replications. These doses will then be tested in the basic bioassay. As long as the experiment is replicated three times with five doses in each replication, the bioassay will be valid.

B. Specialized bioassays At least two dose-fixing experiments are usually required for a specialized bioassay. The first is the same type done for the general bioassay: a logarithmic series of dilutions must be done to tentatively identify the effective range for 5–95% mortality. In this series, a tentative LD5–80 and doses in the upper range (90–99% mortality) should be identified. When the specialized bioassay is done to estimate an LD95, 5–10 doses should then be tested with about 50 test subjects per dose. In the next replication, doses can be adjusted further to achieve 90–99% mortality. When the specialized bioassay is done to estimate an LD99, two dose-fixing experiments should be done, followed by selection of 7–10 doses that cause 97–99.99995% mortality. Each of the final doses should then be tested as many times as necessary to achieve the total required sample of >700,000 test subjects.

V. Reality checklist for bioassays The various sample sizes and the way doses must be placed for precise estimation of LD50 and LD90 are fairly flexible compared with the stringent requirements for estimation of an LD95. The requirements for estimation of an LD99 are complicated and the numbers of test subjects are huge. Historically, entomologists have tended to make blithe recommendations about LDs that should be estimated for specific purposes such as quarantine or resistance testing to separate different genotypes, without realizing the numbers of test subjects that would be required to estimate that LD, or how the doses

2331_C005.fm Page 68 Wednesday, May 9, 2007 5:44 AM

68

Bioassays with arthropods, second edition

would need to be placed for purposes of precise estimation. These types of recommendations have been intended to make bioassays definitive, but have instead made them impossible to do with any degree of precision. Sample sizes are limited by the realities of insect production or collection even on a mass scale. If arthropods were like bacteria and each species could be easily reared in huge numbers in a small area, numbers of test subjects would not be a concern. However, arthropod rearing is an activity that usually requires large areas of laboratory space if the species can be reared at all. Of more than one million species that have been identified, fewer than 1,500 arthropod species have been reared continuously and on a large scale.16 Blanche has added another species to the list, but as with most, the wicked witch is a phytophagous insect. With Lepidoptera such as Dr. Maven’s wicked witches, collections of population samples and subsamples of laboratory populations are extremely time and labor intensive. Theoretical requirements cannot be changed, but the type of bioassays used with general groups of arthropods can certainly be adjusted to achieve the best possible precision. Paula Maven considers which bioassays can be done given the capacity of her rearing operation of wicked witches. Like most Lepidoptera, vast numbers of insects are not available even with a well-established and highly efficient rearing operation. For most experiments with Lepidoptera, 300–500 insects are available for testing. For experiments in which comparisons are involved—screening, population responses, natural variation in response—a basic design for estimation of the LD50 will suffice and comparisons at the LD90 should be avoided. Both the LD50 and the LD90 should only be estimated for comparisons of relative effectiveness when >500–750 test subjects are available. This usually occurs with organisms such at ticks and many species of Diptera; these organisms are generally available in large numbers even in laboratory situations.

References 1. Robertson, J. L., Smith, K. C., Savin, N. E., and Lavigne, R. J., Effects of dose selection and sample size on precision of lethal dose estimates in dose-mortality regression, J. Econ. Entomol. 77, 833, 1984. 2. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 3. Robertson, J. L., Toxicity of Zectran aerosol to the California oakworm, a primary parasite, and a hyperparasite, Environ. Entomol. 1, 1, 115-117, 1972. 4. Robertson, J. L., Preisler, H. K., Ng, S. S., Hickle, L. A., and Gelernter, W. D., Natural variation: a complicating factor in bioassays with chemical and microbial insecticides, J. Econ. Entomol. 88, 1, 1995. 5. Robertson, J. L., Boelter, L. M., Russell, R. M., and Savin, N. E., Variation in response to insecticides by Douglas-fir tussock moth, Orgyia pseudotsugata (Lepidoptera: Lymantriidae), populations, Can. Entomol. 110, 325, 1978.

2331_C005.fm Page 69 Wednesday, May 9, 2007 5:44 AM

Chapter five: Binary quantal response

69

6. Robertson, J. L. and Rappaport, N. G., Direct, indirect, and residual toxicities of insecticide sprays to western spruce budworm, Choristoneura occidentalis (Lepidoptera: Tortricidae), Can. Entomol. 111, 1219, 1979. 7. Robertson, J. L., Gillette, N. L., Lucas, B. A., Savin, N. E., and Russell, R. M., Comparative toxicity of insecticides to Choristoneura species (Lepidoptera: Tortricidae), Can. Entomol. 110, 399, 1978. 8. Bergh, J. C., Rugg, D., Jansson, R. K., McCoy, C. W., and Robertson, J. L., Monitoring the susceptibility of citrus rust mite (Acari: Eriophyidae) populations to abamection, J. Econ. Entomol. 92, 781, 1999. 9. Smith, K. C. and Robertson, J. L., DOSESCREEN: a computer program to aid dose placement, USDA Forest Service Gen. Tech. Rep. PSW-78, 1984. 10. Brown, B. W. Jr., Planning a quantal assay of potency, Biometrics 22, 322, 1966. 11. Freeman, P. R., Optimum Bayesian sequential estimation of the median effective dose, Biometrika 57, 79, 1970. 12. Tsutakawa, R. K., Selection of dose levels for estimating a percentage point of a logistic quantal response curve, Appl. Statistics 29, 25, 1980. 13. Müller, H-G., and Schmidtt, T., Choice of number of doses for maximum likelihood estimation of the ED50 for quantal dose-response data, Biometrics 6, 117, 1990. 14. LeOra Software, 1007 B St., Petaluma, CA 94952, 2005. See http://

www.LeOraSoftware.com. 15. Robertson, J. L. and Preisler, H. K., Pesticide Bioassays with Arthropods, CRC Press, Boca Raton, FL, 1992. 16. Singh, P. and Moore, R. F., Handbook of Insect Rearing, Vols. I and II, Elsevier, Amsterdam, 1985.

2331_C005.fm Page 70 Wednesday, May 9, 2007 5:44 AM

2331_C006.fm Page 71 Wednesday, May 9, 2007 5:44 AM

chapter six

Natural variation in response Paula and Blanche now have a great system: Paula plans the experiments, Blanche completes the bioassays, and Paula does the data analyses. Or, as Blanche puts it, she does all the work and Paula thinks a lot. Once the laboratory colony has been well-established, Blanche does repetitive bioassays with three chemicals representative of different chemical classes, and a standard preparation of the microbial toxicant Bacillus thuringiensis subsp. kurstaki. Paula wants to monitor the quality of the insect colony with these tests. After about six months, Paula becomes concerned and calls Blanche into her office to talk about the results thus far. Something is causing the results to vary from one bioassay to another, and Paula is fretting about the quality of the insect colony, the purity of formulated samples, and everything else including the number of sunspots that occurred during the bioassays. In other words, she has become frantic, irrational, and a raving lunatic. “I don’t understand what’s happening here, Blanche. Is it possible that you are measuring the amounts of materials slightly differently each time you do the formulations? What about the volumes? Is . . .” Blanche stops Paula mid-litany to reassure her that yes, everything is done exactly the same way every time: “Look here, we even store the samples at -40º. The volumes are always the same—that’s why you bought all the fancy titration equipment, remember? Now what else do you want me to do? You’re the brains of this outfit, supposedly.” She suggests that either Paula go to the emergency room for treatment of this anxiety attack, call her pal Dr. Tarleton for advice, or, at the very least, reread her notes from his course. So, Paula finds her old course notebook plus her copy of Finney’s Statistical Methods in Biological Assay.1 The very sight of the equations is like electroshock therapy, and she begins reading about “Standard Curve Estimation.” Here she finds the answer to the problem: “In general, the assumption that a response curve once determined can be used in future assays is inadmissible”.1 Now she also remembers the corollary of Robertson et al.2: Because of natural variation, responses of groups of insects tested at any one time will therefore

71

2331_C006.fm Page 72 Wednesday, May 9, 2007 5:44 AM

72

Bioassays with arthropods, second edition

never be exactly the same as responses of another group tested either at the same time or a different time, regardless of the extent to which bioassay techniques are standardized.

I. Definition Natural variation is best defined as a numerical difference in response that is detected each time a bioassay is repeated with one genetic strain, either within a single generation or >1 generation (Robertson et al.2). Such variation is akin to background noise and can never be eliminated: it is another reminder that each bioassay provides an estimate of response, not a measurement.

II. Statistical boundaries of natural variation For individual data sets, probit or other regression techniques capture the variation among data points. Standard errors and 95% confidence limits for individual lines thus do not define natural variation among data sets. Instead, repeated bioassays are essential. As more and more bioassays are done, estimates of natural variation become more and more reliable. Either lethal doses (LDs) or lethal dose ratios can be used to determine the boundaries. Based on large sample theory and assuming that the samples in all bioassays provide a random sample of responses of n present and future bioassays, the approximate 95% limits of natural variation are MEAN ± 1.96 (SD) where MEAN and SD are the mean and standard deviation of the LD’s from the n samples. When lethal dose ratios are used, as in bioassays with microbial preparations, the equation is the same, with MEAN and SD calculated from the LT’s from the n samples. Dr. Maven next considers some possible sources of natural variation.

III. Levels of variation A. Sibling groups The smallest unit in population formation is the egg mass, which Dr. Maven calls the sibling group. Information about the quantal responses of sibling groups can be difficult to obtain because of limitations in sample sizes (i.e., total number of eggs laid) and demographic factors such as percentage hatch and subsequent survival. For example, Robertson (unpublished data) tested western spruce budworm (Choristoneura occidentalis Freeman) and green budworm (C. viridis Freeman) that were reared from single egg masses and isolated throughout their development. As sixth instars, the insects were tested with either acephate and carbaryl by topical application. Despite the small total sample sizes available for each regression, results of hypotheses tests indicated that the hypothesis of equality was rejected except when C. viridis sibling groups were exposed to acephate (see Table 6.1). In contrast,

2331_C006.fm Page 73 Wednesday, May 9, 2007 5:44 AM

Chapter six: Natural variation in response

73

Table 6.1 Results of Hypotheses Tests for Parallelism or Equality for Choristoneura occidentalis Freeman and C. viridis Freeman Sibling Groups Chemical Acephate Carbaryl

Species

Groups Tested

Equality

Parallelism

C.o C.v C.o C.v

34 12 15 11

R NR R R

R NR NR NR

the hypothesis of parallelism was rejected only when C. occidentalis was treated with carbaryl. These results may indicate the incremental contribution of each sibling group to the natural variation among cohorts within a generation.

B. Cohorts within a single generation Egg masses hatch asynchronously so that larvae from different sibling groups are present within a given developmental stage and different developmental stages may be present at a given time during population development (e.g., Price,3 Morris and Miller4). One of the reasons that Paula and Blanche established a laboratory colony of wicked witches was to ensure a ready supply of insects of uniform age or size for testing on a year-round basis. They used mass-production methods common to many rearing facilities; these methods include provision of the insects with an overabundance of food, exclusion of predators and parasites, and manipulation of development by storage of egg masses for weekly infusion into the colony. The end result is a population with cohorts defined by time and with generations that can be precisely delimited. These factors permit definition of natural variation without interference from outside factors that would also cause responses to vary. Results of repeated bioassays suggest the extent to which natural variation within strains of arthropod species reared even under highly controlled conditions can complicate detection of other differences related to pesticide resistance, varietal differences of host plants, or product quality. However, Paula remembers that 5% of the values or ratios will always fall outside the limits estimated by the equation. If she observes a trend in decreasing response in repeated bioassays, then tentative conclusions about resistance and other biochemical or genetic phenomena may be justified. Likewise, in repeated bioassays with microbial products, consistent shifts in responses at the LD50 must be observed before concerns about product quality would be justified (see Chapter 8, “Statistical Analyses of Data from Bioassays with Microbial Products”). Robertson et al.2 showed six sets of results that demonstrate natural variation in diamondback moth (Plutella xylostella [L.], exposed to Bacillus thuringiensis subsp. kurstaki); Colorado potato beetle (Leptinotarsa decemlineata

2331_C006.fm Page 74 Wednesday, May 9, 2007 5:44 AM

74

Bioassays with arthropods, second edition

[Say], exposed to B. thuringiensis subsp. tenebrioni); and western spruce budworm (treated with pyrethrins, mexacarbate, or DDT). For diamondback moth (late second to early third instar), the means (95% limits of natural variation) of LD50s based on these results were 0.36 (0.04–0.67) μg/g of diet; for second instar Colorado potato beetle, values were 80.0 (0-153) μg/g of diet. For western spruce budworm (sixth instar), results of bioassays with pyrethrins, mexacarbate, or DDT indicate that the means (95% limits of natural variation) of LD50s were 0.07 (0.03–0.10), 0.11 (0.07–0.15), and 2.35 (0.6.9) μg/ μl of solvent, respectively. The mean (95% limits of natural variation) at RT50 for diamondback moth was 2.0 (0.97–3.1); for Colorado potato beetle, limits were much wider 3.97 (0.32–7.62). When pyrethrins was topically applied to western spruce budworm, limits of natural variation at RT50 were quite narrow 1.81 (0.84–2.78). Limits for mexacarbate were intermediate 1.63 (0.85–2.41) and very wide for DDT 2.1 (≈0–4.24).

C. Developmental stage Biotic and abiotic factors affect arthropod development with the result that a range of different developmental stages is present at any given time. A primary source of variation in response at the population level is differential responses of these life stages. Just after the wicked witch laboratory colony was safely established, Paula had Blanche mix a conventional insecticide, permethrin, as a commercial formulation (Overkill) into artificial diet upon which larvae fed for the next seven days. Results of their bioassays (see Table 6.2) were typical of the results usually observed by many other investigators (see, e.g., Robertson and Boelter,5 Elek and Beveridge,6 Biddinger et al.7): younger stages were most susceptible and the last instar was the least susceptible. This source of variation is one of the reasons that Paula, Blanche, and other investigators (see, e.g., Bolin et al.,8 Toledo et al.9) use only one instar or stage in their experiments to identify possible significant differences in arthropod response related to host plant varieties, production lots of microbial pesticides, and source or genetic status of different populations. Life table analyses have been adapted to identify causes of mortality at a specific age interval (see, e.g., Morris and Miller4), and demographic toxicology has developed as an approach to define the effects of toxicants at Table 6.2 Results of Bioassays with Overkill Incorporated into Diet upon which Wicked Witches Fed Instar n Slope (SE) LD50 (95% CL) 1 2 3 4 5 6

500 625 376 425 525 400

2.23(0.24) 3.65(0.39) 2.03(0.24) 2.19(0.23) 2.37(0.35) 1.89(0.27)

0.0084(0.0056-0.014) 0.061(0.054-0.067) 0.14(0.091-1.3) 0.19(0.051-0.34) 0.22(0.18-0.26) 0.40(0.21-0.65)

2331_C006.fm Page 75 Wednesday, May 9, 2007 5:44 AM

Chapter six: Natural variation in response

75

the population level (see Stark and Banks10). One way to understand the differences between quantal response bioassays and the models used in demographic toxicology is to compare their purposes. Quantal response bioassays are done to identify the significance of variables within the framework of statistical models. In contrast, demographic toxicology uses conceptual ecological models to predict effects at the population level. These two approaches need not be mutually exclusive. Some bioassay techniques (e.g., topical application, diet incorporation) produce data that are not amenable for use in forecasts of effects age structure on population response. Others methods such as spray application to insects on foliage can produce data that are a better simulation of conditions in the field (e.g., Robertson and Rappaport11). Results of foliage spray bioassays (Robertson et al.12) were used to develop a contour plot method that shows the variability of response within a population based on both time and age structure. This method is as follows: For a given pair (x, y) of days x after emergence and concentration y, the probability P( D|x , y ) of an insect dying (D) before reaching adulthood was calculated as 6

P( D|x , y ) =

∑ P(D|I , y )P( I |x) i

i

i=2

where P( D|I i , y ) is the probability that an insect in instar i, sprayed with a concentration y, died before successful adult emergence and P( I i |x ) is the probability that the insect is in instar i x days after emergence. P( D|I i , y ) is estimated by Pˆ ( D|I i , y ) = Cˆ + (1 − Cˆ )Φ (αˆ i + βˆ i log y ) —that is, the probit concentration-response curve for the i-th instar) where C is mortality observed in controls and P( I i |x ) is the relative frequency of instar i on day x.

References 1. Finney, D. J., Statistical Methods in Biological Assay, Griffin, London, 1964, pp. 91–92. 2. Robertson, J. L., Preisler, H. K., Ng, S. S., Hickle, L. A., and Gelernter, W. D., Natural variation: a complicating factor in bioassays with chemical and microbial pesticides, J. Econ. Entomol. 88, 1, 1995. 3. Price, P. W., Insect Ecology, John Wiley and Sons, New York, 1997. 4. Morris, R. F. and Miller, C. A., The development of life tables for the spruce budworm, Can. J. Zool. 32, 283, 1954. 5. Robertson, J. L. and Boelter, L. M., Toxicity of insecticides to Douglas-fir tussock moth, Orgyia pseudotsugata (Lepidoptera: Lymantriidae) I. Contact and feeding toxicity, Can. Entomol. 111, 1145, 1979. 6. Elek, J. and Beveridge, N., Effect of Bacillus thuringiensis subsp. tenebrioni insecticidal spray on the mortality, feeding, and developmental rates of larval Tasmanian eucalyptus leaf beetles (Coleoptera: Chrysomelidae), J. Econ. Entomol. 92, 1062, 1999.

2331_C006.fm Page 76 Wednesday, May 9, 2007 5:44 AM

76

Bioassays with arthropods, second edition 7. Biddinger, D. J., Hull, L. A., and Rajotte, E. G., Stage specificity of various insecticides to tufted apple bud moth larvae (Lepidoptera: Tortricidae), J. Econ. Entomol. 91, 200, 1998. 8. Bolin, P. C., Hutchison, W. D., and Andow, D. A., Long-term selection for resistance to Bacillus thuringiensis Cry1Ac endotoxin in a Minnesota population of European corn borer (Lepidoptera: Crambidae), J. Econ. Entomol. 92, 1021, 1999. 9. Toledo, J., Liedo, P., Williams, T., and Ibarra, J., Toxicity of Bacillus thuringiensis δ-exotoxin to three species of fruit flies (Diptera: Tephritidae), J. Econ. Entomol. 92, 1052, 1999. 10. Stark, J. D. and Banks, J. E., Population-level effects of pesticides and other toxicants on arthropods, Ann. Rev. Entomol. 48, 505, 2003. 11. Robertson, J. L. and Rappaport, N. G., Direct, indirect, and residual toxicities of insecticide sprays to western spruce budworm, Choristoneura occidentalis (Lepidoptera: Tortricidae), Can. Entomol. 111, 1219, 1979. 12. Robertson, J. L., Richmond, C. E., and Preisler, H. K., Lethal and sublethal effects of avermectin B1 on the western spruce budworm (Lepidoptera: Tortricidae), J. Econ. Entomol. 78, 1129, 1985.

2331_C007.fm Page 77 Wednesday, May 9, 2007 5:44 AM

chapter seven

Quarantine statistics Idaho may have famous potatoes, but Schaeferville has famous ‘Rednecks.’ This tomato cultivar is pear-shaped, large, and bicolored. The globular portion is as big as a navel orange, and has about the same bright orange color. The neck is scarlet and as long as a small cucumber. The large portion of this tomato is ideal for slicing, canning, or preparation of sauce; a single neck is sufficient for a large salad for one person. And, this tomato is seedless. ‘Rednecks’ are highly desirable in the fresh market, but they have a unique ability to withstand cold storage for up to six months without rotting. Best of all (and in contrast to all other tomato cultivars), wicked witches do not eat ‘Rednecks.’ Located just outside the city limits of Schaeferville, the Jones Family Farm is one of the largest operations in California. The patriarch of the clan, Jerry Jeff Jones, and his wife of 65 years, “Miz” Emmylou Dolly, started their farm with a few acres. Every year they bought a few more parcels so that by the time Paula Maven moved to Schaeferville with her husband, the Joneses owned much of the agricultural land in the county. The Jones’ Family Farm developed ‘Rednecks’ and propagate the plants by a patented and highly secret process. The Jones family also made huge donations to the university every year. Dr. Maven is so deeply engrossed in thought about the design of yet another bioassay with wicked witches that she does not hear her visitor enter. Finally, Hank Williams Jones clears his throat to attract her attention. “Dr. Maven, I’m Hank Jones—Jerry Jeff and Miz Emmylou’s oldest son. I run Jones’ Farm these days and I need your help if you have time.” In essence, Jones’ Farm wants to export Rednecks to New Zealand. Hank explains that he recently returned from a trip to Hokitika, Schaeferville’s sister city, and that he specifically wants to export ‘Rednecks’ to this west coast location where a cousin now lives. The USDA has refused to approve transport of these tomatoes without fumigation based on the susceptibility of other tomato cultivars (varieties). In the Schaeferville area, the most common varieties are ‘Julia Sugarbaker’ (noted for being beautifully tart), ‘Golden Girl’ (late maturing, with wrinkled skin but with a zesty flavor),

77

2331_C007.fm Page 78 Wednesday, May 9, 2007 5:44 AM

78

Bioassays with arthropods, second edition

‘Pinole’ (a nondescript paste tomato) and ‘Elmer’ (a pungent, round salad tomato with an almost overpowering flavor). Fields of these four varieties can be devastated by the offspring of just one breeding pair of wicked witches. Hank Jones does not understand why any type of tomato besides ‘Redneck’ should have anything to do with his export application. Quarantine problems are a new subject for Dr. Maven. She has not considered the bioassays that must be done to ensure that wicked witches do not become established in another country, nor is she familiar with USDA export or pest exclusion regulations. After assuring Hank Jones that she will get back to him as quickly as possible, she begins reviewing the literature. Two books1,2 provide her starting point. She quickly realizes that quarantine of a particular species is not strictly a matter of its life and death after treatment. Instead, as indicated by Worner,3 decisions are based on biological, economic, and environmental features of a region or country. Quarantine statistics concern not only the relationships between dose and response, or time and response (see Time as a Variable, chap. 11), but population ecology as well. However, an antiquated and overly stringent requirement that was imposed over 50 years ago for fruit heavily infested with one species of Tephritid fruit fly has stifled research in quarantine statistics until relatively recently. In 1939, A. G. Baker, the chief entomologist for the USDA, stated, “The security demanded as a basis for recommendation is determined by reading on the regression line the exposure coordinated with a probit of 9. In percentages this probit represents a mortality of 99.9968, or a survival of approximately 32 of 1,000,000.”4 The basis for Baker’s recommendation was quite simple: like his contemporaries, he probably considered probit analysis to be the standard method for analysis of dose-response data. He also concluded that 99.9968% mortality would ensure that accidental introduction of an exotic arthropod (or plant disease) would be impossible.

I. Tolerance distributions in quarantine security The “probit of 9” was codified by the USDA as the requirement for “probit 9 security.” The same requirement still remains as the legal basis of USDA plant protection and quarantine treatment schedules.5 Three related assumptions are inherent in the probit 9 requirement: (1) the probit model is always appropriate for data analyses from commodity treatment bioassays; (2) probability of death is the only criterion relevant to the future establishment of a pest species in a new environment; and (3) 99.9968% effectiveness is the minimum level necessary for quarantine security. Even if the first two assumptions were true, no investigations have ever shown that the probit model is a matter of universal truth. As we indicated in Chapter 3 (Binary Quantal Response with One Explanatory Variable), the debate over probit versus logit analysis has been ongoing among statisticians for over 50 years, and other alternatives have been proposed. For example, distribution functions such as the log and Gompertz (complementary

2331_C007.fm Page 79 Wednesday, May 9, 2007 5:44 AM

Chapter seven: Quarantine statistics

79

log-log) transformations6 were recommended for use in quarantine entomology 20 years ago because results could be easily obtained with a pocket calculator. Now, laptop computers can be loaded with statistical packages that include as many distribution functions as an investigator can possibly use for analyses of binary data. Robertson et al.7,8 have suggested that a general term, Q, be substituted for the word probit in the context of insect quarantine. This simple change in notation would eliminate the implication that the standard normal is the only distribution function that can or should be used to estimate 99.9968% mortality. We will refer to the lethal dose, LD99.9968, as the Q9 here.

A. Laboratory bioassays to estimate the Q9 in a confirmatory test The progression of testing for quarantine problems is the same for any other treatments in pest management. Laboratory tests are used to test possible treatments,9 identify the most susceptible life stages of the arthropod10 that is to be excluded from a new area, and, if the treatment appears to be sufficiently effective, recommend the dose to be tested in a larger test to confirm treatment efficacy. Until relatively recently, different cultivars of a commodity were considered as different entities with respect to a quarantine treatment; a different test protocol was necessary for each cultivar. Each cultivar was subjected to a separate (unreplicated) confirmatory test. Evidence presented by Tebbetts et al.,11,12 Yokoyama et al.,13 Maindonald et al.,14 and Robertson and Yokoyama15 has shown conclusively that cultivar differences are no more than a reflection of natural variation in response of the insect. Periodically, an importing nation will attempt to impose trade barriers based on results of bioassays of an arthropod on a variety of a particular commodity. In 1997–98, such an issue was finally resolved with the government of Japan through negotiations at the World Trade Organization.16 Is the USDA being overly cautious about ‘Rednecks’? Paula Maven must find the basis of their permit denial. Whatever their reason, Blanche may have to do a fumigation bioassay to answer their requirements.

1. Differences in estimates depending on tolerance distribution Robertson et al.7,8 used data from three typical bioassays to show differences at the Q9 when the probit or logit model was used (see Table 7.1). The bioassays were two commodity treatment experiments: (1) Bactrocera dorsalis Hendel exposed to heat treatment for a increasing times in days, and Ceratitis capitata (Wiedemann) in mangoes immersed in hot water for increasing times in minutes; and (2) topical application of a pesticide (mexacarbate) on western spruce budworm. The choice of a model had a large effect on estimates of the Q9, especially in the bioassay with western spruce budworm. For the two generations of B. dorsalis, the Q9 estimates were substantial despite use of ≥ 28,000 individuals in each bioassay, and regardless of model assumed. Large values of the χ2 goodness-of-fit statistic versus degrees of

2331_C007.fm Page 80 Wednesday, May 9, 2007 5:44 AM

80

Bioassays with arthropods, second edition Table 7.1 Results for Seven Generations of B. dorsalis Treated with Cold Generation

Q9 (95% CL)

χ2

Df

30 31 32 33 34 35 37

9.52 (8.79–10.24) 10.64 (8.47–12.82) 9.46 (8.71–10.21) 9.38 (8.46–10.30) 9.30 (7.89–10.70) 10.10 (9.17–11.04) 10.54 (10.34–10.75)

2.68 1.52 8.96 2.54 1.69 3.12 7.25

6 4 7 5 6 6 9

Note: Estimates were obtained by fitting a probit model with a random effect factor to account for extra-binomial variation. From Robertson et al.7

freedom indicated that neither the probit nor logit model adequately fit the data. Such large χ2 values are usually managed by multiplication of variances and covariances by the heterogeneity factor (SAS; 1 7 Sharp and Picho-Martinez18). This practice assumes that the causes of poor fit affect only the calculations of the standard error, but not each point estimate. Residual plots for both the F30 and F31 generations showed evidence of extrabinomial variation, so further analyses of seven generations was done with a compound probit model that incorporates a random error effect at the level of dose (see Preisler19). Even when the random effects model was used, estimates of the Q9 differed (see Table 7.1). This observation is consistent with the general phenomenon of natural variation in response to chemical and microbial agents reported by Robertson et al.20

2. General formula for selection of dose in a confirmatory test based on laboratory bioassays For selection of dose (or time at a given dose) to be tested in the next phase (confirmatory tests), Robertson et al.7 suggested that computation of the mean value of Q9 and its SD could be used along with the value of xπ. Assuming that the samples included in the experiment provide a random sample of the responses of present and future generations of n insect populations, the confirmatory dose is the (Q9)/n + 1.96(SD) where xπ is the π-th percentile point of the distribution curve. Thus, for the seven B. dorsalis generations, 95% of the generations would have a Q9 that is less than 9.855 + (1.65 x 0.56) = 10.78 days. The confirmatory test to verify that quarantine security requirements are met would be done with 2.8ºC for a period of 10.78 days.

3. Dose placement and sample size requirements for estimation of a Q9 in bioassays Dr. Maven decides to use PoloDose to examine the problems of dose placement and sample size that she would ask Blanche to test if they decide to undertake this research problem for the Jones family. In other words, if their grant application is funded, how would they do the experiments? Based on the general information about specialized bioassays to estimate the LD99, Paula uses a seven-dose design with cell sizes from 1,500 to 4,000

2331_C007.fm Page 81 Wednesday, May 9, 2007 5:44 AM

Chapter seven: Quarantine statistics

81

(total sample sizes, 10,500–28,000) to examine where doses should be placed based on the width of L* (see Table 7.2). These results show that all of the designs except the one that includes 0.80 as the lowest dose provides acceptable precision for total sample sizes from 10,500 to 28,000. However, the highest dose in each design must have five survivors out of 10,000 individuals. This means that each bioassay should include 70,000 individuals. Paula can hardly wait to hear the screams when she tells Blanche how many wicked witches would have to be reared and then tested just for one bioassay. Smaller sample sizes can be tested with the understanding that no extrapolation is permissible, and that doses should be placed approximately as shown in Table 7.2. However, even the use of 3,000 individuals (such as would be needed for precise estimation of the LD99; see 5.IV, “Practical Considerations”) would be beyond the capacity of most laboratory rearing programs. Even if Blanche wanted to test a treatment with wicked witches, she could not do so simply because of the sample sizes required. Paula concludes that the arbitrary standard that was set for one species of Tephritid fruit fly is not universally applicable to other insect species, particularly Lepidoptera.

4. Varietal differences Natural variation in response occurs whenever a bioassay is repeated (see Chapter 6, “Natural Variation in Response”).15 Evidence that cultivars significantly affect dose-responses of an arthropod subjected to quarantine treatments is overwhelming.11–15 Based on the procedures described by Robertson and Yokoyama,15 Paula gives Blanche the bioassay method to use. First, she will not use methyl bromide fumigation because the government of New Zealand is discouraging its use and ‘Redneck’ tomatoes are organically grown. Instead, she will use the combined effects of low oxygen, elevated carbon dioxide with short duration high temperature (CATTS) in bioassays of wicked witches on five tomato cultivars (‘Redneck,’ ‘Golden Girls’, ‘Julia Sugarbaker,’ ‘Elmer,’ and ‘Pinole’). The objective of a test of varietal differences is comparison and nothing more, so the best point of comparison is not the Q9 but the LD50. The general design of this type of experiment should include pairwise comparisons of wicked witches reared on each cultivar versus those reared on ‘Redneck’ so that the natural variation of ‘Rednecks’ can be estimated, together with an overall comparison of relative susceptibility of wicked witches that feed on the other cultivars. If enough wicked witches were available (and if they fed on ‘Rednecks’), Blanche would test about 500 individuals in the same way that she does a screening experiment with a chemical. Hypothetical results of such analyses with the PoloPlus software program are shown in Table 7.3. ‘Julia Sugarbaker’ and ‘Elmer’ have LD50s that are equal to those of ‘Rednecks’ in their respective experiments. The response of ‘Golden Girls’ is significantly longer than that of ‘Rednecks,’ and that of ‘Pinoles’ is significantly shorter. However, the mean ± SD of the LD50s of ‘Rednecks’ in these

2331_C007.fm Page 82 Wednesday, May 9, 2007 5:44 AM

82

Bioassays with arthropods, second edition

Table 7.2 Confidence Interval Estimates for the Q9 in a Seven-Dose Design CELL SAMPLE

P0

L* PROBIT

1500

10,500

0.0125, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.025, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.05, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.10, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.25, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.50, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.80, .90, 0.925, 0.95, 0.97, 0.99, 0.9995

0.263 0.241 0.230 0.228 0.245 0.302 0.513

2000

14,000

0.0125, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.025, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.05, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.10, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.25, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.50, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.80, .90, 0.925, 0.95, 0.97, 0.99, 0.9995

0.228 0.209 0.199 0.197 0.212 0.261 0.444

3000

21,000

0.0125, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.025, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.05, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.10, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.25, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.50, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.80, .90, 0.925, 0.95, 0.97, 0.99, 0.9995

0.186 0.171 0.162 0.162 0.173 0.213 0.444

3500

24,500

0.0125, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.025, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.05, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.10, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.25, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.50, .90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.80, .90, 0.925, 0.95, 0.97, 0.99, 0.9995

0.172 0.158 0.150 0.149 0.161 0.197 0.334

3750

26,250

0.0125, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.025, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.05, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.10, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.25, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.50, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.80, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995

0.166 0.153 0.145 0.144 0.155 0.191 0.323

4000

28,000

0.0125, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.025, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.05, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.10, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.25, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.50, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995 0.80, 0.90, 0.925, 0.95, 0.97, 0.99, 0.9995

0.161 0.148 0.141 0.139 0.150 0.185 0.313

2331_C007.fm Page 83 Wednesday, May 9, 2007 5:44 AM

Chapter seven: Quarantine statistics

83

Table 7.3 Results of Tomato Cultivar Tests with Wicked Witches in CATT Tests LD50 (95% CL) (time in minutes)

LD50 ratio

495 3.180 (0.423) 422 2.543 (0.308)

9.4 (6.6–11.8) 11.5 (7.7–15.1)

0.846 (0.697–1.027)

94 94

492 3.622 (0.500) 561 3.093 (0.468)

11.3 (8.8–13.7) 23.7 (11.5–30.7)

0.477 (0.382–0.594)

Redneck Pinole

90 90

498 2.155 (0.186) 596 1.998 (0.202)

16.8 (10.6–23.7) 4.3 (2.7–5.8)

3.193 (2.942–5.204)

Redneck Elmer

95 94

429 2.463 (0.312) 566 3.142 (0.318)

9.6 (3.7–14.3) 10.0 (8.0–11.9)

0.958 (0.772–1.190)

Cultivar

nc

Redneck Julia Sugarbaker

97 92

Redneck Golden Girl

N

Slope(SE)

experiments is 11.7 ± 1.7 days. Using the general equation for natural variation discussed in Chapter 6, and assuming that the cultivars represent a random sample of past and future cultivars upon which ‘Rednecks’ might feed, natural variation would be reflected by any LD50 between 8.4 and 15.3 days.

B. Confirmatory tests In a confirmatory test, large numbers of the target species are tested with a fixed treatment level (usually the Q9), and the upper 95% boundary for the probability of at least one survivor is calculated. For example, if n individuals are treated and no survivors are observed, the 95% upper boundary is 1 – (0.05)1/n. If n = 95,000, for example, then pu = 31.53 per million. To meet the Q9 criterion, <32 survivors per million are required. Any assumptions about a particular tolerance distribution are unnecessary at the stage of confirmatory testing. The correct equation21 to relate sample size (n) and the number of survivors (s) observed in confirmatory tests to true survivorship (pu) where one or more survivors is observed is x =s

∑e

–m

mx/x! = 1 – C

(7.1)

x =0

In this equation, m is the product of n and pu at a given confidence limit C (usually 0.95) for s survivors. The methods of Couey and Chew22 can be used to calculate pu.

2331_C007.fm Page 84 Wednesday, May 9, 2007 5:44 AM

84

Bioassays with arthropods, second edition

II. Ecological approaches to quarantine security: risk Death is not the only criterion for the effectiveness of quarantine treatments. Scientific knowledge about exotic pest species increased substantially between 193923–25 and the present. These ecological studies clearly showed that mortality alone is not the only criterion that should be used to evaluate treatment efficacy.23–28 As Paula Maven is well aware, the science of ecology is relatively new.23–24 With a more ecological approach, emphasis in applied entomology shifted from control of arthropod pests to arthropod population management in the mid-1970s. In quarantine entomology, the role of ecological parameters such as percentage infestation of a commodity, host suitability, pest distribution in a commodity, and arthropod survival on various hosts indicated that a distinction must be made between commodities that are good hosts or that are heavily infested, versus those that are poor hosts or that are rarely infested.

A. The alternative efficacy approach for species on poor hosts The alternative efficacy approach measures risk as the probability of a mating pair, gravid female,25,29 or parthenogenic individual surviving in a shipment. Many factors can be involved in calculations of risk. These include lot size, mean numbers of arthropods per unit of the commodity, and the proportion of the commodity infested.26,28 One general expression of the risk of infestation is e−λ λ r r!

(7.2)

where λ = Nϕμp, N = lot size , ϕ = treatment efficacy, µ = mean number of arthropods per unit of the commodity, and p = proportion of the units infested. Therefore, −λ ⎞ ⎛ q = Pr ⎡⎣r ≥ 2⎤⎦ − ⎜1 − e 2 ⎟ ⎠ ⎝

2

(7.3)

A modification of this equation and the subsequent calculations is shown in Equations 1–4 of Follett and McQuate;29 these equations can then be used to calculate pest risk and the numbers of insects that must be tested to reduce the numbers of test subjects required for quarantine treatment development when the commodity is a poor host for the arthropod. Such arthropod pest-host combinations include Bactrocera dorsalis (Hendel) on rambutan (Nephelium lappacium L.),29 oriental fruit fly on avocados,30 and codling moth on nectarines31 or sweet cherries.32

2331_C007.fm Page 85 Wednesday, May 9, 2007 5:44 AM

Chapter seven: Quarantine statistics

85

B. Risk for preferred hosts and heavy infestations: systems approach Mangan et al.21 describe a landmark investigation in which Equations 7.1–7.3 were used to show that probability of accidental introduction of a single mating pair of Mexican fruit fly (Anastrepha ludens [Loew]) was so high that insecticide application that produced a Q9, sterile insect release, and selective harvest of fruit combined would allow the survival of <1 reproductive pair of flies per shipment of mangoes and citrus. This study is unique because it provides the only example of a true scientific systems approach, including risk analysis, applied to an actual commercial cropping system. Robertson et al.7,8 had recommended that such analyses were crucial to the improvement of scientific pest exclusion systems in entomology.

III. Conclusions The probit 9 and the automatic requirement for 99.9968% mortality in a quarantine treatment is that last lingering remnant of antiquated pest management practices of the early 20th century. As a USDA staff entomologist, A. C. Baker was doubtless familiar with the use of Paris green and other arsenical pesticides on crops and export commodities. Once the USDA had a regulation in place, DDT and later synthetic organic pesticides replaced arsenicals as the control agents of choice on crops and as fumigation agents. Rather than a practice based on sound science, the probit 9 requirement is an anachronism based in bureaucracy. If quarantine entomology had developed to provide knowledge to producers and potential exporters (or importers) in the same way that epidemiology has developed in conjunction with medical science, the statistics of risk analysis would have been the primary methods described here. As this entomological specialty actually has evolved, risk analyses have been a recent addition. The studies of Landolt et al.,25 Vail et al.,26 and Baker et al.27 were just the initial steps toward building the scientific basis that will be the postmortem for the probit 9. Even though Mangan et al.21 assumed that 99.9968 mortality had occurred in their study, the statistical methods that they use will allow the development of even more thorough risk analyses in the future. Paula Maven concludes that the three assumptions inherent in the probit 9 are unfounded. The probit model is not always appropriate for data analyses from commodity treatment bioassays simply because (1) the normal distribution is one of many available, and there is no basis to assume that (2) probability of death is the only criterion relevant to the future establishment of a pest species in a new environment; and (3) 99.9968% effectiveness is the minimum level necessary for pest exclusion.

2331_C007.fm Page 86 Wednesday, May 9, 2007 5:44 AM

86

Bioassays with arthropods, second edition

References 1. Paull, R. E. and Armstrong, J. W., eds., Insect Pests and Horticultural Products: treatments and Responses, CAB International, Wallingford, England, 1994. 2. Sharp, J. L. and Hallman, G. J., eds., Quarantine Treatments for Pests of Food Plants, Westview Press, Boulder, CO, 1994. 3. Worner, S. P., Predicting the establishment of exotic pests in relation to climate, in Sharp, J. L. and Hallman, G. J., eds., Quarantine Treatments for Pests of Food Plants, Westview Press, Boulder, CO, 1994, pp. 11–31. 4. Baker, A. G., The basis for treatment of products where fruit flies are involved as a condition for entry into the United States, USDA Circular 551, Washington, DC, 1939. 5. USDA (United States Department of Agriculture), Plant protection and quarantine treatment manual, USDA, APHIS, Washington, DC, 1998. 6. Chew, V., Statistical methods for quarantine treatment data analysis, in Sharp, J. L. and Hallman, G. J., eds., Quarantine Treatments for Pests of Food Plants, Westview Press, Boulder, CO, 1994, pp. 33–46. 7. Robertson, J. L., Preisler, H. K., and Frampton, E. R., Statistical concept and minimum threshold concept, in Paull, R. E. and Armstrong, J. W., eds., Insect Pests and Horticultural Products: treatments and Responses, CAB International, Wallingford, England, 1994, pp. 47–65. 8. Robertson, J. L., Preisler, H. K., Frampton, E. R., and Armstrong, J. W., Statistical analyses to estimate efficacy of disinfestation treatments, in Sharp, J. L. and Hallman, G. J., eds., Quarantine Treatments for Pests of Food Plants, Westview Press, Boulder, CO, 1994, 47–65. 9. Zettler, J. L., Follett, P. A., and Gill, R. F., Susceptibility of Maconellicoccus hirsutus (Homoptera: Pseudococcidae) to methyl bromide, J. Econ. Entomol 95, 1169, 2002. 10. Neven, L. G., Combined heat and controlled atmosphere quarantine treatments for control of codling moth in sweet cherries, J. Econ. Entomol. 98, 709, 2002. 11. Tebbetts, J. S., Hartsell, P. L., Nelson, H. D., and Tebbetts, J. C., Methyl bromide fumigation of tree fruits for control of Mediterranean fruit fly, J. Agric. Food Chem. 31, 247, 1983. 12. Tebbetts, J. S., Vail, P. V., Hartsell, P. L., and Nelson, H. D., Dose/response of codling moth (Lepidoptera: Tortricidae) eggs and nondiapausing and diapausing larvae to fumigation with methyl bromide, J. Econ. Entomol. 79, 1039, 1986. 13. Yokoyama, V. Y., Miller, G. T., and Hartsell, P. L., Evaluation of a methyl bromide quarantine treatment to control codling moth (Lepidoptera: Tortricidae) on nectarine cultivars proposed for export to Japan, J. Econ. Entomol. 83, 466, 1990. 14. Maindonald, J. H., Waddell, B. C., and Birtles, D. B., Response to methyl bromide fumigation of codling moth (Lepidoptera: Tortricidae) eggs on cherries, J. Econ. Entomol. 85, 1222, 1992. 15. Robertson, J. L. and Yokoyama, V. Y., Comparison of methyl bromide LD50s of codling moth (Lepidoptera: Tortricidae) on nectarine cultivars as related to natural variation, J. Econ. Entomol. 91, 1433, 1998.

2331_C007.fm Page 87 Wednesday, May 9, 2007 5:44 AM

Chapter seven: Quarantine statistics

87

16. SICE Dispute Settlement WTO Report, Japan—Measures affecting agricultural products, report of the panel, Probit 9, dose-mortality tests and confirmatory tests, http://www.sice.oas.org/dispute/wto/ds76/76r07.asp, 1999. 17. SAS Institute, http://www.sas.com/technologies/analytics/statistics/stat. 18. Sharp, J. L. and Picho-Martinez, H., Hot-water quarantine treatment to control fruit flies in mangoes imported into the United States from Peru, J. Econ. Entomol. 83, 1940, 1990. 19. Preisler, H. K., Assessing insecticide bioassay data with extra-binomial variation, J. Econ. Entomol. 81, 759, 1988. 20. Robertson, J. L., Preisler, H. K., Ng, S. S., Hickle, L. E., and Gelernter, W. D., Natural variation: a complicating factor in bioassays with chemical and microbial pesticides, J. Econ. Entomol. 88, 1, 1995. 21. Mangan, R. L., Frampton, E. R., Thomas, D. B., and Moreno, D. S., Application of the maximum pest limit concept to quarantine security standards for the Mexican fruit fly (Diptera: Tephritidae), J. Econ. Entomol. 90, 1433, 1997. 22. Couey, H. M. and Chew, V., Confidence limits and sample size in quarantine research, J. Econ. Entomol. 79, 887, 1986. 23. Andrewartha, H. G. and Birch, L. C., The Distribution and Abundance of Animals, University of Chicago Press, Chicago, 1954. 24. Huffacker, C. B. and Rabb, R. L., eds., Ecological Entomology, John Wiley & Sons, New York, 1984. 25. Landolt, P. J., Chambers, D. L., and Chew, V., Alternatives to the use of probit 9 mortality as a criterion for quarantine treatments of fruit fly (Diptera: Tephritidae)–infested fruit, J. Econ. Entomol. 77, 285, 1984. 26. Vail, P. V., Tebbetts, J. S., Mackey, B. E., and Curtis, C. E., Quarantine treatments: a biological approach to decision making for selected hosts of codling moth (Lepidoptera: Tortricidae), J. Econ. Entomol. 86, 70, 1993. 27. Baker, R. T., Cowly, J. M., Harte, D. S., and Frampton, E. R., Development of a maximum pest limit for fruit flies (Diptera: Tephritidae) in produce imported into New Zealand, J. Econ. Entomol. 83, 13, 1990. 28. Liquido, N. J., Barr, P. G., and Chew, V., CQT_STATS: biological statistics for pest risk assessment in developing commodity quarantine treatment, USDA-ARS Publ. Series (available at http://www.pbarc.ars.usda.gov), 1996. 29. Follett, P. A. and McQuate, G. T., Accelerated development of quarantine treatments for insects on poor hosts, J. Econ. Entomol. 94, 1005, 2001. 30. Liquido, N. J., Chan, H. T., and McQuate, G. T., Hawaiian tephritid fruit flies (Diptera): integrity of the infestation-free quarantine procedure for ‘Sharwil’ avocado, J. Econ. Entomol. 88, 85, 1995. 31. Curtis, C. E., Clark, J. D., and Tebbetts, J. S., Incidence of codling moth (Lepidoptera: Tortricidae) in packed nectarines, J. Econ. Entomol. 84, 1686, 1991. 32. Data and report cited by Follett, P. A. and McQuate, G. T., note 29 above.

2331_C007.fm Page 88 Wednesday, May 9, 2007 5:44 AM

 

 

2331_C008.fm  Page 89  Wednesday, May 9, 2007  5:45 AM

chapter eight

Statistical analyses of data from bioassays with microbial products Every university town seems to have a genetic engineering laboratory, and Schaeferville is no exception. Dr. Waylon Jennings Jones, a first cousin of Hank Jones, is the director and production manager of Jones Genetically Engineered Products. His curriculum vitae—a B.S. in biology from the University of Connecticut, an M.S. in bacteriology from the University of Texas, and a Ph.D. in molecular biology from Stanford University—is impressive. Waylon returned to his hometown to found a company that produces Bacillus thuringiensis varieties for insect management. After long days and nights of research, his staff has isolated the strain that affects wicked witches; Waylon names it B. thuringiensis var. giganticus. The federal registration process1,2 begins, and the Jones company product HurricaneDubya  is registered for use on tomatoes and the other crops that are demolished by infestations of wicked witches. Waylon Jones becomes concerned about the quality of the HurricaneDubya production process after various batches from the fermentation vats are tested in laboratory bioassays. Results seem to be erratic, and response lines are not parallel. Even when bioassays are done in several different laboratories, differences are observed not only in response to HurricaneDubya but also in response to the standard B. thuringiensis var. kurstaki. At the suggestion of his cousin Hank, Waylon makes an appointment to see Paula Maven, who must now review the idiosyncrasies involved with bioassays of microbial products. Or are they idiosyncrasies? Microbial pesticides are unique because their active ingredient is a mixture of large proteins whose activity is stated in terms of standardized units that must be estimated biologically rather than defined chemically. This difference is recognized in the U.S. Environmental Protection Agency guideline, but it merits a thorough examination of all the statistical procedures that are involved. Dr. Maven, mindful of all that she has recently discovered about natural variation in response, begins her review by rereading a key reference.3 89

 

2331_C008.fm  Page 90  Wednesday, May 9, 2007  5:45 AM

90

Bioassays with arthropods, second edition

I. Biological units and standards When formulated for a bioassay, the active ingredient of the toxicant is known in terms of its chemical purity. Thus, Blanche has applied a measured volume containing a precise amount of toxicant in each bioassay with sibling groups, population samples, different generations, and other samples. When she tests microbial pesticides, in contrast, the amount of active material is based on arbitrary units assigned to standard preparations. The historical development of standard bioassay methods for various strains of Bacillus thuringiensis has been reviewed by Beegle,4 but a critical assessment of the statistical methods used for data analyses of bioassays with these products has never been done and is urgently needed. Commercial development and production of microbial products depends not only on standardized bioassay procedures, but also on the use of valid statistical methods. Early in the development of products based on B. thuringiensis, investigators recognized the lack of a relationship between spore count and biological activity of a preparation. As a result, an alternative approach was adopted so that a standard preparation (expressed in arbitrary units called International Potency Units, or IUs) were tested concurrently with each test preparation, and a lethal dose, LD50, for each preparation was estimated as a ratio. The ratio was then multiplied by the IUs of the standard to obtain the putative potency. This procedure avoids an extremely complex computational problem because the binary response for each test preparation is not simply yt = α + βxt. Instead, a more complicated regression line is needed.

II. A revised definition of relative potency Dr. Maven then reads, “Standards are used to determine relative toxicities for different preparations, correct day-to-day fluctuations, and to some extent, correct for different assay conditions and methodologies between different laboratories.”4 Here she detects a semantic problem. In the dictionary, and certainly by logic, potency should be the same as toxicity. In the context of probit and logit regression, however, the terms are not synonymous because Finney’s5 statistical definition of potency is predicated on the assumption that response lines are parallel. At the time Finney’s equations were published, calculations were derived and problems were solved by hand; modern computer technology had not yet made possible the solution of likelihood ratio tests to test the hypotheses of parallelism and equality.6 Likewise, the toxicity ratio test (see 3.II.A.2, “Lethal Dose Ratios”) had not yet been derived. Invertebrate pathologists therefore assumed that a potency estimation was not valid if slopes were significantly different, while at the same time they lacked a statistical method to test the hypothesis of parallelism. As a result, solutions

 

2331_C008.fm  Page 91  Wednesday, May 9, 2007  5:45 AM

Chapter eight: Statistical analyses of data from bioassays

91

to this problem such as those discussed by Beegle4 involve assumptions about corrections for parallelism that are both improper and unnecessary. The terms relative toxicity and relative potency can be used synonymously so long as no assumptions about parallelism are made. Invertebrate pathologists have two choices: discard the assumption of parallelism because it is a statistical relict, or provide biological evidence that parallelism is necessary for a simple point comparison at the 50% level. The logical choice is to discard the unnecessary assumption and stop the dangerous practice of discarding data for no good reason. Remember that parallelism means that the models for toxic action of the two stimuli are the same. The correct calculation for relative potency involves a simple modification of the calculations previously given (in section 3.II.A.2), so that upper and lower 95% confidence limits are estimated along with mean relative potency. By convention, relative potency is estimated at the 50% response level. For example, Blanche has completed five bioassays in which the potency of experimental fermentation batches of B. thuringiensis var. giganticus must be estimated in comparison with the standard B. thuringiensis var. kurstaki. Results produced by probit analysis done with PoloPlus7 provide an ideal means to calculate the relative toxicities with 95% limits in terms of IUs. If the potency of B. thuringiensis var. kurstaki is 12,000, B. t. var. giganticus lots 1–5 had potencies (95% CL) of 0.23 (0.21–0.26), 0.26 (0.23–0.30), 0.35 (0.30–0.39), 0.38 (0.33–0.42) and 0.14 (0.12–0.15) IUs. If other software is used for the data analyses, lethal dose ratios of each lot compared with the standard can be computed by the methods given in 3.II.A.2. Because it is based on the assumptions of the probit model, mean potency is an estimate, not a measurement. Therefore, sampling error and natural variation will contribute to the appearance of different potency values from the same sample in repeated bioassays at the same time and to different values over time.

III. Effects of natural variation on product quality Large-scale commercial production of any material used for arthropod population management involves strict measures to ensure product quality. When a conventional chemical is involved, analytical methods such as gas-liquid chromatography or high pressure liquid chromatography are used to ensure the chemical purity of the product. For the biological insecticide industry, the most reliable method to estimate product quality during production is arthropod bioassay, because no chemically based analytical methods are available to determine biological activity. According to usual practice, an aliquot from each lot is tested in four replicated bioassays and average potency of the lot is then computed.8 That single number, the average, is the only potency reported for the lot. A practical guideline that also more than exceeds the sample size recommended for screening experiments outlined in Chapter 5 (see 5.II,

 

 

2331_C008.fm  Page 92  Wednesday, May 9, 2007  5:45 AM

92

Bioassays with arthropods, second edition

“Basic Binary Bioassays”) is to use at least six doses per bioassay, each with 30 test subjects per dose, with at least four replications. The total sample size of such a bioassay as a whole is 720. As long as each bioassay is done with separate dilutions from the initial aliquot, the experiment can be considered to be replicated regardless of whether two bioassays are done on the same day. Assuming that the samples in the bioassays for the lot represent a random sample of responses of n present (and future) bioassays of the same lot, the approximate 95% limits of natural variation are MEAN ± 1.96 (SD) where MEAN and SD are the mean and standard deviation of the LD’s from the n samples. When lethal doses ratios are used, as in bioassays with microbial preparations, the equation is the same, with MEAN and SD calculated from the LR’s from the n samples. For example, suppose that four replicated bioassays with lot #707 of B. t. giganticus produce LD50s of 12,250; 11,671; 10,600; and 14,310 IUs. The mean  SD, and approximate 95% CL are 12,207 and 1,559 with approximate 95% CL of natural variation of 9,151 to 13,766 IUs. When the label for the product is finalized, mean potency and the 95% interval should be reported so that variation is clearly acknowledged to exist. However, formulation instructions of the commercial product will continue to be based on its mean potency. Efforts to standardize the laboratory methods used in bioassays of microbial products have been extraordinary and are part of the overall attempt to eliminate variation in response to standard microbial preparations of B. t. thuringiensis, B. t. kurstaki, B. t. israeliensis, and B. tentomocidus. The variables under strict control in a given laboratory are usually method of exposure, insect developmental stage, incubation conditions, and duration of exposure. For example, the microbial preparation can be applied to the surface of meridic diet or mixed with molten diet; the numerous other methods are described by Beegle.4 In a specific bioassay, only one developmental stage of the arthropod is used and individuals in that stage are, as much as is possible, the same age. Even when all of these experimental variables are controlled, variable results in response to standard preparations will be observed in the same laboratory under exactly the same treatment conditions. Tables 8.1 and 8.2 show the results of repeated tests of B. t. tenebrioni on early-second-instar Colorado potato beetle and B. t. kurstaki on late-second to early-third-instar diamondback moth.9 The same type of variation can be expected when results from bioassays in one laboratory are compared with results from another laboratory, when results for the same microbial preparation are tested after various periods of storage, or when the responses of populations are compared. As will be shown in Chapter 9, “Pesticide Resistance,” numerical differences in toxicity ratios or relative potencies alone cannot be used to identify resistance without further biological evidence and identification of the extent of natural variation.

  

2331_C008.fm  Page 93  Wednesday, May 9, 2007  5:45 AM

Chapter eight: Statistical analyses of data from bioassays Table 8.1 Toxicity of B. thuringiensis subsp. tenebrioni to Colorado Potato Beetle over 83 Weeks Week 5 4 28 6 3 8 54 2 15 19 48 40 72 9 53 23 33 56 20 1 46 70 80 7 55 76 75 59 34 50 71 18 17 14 57 31 58 79 73 22 16 10 69 49 81 74

n

Slope ± SE

LD50 (95% CI) 

989 898 992 981 1444 980 693 1393 1979 2474 1481 987 1988 993 1331 976 1470 1042 998 989 1475 2387 1719 1473 1026 1395 1977 1945 1979 1983 804 1494 1981 1977 1030 975 1194 683 1981 992 995 987 1995 1496 1731 1971

1.87 ± 0.15 2.26 ± 0.16 1.67 ± 0.15 2.30 ± 0.15 1.13 ± 0.10 2.12 ± 0.15 3.97 ± 0.27 1.13 ± 0.10 3.01 ± 0.12 2.30 ± 0.10 1.12 ± 0.10 1.72 ± 0.14 2.17 ± 0.11 2.94 ± 0.17 3.05 ± 0.15 2.72 ± 0.16 2.01 ± 0.11 3.70 ± 0.25 2.14 ± 0.14 2.49 ± 0.17 1.12 ± 0.11 2.26 ± 0.09 2.52 ± 0.13 1.63 ± 0.11 3.39 ± 0.19 2.54 ± 0.15 2.27 ± 0.10 2.86 ± 0.13 1.42 ± 0.09 1.27 ± 0.06 1.74 ± 0.15 3.00 ± 0.14 2.72 ± 0.12 2.57 ± 0.10 2.18 ± 0.15 3.18 ± 0.17 2.60 ± 0.14 2.98 ± 0.22 1.84 ± 0.10 2.31 ± 0.22 2.61 ± 0.15 2.28 ± 0.15 2.89 ± 0.11 1.29 ± 0.10 2.28 ± 0.13 2.08 ± 0.10

20.1 23.4 30.9 31.6 35.3 39.5 40.1 39.9 44.3 45.4 46.3 46.8 48.7 48.2 48.8 49.9 51.2 52.3 53.5 55.4 56.0 57.0 56.9 59.1 59.9 62.4 62.5 64.1

(15.4–24.8) (20.4–26.3) (23.0–38.4) (25.3–38.5) (10.6–59.7) (34.0–45.5) (37.2–13.1) (32.2–17.3) (37.9–51.3) (40.0–50.1) (31.4–60.3) (36.5–56.9) (42.1–55.7) (43.3–53.9) (38.8–59.8) (44.2–55.7) (43.0–59.4) (48.7–56.0) (45.7–61.7) (46.8–63.7) (35.9–75.5) (50.3–63.9) (48.3–65.6) (42.2–95.5) (53.8–67.4) (52.4–72.6) (50.7–80.0) (36.0–97.4) 66.8 69.4 (42.4–111.3) 68.8 (37.6–105.2) 69.2 (61.6–77.1) 70.3 (56.2–85.8) 70.9 (63.9–78.6) 69.8 (58.7–84.4) 71.6 (65.5–78.1) 72.6 (67.3–78.4) 72.4 (65.8–79.4) 72.4 (54.8–93.1) 74.9 (48.7–97.9) 75.3 (62.2–91.1) 76.3 (65.5–91.6) 76.4 (69.1–84.5) 77.6 (63.3–92.3) 79.8 (57.0–106.4) 80.1 (66.8–95.7)

93

 

 

2331_C008.fm  Page 94  Wednesday, May 9, 2007  5:45 AM

94

Bioassays with arthropods, second edition Table 8.1 Toxicity of B. thuringiensis subsp. tenebrioni to Colorado Potato Beetle over 83 Weeks (continued) Week 60 62 11 61 35 29 77 13 30 67 32 65 26 36 82 39 24 42 66 37 52 12 68 51 63 78 38 47 83 64 21 27 41 25 45 43 44

n

Slope ± SE

1398 1583 985 1894 1936 1993 1397 977 1495 2776 1493 794 1490 2870 1189 1475 2468 1957 1931 1978 1790 993 2344 1493 2398 689 1937 1950 591 1189 1499 1476 1476 995 1945 1984 1992

2.83 ± 0.16 2.84 ± 0.12 2.25 ± 0.17 2.78 ± 0.11 2.70 ± 0.11 2.47 ± 0.12 2.07 ± 0.13 2.17 ± 0.14 1.49 ± 0.11 2.77 ± 0.09 2.58 ± 0.14 2.44 ± 0.16 1.40 ± 0.12 2.83 ± 0.13 2.23 ± 0.13 2.20 ± 0.14 2.36 ± 0.12 1.48 ± 0.10 2.54 ± 0.11 2.33 ± 0.11 2.33 ± 0.11 1.61 ± 0.13 2.84 ± 0.11 1.71 ± 0.09 2.49 ± 0.10 1.82 ± 0.18 2.28 ± 0.12 1.08 ± 0.09 2.07 ± 0.20 2.45 ± 0.16 1.25 ± 0.10 1.66 ± 0.14 1.99 ± 0.15 1.92 ± 0.17 1.63 ± 0.09 1.95 ± 0.16 1.18 ± 0.09

LD50 (95% CI)  80.8 (70.9–92.4) 81.5 (74.1–89.9) 83.6 (42.1–133.5) 83.7 (65.6–107.1) 85.2 (78.6–92.3) 84.6 (77.2–92.3) 85.7 (67.4–111.1) 88.9 (68.5–118.6) 89.6 (73.3–108.6) 89.3 (80.2–99.4) 93.1 (83.0–103.8) 93.4 (85.0–103.1) 94.6 (79.1–111.6) 92.6 (77.8–106.8) 94.9 (78.5–115.2) 94.7 (79.3–111.3) 97.1 (89.8–104.6) 99.5 (86.1–115.0) 98.1 (86.1–111.9) 99.5 (88.7–111.3) 100.1 (80.5–126.4) 100.4 (86.1–118.8) 100.1 (92.8–107.9) 104.7 (85.6–126.13) 104.9 (92.7–117.4) 104.9 (74.0–178.4) 106.3 (96.5–116.8) 109.9 (70.5–109.6) 110.9 (85.0–146.4) 109.9 (97.6–122.4) 109.9 137.2 (107.8–174.0) 144.8 (115.3–184.2) 156.1 (122.6–212.4) 164.1 (136.0–197.4) 218.8 (182.7–271.7) 252.1 (294.0–370.8)

Notes: The regression for week 5 had the lowest LD50 and was used for the standard for comparison for all other LD50s. For weeks 21 and 34, 95% confidence limits could not be estimated because the value of g was ≥0.50; see Savin, N. E., Robertson, J. L., and Russell, R. M., A critical evaluation of bioassay in insecticide research: Likelihood ratio tests of dose–mortality regression, Bull. Entomol. Soc. Am. 23, 257, 1977. Source: Reprinted from Robertson, J. L., Preisler, H. K., Ng, S. S., Hickle, L. A., and Gelernter, W. D., Natural variation: A complicating factor in bioassays with chemical and microbial pesticides, J. Econ. Entomol. 88, 1, 1995.

 

2331_C008.fm  Page 95  Wednesday, May 9, 2007  5:45 AM

Chapter eight: Statistical analyses of data from bioassays Table 8.2 Responses of Diamondback Moth to B. thuringiensis subsp. kurstaki over 37 Weeks Week

n

Slope ± SE

LD50 (95% CI)

3 19 15 4 7 22 23 20 27 25 33 10 5 34 29 17 28 8 6 31 35 16 14 32 26 18 36 13 9 37 1 11 2 30 12 21 24

1642 724 414 1741 576 567 1587 992 1247 1590 1136 367 2069 1804 325 1444 646 1145 1669 1181 1469 1445 1100 2396 979 1796 955 2169 746 1825 382 2173 1465 1510 1070 308 651

2.33 ± 0.14 3.22 ± 0.27 3.68 ± 0.34 2.42 ± 0.12 4.29 ± 0.39 5.55 ± 0.45 3.02 ± 0.14 3.53 ± 0.19 3.86 ± 0.21 3.66 ± 0.17 2.61 ± 0.15 3.33 ± 0.29 2.51 ± 0.11 3.19 ± 0.10 2.41 ± 0.28 3.20 ± 0.22 3.20 ± 0.25 2.31 ± 0.40 3.06 ± 0.16 3.05 ± 0.17 2.96 ± 0.15 2.59 ± 0.12 2.59 ± 0.18 3.21 ± 0.15 2.94 ± 0.21 3.38 ± 0.15 2.09 ± 0.16 2.88 ± 0.11 3.72 ± 0.25 2.32 ± 0.11 3.69 ± 0.42 3.03 ± 0.12 2.71 ± 0.16 2.66 ± 0.21 2.70 ± 0.15 3.37 ± 0.32 2.22 ± 0.27

0.18 (0.14–0.22) 0.19 (0.14–0.23) 0.26 (0.16–0.37) 0.26 (0.13–0.39) 0.28 (0.25–0.30) 0.28 (0.19–0.36) 0.28 (0.23–0.33) 0.29 (0.26–0.32) 0.30 (0.21–0.39) 0.30 (0.24–0.37) 0.31 (0.25–0.38) 0.32 (0.20–0.45) 0.33 (0.31–0.35) 0.33 (0.24–0.45) 0.33 (0.24–0.45) 0.34 (0.25–0.42) 0.34 (0.28–0.44) 0.34 (0.23–0.46) 0.35 (0.29–0.40) 0.36 (0.33–0.38) 0.36 (0.33–0.40) 0.34 (0.26–0.43) 0.37 (0.31–0.44) 0.38 (0.27–0.48) 0.38 (0.27–0.50) 0.39 (0.33–0.44) 0.39 (0.32–0.48) 0.39 (0.33–0.46) 0.39 (0.34–0.45) 0.40 (0.36–0.43) 0.47 (0.24–0.67) 0.47 (0.43–0.51) 0.47 (0.38–0.56) 0.50 (0.42–0.47) 0.52 (0.46–0.58) 0.54 (0.47–0.60) 0.66 (0.57-0.78)

Note: The regression for week 3 had the lowest LD50 and was used for the standard for comparison for all other LD50s. Source: Reprinted from Robertson, J. L., Preisler, H. K., Ng, S. S., Hickle, L. A., and Gelernter, W. D., Natural variation: A complicating factor in bioassays with chemical and microbial pesticides, J. Econ. Entomol. 88, 1, 1995.

95

 

2331_C008.fm  Page 96  Wednesday, May 9, 2007  5:45 AM

96

Bioassays with arthropods, second edition

IV. Conclusions Paula Maven presents Waylon Jennings Jones with a plaque for his office wall that reads, “In general, the assumption that a response curve once determined can be used in future assays is inadmissible. Because of natural variation, responses of a group of insects tested at any one time will therefore never be exactly the same as responses of another group tested either at the same time or at a different time, regardless of the extent to which bioassay techniques are standardized.”9,10 She advises Dr. Jones to continue the side-by-side bioassays of the reference standard versus each test sample. To estimate the relative potency of the test material, the potency of each sample can be calculated directly from the relative toxicity value produced by PoloPlus.7 No assumption that lines are parallel is warranted. Each potency with its 95% confidence intervals should be recorded simply to ensure that the results are fairly consistent, but no results or data should be discarded. The estimate of potency for the entire lot should be computed from the mean potency estimated from four replicated bioassays, along with the 95% confidence interval for natural variation. Collection of data from side-by-side bioassays serves another purpose by permitting a continually updated database from which natural variation can be computed. Because of natural variation, potencies of both the standard and lots will vary around a mean value. In 95% of the bioassays, the mean will lie within the limits estimated by 1.96 times the SD of the mean. However, 1 in 20 (5%) of the means will be outside the limits simply by chance. Unless a trend is observed over time, a decrease in potency is no cause for alarm.

References 1. United States of America Federal Code, Federal Insecticide, Fungicide, and Rodenticide Act; Act of June 25, 1947, as amended through P.L. 108-199, January 23, 2004 (http://www.epa.gov). 2. United States of America, Environmental Protection Agency, Office of Prevention, Pesticides and Toxic Substances, Microbial Pesticide Test Guidelines, February 1996 (http://www.epa.gov). 3. Hickle, L. A. and Fitch, W. L., eds., Analytical Chemistry of Bacillus thuringiensis, ACS Symposium Series 432, American Chemical Society, Washington, DC, 1990. 4. Beegle, C. C., Bioassay methods for quantification of Bacillus thuringiensis δ-endotoxin, in Hickle, L. A. and Fitch, W. L., eds., Analytical Chemistry of Bacillus thuringiensis, ACS Symposium Series 432, American Chemical Society, Washington, DC, 1990, pp. 14-21. 5. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 6. Savin, N. E., Robertson, J. L., and Russell, R. M., A critical evaluation of bioassay in insecticide research: likelihood ratio tests of dose-mortality regression, Bull. Entomol. Soc. Am. 23, 257, 1977.

 

2331_C008.fm  Page 97  Wednesday, May 9, 2007  5:45 AM

Chapter eight: Statistical analyses of data from bioassays

97

7. LeOra Software, 1007 B St., Petaluma, CA 94952, 2005. See http:// www.LeOraSoftware.com. 8. Ng, S. S., personal communication, December 8, 2005. 9. Robertson, J. L., Preisler, H. K., Ng, S. S., Hickle, L. A., and Gelernter, W. D., Natural variation: a complicating factor in bioassays with chemical and microbial pesticides, J. Econ. Entomol. 88, 1, 1995. 10. Finney, D. J., Statistical Methods in Biological Assay, Griffin, London, 1964.

 

2331_C008.fm  Page 98  Wednesday, May 9, 2007  5:45 AM

2331_C009.fm Page 99 Wednesday, May 9, 2007 5:45 AM

chapter nine

Pesticide resistance Carl and Paula Maven live next door to Ernestine Feasor, whose grandnephew shares her home. Young Ernest Lionel Feasor, also known as Elf, is a wily young man prone to excess. So, when his great aunt asks him to spray their tomato seedlings with an insecticide every two weeks during the month she will be on vacation in Fresno, he decides that spraying every two days will be even better. Aunt Ernestine also leaves Elf with explicit instructions about which insecticide (a pyrethroid) to use, and how to mix it (in very small amounts). Well, he decides, I’ll use some of Great Uncle Fred’s old powder—the stuff Fred used to mix into paint to control termites—instead. The powder worked great for termites, so it should protect the little tomato plants from the giant nasty caterpillars. And so, every two days, Elf coats the entire garden with a thick slurry of toxic waste. A few surviving giants lumber off into the many shrubs and bedding plants around the entire yard, carefully avoiding the area of the garden where so many of their kin have died. There they manage to thrive despite the white goo that lands in their vicinity. These larvae pupate and become adults very quickly, and then the moths fly off to reproduce. This life cycle is repeated several times, so that by the end of Miss Feasor’s vacation, her own plants and those in the Mavens’ yard are covered with newly hatched larvae. This horrible infestation has Paula Maven baffled because she and her husband Carl have carefully abided by the same spray schedule and application rate that has controlled the wicked witches on tomatoes at the Jones’ Family Farm and at the other, smaller, commercial operations near Schaeferville. Obviously, something has happened. Then the phone calls begin! Windy Acres, Truckee Meadows, and Tomato Pie Farms are having control failures, and so is the Jones’ Family Farm. The problem is spreading. Paula first asks Blanche to collect as many wicked witches as she and her student volunteers can get, from as many sites as possible in Schaeferville, and from as many farms outside town as they can visit. Next, she visits Ernestine Feasor, who recounts the details of her trip to Fresno and then complains about the condition of her tomato plants and all of her other plants.

99

2331_C009.fm Page 100 Wednesday, May 9, 2007 5:45 AM

100

Bioassays with arthropods, second edition

During the next few weeks, Blanche and her conscripts collect wicked witches from numerous host species. They find larvae on tomatoes (and on parsley, sage, rosemary, and thyme, as well as cilantro), but also on such diverse plant species as plum, pomegranate, pigweed, thistle, and pine. Paula and Carl Maven also spend many evenings with their flexible forceps collecting caterpillars. While collecting, Paula considers which chemical to use in tests for possible resistance and cross-resistance to the pyrethroid. Because the material that Elf used was so old, and because it was a powder, she decides that the culprit is probably a vintage, chlorinated hydrocarbon pesticide. So, she settles on DDT as her test material. As the insects are collected and the caterpillars reach the proper stage of development, Blanche transfers them to foliage of the same species of plant from which they were collected. After 24 hours, she applies both the pyrethroid and DDT in rates equivalent to ounces per acre.1,2 As part of her quality control bioassays, Blanche had already gathered data from laboratory-reared insects founded with parents collected from hers and Miss Feasor’s tomato plants, and from several other locations in Schaeferville. When all of the results are in, Dr. Maven discovers that DDT is not as toxic to wicked witches from her yard or Miss Feasor’s as it is to caterpillars from other locations; nor is it as toxic as it was to the original groups that Blanche tested when the laboratory colony was established. Paula also notes that larvae on different host plant species collected from the same location seem to differ in response. Responses to the pyrethroid seem to have shifted so that it is generally less toxic and in some collections substantially so. Dr. Maven has entered a new area of research—pesticide resistance. But before she does anything further, she needs a good working definition of resistance.

I. Resistance defined The traditional definition of resistance, paraphrased by ffrench-Constant and Roush3 as “the development of a strain capable of surviving a dose lethal to a majority of individuals in a normal population,” has evolved with the completion of increasing research over the past 35 years. Among other problems, a “normal” population response does not exist (see Chapter 6, “Natural Variation in Response”). Ball4 was probably the first to advocate definition of resistance based on failure of a pesticide to control populations in the field, despite the fact that the same agent adequately controlled the arthropod in the past. This general definition can easily be extended to other chemical or biological materials used to manage a disease, behavior, or another physiological process. Sawicki5 has proposed an improved definition of resistance as “a genetic change in response to selection by toxicants that may impair control in the field.” Paula Maven defines resistance as a significant, genetically based shift in the molecular, biochemical, or behavioral bases of quantal responses in populations of an arthropod species. Resistance

2331_C009.fm Page 101 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

101

represents one extreme of response, compared with susceptibility, the other extreme. Various degrees of tolerance lie between the two extremes.

II. Natural variation versus resistance Resistance can be distinguished from a major confounding factor—natural variation—by the 95% limits for natural variation of susceptible populations. Approximate limits of natural variation for susceptible populations from the same host and subjected to identical types of bioassays are MEAN ± 1.96(SD), where MEAN and SD are the mean and standard deviaions from the n samples. If the arthropod species is polyphagous, all comparisons should be made from population samples collected from the same host plant species, because factors from the plants might also affect the manifestation of resistance (see section V, “Host-Insect Interaction and the Expression of Resistance,” below). For example, Rust et al.6 have calculated a mean LD50 ± SD of 0.52 ± 0.17 ppm of imidacloprid fed to four susceptible cat flea (Ctenocephalides felis [Bouch]) strains tested in three different laboratories. Paula Maven calculates the 95% limits of natural variation for these susceptible cat flea strains to be 0.19–0.85 ppm. Resistance to imidacloprid in cat fleas has not been documented, but these limits are useful for documenting the status of present and future field-collected strains. For example, the LD50s in 7 of 18 bioassays of field-collected cat flea isolates were >0.85; 11 strains can be considered to be susceptible and the 7 other strains are tolerant to imidacloprid. Baseline studies such as this and others are important because they provide documentation both before2,7–9 and after resistance develops.

III. Use of bioassays to separate populations and strains Quantal response bioassays are useful to identify and monitor shifts in population tolerance. They provide information that can be used for statistical comparisons of entire regression lines and individual dose levels of interest. Although full-scale bioassays are crucial to toxicological research programs concerning resistance, they are impractical for resistance monitoring programs because of the time and resources involved in their completion. Instead, resistance monitoring programs may use only one dose for testing.

A. Population bioassays Bioassays to compare susceptible populations both among themselves and versus resistant populations should be performed as described in Chapter 3, “Binary Quantal Response with One Explanatory Variable.” Likelihood ratio tests (see 3.B.1) can be used to test whether regression lines are parallel or equal, and the ratio test (see 3.B.2) can be used to test whether a given LDx is significantly different from the LDx of the most susceptible population.

2331_C009.fm Page 102 Wednesday, May 9, 2007 5:45 AM

102

Bioassays with arthropods, second edition

The alternative procedure—examination of 95% CL to detect overlap—must not be used because it lacks statistical power.10 Regression lines of each population can also be plotted to visually assess appropriate groupings of response.6,7 Proper dose placement and adequate sample sizes must always be used in all bioassays done to estimate relative tolerance (or resistance) of populations or strains. Sample sizes will dictate the LD that can reliably used for comparisons and for fairly reliable estimation of a single dose or set of doses that will discriminate between susceptible and resistant groups. If sample sizes from field-collected populations range from 250 to 500, comparisons at LD50 are justified. If ≥ 750 arthropods are tested in each bioassay, then both the LD50 and LD90 can be used as long as doses are placed as described in Chapter 5, “Binary Quantal Response: Dose Number, Dose Selection, and Sample Size.” Comparisons at LD95 require sample sizes ≥ 1,000; comparisons at LD99 require bioassays with 3,000–3,600 (see Chapter 5); both LDs also require special placement of doses. Unless these very large numbers of subjects are available for bioassays and doses are placed extremely carefully, estimates of these extreme levels are so imprecise that they are meaningless because of their extremely wide confidence intervals.

B. Response ratios Many investigators use response ratios to estimate the magnitude of tolerance or resistance. In much of the literature about resistance, these ratios have been reported as simply as LD (population A)x ÷ LD (population S)x where x is the response level, A is the population being compared, and population S is the population with the greatest susceptibility. However, each ratio has an associated error term (see 3.II.A.2, “Lethal Dose Ratios”), and the error must be reported in the form of 95% confidence limits.11 Responses ratios alone cannot identify resistant populations, but they are useful in the documentation of spatial and temporal differences among populations.

C. Selection of a discriminating dose A discriminating dose is a single dose that will theoretically affect a high percentage of susceptible genotypes in a population without affecting resistant genotypes in a resistant population.12 In the context of resistance monitoring, the use of single doses clearly requires less time and resources than does estimation of a valid dose-mortality regression,13,14 but the dose or doses must be chosen cautiously. The best such choice represents a compromise that minimizes the likelihood of false positives and maximizes the probability of detection at the earliest possible stage of development.6 Roush and Miller12 have discussed various aspects of the statistical design of bioassays that would provide reliable estimates. Their premise was that dose selection and sample size guidelines presented for the LD90 by Robertson et al.15 were applicable to more extreme levels such as the LD95

2331_C009.fm Page 103 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

103

and LD99. Paula Maven has learned that, although the guidelines for dose selection at the more extreme doses are generally applicable, the guidelines for sample sizes are not (see 5.II). Sample sizes for estimation of reliable LD95s are about three times larger than sample sizes required for precise estimation of an LD90.. For estimation of an LD99, at least 30 times more test subjects are required. Collection, handling, and testing of 3,000–3,600 test subjects in a bioassay done to estimate an extremely high LD is clearly too labor intensive to be done on a routine basis in resistance monitoring. A further complication for the use of discriminating doses LD≥90 is the choice of the mathematical model used for data analyses. Savin et al.16 showed that, for mexacarbate applied to laboratory-reared (nondiapausing) western spruce budworm, estimates of LD50s for probit and logit models varied by 1.4% and LD90s varied by 0.48%. At the LD99, however, logit values were consistently higher (25%). The best general approach to selection of a discriminating dose is an empirical compromise based on a two-stage approach to the problem.6,7,17 First, a survey of population responses is done by the same methods described for basic bioassays in Chapter 5. An estimate of relative resistance (or tolerance) levels among resistant and susceptible populations at the LD50 can be obtained. Next, a discriminating dose that approximates the LD90–95 of the susceptible population(s) can be selected. This dose (or array of doses) is then multiplied by a factor of two or three, then tested in a separate bioassay to quantify numbers of putative susceptible and resistant individuals that respond.

IV. Statistical models of modes of resistance inheritance18 Having once been a Girl Scout, Paula Maven is prepared! If necessary, she and Blanche are ready to investigate the modes of inheritance of pesticide resistance in wicked witches. Studies of resistance inheritance usually begin with dose-response bioassays to study aspects of simple Mendelian genetics; these investigations serve as the bases of more sophisticated biochemical and molecular genetic analyses.19–20 Statistical methods used for genetic analyses must be based on the experimental design of the study and the sources of variation in the experiments. Because most bioassays include uncontrollable sources of variation beyond those assumed by the binomial model, these sources of variation must be identified and included in the statistical models. As a guide Paula will use data analyses from studies of cyhexatin and propargite resistance in Pacific spider mite. With some modifications, similar methods can be adapted to wicked witches and other arthropod species.

A. Standard method of analysis with bioassay data Luckily, Paula remembers possible causes of lack-of-fit, use of the χ2 statistic, and the definition of a residual (see Chapter 3.II.A.1). Hypotheses about

2331_C009.fm Page 104 Wednesday, May 9, 2007 5:45 AM

104

Bioassays with arthropods, second edition

mode of inheritance are tested by using a χ2 test to compare expected dose-mortality curves calculated from parent (resistant and susceptible) strains and F1 progeny, versus observed dose-mortality curves of the backcross progeny.21–24 Significantly large values of the χ2 statistic may indicate that the putative mode of inheritance is wrong or may require some modification. However, other interpretations are possible including the presence of extra sources of variability in the bioassay that were not included in the model.25

1. Degree of dominance Data from dose-response experiments done with susceptible (S), resistant (R), or heterozygous reciprocal F1 (RS or SR) colonies of arthropods can be analyzed by fitting probit or logit regressions with a standard probit analysis program.26 The degree of dominance (D) of the resistance trait is calculated by the equation

D=

2θˆ3 − θˆ2 − θˆ1 θˆ2 − θˆ1

(9.1)

where θˆ1 = log10 ( LC 50 ) of the susceptible (S) colony, θˆ2 = log10 ( LC 50 ) of the resistant (R) colony, and θˆ3 = log10 ( LC 50 ) of the heterozygous RS and SR colonies.27 The standard error of D can be calculated based on the asymptotic formula for variances of functions of random variables28 by taking the square root of

var( D) =

4

(

θˆ2 − θˆ1

)

2

⎡ θˆ3 − θˆ1 ⎢ ⋅ ⎢var(θˆ 3 ) + θˆ2 − θˆ1 ⎢⎣

( (

) )

2

2

var(θˆ2 ) +

(θˆ − θˆ ) (θˆ − θˆ ) 3

2

2

2

1

2

⎤ ⎥ ˆ var(θ 1 )⎥ ⎥⎦

(9.2)

This standard error is used to determine whether D is significantly different from ±1 (i.e., whether the resistance trait is completely dominant or completely recessive). For a completely recessive trait, D = –1; for a completely dominant trait, D = 1. For example, if D = –0.87 and SE= var( D) = 0.09 , then the resistance trait may be completely recessive because D is not significantly different from –1. The approximate 95% confidence interval for D (D ± 2 SE = [–1.15, –0.69]) includes the value –1.

2. Hypothesis testing Expected mortalities for the various crosses (SR × R, RS × S or RS × RS) are then calculated assuming a particular model for mode of inheritance. For example, assuming one major gene and Mendelian mode of inheritance, response probabilities at each concentration for the backcross RS × SS colony (produced by crossing RS females with SS males) should be the average of

2331_C009.fm Page 105 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

105

the mortality probabilities for the RS and SS individuals. The standard χ2 test is based on the statistic

Xi

2

(O =

i

− Ei Ei

) + (O 2

i

− Ei Ei

2

)

(9.3)

where O i and Ei are the numbers of observed and expected responses at a given dose di, and O i and Ei are numbers of observed and expected subjects that do not respond. If ni = total number of subjects from the backcross colony treated with the i-th level of toxicant, ri = observed number of deaths out of ni subjects, and πˆ i = estimated response probability under the proposed genetic model, 2

Xi 2 =

(ri − ni πˆ i ) ni πˆ i (1 − πˆ i )

(9.4)

The genetic hypothesis is then tested by comparing the test statistic X i 2 (for each i = 1, . . . , N) with values from a χ2 table with 1 df, or by comparing the sum X2 =

∑

N 1

Xi 2

with values from a χ2 table with N df.

B. Inferences using the standard method When the test statistic is not significantly large, Dr. Maven might be tempted to conclude that the hypothesis about mode of inheritance is correct. However, statistical tests can only be used to reject hypotheses, not to accept them. The only conclusion that she can make about a small χ2 value is that her hypothesis cannot be rejected and that her model describes the data adequately. Other models may also describe the data adequately; such alternative models cannot be rejected unless they are tested individually. If the value of X i 2 in Equation 9.4 is large and significant, Paula might conclude that her assumptions about the mode of genetic inheritance are incorrect. However, other factors listed next may be the source(s) of a large χ2 value.

1. Mode of inheritance The formula for estimating π i in Equation 9.4 may be inadequate for at least one dose level. For example, if πˆ i were calculated assuming a one-major-gene

2331_C009.fm Page 106 Wednesday, May 9, 2007 5:45 AM

106

Bioassays with arthropods, second edition

model, then large values of X i 2 could mean that the single gene model is inadequate and that some other model (e.g., multiple genes or modifier genes) is necessary to describe the mode of inheritance.

2. Binomial distribution Binomial variation, which is always present in dose-response experiments, is similar to the variation expected in the outcome of a coin-flipping experiment. Other sources of variation (e.g., slight differences in temperature and humidity over time, or slight differences in dose between replicates) might also be present. This type of fluctuation has been called overdispersion.18 Experiments in which precise amounts of a material are applied to each test subject, such as topical application to single insects, exhibit less overdispersion between replicates than do other types of experiments such as those in which the material is sprayed or incorporated into a diet fed to test subjects.29 The χ2 statistic in Equation 9.3 also assumes that random fluctuations of responses around expected values follow the binomial distribution and that sample sizes are large. The denominator in Equation 9.3 is the variance of binomial variables and the equation includes no other source of variation. Therefore, any source of variation beyond that of the binomial variation will cause the χ2 statistic to be large even when the hypothesis about the mode of inheritance is not rejected.

3. Both mode of inheritance and binomial distribution Assumptions about the mode of inheritance and the binomial distribution have the same effect on the χ2 statistic in Equation 9.3 (i.e., they can cause large values of Xi 2 ). The first indication of possible overdispersion in bioassay data is a large value of the χ2 goodness-of-fit statistic for the susceptible (S) or the resistant (R) colonies. The only assumptions involved are that the data fit the probit model and the distribution of responses is binomial. If the probit curve is adequate but the χ2 goodness-of-fit statistic is still large, then the bioassay data probably show overdispersion. A second (and probably a more satisfactory method) to detect overdispersion in bioassays with pure R or S colonies or the backcross colonies is to calculate a χ2 statistic without any assumptions about the “shape” of the response probabilities. One such statistic is given by I

X2 =

Ji

(r

ij

− n ij pˆ i

ij

i

2

)

∑ ∑ n pˆ (1 − pˆ ) i=1

j=1

(9.5)

i

where the subjects are divided into I dose groups (indexed with i from 1 to I). In the i-th dose group there are Ji subject groups (indexed with j from 1 to Ji), all of which receive the same dose, di. In a dose group i, subject group

2331_C009.fm Page 107 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

107

j, there are rij responses out of nij subjects (all getting dose di); pˆ i is the average fraction of responses at dose di—i.e., pˆ i = (1 / J i )

∑

Ji j =1

( rij / nij ) . The only

assumption involved is that the responses are independent binomial variables. Therefore, a large χ 2 value will indicate that the data do not consist of independent binomial variables and that the data are overdispersed. Other procedures for testing the assumptions of the binomial distribution are also available.30 If Dr. Maven makes an incorrect assumption about the mode of inheritance (e.g., that a one-major-gene model is correct when the mode of inheritance is better described by a multiple gene model), she will see large values of the χ2 statistic in Equation 9.4, but not extra variation beyond the binomial variation. Consequently, a test statistic such as the one in Equation 9.5 can be used to detect and characterize extra sources of variation that could then be incorporated in the model. One way that she can include overdispersion in a χ2 test is to calculate a modified statistic

Xi

2

( ri − ni πˆ i ) = var( ri )

2

(9.6)

where Ji

ri =

∑w r

ij ij

(9.7)

j=1

Ji

w ij = n i / ( J i n ij ) , n i =

∑n

ij

, and where the form for var( ri ) depends on the

j=1

characteristics of the random sources of variation in the particular experiment. For example, if the only source of variation in the experiment is the binomial fluctuation, then var( ri ) can be estimated by ni πˆ i (1 − πˆ i ) and the modified statistic in Equation 9.6 is the same as the standard statistic in Equation 9.5 when the sample sizes, nij, are the same at each replicate. A second form for var( ri ) is given in section C, “Examples,” below.

4. Other causes for bad fit a. Variation between replicates. Other problems that will result in large values of the χ2 statistic are outliers and variation between experiments (see 3.II.A.1). Except in cases where precise amounts are applied, the actual dose received by each test subject varies even when the amount administered is

2331_C009.fm Page 108 Wednesday, May 9, 2007 5:45 AM

108

Bioassays with arthropods, second edition

the same. This source of variation affects the slope and intercept of the fitted probit (or logit) lines. The larger the imprecision, the smaller are the absolute values of the slope and intercept.31 This source of variation is incorporated in the model automatically because the slope and intercept are estimated from the data; it is not the same as the variation between replicates that is introduced because of differences in dose. b. Genetic heterogeneity. In almost all bioassays, the R or S colonies are not totally genetically pure. This problem introduces an additional source of variation that affects the slope of the probit (or logit) line. The larger the heterogeneity in a colony, the lower the slope of the probit line.32 In some cases, heterogeneity in a colony will cause a plateau in the line to appear. However, heterogeneity affects the shape of the response curve but not the variation around that curve.

C. Examples Hoy et al.23 and Hoy and Conley24 have described experiments done to determine modes of inheritance of cyhexatin/fenbutatin oxide and propargite resistances in Pacific spider mite, Tetranychus pacificus McGregor. These examples demonstrate the analyses necessary to derive a test statistic or a statistical testing procedure that is appropriate to this set of experiments, and they provide a general guide to statistical analyses for other resistance studies.33

1. Dose-response bioassays Both studies involved selection with the acaricide to obtain homogeneous resistant colonies; comparison of dose-mortality regressions of resistant and susceptible colonies, F1, and backcross progeny; and analysis of observed and expected dose-mortality relationships with standard χ2 tests. Because this species is arrhenotokous, F2 females are genetically the same as backcross females. Haploid F2 males would respond in a 1:1 (R:S) ratio of phenotypes if resistance was conferred by a single major gene and they inherited resistance genes from their mothers. In both studies, two sets of bioassays were done. In the first set, simultaneous bioassays were done for the S, R, SR, and RS colonies. In the second set, simultaneous bioassays were done for the S, R, and backcross SR × S and RS × R colonies.

2. Dose-mortality lines Except for the backcross SR × S and RS × R colonies, dose-mortality data from all bioassays were analyzed with the GLIM34 statistical package, assuming the probit model and binomial errors. In each experiment, the χ2 goodness of fit statistic was too large (see Table 9.1), suggesting that the model was not appropriate. A probit line seemed to fit each set of data adequately and the scatter of residuals was apparently random. However, the number of points with an absolute value >2 (see 3.II.A.1) suggested overdispersion in the bioassay data of S, R, SR, and RS colonies. Because bioassays of

2331_C009.fm Page 109 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

109

Table 9.1 Goodness of Fit of the Probit (Binomial) Model to Concentration-Response Data for Pacific Spider Mitesa

Test

Female colony

Test statistic for goodnessof-fit of model

Experiment

Number of mites treated

1 2 1 2 1 1

600 1125 800 1140 640 610

** ** ** ** ** **

187.1 380.8 214.7 276.8 201.8 154.6

118 157 158 172 126 120

1 2 1 2 1 1

1431 1786 1559 1623 2042 2158

** ** ** ** ** **

181.9 188.9 230.8 197.7 360.9 264.9

69 98 86 90 114 122

df

Statistic for equality of probit lines

Cyhexatinb SS RR SR RS

** 20 *9 *9

Propargitec SS RR SR RS

** 24 ** 12 1.2

Notes: aLikelihood ratio test statistic (df = 2) for overdispersed binomial data.25 bData from Hoy et al.23 cData from Hoy and Conley.24 **Indicates that the value is highly significant (P = 0.01). *Indicates that the value is significant (P = 0.05) but not highly significant. Source: Reprinted from Preisler, H. K., Hoy, M. A., and Robertson, J. L., Statistical analyses of modes of inheritance for pesticide resistance, J. Econ. Entomol. 83, 1649, 1990.

backcross SR × S and RS × R mites were done simultaneously with those of the S and R colonies, overdispersion was also likely to be present. The X2 statistic (Equation 9.5) for each of the backcross colonies also indicated overdispersion (see Table 9.2). Because both types of statistical tests were done for each experiment separately, the extra variation observed could not be attributed to variation between experiments. Instead, extra variation between replicates at the same dose was likely. Responses of spider mites from the same replicate thus seemed to be more alike than those from different replicates.

3. Estimation of overdispersion Methods for estimation in the presence of overdispersion at the dose level include the beta-binomial method,35,36 the method of moments,37,38 and maximum likelihood method.25 Maximum likelihood procedures were used to compute the mortality probability estimates Pˆ ( R ) , Pˆ (S ) , Pˆ ( RS ) , and Pˆ (SR ) , and corresponding LC50s and standard errors. This procedure incorporates extra variation into the model by adding a random effect variate to the fixed effect regressors at the probit scale. The same procedure can also be used to test hypotheses about equality of probit lines. When the equality of the probit

2331_C009.fm Page 110 Wednesday, May 9, 2007 5:45 AM

110

Bioassays with arthropods, second edition

Table 9.2 Goodness of Fit Tests for the Binomial Error Model ( X 12 )a and the Single Major Gene (Mendelian) Inheritance Model ( X 2 2 )b Females from backcross

X 12 for

Number of mites treated

binomial error

df

gene model

df

1300 1335

**285 **315

189 186

14.0 11.4

9 11

1852 2309

**237 **199

94 166

**42.1 **32.1

12 13

X 2 2 for single

c

Cyhexatin SR × S RS × R Propargited SR × S RS × R 2

2

Notes: a X 1 was calculated using Equation 9.4. b X 2 was calculated by summing the 2 values of X 1 in Equation 9.5 over all i. cData from Hoy et al.23 dData from Hoy 24 and Conley. **Indicates that the value is highly significant (P = 0.01). *Indicates that the value is significant (P = 0.05) but not highly significant. Source: Reprinted from Preisler, H.K., Hoy, M.A., and Robertson, J.L., Statistical analyses of modes of inheritance for pesticide resistance, J. Econ. Entomol. 83, 1649, 1990.

lines for the F1 colonies (SR and RS colonies) was tested in the cyhexatin and propargite studies, differences in the probit lines were not highly significant (see Table 9.1). Therefore, data from the two F1 colonies were pooled and an estimate for P ( F1 ) was obtained from the pooled data. When tests of equality of probit lines were done for the S and R colonies from experiments with cyhexatin and propargite, probit lines from the various experiments were highly significant different in almost all cases (see Table 9.1). Preisler et al.18 then attempted to incorporate the variability between experiments into the model by fitting a model with a probit line

α k + β k log( d ) + δl

(9.8)

where k is the indicator for the various colonies, and l is the indicator for the various experiments. In this model, the experiment effect δl is incorporated as an additive effect on the probit scale. This model seemed to fit the data from the propargite studies but not those from the cyhexatin studies. A further search for an appropriate model describing the variation between experiments in the cyhexatin studies was not done.

4. Mode of inheritance of cyhexatin resistance Resistance to cyhexatin in Pacific spider mite was incompletely recessive (D ± SE = –0.18 ± 0.05 calculated with the pooled F1 data). Expected response probabilities for the backcross females (RS × R and SR × S) were calculated assuming that resistance to cyhexatin is determined by a single major gene with Mendelian mode of inheritance—that is,

2331_C009.fm Page 111 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

111

πˆ i = 0.5 Pˆi( Fl ) + 0.5 Pˆi( R )

(9.9)

for the RS × R backcross colony, and

πˆ i = 0.5 Pˆi( Fl ) + 0.5 Pˆi(S )

(9.10)

for the SR × S backcross colony. The standard χ2 test statistics, calculated with Equation 9.4, were too large in each case. This result was not surprising because the χ2 statistic (assuming binomial error) was too large even when a nonparametric formula (Equation 9.5) was used to estimate π i . Because of the overdispersion detected in these data, Equation 9.6 was used with a variance function that incorporates the extra variation to calculate a modified test statistic. One simple way to incorporate the overdispersion in the variance function is to use the formula var( ri ) = ni πˆ i (1 − πˆ i )h

(9.11)

where

h=

X2

∑ J −I i

i

and where X 2 is calculated using Equation 9.5. The value h is an estimate of the heterogeneity factor.32 Equation 9.10 is a reasonable estimate for the variance of ri when the number of subjects nij treated at each replicate are equal. A more appropriate formula for the case when the sample sizes at each replicate are not equal is given by var( ri ) =

ni 2 Ji2

⎡mi πˆ i (1 − πˆ i ) + ( J i − mi )σˆ i 2 ⎤ ⎣ ⎦

(9.12)

where w ij = n i / ( J i n ij ) , m i =

∑ (1 / n ) j

ij

and where πˆ i , σˆ i 2 are estimated by fitting probit curves to the R, S, RS, and SR mortality data as described by Preisler.25 Values of the modified χ2 statistics for the cyhexatin experiments calculated with Equations 9.6, 9.7, and 9.12 are listed in Table 9.2. These values seem to indicate no significant departure of the expected responses from the single major gene model as given by Equations 9.9 and 9.10.

2331_C009.fm Page 112 Wednesday, May 9, 2007 5:45 AM

112

Bioassays with arthropods, second edition

5. Mode of inheritance of propargite resistance Values for degrees of dominance indicated that resistance to propargite was incompletely recessive (D ± SE = –0.30 ± 0.03, calculated with the pooled F1 data). Modified χ2 values, assuming a single major gene Mendelian model, were large (see Table 9.2). When the modified X i 2 values were examined individually, 4 of the 12 values from the SR × S cross and 2 of the 13 values from the RS x R cross were significant (P < 0.01). In each case, responses of Pacific spider mites to propargite in the backcross colonies seemed significantly larger than expected. Reasons for this significant difference between observed and expected are not clear. Possibly, the assumption that a model with one major gene describes the expected responses was not correct. The mode of inheritance of propargite resistance might be better explained by a polygenic model or a model with modifier genes. Also, the model for incorporating the variation between experiments (Equation 9.10) might not be appropriate for the RS and SR colonies. However, this possibility could not be checked because the bioassays on these colonies were done only in one set of experiments.

V. Host-insect interaction and the expression of resistance Factors that affect the phenotypic expression of genetic resistance might affect not only the results of bioassays done in toxicological experiments, but also the results of resistance detection with discriminating doses. Robertson et al. 39 examined levels of nonspecific esterases and glutathione-S-transferase in resistant and susceptible strains of light brown apple moth, Epipyas postvittana (Walker), last instars that fed on different host plant species. This insect species, which is resistant to the organophosphorous pesticide azinphosmethyl, is polyphagous and feeds on such diverse hosts as gorse and broom, in addition to apple. Although higher glutathione-S-transferase activities in resistant insects fed blackberry, apple, gorse, broom, or artificial diet may be responsible for decreased toxicity of azinphosmethyl in the resistant strain, an allelochemical in blackberry foliage may inhibit or prevent induction of nonspecific esterase activity in the same strain. In resistance detection in the field, resistant larvae off of blackberry might mistakenly be identified as susceptible when they are not. These results indicate the need for a careful and additional exploration of the factors, including those related to host plants, that affect the phenotypic expression of resistance.

References 1. Robertson, J. L. and Rappaport, N. L., Direct, indirect, and residual toxicities of insecticide sprays on western spruce budworm, Choristoneura occidentalis (Lepidoptera: Tortricidae), Can. Entomol. 111, 1219, 1979.

2331_C009.fm Page 113 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

113

2. Bergh, J. C., Rugg, D., Jansson, R. K., McCoy, C. W., and Robertson, J. L., Monitoring the susceptibility of citrus rust mite (Acari: Eriophyidae) populations to abamectin, J. Econ. Entomol. 92, 781, 1999. 3. ffrench-Constant, R. H. and Roush, R. T., Resistance detection and documentation, in Roush, R. T. and Tabashnik, B. E., eds., Pesticide Resistance in Arthropods, Chapman & Hall, NY, 1990. 4. Ball, H. J., Insecticide resistance: a practical assessment, Bull. Entomol. Soc. Amer. 27, 261, 1981. 5. Sawicki, R. M., Definition, detection and documentation of insecticide resistance, in Ford, M. G., Holloman, D. W., Khambay, B. P. S., Sawicki, R. M., eds., Combating Resistance to Xenobiotics; Biological and Chemical Approaches, Ellis Harwood, Chichester, England, 1987, pp. 105-117. 6. Rust, M. K., Denholm, I., Dryden, M. W., Payne, P., Blagburn, B. L., Jacobs, D. E., Mencke, N., Schroeder, I., Vaughn, M., Mehlhorn, H., Hinkle, N. C., and Williamson, M., Determining a diagnostic dose for imidacloprid susceptibility testing on field-collected isolates of cat fleas (Siphonaptera: Pulicidae), J. Med. Entomol. 42, 631, 2005. 7. Pree, D. J., Archibald, D. E., Ker, K. W., and Cole, K. J., Occurrence of pyrethroid resistance in pear psylla (Homoptera: Psyllidae) populations in southern Ontario, J. Econ. Entomol. 83, 2159, 1990. 8. Scott, J. G., Roush, R. T., and Rutz, D. A., Insecticide resistance of house flies from New York dairies (Diptera: Muscidae), J. Agric. Entomol. 6, 53, 1989. 9. Staetz, C. A., Susceptibility of Heliotis virescens (F.) (Lepidoptera: Noctuidae) to permethrin across the cotton belt: a five year study, J. Econ. Entomol. 78, 505, 1985. 10. Wheeler, M. W., Park, R. M., and Bailer, A. J., Comparing median lethal concentration values using confidence interval overlap or ratio tests, Environ. Toxicol. Chem. 25, 1441, 2006. 11. See Robertson, J. L., Preisler, H. K., Ng, S. S., Hickle, L. E., and Gelernter, W. D., Natural variation: a complicating factor in bioassays with chemical and microbial pesticides, J. Econ. Entomol. 88, 1, 1995. 12. Roush, R. T. and Miller, G. L., Considerations for design of insecticide resistance monitoring programs, J. Econ. Entomol. 79, 293, 1986. 13. Sawicki, R. M., Denholm, I., Forrester, N. W., and Kershaw, C. D., Present insecticide-resistance management strategies in cotton, in Green, M. B. and de B. Lyon, D. J., eds., Pest Management in Cotton, Ellis Harwood, Chichester, England, 1989, pp. 21-43. 14. Forrester, N. W., Cahill, M., Bird, L. J., and Layland, J. K., Management of pyrethroid and endosulfan resistance in Helicoverpa armigera (Lepidoptera: Noctuidae) in Australia, Bull. Entomol. Res. Suppl. 1, 1990. 15. Robertson, J. L., Smith, K. C., Savin, N. E., and Lavigne, R. J., Effects of dose selection and sample size on precision of lethal dose estimates in dose-mortality regression, J. Econ. Entomol. 77, 833, 1984. 16. Savin, N. E., Robertson, J. L., and Russell, R. M., A critical evaluation of bioassay in insecticide research: likelihood ratio tests of dose-mortality regression, Bull. Entomol. Soc. Am. 23, 257, 1977. 17. Zhao, J.-Z., Li, Y.-X., Collins, H. L., Gusukuma-Minuto, L., Mau, R. F. L., Thompson, G. D., and Shelton, A. M., Monitoring and characterization of diamondback moth (Lepidoptera: Plutellidae) resistance to spinosad, J. Econ. Entomol. 95, 430, 2002.

2331_C009.fm Page 114 Wednesday, May 9, 2007 5:45 AM

114

Bioassays with arthropods, second edition

18. This section is based entirely on the statistical methods described by Preisler, H. K., Hoy, M. A., and Robertson, J. L., Statistical analyses of modes of inheritance for pesticide resistance, J. Econ. Entomol. 83, 1649, 1990. 19. Hemingway, J. and Ranson, J., Insecticide resistance in insect vectors of human disease, Ann. Rev. Entomol. 45, 371, 2000. 20. ffrench-Constant, R., Anthony, N., Aronstein, K., Rocheleau, T., and Stilwell, G., Cyclodiene insecticide resistance: from molecular to population genetics, Ann. Rev. Entomol. 45, 449, 2000. 21. Halliday, W. R. and Georghiou, G. P., Inheritance of resistance to permethrin and DDT in the southern house mosquito (Diptera: Culicidae), J. Econ. Entomol. 78, 762, 1985. 22. Roush, R. T., Combs, R. L., Randolph, T. C., Macdonald, J., and Hawkins, J. A., Inheritance and effective dominance of pyrethroid resistance in the horn fly (Diptera: Muscidae), J. Econ. Entomol. 79, 1178, 1986. 23. Hoy, M. A., Conley, J., and Robinson, W., Cyhexatin and fenbutatin-oxide resistance in Pacific spider mite (Acari: Tetranychidae): stability and mode of inheritance, J. Econ. Entomol. 81, 57, 1988. 24. Hoy, M. A. and Conley, J., Propargite resistance in Pacific spider mite (Acari: Tetranychidae): stability and mode of inheritance, J. Econ. Entomol. 82, 11, 1989. 25. Preisler, H. K., Assessing insecticide bioassay data with extra-binomial variation, J. Econ. Entomol. 81, 759, 1988. 26. LeOra Software, PoloPlus, LeOra Software, 1007 B St., Petaluma, CA 94952, 2003. See http://www.LeOraSoftware.com. 27. Stone, B. F., A formula for determining degree of dominance in case of monofactorial inheritance of resistance to chemicals, Bull. W.H.O. 38, 325, 1968. 28. Lehmann, E. L., Testing statistical hypotheses. Wiley, New York, 1966. 29. Preisler, H. K. and Robertson, J. L., Analysis of time-dose-mortality data, J. Econ. Entomol. 82, 1534, 1989. 30. Mosteller, F. and Tukey, J. W., The uses and usefulness of binomial probability paper, J. Am. Stat. Assoc. 44, 174, 1949. 31. Burr, D., On errors-in-variables in binary regression—Berkson case, J. Am. Stat. Assoc. 83, 739, 1988. 32. Finney, D. J., Probit Analysis, 3rd ed., Cambridge University Press, Cambridge, England, 1971. 33. Brun, L. O., Suckling, D. M., Roush, R. T., Caudichon, V., Preisler, H., and Robertson, J. L., Genetics of endosulfan resistance in Hypothenemus hampei (Coleoptera: Scolytidae): implications for mode of sex inheritance, J. Econ. Entomol. 88, 470, 1995. 34. Payne, C. D., ed., The GLIM System Release 3.77 Manual, Numerical Algorithms Group, Oxford, England, 1978. 35. Williams, D. A., The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity, Biometrics 31, 949, 1975. 36. Crowder, M. J., Beta-binomial Anova for proportions, Appl. Stat. 27, 34, 1978. 37. Williams, D. A., Extra-binomial variation in logistic linear models, Appl. Stat. 31, 144, 1982.

2331_C009.fm Page 115 Wednesday, May 9, 2007 5:45 AM

Chapter nine: Pesticide resistance

115

38. Moore, D. F., Modeling the extraneous variance in the presence of extra-binomial variation, Appl. Stat. 36, 8, 1987. 39. Robertson, J. L., Armstrong, K. F., Suckling, D. M., and Preisler, H. K., Effects of host plants on toxicity of azinphosmethyl to susceptible and resistant light brown apple moth (Lepidoptera: Tortricidae), J. Econ. Entomol. 83, 2124, 1990.

2331_C009.fm Page 116 Wednesday, May 9, 2007 5:45 AM

2331_C010.fm Page 117 Wednesday, May 9, 2007 5:45 AM

chapter ten

Mixtures A few weeks after the Elf-induced resistance scare, Paula Maven takes an afternoon off from work to tend to what remains of her vegetable garden. She has been so busy that she cannot remember even watering the plants during the past ten days. The prime casualty in the Maven yard seems to have been the tomato plants. The poor little things look terrible: besides being wilted, the jaws of small wicked witches have clearly been at work. Over the fence, she notices that Ernestine Feasor is also gardening. Miss Feasor had planted her replacement tomatoes at exactly the same time as Paula, but the leaves of her plants are undamaged (and of course, they are infinitely more turgid). Dr. Maven just has to find out why Ernestine’s plants have escaped damage. “Miss Feasor, may I ask you a question?” “Surely, dearie, what is it?” “Well, why do your tomatoes look so healthy? I don’t see any signs of insect damage, and I was just wondering. . .” “Oh, it’s simple. First of all, your plants can stand some watering, if you don’t mind my saying so. Person with your education should know that! Besides, I’ve been spraying them with the chemical you told me to use, but for good luck I add just a pinch of another special white powder that my late brother Fred left in the shed. Fred worked for a chemical company for years, you know, and he just brought bags and bags of samples home with him. And he’d be doing it still, but the cancer finally got him. In his liver, it was. Why, he even showed my nephews how to mix that white powder into paint. Fred also owned a house painting business along with his sons Ellsworth and Lester. Well, anyway, they were very successful painters, and fast, too. Know the secret to house painting, dearie? Well, it’s brooms. If you put the paint on with a broom, you’d be surprised how fast it goes. . . ” Fifteen stories later, Dr. Maven politely excuses herself and flees to the quiet of her kitchen. The thought of living next door to Fred’s shed filled with mysterious white powders is disconcerting; what a toxic waste dump! Paula now considers the merits of adding a pinch of one chemical to another. Perhaps the idea just might work. She has identified several pesti-

117

2331_C010.fm Page 118 Wednesday, May 9, 2007 5:45 AM

118

Bioassays with arthropods, second edition

cides that seem both environmentally safe and sufficiently effective against wicked witches. Of all the candidates, she prefers juvenile hormone analogues and chitin synthesis inhibitors because they are most specific. But these chemicals are very expensive, perhaps prohibitively so for most local growers. Suppose that a trace amount of a chitin synthesis inhibitor could be mixed with a less expensive (but also, less effective) type of pesticide. Would toxicity increase significantly? Another alternative might be adding a synergist—that is, a chemical that is not toxic in itself but that blocks one of the steps involved in detoxification of a pesticide. As a result, toxicity of the pesticide would also increase significantly. Back at work the next morning, Dr. Maven does an online literature search regarding bioassays of mixtures. Experiments with synergists are indeed simple, as are data analyses. But her review of the literature convinces her that practical aspects of the problem of mixtures of one component with another have been unnecessarily complicated by descriptions of elaborate statistical models developed without biochemical information, let alone any means of experimental verification. The original approach of Bliss seems to her to be the most sensible.1 Bliss developed the first statistical models of joint action of pesticide mixtures based on three theoretical modes of physiological interaction: independent joint action, similar joint action, and synergistic action. Efforts to extend and elaborate upon Bliss’s categories resulted in development of increasingly complex mathematical formulas to describe physiologically more complex situations.2–12 As an example of what can happen when statistical theory is developed in the absence of biological or biochemical data, the resultant statistical methods are of minimal practical value to biologists. In her review of the subject, Dr. Maven notices that such elaborate statistical methods have rarely been used in biological investigations because they rely on assumptions that are impossible to verify and because they are founded on unsubstantiated theories of toxicology. Problems with these alternative methods and their underlying hypotheses will be discussed in more detail in section III, “Other Theoretical Hypotheses of Joint Action of Pesticides,” below.

I. Independent, uncorrelated joint action of pesticide mixtures In a reexamination of the mixture problem, Robertson and Smith13,14 have described statistical methods that can be used to test a very simple null hypothesis that was first defined by Bliss.1 This simple hypothesis—independent, uncorrelated joint action—means that the toxicity of each component in the mixture is not affected by toxicity of the other component and that susceptibility to one mixture component is not correlated with suscep-

2331_C010.fm Page 119 Wednesday, May 9, 2007 5:45 AM

Chapter ten: Mixtures

119

tibility to the other. A response will occur only if the concentration of at least one of the two components is greater than the tolerance of the test subject. Biochemically, this type of response will be observed if the action sites of the two components are different (i.e., if each one has a completely different mode of action and these modes of action are totally independent). Assuming that this type of interaction occurs, synergism is the occurrence of significantly greater mortality than that predicted by the model. The opposite effect, significantly reduced mortality, is defined as antagonism. These definitions are implicit in the original definition of synergistic action given by Bliss1: “The effectiveness of the mixture cannot be assessed from that of the individual ingredients but depends upon a knowledge of their combined toxicity when used in different proportions. One component synergizes or antagonizes the other.”

A. A statistical model In experiments with a mixture of two components, test subjects can die of three possible causes. The first cause is natural mortality, with a probability po (a constant). The other two causes of mortality are component 1 and component 2. For the first component, the probability of response (p1) is a function of dose d1. Usually, the probit or logit of X1 = log(d1). For the second component, the probability of response (p2) is a function of d2. If these three causes of mortality are independent, the probability of death (p) is: p = p0 + ( 1 − p0 ) p1 + ( 1 − p0 )( 1 − p1 ) p2 If each plus sign means “or” and each product means “and,” this equation can be interpreted as follows: The total probability of death equals death from natural causes (p0), or no death from natural causes (1–p0) and death from the first component [e.g.,(1–p0)p1], or no death from natural causes or from the first component [i.e.,(1–p0)(1–p1)p2].

B. A test of hypothesis of independent joint action A χ2 statistic can be used to test the hypothesis of independent joint action. This test is done by obtaining an estimate for the probability of mortality (p) for several dose or concentration levels of the two components and then comparing pˆ (the estimate of p) with the observed proportion killed at the corresponding dose levels. The three contributions to p are estimated separately. First, p0 is calculated as the proportional mortality observed in the control group. Next, p1 and p2 are estimated from bioassays of components 1 and 2, with data analyzed using a computer program such as PoloPlus15 or R.16 Finally, the χ2 test statistic is calculated with PoloMix,17 a computer program written specifically for this purpose.

2331_C010.fm Page 120 Wednesday, May 9, 2007 5:45 AM

120

Bioassays with arthropods, second edition

C. PoloMix17 The Microsft Windows–compatible program PoloMix was designed to identify pairs of chemicals whose interaction results in a response that departs from the hypothesis predicted by the model of independent, uncorrelated joint action. The program is based on the general procedure described in the previous section and the corrected procedure originally described by Robertson and Smith.13,14

1. Data input files Parameter estimates from statistical analyses for each component and dose-response data for the mixture are put in three data files for use by the program. Any word processing program can be used to create the file, but it must be saved to text format. For example, Blanche enters the data for a mixture experiment as shown below: Data for component 1 permethrin 2.53 5.09 0.1097 0.6959 0.2483 1.182 Data for component 2 dimilin 1.43 1.47 .015 .0392 .0156 2.2685 Data for mixture of components dose-response permethrin dimilin .001 10 6 .01 10 5 .1 68 29 .2 60 38 .3 60 48 .5 59 48 .7 60 53

2331_C010.fm Page 121 Wednesday, May 9, 2007 5:45 AM

Chapter ten: Mixtures

121

1. 70 69 2. 60 60 3. 60 60 10. 10 10 For each component, the first file line is used only for identification. Entries on the second (left to right) file line are estimated intercept, estimated slope, estimated variance of the intercept, estimated variance of the slope, estimated covariance of the slope and intercept, and the heterogeneity adjustment factor. These values are obtained from the output of a probit or logit regression program such as PoloPlus.15 The first line of the dose-response data set is also for identification only. The actual data follow on subsequent lines. Each line has three columns. The first is dose (x), the second is the number (n) of test subjects, and the third is the number responding (r).

2. Running PoloMix Blanche opens the PoloMix window and fills in the information on the two chemicals and their parameter files (see Figure 10.1) and then fills in the mixture information on the controls and the dose-response data (see Figure 10.2). PoloMix is now ready so she clicks the Compute button and the analysis appears. She saves it to a “Results” file (see Figure 10.3).

3. Program output PoloMix calculations of expected mortality and χ2 values for each dose calculated as described in earlier in this chapter (section A, “A Statistical Model”). These calculations appear in the last two columns of lines for the mixture doses. The total χ2 for the appropriate degrees of freedom (i.e., number of doses including the control, minus 1) is listed next. To determine whether significant departures from the null hypothesis occur, the critical tabular value of χ2 at the probability level of choice (e.g., P = 0.05) can be compared with the value calculated by PoloMix. If the calculated value is less than the tabular value, the null hypothesis cannot be rejected. Conversely, if the calculated χ2 value is greater than the tabular value, then the hypothesis of independent joint action is rejected. In this example, the critical value of χ2 is 14.1 for 7 df (P = 0.05) and the hypothesis of independent joint action cannot be rejected. When the hypothesis is rejected, a plot of the data should be examined to determine the direction of significant departures from values predicted by the hypothesis. Ideally, all the values will lie to the left (significant antagonism) or to the right (significant synergism) of expected values. However, points on either side of the expected line occur when the expected line is not equal or parallel to the observed line; in this situation, χ2 values for the

2331_C010.fm Page 122 Wednesday, May 9, 2007 5:45 AM

122

Bioassays with arthropods, second edition

Figure 10.1 The Opening PoloMix Window that Blanche Has Filled in with the Information on the Two Chemicals and the Parameter Files.

parts of the line above and below the 50% response level can be examined.13 Degrees of freedom are equal to the number of doses (including controls) minus 1 for the subset of the data. The calculated χ2 value is then compared with the tabular value at the appropriate degrees of freedom and probability of choice to determine the significance of the results.

II. Similar (additive) joint action A second hypothesis that can be tested about the joint action of components is simple similar action. When each of the two components is toxic and their dose-response lines are parallel, their joint action is additive if dose d1 of component 1 has the same effect as dose ρd2 of component 2, where ρ is the relative potency. Such a relationship could occur if two components are closely related structurally, but have different potencies. An additive relationship thus suggests that treating an organism with d1 of 1 and d2 of component 2 is the same as treating it with d1 + ρ d2 of component 1 alone. A general parametric equation for similar action is y = α + β log( d1 + ρ d2 )

2331_C010.fm Page 123 Wednesday, May 9, 2007 5:45 AM

Chapter ten: Mixtures

123

Figure 10.2 After Blanche Opens the Dose-Response File, She Sees Its Data on the Right.

where y is the probit or logit line. Diagnostic tests for similar action compared with alternatives corresponding to antagonistic or synergistic joint action are described by Giltinan.18 However, no computer programs are currently available for doing these tests.

III. Other theoretical hypotheses of joint action of pesticides Finney19 reconsidered Bliss’s three types of interaction and added some minor modifications. Hewlett and Plackett2–4 and vice versa5–8 have contributed several new theories of interaction that are so subtle in their differences that they cannot be demonstrated biologically. Sakai20 subsequently expanded the types of interactions described by Hewlett and Plackett to include the following possible types of joint action: true, similar (similar and complex), dissimilar (dependent and independent), compound (similar and dissimilar), actuated, offset, converted, synergistic, antagonistic, pseudo-, physiological (similar and dissimilar), physico-chemical, pseudosynergistic, and pseudo-antagonistic. Dr. Maven agrees with Busvine’s21 comment made in reference to Sakai’s20 modifications: “His latest contribution displays a subtlety that may deter many insect toxicologists (including the writer).”

2331_C010.fm Page 124 Wednesday, May 9, 2007 5:45 AM

124

Bioassays with arthropods, second edition

Figure 10.3 The PoloMix Results for This Set of Data.

IV. Synergists Synergists are chemicals that are not toxic to an arthropod. When mixed with a pesticide, however, they block a step of the detoxification of the pesticide so that that pesticide becomes significantly more toxic. For exam-

2331_C010.fm Page 125 Wednesday, May 9, 2007 5:45 AM

Chapter ten: Mixtures

125

ple, Corbett et al.22 list four chemicals that continue to be of commercial interest: N-(2-Ethylhexyl)-8,9,10-trinorborn-5-ene-2,3-dicarboximide; piperonyl butoxide; sesamex; and sulfoxide. Piperonyl butoxide interferes with oxidative breakdown of the insecticide that is catalyzed by cytochrome P-450. Piperonyl butoxide and the three other synergists are used to enhance the toxicity of pyrethroids, a group of insecticides that tend to be very expensive and unstable. Hewlett and Plackett23 have proposed the following probit model for response of an organism to drug A (applied at dose d1) plus synergist B (applied at dose d2): Y = β0 + β1 log d1 + β 2

d2 γ + d2

where Y is the probit line and β0, β1, β2, and γ are unknown parameters. R16 or another computer package, such as Stata,24 GLIM,25 or Mathematica,26 can be used to calculate estimates of the parameters; however, Hewlett and Plackett23 admit that the model has no “definite biological basis.” As Dr. Maven has found early in her reading on the problem of mixtures, this description seems to apply to most of the statistical methods published after Bliss’s1 initial work. A more sensible approach to analyzing the effects of a synergist is to derive a dose-response model for the synergist based on knowledge or a theory about its biological mode of action. For example, Preisler27 derived a dose-response model to describe the synergistic effect of an enzyme, chitinase, on the biological activity of gypsy moth (Lymantria dispar [L.]) nuclear polyhedrosis virus (NPV). The model was based on the mode of action for chitinase suggested by Shapiro et al.28 who indicated that the enzyme might disrupt the insects’ peritrophic membrane. Once the peritrophic membrane is disrupted, greater numbers of viruses can penetrate the midgut and infect susceptible cells. The mode of action of chitinase was modeled as follows: If D(t) = the amount of NPV reaching susceptible cells by time t, then D(t) is an increasing function of time, the amount of NPV present at time zero, and the dose of enzyme administered at time zero. Preisler27 has used the complementary log-log model to estimate the dose-response curve. GLIM was used to calculate values of the parameters.

V. Conclusions For practical purposes, the simplest hypothesis of pesticide interaction that can be tested experimentally is that of independent, uncorrelated, joint action. This hypothesis means that the effect of one component of the pesticide mixture is not correlated with the effect of the other and is applicable to data from experiments with mixtures consisting of pesticides of different chemical types. If the hypothesis is rejected, two effects are possible. Syner-

2331_C010.fm Page 126 Wednesday, May 9, 2007 5:45 AM

126

Bioassays with arthropods, second edition

gism is the occurrence of significantly greater mortality than predicted by the model, while antagonism is the occurrence of significantly reduced mortality. Another simple hypothesis that can be tested is that of similar (or additive) joint action. This hypothesis is probably applicable when one mixture component is structurally related to the other mixture component. Other hypotheses about pesticide interactions cannot be distinguished in quantal response bioassays because they are based on statistical rather than biological theories. Effects of synergists (nontoxic chemicals that increase the toxicity of a pesticide by blocking some stage of the detoxification process) are most sensibly modeled by deriving a dose-response model based on a particular biological mode of action.

References 1. Bliss, C. I., The toxicity of poisons applied jointly, Ann. Appl. Biol. 26, 585, 1939. 2. Hewlett, P. S. and Plackett, R. L., Statistical aspects of the independent joint action of poisons, particularly pesticides. II. Examination of data for agreement with the hypothesis, Ann. Appl. Biol. 37, 527, 1950. 3. Hewlett, P. S. and Plackett, R. L., A unified theory for quantal responses to mixtures of drugs: non-interactive action, Biometrics, 15, 591, 1959. 4. Hewlett, P. S. and Plackett, R. L., A unified theory for quantal response to mixtures of drugs: competitive interaction, Biometrics, 20, 566, 1964. 5. Plackett, R. L. and Hewlett, P. S., Statistical aspects of the independent joint action of poisons, particularly insecticides. I. The toxicity of a mixture of poisons, Ann. Appl. Biol. 35, 347, 1948. 6. Plackett, R. L. and Hewlett, P. S., Quantal responses to mixtures of poisons, J. R. Stat. Soc. B. 14, 141, 1952. 7. Plackett, R. L. and Hewlett, P. S., A unified theory for quantal responses to mixtures of drugs: the filling to data of certain models for two non-interactive drugs with positive correlation of tolerances, Biometrics 19, 517, 1963. 8. Plackett, R. L. and Hewlett, P. S., A comparison of two approaches to the construction of models for quantal responses to mixtures of drugs, Biometrics 23, 27, 1967. 9. Ashford, J. R., Quantal responses to mixtures of poisons under conditions of simple similar action: the analysis of uncontolled data, Biometrika 45, 74, 1958. 10. Ashford, J. R., General models for the joint action of mixtures of drugs, Biometrics 37, 457, 1981. 11. Ashford, J. R. and Smith, C. S., General models for quantal response to the joint action of mixtures of drugs, Biometrika 51, 413, 1964. 12. Ashford, J. R. and Smith, C. S., An alternative system for the classification of mathematical models for quantal responses to mixtures of drugs in biological assay, Biometrics 21, 181, 1965. 13. Robertson, J. L. and Smith, K. C., Joint action of pyrethroids with organophosphorous and carbamate insecticides applied to western spruce budworm (Lepidoptera: Tortricidae), J. Econ. Entomol. 77, 6, 984. 14. Robertson, J. L. and Smith, K. C., MIX: a computer program to evaluate interaction between chemicals, USDA Forest Service Gen. Tech. Rep., PSW-112, 1989.

2331_C010.fm Page 127 Wednesday, May 9, 2007 5:45 AM

Chapter ten: Mixtures

127

15. LeOra Software, PoloPlus, LeOra Software, 1007 B St., Petaluma, CA 94952. See http://www.LeOraSoftware.com. 16. See http://www.r-project.org. R version 1.9.1 was released on June 21, 2004. 17. LeOra Software, PoloMix, LeOra Software, 1007 B St., Petaluma, CA 94952. See http://www.LeOraSoftware.com. 18. Giltinan, D. M., Capizzi, T. P., and Malani, H., Diagnostic tests for similar action of two compounds, Appl. Stat. 37, 39, 1988. 19. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 20. Sakai, S., Joint action of insecticides, Bull. Daito Bunko Univ. 1, 1969, p. 279. 21. Busvine, J. R., A Critical Review of the Techniques for Testing Insecticides, Commonwealth Agricultural Bureaux, London, 1971. 22. Corbett, J. R., Wright, K., and Baillie, A. C., The Biochemical Mode of Action of Pesticides, Academic Press, London, 1984. 23. Hewlett, R. L. and Plackett, P. S., The Interpretation of Quantal Responses in Biology, University Park Press, Baltimore, MD, 1979. 24. Stata Corporation, Stata 9 software, 4905 Lakeway Dr., College Station, TX 77845. 25. Baker, J. R. and Nelder, J. A., The GLIM Manual: Release 3. Generalized Linear Interactive Modelling, Numerical Algorithms Group, Oxford, England, 1978. 26. Wolfram Research Mathematica software, Champaign, IL. 27. Preisler, H. K., Analysis of toxicological experiment using a generalized linear model with nested random effects, Intl. Stat. Rev. 57, 145, 1989. 28. Shapiro, M., Robertson, J. L., and Preisler, H. K., Enhancement of baculovirus activity on gypsy moth, J. Econ. Entomol. 80, 1113, 1987.

2331_C010.fm Page 128 Wednesday, May 9, 2007 5:45 AM

2331_C011.fm Page 129 Thursday, May 10, 2007 11:20 AM

chapter eleven

Time as a variable Hank Jones returns to see Dr. Maven about another problem. It seems that his mother has a very special question about another pest of ‘Redneck’ tomatoes. Just when the wicked witches seem to be under control, her select crop of ‘Rednecks’ grown and sold for canning is under attack by a subspecies of the Texas leafcutting ant (Atta texana [Buckley])—the tomato stem cleaver (Atta texana severalis [Amputeé]): “So you see, ma’am, once a gang of them ants start chewing on the stem, the tomato drops off in ’bout six hours. And it’s always a green tomato, not a ripe one. We’ve already got a fourth of the crop just laying on the ground. We can’t sell the green tomatoes, Paula Deen1 can’t come up with enough recipes for the blasted things, and Momma says she’s too blamed old to put up pickled green tomatoes by the carload. Anyhow, what we need is something that’ll kill the ants in less than six hours. Can you help?” In truth, our heroine had never really thought about the speed at which a toxicant acted, except in passing. Of course, she has noticed that some pesticides such as the pyrethroids or pyrethrins acted very quickly at low doses. Other kinds of pesticides (e.g., molt inhibitors, juvenile hormone analogues) act comparatively slowly even at high doses. For the sake of the ‘Redneck’ canning tomatoes, Paula and Blanche now examine the matter of time in response of tomato stem cleavers ants to pesticides in more detail.

I. Purposes of studies involving time Time-dose-mortality relationships are of practical and theoretical importance in studies of pesticide activity on arthropods. For some species such as the cone beetle, Conophthorus ponderoase Hopkins, the most important criteria for choice of a pesticide are speed of kill and residual activity that persists during the period in which females attack host cones.2 Female C. ponderosae rapidly sever connective tissue in the cone stalk; once contacted, an insecticide must cause death quickly if cone death is to be prevented. In theoretical studies, time trends may also be preliminary indicators of chemical mode of action and detoxification mechanisms.

129

2331_C011.fm Page 130 Thursday, May 10, 2007 11:20 AM

130

Bioassays with arthropods, second edition

Data from time-dose-response experiments have frequently been analyzed by modeling time trends separately for each dose,3,4 or by separately estimating dose trends for each time.5 However, these methods are inefficient because the entire data set is not used in the estimation procedure. In addition, activity over time is difficult to describe when time and dose trends are considered separately. Time-dose-response data have also been analyzed by fitting probit lines (with time replacing dose) to mortality data for a fixed dose over time.5 Unless different groups are used for each observation period, however, this method is inappropriate for time-response data because responses at different time points are correlated. Methods for the analysis of correlated data have been described,6 and a computer program written in the Mathematica7 language is now available, but use of the program depends on access to this software.

II. Sampling designs A. Alternatives Bioassays that include both time and dose as variables can have one of two possible designs. With the independent sampling design, separate groups of test subjects are treated with a given dose. Each group is then observed for a different period of time, and numbers of responses are recorded at each observation period. For the experiment to be valid, responses that occur in a given test group must be recorded only once. The other alternative, the serial sampling design, involves treatment of subjects with a given dose, use of several doses for the experiment as a whole, and recording of responses for each dose group at a series of times after treatment. Numerous observations are necessary because responses differ with each dose group (i.e., a high dose will kill more test subjects in a short period of time, but a low dose will kill fewer subjects during the same interval). In summary, a serial design involves treatment with a series of observations for each treatment group.

B. General statistical models For the independent design, statistical models of time-response data for a fixed dose are straightforward. The probability of response by a given time t can be modeled by the probit, logit, or complementary-log-log (CLL) curves with time (or some function thereof such as the logarithm of time) as the single independent variable. The statistical statement of the binary response with time as the explanatory variable is Pi = F(α + βti )

(11.1)

2331_C011.fm Page 131 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

131

where Pi is the probability of response, ti is the ith time (or the logarithm of time), α is the intercept of the regression line, β is the slope of the regression line, and F is a distribution function (probit, logit, or complementary log-log). The probit and logit models are as defined as in Chapter 3 (see 3.II.A., “Probit or Logit Regression”). The general statement of the CLL relationship is as follows: For a fixed exposure time tj (j = 1,...,J), to a chemical at a concentration di (i = 1,...,I), the model for mortality of a test subject by time tj is pij = 1 − exp[− exp(τ j + β log10 di )]

(11.2)

where exp(y) ≡ ey, β is an unknown parameter and τj are unknown categorical variables corresponding with the times tj. The linear part of Equation 11.2, τ j + β log10 di , is the CLL line (i.e., the linear predictor of the CLL model). The model assumes that loge(-loge(1 - pij)) is linear in the covariates. For the independent time-mortality design, τj is replaced by the logarithm of tj and log10(di) is replaced by the constant log10(D) where D is the fixed dose used in the experiment. This statement of the CLL relationship corresponds with the Weibull function, which has been used to model responses to some chemicals over time.3

III. Analysis of independent time-mortality data A. Experimental design The experimental design of time-dose-response experiments done with an independent sampling design is analogous to designs described in Chapter 4, “Binary Quantal Response: Data Analyses,” for dose-response experiments in which responses are tallied after a constant time. Instead of time being constant (e.g., mortality tallied after seven days or some other fixed time), dose is constant and time is varied. At first, Dr. Maven is slightly confused by this requirement. However, the analogy with a dose-response experiment clarifies her thinking. In a dose-response bioassay, test groups are treated with different doses or concentrations. In time experiments at a constant dose, responses of different treatment groups are recorded at each observation period. Once the experimental dose or concentration has been selected, preliminary experiments are necessary to bracket the times at which 5% to 99% mortality occurs. At least three replications with all time groups should then be done. The same guidelines described in Chapter 5, “Binary Quantal Response: Dose Number, Dose Selection and Sample Size,” pertain to time studies. As with the dose-response experiments, selection of the optimal times depend on the lethal time (LT) of interest and the number of times used. The information in Chapter 4 (Table 4.1) can be used for selection of

2331_C011.fm Page 132 Thursday, May 10, 2007 11:20 AM

132

Bioassays with arthropods, second edition

the optimal experimental design (placement of time points, number of individual times tested) by substituting LT for effective dose (ED) throughout. The second column (number of doses) should be replaced with the heading “Number of Times.”

B. Limitations and constraints For an experiment with an independent design, each time group must be independent: a different group of test subjects must be used for assessment of response at each time. If the same group of test subjects is observed at several time intervals, responses at different time points will be correlated. Analysis of correlated response data requires the use of computer programs that do multinomial analysis because use of responses at different time points violates the premise of independent binomial response assumed in PoloPlus8 or SAS.9 (As noted previously, an alternative special program specifically for correlated data6 is written in Mathematica7 language.) Unfortunately, many published reports5,9 describe analyses of data collected by sequentially recording the mortality within the same group of individuals, followed by probit or logit analysis with time as the independent variable. Results of such analyses are not valid. A final problem must be kept in mind when time or the logarithm of time is used as the independent variable in probit, logit, or CLL models. If the function of time used in the regression line increases indefinitely as time increases, then the probabilities of mortality will increase to 1. Such a model suggests that all test subjects will eventually die from the treatment. Especially at low doses or concentrations, this is not true: Many insects will die from causes other than the pesticide. Therefore, mortality will reach a plateau that is usually < 1. As a result, a probit, logit, or CLL model with time (or logarithm of time) as the independent variable will not be appropriate for the data except at higher doses. The problem of plateaus of <100% mortality (i.e., maximum P < 1) is especially relevant to studies of pesticide resistance in which LTs are used to compare population responses.10,11 A dose selected on the basis of responses of susceptible populations will probably not kill all members of resistant populations regardless of the observation times. A dose that will affect all members of the most resistant population might be used instead, but the observation times for each susceptible population should be chosen carefully so that most test subjects are not dead when the first count is made. Careful preliminary experiments will be necessary to select the times that are appropriate for each population; use of PoloDose12 can facilitate their selection to obtain the most precise estimate of the LT of interest. A model with a categorical time variable can be fitted when the data for all doses are analyzed simultaneously. Such a model is more general than one with time or logarithm of time as the independent variable (e.g., Equation 11.1) and it includes models with plateaus at values <1. As Paula explains the situation to Blanche, a plateau can be modeled as if the two of

2331_C011.fm Page 133 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

133

them are writing a textbook: they begin writing and make a lot of progress quickly, things drag on (and on, and on), and then all of a sudden, they finish within the space of two weeks. That long, flat interval between start and finish is the plateau.

IV. Analysis of serial time-mortality data For Paula Maven’s problem with tomato stem cleaver ants on ‘Redneck’ tomatoes, use of the serial time–mortality design is ideal. This design, in which the same test subjects are followed over time, is the most economical way to use test subjects. (Not that Blanche’s supply of ants is running out.) Another advantage of using the serial design is that Paula and Blanche can gain more insight into the mode of action of a particular pesticide and the effect of dose on speed of lethal action.

A. Experimental design For this kind of experiment, application rates should be selected as described in Chapter 5. Times at which mortalities are tallied should be chosen so that 5% to 95% of the total mortality that occurs with each dose is included in the observations. At each observation period when mortality is recorded, each dead test subject should be removed from the treatment container, held in a separate container, and its condition verified at the time of the next observation. (This procedure ensures that a test subject is counted as dead at only one observation interval and that a subject categorized as dead is, in fact, dead.) Unless other variables such as body weight are intentionally included in an experiment, they must be controlled. For example, a narrow range of body weights (average or individual) can be used to exclude body weight as a variable. An alternative procedure is to record all body weights and test for the significance of body weight as a variable in the time-dose-response regression. Paula chooses to have Blanche test commercial formulations of two pesticides (pyrethrins, acephate) that have acted quite quickly on the tomato stem cleaver ants in preliminary experiments. In the time-concentration-response experiments, Blanche places ten adults of one sex on each potted ‘Redneck’ tomato plant. (Males have a red cross on their dorsal prothorax, and females have no markings.) Each plant bears at least ten green ‘Rednecks’; the plant is sprayed with one of five concentrations of each chemical. Two plants are sprayed in a replication with each concentration, and each experiment is replicated three times for each sex. Controls for each pesticide are sprayed with water only; a control group is included with each replication with each chemical. All concentrations, from lowest to highest, of a pesticide are sprayed in each replication, and both pesticides are tested in a replication. With help from the entire faculty, staff and student body, Paula and Blanche then obtain mortality counts at 4, 8, 12, 24, 48, 72, 96, 120, 144, and

2331_C011.fm Page 134 Thursday, May 10, 2007 11:20 AM

134

Bioassays with arthropods, second edition

168 hours after treatment. Because changes in observers (and detachment of their minds and, possibly, retinas) introduce another possible variable into the experiment, Dr. Maven holds a group session about how to tell whether an ant is dead. The criteria to be used by all observers are (1) lack of movement of any legs when a stream of air is blown over the body; (2) generalized writhing of the body; and (3) presence of a tiny white lily clasped between the first pair of legs. Possible differences in observer decisions about whether death has occurred pale in comparison with the tedium involved if one person were to do all of the observations.

B. Statistical methods With the serial design, standard techniques that are suitable for the independent design are not applicable for data analyses because responses of test subjects over time are not independent. Thus, analyses such as those described by Su et al.5 and Cochran10 are not appropriate: When counts are made on the same individuals at each time period, standardized probit or logit techniques with time as the independent variable should not be used. For a given dose, the numbers of responses at each time out of the total number treated with that dose have a multinomial distribution. Therefore, analyses of dose-mortality data over time can be done with the procedure described in Chapter 14, “Polytomous (Multinomial) Quantal Response.” The conditional probability that a test subject responds by time tk given its failure to respond at time tk-1 is modeled by yijk = γ jk + β j log10 ( di + d0 )

(11.3)

where yijk is the probit, logit, or CLL line for test subjects in group j treated with dose di at the beginning of the experiment (t0). If group j includes separate subgroups of males and females, then j = 1, 2. γj,k are the intercepts (one for each sex and time interval), βj are the slopes (one for each sex) and d0 = 10a. The value a is defined as

a = log( d0 ) = log( d i ) −

d1 ⎡log( d2 ) − log( d i ) ⎦⎤ d2 − d1 ⎣

(11.4)

where 0 < d1 < d2. Equation (11.4) provides a means to deal with a dose of zero. The CLL model is well-suited for the analysis of time-mortality data from a serial design. In an extensive series of experiments with western spruce budworm, Preisler and Robertson13 have shown that the cumulative probability of a subject responding by time tk can be adequately approximated by this model. The line for cumulative probability of response by time tk is given by

2331_C011.fm Page 135 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

135

yijk = τ jk + β j log10 ( di + d0 )

(11.5)

where βj and d0 are the same as in Equation 11.3 and where

τ jk = loge ( e

γ j1

+e

γj2

+

γ

+ e jk )

(11.6)

The relationship between γ and τ in Equation 11.6 does not hold for the standard probit or logit models. Conditional probabilities given in Equation 11.5 can be used to calculate maximum likelihood estimates of the parameters to test hypotheses or equality. This estimation procedure is appropriate because conditional responses are independent binomial variables. Thus, standard programs for estimation of parameters of probit, logit or CLL lines can be used. Cumulative probabilities in Equation 11.5 are needed to calculate parameters of biological interest, such as estimates of lethal dose over time.

C. Estimation For estimation of Equation 11.5, two data sets are needed: (1) the number of subjects (rijk) in category ij (i.e., of group j that have been treated with dose di) that died in time interval (tk-1,tk); and (2) the number of subjects (nijk) in category ij that were still alive at time tk-1. The latter variable therefore equals the total number of insects in category ij minus all of the insects that died by time tk-1. Because the number of responses rijk out of nijk are independent binomial variables, a software package that performs binomial regressions with the CLL line such as R14 or GLIM15 can be used to estimate the parameters in Equation 11.4 and to compute maximum values of likelihood functions. The significance of variables can then be tested by analysis of deviance.

1. Estimation of response probabilities For estimation of response probabilities, the model with the least number of parameters that fits the data adequately is used to calculate estimates of the probabilities of response (Pijk) up to time tk. For example, if the effect of sex on responses in all time intervals is not significant, then the model with equal lines for both sexes can be used. The CLL model becomes yˆ ijk = γˆ + β log10 ( di + d0 )

τˆ k = loge ( eγˆ1 + eγˆ2 + and

+ eγˆk )

(11.7) (11.8)

2331_C011.fm Page 136 Thursday, May 10, 2007 11:20 AM

136

Bioassays with arthropods, second edition

{

}

Pˆijk = 1 − exp − exp ⎡⎣τˆ k + βˆ log10 ( di + d0 )⎤⎦

(11.9)

Plots of pˆ ijk against time can be used to study the effect of dose on speed of lethal action (see IV.C.3, “Example,” below).

2. Estimation of Lethal Doses over Time The parameter LDx(tk) is the dose that causes x% mortality by time tk. An ˆ estimate of LDx(tk) is 10θ k where a − τˆ k θˆk = x βˆ and ax = log e ⎡⎣ − log e ( 1 − x / 100 ) ⎤⎦

(11.10)

Based on the asymptotic approximation of variances, the equation for the variance of θˆ is var(θˆk ) =

1 ⎡ˆ 2 θ k var( βˆ ) + var(τˆ k ) + 2θˆk cov(τˆ k , βˆ )⎤⎦ ˆ β2 ⎣

cov(τˆ k , βˆ ) =

var(τˆ k ) =

1 e 2τˆ k

1 e τˆ k k

k

∑e

γˆi

cov( βˆ , γˆk )

(11.12)

i=1

k

∑∑ e i=1

(11.11)

γˆi +γˆi′

cov(γˆi , γˆi′ )

(11.13)

i′

Finally, variances and covariances of the estimates βˆ and γˆk are obtained from the output of the statistical program that was used to fit the CLL model to Equation 11.3. Plots of LDx(tk) versus time permit comparisons of effectiveness to be made at selected times after the test subjects are first exposed to different chemicals.

2331_C011.fm Page 137 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

137

Table 11.1 Number of Responsesa of Tomato Stem Cleaver Males or Females in Each Time Interval after Application of Acephate to Tomato Plants Sex

Dose

4

8

Males

0 1 2 3 5 10 0 1 2 3 5 10

0 3 11 12 13 13 0 2 16 12 11 15

0 11 14 17 12 17 0 13 15 20 15 23

Females

Time Interval in Hours after Treatment 12 24 48 72 96 120 144 0 5 5 7 15 9 0 10 9 8 16 8

0 5 7 4 7 16 0 5 6 7 6 12

0 0 3 3 5 5 0 1 1 3 5 2

0 2 3 6 2 0 0 2 0 2 1 0

0 1 1 2 0 0 0 0 1 0 0 0

0 0 0 0 3 0 0 0 0 0 1 0

0 4 6 3 1 0 0 2 4 2 0 0

168 0 5 2 1 2 0 0 5 0 0 2 0

Note: aThe total number of test subjects at each dose is 60.

3. Example Part of the data gathered by Dr. Maven and her assistants are shown in Table 11.1. Dr. Maven uses CLL regression to estimate the conditional binomial model. The GLIM15 output begins with a listing of the data (part of which is shown in Figure 11.1a). Under the column labeled “Sex,” 1 designates males and 2 designates females. “Time” is the time elapsed from the beginning of the experiment until the time an observation was made. “Dose” is self-explanatory, while “Response” is the number of tomato stem cleaver ants that died since the last time an observation was made. Finally, “Conditional Total” is the number of ants, exposed to a given concentration, that were still alive when the time interval began. For example, in Figure 11.1a, in line 4, the conditional total of 57 equals the conditional total in line 3 minus the 3 insects that died in the time interval. Figure 11.1b shows the commands for testing the hypotheses of parallelism and equality of CLL lines for male and female ants. Because control mortality (dose 0) was zero, d0 is set to zero. The output from these commands (Figure 11.1c) shows the information necessary for hypothesis testing. H1 is the hypothesis that the CLL lines for males and females are parallel; statistics for this test are given in lines 2–4 and lines 5–7. The difference in the values of the LR test statistic is 69.094 (i.e., scaled deviance = 69.094; line 6) minus 68 (i.e., scaled deviance = 68; line 3). Degrees of freedom for the test are 69 (line 7) minus 68 (line 4), or 1. The P value for 1.094 with 1 degree of freedom is > 0.05, so H1 cannot be rejected. H2 is the hypothesis that the CLL lines for males and females are equal. The LR test statistic is 75.758 (line 9) minus 68 (line 3). This value, 13.758, is less than the critical χ2 value for 11 degree of freedom (79[line 10] - 68[line 4]). Therefore, the hypothesis of equality cannot be rejected.

2331_C011.fm Page 138 Thursday, May 10, 2007 11:20 AM

138

Bioassays with arthropods, second edition

Figure 11.1a Complementary-Log-Log (CLL) Regression of Time-Dose-Mortality Data Done with the GLIM Program.

2331_C011.fm Page 139 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

Figure 11.1b–d (continued)

139

2331_C011.fm Page 140 Thursday, May 10, 2007 11:20 AM

140

Bioassays with arthropods, second edition

Figure 11.1e (continued)

Because responses of males and females are not significantly different, parameters of the conditional binomial model with equal slopes and intercepts for both sexes are computed next (see Figure 11.1d). In Figure 11.1e (the output from running Figure 11.1d), lines 4–13 are the estimates for the intercepts δk for each of the ten time intervals. The estimated slope, β(= 1.348 + 0.1859), is shown in line 14. This model (see Figure 11.1e), which includes only those parameters that were significantly different from zero, produces parameter estimates that are used to calculate the cumulative probabilities from Equations 11.8 and 11.9. For example, the probability of an insect dying eight hours (i.e., the second time interval with k = 2) after treatment with the second dose level of acephate (i.e., i = 2 and d2 = 2 [g/ha]) is calculated as follows: From Equation 11.6,

τˆ 2 = loge ( e −2.376 + e −1.679 ) = −1.275 From Equation 11.7,

{

}

p22 = 1 − exp − exp ⎡⎣ −1.275 + 1.348 log 10 ( 2 ) ⎤⎦ = 0.342 . Thus, a tomato leaf cleaver ant has a 34% chance of being dead eight hours after being sprayed with 2 g/ha of acephate. Figures 11.2a and 11.2b show plots of the probabilities for all time points between 0 and 168 hours after treatment, for all application rates of acephate (Figure 11.2a) and pyrethrins (Figure 11.2b). As the application rates for either

2331_C011.fm Page 141 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

141

0.4

highest dose second highest dose third highest dose lowest dose

0.0

Probability

0.8

a

0

50

100

150

Hours after treatment

Figure 11.2a Probabilities of Death over Time for Pesticides for Which the Amount Applied Has no Effect on Speed of Lethal Action (a and b). Examples c and d Are for Pesticides for Which Speed Is Affected by the Amount Applied.

pesticide increase, probabilities of mortality also increase. But the time required to reach the plateau when all of the ants that will die have done so appears to be the same regardless of application rate. Thus, the amount of acephate or pyrethrins applied does not affect the speed of lethal action. For acephate treatments, Dr. Maven notices that mortality probabilities reach a plateau at about the same time (around 24 hours). With pyrethrins, the plateaus are reached more quickly (i.e., < 30 minutes after treatment). Based on these results, Dr. Maven recommends that Hank Jones apply pyrethrins to his crop of ‘Redneck’ tomatoes because the highest rate kills almost all of the tomato leaf cleaver ants within 30 minutes. Examples of pesticides whose speeds of action are apparently affected by application rate are shown in Figures 11.2c and 11.2d. The time required for the plateau to be reached clearly changes from the lowest to highest rate. In fact, the plateau for the lowest rate in Figure 11.2c has not been reached by 168 hours. Table 11.2 lists the estimates of LD50 and LD90 (with their 95% confidence intervals) for the tomato leaf cleaver ants treated with acephate and for increasing times of exposure. These values were calculated using Equations 11.10–11.13. For example, the LD50 for eight hours of exposure is calculated from Equation 11.10, with k = 2 and x = 50% as: a50 = log e ⎡⎣ − log e ( 1 − 0.5) ⎤⎦ = −0.367 −0.367 − (−1.275) θˆ2 = = 0.674 and LD50(8) = 100.674 = 4.72. 1.348

40

Hours after treatment

20

60

lowest dose

third highest dose

highest dose second highest dose

142

Probability

Figure 11.2b (continued)

0

b

2331_C011.fm Page 142 Thursday, May 10, 2007 11:20 AM

Bioassays with arthropods, second edition

2331_C011.fm Page 143 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

143

0.4

highest dose second highest dose third highest dose lowest dose

0.0

Probability

0.8

c

0

50

100

150

Hours after treatment

Figure 11.2c (continued)

0.4

highest dose second highest dose third highest dose lowest dose

0.0

Probability

0.8

d

0

50 100 Hours after treatment

150

Figure 11.2d (continued)

Table 11.2 Estimates of LD50 and LD90 for Texas Stem Cleaver Ants on Tomato Plants with Increasing Times of Exposure to Acephate LD

4

8

50 90

30.9 240.6

4.7 36.7

Hours after Exposure 12 24 48 2.1 16.3

1.1 8.5

0.8 6.4

72

96

0.7 5.3

0.6 5.0

2331_C011.fm Page 144 Thursday, May 10, 2007 11:20 AM

144

Bioassays with arthropods, second edition

V. Conclusions Bioassays involving both time and dose as independent variables can have one of two possible designs. Separate groups of test subjects are treated with a given dose when the independent sampling design is used. Each group is observed for a different period of time, when responses are tallied. Counts cannot be made on the same individuals at each time period. With the serial sampling design, subjects are treated with a series of doses and responses for each dose are recorded at different times. Of the two designs, the serial sampling design is more efficient.

References 1. See Deen, Paula H., The Lady & Sons Savannah Country Cookbook, Random House, NY, 1998, and Deen, Paula H., The Lady & Sons Too!, Random House, NY, 2000 for two wonderful recipes for fried green tomatoes. Both Paula and Carl Maven swear that Paula Deen has the best recipes for green tomatoes (and other fantastic Southern food) that they have ever tasted. 2. Haverty, M. I. and Wood, J. R., Residual toxicity of eleven insecticides to the mountain pine cone beetle, Conophthorus monticolae Hopkins, J. Ga. Entomol. Soc. 16, 77, 1981. 3. Hewlett, P. S., Time from dosage to death in beetles, Tribolium castaneum, treated with pyrethrins or DDT, and its bearing on dose-mortality relations, J. Stored Prod. Res. 10, 27, 1974. 4. Shapiro, M., Preisler, H. K., and Robertson, J. L., Enhancement of nucleopolyhedrosis virus activity on gypsy moth (Lepidoptera: Lymantriidae) by chitinase, J. Econ. Entomol. 80, 1113, 1987. 5. For example, Su, N-Y., Tamashiro, M., and Haverty, M. I., Characterization of slow-acting insecticides for remedial control of the Formosan subterranean termite (Isoptera: Rhinotermitidae), J. Econ. Entomol. 80, 1, 1987. 6. Throne, J. E., Weaver, D. K., Chew, V., and Baker, J. E., Probit analysis of correlated data: multiple observations over time at one concentration, J. Econ. Entomol. 88, 1510, 1995. 7. Wolfram, Stephen, Mathematica, Champaign, IL. 2005. 8. LeOra Software, PoloPlus, LeOra Software, 1007 B St., Petaluma, CA 94952, 2003. See http://www.LeOraSoftware.com. 9. SAS Institute, http://www.sas.com/technologiest/anaytics/statistics/stat. 10. For example, Cochran, D. G., Selection for pyrethroid resistance in the German cockroach (Dictyoptera: Blatellidae), J. Econ. Entomol. 80, 1117, 1987. 11. Preisler, H. K., Hoy, M. A., and Robertson, J. L., Statistical analyses of modes of inheritance for pesticide resistance, J. Econ. Entomol. 83, 1649, 1990. 12. LeOra Software, PoloDose, 1007 B St., Petaluma, CA 94952, 2005. See http:/ /www.LeOraSoftware.com.

2331_C011.fm Page 145 Thursday, May 10, 2007 11:20 AM

Chapter eleven: Time as a variable

145

13. Preisler, H. K. and Robertson, J. L., Analysis of time-dose-mortality data, J. Econ. Entomol. 83, 1990. 14. See http://www.r-project.org. R version 1.9.1 was released on June 21, 2004. 15. Payne, C. D., ed., The GLIM System Release 3.77 Manual, Numerical Algorithms Group, Oxford, England, 1978.

2331_C011.fm Page 146 Thursday, May 10, 2007 11:20 AM

2331_C012.fm Page 147 Thursday, May 10, 2007 11:20 AM

chapter twelve

Binary quantal response with multiple explanatory variables Blanche has watched the wicked witches become heavier with each successive generation of laboratory colonization. During the first year of bioassays, Dr. Maven had her select and test insects within a very narrow weight range. But the insects’ weights have increased so much that the shelves supporting the insect colony are pulling away from the walls. Worse yet, Blanche simply cannot find enough insects in the weight range that she had been testing previously. She brings the matter to Paula’s attention. Dr. Maven ponders this situation—what should they do? They certainly cannot ask Weight Watchers for advice. Blanche might use a weight range with a higher upper limit, but how can Paula be sure that body weight does not affect responses of the insects to toxicants? After reading the material in yet another online literature search, Dr. Maven suspects that multiple probit or logit regression might be the most efficient method to handle this burdensome problem. As before, she has Blanche record a binary response (dead or alive). But now Blanche will also record dose and body weight as possible variables affecting response. This type of a bioassay is a binary quantal response experiment with multiple explanatory variables.

I. Early examples and inefficient alternatives Examples of the use of multiple regression techniques in bioassays with arthropods were scarce in the biological literature before publication of the first edition1 of this book. Finney2 confined his discussion to multiple probit analyses with two quantitative variables. In the particular situation that he discusses, the logarithm of each variable is linearly related to the probit of response when the other variable is fixed. Details of the manual calculations for this “probit plane” problem are also provided. In our first edition, we1 improved the situation slightly by providing a discussion of a computer 147

2331_C012.fm Page 148 Thursday, May 10, 2007 11:20 AM

148

Bioassays with arthropods, second edition

program, interpretation of its output, and guidance for the information necessary for hypothesis testing. However, we did not show any user-friendly computer programs among our examples. Perhaps to avoid complicated calculations and confusing computer outputs, many biological scientists chose (and continue to choose) an alternative that is primitive compared with estimation by multiple regression. Rather than using multiple regression techniques, these investigators have done multiple experiments (with univariate analyses) in attempts to show the effects (but not necessarily test the significance) of variables other than dose on response. For example, early research on the role of insect body weight on response was done by testing separate groups of selected weights, estimating their responses by simple (univariate) probit analysis, and making comparisons at the LD50 or LD90 as the basis for concluding that weight did or did not significantly affect response.3–6 The primary reason for use of binary quantal response bioassays with multiple explanatory variables is simple: compared with a single experiment in which the significance of several variables is tested simultaneously, multiple experiments with single variables are grossly inefficient.

II. A general statistical model The general model for solution of a multiple probit or logit problem is y = β1x1 + + β k xk , where y is the probit or logit of response and x1 through xk are the explanatory variables (including constant x1=1). Regression coefficients are β1 through β k for the constant term and explanatory variables. The presence of more than one explanatory variable makes the statistical methods used to estimate the probability of response and values of the coefficients far more complex than those previously described for binary quantal response with only one explanatory variable. As in any binary quantal response model, an individual can respond in one of two ways—dead or alive. The probability p that an individual is dead is F(β´xi) where F is a distribution function, β´ = (β1,...,βK) is a K × 1 vector of unknown regression coefficients and xi = (x1i,...,xKi) is a K × 1 vector of explanatory variables (including a constant term) for individual i. For the probit model, pi = F(β´xi) = Φ(β´xi) where Φ is the standard normal distribution function. For the logit model,

pi = F( β ′xi ) =

1 1 + e − β′xi

The maximum likelihood method can be used to estimate either model. Details of the statistical methods for these estimation procedures are described by Finney,2 Domencich and McFadden,7 Russell et al.,8 Maddala,9 and LeOra Software.10

2331_C012.fm Page 149 Thursday, May 10, 2007 11:20 AM

Chapter twelve: Binary quantal response

149

III. Types of variables in multiple regression models As specified by the multiple regression model, the linear predictor (e.g., probit or logit line) is modeled with additional variables besides dose. These models are appropriate for many kinds of bioassays. For example, the effects of continuous variables such as body weight and temperature on response can be estimated. When these kinds of covariates are included in the model, variability in response usually decreases. The subject of body weight as a variable will be discussed in more detail in Chapter 13, “Multiple Explanatory Variables: Body Weight.” Multiple regression models can also be used to study differences in response among groups of experiments by the addition of categorical covariates (e.g., sex, source of test subjects, types of diets) to the linear predictor. Examples discussed here demonstrate analyses with such variables. Finally, as was discussed in Chapter 10, “Mixtures,” use of multiple regression models is appropriate in the study of the joint action of pesticide mixtures. In mixture experiments, the multiple covariates are doses of the various pesticides in the mixture.

IV. Computer programs Historically, multiple probit or logit regression techniques have been used more frequently (and routinely) in studies of travel patterns 6 and economics7 than they have been in the analyses of data from pesticide bioassays. One reason for this disparity may be that economists and sociologists have had more ready access to efficient computer programs and became more familiar with statistical packages as part of their graduate education. Reichenbach and Collins11 have used two programs in the UCLA Biomedical Computer Program P Series12 (BMDP) to examine the effects of temperature and humidity on the toxicity of propoxur to German cockroaches ( Blattella germanica [L.]) and western spruce budworm. GLIM13 was also used to estimate multiple probit or logit regressions, as illustrated by analyses to show that an enzyme, chitinase, significantly enhanced the activity of a baculovirus ingested by gypsy moth, Lymantria dispar (L.), larvae.14 With any large statistical package, specific programs can be written in the appropriate programming language to handle specific multiple regression problems. A new computer program, PoloEncore,10 is shown here for the first time. This program is the Microsoft Windows-compatible version of a previous DOS program, POLO28, that we illustrated in the first edition1 of this book. This program should facilitate use of multiple regression techniques for results of bioassay on arthropods because intermediate output and statistical jargon have been removed from the DOS version.

2331_C012.fm Page 150 Thursday, May 10, 2007 11:20 AM

150

Bioassays with arthropods, second edition

V. Multiple probit analysis: an example from PoloEncore Because of her previous experience in coming to understand univariate probit and logit analyses, Dr. Maven begins her education in multiple regression methods by working through a sample problem. Among the examples of multiple probit analyses given in the POLO2 manual, Russell et al.8 used data from experiments done by Tattersfield and Potter15 to illustrate a relatively simple analysis with two covariates. Based on manual computation procedures, the same problem—parallel planes—was also described in detail by both Finney2 and Busvine.16 Tattersfield and Potter15 exposed red flour beetle, Tribolium castaneum (Herbst), to pyrethrum either as a direct spray or as a film deposited on glass (see Table 12.1). The response variable for each bioassay is binary (dead versus alive); the explanatory variables are pyrethrum concentration and spray or film deposit (i.e., the amount of the carrier solvent). If both explanatory variables are significant, then the response will be predicted by a plane. This means that the probit or logit of response might be linearly related to the logarithm of the measurement of each factor when the other factor is held constant. Table 12.1 Tattersfield and Potter: Beetles Exposed to Pyrethrum Either as Spray or Deposit15 Plane 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2

Pyrethrum concentration 5. 10. 20. 40. 5. 10. 20. 40. 5. 10. 20. 40. 5. 10. 20. 40. 5. 10. 20. 40. 5. 10. 20. 40.

Weight of deposit 2.9 2.9 2.9 2.9 5.7 5.7 5.7 5.7 10.8 10.8 10.8 10.8 2.9 2.9 2.9 2.9 5.7 5.7 5.7 5.7 10.8 10.8 10.8 10.8

Exposed

Responses

27 29 30 28 29 29 27 30 30 24 31 19 29 30 29 29 27 28 28 29 28 28 28 17

1 15 27 28 4 19 26 30 6 15 31 19 3 10 24 29 4 14 27 29 8 17 26 17

2331_C012.fm Page 151 Thursday, May 10, 2007 11:20 AM

Chapter twelve: Binary quantal response

151

A. Statistical model The probit model that expresses the effect of pyrethrum spray is ys = αs + β1s x1 + β2s x2

(12.1)

where ys is the probit of percent mortality, x1 is the pesticide concentration in mg/ml (a continuous variable), and x2 is the spray deposit in mg/cm2 (another continuous variable). The regression coefficients are αs for the constant, β1s for spray concentration, and β2s deposit weight. For the lethal effect of pyrethrum film, the model is y f = α f + β1 f x1 + β 2 f x2

(12.2)

where yf is the probit of percent mortality, x1 is concentration, and x2 is weight of the deposit on the glass. The regression coefficients are αf for the constant, β1f for concentration, and β2f for weight of the deposit.

B. Hypothesis tests Likelihood ratio tests can be used to test three hypotheses about these data. These hypotheses are (1) that the planes for the spray and residual film data are parallel; (2) that the planes are equal assuming that they are parallel; and (3) that the planes are equal assuming nothing about parallelism. “What’s the difference?” says Carl Maven to his wife Paula. She tries to think of a suitable analogy: “Okay, my dear, suppose that you’re the quality control inspector at the Oreo17 cookie factory. If your machinery is doing what you want, the two chocolate biscuits of the cookie will be parallel, with exactly the same thickness of white filling between them. The two biscuits will also be the same size. So, the first hypothesis tests whether the two parts are parallel, but that could mean that one side is smaller than the other and the filling might fall off the edges. The third hypothesis tests whether the two parts are equal, but one of them could be at an angle with the other and you don’t want that either. As the guardian of the Oreo cookie, you are interested in the second hypothesis because you want the parts to be parallel and equal. Got it?” “Now I understand! Where are the Oreos anyway? I’m hungry.” And Dr. Maven returns to her hypotheses. The LR test compares two values of the logarithm of the likelihood function. The first, L(ω), is the value when the log likelihood is maximized with no restrictions. The second, L(ω), is the maximum of the likelihood function subject to the restrictions of the hypothesis being tested. The hypothesis of parallel planes is H:(P): β1s = β1f, β2s = β2f. Ls and Lf are the respective values of the maximum of the log likelihood for Equations

2331_C012.fm Page 152 Thursday, May 10, 2007 11:20 AM

152

Bioassays with arthropods, second edition

12.1 and 12.2. The value of L(Ω) is the sum of Ls and Lf. The model with the restrictions imposed is y = αsxs + αf xf + β1x1 + β2x2

(12.3)

Categorical variables are used to solve this equation, so that xs = 1 for spray; xf =1 for film; xs = 0 for film; and xf = 0 for spray. The value L(Ω) is obtained by estimating Equation 12.3 by maximum likelihood. For large samples, the LR statistic is distributed approximately as a χ2 with 2 degrees of freedom. The number of degrees of freedom is the number of restrictions imposed by the hypothesis. For this test, the number of degrees of freedom equals the number of parameters constrained to be the same. By the LR test, the hypothesis is rejected at significance level α if LR > χ2(n) where χ2(n) is the upper significance point of a χ2 distribution with n degrees of freedom. The hypothesis of equality given parallelism is H(E⏐P): αs= αf. The unrestricted model is Equation 12.3 and the restricted model is y = α + β 1 x1 + β 2 x 2

(12.4)

In Equation 12.4, the coefficients for spray and film are restricted to be the same. The maximum log likelihood values required for this test are L(Ω) (the ML estimate of Equation 12.3) and L(ω) (the ML estimate of Equation 12.4). When H(E|P) is not rejected, LR = 2[L(Ω) – L(ω)] ∼ χ2(1). The hypothesis is rejected at significance level if LR ≥ χ2(1). Once H(P) is not rejected, H(E|P) can be tested. The hypothesis of equality is H(E): αs = αf, β1s = β1f, β2s = β2f. The unrestricted models are Equations 12.1 and 12.2, and the restricted model is Equation 12.4. The maximum log likelihood values required are L (Ω) and L(ω), where L(Ω) = Ls + Lf (i.e., ML estimations of Equations 12.1 and 12.2) and L(ω) is the maximum likelihood estimation of Equation 12.4. When H(E) is not rejected, LR = 2[L(Ω) – L(ω)] ∼ χ2(3).

C. Data analysis with PoloEncore PoloEncore is the Microsoft Windows–compatible version of the older DOS program POLO28, but PoloEncore is vastly improved in user friendliness and easy comprehension of results. The program is designed to analyze the effects of up to nine explanatory variables on a binary response (e.g., dead vs. alive). Figures 12.1a–12.1c show the PoloEncore screens that produce the solutions to Equations 12.1 through 12.4. Solutions to the hypothesis tests are shown in Figure 12.2, which is actually the last portion of a 199 line output. The hypotheses and results of testing are (1) H(P) [Hypothesis of parallelism]

2331_C012.fm Page 153 Thursday, May 10, 2007 11:20 AM

Chapter twelve: Binary quantal response

153

Figures 12.1a PoloEncore Screens for Tattersfield and Potter study.

L(Ω) = –223.8762 L(ω) = –225.1922 LR = 2.6321; df = 2; H0 cannot be rejected Dr. Paula Maven concludes that the planes are parallel. Dr. Carl Maven deduces that the two biscuits of the Oreo are evenly separated by the white filling. (2) H(E⏐P) [Hypothesis of equality given parallelism] L(Ω) = –225.1922

2331_C012.fm Page 154 Thursday, May 10, 2007 11:20 AM

154

Bioassays with arthropods, second edition

Figures 12.1b (continued)

L(ω) = –225.8635 LR = 1.3425; df = 1; H0 cannot be rejected. Paula concludes that the planes are parallel and equal; Carl has found the perfect Oreo. (3) H(E) [Hypothesis of equality] L(Ω) = –223.8762 L(ω) = –225.8635 LR = 3.9746; df = 3; H0 cannot be rejected

2331_C012.fm Page 155 Thursday, May 10, 2007 11:20 AM

Chapter twelve: Binary quantal response

155

Figures 12.1c (continued)

Paula concludes that the planes are equal; Carl is too busy eating Oreos to care.

VI. Multiple logit analysis: sample of analysis with GLIM An unpublished study in which nine groups of experiments were done to study the effects of temperature and photoperiod on response of the western spruce budworm to pesticides demonstrates estimation of multiple logit regressions by addition of categorical covariates to the linear predictor. In this study, three temperatures 10, 24, and 28°C and three photoperiods 8:16, 12:12, and 16:8 (light [L]:dark [D]) were tested. The average body weight of each treatment group (ten last instars in a Petri dish lined with filter paper) was used as the weight variable. Each experiment was replicated three or four times.

2331_C012.fm Page 156 Thursday, May 10, 2007 11:20 AM

156

Bioassays with arthropods, second edition

Figure 12.2 PoloEncore Output for Tattersfield and Potter Study Showing Likelihood Ratio Tests.

A. Statistical model The logit model that expresses the effect of the two categorical covariates (temperature and photoperiod) and two continuous covariates (dose and weight) is yij = α ij + β ij log10 ( d + d0 ) + γ ij log10 ( W )

(Model 1)

where yij is the logit of the probability of mortality, i = 1,2,3 corresponds with the three temperature levels and j = 1,2,3 corresponds with the three photoperiods. The term d is dose in μg, W is average body weight in milligrams, and d0 = 10a, with

2331_C012.fm Page 157 Thursday, May 10, 2007 11:20 AM

Chapter twelve: Binary quantal response

a = log 10 ( d0 ) = log 10 ( d1 ) −

157

d1 [log 10 ( d2 ) − log 10 ( d1 )] d2 − d1

and 0 < d1 <...< dI. This method for dealing with dose zero is discussed by Tukey et al.18 This model contains 27 = 3 × 3 × 3 parameters and is equivalent to fitting separate logit planes to each of the nine groups. Many models could be fitted to the data. For example, the logit plane yij = α ij + β log10 ( d + d0 ) + γ log10 ( W )

(Model 2)

with 11 parameters fits parallel logit planes to the nine groups. In this case, the slopes β and γ do not change when temperature, photoperiod, or both change. The logit line yij = α i + β i log10 ( d + d0 )

(Model 3)

with six parameters fits a model with no effects of weight or photoperiod. The slopes (βi) and the intercept (αi) depend on the three temperature levels but do not depend on the photoperiods (j = 1,2,3).

B. Hypothesis tests The first step in hypothesis testing consists of fitting the logit model as specified by Model 1. Next, the restricted models with fewer parameters (e.g., Models 2 and 3) are fitted. The LR test statistic is then calculated to test various hypotheses about the general Model 1 based on the difference in values of the maximum log likelihoods (or deviances) of various models. For example, the difference in the deviances of the models given by Models 1 and 2 can be used to test the hypothesis of parallelism of the logit planes. If the LR test statistic is larger than the corresponding value from a χ2 table, the hypothesis is rejected. The degrees of freedom for a particular test is the difference between the number of parameters for the models. Use of the P = 0.01 level of significance is appropriate because more than one hypothesis will usually be tested on the same data set. Testing at this low level will probably ensure that the overall P-value will not be greater than (1–0.99k), where k is the number of hypotheses tested. For example, if k = 5, then the overall P-value of the experiment will not be >0.049 (i.e., about 5%).

C. Search for the best-fitting dose-mortality model The LR test statistic can be used to search for the “best fitting” logit (or probit) plane, given the set of covariates (e.g., temperature, body weight)

2331_C012.fm Page 158 Thursday, May 10, 2007 11:20 AM

158

Bioassays with arthropods, second edition

recorded in the experiment. The search method consists of computing a sequence of logit planes starting with the model for separate planes given by Model 1, then fitting a model with a smaller subset of parameters at each consecutive step. The search is complete when any further reduction in the parameters produces a significant LR test statistic.

D. An example: acephate One of the pesticides that was tested in the temperature-photoperiod-dose-response experiment was acephate. Some of the data from this experiment are shown in Figure 12.3a. Under the “Temp” column, 1, 2, and 3 designate 10˚C, 24˚C, and 28°C, respectively. In the “Photo” column, 1, 2, and 3 designate photoperiods of 8:16, 12:12, and 16:8 (L:D), respectively. Figure 12.3b shows the commands for testing the various hypotheses; Figure 12.3c lists the information necessary for calculating the LR test statistics. Several hypotheses are of interest, as described below.

1. Significance of average body weight A test of this hypothesis involves comparison of the deviances for Model 1 and the model with the logit line yij = α ij + β ij log10 ( d + d0 )

(Model 4)

The differences in the deviances between the two models is 489.29 – 476.00 = 13.29 with 9 df (see Figure 12.3c). Therefore, the weight covariate does not appear to significantly affect response of the larvae to acephate (P = 0.16, where P is the probability of falsely rejecting the null hypothesis).

2. Parallelism of the logit lines The differences in the deviances between the model specified in Model 4 and the model for parallel logit lines given by yij = α ij + β log10 ( d + d0 )

(Model 5)

is 579.07 – 489.29 = 89.78 with 8 df (see Figure 12.3c). So, the logit lines are not parallel (P < 0.01). In this case, the slope of the logit line is affected by changing temperatures, photoperiods, or both.

3. Best-fitting logit line The model with the best-fitting logit curve is the logit line yij = α ij + β i log10 ( d + d0 )

(Model 6)

2331_C012.fm Page 159 Thursday, May 10, 2007 11:20 AM

Chapter twelve: Binary quantal response

159

Figure 12.3a Multiple Logit Analysis of Dose-Weight-Temperature-Photoperiod-Response Data with GLIM.

2331_C012.fm Page 160 Thursday, May 10, 2007 11:20 AM

160

Bioassays with arthropods, second edition

Figures 12.3b–c (continued)

In this model, the slope depends on temperature (i) but not on photoperiod (j). Estimates of the parameters in Model 6 are listed in lines 1 to 9 of Figure 12.3c. Values of the LD90 (Table 12.2) were calculated by LD90 = 10a where a = ( x − αˆ )/ βˆ and x = log e ( 0.0 / 0.1) = 2.197 and αˆ , βˆ are estimates of the parameters. For these experiments, the slope of the line is largest at the lowest temperature.

2331_C012.fm Page 161 Thursday, May 10, 2007 11:20 AM

Chapter twelve: Binary quantal response

161

Table 12.2 Estimates of LD90, Intercepts (α), and Slopes (β) for Western Spruce Budworm Held for Different Photoperiods (L:D) and Temperatures (°C) after Treatment with Acephate Temp.

L:D

α ± SE

β ± SE

LD90

10

8:16 12:12 16:8

–3.0 ± 0.3 –3.0 ± 0.3 –3.4 ± 0.3

5.9 ± 0.5 5.9 ± 0.5 5.9 ± 0.5

7.5 7.5 8.8

24

8:16 12:12 16:8

–1.1 ± 0.2 –1.8 ± 0.2 –1.5 ± 0.2

3.2 ± 0.3 3.2 ± 0.3 3.2 ± 0.3

10.8 18.2 14.1

28

8:16 12:12 16:8

–0.5 ± 0.2 –0.8 ± 0.2 –0.4 ± 0.2

2.3 ± 0.2 2.3 ± 0.2 2.3 ± 0.2

14.0 19.8 13.6

VII. Conclusions Quantal response bioassays with more than one explanatory variable are far more efficient than multiple, single variable experiments in demonstrating the effects of variables other than dose on response. Compared with a single experiment in which the significance of several variables is tested simultaneously, multiple, single variable experiments waste time, test subjects, and financial resources. Reliable computer programs—PoloEncore,10 GLIM,13 and BMDP11—are available for multiple regression analyses. Estimation can be done with categorical or continuous variables. Use of a user-friendly program such as PoloEncore10 is preferable for most users with no interest or skills in experimental statistics.

References 1. Robertson, J. L. and Preisler, H. K., Pesticide Bioassays with Arthropods, CRC Press, Boca Raton, FL, 1992. 2. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 3. Gast, R. T., The relationship of weight of lepidopterous larvae to effectiveness of topically applied insecticides, J. Econ. Entomol. 52, 1115, 1959. 4. Gast, R. T., Guthrie, F. E., and Early, J. D., Laboratory studies on Heliothis zea (Boddie) and H. virescens (F.), J. Econ. Entomol. 49, 408, 1956. 5. MacCuaig, R. D., Determination of the resistance of locusts to DNC in relation to their weight, age, and sex, Ann. Appl. Biol. 44, 634, 1956. 6. Way, M. J., The effect of body weight on the resistance to insecticides of last-instar larva of Diataraxia oleracea, the tomato moth, Ann. Appl. Biol. 41, 77, 1954. 7. Domencich, T. A. and McFadden, D., Urban Travel Demand, American Elsevier, New York, 1975.

2331_C012.fm Page 162 Thursday, May 10, 2007 11:20 AM

162

Bioassays with arthropods, second edition

8. Russell, R. M., Savin, N. E., and Robertson, J. L., POLO2: a user’s guide to multiple probit or logit analysis, USDA Forest Service Gen. Tech. Rep., PSW-55, 1981. 9. Maddala, G. S., Econometrics, McGraw-Hill, New York, 1977. 10. LeOra Software, PoloEncore, LeOra Software, 1007 B St., Petaluma, CA 94952, 2006. See http://www.LeOraSoftware.com. 11. Reichenbach, N. C. and Collins, W. J., Multiple logit analyses of temperature and humidity on the toxicity of propoxur to German cockroaches (Orthoptera: Blatellidae) and western spruce budworm (Lepidoptera: Tortricidae), J. Econ. Entomol. 77, 31, 1984. 12. Brown, M., ed., Biomedical Computer programs, P Series, University of California, Los Angeles, 1981. 13. Baker, J. R. and Nelder, J. A., The GLIM Manual: Release 3. Generalized Linear Interactive Modelling, Numerical Algorithms Group, Oxford, England, 1978. 14. Shapiro, M., Preisler, H. K., and Robertson, J. L., Enhancement of baculovirus activity on gypsy moth (Lepidoptera: Lyantriidae) by chitinase, J. Econ. Entomol. 80, 1113, 1987. 15. Tattersfield, F. and Potter C., Biological methods of determining the insecticidal values of pyrethrum preparations (particularly extracts of heavy oil), Ann. Appl. Biol. 30, 259, 1943. 16. Busvine, J. R., A Critical Review of the Techniques for Testing Insecticides, Commonwealth Agricultural Bureaux, London, 1971. 17. Apologies to the Nabisco Baking Company for this analogy. For the benefit of readers outside of the United States, an Oreo consists of a layer of white filling between two chocolate cookies (biscuits). 18. Tukey, J. W., Ciminera, J. L., and Heyse, J. F., Testing the statistical certainty of a response to increasing doses of a drug, Biometrics 41, 295, 1985.

2331_C013.fm Page 163 Wednesday, May 9, 2007 5:46 AM

chapter thirteen

Multiple explanatory variables: body weight The assumption that insects generally respond to toxicants in direct proportion to their body weight has led some investigators1,2 to compensate for effects of weight by proportionally adjusting doses to the weight of the test subjects during the application process. The adjustment—for example, the application of l μl/100 mg body weight—was (and unfortunately still is) used routinely. Results of experiments with locust species,3 and several species of lepidoptera,1,4 suggested that such dose adjustments were appropriate. But evidence that responses do not vary as simple functions of body weight was also described by Bliss5 and Way.6 The example with acephate in the previous chapter (12.IV) also indicates that body weight is not a significant variable in the dose-response regression. Such contradictory evidence, summarized first by Busvine7 and later by Robertson et al.8 should have alerted investigators about the possible significance of weight in the response of a particular arthropod species, and the fact that the significance of the weight variable should be tested before any adjustment is made. Yet many researchers do not do so, either because they do not know how or because weight adjustment has been used so often in the past. For example, Paula Maven does a complete search for just one entomologist’s publications. This scientist published the results of many pesticide bioassays, but those published after 1979 emphasize methods to deal with body weight as a variable. What about the papers before 1979? When Dr. Maven scans these reports,9–33 she finds that they all reflect the assumption that responses of insects are proportional to body weight. Quite simply, the investigator applied l μl/100 mg body weight no matter what the pesticide and regardless of the species being tested. Dr. Maven is slightly skeptical about proportional response occurring in orange tortrix (Argyrotaenia citrana [Fernald]) and western spruce budworm [Lepidoptera: Tortricidae]; California oakworm, Phryganidia californica Packard [Lepidoptera: Dioptidae]; forest tent caterpillar (Malacosoma disstria [Hübner]) and western tent caterpillar (M. californicum [Packard]) [Lepi-

163

2331_C013.fm Page 164 Wednesday, May 9, 2007 5:46 AM

164

Bioassays with arthropods, second edition

doptera: Lasiocampidae]; Symmerista canicosta Franclemont [Lepidoptera: Notodontidae]; elm spanworm (Ennomus subsignarius [Hübner]), western hemlock looper (Lambdina fiscellaria lugubrosa [Hulst]), and Calocalpe undulata (L.) [Lepidoptera: Geometridae]; Douglas-fir tussock moth, Orgyia pseudotsugata (McDunnough) [Lepidoptera: Lymantriidae]; pales weevil, Hylobius pales (Herbst)[Coleoptera: Curculionidae]; and western pine beetle, Dendroctonus brevicomis LeConte [Coleoptera: Scolytidae]. Before 1979, for example, response to approximately 300 different pesticides was proportional to body weight of western spruce budworm. After 1979, proportional response abruptly ceased. Was there something in trees that caused proportional response of western spruce budworm and all of the other species to occur only before 1979? A terpene or two? What else could account for this strange phenomenon? Simple: Dr. Maven concludes that this scientist was probably just following contemporary convention. Then she begins to wonder how many others still blindly follow one convention or another without thinking about what they are doing. She suspects that there may yet be quite a few. Well, at least she has not been so foolish. Anyone who has spent the time rearing arthropods in a laboratory culture or collecting them from a field population cannot afford to compromise the bioassay by not identifying and testing hidden assumptions in either the application method or in the data analysis. In particular, any a priori assumption about the role of body weight in response to pesticides must be avoided.

I. Effects of erroneous assumptions about body weight In Dr. Maven’s opinion, two publications should be required reading for any investigator who is doing a topical application bioassay. In the first report, the authors8 tested the hypothesis that response of western spruce budworm to mexacarbate, pyrethrins, or DDT is proportional to body weight. Different sampling methods, weight ranges, and dose adjustment procedures were compared for each chemical. Tolerance to mexacarbate and DDT appeared to increase roughly as a function of the square of body weight rather than as a simple proportion. In a few instances, tolerance to pyrethrins seemed to increase as a simple proportion of body weight. Mostly, however, the square of weight more adequately described the relationship between tolerance and weight. In the second report,34 the authors used the same data set to describe calculation of lethal doses and confidence intervals for insects of a given body weight. The calculations were based on multiple probit and logit regression techniques. Average, as well as individual, body weights were used. Effects of imposing the restriction that response is proportional to body weight were also examined. Finally, a general method for doing topical application experiments so that the role of body weight is tested (rather than assumed to be a particular function of response) was suggested. One of the conclusions of this investigation was that the unquestioned use of proportional adjustment of response for body weight may result in

2331_C013.fm Page 165 Wednesday, May 9, 2007 5:46 AM

Chapter thirteen: Multiple explanatory variables: body weight

165

erroneous inferences about relative toxicities. A crossover effect (see Figure 13.1) occurred. Lethal doses for the 60 mg weight class (the smallest group of western spruce budworm tested) were higher assuming proportional response than when no assumption was made, and lethal doses for the higher weight classes were generally lower assuming proportional response than when no assumption was made. This pattern thus suggests that, at lower body weights, use of proportional adjustment for body weight will indicate that a chemical is less toxic, and at higher weights that it is more toxic, than is actually the case. In addition, confidence limits for the lethal doses were generally larger when no assumption about proportional response was made. In essence, use of the proportional response adjustment appears to bias lethal dose estimates and give an overly optimistic impression of their precision. The results of this investigation with western spruce budworm certainly cannot be generalized to all other arthropods. Increased tolerance with increased weight, for example, was observed in the granary weevil, Sitophilus granarius (L.).35 Regardless, dose adjustment should never be used without testing the hypothesis that response is proportional to body weight. Grouping of test subjects tended to mask the absence of a proportional response in these experiments.34 Proportional response was rejected in 73% of the experiments in which individual insect data were used, but in only

30 Basic-grouped Basic-individual Proportional-grouped Proportional-individual

20

15

10

7 6 5 4 60

70

80

90

100

Figure 13.1 Estimated LD90s for DDT Applied to Last Instar Western Spruce Budworm in Experiments with Four Designs. From Savin et al.34

2331_C013.fm Page 166 Wednesday, May 9, 2007 5:46 AM

166

Bioassays with arthropods, second edition

44% of the experiments in which grouped data were used. In practice, a bioassay in which individual test subjects are weighed are rare because they are so costly and time-consuming. So, when group weights (such as the average weight of 10 test subjects in a Petri dish) are used to test the hypothesis of proportional response, results must be viewed with caution if the hypothesis is not rejected. Finally, these authors suggest that the most prudent procedure is use of a convenient uniform application volume such as 1 μl. The hypothesis of proportionality can then be tested by simply including body weight as an additional variable in the multiple probit or logit regression.

II. Testing the hypothesis of proportional response The model with dose and weight and covariates (i.e., proportional response) is y = δ0 + δ1 log( D) + δ2 log( W )

(13.1)

where y = the probit or logit of the response, D = dose, and W = weight. If β0 = δ0, β1 = δ1, and β2 = δ1 + δ2, Equation 13.1 can be rewritten as y = β0 + β1 log( D / W ) + β 2 log W

(13.2)

The hypothesis of proportionality is H: β2 = 0. The hypothesis that assumes proportional response is (13.3)

y = β0 + β1 log( D / W )

The hypothesis of proportional response is rejected at the P = 0.05 significance level if the likelihood ratio (LR) statistic LR = 2[L(Ω) – L(ω)] > χα

2

where L(Ω) is the maximum log likelihood for Equation 13.2 and L(ω) is the maximum log likelihood for Equation 13.3. The test statistic LR can be calculated after fitting Equations 13.2 and 13.3 with any of the computer programs (PoloEncore,36 GLIM,37 BMDP38) mentioned in Chapter 12, “Binary Quantal Response with Multiple Explanatory Variables.” In PoloEncore, calculations for this hypothesis test are done when the options shown in Figures 13.2a–13.2c are chosen. Figure 13.3 shows the results for Dr. Maven’s data for wicked witches analyzed with PoloEncore. Lines 7–18 summarize the data file and list the parameters in the full (four-parameter) model. Besides the constant term,

2331_C013.fm Page 167 Wednesday, May 9, 2007 5:46 AM

Chapter thirteen: Multiple explanatory variables: body weight

167

Figure 13.2a PoloEncore Options for the Proportional Response Hypothesis Testing and for Confidence Limits and Lethal Doses (LDs) for Specified Weights.

the full model include natural response, logarithmic transformations of body weight, and logarithmic transformations of dose divided by weight (dose over weight, or D over W). Parameter values (lines 31–33), their standard errors (lines 35–37) , and values of each t-ratio (parameter value ÷ S.E.) (lines 39–41) follow. (If the value of a t-ratio for any term is below the critical value of 1.96, it is not significant in the regression.) The prediction success table (lines 50–58) lists the number of individual test subjects that were predicted to respond and that actually did so, predicted to respond but that actually did not, predicted to be unresponsive and that actually responded, and predicted to be unresponsive and that actually were unresponsive. These groups are listed in increments of 0.00 to 0.50 and 0.50 to 1.00. These numbers are calculated by using maximum probability as a criterion.39 Results of the LR test of the hypothesis are given next, in lines 60–64. The value of χ2 (=106.227) indicates that the hypothesis that the logarithm

2331_C013.fm Page 168 Wednesday, May 9, 2007 5:46 AM

168

Bioassays with arthropods, second edition

Figure 13.2b (continued)

of body weight and the logarithm of dose over weight are significant variables in the response. The LR statistic for the test of proportional response is LR = 2[L(Ω) – L(ω)] = 2[–94.9087 + 99.4885] = 2[4.5788] = 9.160. Dr. Maven rejects the hypothesis of proportionality because the critical value for χ2 at the 0.05 significance level is 3.84. She can also reject the hypothesis on the basis of the t-ratio for β2 (= –2.92). These results indicate that she cannot justify adjustment for dose by body weight, and that she should use the model with weight and dose as independent variables for her analyses. The hypothesis can also be tested with the t-ratio for β2. If the hypothesis is not rejected, LD50 and LD90 estimates can be obtained for any body weight desired. If the hypothesis is rejected, two options are available as described in the next section.

2331_C013.fm Page 169 Wednesday, May 9, 2007 5:46 AM

Chapter thirteen: Multiple explanatory variables: body weight

169

Figure 13.2c (continued)

III. When body weight is a significant independent variable If the hypothesis of proportional response has been tested and rejected, another model can be used to estimate selected lethal doses at specific body weights. The model for body weight and dose as independent variables8,34 is: y = δ0 + δ1 (log D) + δ2 (log W ) For W = W*, where W* is a specified weight, the equation can be rewritten as y = A + B(log D)

(13.4)

2331_C013.fm Page 170 Wednesday, May 9, 2007 5:46 AM

170

Bioassays with arthropods, second edition

Figure 13.3 PoloEncore Results of Calculations Produced by Options Chosen in Figures 13.2a–13.2c.

2331_C013.fm Page 171 Wednesday, May 9, 2007 5:46 AM

Chapter thirteen: Multiple explanatory variables: body weight

Figure 13.3 (continued)

171

2331_C013.fm Page 172 Wednesday, May 9, 2007 5:46 AM

172

Figure 13.3 (continued)

Bioassays with arthropods, second edition

2331_C013.fm Page 173 Wednesday, May 9, 2007 5:46 AM

Chapter thirteen: Multiple explanatory variables: body weight

Figure 13.3 (continued)

173

2331_C013.fm Page 174 Wednesday, May 9, 2007 5:46 AM

174

Figure 13.3 (continued)

Bioassays with arthropods, second edition

2331_C013.fm Page 175 Wednesday, May 9, 2007 5:46 AM

Chapter thirteen: Multiple explanatory variables: body weight

175

where A = δ0 + δ2 (log W * ) and B = δ1 . Equation 13.4 can be used to estimate the lethal dose for body weight W* by simple linear regression. Confidence limits for the lethal dose, given body weight W*, can then be calculated because A and B are linear functions of the original coefficients δ0, δ1, and δ2. Details of the calculations involved are described by Savin et al.34 and by LeOra Software.36 The multiple regression equation for Dr. Maven’s wicked witch data is y = 15.9899 + 3.3068(log D) – 7.1859(log W) (see Figure 13.3, line 124). Lines 158–281 in Figure 13.3 list the lethal dose estimates for wicked witches of average weight (77.3671 mg) and the body weights that Dr. Maven has specified (60, 70, 80, 90, and 100 mg). For each weight class, the first line shows the weight and the logarithm of weight to the base 10. Values of parameters, standard errors, and covariances of the parameters are listed next (e.g., lines 161–72). Values of g and t, used to calculate confidence limits for point estimates on the probit or logit line, appear next (e.g., line 174). Finally, values of the lethal dose necessary for 50% and 90% mortality at each weight, together with their 95% confidence limits, are listed (e.g., lines 175–76). Results for each weight specified are given in the same format.

IV. Standardized bioassay techniques involving weight Use of insects in a very narrow weight range has been recommended in standardized tests for resistance (or relative susceptibility) of the Heliothis species.40 This recommendation has some merit because it helps ensure uniformity among different investigators testing different test subjects in different laboratories. However, the concomitant recommendation that results should be reported in units proportional to body weight is fallacious. For Heliothis species, LD50s are to be presented in standard units of μg/g of larval weight. Yet the hypothesis of proportionality has never been tested. Such recommendations simply perpetuate the erroneous assumption that response is proportional to body weight. Depending on the purpose of the study, body weight can be included in an experiment in several ways, but never when the pesticide is applied. Instead, a uniform application volume such as 1μl per insect should be used. A narrow weight range might be also used with this uniform application volume. Because weight does not differ among test groups, it can be ignored in estimating dose-mortality regressions. Even in studies of resistance, however, use of a narrow weight range may be impossible even under highly controlled conditions. If so, then test subjects must be weighed individually if valid and meaningful comparisons between or among responses are to be made. For example, Robertson et al.41 compared responses of lightbrown apple moth, Epiphyas postvittana (Walker), strains that were resistant and susceptible to azinphosmethyl. Both strains were reared on apple, gorse,

2331_C013.fm Page 176 Wednesday, May 9, 2007 5:46 AM

176

Bioassays with arthropods, second edition

broom, blackberry, or a general-purpose diet. Larvae on natural plant foliage, especially those on blackberry, were smaller than larvae on general purpose diet. One result of bioassays was that responses of resistant larvae from blackberry were similar to responses of susceptible larvae from general purpose diet. The average weight of larvae from blackberry was 18 mg, while the average weight of larvae from general purpose diet was 30 mg. Did the difference in response result from the difference in body weight, or was its effect related to the host plant?

V. Conclusions To date, the most important application of multiple regression techniques (multiple probit or logit analysis) to pesticide bioassays has been examination of the role of body weight in response.8,34 Results of these investigations showed that the unquestioned use of proportional adjustment of dose to body weight may result in erroneous inferences about relative toxicities. Regardless of the arthropod species tested, the hypothesis that body weight must be tested before response is expressed in terms of body weight. Adjustments for weight should never be made when a pesticide is applied. Finally, standardized protocols for tests of pesticide resistance must be changed so that response is not expressed in terms of body weight. Instead, response should be expressed on a per insect basis. Either test subjects should be selected within a very narrow weight range, or they should be weighed individually or in groups of uniform size.

References 1. Gast, R. T., Guthrie, F. E., and Early, J. D., Laboratory studies on Heliothis zea (Boddie) and H. virescens (F.), J. Econ. Entomol. 49, 408, 1956. 2. Metcalf, R. L., Methods of topical application and injection, in Shepard, H. H., ed., Methods of Testing Chemicals on Insects, Burgess Publishing Co., Minneapolis, MN, 1958, p. 92. 3. MacCuaig, R. D., Determination of the resistance of locusts to DNC in relation to their weight, age, and sex, Ann. Appl. Biol. 44, 634, 1956. 4. Gast, R. T., The relationship of weight of lepidopterous larvae to effectiveness of topically applied insecticides, J. Econ. Entomol. 52, 1115, 1959. 5. Bliss, C. I., The size factor in the action of arsenic upon silkworm larvae, J. Exp. Biol. 13, 95, 1936. 6. Way, M. J., The effect of body weight on the resistance of insecticides of last-instar larva of Diataraxia oleracea, the tomato moth, Ann. Appl. Biol. 41, 77, 1954. 7. Busvine, J. R., A Critical Review of the Techniques for Testing Insecticides, Commonwealth Institute of Entomology, London, 1971. 8. Robertson, J. L., Savin, N. E., and Russell, R. M., Weight as a variable in the response of western spruce budworm to insecticides, J. Econ. Entomol. 74, 643, 1981.

2331_C013.fm Page 177 Wednesday, May 9, 2007 5:46 AM

Chapter thirteen: Multiple explanatory variables: body weight

177

9. Schwartz, J. L. and Lyon, R. L., Laboratory culture of orange tortrix and its susceptibility to four insecticides, J. Econ. Entomol. 63, 1788, 1970. 10. Schwartz, J. L. and Lyon, R. L., Contact toxicity of five insecticides to California oakworm reared on artificial diet, J. Econ. Entomol. 64, 146, 1971. 11. Lyon, R. L., Brown, S. J., and Robertson, J. L., Contact toxicity of sixteen insecticides applied to forest caterpillars reared on artificial diet, J. Econ. Entomol. 65, 928, 1972. 12. Robertson, J. L., Lyon, R. L., Shon, F. L., and Gillette, N. L., Contact toxicity of 20 insecticides to Symmerista canicosta, J. Econ. Entomol. 65, 1560, 1972. 13. Robertson, J. L. and Lyon, R. L., Western spruce budworm: nonresistance to Zectran, J. Econ. Entomol. 66, 801, 1973. 14. Robertson, J. L. and Lyon, R. L., Elm spanworm: contact toxicity of 10 insecticides to larvae, J. Econ. Entomol. 66, 627, 1973. 15. Robertson, J. L. and Gillette, N. L., Western tent caterpillar: contact toxicity of 10 insecticides applied to the larvae, J. Econ. Entomol., 66, 629, 1973. 16. Robertson, J. L. and Lyon, R. L., Douglas-fir tussock moth: contact toxicity of 20 insecticides applied to the larvae, J. Econ. Entomol. 66, 1255, 1973. 17. Robertson, J. L., Page, M., and Gillette, N. L., Calocalpe undulata: contact toxicity of 10 insecticides to the larvae, J. Econ. Entomol., 67, 706, 1974. 18. Robertson, J. L., Lyon, R. L., and Gillette, N. L., Contact toxicity of 38 insecticides to pales weevil adults, J. Econ. Entomol. 68, 124, 1975. 19. Page, M. and Robertson, J. L., Western spruce budworm, bioactivity of mexacarbate during storage, Insecticide Acaricide Tests 1, 104, 1975. 20. Savin, N. E., Robertson, J. L., and Russell, R. M., A critical evaluation of bioassay in insecticide research: likelihood ratio tests of dose-mortality regression, Bull. Entomol. Soc. Am. 23, 257, 1977. 21. Robertson, J. L., Boelter, L. M., and Gillette, N. L., Laboratory tests of insecticides on western spruce budworm, 1974-76, Insecticide Acaricide Tests 2, 110, 1977. 22. Russell, R. M., Robertson, J. L., and Savin, N. E., POLO: a new computer program for probit analysis, Bull. Entomol. Soc. Am. 23, 209, 1977. 23. Robertson, J. L., Gillette, N. L., Lucas, B. A., Savin, N. E., and Russell, R. M., Comparative toxicity of insecticides to Choristoneura species, Can. Entomol. 110, 399, 1978. 24. Robertson, J. L., Boelter, L. M., Russell, R. M., and Savin, N. E., Variation in response to insecticides by Douglas-fir tussock moth, Orgyia pseudotsugata (Lepidoptera:Lymantriidae), populations, Can. Entomol. 110, 325, 1978. 25. Robertson, J. L., Laboratory tests of insecticides on western spruce budworm, Insecticide Acaricide Tests 3, 148, 1978. 26. Robertson, J. L. and Gillette, N. L., Contact toxicity of insecticides to western pine beetle, Insecticide Acaricide Tests 3, 147, 1978. 27. Robertson, J. L., Crisp, C. E., and Look, M., Toxicity of O,0-dimethyl 2,2,2-trichloro-1-hydroxyethyl phosphonate and its acyloxy and vinyl derivatives, Insecticide Acaricide Tests 3, 144, 1978. 28. Robertson, J. L. and Boelter, L. M., Toxicity of insecticides to Douglas-fir tussock moth Orgyia pseudotsugata (Lepidoptera: Lymantriidae): I. Contact and feeding toxicity, Can. Entomol. 111, 1145, 1979.

2331_C013.fm Page 178 Wednesday, May 9, 2007 5:46 AM

178

Bioassays with arthropods, second edition

29. Stock, M. W. and Robertson, J. L., Differential response of Douglas-fir tussock moth, Orgyia pseudotsugata (Lepidoptera: Lymantriidae), populations and sibling groups to acephate and carbaryl: toxicological and genetic analyses, Can. Entomol. 111, 1231, 1979. 30. Robertson, J. L. and Kimball, R. A., Toxicities of topically applied insecticides to western spruce budworm, Insecticide Acaricide Tests 4, 174, 1979. 31. Robertson, J. L. and Kimball, R. A., Effects of insect growth regulators on western spruce budworm (Choristoneura occidentalis) (Lepidoptera: Tortricidae): I. Lethal effects of the last instar treatments, Can. Entomol. 111, 1361, 1979. 32. Robertson, J. L. and Kimball, R. A., Toxicities of topically applied insecticides to western spruce budworm, 1979, Insecticide Acaricide Tests 5, 203, 1980. 33. Robertson, J. L. and Kimball, R. A., Toxicities of insecticides to Douglas-fir tussock moth, 1979, Insecticide Acaricide Tests 5, 202, 1980. 34. Savin, N. E., Robertson, J. L., and Russell, R. M., The effect of body weight on lethal dose estimates for the western spruce budworm, J. Econ. Entomol. 75, 538, 1982. 35. Lavadinho, A. M. P., Toxicological studies on adult Sitophilus granarius (L.). Influence of individual body weight on the susceptibility to DDT and malathion, J. Stored Prod. Res. 12, 215, 1976. 36. LeOra Software, PoloEncore and PoloEncore User’s Guide, 1007 B St., Petaluma, CA 94952, 2007. See http://www.LeOraSoftware.com. 37. Baker, J. R. and Nelder, J. A., The GLIM Manual: Release 3. Generalized Linear Interactive Modelling, Numerical Algorithms Group, Oxford, England, 1978. 38. Brown, M., ed., Biomedical Computer Programs, P Series, University of California, Los Angeles, 1981. 39. Domencich, T. A. and McFadden, D., Urban Travel Demand, American Elsevier, New York, 1975. 40. Anonymous, Standard method for detection of insecticide resistance in Heliothis zea (Boddie) and H. virescens (F.), Bull. Entomol. Soc. Am. 16, 147, 1970. 41. Robertson, J. L., Armstrong, K. F., Suckling, D. M., and Preisler, H. K., Effects of host plants on toxicity of azinphosmethyl to susceptible and resistant light brown apple moth (Lepidoptera: Tortricidae), J. Econ. Entomol. 83, 2124, 1990.

2331_C014.fm Page 179 Wednesday, May 9, 2007 5:47 AM

chapter fourteen

Polytomous (multinomial) quantal response Ugly rumors have been circulating in Schaeferville. Bluehaired matrons at the drugstore whisper behind Paula Maven’s back and shake their heads in dismay as she pays for her ibuprofen (Dr. Maven now has chronic headaches and excruciating neck pain, the direct results of long hours of work at her computer screen performing online literature searches). Usually chatty, the clerk at the market now grabs Paula’s money without a word. Her acquaintances and neighbors outside the university, including Ernestine Feasor, shun her. To all of these slights Dr. Maven is oblivious because she is so preoccupied with the complexities of experiments with wicked witches. Blanche St. James, however, has noticed the difference both in the number of phone calls to their lab asking for advice about pests of tomatoes and when they go out to lunch at the local taco stand: no one even bothers to say hello to Dr. Maven. Blanche calls Paula’s mother-in-law Hilda to ask what is going on, and Hilda Maven promises to do some detective work; she discovers the source of the problem when her daughter-in-law becomes the subject of the Sunday pastoral prayer at the senior Maven’s church. “They’re accusing you of being a recruiter for a strange cult that practices polygamy. The preacher called it the Cult of Polygamous Logits. Not only that, people are afraid that you’re raising those giant wicked witches so that some day you can set them loose on the streets of Schaeferville. What are you and my son up to?” Dr. Maven is stunned. Then she remembers that a few weeks earlier she had done a literature search on polytomous logits and multinomial logits and accidentally left the printout on Ernestine’s front porch along with printed instructions on management of hazardous materials. She suspects that Ernestine misunderstood what she should have not been reading in the first place. And sure enough, all that Ernestine gleaned from Dr. Maven’s output was “polygamous logit.” Well, that must have been quite enough to start the juicy gossip. That and Dr. Maven’s preoccupation with what Miss Feasor calls “those disgusting giant varmints.”

179

2331_C014.fm Page 180 Wednesday, May 9, 2007 5:47 AM

180

Bioassays with arthropods, second edition

I. Example Once mother-in-law Maven has set the town straight, Paula and Blanche begin a study that involves a far more complicated experimental design and statistical analysis than the binary or multiple quantal response analyses that they have done before. This time Blanche treats the wicked witches with each of several juvenile hormone analogues (JHAs). Males and females are treated as separate groups. Not only does the chemical cause some larvae to die, but it causes some to develop into abnormal pupae that die, some into pupae that form adults with major morphological abnormalities, and some into normal pupae which in turn form adults with minor abnormalities. In this experiment, the explanatory variables are concentration of the JHA and sex, but multiple response variables (i.e., the various effects caused by the hormone) are also present. Dr. Maven carefully records the following effects as possible results from treatment of wicked witches with each JHA: 1. Died as larva before metamorphosis, or in transition between larval and pupal stages. 2. Pupa malformed, died before or during larval-pupal ecdysis. 3. Pupa malformed, adult with major morphological abnormalities. 4. Pupa malformed, adult normal or with only minor morphological abnormalities. 5. Pupa normal, but died before or during pupal-adult ecdysis. 6. Pupa normal, but adult had major morphological abnormalities. 7. Pupa normal, adult normal or with only minor abnormalities. Just as polytomous logit analysis presents a problem of homonymy for the hearing impaired, polytomous (or multinomial) quantal response bioassays present a problem for most biologists who are not familiar with the statistical methods involved in data analyses. Many investigators collect information about the multiple effects that occur after treatment with classes of pesticides such as JHAs or benzoyl phenylureas, but then do not know how to analyze their data. Either the data remain unanalyzed, or the information is collapsed into a binomial structure (dead versus alive) to facilitate use of regular binary probit or logit analysis. Doing an experiment without knowing how the data will be analyzed might be called the Scarlett O’Hara method of experimental design.1 In the case of a polytomous quantal response bioassay, a Scarlett O’Hara design is understandable because only a few examples of analyses of polytomous data are available in the biological literature. Finney2 has described statistical methods for analysis of multiple classification data; the data set used was that of Gurland et al.,3 in which insects exposed to guthion residues were classified as dead, moribund, or alive. The situation with three possible outcomes represents the simplest case for which the polytomous model is appropriate.

2331_C014.fm Page 181 Wednesday, May 9, 2007 5:47 AM

Chapter fourteen: Polytomous (multinomial) quantal response

181

Hughes et al.4 have described multinomial logit analyses of a large data set in which effects of three types of chemicals on western spruce budworm were compared. More recently, very large data sets collected in the course of studies of chemicals in the environment have also been analyzed by principal response curves,5 which are a form of principal components analysis.6,7 However, Dr. Maven is totally bewildered by the statistical methods described in these sources. In desperation, she once again calls Garland Tarleton for help. Dr. Tarleton, who has heard the rumors of about the polygamous logit cult, immediately informs Paula that he would like to join. After Paula straightens out that little matter, she asks for help. Dr. Tarleton suggests a procedure that Dr. Maven can use to analyze her data.8 Because a program that is user friendly to the biologist has yet to be developed, she will have to use an experimental statistical program for the analysis.

II. The multinomial logit model A sample data set from Dr. Maven’s experiments is shown in Table 14.1. The wicked witches were topically treated with increasing concentrations of the JHA hydroprene in acetone; males and females were tested separately. Each insect responded in one of K categories (i.e., one of the seven effects that Blanche recorded). The statistical analysis will first test whether any of the covariates significantly affect the response. For Dr. Maven’s problem, the covariates are sex and JHA concentration. Next, the analysis will calculate Table 14.1 Sample Data Set for Male or Female Wicked Witches Exposed to the Insect Growth Regulator Hydroprene, Showing the Number of Responses in Each Category, by Sex and Concentration. Sex

Concentration

1

2

Response category 3 4 5 6

7

Total

Male

0 0.1 1.0 10.0

2 8 10 26

0 1 5 11

0 0 3 2

0 0 13 6

5 14 19 51

6 10 3 4

87 63 32 6

100 96 85 106

Female

0 0.1 1.0 10.0

4 8 6 18

0 2 6 11

1 0 1 8

0 0 4 12

5 13 17 31

19 21 14 10

69 43 37 19

98 87 85 109

Note: Response categories are: (1) dead larva; (2) malformed, dead pupa; (3) malformed pupa that developed into an adult with major abnormalities; (4) malformed pupa that developed into a normal adult; (5) normal pupa that died before adult emergence; (6) normal pupa that developed into an adult with major abnormalities; and (7) normal pupa that developed into a normal adult.

2331_C014.fm Page 182 Wednesday, May 9, 2007 5:47 AM

182

Bioassays with arthropods, second edition

estimates of the conditional probabilities of response for each of the seven categories.

A. Statistical model In Dr. Maven’s experiment with one continuous variable (concentration) and a categorical covariate (sex), the probability that an insect responds in state k is modeled by: e

qijk =

y ijk

(14.1)

K −1

1+

∑e

y ijk

k =1

where yijk = α jk + β jk log( di + d0 )

(14.2)

and in which qijk is the probability of response in state k at concentration di and covariate j (if the covariate is sex, then j = 1,2 for males and females, respectively); where αjk are the intercepts (one for each state and sex), βj are the slopes (one for each state and sex); and where do = 10a, with

a = log( d0 ) = log( d i ) −

d1 ⎡log( d2 ) − log( d i ) ⎦⎤ d2 − d1 ⎣

(14.3)

and 0 < d1 < d2 < ... < di. The use of Equation 14.2 as a method for dealing with dose zero is discussed by Tukey et al.9 The number of responses, rijk, out of the total nij treated with the concentration di, are used to estimate the parameters in Equation 14.3. The vector (rij1,...,rijK) has a multinomial distribution with probabilities of response in state k given by (qij1,…,qijK).

B. Estimation of parameters For estimation of Equation 14.2, rijk equals the number of insects in category ij (i.e., of covariate j that have been treated with dose di) that responded with effect k. The vector (rij1,...,rijK) has a multinomial distribution. Estimation of the parameters in a multinomial model can be done using the software package R.10 The program (multinom) that will run multinomial analyses in R must first be downloaded from the nnet (Neural Network) library (e.g., http://web.csb.ias.edu.library/nnet/html/multinom.html. multinom can be used to estimate the parameters in Equation 14.1 and compute maximum values of likelihood functions. The significance of covariates such as sex can then be tested with likelihood ratio tests.

2331_C014.fm Page 183 Wednesday, May 9, 2007 5:47 AM

Chapter fourteen: Polytomous (multinomial) quantal response

183

C. Data analysis Analysis of the data with R is shown in Figures 14.1–14.3. The data are listed in Figure 14.1. Column 1 is “Sex,” column 2 is “Dose,” and columns 3 to 9 are the responses. Figure 14.2 shows the R commands for reading the data, testing the hypotheses of equality, and producing estimates of the probabilities of response. In line 6, do= 0.077 is the solution to Equation

Figure 14.1 Data from Table 14.1 Prepared for the R Analysis.

Figure 14.2 The R Commands for Reading the Data, Testing Hypotheses, and Estimating Probabilities of Response.

2331_C014.fm Page 184 Wednesday, May 9, 2007 5:47 AM

184

Bioassays with arthropods, second edition

Figure 14.3 The Output from Running the Commands shown in Figure 14.2.

14.3. Figure 14.3 is the output from running the commands in Figure 14.2. At the end of line 7 under the column headed “Pr(Chi)” is the number 1. This is the P value for testing the hypothesis of equality of male and female lines. The P value is greater than the critical value for χ2 at the 5% level,

2331_C014.fm Page 185 Wednesday, May 9, 2007 5:47 AM

Chapter fourteen: Polytomous (multinomial) quantal response

185

so the hypothesis that the logit lines for males and female wicked witches are equal cannot be rejected. Because responses of males and females are not significantly different, parameters of the model without sex as a variable are computed next (see Figure 14.2, line 10). Estimates of the parameters with their standard errors are listed in Figure 14.3, lines 11–27. Lines 13–18 show the estimate for the intercepts k and slopes for the states 2–7. The corresponding standard error values are shown in lines 22–27. No values are given for state 1 because the multinomial probabilities are such that qij1 = 1 – (qij2 + qij3 + … + qijK ). This means that probabilities for state 1 are obtained by summing the probabilities for all other states and subtracting the result from 1. The sum of the multinomial probabilities over all states equals 1, a consequence of the fact that an insect has to be in one of the seven states. The model with the fewest parameters and that describes the data adequately (i.e., same slope and intercept for male and female) produces parameter values that are used to calculate the probabilities in Figure 14.3, lines 33–36. According to this analysis, the probability of a wicked witch being seriously malformed as an adult (state 6) does not seem to be related to the concentration of hydroprene applied. Dr. Maven concludes that some other factor besides hydroprene must be responsible for the other malformations, but she will have to design other experiments to identify the causes. Dr. Maven is also interested in other probabilities, among them whether the probability of a malformed pupa increases with increased concentration of hydroprene. Such probabilities can be calculated from the conditional probabilities (see Figure 14.3, lines 33–36); by adding the values in columns 2, 3, and 4, Dr. Maven finds that the probability of a malformed pupa increases with concentration (for concentration 0.1, P = 0.036; for concentration 1.0, P = 0.11; for concentration 10, P = 0.262).

III. Conclusions Use of the polytomous (multinomial) model permits quantification of effects that are masked by collapsing all effects into a binary model in which dead or alive are the only categories (e.g., Robertson and Kimball11); it also permits estimation of individual dose-response probit lines for each effect.12 Polytomous quantal response analyses are more informative, especially for data that concern the effects of JHAs or other chemicals that are not classic poisons. As discussed by Hughes et al.,4 polytomous analyses are also well-suited to studies of chemical modes of action. Among the reasons that this type of quantal response analysis has not been widely used in investigations with pesticides, the most important is probably the limited number of examples readily understandable to biological scientists. Another important deterrent has been the availability of few computer programs that can perform the required analyses. One such program was shown above. Using the multinomial program in R, we were able to analyze polytomous data without having to collapse the categorical

2331_C014.fm Page 186 Wednesday, May 9, 2007 5:47 AM

186

Bioassays with arthropods, second edition

effects. A user-friendly, well-documented polytomous probit or logit computer is needed for routine use by biologists.

References 1. "I'll think of it all tomorrow...I can stand it then. Tomorrow, I'll think of some way..." from Mitchell, M., Gone with the Wind, 14th printing, Avon, New York, 1936, p. 1024. 2. Finney, D. J., Probit Analysis, Cambridge University Press, Cambridge, England, 1971. 3. Gurland, J., Lee, I., and Dahm, P. A., Polychotomous quantal response in biological assay, Biometrics 16, 382, 1960. 4. Hughes, G. A., Robertson, J. L., and Savin, N. E., Comparison of chemical effectiveness by the multinomial logit technique, J. Econ. Entomol. 80, 18, 1987. 5. van den Brink, P. J. and Ter Braak, C. J. F., Principal response curves: analysis of time-dependent multivariate responses of biological community to stress, Environ. Toxic. Chem. 18, 138, 1999. 6. Ter Braak, C. J. F., Ordination, in Jongman, R. G. H., Ter Braak, C. J. F., and van Tongeren, O. F. R., eds., Data Analysis in Community and Landscape Ecology, Cambridge University Press, Cambridge, England, 1995, pp. 91-173. 7. Jolliffe, I. T., Principal Component Analysis, Springer-Verlag, New York, 1986. 8. This method has permitted the analysis of a huge body of data about JHA effects that has been sitting in my archives for over 15 years. 9. Tukey, J. W., Ciminera, J. L., and Heyse, J. F., Testing the statistical certainty of a response to increasing doses of a drug, Biometrics 41, 295, 1985. 10. See http://www.r-project.org. R version 1.9.1 was released on June 21, 2004. 11. Robertson, J. L. and Kimball, R. A., Effects of insect growth regulators on the western spruce budworm (Choristoneura occidentalis) (Lepidoptera: Tortricidae). I. Lethal effects of last instar treatments, Can. Entomol. 111, 1361, 1979. 12. For example, Granett, J., Juvenile hormone toxicity to laboratory reared gypsy moth larvae, Prothetria dispar (Lepidoptera: Lymantriidae), Can. Entomol. 106, 695, 1974.

2331_C015.fm Page 187 Wednesday, May 9, 2007 5:47 AM

chapter fifteen

Improving prediction based on dose-response bioassays What has Paula Maven gleaned from her basic education in the subject of dose-response bioassays? She has learned the statistical definitions of a dose response with one variable and all of the ways in which this type of linear regression can be used for special purposes such as quarantine statistics, evaluation of the quality of microbial products, and studies of pesticide resistance. Data from bioassays involving time or more than one chemical applied together (i.e., mixtures) represent more elaborate regressions because they include more than one explanatory variable. The most complex regressions to solve involve both multiple explanatory variables and multiple response variables. In the course of her education, Paula has found that computer programs can range from undocumented, experimental statistical programs with no instructions to well-documented and user-friendly programs with user’s guide. Biologists need more of the latter. In their absence, large computer packages such as Stata1 contain large libraries of programs that should be adaptable for many purposes. The problems that Paula has studied all concern estimation of response of laboratory populations. Precise estimation of response in a bioassay can be ensured by use of adequate sample sizes, careful attention to dose placement, and careful attention to sound experimental design. Any estimate from a laboratory bioassay analyzed by standard statistical models is experiment-specific because it does not predict the results of a future experiment. Prediction statistics have been used in econometrics2 and studies of travel demand3 for many years; their use in ecotoxicology4 emphasizes effects of human activities on the environment. Available statistical methods for prediction4 should be used, adapted, and, where necessary, developed for routine use in toxicological studies with invertebrates and other organisms besides humans.

187

2331_C015.fm Page 188 Wednesday, May 9, 2007 5:47 AM

188

Bioassays with arthropods, second edition

Robertson and Worner5 have examined attempts to make laboratory bioassays realistic predictors of effects in terms of natural populations and explained why such attempts have failed. Finally, they suggest a new approach—population toxicology—that should provide more reliable predictions. In the past, one way to attempt realistic prediction was definition of separate aspects of pesticide effectiveness, followed by attempts to synthesize results into overall estimates of effectiveness on a population. Robertson and Haverty,6 for example, defined effects by ingestion and contact, residual toxicities, and rainfastness in experiments with western spruce budworm. They then devised a scoring system based on these four factors and predicted field effectiveness. Later field trials showed that efficacy of two of the six pesticides had been grossly overestimated and efficacy of another pesticide had been grossly underestimated.7 An underlying problem in the multiple bioassay approach is that the relative importance of separate aspects of pesticide effectiveness in overall efficacy is unknown. For example, is contact toxicity as important as toxicity by ingestion when chemical Y is applied to a population of western spruce budworm? The answer to both questions is that no one knows because relative importance has not been quantified. One definition of optimal time of application is the time during population development when a treatment will achieve maximum effect with minimum active ingredient. Early attempts to identify optimal time consisted of simple empirical estimates. First, the chemical was applied to each developmental stage (selected to be of uniform ages within the stage) and effects on each stage was estimated. Based on relative toxicities (e.g., LD50 stage X ÷ LD50 most susceptible stage), an empirical estimate of optimal time was made. For example, if chemical X was most toxic to second instars, optimal time of application would be when a population consisted mainly of second instars.8,9 Haverty and Robertson10 used a more refined procedure that was based on instar distribution of a small number of western spruce budworm over time. Not only was the sample size small (n = 100), but larvae were reared individually on artificial diet under highly controlled laboratory conditions. Next, Robertson et al.11 developed a contour plot procedure to estimate optimal time of application. Another consideration may be the use of insects reared on artificial diets. Even if a bioassay predicted efficacy at the population level for a species fed artificial diet, would the predictive value of results be relevant to a population of the same species feeding on natural hosts? Evidence reviewed by Rose et al.12 suggests that that answer might be no. For phytophagous insects, evidence that responses to toxicants are significantly affected by host plant species or quality continues to accumulate. A new approach is clearly needed for laboratory bioassays to approximate responses likely to occur in a field population. Robertson and Worner5 suggest that population response, rather than response of individuals selected for their uniform characteristics, must be emphasized. Researchers have probably not considered a population approach to laboratory bioassays

2331_C015.fm Page 189 Wednesday, May 9, 2007 5:47 AM

Chapter fifteen: Improving prediction based on dose-response bioassays

189

because definition of population age is difficult and analyses of results for anything beside instar categories of uniform age and weight present another problem. Numerous methods to define the physiological age distribution of a population have been described. These range from simple degree-day approaches to complex distributional models.13,14 While the accuracy of these methods may be questionable, they at least provide a means to describe physiological age of a population relative to some measurable, biologically significant, point in time (e.g., first egg deposition, termination of diapause). Similarly, effects of treatment on a developing population can now be assessed using ridit analysis.15 Another approach may be to collect and test samples of field populations in the laboratory. The age of individuals in the sample cannot be determined specifically, but the sample itself would represent individuals from a population of a particular age distribution relative to physiological time (e.g., the sample is of a population X degree days from first egg hatch). The particular method used to describe a field population in terms of physiological time, whether degree days (linear development rates) or proportion of development over time (nonlinear development rates) must be appropriate to the insect population sampled. Close cooperation with ecologists will therefore be required. Precedents of evaluation of effectiveness in relation to arthropod phenology are found in the published literature concerning field tests with pesticides. Walker et al.16 described efficacy of pesticide spray applications for California red scale relative to male flight phenology. Similar studies with San Jose scale have been reported.17,18 Just as these investigations, all of which were based on physiological development of populations, provided reliable estimates of timing, efficacy or both should be possible if laboratory bioassays are based on population age. An alternative procedure would be to simulate selection of test subjects from a field population in the laboratory if population samples cannot be collected from the field because of economic or practical constraints (such as tree height). With this alternative, arthropods reared in the laboratory would constitute the population. Physiological time, rather than chronological time, would be used as the basis of selection of individuals for testing. Such a selection process should be equally applicable to routine activities, such as screening, as well as more complex problems, such as optimal time of pesticide application. The contour plot method12 might be used to assess optimal time of application at minimum application rates, but with physiological time rather than chronological time as the means to describe the age of the population. At least for the generation being tested in the bioassay, we recommend that the population be fed natural substrates rather than artificial diet. For most phytophagous species, potted plants or a continuous supply of fresh host-plant material could be used. Artificial diet should only be used in the bioassay when the diet itself does not significantly response.

2331_C015.fm Page 190 Wednesday, May 9, 2007 5:47 AM

190

Bioassays with arthropods, second edition

Once the arthropods have been exposed to the treatment that is as realistic a way as possible (e.g., spray application), monitoring of their development should continue throughout completion of the life cycle. An arbitrary evaluation period after treatment, such as seven days, should not be used because long-term effects are liable to be overlooked when in fact they are important at the population level. If possible, survivors should be mated and development of the F1 generation monitored. Ideally, table parameters obtained from these data might be used to identify second generation treatment effects that should otherwise go undetected. Because life table studies are so time- and labor-intensive, a simpler approach is to hold test subjects until they reach sexual maturity, allow a subsample to mate, and maintain the progeny until they too reach maturity. Fitness of treated survivors, untreated survivors and their respective progeny can then be compared. Kogan19 has emphasized the need to base pest management decisions in the field on sound principles of population ecology. Robertson and Worner,5 and Stark and Banks,20 have emphasized the same concerns for laboratory bioassays done to predict pesticide efficacy to populations in the field. Costs of doing population toxicology may exceed the expense presently incurred in doing a laboratory bioassay, but the reliability of the resultant predictions would be well worth both the extra time and money involved.

References 1. Stata Corporation, Stata 9 software, 4905 Lakeway Dr., College Station, TX, 77845. 2. Domencich, T. A. and McFadden, D., Urban Travel Demand, American Elsevier, New York, 1975. 3. Maddala, G. S., Econometrics, McGraw-Hill, New York, 1977. 4. Cairns, J. Jr and Niederlehner, B. R., Predictive ecotoxicology, in Hoffman, D. J., Rattner, B. A., Burton, G. A. Jr., and Cairns, J. Jr., eds., Handbook of Ecotoxicology, CRC Press, Boca Raton, FL, 2003, pp. 911-924. 5. Robertson, J. L. and Worner, S. P., Population toxicology: suggestions for laboratory bioassays to predict pesticide efficacy, J. Econ. Entomol. 83, 1, 1990. 6. Robertson, J. L. and Haverty, M. I., Multiphase laboratory bioassays to select chemicals for field testing on western spruce budworm, J. Econ. Entomol. 74, 148, 1981. 7. Markin, G. P. and Johnson, D. R., Western spruce budworm aerial field test, Insecticide Acaricide Tests 7, 203, 1982. 8. Granett, J. and Retnakaran, A., Stadial susceptibility of eastern spruce budworm (Choristoneura fumiferana) (Lepidoptera: Tortricidae) to the insect growth regulator Dimilin, Can. Entomol. 109, 893, 1977. 9. Robertson, J. L., Contact and feeding toxicities of acephate and carbaryl to larval stages of the western spruce budworm, Choristoneura occidentalis (Lepidoptera: Tortricidae), Can. Entomol. 112, 1001, 1980. 10. Haverty, M. I. and Robertson, J. L., Laboratory bioassays for selecting candidate insecticides and application rates for field tests on the western spruce budworm, J. Econ. Entomol. 75, 179, 1982.

2331_C015.fm Page 191 Wednesday, May 9, 2007 5:47 AM

Chapter fifteen: Improving prediction based on dose-response bioassays

191

11. Robertson, J. L., Richmond, C. E., and Preisler, H. K., Lethal and sublethal effects of avermectin B1 on the western spruce budworm (Lepidoptera: Tortricidae), J. Econ. Entomol. 78, 1129, 1985. 12. Rose, R. L., Sparks, T. C., and Smith, C. M., Insecticide toxicity to the soybean looper and velvetbean caterpillar larvae (Lepidoptera: Noctuidae) as influenced by feeding on resistant soybean (PI 227687) and coumestrol, J. Econ. Entomol. 81, 1288, 1988. 13. Hudes, E. S. and Shoemaker, C. A., Inferential method for modelling insect phenology and its application to the spruce budworm (Lepidoptera: Tortricidae), Environ. Entomol. 17, 97, 1988. 14. Wagner, T. L., Wu, H., Sharpe, P. J. H., and Coulson, R. N., Modelling distributions of insect development time: a literature review and application of the Weibull function, Ann. Entomol. Soc. Am. 77, 475, 1984. 15. Howard, P. J. A. and Howard, D. M., The application of ridit analysis to phenological observations, J. Applied Statistics 12, 29, 1985. 16. Walker, G. P., Aitken, D. C., O’Connell, N. V., and Smith, D., Using phenology to time insecticide applications for control of California red scale (Homoptera: Diaspididae) on citrus, J. Econ. Entomol. 83, 189, 1990. 17. Rice, R. E. and Jones, R. A., Timing post-bloom sprays for peach tree twig borer (Lepidoptera: Gelichiidae) and San Jose scale (Homoptera: Diaspididae), J. Econ. Entomol. 81, 293, 1988. 18. Downing, R. S. and Logan, D. M., A new approach to San Jose scale control (Hemiptera: Diaspidae), Can. Entomol. 109,1249, 1977. 19. Kogan, M., ed., Ecological Theory and Integrated Pest Management Practice, Wiley-Interscience, New York, 1986. 20. Stark, J. D. and Banks, J. E., Population-level effects of pesticides and other toxicants on arthropods, Annu. Rev. Entomol. 48, 505, 2003.

2331_C015.fm Page 192 Wednesday, May 9, 2007 5:47 AM

 

2331_Index.fm  Page 193  Thursday, May 10, 2007  11:21 AM

Index χ2 test, 24. See also Goodness of fit

A Acephate, 158 Activity residual, 129 Actuated joint action, 123 Additive joint action, 122. See also Similar joint action Age, population distributions, 189 Alternative hypotheses problems with, 105, 123 Analysis, 4. See also specific methods of analysis life-table, 74 quantit, 31 regression, 5 Analysis of variance, weighted, 31 Antagonism, 126 Antagonistic joint action, 123 Application bioassay techniques and, 75 cleaning of devices, 17 Arthropod rearing, 68 Arthropod survival, quarantine entomology and, 84 Artificial diet, 6, 74, 188 Assumptions. See Hypothesis tests; specific models

B Basic binary bioassays, 55, 58 practical considerations, 66 Beneficial microorganisms, 3 Best-fitting dose-mortality model, 157 Binary bioassays basic, 55, 58 practical considerations, 66 specialized, 56, 62 practical considerations, 67

Binary model, basic, 4 Binary response assays, primary types of, 55 Binary response experiment with multiple explanatory variables, 4, 147 Binary response experiment with one explanatory variable, 4, 12 statistical statement of, 23 Binomial error model, goodness of fit tests for, 110 Binomial model conditional, 137 probit, 25 Binomial regressions, 135 Binomial variation, 106 Bioassays, 3 data, standard method of analysis for, 103 dose-response, 4 effect of natural variation on, 71 foilage spray, 75 laboratory, estimation of Q9 using, 79 mixtures, 118 multiple regression techniques for, 147 prediction statistics and, 187 quantal response, 3 (See also specific types of bioassays) polytomous, 180 standardized techniques involving weight, 175 topical application, 164 use of to estimate insecticide purity, 91 use of to separate populations and strains, 101 with mixtures, 6 Biological units, 90 BMDP, 161, 166 multiple regression models using, 149 Body weight, 163 as an independent variable, 169 proportional adjustment of response for, 164 significance of, 158

193

 

2331_Index.fm  Page 194  Thursday, May 10, 2007  11:21 AM

194

Index

C

D

California red scale, 189 Cat flea, 101 Categorical covariates, 149 logit model for, 156 Categorical time variable, 132 Categorical variables, 152 CATTS, 81 Chemical mode of action, time trends as indicators of, 129 Chi-square function, 24 SAS, 51 Chitin synthesis inhibitors, 118 Chitinase, 125, 149 Chronological time, 189 CLL. See Complementary log-log model Cohorts within a single generation, 73 Collection, limitation on sample size due to, 68 Colorado potato beetle, 73, 93 Commodity treatment, 5, 79 Common controls, 15 Complementary log-log model, 7 regression, 138 time-response data, 130 use of in serial experimental design, 134 Compound binomial probit model, obtaining maximum likelihood estimates for parameters in, 26 Computer programs, 4, 18. See also specific programs Concentration-response, 13 Conditional binomial model, 137, 140 Conditional probability, 134 Confidence intervals, 27, 29, 57, 82, 96, 164 width, 102 Confirmatory tests, 83 Constrained slopes, estimations of with PoloPlus, 41 Continuous variables, 149 Contour plot method, 189 Controls, 15 Converted joint action, 123 Correlated response data, analysis of, 132 Covariates, 149 multinomial logit models, 181 Cultivars dose-responses due to differences of, 81 quarantine treatment and, 79 Cumulative probability of response, 134 Cyhexatin resistance, mode of inheritance of, 110 resistance to in Pacific spider mites, 103, 108

Definitions. See specific terms Degree of dominance, 104 Degrees of freedom, 152 Demographic toxicology, 5 models of, difference from quantal response bioassays, 75 Dependent variables, 3 Design, 4 Detoxification mechanisms, time trends as indicators of, 129 Developmental stage, effect of on natural variation, 74 Deviance, 24 analysis of, 135 Diamondback moth, 73, 92, 95 Discriminating dose, 56 resistance detection with, 112 selection of, 102 Dissimilar joint action, 123 Distribution functions, 78 Dose adjustment, body weight and, 165 definition of, 22 dilutions, 67 discriminating, 56 resistance detection with, 112 selection of, 102 placement, 55, 80 estimating relative tolerance and, 102 selection of, 80 lethal doses and, 103 Dose-mortality lines, 108 Dose-mortality model, best-fitting, 157 Dose-response, 13 bioassays, 4, 108 experiments, binomial variation in, 106 regression, 163 relationship, 3

E Ecological models, 7, 84 Ecotoxicology, definition of, 7 Effective dose, 23 Equal response, separation of probit or logit lines into groups, 31 Equality, 26, 29 CLL lines, 137 hypothesis of given parallelism, 152 tests of in PoloPlus software, 35 Error terms, 102 independence of, 26 Estimated lethal doses, 58, 67

 

2331_Index.fm  Page 195  Thursday, May 10, 2007  11:21 AM

Index

195

calculation of with calculation of with PoloPlus, 44 designs for testing, 59 precise, designs for, 63, 65 Estimation, 23 Experimental design, 4, 13 independent, analysis of time-mortality data, 131 serial, 7 serial, analysis of time-mortality data, 133 Experimental unit, 13 Explanatory variables, 3, 12, 148 Exposure methods, 14 Extrabinomial variability, 17, 26, 80

F Field populations, predicting responses of, 188 Fit. See goodness of fit; lack-of-fit Fitted response curves, 36 Foilage spray bioassays, 75

G Genetic heterogeneity, 108 Genetic hypothesis for mode of inheritance, 105 Genetic resistance, 112 GLIM, 125, 137, 161, 166 analysis of dose-mortality data using, 108 multiple logit analysis of dose-weighttemperature-photoperiodresponse data, 159 multiple regression models using, 149 performing binomial regressions with the CLL line with, 135 regression of time-dose-mortality data with, 138 same of multiple logit analysis with, 155 Goodness of fit, 24, 79, 104 PoloPlus, 43 SAS, 51 Green budworm, 72

H Heterogeneity, 108 Host suitability, quarantine entomology and, 84 Host-insect interaction, resistance expression and, 112 Hydropene, 181, 185 Hypothesis tests, 28 logit model with covariates, 157

mode of inheritance, 104 multiple probit analysis, 151 use of PoloPlus for, 44

I Independence of error terms, 26 Independent joint action, 118 test hypothesis of, 119 Independent sampling design, 130 limitations and constraints, 132 time-dose response experiments, 131 Independent variables, 3 body weight, 169 Individualized randomized procedures, 14 Infestation, calculating risk of, 84 Inheritance mode of, 104 genetic hypothesis for, 105 mode of', inferences using standard statistical methods, 105 Inhibitory dose, 23 Insect phenology, 189 Insect production, limitation on sample size due to, 68 Insecticides, use of bioassays to estimate purity of, 91 Interaction, theories of, 123 International Potency Units, 90

J Joint action, pesticide mixtures, 118 theoretic hypotheses of, 123 use of multiple regression modes to study, 149 Juvenile hormone analogues, 118, 180

K Kill speed of, 129

L Laboratory methods, standardization of, 92 Lack-of-fit, 103, 106 causes for, 107 Lethal concentration, 23 Lethal dose, 5, 23. See also Estimated lethal doses body weight and, 169, 175 estimates, proportional response adjustment, 165 estimation of over time, 136

 

2331_Index.fm  Page 196  Thursday, May 10, 2007  11:21 AM

196

Index

guidelines for dose selection and sample size, 103 point estimates of, 29 precise estimation of, 63, 65 ratios, 26 calculation of using PoloPlus, 44 resistance and, 101 use of to determine boundaries of natural variation, 72 Lethal time, 23, 131 Life tables, 5 analyses of, 74 Likelihood ratio tests, 29, 101, 151 in PoloPlus software, 35 Linear predictor, 149 Log-likelihood function, 24 Logarithmic transformations, 167 Logistic distribution, 31 Logit lines, parallelism of, 158 Logit model, 7, 23 hypothesis tests, 157 in PoloPlus software, 35 polytomous, 180 regression lines, 28 time-response data, 130 Logit plane, best fitting, 157 Logit problem, multiple, solution of, 148 Loss functions, 24

types of variables used in, 149 use of in bioassays, 147

N Natural mortality, 119 Natural response, 29, 167 estimations of with PoloPlus, 41 Natural variation, 5, 71, 80 definition, 72 effect of developmental stage on, 74 effects of on product quality, 91 resistance vs., 101 sibling groups, 72 Normal distribution, 23 Nuclear polyhedrosis virus, 3, 125

O Offset joint action, 123 One-major-gene model, 104 Optimal time, 188 Order of treatments, 17 Organic gardening, 3 Outliers, 17, 25 Overdispersion, 106 estimation of, 109 incorporation of in variance function, 111

M

P

Mathematica, 125, 130, 132 Maximum likelihood, 148 mortality probability estimates using, 109 procedure, 24 Microbial preparations, standardization of, 92 Microclimate, use of to affect numbers of pests, 3 Minimum χ2 method, 24 Mixtures, bioassays with, 6, 118 Models. See specific models Mortality, causes of, 119, 132 Multinomial model, 4, 13, 180 estimation of parameters, 182 Multiple classification data, analysis of, 180 Multiple gene model, 107 Multiple logit analysis, sample analysis of with GLIM, 155 Multiple probit problem PoloEncore, 150 solution of, 148 Multiple quantal response experiment, 13. See also Multinomial model Multiple regression techniques, 161

Pacific spider mite, 103, 108 Parallel planes, hypothesis of, 151 Parallelism, 26, 28, 90, 151 CLL lines, 137 logit lines, 158 tests of in PoloPlus software, 35 use of PoloPlus for tests of, 44 Percentage infestation of a commodity, 84 Pest distribution in a commodity, 84 Pesticides, 3 effectiveness of, predicting, 188 mixtures, bioassays of, 118 resistance, 6 plateaus of, 132 resistance to, 92 role of body weight in response to, 164 time-dose-mortality relationships of, 129 Physico-chemical joint action, 123 Physiological age, population distributions, 189 Piperonyl butoxide, 125 Plateaus, 132 Point estimates, 29 POLO2. See PoloEncore

 

2331_Index.fm  Page 197  Thursday, May 10, 2007  11:21 AM

Index PoloDose, 57, 132 PoloEncore, 149, 161, 166 data analysis with, 152 options for proportional response hypothesis testing, 167 output, 156 PoloMix data input files, 120 output, 121 running, 121 PoloPlus, 29, 35, 119 analysis of correlated response data using, 132 calculating relative toxicities using, 91 calculation of estimated lethal doses with, 44 dose dilution estimation using, 67 plots, 46 sample output, 41 summary information, 45 warning about t-ratio, 43 Polytomous logit analysis, 180 Polytomous model, 4, 7. See also Multinomial model Population bioassays, 101 ecology, 78, 190 levels, effect of toxicants at, 75 pest, 3 response, 5 toxicology, 188 Potency, 6 toxicity and, 90 Precision, 58 optimal designs for estimation of lethal dose, 63 Prediction statistics, 187 Probability of mortality, 119 Probability of response, 57 Probit model, 5, 7, 23, 85, 150 binomial, 25 compound binomial, obtaining maximum likelihood estimates for parameters in, 26 goodness of fit to concentration-response data, 109 mean potency, 91 natural variation and, 72 regression lines, 28 time-response data, 130 univariate analysis, 148 USDA probit of 9 requirement, 78 Probit plane best fitting, 157 problem, 147

197 Product quality, effects of natural variation on, 91 Propargite resistance, mode of inheritance of, 112 resistance to in Pacific spider mites, 103, 108 Proportional response, 163 testing hypothesis of, 166 Proportionality. See also Proportional response hypothesis of, 168 Pseudo-physiological joint action, 123 Pseudoreplication, 16 Pseudosynergistic joint action, 123 Putative potency, 90 Pyrethroids, 125 Pyrethrum, probit model for, 151

Q Q9 confidence interval estimates for, 82 dose selection and placement for estimation of, 80 estimation of using laboratory bioassays, 79 Quantal response, 3 Quantal response bioassays, 12 difference from demographic toxicology models, 75 natural variation in, 5 treatment methods for, 14 Quantit analysis, 31 Quarantine entomology, 5, 67 distribution functions and, 79 ecological approaches to security, risk, 84 tolerance distributions in quarantine security, 78

R R, 18, 52 equality and parallelism tests, 53 multinomial logit model data analysis, 183 performing binomial regressions with the CLL line with, 135 Radiation, use of to affect numbers of pests, 3 Random effects model, 80 Randomization, 14 Rearing, 68, 73 Rectangular data sets, computational scheme for in SAS, 51 Red flour beetle, 150 Regression analysis, 5

 

2331_Index.fm  Page 198  Thursday, May 10, 2007  11:21 AM

198

Index

Regression lines, 28 population bioassays, 102 Relative potency, 6, 26 definition of, 90 Relative susceptibility, 175 Relative toxicity, 91 Replicates, variation between, 107 Replication, 16 Residual plots, 24, 80 PoloPlus, 43 Residuals, 24, 103 Resistance, 92 definition of, 100 host-inset interaction and the expression of, 112 inheritance, statistical models of modes of, 103 natural variation vs., 101 standardized tests for, 175 Resistance ratios, 36 Resistance testing, 67 Response probabilities, estimation of, 135 Response ratios, estimating the magnitude of tolerance using, 102 Response threshold, 28 Response variables, 3, 12 Ridit analysis, 189 Risk, calculations of, 84

S S-PLUS, 18, 52 Safety and selectivity in the environment principles, 4 Sample size, 55, 66, 92 estimating relative tolerance and, 102 lethal doses and, 103 San Jose scale, 189 SAS analysis of correlated response data using, 132 probit procedure in, 51 Proc-Probit, 35 Scoring, 188 Separation of probit or logit lines into groups of equal response, 31 Serial experimental design, 7 analysis of time-mortality data using, 133 use of complementary log-log model in, 134

Serial sampling design, 130 Seven-dose design, confidence dose estimates for Q9 using, 82 Sibling groups, 72 Similar joint action, 118, 122 Simultaneous precise estimation, 58 designs for, 62 Slope, 28 Specialized binary bioassays, 56, 62 practical considerations, 67 Standard curve estimation, 71 Standards, 90 Stata, 125 Statistical models, 3, 7 computer programs for, 18 genetic analyses, 103 multinomial, 182 pesticide mixtures, 119 serial experimental design, 134 time-response data, 130 Strains, use of bioassays to separate, 101 Subsets, 16 Susceptibility, 101 relative, 175 Symmetric tolerance distributions, twoparameter, 31 Synergism, 126 Synergistic action, 118, 123 definition of, 119 Synergists, 118, 124 Systems approach, risk analysis using, 85

T Temperature, use of to affect numbers of pests, 3 Time categorical variable, 132 estimation of lethal dose over, 136 optimal, 188 replication and, 16 Time-dose-mortality data, CLL regression of, 138 Time-dose-response experiments data analysis from, 130 design of, 131 Tolerance, 101 distributions, 78, 83 increase in with increased body weight, 165 Topical application bioassay, 164

 

2331_Index.fm  Page 199  Thursday, May 10, 2007  11:21 AM

Index

199

Toxicity, 188 potency and, 90 Toxicity ratio test, 90 Treatments, 13 efficacy of, evaluating, 84 methods, 14 sequence, randomization of, 17 True joint action, 123 Two-parameter symmetric tolerance distributions, 31

U UCLA biomedical Computer Program P Series. See BMDP Unconstrained slopes, estimations of with PoloPlus, 40 Untreated controls, 15

V Variability of response, 75. See also Natural variation elimination of, 92 Variables, types of in multiple regression models, 149 Variance function, incorporation of overdispersion in, 111 Variance-covariance matrix, PoloPlus, 43

W Weibull function, 131 Weight, dose response and, 148 Weighted analysis of variance, 31 Western spruce budworm, 23, 72, 74, 134, 149, 155, 163, 164

 

2331_Index.fm  Page 200  Thursday, May 10, 2007  11:21 AM