.x‘k A.\>v5:\‘ .»,:..J.«;3§.7.~c..u .32...) fi1.l\nL\)..¢{‘\S \ » {$.81}? ill-kn.) {3.3“}? 111.1.1$);09\~‘\1k€. 20%; {25‘ z.“ ‘8. $5.04..- .9 ; ., ls... ..,.....Y.,,.r....:.§\ .1, .,A.D..w....m...‘r¢. .._. .. . . . .4 .v :4. A tn tobfyu‘ i3)». » t 551‘ 5). 79),. . v , {1‘ .05 . . lam/)2 amp. .Y..a.a»r u... ...I. rigvoviflg. 7.05 , ‘ .‘v‘ . 1.1 rig . 2.112%... . x __.J‘elllsz f )1)... i314. A. ,1 ‘ 1111' 333411;} 31.15... ‘ 211}J\\\<.\:§§\ .3314; I‘d... .éigixiflfii i A . .. , . . . ‘ 31.33....- V .13.,“ . . 9...... vs 1113924321144 zxiiiig . .. $11 2 ‘ v I «f to, . . .§ . . . .slft‘h‘gggg 3...... i165 LUHTIH on ‘ o , 3.1%.}?! fin! gngkft . . . ‘ Silii..3§fl3wfl!\3i.i\1wir .ui‘i‘i . 5.. til 5%.;}. at? ‘ PEN?.W.!"0ILV {titu’viirt 31.: ‘ .- gggiagzfigsg Q £13“... 6.3.! $.- HP’ . I . L) n . 1") Int?! 4. . It; .. . __. If. . . €310.31... u..u§..ii . ‘53)} ‘ V. .- u ‘ axitgx leW . I, l”. . . (u ‘ 5:315}: \ . 11 \‘351142‘41 .13, has .V 33051;: , 51.! t} x .hAHVix tmzfunlr .lrrrt. (Hrvh ‘4‘}..r1ufit‘1aa 1.139%...) .T . , 3‘6.“ch gxfi§§..2§fl\; gas 3.73;; 0 i a £1th $1.11!!» . all] if! n .)f , $321322 :1. .ziii‘. $4 fir! git).tn.fi8 it???» %§)§i}2\d{;¢§3~1‘1§ t V . Danton $1.. \. r I; a .égbhr.l.rrv #5.}! tr. on!!! . . . . 53%. . 5.... Fagin... . .1... x . n . . . ._ a“; 5. 1 , ! \lILL .; . . L‘ 5; PI. . if is! ‘ ; A3134§v§§ .‘ . ‘ . V ‘ . frivi.‘ nitrvOrk.‘ , 4g: 5. 33,151.}; 31. :13; tit.) ,. kiwi. rinnittlftfleti (gifgt..irf5r L giggi £12:szii:zz£:§§>.>lxu<§x§32w3333i§i 23241234.? ta! 53.4%! it?! . u l. .l: v. ‘ v . a . ‘ lv :52. 312.... ‘ . . .2: 1.1.54 ,..L.n.. £11.15: ‘3h.ll,}.ul+klr:r€vsnnvrrrr ‘ PI: .11:- . ‘ gifl“§4}\3’q§§\ g #5111}. 1 “it. . . . x ((3.4 1;: .\ I . , iiiig‘; , VJ“? éfi ‘ figgg .flsfi . fifti‘ g ‘ g; n . 311. \ ’21 ’31). .i. . It‘ll-L. {A}! 33:33:. 3.1 31.25.33. 13% L .i .1 tfllEtit truss? A . \..Ss§§§ xleggig .guufigliliuiliiég . 3(5):? sinisxbg... ilftr. giu I. {gianiiii W... . .. A gil‘ix“) 3v?! . I11!l§.,u1}§..3.§§§ifi3§y‘i \ L gt?! 1.31:5... ‘ , §X§511§§1131 1201:... gysiniadfi +1.. . . .5: A. 521 «3.11.! ‘ a A; I I ‘ , K. (- ’Lq‘LL at; a} . r . ‘ .-ck.--1n.¥.§t ‘ 41.!» . 1.1 tttt t. r :. ,ylLturvfi. AL. {rtr ‘ . . I) 2!)?! I'VE; .{.a it; Alb (3)3": . (C’tifr’ . I.“ P21! 3}} ”I“ I A,— AL. A ‘ I; , . ‘ f in \ .f‘kfth‘i IVJSWI» sin-35¢; 1.1% , 31“?) g . DIEK‘ZE“. . c . x ‘ . , 33...: 3.... pl; in \- t 15‘; . é “Liblvigll‘stltlltfi’ , . ‘ ‘ 1%;‘3; . ’1’ .I. in: ‘ ‘ ‘1! 1.5.9.140... ||rl .K bl} betlrtlttm. vl’rturifirtrtvfrf . . . . . ‘ . _ . . ‘ ii «(:1 l _ ‘ o l . 1|? ‘ E» A . x V ‘ Ab ., . t$\..a1t.c\t..bb;f{7o} xiigui. 4115:7113.- .l!‘ 31.11.}; ‘ thgiltth‘X :wAmtlei l. é.331314.,...,4E§§3§§§§§J§is§i~i§sh¢ 53+, 555i {39:11:14 . igklgxtifaifiztfinwfizirh . r ii.) 3‘2? g . . .23.. . , 4. , i511 . $3145 15193! $1335 “Lamvatmzzlf. \i ‘11:; gs is! ‘ .121! 2, t r x x. . , iggggigéig . is: L. .4 itlkrubll‘lL . . tr‘ .: ‘ r i» £¥ §§ y {‘1 .a fOJL. Mb: 3 34323:; in... :3.- ‘ V « . . L “mtg... 3.1.1311: m i. 2.5.3. : ifttsfig: a}? «at»: b§«x%. nu, . ttHrrfienJfiH «lib, i5??? “Q a. it a: . 4 hunky .. L $.15: .35.“ \. Afil‘ukh buff 4‘ . . x... . ‘ ‘ 3 113?er . . ‘ (If 5)... « V 4‘31”} 3.3.3.13. 5... i9..- , , . gait; .ttinnnutz}1tn+3 . . . A . Lt £101 ; ct :58}.th .. 33% It. ‘ isttiih AL V .;.I§§§. . .1‘123 1511; » 31$}de «(41.9. ¢ “.393. A . ‘5. c. . ii: , ‘ [Eif4égrr‘fgl’ Is”. (1...! ’33.}! «JE . Air} . . ..l.vlu!fi$£.€!lr.v§fs+; . u’ALE‘."I\( .I.Jx.!.}rrr - - 0 - » '(‘P HI‘ 3“) t‘ " WIN"!llll|Hili|iW|lWillillillilii 31293 00667 8076 9‘3. ' f t teaéfigéfiv i ifiiichigan State E University i This is to certify that the dissertation entitled An Economic Analysis of Pest Management Information Systems with Application to Aifalfa Weevii Control presented by Karen Kionsky has been accepted towards fulfillment of the requirements for EhJD. ckgnmin_Ag£iQulLufid] Economics WWW d ‘ Major professor Date FM amqgé MSU is an Affirmative Action/Equal Opportunity Institution 012771 MSU LIBRARIES RETURNING MATERIALS: Piece in book drop to remove this checkout from your record. FINES wiII be charged if book is returned after the date stamped beIow. my 9 31992‘ 5?) AN ECONOMIC ANALYSIS OF PEST MANAGEMENT INFORMATION SYSTEMS NITH APPLICATION TO ALFALFA WEEVIL CONTROL By Karen Klonsky A DISSERTATION Submitted to . Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1986 ABSTRACT AN ECONOMIC ANALYSIS OF PEST MANAGEMENT INFORMATION SYSTEMS WITH APPLICATION TO ALFALFA WEEVIL CONTROL By Karen Klonsky Pest management decisions are made under conditions of imperfect knowledge. Pest management programs are information systems developed to aid in the pest management decisions making process. Any pest management program involves: l) design, 2) implementation and 3) evaluation. Pest control guidelines are developed in the design phase. Usually, implementation of the guidelines requires field specific information. Evaluation means determining the value of the information made available through the pest management program. A systematic way of evaluating alternative pest control guidelines is developed in the study. First, a probability distribution for possible outcomes for each alternative pest management practice is determined. The use of mathematical models to generate a distribution is discussed. The distributions are then compared using methods developed for selecting among risky alternatives. The value of information is calculated by comparing the outcomes of decisions made with the information to the outcomes made without the information. The evaluation method developed is applied to control crop loss of alfalfa due to alfalfa weevil. Seven alternative control strategies are considered. Four of the strategies involve the use of pesticides. One uses a single routine spray and another uses two routine sprays per Klonsky season. The third uses a static threshold and the fourth uses a dynamic threshold for deciding on the timing of a spray application. Two of the control guidelines use early harvesting to control weevils. One of these uses accumulated degree days to schedule the first harvest. The other' uses the pest population and accumulated degree days to set the harvest date. The last alternative is to use a routine harvest date and no sprays. The outcomes for each control strategy are simulated using a mathematical model of the alfalfa-alfalfa weevil agroecosystem. The model simulates single field for a single .year. Fifteen ‘years of weather data for Gull Lake Michigan are used to generate a probability distribution for each management strategy. The strategies are compared using several methods for comparison of decisions made under uncertainty. In all cases the early cutting schedules are preferred to the spray rules and the no control strategy. The effects of altering the intensity of monitoring on the outcomes for these alternatives involving monitoring are also evaluated. Sampling intensity did not affect the results. to Peggy i7: __—. _ ACKNOWLEDGMENTS I am forever indebted to Dr. James Bonnen and Dr. J. Roy Black for their unfaltering support and guidance during the seemingly unending dissertation process. Each in his own way provided a model for integrity in research. I hope I can always meet the high standards they have set. Several other faculty should be acknowledged. Dr. Glen Johnson‘s ideas greatly influenced this work. Dr. Thomas Edens introduced me to pest management and Dr. A. Alan Schmid's teachings were important throughout my graduate education. I would like to thank Paul Winder and Paul Wolberg for their invaluable assistance in computer programming. I would also like to thank Susan, Susan and the Monday Night Supper Club for their moral support and of course the Lost World String Band for giving me a chance at an alternative career. TABLE OF CONTENTS LIST OF TABLES .......................... vii LIST OF FIGURES ......................... ix 1. INTRODUCTION ....................... l 1.1 Problem Statement ..................... l l.2 Objectives ........................ 7 l.3 Dissertation Organization ................ 9 II. PEST MANAGEMENT ..................... ll 2.l Introduction ....................... ll 2.2 The IPM Concept ...................... l3 2.3 Operationalizing the Economic Threshold ......... 29 2.4 Pest Management of the Alfalfa Weevil ........... 45 III. INFORMATION AND PEST MANAGEMENT .............. 48 3.1 Introduction ....................... 48 3.2 The Role of Information in Decision Making ........ 49 3.2.l Information and Resource Allocation ........... 50 ‘ 3.2.2 An Information System Paradigm .............. 54 ‘ 3.2.3 Application of the Inforamtion System Paradigm ...... 62 3.2.4 Decision Making Under Risk and Uncertainty ........ 72 3.2.5 Information Learning and Decision Making ......... 94 3.2.6 Risk Preferences and Pest Management Decision Making - . . lOO l Empirical Results l 3.2.7 Application to Alfalfa Weevil Pest Management ...... . lO6 Lu w o o 0) w w o o o .—J (A) ppkww u—l #h-b N b-b-Pb-bw 01 5.441 The Public Goods Nature of Information .......... Private vs. Public Goods ................. Public Goods, Externalities and Market Failure ...... Information, Market Value and Pest Management ....... Evaluation of Information Systems ............. Decision Theory Approach ................. Net Social Benefits Approach ............... Production Function Appraoch ............... SIMULATION AND PEST MANAGEMENT .............. Introduction ....................... The Use of Mathematical Models in Pest Management ..... Model of the Alfalfa-Alfalfa Weevil Agroecosystem ..... Alfalfa Plant Simulation - ALSIM ............. Alfalfa Weevil Model ................... Linking the Alfalfa Plant and Alfalfa Weevil Models . . . . Modification of the Model to Include Hay Quality ..... Management Model ..................... Modification of the Model for Michigan Conditions ..... Validation and Vertification of the Alfalfa-Alfalfa . . . . Weevil Model Modification of Simulation Results ............. . METHOD FOR EVALUATION ................... Net Income ........................ Value of Pest Management Programs, Monitoring, and Insecticide Applications Sampling Interval ..................... Analysis of Simulation Results .............. Analysis of Simulation Results by Comparison of Means . . . U 125 138 148 157 162 177 184 193 207 213 223 228 228 230 230 220 231 5.4.2 VI. 6.1 6.1.1 6.1.2 6.2 6.3 6.4 6.5 VII. Comparison of Income Distributions Using Stochastic . . . . 236 Dominance EVALUATION OF ALFALFA PEST MANAGEMENT PROGRAMS ....... 239 Net Income Above Spray and Monitoring Costs ........ 240 Comparison of Means .................... 244 Ordering by Stochastic Dominance ............. 252 Value of Pest Management Programs ............. 255 Value of Insecticide Applications and Monitoring ..... 257 Sampling Frequency .................... 261 Recommended Spray Dates and Harvest Dates ......... 266 SUMMARY AND CONCLUSION .................. 27O UL LIST OF TABLES Table 3.1 Decision Matrix for Decision Making Under ....... 74 Uncertainty Table 3.2a Hypothetical Income Data for Two Action Choices, . . . 87 Corresponding Cumulative Distribution Functions, and Tests for F30 and SSD Table 3.2b Alternative Tests for First and Second Degree ..... 87 Stochastic Dominance Using Data from Table 3.2a Table 3.3 Summary of Paired Comparison Tests of Means and . . . . 102 Variances of Actual and Subjective Probability Distributions Table 3.4 Interaction of Avoidance and Exclusion Costs with . . . 112 Respect to Joint-Impact Goods Table 4.1 Survival Rates due to Insecticide and Harvesting . . . 174 and Other Causes Table 4.2 Means of Yield and Quality of Treated and Untreated . . 187 Alfalfa Cut at Different Dates Table 4.3 The Effect of Temperature Accumulation on Quality . . . 189 Measures of Alfalfa Table 4.4 Ration Composition and Ingredient Costs for Feeding . . 192 High Quality and Low Quality Alfalfa for a Constant Level of Dairy Production and Ration Cost Table 4.5 Alfalfa Weevil Pest Management Recommendation Charts . 198 Table 4.6 Costs and Recommended Application Rates for ...... 208 Insecticides Used to Control Alfalfa Weevil Table 4.7 Effect of Change in Dormancy Logic, 1966-1969 ..... 212 Table 4.8 Number of Larvae Per Twenty Sweep Sample ....... 216 Table 4.9 Comparison of Field Data for Treated Plots and . . . . 221 ALSIM Predictions Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Gammon .10 .3a .3b .3c .10 .11 .12 Estimates of the Year and Decision Rule Effects on . . Gross Income Net Income Above Monitoring and Spray Costs for Each . Year Net Income Above Monitoring and Spray Costs Ordered from Lowest to Highest Income Ranking of Decision Rules Based on Net Income Using Waller-Duncan k-Ratio Test Ranking of Decision Rules Based on Net Income Using Fisher's Least Significant Difference Test at the .10 Significance Level Ranking of Decision Rules Based on Net Income Using Fisher's Least Significant Difference Test at the .05 Significance Level Ordering of Decision Rules by F50 and SSD Based on Net Income Grouping of Decision Rules Based on Net Income Using F50 and SSD Value of Pest Management Programs Value of Spray Applications Value of Monitoring Effect of Sampling Frequency on Net Income Above . . . Spray and Monitoring Costs for Decision Rule 3 - Static Threshold Effect of Sampling Frequency on Annual Net Income Above Monitoring Costs for Decision Rule 5 - Dynamic Threshold Spray Dates Recommended by Decision Algorithms . . . . Harvest Dates Recommended for the First Cutting by . . Decision Algorithms U... .......... OOOOOOOOOOOOOOOOO . 227 . 241 . 243 . . 246 . 248 . 249 . 251 . 252 . 263 . 264 . 267 . 268 LIST OF FIGURES Figure 3.1 The elements of an information system ........ 56 Figure 3.2 B-E method for calculating daily degree days by . . . 65 means of a sine curve. Figure 3.3 Calculation of larvae degree days .......... 71 Figure 3.4A First degree stochastic dominance (FSD)--F(X) . . . . 85 and G(Y) are discrete probability distributions. Figure 3.48 First degree stochastic dominance (FSD)—-F(X) . . . . 85 and G(Y) are continuous probability distributions. Figure 3.5A Second degree stochastic dominance (SSD)--F(X) . . . . 89 and G(Y) are discrete probability distributions. Figure 3.53 Second degree stochastic dominance (SSD)--F(X) . . . . 89 and G(Y) are continuous probability distributions. Figure 3.6 Private goods joint supply .............. 116 Figure 3.7 Public goods joint impact--vertica1 summation . . . . 117 over all consumers. Figure 3.8 Supply adjustment with imperfect information ..... 144 Figure 4.1 Flow chart description of the alfalfa weevil and . . . 158 B. Curculionis life cycles. Figure 4.2 ALSIM 1 (LEVEL 1) is based on this model of ..... 160 material flow in the alfalfa crop. Figure 4.3 Simulated and actual percentages of larvae ...... 218 degree days for 1972 and 1974. Figure 4.4 Comparison of field observations of average larval . . 219 populations to simulation results, 1972 and 1974. Figure 4.5 Comparison of field data and TNC values generated . . 222 by ALSIM 1 for Aurora, New York. ix CHAPTER I INTRODUCTION 1.1 Problem Statement Our chemically-oriented, high—energy technology has increased agriculture's productivity. It has also created perplexing problems concerning the quality and safety of the environment and food supply. Some of the chemical inputs that the farmer finds profitable to use are considered toxic substances in a broader context. A rnarket economy allows farmers to ignore unpriced externalities arising from pesticide use. Externalities that cannot be associated with direct monetary costs are not taken into account in his ”to use, or not to use" decision. In recognition of this dilemma, regulations have been introduced by the public sector to modify pest control practices. However, regulation of pesticide use in order to reduce environmental damage and related health hazards need not mean a reduction of the quality and quantity of agricultural products. As a result of rising energy costs and decreasing effectiveness of pesticides, chemical controls by themselves may no longer be as econmically viable as they were once perceived to be. An alternative approach to crop protection based on the eradication of pests is the management of agro-ecosystems based on maintaining pest populations at tolerable low levels. The latter approach called integrated pest management (IPM), relies on ecological principles for the development of pest control strategies. The objectives of IPM are often assumed to include a reduction in pesticide use. This is not quite accurate. Limiting pesticide use is 1 2 not part of the design of pest management programs. Theoretically, IPM could increase the use of pesticides. In practice, however, growers employing IPM strategies have reduced their use of pesticides on average. Thus, pesticide reduction has been a consequence but not a requirement of IPM. It is clear that the success of pest management is contingent upon implementation at the grower level. Pest management programs must be incorporated into farm management practices. However, there are numerous obstacles to the adoption of IPM. While IPM may reduce expenditure for pesticides it may also increase demands on management. The decision-making process incorporating IPM is typically more complex than adherence to routine spray schedules. Monitoring of fields for stages of crop development and pest population levels are typically required. In contrast, routine spray schedules simplify overall planning on the farm. In addition, growers may want the maximum protection afforded by routine spraying. They may be willing to spend more on spray materials to guarantee maximum yield and reduce risk of crop loss. Where aerial sprays are used, IPM creates other management problems. It is probable that when one person is given a spray recommendation from an IPM program so will his neighbor. Where spray equipment is hired, all fields requiring treatment may not be sprayed in time. If a routine spray schedule is followed, on the other hand, a contract can be set up with the spray operator at the beginning of the season to guarantee services. Growers frequently apply several pesticides for the control of numerous pests in one spray. They may be unwilling to apply each pesticide at a cfifferent time. Further complications arise when pest nmnagement programs are available for one pest but not others. If a grower is following a routine spray schedule for one pest, he is likely to throw in an "insurance" application for others. Ideally, reliable pest control guidelines should be developed for each cropping system and each region of the country individually. This goal has not been reached and indeed may never be. IPM involves multiple pests, parasites, predators, crops and control techniques. While this is appealing on a theoretical level, it may be unmanageable in an applied sense. Even looking at a single crop, understanding the relationships among pests, controls, yield and weather is not a minor task. Some problems involved in adoption of pest management practices have been outlined. In order to facilitate implementation of IPM at the grower level the expected returns to alternative pest management programs must be established. With this objective in mind, a framework for the analysis of pest management programs will be put forth. Any pest management program involves three phases: 1) design; 2) implementation; and 3) evaluation. Each phase involves the acquisition and analysis of information to generate decisions. What is meant by a pest management program is sometimes ambiguous because IPM programs exist at both the research/extension level and the grower level. At the research/extension level, guidelines for pest control are developed in the design phase along with a means for providing information to growers. First, the problem to be solved must be clearly defined. The design process also involves the acquisition and analysis of information. The end product is the development of control guidelines and a practical means of applying the guidelines. Monitoring may or may not be included in the program. Implementation at the research/extension level is the transmission of information to decision makers at the firm level. Once the program is being executed, its performance should be evaluated and the program design modified if necessary. No matter how eloquent its design a pest management program in this context is not successful unless the information it provides is utilized in production decisions. At the grower level, the design of a pest management program is the choice among alternative pest management programs and control guidelines developed at the research/extension level. The precursor of this decision is recognizing the problem at hand. Application of the control guidelines usually involves acquisition of field specific information. Setting In) a procedure fOr collecting the information required by the control guidelines is also part of the design process. Implementation at the grower level means using the problem specific information and control guidleines to generate the recommendation of a control practice cu" technique. Execution (Hi the control practice is also part of the implementation stage. The performance of the system in response to the control practice employed should be evaluated in the context of crop loss and feedback given to the manager and research/extension personnel. To avoid ambiguity, the term pest management program will be used throughout to refer to programs at the research/extension level. The term pest management strategy will be used in reference to the grower level. Information is needed at the research/extension level and the grower level and at each phase. Detailed information encompassing several locations and several years is analyzed at the research extension level to develop control guidelines. Growers need information to choose among guidelines. In order to operationalize a set of guidelines, growers must have information regarding their specific situation. Information collected at the grower level can be used to develop and refine guidelines at the research/extension level. Thus, information flows from the grower to research and extension as well as from research and extension to the grower. IPM depends upon information about the current state of the pest-crop ecosystem to predict future states based upon a priori information. From these predictions control recommendations are made. The need is not simply for a monitoring program, but for an information acquisition/delivery system capable of collecting, interpreting and transmitting data in a timely and efficient manner. This involves development and implementation of regional monitoring programs, data analysis technologies and capabilities, and information delivery systems. Each dimension can be designed and administered in a number of different ways. Pest management programs may be coordinated by Cooperative Extension, chemical fieldmen, private consultants, grower-owned cooperatives or individual growers. The information provided may be either field specific or regional. Monitoring may be administered by any of these institutions. Monitoring also varies in terms of how often samples are taken and the number of points sampled as well as the size of the geographic area 6 covered. Information from several regions can be utilized to predict emergence and movement of pests. Regional coordination is particularly important for control of pests that are not problems every year (e.g., army worm). If data are processed at a central location, information must be interpreted and transmitted back to the field quickly in a usable form. Information can be disseminated by radio announcements, recorded telephone messages, printed pest alerts sent by mail, personal contact or any combination of these. Computer terminals in Cooperative Extension offices are used to establish effective communication networks to meet these needs in a number of states. Control recommendations depend on timely information describing the state of the agroecosystem such as accumulated degree days, pest population levels or stage of plant development. While information need not be quantitative, in practice it is presented as a cardinal or ordinal measure. Ordinal measures involve a rating system. For example, the abundance of insects can be described by the following: 1) none; 2) few; 3) common; 4) abundant; and 5) extreme. In contrast, a cardinal measure is the number of insects collected in 20 sweeps of a field. Data in either format is subject to error for at least two reasons. Sampling errors are attributable to uneven distribution in the field, wind velocity, rainfall, the skill of the scout and other reasons. Errors in sampling procedure take place when measurements made in a small area are extrapolated to a larger area. Even when measurements are accurate, the population to be estimated “my differ from one location to another location or from one time period 7 to another. In other words, the mean and variance of the sample taken, regardless of measurement error, may be correct for one location or time period but not another. These errors arise from a poor design of the sampling procedure. It follows that frequent sampling in numerous locations reduces error. However, it is not feasible to monitor all locations at all times for all pests. There is a tradeoff between accuracy in information and the cost of information. Pest management programs can be viewed as information systems. As such, expected returns to a pest management program are equivalent to returns to the information provided by the program. Therefore, by assessing the value of information afforded by alternative designs of pest management programs, the performance of the programs can be evaluated and compared. This will aid in the design, implementation and modification of IPM programs. 1.2 Objectives Pest management programs are information acquisition/delivery sytems. The information generated is utilized in the pest management decision making process for selection of pest control strategies. This study serves two purposes. First it proposes to develop a means for evaluating IPM programs and strategies. There are countless possibilities for the format and content of the information presented through pest management programs. Even when programs and strategies have been developed and used for specific pest-crop problems, there needs to be a systematic way of evaluating them. The evaluation process can be used to choose among pest management programs and to improve the design of a particular pest management program. The procedure followed in this study is applicable to any pest crop situation. Second, the study provides information for the control of alfalfa weevil and the design of monitoring programs for alfalfa weevil control 'in alfalfa. The results are appropriate at least for the Great Lakes States and the northeastern United States where fall—laid eggs of alfalfa weevil adults do not survive the winter. This means there is no larval feeding in the spring as there is in warmer climates. There are several known methods for control of alfalfa weevil in alfalfa. Some of these methods involve the proper timing of implementation which in turn means monitoring of the pest and crop conditions during the growing season. This study identifies alternative pest control strategies and compares their effectiveness in controlling a7Falfa weevil during a single season. In order to accomplish this, a mOdel was developed to simulate the alfalfa—alfalfa weevil agiro-ecosystem and the impact of alternative management strategies on weeV'il population and ultimately on alfalfa yield and quality. The model was run for 15 years of weather data from Gull Lake Michigan and seVen different management strategies. Multiple years were used to es“'T-ablish a probability distribution of income for each strategy. Several evaluation methods were used in order to compare the income d1. Stributions generated by each management strategy. The results from each method were compared. The effects of altering the intensity and E"(:(Nlracy of monitoring on the probability distributions were also e" a 1 uated. l.3 Dissertation Organization In this chapter the concept of IPM has been introduced. Pest nmanagement programs have been described as information systems used to make pest control decisions. The objectives of the study have been discussed. Chapters II, III, and IV present the background necessary for evaluation of pest management programs. In each of these chapters topics are discussed under the general rubric of pest management and then applied to the alfalfa weevil control problem. Each of these chapters provide the building blocks needed to design and execute an evaluation of pest management programs. Chapter II discusses the pest management concept in detail. Several models for development of pest control guidelines are presented. Pest management strategies for alfalfa weevil control are described in the context of the ideas develOped. Chapter III is divided into three major sections and an in‘tr'oduction. The first section explores the design of an information System and the role of information in pest management decision making. Decision making is discussed under conditions of imperfect information. -rr“3' [Drocess of incorporating new information into the decision making p"QC—e55 is described and then formalized. Several methods for comparing the income flows resulting from alternative information systems are pr‘e'sented. Application is made to the alfalfa weevil problem. In the second section of Chapter III, the public and private goods natUre of information is discussed. Examples of alternative ~”‘St‘itutional arrangements for pest management programs are sketched. In the last section several approaches to measuring the value of information are presented. Empirical studies are discussed. Chapter IV discusses the use of mathematical models in the design and analysis of pest management programs. An alfalfa—alfalfa weevil simulation model is described in detail. The model is used in the analysis of Chapter VI. Validation and limitations of the model attributable to the abstractions from reality required by the modeling process are presented. Chapter V draws upon the foundation built in the previous chapters to develop a method for analysis of the value of real time information for various alfalfa weevil control strategies. A management model is 1 inked to the alfalfa-alfalfa weevil model to simulate alfalfa production for each control strategy and under conditions of different information flows. Chapter VI presents the results of the simulation runs and analysis of the results. The final chapter, Chapter VII, summarizes the study and implications of the results of the design and evaluation of pest management programs in general and for alfalfa weevil control in pa Pticular. CHAPTER II PEST MANAGEMENT 2.1 Introduction The term "pest" has no biological meaning. An organism becomes a pest to crop production only in an economic context. A pest alters the condition of a crop in such a way that the value of production is reduced for a given set of inputs and economic conditions. Each year substantial crop damage occurs due to insects, weeds, pathogens, nematodes and other pests. The reduction in potential crop production ‘For the U.S. in 1974 has been valued at $55 billion (Pimental 1976). Pest control is a broad term encompassing all procedures used to reduce the detrimental effects of organisms on yield or quality in agricultural production. Pesticides are the most common method of pest Control in the U.S. Damage occurs despite extensive use of pesticides and other means 0": pest control. Total sales of pesticides have averaged more than 1 b". 1 1 ion pounds per year since 1970. In 1980, 846 million pounds were us'Ed for crop protection, almost twice the amount used 10 years earlier and 2 1/2 times the amount used in 1966 (USDA, 1981). As the volume of pesticide use has grown, so has the number of Spe(ties that have developed resistance to pesticides (Figure 2.1). other unfavorable consequences of pesticide use include resurgence of ta‘r‘ge’c pest populations and outbreaks of secondary pests. These heQative consequences are the result of ignoring the adaptive CapaL‘lilities of the environment and the interrelationship between agb0~ecosystems and the total ecosystem. It is not surprising then, NUMBER oE PESTICIDE RESISTANT SPECIES 1900 Flgure 2.1 SSOurce: 12 F 281 AMHRDPOD PESTS 250 - 200 ' 150 — loo _ USE OF DDT ‘1 j>67 PLANT PATHOGENS I 50 - / SAN JOSE SCALE 0’ LIME SULFUR [I 1908 [I 3'“ l7 WEEDS ,4)? A n T -n d n \ n g l L L 1960 1980 2000 2020 1920 1940 The Development of Pesticide Resistant Species of Arthropod, Pathogen, and Need Pests Since 1908. B. Croft, "Potentials for research and implementation of integrated pest management on deciduous tree-fruits,” pages 101—115 in E. Smith and D. Pimental (eds.). Pest Control Strategies, 1978. 13 that use of chemical pesticides has also created a hazard for fish, wildlife and man. The purpose of this chapter is to provide some background in the theoretical basis of pest management. In the second section the historical development of the philosophy of pest control is outlined. The definition of pest control in its current usage is broken down into several major concepts. Each of these concepts is explored. It is apparent from this exercise that the "best" management strategy depends upon the objectives of the decision maker and the performance criteria used to evaluate the strategy employed. In the third section several theoretical models are presented which act to develop further the concept of pest management. They help identify the type of information which is necessary for developing pest control guidelines. Difficulties encountered in these simple models i lluminate the complexity of practical application of the ideas presented in the first section. The fourth section outlines the methods available for control of the alfalfa weevil based on the IPM philosophy. The use of biological '7 "formation to develop pest control strategies is demonstrated. 2 - 2 The IPM Concept Integrated pest management (IPM) is an approach to cr0p protection based on ecological principles. Management strategies are developed in the context of an agro-ecosystem. These strategies include an integration of well-timed chemical applications, bi01091C31 controls, FEST stant plant varieties and cultural practices. The methods used in IPM are not new. Cultural control practices 14 are the earliest form of crop protection used by man. The concept of biological control dates from the late 19th century and the conscious development of pest-resistant plant varieties began around 1900. The use of chemical compounds for crop protection also has a long history. During the 18th century various combinations of tobacco, animal manures, soot, dry ashes, sea water, urine, soap, turpentine and alcohol were recommended for insect and/or disease control. Because of the immense success of chemical controls following World War II, the emphasis in research shifted away from resistant varieties and other forms of control. The chemical approach dominated applied entomology from the 19205 through the 1960s with some notable exceptions. In the past 15 years, recognition of the negative consequences of dependence on chemical controls revived interest in other control methods. The idea of integrating control strategies also has a historic base. The term integrated control was originally applied in the 19505 to control insects using both biological and chemical control (Smith and A7 Tenn, 1954; Stern et al., 1959). The fundamental idea is to attack peSt populations at their peak while leaving parasite populations intact. It was later broadened to include all control methods (Smith and Reynolds, 1965). Later the term "pest management" replaced "1. ntegrated control" (Geier, 1970). The concept of pest management has been broadened to include all classes of pests (diseases, insects, netnatodes and weeds). Pest management and IPM are now used inteY‘changeably. IPM implies an integration of disciplines (entomology, plant paLthology, agronomy, and economics) as well as an integration of control 15 methods. The development of the IPM concept has been described by .Snfith, Apple and Botrell (1976). The evolution of the concept and its terminology spans a period of several decades and has been influenced greatly by changing technologies and societal values. Some crop protection specialists continue to discredit the concept as representing only new jargon applied to long established crop protection practices. We acknowledge that IPM is not a disjunct development in crop protection - it is an evolutionary stage in pest control strategy - but it represents a new conceptual approach that sets crop protection in a new context within a crop production system. As defined by the Office of Technological Assessment, IPM is a "<30mprehensive approach to the use of various control methods that takes 'irito account the role of' all kinds of’ pests in their' environment, [JCJSslble interrelationships among pests, and other factors". The FAO panel of experts on integrated pest control (1967) defined ‘irrtegrated pest management as: . a pest management system that in the context of the associated environment and the population dynamics of the pest species, utilizes all suitable techniques and methods in as compatable a manner as posible and maintains the pest populations at levels below those causing economic injury. Both definitions advocate pest management as a systems approach to FPEESS‘t. control based on ecological principles not only focused on Satisfying the short run needs of an individual firm. The full advantages and limitations of any control method cannot be identified For a single firm during one season. The pest management approach is designed to recognize the benefits and losses, experienced by all '“S3'71t>£ars of society over time, associated with pest control practices. By taking a broad perspective, the list of control strategies alva1°lable is increased but so is the complexity of choosing a control S§‘3"iitegy. Choosing a control strategy requires knowledge of the effects 1mpTementation of each available strategy will have on the pest and the 16 environment and an evaluation of these effects. In other words, the overall impact of each strategy must be predicted from our understanding of the system being managed and compared using some performance criteria. In order to accomplish this, the characteristics of the system to be analyzed must be identified. Any definition of pest management is purposefully general and thus vague as to what characteristics should be considered in selecting a pest control strategy and how to evaluate those factors. However, the definitions do serve as general guidelines. Components of the FAO definition of IPM quoted above will be addressed individually to elaborate the ideas presented in the definition. ASSOCIATED ENVIRONMENT Pest management decisions are made based on the characteristics of the environment that effect crop loss attributable to pests. The most critical environmental factor is weather. Temperature, precipitation, solar radiation and wind influence the status of the plant, pest and natural enemies directly or indirectly. For example, the emergence of pests and overwintering behavior are determined by temperature. The pest problems in a particular field are also related to the phA’Sical characteristics of the field and the area surrounding the fie—Id. The slope of the land, drainage, elevation and proximity to dra ‘3 nage ditches and natural waterways affect pest levels as well as the entry of any pesticides into the food chain. Wooded areas provide OveY‘wintering sites for pests. Weeds bordering a field harbor pests th V‘OUghout the year. 17 The hazards posed by pest control (primarily pesticide use) to humans, domestic animals and wildlife are usually referred to as social costs. Social costs are rarely if ever included in the calculation of costs and benefits of pest control strategies at the firm level. The term associated environment has a broader interpretation when social costs are being considered than when they are not. POPULATION DYNAMICS OF PEST SPECIES Pests compete with members of their own species and other species for food. Some insect species will feed at a constant rate until a crop is destroyed while others will adjust their feeding rate to the population density. When a pest population is reduced, this will make ‘Food available for another species. The problem of a secondary outbreak occurs when an increase in the population of a second species is attributable to control of the target pest. Pest populations also interact with predators, parasites and pathogens. Enemies of the pest may compete with each other. TECHNIQUES AND METHODS OF CONTROL Pesticides provide an immediate reduction of pest populations and Y‘emain an important tool for pest management. However, pesticides need not be applied as a prophylactic. The proper timing of pesticides based on the level of pest infestation and plant status can reduce the number of applications and improve control. Pesticides are often injurious to "atUral enemies of the pest. This negative effect can also be diminished by careful timing of applications. Although pesticide use is “0‘" the most common method of pest control, several other methods exist 1“(:luding biological controls, resistant plant varieties, and cultural Pl‘actices . 18 Biological control is provided by predators, parasites or pathogens that are natural enemies of the pest. These organisms may be propagated in the laboratory and released into the environment. Because so many pests are not native to the areas they infest, the natural enemies of the pest must often be imported. The release of a predatory lady beetle and a fly imported from Australia in 1888 to control cottony cushion scale on citrus in California is probably the earliest U.S. example of biological control introduced by man. These two predators eliminated the scale as an economic pest within a year. Biocontrol agents are very specific and are less likely to produce undesirable side effects than is conventional pesticide use. Several other more recently developed techniques show potential for insect control. Insect pheromones are a means of direct control by trapping. They can also be released to inhibit mating as can sterilized males. Juvenile hormones introduced to the environment work by interfering with the maturation of insects. The use of resistant plants has been effective in the control of certain nematodes, plant pathogens and a few insects. Damage is reduced due to some physical characteristics of the plant. Some plants contain chemicals that are toxic to insects feeding on them. Others avoid damage by maturing rapidly. This allows for early harvesting before extensive damage from pests occurs. Still others do not avoid damage b“ l‘egenerate lost plant materials quickly. Mmral or physical practices regulate pests by changing their environment. Cultural control practices were the earliest form of crop protection instituted by man developed mostly by trial and error. 19 Control methods now include removal of crop stubble (sanitation) to reduce overwinter survival, tillage to destroy overwintering pests, removal of alternative hosts, rotation of crops to limit the build up of pest populations and the timing of planting and harvesting. Other physical practices include pruning, defoliation, isolation from other crops, the use of trap crops, and the management of water and fertilizer. Crop rotation can be used to control insects, weeds, diseases and nematodes. Crops should not be followed by similar crops (e.g. grains followed by grains) to benefit from crop rotation. Some weed problems can be controlled in one crop better than in another. In this case, crop rotation does not directly control weeds but makes it possible for other technologies to provide control. The increase in narrow row spacing, broadcast seeding, and VIC-tillage has meant a decrease in using mechancial weed control after Planting and an increased reliance on herbicides. Although no-till results in a lower percentage of weed germination, no-till requires greater use of chemicals than conventional tillage. Public actions are usually not included in a list of pest management tactics. However, they play a critical role in pest ma“Mement. Regulations restrain, encourage or require the utilization 01’ certain pest control methods. Government regulations take many 1’Orms. Most are directed at pesticide use. Restrictions on pesticide use affect farmers' pest control choices. Legislation - The first federal law designed to control pesticides was the Federal Insecticide Act of 1910 which pertained to only insecticides and fungicides. Its main purpose was to protect farmers 20 against poor quality or fraudulent products. The 1938 amendment of the Pure Food Law of 1906 set tolerances for certain pesticide residuals in foods. The Federal Insecticide, Fungicide and Rodenticide Act (FIFRA) was signed into law in 1947. It required that any of these products be registered with USDA before they could be marketed in interstate (xnmnerce. The main purpose of the law was to make pesticides safe to the user. This was accomplished by requiring complete and useful labeling by the manufacturer and further requiring that the label instructions for application be followed by the user. FIFRA was administered by the Pesticide Regulation Division of USDA until 1970 when responsibility was transferred to the newly established Environmental Protection Agency (EPA). In 1972 FIFRA was amended to include the classification of pesticides, the registration of applicxitors and identify EPA as the responsible agency. A more detailed descrilation of the current legislation follows. 'Thee procedure for registration begins with a statement filed with EPA by’ the applicant which includes a statement of all claims to be made for thee pesticide, the complete formula for the pesticide, a copy of the labelirig of the pesticide, and any directions for its use. The aPPIlCtantmust furnish any information required by EPA for registration. REQIStY‘ation will be approved if the pesticide is found to meet the (31311115 made for it and "when considered with any restrictions imposed [Under~ FIFRA] it will perform its intended function without unreasonable adverse effects on the environment; and when used in accordance with WidesDread and commonly recognized practice it will not generally cause unreasonable adverse effects on the environment." 21 As part of the registration of a pesticide it is classified for general use or restricted use. A pesticide is classified for restricted use if it is determined that "without additional regulatory restrictions [the pesticide may cause] unreasonable adverse effects on the environment, including injury to the applicator." Certifications require passing a written exam administered at the state level. Applicators are given either private or commercial status. Private applicators are limited to use of pesticides on property owned or rented by themselves or their employer. The most important source of information to the layman for pesticide use is the label on the container. Labeling of all registered pesticides is required under FIFRA. Highly toxic pesticides must carry the unards "Danger-Poison“ on the label, moderately toxic pesticides the word "Warning" and slightly toxic pesticides the word "Caution". Other inforination required on the label includes: —l . Product name . Company name and address Ingredients ewm . Precautionary statements including hazards to humans and domestic animals, environmental hazards and physical or chemical hazards 5. Classification of pesticide (restricted or general use) 6. Category of applicator 7- Storage and disposal directions 8. Directions for use on each crop for which the pesticide is registered including application rates. 22 Knowledge of IPM techniques cannot be required for certification. However, the legislation requires federal standards and state plans for certification to provide information concerning integrated pest management to potential users upon request. In other words, it must be possible for growers to put IPM into practice. A major part of the registration process is the Rebuttable Presumption Against Registration Process (RPAR). The RPAR activity is a review process for selected registered pesticides which allows for public participation. There were about 45 chemicals or groups of chemicals involved in the RPAR process in 1980. As of 1980, the registration for 6 pesticides had been cancelled or suspended by EPA and 15 pesticides had been voluntarily cancelled by the registrants. Federal grades and quality standards set maximum tolerable levels for pest damage to food and insect parts in food. Although some standards are set for health purposes, quite often they reflect a demand for attractive fruit and vegetables. Pesticides have been used extensively for cosmetic purposes. It would be expected that a downward revision of grades and standards would reduce pesticide use while an Upward revision would invite increased use (Carlson and Castle, 1972). Ta‘xes and subsidies can be used to alter pesticide use. Taxes on pesticide use increase the cost of this means of control. Theoretically they Can be adjusted upward or downward until the 'optimal' level of a‘9‘~11‘99i1te pesticide use is attained. SMbsidies can be used to make one form of pest control more attractive than another. Subsidies to agricultural chemical companies to develop narrow-spectrum pesticides that kill only a few species make them more profitable to produce. Subsidies to public or private 23 agencies such as The Federal Crop Insurance Corporation encourage the substitution of crop insurance for pesticide application. Shifting production to areas where pests are not problematic reduces the need for artificial controls. Acreage shifts can also be used to isolate pollution producing activities from other activities or locate pollution producing activities in areas where the absorptive capacity of the environment is greatest. Spatial shifts can be encouraged by changes in market prices, taxes, subsidies or acreage allotments. Other examples of regulations include the certification of disease free seeds and plants and guaranteeing the removal of abandoned orchards. Connecticut and Massachusetts recently passed laws to erradicate the barberry, an alternative host for the stem rust of wheat. Societal values concerning pest control methods are expressed through the scope and form of regulation. Pest management techniques are Chosen at the farm level within the constraints of regulation. The selection process of an individual grower must be consistant with the results of the regulatory process. ECONOMIC INJURY The FAO definition of IPM states that a pest management system Should "maintain pest populations below those causing economic injury." The term economic injury was developed by entomologists to determine When Pest control is appropriate. The economic injury level is defined as "the lowest population density that will cause economic damage" (Stern et a1. 1959). Economic damage is the amount of injury that will justify the cost of artificial control measures. The implication is 24 crop damage should be tolerated when the trade-off between damage and control costs is recognized. Usually there is a lag between recognition of the need for control and the initiation of control and a second lag before the control takes effect. For this reason it may be necessary to implement controls before the injury level is reached. To capture this distinction, another term, economic threshold, was introduced by Vernon Stern in his pioneer article "Economic Thresholds“ (1959). Based on the definitions of economic injury level and economic damage, economic threshold is defined as "the density at which control measures should be applied to prevent an increasing pest population from reaching the economic injury level ." The economic threshold is always lower than the economic injury level to allow time for the control to take effect. Edward and Heath (1964) defined the economic threshold as the POpUliation large enough to cause damages valued at the cost of practical contrxal. The Subcommittee on Insect Pests of the Committee on Plant and Anhnal Pests established by the National Research Council (National Acadenu/ of Sciences, 1969) defined the economic threshold as ”the level at WIFich damage can no longer be tolerated and, therefore, the level at, or beefore which, it is desirable to initiate deliberate control ac’U’Vities." TI) summarize, the FAO definition of IPM can be interpreted as a Iist 0f characteristics a pest control system should have in order to be C0n51Stent with the IPM philosophy. The control system should utilize mEthOds and techniques that are environmentally sound. The methods and teChnlques should not work against each other in the long run (e.g. use 01 Pesticides may reduce the effectiveness of biological controls over 25 time). A pest management system should be based on ecological principles and draw from control mechanisms found in nature. Finally, the control system should be compatible with producer and user objectives. Thus, it should not tolerate economic damage, but neither should it include control measures that are not economically warranted. The performance objectives of IPM are often assumed to include a reduction in pesticide use. This is not quite accurate. Limiting pesticide use is not part of the design of pest management programs. Theoretically, IPM could increase the use of pesticides. In practice, however, growers employing IPM strategies have reduced their use of pesticides on average. Thus, pesticide reduction has been a consequence, but not a requirement of IPM. Even when the important biological relationships are understood for a Particular pest management problem, the definitions of IPM are amblguous. They provide no insights into several factors which are Critical in Operationalizing the IPM concept. The specific context in “"11 Ch decisions are made indicates what appropriate control methods are aval lable. What is possible and favorable in one context may not be in arjolt—her. The following dimensions must be clearly delineated before IPM c an be put into practice. Time Frame - The planning horizon determines what factors are 1: ~ 1 Xed and what factors can be controlled by the manager. For example, 0 . . . . r"Ce a cropping system and machinery are chosen the grower lS locked in and has fewer control options. In a one year planning scheme, crop r . . . . . . Qtcation lS not an option. Most SOCial costs are not realized in a Sirlgle year. Pesticides move through the food chain over time. 26 Spatial Unit - The spatial unit to which the IPM concept is applied must be designated. Pest management can be oriented to a field, a farm or a region. The factors over which the decision maker has some control are different for each of these units. Similarly, the objectives of pest management vary for a farm, a region, the agricultural sector and society. The consequences of the actions of one producer are rarely independent of the actions of other producers. Consequently, the optimal management scheme for a region will differ from the aggregate of the management schemes of the producers in the region developed from the same information base. The same is true when actions are not independent among time periods. Numerous combinations of spatial and temporal units are feasible 1:01” pest management design. For example, most biological control methOds require regional management over several years. In order to take a whole farm approach to pest management, the potential conflict in implementing control strategies and other farm actl.Vities should be recognized. For example, application of pesticides ‘For protection of one crop may be prescribed at the same time as the hal‘F‘Vesting or planting of another. If pest management is applied in a who1e farm context, then the grower's entire decision agenda must be Considered. Institutional Structure - The structure of an economy determines the conduct of individual actors within that economy. Structure refers to all the factors which constrain the available lines of action open to an individual. The opportunity set for each individual is established by the structure. 27 A distinction can be made between natural factors and institutional factors that compose the structure of an economy. Institutional characteristics refer to social relations as opposed to natural phenomena. In the words of John R. Commons (1950), "An institution is collective action in control, liberation and expansion of individual action." 0r according to A. Allan Schmid (1978) "interacting opportunity sets are what is meant by the institutional structure and can be distinguished from nature, technology, knowledge, tastes and other aspects of personality." These authors1 use the terms institutions, property rights and rules more or less interchangeably. Other authorsz, define institutions as business entities including inctividuals which perform economic activities (Kohls and Downey, 1972). In this context, the most important institution in a market economy is t'‘19 firm. A broader definition includes business entities, rules, laws, Cllslloms and conventions involved in economic activity (Breimyer, 1976). Fl‘r1Zher, the business entities may be either public or private. Adapting the broadened definition land grant colleges, the Extension Service, chemical firm fieldmen, regulations, crop insurance, i "FJUt supplers and marketing orders are all institutions that affect DEBS5t management. Pest management decisions are made within the existing i Y‘EStfitutional structure. A strategy which is possible or feasible in ()"‘E context may not be in another. Institutional change modifies the ()F3F30rtunity set of growers and ultimately their choice of pest control taetics. \________ l ‘éThese examples are drawn from the public expenditure literature. he following definitions are taken from the marketing literature. 28 Risk and Uncertainty3 - Pest management decisions are made without perfect knowledge of the outcomes associated with alternative strategies. Risk and uncertainty enter the pest management decision making process in several ways, through (1) the agricultural biology, (2) technology and (3) institutions. All three are interrelated. New methods of control, including new pesticides, are continuously introduced,changing the technology available for production. Changing regulation of pest controls contributes to the variation in technology. Organization of the delivery of pest control information is changing rapidly. Economic events change prices. With price changes the value of crop loss and the cost of control vary. The primary source of variation in crop production is weather. Stochastic factors in agriculture include spatial and temporal variation 1" Pest types and population levels and variation in damage (both yield Susceptibility of pests to controls also varies The effect and quality) per pest. as the genetic characteristics of the pest change over time. of Controls on other crops and the quality of crops is not known with Certainty. Uncertainty in pest management suggests the potential for using a declsion framework incorporating risk. Decisions made with imperfect knoWledge can be characterized by a probability distribution function f or all possible outcomes. This distribution can be used to choose a c Ontrol strategy once an individual's attitude toward risk (willingness to gamble) is known. An individual's attitude toward risk will affect x— 3 The terms risk and uncertainty will be used interchangeably. A more “lgorous approach to this topic is presented in section 3. . 29 the selection of a control strateQY, all other factors held equal. Given that individuals' preferences for risk vary, it is not possible to determine a unique optimal control strategy that will maximize utility for individuals with different risk preferences. However, by categorizing individuals as risk averse, risk neutral or risk preferers, it is possible to rank control strategies. 2.3 Operationalizing the Economic Threshold As a science of resource allocation, economic theory can be applied tC) deciding l) which combination of available pest management inputs to U39, 2) what quantities of each input to use and 3) when to apply those inputs. programs the decision process includes the Other For certain control "UHNDer of applications or an amount of material to be applied. Str‘ategies are either implemented or they are not implemented. It is "()t really meaningful to ask what proportion of a field to plant in a 'fleis‘lstant variety, or what percentage to harvest early. Similarly, for Some strategies the timing of application is not a major concern. For exiarnple, a grower is concerned with whether or not it pays to construct ii (jeeer fence but not when to build it. For these reasons, although the (1(3'frinition of economic threshold refers to all pest control techniques, tlr‘SE threshold concept has been applied primarily to insecticide E‘F3F31ications. Any resource allocation problem consists of a description of the p“"Oduction process and a decision criterion for selecting inputs into t1lat production process. Various theortical approaches to 0Perationalizing the economic threshold will be presented below. They 3O vary in the complexity of the description of the production process, the possible control strategies, and the decision criteria for choosing among the control strategies. The earliest attempt at a systematic approach to determining the economic threshold based on economic theory was developed by Headley (1972). Headley used marginal analysis to derive a rigorous definition for the economic threshold from a simple pest control model. The model developed by Headley has four components. 1) Pest population growth function Pt = Pt_n(l+r)n (2-1) 2) Crop production function y = N - th (2-2) 3) Pest damage function pt = bPE - A (2-3) 4) Pest control cost function 0 =L_ (2-4) Pt-n Where. Pt = the pest population at time t Pt-n = the population at time t—n r = growth rate of the population per time period (1+r)n = compound growth factor y = product yield N = maximum possible yield c = a constant parameter measuring incremental yield effects Dt = pest damage in time t 31 b = constant parameter which enters into the incremental damage resulting from Pt A = constant to define the damage tolerance level 0 = total control cost L = a constant parameter influencing incremental costs The equation for Pt (2—1) can be substituted into the damage function (2-3) to derive Dt as a function of Pt-n' _ n 2 Dt — b[Pt_n(1+r) ] — A (2-5) Froni this equation pest damage attributable to various pest levels at tlfne t-n can be determined. Substituting (2-5) into (2-2) a production fWICtion can also be expressed in terms of Pt—n' y = N - c{b[Pt_n(l+r)n]2 - A} (2-6) 17111 S equation presents the relationship between pest population at time t:“'l and yield at time t. Headley uses profit maximization as the decision criteria. I\S§55l1ming that the producer is a price taker, the marginal revenue with resbpect to P t—n lS. dy 2n MR = = -2cb(l+r) P (2‘7) t-n 32 and the marginal cost of control is: _ d0 _ L MC — _ — - 15—_2 (2—8) dPt-n t-n Assuming profit maximization is the objective of the manager, the optimal pest level Pt—n to which the pest population should be reduced in period t-n is obtained by equating marginal revenue to marginal cost. p = L i t- [—————1 - 2—9 n 2cb(l+r)2n 3 ( ) This value of Pt-n is the economic threshold defined as the popLilation level where the marginal cost of reducing the pest population by one increment is equal to the marginal increase in the value of ProchJction that results. Headley interprets the definition of economic threshold to pertain tc’ a single producer considering a single pest for a single season. The Head'ley model is essentially static. It provides no information on the Optlmal timing of applications during the season. He implicitly assumes 1:115111 the optimal period for pest control (from time t-n to t) 18 ..E3'll:omologically determined.“ The amount of damage realized before time 1:77'1 does not enter into the computations. Improvements in the Headley n1()<3631 have been made by a number of authors including Hall and Norgaard ( 1 S373), Talpaz and Borosh (1974), Heuth and Regev (1974) Shoemaker (1 977) and Feder (1979). Hall and Norgaard (1973) refine the Headley model to allow the time a"<1 dosage of pesticide application to vary. The simplifying assumption .13 made that there is a single optimal time of application which 15 determined simultaneously with the optimal quantity of pesticide aDplied. A "kill function" is added to Headley's model which determines 33 the number of pests killed by a pesticide application as a function of the pesticide dosage and the time of pesticide application. A more complex pest population growth function is used which determines population as a function of the time of pesticide application and the kill function. Unlike the Headley model, the pest population is calculated from the beginning of the season and not from the time of pesticide application. Damage occurring before the pesticide treatment is used in determining the economic threshold. The cost of control is determined by the quantity of pesticides used and not the number of pests killed. The damage and yield functions have the same form as in the Headley model. The optimum time and quantity of pesticide application are found by maximizing profit with respect to these two inputs simultaneously. While the Hall and Norgaard model is an important extension of Head'ley's work, it is not rigorous enough for application to a specific p‘Coblem. In the words of the authors "...We never meant for our model to be 'applied.‘ Our paper was a basic exploration of the definition of the [economic] threshold ...In our conclusion we stated that our model . pl"Ovides rigor to the definition of the concept of economic threshold but is too simple for practical application."' Talpaz and Borosh (1974) refine Headley's basic model by allowing For multiple treatments within a season. A setup cost for each aleication is added to the cost function. An explicit kill function is Used so that numerical computations can be carried out for a specific best and crop. The control parameters are the quantity of pesticides applied for each treatment, and the number of applications. The timing of the 34 applications is not a control parameter. If n is the optimal number of applications, the timing of applications is determined by dividing the growing period for the crop into n+1 equivalent periods. Sprays should be applied at the end of the first n periods and the harvest made at the end of period n+1. Heuth and Regev (1974) also use a single crop, single pest, single year model and relax the assumption of a single chemical application. They make an important contribution by including long run impacts of pest control in their analysis to consider what they call "the dynamic properties of the economic threshold." Specifically, they include increasing pest resistance over time by characterizing pest susceptibility to chemical control as an exhaustible resource. User costs4 associated with pest resistance are included in the analysis in addition to monetary costs of control to capture the effects of pest resistance. The user costs considered are "increased future costs of controlling the pest as a result of a decision to apply chemicals today“ resulting from the depletion of the stock of susceptible pests (i.e. ilicreasing pest resistance). The economic threshold is determined as follows: "If the marginal VEillJe of insecticides in plant growth and pest growth is less than the r"alcginal unit cost of insecticides plus the marginal cost of their use in reducing the stock of susceptibility, none will be used. If any 1Y‘lsecticides are used, the level of use will be such that the marginal bev‘iefit equals the marginal cost." \—— 4The term 'user cost' was coined by Keynes and is used extensively in resource economics. As defined by Scott (1967) user cost is "The present value of the future profit foregone by a decision to produce a unit of output today." x ‘\" "'\ ~ / 35 Following this analysis, profit maximization that ignores user costs of pesticides results in nonoptimal behavior. However, the activities of an individual grower have essentially no impact on pest resistance. The solution presented is a regional solution for several growers with a multi-year planning horizon that maximizes regional profit. Some institutional change is necessary before user cost of reducing the stock of susceptibility will be included in the decision making process. The authors suggest "....appropriate Pigouvian taxes and subsidies may be defined for the region to achieve the centralized solution with decentralized decision making and thus maximize regional profits." Of course, this is only one of several possibilities. Heuth and Regev's study is important for at least two reasons. First, they showed that the definition of economic threshold can include future effects of pest management beyond the current season. Second, if interdependencies between growers and time periods are to be considered in developing pest management strategies, profit maximization for a single firm is not an adequate decision rule. All but the last of the studies discussed assumed that pest control de(:isions are independent of the pest population in subsequent time Per"i<)ds or seasons. When populations are not independent from year to ~Ye€iY‘, combining the optimal strategies for each year independently will "013 result in an optimal strategy over the entire period. Headley 11975) illustrated this point with a hypothetical management system cons‘lsting of three available control methods and a two year planning horizon. The costs and percent mortality vary for each control method. 36 The functions implicit in Headley's example are: 1. Pest population function P(t+1) = 3(l-Mi)P(t) (2-10) 2. Value of crop production Yi(t) = 200 Di(t) (2-11) 3. Pest damage function Di(t) = (l-Mi)P(t) (2-12) 4. Cost of control C1 = 0 C2 = 10 C3 = 30 where: P(t+1) = pest population in period t+1. P(t) = pest population in period t. Mi = mortality rate for control measure i in any single period. Yi(t) = value of crop production using control i in period t. Di(t) = value of crop loss attributable to pest population in period t using control i. C. = cost of control i for a single period. The three control methods considered are 1) no control; 2) a CCHnt>ination of biological and chemical controls; and 3) chemical Corrtrol. Costs and mortality for each are summarized below. 37 Control Method % Mortality Cost/Acre l - no control 0 $ 0 2 — combination 75 $ 10 3 - chemical 90 $ 30 Headley shows through this simple example that maximization of net income, for' each time period separately' will not lead to the same selection of methods as will maximization of net income over several time periods. Further, the total incomes will not be equivalent. Letting I1.(t) be the net income in period t using control i, the objective function can be represented as: Max(Ii(t) + Ii(t+l)) (2-14) 1 where: 11(t) = Yi(t) - C1(t) i = l, 2, 3 The problem of maximization over two time periods can be solved by «:onstructing a decision tree for each possible combination of controls arni finding the maximum net income by inspection (Figure 2.2). An initial population of lCK) is assumed. Maximization for each Period individually leads to using method 2, a mix of biological and Cliennical controls, in each period. The total income for the two periods 155 $336.25. Optimization over the two periods leads to using method 3, Chemical control, in period 1, and method 2 in period 2. The total lncome in this case is $342.50. Shoemaker (1977) establishes a "multi-dimensional economic threshold" as a function of several variables including pest population density, natural enemy population density, plant vigor and maturity and 100 Figure 2.2 PERIOD 1 PERIOD 2 v v ‘$ 0.00 i $215.00 P $240.00 ’ $290.00 , $336.25 $327.50 $330.00 $342.50 $327.00 TOTAL REVENUE FOR TWO PERIODS The nine possible outcomes for a hypothetical two-period pest control problem with an initial population level of 100 and three alternative control strategies. The numbers in parentheses are net incomes for each period. The numbers to the left of each branch are the initial popula- tion levels at the beginning of each period. 39 weather. She discusses the use of dynamic programming and a multiple-season objective function to develop pest management guidelines. Using this approach, the best combination of chemical, cultural and biological methods of control can be estimated. The ecosystem model utilized by Shoemaker can easily be described in the framework developed by Headley. 1. Population model P](t+l) = G](P1(t), P2(t), Z(t), h(t), v(t)) (2-15) P2(t+1) = G2(P1(t), P2(t), Z(t), h(t), v(t)) (2-16) 2. Crop production function Y(t) = G3(Z(t), h(t)) (2-17) 3. Pest damage function D(t) =G4(P,(t>, P2(t). Z(t). h(t). v(t)) (2-18) 4. Cost of control em = 65(V(t)) (249) where: P](t+l) = pest population in the spring of year t+1. P1(t) = pest population in the spring of year t. P2(t+l) = parasite population in the spring of year t+1. P2(t) = parasite population in the spring of year t. Z(t) = weather pattern for year t. h(t) = time of harvest for year t. v(t) = amount of insecticide applied after harvest. Y(t) = yield expected in the absence of pest damage in year t. D(t) = amount of yield lost to pest feeding in year t. C(t) = cost of insecticide treatment. 40 The objective function used is profit maximization over several years. The best management policies are assumed to be those which maximize the present value of net income. Formulating the maximization problem as a dynamic programming problem results in the following: Max T h(i), V(i) [ 2 1 [Pi Y(t) - C(t)] (2-20) i= , T i=1 (1+r) where: r = discount rate P. = price of alfalfa in year i 1 subject to the constraints of equations (2-15)—(2—l9). The optimal management strategy has two components, the time of harvesting and the amount of insecticide applied. The population of natural enemies is considered in determining the control methods by describing the pest population as a function of the natural enemy population and the natural enemy population as a function of the control methods in the model. Only the general form of the model is presented here. In aIDplication, each component of the model may be expressed by a series of EHJIJations to include greater detail in the model than is possible in a Si ngle equation. The optimization procedure utilized by Shoemaker is dynamic PYWngramming. The procedure eliminates the need for estimating results TOY‘ each possible combination of control strategies and initial Populations. One of the major limitations of dynamic programming is that the process must be Markovian. That is, the value of a variable at time t 41 can depend on values at time t-l but not on t—2, t—3, etc. A second problem with dynamic programming is that the number of state variables must be small for the optimization to be computationally feasible. These problems are circumvented by defining the objective function in terms of three variables (the initial pest population, P1, initial population of natural enemies, P2, and the weather pattern Z). The complicated relationships among weather, pest populations, yield, timing of harvest, etc. are all incorporated into the functions G1, G2, G3 and G4, which are calculated outside the dynamic programming problem. Each of these functions can be described in an ecosystem model by a series of 1, P2 and 2. These values, in turn, are used to solve the dynamic programming equations and solved numerically to determine C and Y from P problem. The ecosystem model can then include numerous variables without making the dynamic programming problem impossible. At the same time, the detail of the ecosystem model is not sacrificed. The 'work reviewed so far has assumed that reasonably accurate iecosystem models are available and the outcomes of alternative control preactices are known with certainty. However, in most pest nonagement ESithations, each control alternative has a number of possible outcomes, Some being more probable than others. Feder (1979) introduces stochastic variables into a: simple pest management model. Three sources of uncertainty are identified: 1) the Fate of damage (0); 2) the pest population density (N); and 3) the Effectiveness of pesticides (k). The analysis considers the effect of Allowing each of these factors to be random while the other two are assumed to be nonrandom. Clearly, this simplifies the computational requirements. However, it is not obvious that the same results would be 42 obtained if all three factors were assumed to be stochastic simultaneously. The model is applicable to a single firm decision making process. In the words of the author "The optimal amount of pesticides implied...is 'private', not social because the farmer ignores the damage inflicted on wildlife and humans by pesticide drifts and residues and because of the other externalities related to pesticides used." The model can be described as follows: 1. Pest population function N* = (l—k)N (2—21) 2. Crop production function Y = Y*(l-D) (2—22) 3. Damage function D = bN (2-23) 4. Kill function k = k(x) (2-24) 5. Cost of control C = pxx+F (2-25) where: N* = pest population level after control is implemented. k = proportion by which pest population is reduced by pesticides. N = pest population level before control is implemented. Y = crop yield. Y* = crop yield in the absence of pests. D = crop loss to pests. b = damage caused by a single pest. 43 x = amount of pesticides applied. C = cost of control. PX = price of pesticides. F = fixed costs of control. The cost of management techniques other than pesticides is assumed to be fixed. The only control variable in this system is the amount of pesticides to be applied. Feder assumes risk averting behavior and consequently the objective function is maximization of expected utility as follows: Max E [U(P Y - bN*[l-k(x)] - p x-F)] (2-26) x y x The first order conditions for an optimum are given by: 35:”) = E [U'(ka'—Px)]<0 (2'27) and X aE(U) = 0 (2-28) 3X While some of the variability in b is caused by random factors, the mean (6) may be decreased by pest resistant varieties, timing of fertilizer and water application or other techniques. Farmers can be charged a fixed cost for information about these technologies because they increase the farmer's expected utility. A farmer will pay for information up until the point his expected utility is unchanged. Uncertainty regarding N can be reduced by monitoring of fields. The cost of monitoring is on a per acre basis. In this case, growers should also be willing to pay for information. The result of information is a reduction in the frequency and quantity of pesticide use. 44 Feder looks at two alternative specifications of uncertainty in the kill function; (1) the variation in pest response to the pesticide declines for higher dosages; and (2) the variance increases with the dosage. In the first case pesticides are a risk reducing input. With a more effective pesticide, less is needed to maintain the pest population below a certain level and pesticide use will decrease. Growers will be willing to increase costs for a better quality chemical or information that will increase the effectiveness of current pesticides. In the second case, pesticides are not a risk reducing input. With larger amounts of pesticides the variance of the utility function increases. A decrease in uncertainty regarding pesticide effectiveness will cause an increase in the amount and frequency of pesticides applied by lowering the economic threshold. Consequently, growers will pay for information to improve the efficacy of the pesticides and increase pesticide use. The major contribution to the literature by Feder is the recognition that uncertainty affects pest nwnagement decisions. Most attempts to develop pest management programs have relied on the assumption that growers are risk neutral. Consequently, the objective function has been to optimize expected profit. Optimization implies control over pest management variables and perfect knowledge of the relationship between pest management variables and crop loss. In practice, the grower does not know with certainty either the amount of damage that will occur if a pest control strategy is not implemented or the outcome if a pest control strategy is implemented. If the variability in pest damage is different for alternative pest management strategies, then growers with differing risk preferences may 45 choose different pest control methods. Put another way, it may not be possible to identify a pest management program acceptable to a group of rational decision makers operating under uncertainty if their risk preferences differ. In fact, risk averse growers may prefer routine spray schedules if they reduce the variability in crop loss. Decision making under uncertainty will be discussed in 3.2.4. Empirical studies of the relationship between risk preference and pest management decisions are discussed in 3.2.6. 2.4 Pest Management of the Alfalfa Weevil The alfalfa weevil Hypera postica (Gyllenhal) is a European species that was first discovered in Michigan in 1966 (Dowdy, 1966) and has since spread and increased to damaging numbers over the lower peninsula (Ruppel and Guyer, 1972). It is now the most serious pest of alfalfa, threatening roughly half of the alfalfa acreage throughout the state. The adult weevils are gray to brown beetles, one-quarter inch long. A broad dark band extends to the middle of their wings. The larvae have black heads and green bodies when fully grown with a white stripe down their backs. They are less than three-eights of an inch long. Adult weevils overwinter in protected areas and become active in early spring. During this time, they feed on the leaves of the alfalfa and lay eggs inside the hollow stems of the plants. The larvae hatch from the eggs beginning in late April and feed on the alfalfa leaves for three to four weeks. When full grown, they spin silken cocoons on the plant and enter a pupal stage. After one or two weeks, adults emerge from these cocoons from mid-June to mid-July. They 46 feed for about a week and then move out of the alfalfa fields to protected areas. Most adults remain in a resting period until the following spring. Although some become active and lay eggs in the fall, these eggs do not survive the winter in northern climates. The alfalfa weevil became well-established in the New World, in part, due to the absence of natural enemies (parasites, predators, and diseases) that suppress its numbers in Europe. One method of control involves the introduction of biological control agents. Parasitic wasps have been introduced throughout Michigan for this purpose. The wasps lay their eggs in either the eggs or larvae of the alfalfa weevil. Insecticides applied during the growing season have been the most widely used method of control. Proper timing of a spray is critical because of the short residual activity of the insecticides used. A spray applied too early will leave the crop unprotected, while a late spray may not avoid economic loss. When the weevil was first discovered, it was feared insecticides would be the only means of avoiding economic losses. However, field observations indicated damage was not extensive until the alfalfa was flowering and, therefore, early cutting could be used to avoid loss and reduce the need for the use of insecticides. Montana investigators (Hastings and Pepper, 1951) proposed this strategy in 1950 but their recommendation was not accepted by the growers because they believed the value of the yield loss incurred by the early cutting more than offset the cost of chemical application. Hamlin et al. (1949) observed high larval and pupal mortality following cutting in Utah. Casagrande and 47 Stehr (1973) reported between 60 and 80 percent of the larvae present killed by harvesting. Early harvest can also reduce loss since much of the damage attributable to the weevil occurs after the plants reach the late bud stage. While the early cutting reduces yield in the absence of pest populations, it improves the quality of the hay. Early harvest of the first cutting is now considered a viable alternative to insecticide application (Tesar, 1968). Several guidelines for the timing of spray application and first cutting exist. They include advising growers to take the first cutting at the late bud stage for growers using a three-cut-per-season system (Tesar, 1968); apply insecticide when 25 to 50 percent of the alfalfa tips show damage (Janes and Ruppel, 1969); and spray if 25 percent of the tips show damage and will not be cut for a week or more (Ruppel et a1. 1976). The underlying hypothests is that crop yield and quality will be reduced if the recommendations are not followed. However, these criteria, while useful as rules of thumb, are not based on experimental data or controlled field trials. Developing rigorous guidelines for the timing and implementation of alfalfa weevil control strategies requires knowledge of the impact of alfalfa weevil feeding on the yield and quality of alfalfa for a particular region. To summarize, at least three methods of control are available for control of alfalfa weevil. They are biological control, early harvesting and insecticide application. The latter two involve proper timing of implementation. CHAPTER III INFORMATION AND PEST MANAGEMENT 3.1 Introduction In the preceeding chapter the fundamental ideas of pest management were discussed. A distinction was made between pest control guidelines and pest management programs. Pest control guidelines are decision rules for allocating resources to pest control. Site specific information is necessary for applying the pest control guidelines to a particular situation. Pest management programs are information systems that make available pest control guidelines and the information necessary for utilizing the guidelines and ultimately making pest control decisions. Information is an input into the managerial process from which decisions are the output. In this sense, information is a commodity for which there is ii supply, demand and a nmrket value. Information derives its value by improving decisions concerning the allocation of other resources. The ultimate objective of this chapter is to develop a method for evaluating pest nonagement programs. Pest management programs can be distinguished by the information they make available. It follows that pest management programs can be evaluated by looking at the impact of the information provided for management decisions. Various topics in the study of information will be explored. The remainder of this chapter is divided into three sections. The next section looks at the role of information in the decision making process. The implications of perfect and costless 48 49 information for resource allocation are explored briefly. The restriction of perfect knowledge is then relaxed and decision making under uncertainty is discussed in the remainder of the section. The third section looks at the characteristics of information as a commodity. These characteristics determine the supply and demand for information. The public goods nature of information and its implications are discussed. The theory presented is not appropriate for assigning a dollar value to information but provides insight into the difficulties of determining what information should be provided and whether or not the information should be provided by the public or private sectors or some combination of the two. Some alternative institutional arrangements for the provision of pest management information are presented. The fourth section presents several quantitative approaches to computing the value of information provided by alternative information systems. 3.2 The Role of Information in Decision Making This section is divided into six subsections. The first subsection describes the relationship between information and resource allocation. The second subsection presents an information system paradigm and the components of our information system are discussed. The paradigm is useful in identifying some major ideas to be considered in evaluating information systems. The integral role played by the decision maker in the design of an information system is emphasized. The point is made that the problem to be solved impacts the design of the information system. Perhaps the most important implication of 50 the paradigm is that information only gains market value as an input into the decision making process. The paradigm is applied to pest management in the third subsection. The information system paradigm points out the role of the decision maker in the design of an information system and the existence of a relationship between the generation of information and problem solving. The fourth subsection attempts to describe the decision making process and the impact of information on problem solving. The concept of subjective probabilities for possible states of nature is introduced. Several decision criteria and algorithms for selecting among risky ventures are presented. The impact of the decision maker's attitude toward risk on resource allocation is also discussed. The fifth subsection uses these ideas and looks at the role of learning in decision making. Bayes rule for revising subjective probabilities is defined. In the sixth subsection empirical results of studies looking at attitudes toward risk and the impact on pest management decisions are presented. 3.2.1 Information and Resource Allocation The fundamental activity of an economic actor is to allocate . . . 1 resources based on available information. The performance of a market economy can be viewed as the result of decisions made in the process of allocating resources. Goods and services are rationed among consumers. The factors of production are allocated among producers. 1Throughout this chapter the terms knowledge and information will be used interchangeably. 51 The following discussion will focus on the production side of the economy and in particular on pest control as an input to agricultural production. The business firm will be viewed as the principal organization for production activities. The firm must make several decisions regarding production. The firm must.choose the level of output for each product and how to produce the output. The firm must also determine what prices to charge for its outputs and pay for its inputs. Of course, the set of attainable combinations of activity and price levels is bounded. In making production decisions the firm faces three kinds of constraints: 1) technical; 2) government; and 3) market.2 Technological constraints define the production possibilities of a firm. That is, they describe all patterns of inputs and outputs that are feasible. These constraints stem from the physical laws of nature, the actions of others, and the current state of technology. The basis of‘ technological constraints is incompatible use of finite resources. For a physical factor allowing several uses, the resource must be allocated among these uses. The set of possible uses changes with changes in technology. The output and factor utilization of others limits the Opportunity set of a firm. In the simplest case, if A uses a resource then it is not available for use by 8. Also, unless a firm supplies all of its own inputs, it is dependent on the production of inputs by other firms. The activities of other firms may entail the production of byproducts which 2Technical and market constraints are suggested by Varian (1978) as constraints faced by a firm in determining a profit maximizing policy. The constraints may also be interpreted as three categories of externalities following the approach taken by Schmid (1978). 52 become unplanned inputs into the firm's own production function. Fruit production provides pollen for the honey producer. Smoke produced by one firm may necessitate the installation of air filters by another. Government constraints are those constraints that influence the production activities of the firm through public action, i.e. property rights and rules that affect the opportunities of the firm. Government constraints can be viewed as costs imposed and benefits conferred on individuals by collective action. Political action alters price and output levels. In so doing, cost of production is increased for some and revenue is increased for others. Government constraints are really market constraints or technical constraints created through the legal system. While government constraints are the result of collective action, market constraints concern the impact of the independent actions of individuals on the opportunity set of the firm. The consumption patterns of consumers and the demand for inputs by other producers affect the price levels of the inputs and outputs of a firm. Prices act as signals transmitting market values for the allocation of resources. Government constraints are also signals transmitting information concerning nonmarket or social values. Thus, what is produced, how it is produced, and in what quantity is a function not only of market values but of nonmarket values. The three categories of constraints facing a firm are by no means independent. Private sector markets, public sector decisions, and adoption of technology are all causally related. The technical constraints determine what can be produced and the available methods of 53 production. Changes in technology alter the value of’ resources in production. Market constraints provide prices which determine the allocation of resources to produce various outputs and the choice of input mix. Government constraints alter the production possibilities and exchange values of inputs and outputs of production. One of the ideal conditions often assumed in the analysis of a market economy is that producers and consumers possess perfect knowledge of all constraints facing them. Several consequences follow. On the production side, all firms have access to the same technology and all market prices are known with certainty. Firms can control the quantity and quality of their output. On the consumer side, consumers know what goods are available and the quality and price of the goods. Under these conditions, it follows that no buyers will pay above the market price for any product. No producers will be able to price their products above the market price or be willing to accept less than the market price. Under the assumption of perfect knowledge there is a single price, markets clear, all individuals and firms are price takers, all products are produced with the least cost combination of inputs and a static equilibrium is reached. However, when imperfect information prevails, none of these conclusions necessarily holds. The assumption of perfect and costless knowledge does not allow a market for information. When the assumption is relaxed, the activities of seeking information and supplying information become questions of resource allocation. Application of this approach to pest management views an agricultural producer as a consumer of pest control information and a pest management program as a commodity consisting of information. 54 Ideally pest management programs provide at least three categories of information: 1) information describing the relationship of crop loss to biological and environmental factors; 2) timely information about pest population levels, crop stage, and weather and 3) pest control guidelines. The categories of information are interdependent. The first category of information constitutes a general knowledge of the agro—ecosystem being managed and is encompassed in pest control guidelines developed from past experience and observations. The second category is specific to the particular decision maker and is necessary for Operationalizing the guidelines. Pest control guidelines are a synthesis of the technical, market and government constraints cogent to the control decision. A control strategy will not be recommended if the expected cost is greater than the expected return given current prices. A pesticide that is not currently registered for use on a particular crop will not be recommended. Hence, as market and government constraints change, pest control guidelines must also change. In practice pest management programs may not provide explicit information concerning technical, market or government constraints. However, this information is implicit in the pest control guidelines. 3.2.2. An Information System Paradigm3 In the preceding subsection the assumption of costless knowledge was relaxed. Information was described as a critical input into the 3The term paradigm is used here to mean a model or structure. It does not refer to a self-contained theory, science or discipline. II! V 1 f ‘ 55 management process for which decisions are the output. It follows that information only has economic value in the context of decision making under uncertainty. Relaxing the assumption of perfect and costless knowledge leads to the study of information systems responsible for the production of information. In this spirit Bonnen (1975) developed a paradigm to describe the inherent structure of any information system. The paradigm develops a vocabulary for the components of an information system. A distinction is made between data and information. Data systems and information sytems are then placed in a decision making framework. The information system paradigm is a theoretical framework for studying the process of producing information for use in decision making. The paradigm is a useful tool for evaluating an existing or 1 proposed information system by identifying the necessary components. The paradigm is presented here in some detail and applied to pest management in the next subsection (Figure 3.1). DATA AND INFORMATION SYSTEMS Data are an attempt to represent reality through measurement or counting. Data are usually numerical but data need not be in quantitative terms. For example, pest infestations can be described as extreme, moderate, or low. Of course, qualitative terms can be translated into ordinal measures (e.g. low = l, extreme = 10). In any case data can be presented in several forms including tables, graphs and charts. The discussion will focus on statistical data although the ideas presented are equally applicable to qualitative data. Data can be narrowly defined as the quantification of ideas or concepts that describe the world. Therefore, the production of data ‘..—w m wags/(g uououuoiul 56 Decision Making 4 Information for Decision Makers UTVII KW TITIIU ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo 0000000000000000000000000000000000000000000000000000000000 4 oooooooooooooooooooooo IU'fTI’U'V" 552555222522. interpretoiion on c1 .409 0.8. 15 3:5:3:3:5:3:§:3:§:3:3=: 'V—‘T' n 'erVVUTTV'It'f 4 3: Doio Output ? Es“ Measurement;E ? vvvvvvvvvvv vvvvvvvvvv OOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOO ................... ligand Testing :1 :;;§gof Analytical OOOOOOOOOOOOOOOOOOOOOO 0000000000000000000000 55—22 Operoiionolizoiion of ’Ca’r'i‘cepie.’ fiv" W'VV“ T'YV‘Y'YfV' oooooooooooooooooooooo 4 OOOOOOOOOOOOOOOOOOOOOO ooooooooooooo 4 OOOOOOOOOOOOOOOOOOOOOO A‘AAAL‘ __- . + . v 1 vvvv 7W Theoretical Coneeeia.§5§S§E§5§5§3§E§3§5§5§5§3§5§3 /\ Figure 3.1 Source: Bonnen 1977 Reohiy AAAALMLAJ My ' The elements of an information system :13: Framework 53511 . Y tools/(s .(Jinbui F‘_fi 57 requires a conceptualization of the world that simplifies and categorizes reality in such a way as to allow quantification. The concepts are operationalized by selecting and defining variables from the real world that are highly correlated with the categories of empirical phenomena established in the conceptual statement of a problem. Once the variables are defined, a technique for measurement must be developed and carried out. Thus, the production of data involves three steps: 1) conceptualizaton; 2) operationalization of the concepts; and 3) measurement. In the language of the systems scientist, the production of data can be viewed as a data system. The three phases then become; 1) problem definition; 2) selecting and defining variables; and 3) observation. In this context the reliability' of' data has several different meanings, all of which are important. First, the reliability of the conceptual framework raises the question of whether or not the abstract concepts selected provide an adequate and pertinent representation of reality in the context of the decision being made. The accuracy of the measurement technique has nothing to do with whether or not you are measuring the right thing. Second, the reliabiity of the operationalization of a concept refers to the ability of the selected variables to reflect variation in the phenomena they were designed to measure. Finally, reliabiity of measurement technique is what is usually meant by statistical reliability. It is independent of conceptual or operational reliability. Clearly, no amount of statistical sophistication can compensate for errors in the first two stages of data production. The example used by Bonnen is the concept of 'parity price.‘ He states that parity price 58 "no matter how well measured, is a poor representation today of farmer welfare." The demand for data is generated by the need to make decisions. Thus the conceptual framework must be based upon the objective of the inquiry. Otherwise, the resulting set of data may not be adequate or appropriate for the decision being made. Data that are relevant in one decision making context may be superfluous in another, depending upon the question to be answered and the beliefs of the decision maker. Recognition of a decision making problem uncovers the need for data. The corresponding conceptual framework establishes what needs to be measured. But decision makers rarely use the raw product of data collection. Some level of analysis or interpretation is necessary to give the data meaning in a decision making context. The act of interpreting data transforms data into information. An information system, then, contains a data system as ii subcomponent. The analysis and interpretation of the data produces information relevant to the decision making problem. In Bonnen's formulation the decision maker is endogenous to the information system and performs the function of a user as well as implicit designer of the system (Bonnen 1977). The distinction between data and information is recognized by several authors (Eisgruber, 1967; Dunn, 1974; Davis, 1963). Davis points out that despite an abundance of data, in many cases the available data is insufficient for decision making. He defines data as groups of nonrandom symbols that represent quantities, actions, things, goals, etc. Data is only useful for decision purposes when processed and transformed into information. 59 Although it is clear that decision makers rarely use raw data, it is also clear that analysts rarely use raw data in the production of information (Rossmiller et al., 1977). The formatting of data is the most rudimentary form of interpretation. Nonetheless, it provides an important function in giving meaning to data. It facilitates communication among the producers of data, analysts and decision makers. Most data is highly processed before an analyst or decision maker sees it. Data can be reformatted, combined with other data, aggregated, or described in word form. Clearly, a sharp distinction between data and information does not exist. A more accurate description is a continuous processing of data to get narrower and more decision specific information. While at an applied information system level the distinction between data and information is important, it is also crucial to note that at an epistemological level there is no difference. This follows from the fact that all inductive products have deductive priors, and vice versa (Chalmers, 1976). In practice, data and analysis reduce uncertainty but never eliminate it. Thus, in reality there is no such thing as perfect information. Data and analysis, when utilized becomes information and gains value. The value of information depends upon the value of the decision in which it is used and the extent to which it effectively reduces uncertainty and the related decision error. Perhaps a working definition of information is data that has been converted into a form useful to the decision maker. The 'conversion' may be a simple tabulation or a sophisticated statistical analysis. In any case, information identifies relationships among datum related to a problem. 60 One other point which will be referred to as the data overload problem deserves mention (Shaffer, 1978). It is possible to render information useless to the decision maker simply by providing too much. There is a point after which the decision maker is unable to incorporate more information into the decisicni making process or integrate the information available. An information system must function not only to process data into information but also to select information and synthesize it into a form compatible with the decision maker's needs. ROLE OF DECISION MAKER IN AN INFORMATION SYSTEM Ultimately, the purpose of the information system is to provide information for problem solving. The decision maker has the clearest insight into the definition of the problem. The decision maker is part of the information system because the goals of the decision maker are essential to the design of the information system. However, the decision maker is rarely the designer of the information system. Also, there may not be a direct loop from the decision maker back to data collection. It is tempting to look at the information system as producing a supply of information and the decision maker as generating the demand for information. But the demand generated by the decision maker is often reflected to the supplier through the analyst depending upon the specific organization of the system. It is important to recognize that the information system paradigm and supply and demand analyses are designed to answer completely different questions. The information system paradigm does not outline production stages. Rather it is an epistemological statement attempting 61 to map the logic of how you know what you can say you know. The paradigm identifies the dimensions of an information system and can act as a set of guidelines for analyzing and improving a system. This is not to say that information cannot be correctly interpreted as a commodity. The important point is that "information only becomes an economically valuable commodity in the context of decision making" (Riemenschneider and Bonnen, 1979). Like any valuable commodity, the characteristics of information influence its production and use within the economy. The factors that affect the supply and demand for information will be addressed in section 3.3. UNDERLYING CONCEPTUAL FRAMEWORK One of the key aspects of the paradigm is the recognition of a conceptual framework underlying all data production. Observations are not independent of theory. This point is emphasized by A.F. Chalmers in his treatise What Is This Thing Called Science? (1976). He states: "Theory of some kind must preceed all observation statements and observation statements are as fallible as the theories they presuppose. Observation statements must be made in the language of some theory, however vague." Chalmers emphasizes the need to develop an appropriate conceptual framework to produce reliable data. He later states, Observation statements...are always made in the language of some theory and will be as precise as the theoretical or conceptual framework as they utilize is precise... Precise, clearly formulated theories are a prerequisite for precise observation statements. In this sense theories preceed observation. 62 The> discussion to ‘this point has focused (N1 the production of information for decision making from the analysis of data. It is also possible to derive information directly from laws and theories. This kind of reasoning is called deductive reasoning and does not involve measurement or observation. Deductive reasoning constitutes the discipline of logic. Logic and deduction cannot establish the truth of predictions or explanations of physical phenomena. Deduction does establish the logical validity of an argument. That is, for a valid argument, if the premise is true, then the conclusion must be true. Whether or not the premises are true cannot be proved by an appeal to logic. Bonnen, adopting Churchman's terminology, refers 1X) the deductive process as an inquiry system. Ideally, in an information system, the data system and the inquiry system utilized in a specific decision making process will be based upon the same set of theoretical concepts. Further, the definitions of variables that operationalize those concepts should also be identical. Unless there is a common conceptual ground and definition of variables, data cannot be used to validate theory. Empirical testing of hypotheses necessitates data which are designed around the same conceptual grounds as the hypotheses themselves. Some examples related to pest management follow to illustrate the ideas presented. 3.2.3. Application of the Information System Paradigm MEASUREMENT OF BIOLOGICAL TIME One of the most critical factors affecting biological processes is ambient temperature. Maximum and minimum daily temperatures are 63 collected in numerous weather stations in every state and published monthly by the National Oceanic and Atmospheric Administration in a volume entitled Climotological Data. In a very short period of time the daily maximum and minimum temperatures become too much data to easily interpret. Further, temperature data in and of itself says nothing about pest emergence or population growth. Some understanding of the relationship between temperature and population dynamics is necessary. Two concepts, temperature threshold and heat accumulation, are often introduced to solve these problems. For a given biological process there exists a temperature threshold below which no activity occurs. Heat accumulation above the appropriate threshold aggregates daily temperature data into a single measure. The effect of temperature on the process can be described or predicted using the measure of heat accumulation over the threshold. The measure most commonly employed is degree days. However, there are several methods available for calculating degree days. All methods begin calculation of heat accumulation on a specified day, usually January 1. Degree days above the specified threshold are calculated daily and added to the previous days' total to provide a measure of accumulated degree days for the year. The simplest method of calculating degree days for any one day uses maximum and minimum daily temperatures. Daily degree days are calculated as the difference between the simple average of the day's high and low temperatures and the threshold as follows: DD(t) = [(TH(t) + TL(t))/2]-B for (TH(t) + TL(t))/2>B DD(t) = 0 otherwise 64 Where: DD(t) = Daily degree days for day t; TH(t) = Daily high temperature; TL(t) = Daily low temperature; and B = Lower threshold. While this method is straightforward and easy to calculate, it may not be sufficiently precise. Take, for example, the case where the threshold is 50°F, the high temperature for the day is 54°F and the low temperature is 44°F. The average is then 49°F and no degree days are accumulated for that day. But the temperature was above 50°F for at least some period of time. Therefore, some activity took place but is not reflected in the degree day measure. A second method for calculating degree days estimates heat accumulation as the area under a diurnal temperature curve was developed by Arnold (1960) and refined by Baskerville and Emin (1969) to include both an upper and lower threshold. The principal assumption of the method is that when temperature is plotted over the period of one day the area under the resulting curve is similar to the trigonometric sine curve constructed with the amplitude equal to the difference between the maximum and minimum temperature and is a good estimate of daily degree days (Figure 3.2). Two interpretations of an upper threshold are possible. If the process is arrested by temperatures above the upper threshold (K2) then no heat units accumulate during the period in which K2 is exceeded. The resulting degree day calculation is the sum of areas A and C. If, on the other hand, temperatures above K2 retard but do not arrest the process then it is assumed that heat is accumulated at a constant rate TEMPERATURE 65 TH"—_— —— —'"_ __.—— ”new? 99 . o’e’e’e’.‘ zezo’o’e’e K1 ______ vastness“. . l 1 1 1 TL"‘ ————— '-%-'f-‘ ———————— :—- ————— 0 2 4 6 8 10 12 14 16 18 20 2224 HOURS Figure 3.2 B-E method for calculating daily degree days by means of a sine curve. K1 is the lower threshold, K2 is the upper threshold, TH is the high temperature for the day, and TL is the daily low temperature. 66 for that period. In this case the degree day measure is the sum of areas A, B and C. Of course, if no upper threshold is imposed, the degree day measure is areas A, B, C and D. The calculation of degree days is a good example of interpreting raw data to produce information. Using the same conceptual framework two methods of analysis were presented. The method used reflects, in part, needs of the decision maker. Quite often degree day measures are used to predict the emergence of a population and stages of development. Unfortunately, the method used to calculate degree days is usually not made explicit in the literature. If an upper threshold is reported, the interpretation is usually excluded. When the underlying methodology is unclear the usefulness of the information is diminished. MEASUREMENT OF PEST POPULATION A second basic measurement in pest management is pest population. Obviously it is not plausible to count the total number of pests in a field. Some subsample must be used as ea proxy. Several alternatives are used in practice. Using alfalfa weevil larvae as an example, common measures include the number of larvae per thirty stem sample, the number of larvae per twenty sweep sample and the number of larvae per square meter. Desirable characteristics of any sampling technique include the ability to repeat similar samples from the same sampling universe and ease in use. A thirty stem sample requires selecting thirty stems of alfalfa at random, shaking the larvae from the alfalfa and counting the number of 67 larvae. The larvae may or may not be sorted into instars4 depending upon the data needs of the decision maker. It is difficult for a scout to select a truly random sample. There also may be great variability within a field. It is difficult for two individuals to get similar counts within the same field. A thirty stem sample has the advantage of recovering each age class of larvae with equal probability. That is, it is not more likely to detect one instar than another. The use of the sweep net as a sampling tool allows a scout to cover a large area relatively quickly. Several problems arise with the use of sweep nets, however. A study by Cbthran and Summers (1972) described differences in the ability to collect larvae of different age classes with a sweep net. In a later study, Cothran, Summers and Franti (1974) made a comparison of two standard sweep net techniques, the 180° sweep and the pendulum (P) sweep. They determined the average ratio of the mean of the 180° to that of the P sweep was about 1.76:1 when counts were low and about 1.8:1 otherwise. They found the two methods to be equally reliable but recommend the 180° sweep for low populations because it is more likely to recover larvae. The study also looked at variation in counts among individuals using each tool. Significant differences in counts resulted among some of the individuals. The authors conclude that the results of sweep net sampling are not precise enough to use as the only basis for insecticide recommendations. The number of larvae per square meter is a concept used only in mathematical models. It is not feasible for field work simply because 4Instars are the stages of an insect between successive molts. A molt in insects and other anthropods is the shedding of the exoskeleton. 68 it is unthinkably labor intensive. If an average number of stems per square meter is estimated and an average number of larvae per thirty stem sample is known, it is a simple matter to estimate the average number of larvae per square meter. It should be emphasized that alfalfa 2 varies stands are uneven within a field and the number of stems per M with variety and age of the stand. Nonetheless, the results of field trials using a thirty stem sample are comparable to the results of simulation models based on an M2 measure, if an assumption is made about the number of stems per M2. No such conversion is possible between sweep net samples and larvae per thirty stem sample without research (similar to the Cothran study) devised specifically to compare the two techniques. The use of different sampling techniques and units of measure makes synthesis of data in the literature difficult, if not impossible. In particular, the effect of larval population on alfalfa yield estimated in various studies cannot be compared when population is estimated using different methods. Sweep net data are usually presented without mention of sampling method again leaving comparison of results potentially inaccurate. This is a perfect example of a situation where the underlying concepts are consistent across research but the definitions of variables are not. Variables are often defined for compatibility with measurement techniques available. The economic threshold is a fundamental concept in pest management (see 2.3). It is the population level beyond which the value of pest damage will exceed the cost of control. The economic threshold provides growers with information about expected loss to aid in pest control decision making. 69 In its simplest form, the economic threshold is a population level. Therefore, it can be presented in at least all of the ways described above for presenting pest populations. A single population level says nothing about dynamics throughout the system. ll specified population level at the beginning of the season is not differentiated from the same p0pulation level at the middle or end of the season. Based on that single piece of information it is impossible to know whether pest populations are expected to increase or decrease in the immediate future. To circumvent this problem the economic threshold is often described in terms of peak population density. Of course, in practice, it is impossible to identify the occurence of the peak population level until after it has passed. This information, while useful to researchers for discovering the relationship between pest population and crop loss, cannot be used for pest control decisions unless peak population can be predicted with some level of accuracy. The expected time of the population peak can be estimated from past experience and is typically expressed in terms of degree days (e.g. peak population always occurs before 950 degree days base 48°F). It can also be predicted using mathematical models. The economic threshold need not be a single measure at a single point in time. The term 'dynamic threshold' refers to a threshold that changes over time. For example, a dynamic threshold may be expressed as a series of pest populations coupled with degree day measures. Alternatively, it may be expressed as a series of pest populations coupled with some measure of plant development (e.g. plant height or plant stage). 70 In order to test any hypothesis about the effect of alfalfa weevil feeding on quality and yield, some unit of measure of pest population over time has to be selected. Several alternatives exist for measuring pest population. Quite often population at peak infestation is used as a gauge to compare infestations in different ,years. However, this measure does not capture the distribution of the population throughout the season. Further, peak population cannot be used for control recommendations unless it can be accurately predicted from prior observations of population level. Procedures are not presently available to satisfactorily predict the date and magnitude of the larvae peak. One method used to circumvent these problems is to construct a variable to measure pest populations over time. For each sample date the number of larvae is plotted against the degree days accumulated from January 1 above the base temperature of 48°F (8.9°C) (Litsinger and Apple, 1973), the threshold for larvae development. The area under the curve obtained by connecting the data points corresponds to the measure of larvae degree days accumulated during the season (Figure 3.3). An estimate of the larval peak is not needed to calculate larvae degree days. Further, using growing degree days allows for comparison of data from different seasons and locations. The measure is also appropriate for a variety of sampling regimes. It requires only that samples be taken using a uniform population measure (e.g., number of larvae per 20 sweeps, number of larvae per stem). The most commonly encountered means of presenting an economic threshold have been outlined above. The list of alternative specifications is endless. The point is, that starting with the 71 1500- H H O N 0 U1 9’ 93 750- 500- ALFALFA MEEVIL POPULATION 250- 1 16 31 15 3O 15 --- "Av --- --- JUNE --- --- JULY ' Figure 3.3 Calculation of larvae degree days 72 theoretical concept of'ani economic threshold, information provided to growers will vary depending upon the definiton of variables, measurement techniques, and format used for presentation. 3.2.4 Decision Making Under Risk and Uncertainty An individual makes decisions in an evironment characterized by uncertainty whenever there is imperfect information regarding the problem to be solved. In this subsection the decision making process under conditions of imperfect knowledge will be given some rigor. The discussion can be interpreted as an elaboration of the final element of Bonnen's information system - “Decision Making" (Figure 3.1). Risk and uncertainty affect production and consumption decisions when the outcome of an action is not known with certainty at the time the action is chosen. Frank Knight (1921) made the classic distinction between risk and uncertainty. He defined risk as a condition in which the possible outcomes of an action choice can be assigned a probability and uncertainty as a condition in which information about the relative chances of the different outcomes is not available. While certain aspects of a decision reoccur over time for many decisions, repeated trials are not possible to discover the frequency with which outcomes occur. This does not mean that decisions are made ad hoc. Rather, people make decisions based upon their own ideas of probability (Ramsey, 1931; Savage, 1964; and Raiffa, 1968). These subjective probabilities are derived from objective evidence, personal experience and other sources. By assuming that for each decision there is a known set of possible outcomes with an associated subjective probability distribution the distinction between risk and uncertainty 73 collapses and the terms can be used interchangeably for all intents and purposes. The choice of a production strategy can be represented in a decision theory framework using El decision matrix (Table 3.1). There are ii action choices (Aj, j == 1, 2, ...n) and ni possible states of nature (Ni’ i == 1, 2, ...m) with a probability (Pi) assigned to each state of nature. For each combination of action choice and state of ij)° The simplest way to select among the action choices is to express nature there is an associated outcome (0 each outcome in terms of a monetary value and maximize expected returns.5 The maximizing principle can be expressed mathematically as: m : . = P. .. - ng E(OJ) 15] 1 013 (3 1) m and 2 P. = 1 (3-2) Behavior under uncertainty is often explored using game theory. Games that cost their expected value to play are called fair games. In the eighteenth century' the inathematician Daniel Bernoulli rigorously investigated the observation that in many situations people will refuse to play fair games. He illustrated this point with the famous "St. Petersburg Paradox". 5For example, the outcome of an agricultural production decision (action choice) can be expressed as 3 tons per acre or $300 dollars per acre (assuming each ton of production is valued at $100). Decision Matrix for Decision Making Under Uncertainty 74 Table 3.1 States Prfibagilities Action Choices of Nature States Al A2 A3 . . An Ni P1 011 012 013 . . 01" N2 P2 021 022 023 . . . 02h N3 P3 031 032 033 . . 03“ Nm Pm 0m] 0m2 0m3 ..... 0mn 75 Bernouillian decision theory offers an alternative to the maximize expected returns rule. The underlying hypothesis is that the relationship between income and utility is not necessarily linear. If the preferences of an individual are consistent with certain behavioral axioms and if an individual's utility function is known, it can be used to predict his choice among risky action choices (for which the probabilities of possible outcomes are known). Bernoulli developed an approach known as the expected utility hypothesis. The steps involved are the following: 1. Identify the possible action choices. 2. Identify the possible outcomes for each of the action choices. 3. Identify a probability density function for the outcomes. 4. Derive utility measures for the outcomes. 5. Determine the expected utility for each action choice by summing the utility measures for the outcomes which are weighted by the associated probability that each outcome will occur. 6. Select the action choice which produces the highest expected utility. This procedure for implementing the Expected Utility Hypothesis can be expressed mathematically as: n n m3x:E[U (Oj)] = U[E(Oj)] = U121:1 Pi(0ij)] = iil P1U(Oij) (3-3) n and X P = 1 (3-4) 76 where: U(Oij) is the utility function for the decision maker and “MB PiU(0ij) is the expected utility of action choice j. i 1 In 1944 the expected utility hypothesis (EUH) was derived by von Newmann and Morgenstern from a set of axioms for "rational" behavior. Alternative sets of axioms can be used to deduce the EUH. Important questions have been raised about the axioms and no universally agreed upon set has been developed. Most proofs of the EUH require at least the following properties: 1. Orderability - An individual's preferences are transitive. For any three probability distributions, h1, h2’ and ii if a person 39 prefers h1 to h2 and h2 to h3 then he necessarily prefers h] to h3. 2. Continuity - There is a continuous complete ordering of preferences. 3. Independence - If h1 is preferred to h2 and h3 is some other probability distribution, then a lottery with h1 and h3 as prizes will be preferred to a lottery with h2 and h3 as prizes. If decision makers have preferences consistent with the above axioms then an ordinal utility function can be drived which reveals his preference ranking of possible outcomes. The utility function is unique up to a linear transformation. If in addition, the decision maker has a subjective probability distribution associated with the set of outcomes for any action choice, then the expected utility of each action can be calculated. Further, the expected utilities can be used to rank or order the action choices according to the decision makers' preferences. 77 Bernoullian decision theory separates decision making under uncertainty into two components, utility and probability. Following this approach, prescriptions can be made for a decision maker as to which action choice should be selected based on an individual's subjective probability function and utility function. In practice, it is difficult to ascertain both an individual's utility function and a probability distribution of the outcomes. Further, while the expected utility hypothesis is appealing because it allows for a complete ordering of stochastic events, it lacks generality. A utility function unique to an individual cannot be used to predict someone else's behavior. Utility functions must be defined for each individual in order to apply the EUH. It can further be argued that utility functions must be defined for each individual and each problem to be solved. That is, an individual may derive more utility from $100 gained from choosing a better seed variety then $100 gained in a wager (even after the costs of making the decision or placing the wager are considered). It follows that a single utility function cannot be derived for an individual to predict behavior in a variety of uncertain situations. In order to apply the EUH it may be necessary to derive a utility function for each individual and each decision situation. Various attempts have been made to establish general properties of utility functions and to construct decision rules based on these properties. The fundamental approach has been to categorize utility functions by the shape of the function without specifying the function precisely. Each category corresponds to an attitude toward uncertainty. 78 Decision rules are then developed for each attitude which can be used to predict behavior.6 The question remains as to whether or not it is meaningful to categorize an individual as having a particular attitude toward risk regardless of the problem to be solved. This does not make it impossible to make statements about behavior without specifying the utility fonction. It does mean that an individual may not follow the same decision rule in every situation. In the following discussion decision makers are described as risk-averse, risk-neutral or showing risk preference, depending on the shape of their utility functions. Precise meaning is given to these terms. It is possible that an individual will be risk-averse in one situation and risk seeking in another. The theory presented below was developed under the simplifying assumption that an individual's utility function does not vary from one situation to another. However, the theory developed is appropriate to the more general case if the reader keeps in mind that one individual can display different behavior at different times, i.e. have more than one utility function. While the theory is intended to categorize groups of individuals according to their attitude toward risk, it may only be appropriate for categorizing utility functions. All decision makers are expected to have positive marginal utility for additional wealth. That is, an increase in wealth is always assumed 6Any decision rule is also a means of predicting behavior when a decision maker is rational. For example, the EUH can be interpreted as a decision rule for selecting among action choices or as a way of predicting an individual's action. 79 to be desirable. If it is also assumed that the utility function is differentiable, then: W (X) > 0 (3-5) If the second derivative, U" (X) exists, then it is the rate of change of marginal utility with respect to wealth. If U" (X) > O, the marginal utility of wealth, U'(X), is strictly decreasing as wealth, X, increases and the decision maker is characterized as a risk averter. If U"(X) = 0, then U'(X) is constant as X changes and risk neutrality is demonstrated. If U"(X) > 0 then U'(X) increases as X increases and the decision maker shows a preference for risk. It appears that the marginal utility (U'(X)) and the rate of change of marginal utility (U“(X)) are meaningful measures for comparison of the risk preferences of individuals. But a utility fuction is unique only up to linear transformation. This means that for a utility function U(X), adding a constant to U(X) or multiplying the function by a positive constant does not change the resulting preference ordering. Adding a constant to U(X) does not change the values of U'(X) or U"(X). However, multiplying U(X) by a positive constant also multiplies U' and U" by the same constant. Therefore, comparing the first or second derivatives of two individual's utility functions is meaningless. Two measures of attitudes toward risk that are invariant under linear transformation of the LHfility fonction have been suggested by Arrow (1965) and Pratt (1964). They are: 1. Coefficient of absolute risk aversion RA(X) - U"(X)/U'(X) 2. Coefficient of relative risk aversion RR(X) - XU"(X)/U'(X) 80 Arrow and Pratt give two different but consistent interpretations of the coefficients. Both assumed that any individual is predominantly risk averse. Arrow considers a lottery that involves a specified prize, h, with probability p of winning and probability 1-p of losing. The willingness of an individual to play will depend on the value of p and his present wealth, X. Absolute risk aversion measures the individual's insistence for more than fair odds. (A risk averter will refuse to play if p<1/2). If the prize is measured in proportion to his present wealth (i.e. h = nX) a similar interpretation can be made for relative risk aversion. Pratt's interpretation is based on the concept of an insurance premium. An individual is offered the choice between a random income with mean, u, and variance, 02 and a certain income of X*. The difference between the expected income and the certain income (u-X*) can be interpreted as an insurance premium. In particular, there exists an income level X** such that the individual is indifferent between the certain income and the random income. This quantity is referred to as the certainty equivalent. The absolute risk aversion and relative risk aversion coefficients measure the absolute and relative size of the corresponding insurance premium, respectively. A more risk-averse person would be willing to pay a higher insurance premium to avoid the risky income. An interesting variation on this approach is presented by Magnusson (1969). Here the utility function has two arguments, the mean and variance of a random income. The certainty equivalent is then that income X** such that: 81 u = U(u, 02) = 0 (X**, 0) (3-5) Holding utility at a constant level (i.e. dU = 0) and differentiating the utility function: 2 U du + U do = O 1 2 U1 and U2 stand for the partial derivatives of the utility function with respect to the first and second arguments, respectively. Then assuming that U1 > O, the marginal rate of substitution between u and 02 can be found from (3-6) as: du U2 du d02 U1 doZ U1 The ratio of differentials can be interpreted as the marginal rate _ 2 (3-7) of substitution between expected income and the variance of the income. If the variance is interpreted as a measure of risk, then the ratio is the marginal rate of substitution between expected income and risk. Any other measure of risk could be used to obtain the same result. The author goes on to say that if the ratio is positive (U2 < 0) there is a risk-aversion, if it: is zero (U2 == 0) risk-neutrality and iii it is negative (U2 > 0) risk-preference. The classification of a decision maker as risk-averse, risk-neutral or a risk-taker can be used to predict his preferences among action choices without deriving his utility function. Ideally, the action choice that would maximize expected utility for all decision makers regardless of their risk preferences could be identified simply from the distribution of the outcomes. Although it is possible to construct a set of action choices and related outcomes such that one action choice would be preferred by all decision makers, for an arbitrary opportunity set, such a universal utility maximizing action choice does not necessarily exist. A less ambitious but more fruitful venture is to 82 identify a subset of the action choices in such a way that the utility maximizing action choice is necessarily contained in that subset for a large number of decision makers. Valuation procedures that make use of a classification of utility functions and the distribution functions of outcomes to reduce the number of desirable action choices are referred to as efficiency criterion. Efficiency criteria have a tendency toward Type II error (Robison 1977). That is, the null hypothesis that a decision maker will be indifferent between two action choices may be accepted when it is false. EFFICIENCY CRITERIA IN DECISION MAKING Several efficiency criteria have been devised which make specific assumptions about attitudes toward risk but do not require specification of a single value utility function. Some examples follow. The first, which has been described above, is to choose the action alternative with the largest expected value. Max:E(0..) = g -) (3'8) 13 This criterion is identical to utility maximization of U(O ) = 0 ij ij’ that is, the decision maker is indifferent towards risk. In this case, the marginal utility of wealth is neither increasing or decreasing. A safety first criterion is another possibility for explaining the behavior of decision makers. This formulation of the decision function assumes that the grower maximizes expected value discounted by some measure of risk. ”2 s.) (3-9) M§X1[E(Oj) - a J 83 The standard deviation of the value of outcomes for action choice Oj is denoted by Sj and a is the critical probability level. By setting a=0 we get the trivial case of risk neutrality. As the absolute value of a increases, the decision maker attributes a higher cost to variability of income and demonstrates increasing risk aversion. The criteria does not allow for a preference for risk. Safety first is consistent with the expectation-variance criteria (E-V criteria). Using the E-V criteria, decision makers faced with two sets of outcomes with the same expected values and different variances will prefer the set with the smaller variance. The maximim criteria represents extreme risk aversion. The decision maker assumes the worst will happen and compares the worst possible outcomes for each action choice. He then selects the action for which the worst possible outcome has the greatest value regardless of probability. The decision function is: M3x:(min: Oij) (3-10) Other examples are first degree stochastic dominance, second degree stochastic dominance and Meyer's stochastic dominance with respect to a function. These criteria are rigorous procedures utilizing the cumulative probability functions of outcomes related to action choices. The criteria differ in the underlying assumptions about the risk preferences of decision makers. Less restrictive assumptions allow the results to be more general but at the same time make it more difficult to reduce the number of action choices in the opportunity set. The probability of Type 11 error is increased. 84 FIRST DEGREE STOCHASTIC DOMINANCE First degree stochastic dominance assumes only that the marginal utility for wealth is positive over the relevant income range (i.e. U'(X) > 0). Then -w :_RA = - g;-: m. The procedure for comparison of action choices is as f0110ws. Suppose X euni‘Y are stochastic income variables associated with action choices A1 and A2 with cumulative distribtution functions F and G, respectively. F and G may be either continuous or discrete functions. Let r be any income level. Then let: F(r) : G(r) for all r (3-11) and F(r) > G(r) for some r (3-12) It follows that U(Y) > U(X) for all U such that U' > O and A1 is preferred to A2. F is said to be the dominant distribution. If G(r) i F(r) for all r and G(r) > F(r) for some r then U(Y) > U(X). In this case G is dominant and A2 is preferred to A1 for all positive utility functions. If’ neither: distribution is dominant, the action choices cannot be ordered by this criteria. Figure 3.4a and 3.40 illustrate first. degree stochastic dominance for continuous and discrete distribution functions. For two discrete income distributions with the same numbers of observations, an equivalent specification of FSD exists. Let Xi and Y, be ordered sets of n income observations (i.e., Y. < Y. X. :_X l 1 —- i+l’ l .< i < n-l) for action choices A1 and A2 respectively. Let X0 and Y0 1+1: equal 0 and Xn+1 and Yn+1 equal infinity. Then cumulative probability functions can be constructed for the income observations as follows: F(X) = g; for x1. :x < xM i O,l,2,...n (3-13) G(Y) %for Y1. iv < rm i O,1,2,...n (3-14) 85 1.0 : ..J 23 g .6 x ‘+—— e . 1 E J1 euJ 22 I g I a .2 1: T F(X) __--.. 1 G(Y) 0.0 ' INCOME Figure 3.4A. First degree stochastic dominance (FSD)--F(X) and G(Y) are discrete probability distributions. LO t .8 3 e g .6 E 3 .4 E 3 2 z I 8 / Fe)---- I G(Y) 0.0 .1 INCOME Figure 3.48. First degree stochastic dominance (FSD)--F(X) and G(Y) are continuous probability distributions. 86 The distributions constructed in this way assure that each observation is equally likely. If we let r represent income level then distribution F dominates G and action choice A1 is preferred to action choice A2 if and only if: G(r) - F(r) :_O for all r :_ 0 (3-15) and G(r) - F(r) > O for some r_: 0 (3-16) This procedure is illustrated in Table 3.20. The values of F(Xi) and G(Yi) are constructed following (3-13) and (3-14). In this example condition (3-15) is satisfied but (3-16) is not. F and G cannot be ordered and the decision maker is indifferent between A1 and A2. An alternative» and consistent test for first degree stochastic dominance can be performed by comparing the values of X1 and Y, for each i. The distribution of X dominates the distribution of Y if and only if X]. is greater than or equal to Y]. for all i and a strict inequality holds for some i. F dominates G and action choice A1 is preferred to action choice A2. Mathematically: X1 - Y, :—O for all i (3-15)* Xi - Yi > O for some i (3-16)* where: F (X1) = G(Yi) for all i and (3-17) U'(r) > (3-18) An example is given in Table 3.2a. Notice that both procedures failed to order the action choices by F50. The difference between the conditions 'hi (3-15) and (3-16) and those 'Hi (3-15)* and (3-16)* is simply that in the former case the probability levels for each distribution are being compared for given income levels while in the latter case the income levels for given probability levels are being compared. Similarly, if Yi is greater than or equal to Xi for all i and 87 Table 3.2a Hypothetical income data for 2 action choices. corresponding cummulafive distribution functions. and tests for F30 and SSD. 1 X1 F(Xi) Y; G(Yi) X3- Y1 XXI-Y1 l 200 .2 100 .2 100 100 2 400 .4 100 .4 300 400 3 400 .6 500 .6 -iOO 300 4 550 .8 550 .8 O 300 5 600 1.0 550 1.0 50 350 Table 3.2b Alternative tests for first and second degree stochastic dominance using data from Table 3.23. income F(r) G(r) G(r)-F(r) ZG(r)-F(r) (r) 100 0.0 .4 .4 .4 200 .2 .4 .2 .6 300 .2 .4 .2 .8 400 .6 .4 -.2 .6 500 .6 .6 .O .6 550 .8 1.0 .2 .8 600 1.0 1.0 .O .8 88 strictly greater for at least one i then G is preferred to F. If neither set of conditions holds then first degree stochastic dominance fails to produce an ordering. SECOND DEGREE STOCHASTIC DOMINANCE Second degree stochastic dominance (SSD) makes an additional assumption about the character of the utility function. The marginal utility of wealth is assumed to be increasing (as with FSD) but at a decreasing rate. This implies that U" (X) < 0 and RA(X) ranges from 0 to positive infinity. The further restriction of the utility function means that SSD results are applicable to a smaller group of decision makers than are FSD results. SSD has the advantage that it can order action choices that are determined to have identical utility under F80. The second degree stochastic dominance criteria works as follows: Let F(X) and F(Y) be continuous cumulative distribtuion functions for the outcomes of actions A1 and A2, respectively. Then F(X) dominates G(X) if and only if: R 6[G(r) — F(r)] dr :_0 for all R (3-l9) and R 6[G(r) - F(r)] dr > O for some R (3-20) U(Y) < U(X) for all U such that O_: RA(r) :_w. In this case F is preferred to G (Figure 3.5a). Intuitively, A1 reduces the probability of a low income in comparison to A2. On the other hand A2 has a higher probability of a very high income. However, if the decision maker is risk-averse, that is, his marginal utility for wealth is decreasing, 89 1.0 . z: .8 - 23 m a“ g .4- EE : F( > 3 l2_ “— i X ---_ E l G()-— ‘J l 0.0 . INCOME Figure 3.5A. 1.“ l): 8" 3 a 35 g; .6 - §§ .4 — '— :5 D g; .2 - U 0.0 Second degree stochastic dominance (SSD)--F(X) and G(Y) are discrete probability distributions. , F(x) -—-- / G(x) ———- Figure 3.5B. INCOME Second degree stochastic dominance (SSD)--F(X) and G(Y) are continuous probability distributions. 90 then the utility gained by avoiding low incomes will more than offset the utility lost by decreasing the probability of very large incomes. If" F and G are interchanged in (3-19) and (3-20) then G is preferred to F for the appropriate utility functions. If strict equality holds in (3-l9) and condition (3-20) is not met, then the action choices cannot be ordered by SSD. The conditions for discrete cumulative distribution functions are: II M: [G(ri) — F(ri)] > for all n (3-2l) i l and HM: [G(rj) - F(ri)] > 0 for some n (3-22) 1 where: 0.: RA(r) : w. Here F is preferred to G (Figure 3.5b). If Xi and Y1 are ordered sets of n observations then F(x) and G(x) can be constructed as in (3-l3) and (3-14). An equivalent set of conditions for SSD is: n+l Z (X. - Y.) > O for all n (3—23) i=0 ‘ ‘ — and n+1 2 (xi - Y1) > 0 for some n (3-24) i=l where: F(Xi) = G(Yi) (3—25) X0 : YO : O (3'26) 9] O _<__Xn+1 = Yn+l g_w (3-27) 0 :RAM :w (3-28) Then U(X) is greater than U(Y) and F is preferred to G. Notice that in the examples illustrated in Figures 3.5a and 3.5b the FSD criteria fails to order the action choices while SSD ranks F preferred to G. It must be emphasized that the latter result is only relevant for risk-averse decision makers. A distribution function may be first degree dominant over some range of income but not dominant over a larger range. In Figure 3.4b F dominates G over the entire income range. In Figure 3.5b F is ffirst degree stochastic dominant over part of the income range but not the entire range. However, F is second degree stochastic dominant over the entire income range. The second degree stochastic dominance criteria applies to a class of decision makers that includes those who are risk neutral and those who show any degree of risk aversion. The resulting preference ordering is dominated by the values of distributions at very low incomes. A distribution F(X) cannot dominate G(X) unless F(X) > G(X) for the lowest observed value of X. This problem is often referred to as the left-hand tail problem. ll second problem vfiifli SSD arises concerning decision makers with Friedman-Savage utility functions. That is, decision makers who are risk-averse over a broad range of incomes but are risk preferers at very high incomes. This form of a utility function was developed to explain participation in lotteries. SSD fails to account for different preferences at different income levels. 92 STOCHASTIC DOMINANCE WITH RESPECT TO A FUNCTION Stochastic dominance with respect to a function is a criterion for ordering uncertain choices developed by Meyer (1977) in response to these difficulties. The criterion relaxes the restrictions on the value of the rfisk-aversion coefficient required tut first and second degree stochastic dominance but at the same time does not require the derivation of a single valued utility function. The criterion requires establishing upper and lower bounds on the risk-aversion coefficients Ur and LV for all feasible income levels. The bounds are functions of income. Mathematically, In practice, upper and lower bounds are established for intervals of income levels. The solution procedure developed tn/ Meyer requires identifying a utility function, u(y), which minimizes, 7 r3[G(y) - F(y)] u'(y) dy (3-29) subject to the constraint, r1(y) _<_-U"(y)/U'(y) : r2(y). for all y (3-30) 7The range of system outputs is normalized so that all values of y fall on the bounded interval [0, l]. 93 It can be shown that equation (3-29) is equal to the difference between the expected utilities of outcome distributions F(y) and G(y).8 For decision makers whose utility functions satisfy the above constraint (3-30), if the minimum value of this difference is positive then the expected utility of F(y) is always greater than the expected utility of G(y). Consequently, F(y) is preferred to G(y) for the appropriate class of decision makers. If the minimum is less than or equal to zero, the decision makers do not unanimously prefer F(y) to G(y). Neither can it be said that G(y) is preferred to F(y). If the minimum is negative, then a second equation .gmyl - G(y)] u' (y) dy (3-31) must be minimized subject to the constraint (3—30). In this case, if the minimum value is positive than G(y) is preferred to F(y). If the results of uninimizing (3-29) and (3-3l) are both negative then the criterion fails to order the distributions. Put another way, neither distribution is unanimously preferred by the class of decision makers included. 8This can be demonstrated in the following manner. Let f(y) and g(y) be the probability density functions associated with F(y) and G(y) f5 f(y)U(y)dy - f8 g(y)U(y)dy = f8 [f(y)-g(y)lu(y)dy is the difference between the expected utilities associated with the two distributions. Integrating by parts, r2, [f(y)-g(y)]u(y)dy = [F(y)-G(y)]uu) 3,43, [F(y)-G(ynu'uidy = f5 [G(y)-F(y)JU'(y)dy since [F(0)-G(O)] and [F(l)-G(l)] are both equal to zero. 94 It should be mentioned that first and second degree stochastic dominance are special cases of stochastic dominance with respect to a function. For FSD, Ur = wand Lr = -m, for all y. For SSD, Ur =w and Lr = O, for all y. 3.2.5 Information Learning and Decision Making From the discussion in 3.2.2, management can be conceived as a process for which information is an input and decisions are an output. In this light information only has value in the context of a decision. The manager must define the problem, collect information, analyze the information and make a decision. These steps involve identifying l) the action choices available, 2) information needed to choose among the action choices, 3) a procedure for analyzing the information and 4) a decision rule for selecting the best of the known action choices. These steps are not necessarily carried out in any order. The gathering of information might reveal additional action choices and reformulation of’ the problem. The analysis procedure inight require gathering additional information, and so forth. A producer typically requires a broad range of information for making a production decision. The three categories of constraints facing a firm that were discussed in Section 3.2.1 can be interpreted as categories of information. They are: l) technical, 2) market and 3) government. A pesticide use decision requires information about the performance of the pesticide in controlling pest populations. The price of the pesticide and the value of the crop loss is also information required for the decision. Regulatory information about each pesticide 95 considered for use is also necessary. This framework was formalized in the Headley model presented in 2.3. The mix of information required to solve the problem is imbedded in the equations of the model. Each type of information has a temporal dimension. Information about the past and present is used to form expectations about the future. In addition each category of information has both a positive and normative dimension. (Johnson et al., l96l).9 Normative information includes market and nonmarket values about the past, present and future. While positive information is used to predict the physical consequences of EH1 action choice, normative information is used to predict the goodness and badness of the consequences. The set of consequences to be considered is determined in the problem definition stage. In the Headley model (Sec. 2.3) the problem is defined for a single field and a single year. The impact of a control decision on pest populations in subsequent years or an adjoining field are not included in the analysis. Consequently, these impacts are not part of the weighing of "goods" and "bads". Further, no information about the probable impact on other fields or future pest populations is required. These consequences will not be part of the decision making process, regardless of the decision rule used, because they have not been specified for inclusion in the analysis. Thus, the values of the decision maker are imbedded in the outcome by design of the problem. 9Johnson identifies three broad categories of information as institutional, technological and human. The third category includes both market and nonmarket values. 96 Once the problem is clearly defined, the Type I and Type 1110 errors that are acceptable to the decision maker must be specified. From this specification the cost and value of additional information can be calculated. The decision maker then must determine not only what form of information is necessary, but also what level of precision. The riskiness of a decision depends on the reliability of all of the information used in all stages of the decision process. The reliability of the decision rule is only one source of uncertainty. In pest management there is a trade-off between uncertainty in modeling and uncertainty in monitoring. The more accurately predictions about future states can be made from current information (models) the less accurately present states need to be measured (monitored). Conversely, an accurate measurement of the present state may compensate for a less accurate predictive model. The information contained in a pest management model used to predict future states of an agro-ecosystem is a synthesis of prior knowledge. Sample observations are collected by monitoring to estimate the current state of the system. Bayes Rule or Bayes Theorem is a formal procedure for combining estimates from sample observations with prior knowledge so that both can be used in the decision making process. Prior knowledge may be the result of observation, purely subjective, or a combination of both. Bayes Theorem can be interpreted as a means of updating probability distributions derived before present information had become available. Alternatively, it can be viewed as a means of combining information from 10A Type I error is accepting a hypothesis when it is false. A Type 11 error is rejecting a hypothesis when it is true. 97 two different sources. The fundamental theorem will be presented below.H Suppose that an event, A, can occur only if events B1 or 32 occur. Further either B1 or 82 must happen but both B1 and 82 cannot occur simultaneously. The occurrence of B1 or B2 does not depend on the occurrence of A. However, either B1 or B2 must occur in order for A to occur. B1 and B2 can be viewed as alternative hypotheses and A as a sample observation. The probabilities of the compound events AB1 can be written as P(AB1) P(B1) P(AIB1) (3-32) Oi" P(AB1) P(A) P(B1'A) (3-33) where P(AlB1) and P(B]|A) are conditional probabilities. The objective of Bayes formula is to infer from the occurrence of A which hypothesis, B1 or B2, to accept. Solving the equations for P(B]|A), P(B1IA) = P(B1) P(A'B1) (3-34) P(A) Quite often it is difficult to assess the probability of A. But since A can only occur when B1 or B2 occur, P(A) = P(B1) P(AIB1) + p(32) P(AlBZ) (3-35) To put Bayes Rule in the context of information systems and decision theory, B1 and 82 can be interpreted as hypotheses about a future state of nature. P(B1) encapsulates a prior knowledge about the likelihood of a particular state of nature. It may be the result of HThe discussion presented follows the presentation of Bayesian analysis in K.J. Cohen and R.M. Cyert, Theory of the Firm, Englewood Cliffs:Prentice Hall, Inc., 1975, p. 459-460. 98 repeated sampling, sequential sampling, subjective probabilities or any combination of these. A is an observation of the current state of nature. In pest management A would be the result of biological and/or environmental monitoring. Then the posterior probability, P(B1 A) is the likelihood that B1 will occur based on previous knowledge and current information about the status of the system. The anlaysis can easily be extended to consider n possible states of' nature B], B2,...Bn. It follows that, the probabilities used to maximize utility are a function of the information system utilized. In Bayesian statistics, information is summarized in a prior probability function. The prior probabilities are revised as new information becomes available. This process is called sequential sampling (Wald, l947). In classical statistical theory, hypotheses are tested by repeated sampling. Given a data set and a choice between two hypotheses the analyst will either: l) accept the null hypothesis; or 2) reject the null hypothesis. The only information utilized is the data set generated from the repeated sampling procedure. Using sequential sampling, an analyst may fail to accept or reject the null hypothesis, and choose to gather more information before making a choice. The sequential sampling procedure is compatible with the mathematical approach to learning develOped in the psychology literature (Bush and Mosteller, l955). Learning is defined as any systematic change in behavior. In a probabilistic view of behavior, an individual has a probability, p, of making a particular response. Learning is measured 99 by the change in the individual's probability of making the response. Learning has ended when there is no longer a change in the probability of a particular response. The definition of learning is meaningful in a decision theory context if learning is interpreted as a change in the decision maker's subjective probability function for the possible states of nature. The decision maker starts with a prior probability function. He gathers additional information and then revises that probability function. In turn, the change in probabilities corresponds to a change in the selection of an action choice. Uncertainty about the states of nature are expressed in the probability function. Any change in the probability function is learning. Glenn Johnson (l96l) has identified five knowledge situations under which decisions are made. In the case of subjective certainty, knowledge is so complete that the decision maker can act without protection from possible mistakes. In essence, the future state of nature is known with certainty and the variance of the probability function is O. The remaining four cases are examples of subjective uncertainty. As stated above, specifications for choices must be set. In particular, the probabilities of Type I and Type II errors that will be tolerated must be specified. The marginal cost (MC) and marginal utility (MU) of additional information can be determined from this specification. Learning is the situation where no decision can be made (MC < MU) and the decision maker continues to gather information. In the jgrggd action situation learning is ‘terminated prematurely even though the 100 decision maker would like more infonnation. For example, poor weather or a court order can terminate the learning process. Inaction occurs when the marginal utility of more infonmation is so low you are not in a learning situation but you do have uncertainty. The specifications for a choice cannot be met but the cost of obtaining additional infonnation exceeds the value of that information (MC > MU). Finally, involuntary learning or forced learning takes place when a decision is made under the constraint of an administrative action. Learning is the internalization of knowledge. New information and past experiences are synthesized to improve decisions made under uncertainty. Learning implies improvements in the prediction of future states of nature. Attitudes toward risk reflect what degree of uncertainty is acceptable with respect to these predictions. Therefore, learning will continue only when this acceptable level is not met. 3.2.6 Risk Preferences and Pest Management Decision Making - Empirical Results Several studies have looked into the question of attitude toward risk with regard to pest management decisions and the demand for infonnation. The results of two studies are presented here. Hanemann and Farnsworth (1980) address the question of adoption of IPM versus conventional control related to risk considerations. They analyzed data collected in the San Joaquin Valley from 44 cotton growers over the period l970—1974. 28 of these growers used IPM and l6 used conventional chemical controls during the interview period. Several hypotheses were tested. l) There exists a difference in risk preference between growers who use IPM and those who employ conventional control. 101 2) The expected returns from IPM are different than for conventional control. 3) The variance of profits under the two strategies is not the same. 4) The subjective probability distributions of returns from IPM and conventional control are different for the two groups of growers. Utility functions for 44 growers were generated using lotteries. The growers were classified according to their risk preferences. Five growers had nonuniform preferences (i.e. risk-prone then risk-averse or risk—averse then risk-prone as income increases). Of the remaining 39 growers, 20 were risk-prone to some degree, six were risk-neutral and I3 were risk-averse to some degree. The results showed no difference in attitude toward risk of growers choosing IPM and those using conventional control. Therefore, the hypothesis that growers using conventional control are risk-averse was rejected. Based on the data set, the expected profits and variance of profits were not significantly different for the two strategies. Combining these results, adoption of IPM could not be explained by risk preference or the difference in risk associated with IPM versus conventional control. The subjective probability distributions of cotton yields, insecticide expenditures and pest damage under both IPM and conventional control strategies were constructed based on the interviews (Table 3.2). The subjective probability distributions matched the actual historic data quite well for yields but not for insecticide expenditures. The means of the subjective distributions for insecticides exceeded those of the actual distributions. The authors suggest that this discrepancy may 102 Table 3.3 Summary of Paired Comparison Tests of Means and Variances of Actual and Subjective Probability Distributions Insecticide Partia11/ Group Yields Expenditure Profits— ----------------------- Actual Probability Distributions----------------------- B°th “IPMZ/ ‘ “cc “IPM ‘ ucc “IPM = ucc Gf°ups , “IPM < “cc “IPM ‘ “cc “IPM = “cc --------------------- Subjective Probability Distributions------- — ——-- IPM _ IPM 1P" “IPM ‘ “IPM “IPM 3-“IPM IPM IPM Growers CIPMlzvolPM PIpM 2.01pM cc _ cc cc “cc ' ucc ucc Z-Vcc CC _ CC - Growers OCC - CCC UCC - CCC IPM IPM IPM IPM g! IPM IPM g/ 1P” uIPM ’ ucc “IPM ‘ “cc “IPM ’ ucc IPM . IPM IPM IPM IPM _ IPM Gr°wers “IPM ‘ “cc “IPM ‘ “cc “IPM ‘ “cc cc cc (cc cc ,cc cc CC LIPM ‘ “cc LIPM ’ “cc LIPM ‘ ”IPM cc cc cc = cc cc cc Growers 01PM > cCC CIPM OCC CIPM > PIpM 1 Partial profit - yield x actual price in l976 - all insecticide expenses. Cotton prices and noninsecticide expenses are assumed to be the same for both groups. 2p is the mean and o is the variance of the probability distribution. The subscript denotes the group to which the distribution pertains. The superscript denotes a groups subjective distribution. Where no superscript is used, the distribution is the actual distribution. For example “CC is the actual mean for conventional control. 3The result holds at the .lO level but not at the .05 level. All other cases hold at the .05 level. Adapted from Wm. Hanemann and R.L. Farnsworth, "Risk Preferences and Perceptions in the Use of IPM," paper presented at the annual meetings of AAEA, Champaign - Urbana, Illinois, 27-30 July, 1980. 103 be a reflection of expected insecticide price increases on the part of the growers. The more interesting results are in the comparison of‘ growers subjective probability distributions for the strategy they employ and the alternative strategy. Each group judged its strategy to have a higher expected profit than the alternative strategy because each underestimated the yields for the alternative strategy. Further, each group perceived the variance in the yields to be lower than for the other group. Hence, each group also perceived the variance in profits to be lower for their group than for the other group. The obvious conclusion is that it is the subjective perceptions of outcomes rather than risk preferences that explains the choice of control method. A particular' attitude toward risk does not Inake a grower a good or bad candidate for pest management services. The findings of this study are consistent with the work of Savage (l964) who argued that people act as though they make decisions based on their own judgmental probability of outcomes which may or may not be consistent with actual probabilities. These subjective probabilities are developed based ("1 evidence from formal and informal information sources. In the study, the conventional control growers obtained information from chemical salesmen and the IPM growers from pest management consultants. The very act of requesting advice, or, in the case of IPM growers, paying for advice, indicates that growers seek information to revise their subjective probability distributions. The implication is that provision of information would increase the adoption of pest management. 104 In another study of attitude toward risk and adoption of IPM, Webster (l979) used Bernoullian decision theory to analyze the problem of whether or not to spray against Septoria, a fungal disease of wheat. The study relies on the theory presented above in 3.2.4. Risky decision making was divided into two components, utility and probability. Application of fungicides was the only management strategy considered. The probability distribution of yield for sprayed fields were obtained from a plant pathologist for all possible combinations of field characteristics. The characteristics considered were: I. the stage of growth of the crop (flag leaf or flowering) 2. the observation of infection in the crop, or not 3. the forecast of an infection period in the next seven days, or not 4. the topography of the crop site-whether favorable to the disease, or not 5. the susceptibility of the variety or not For each stage of growth, there are 2 x 2 x 2 x 2 = l6 sets of characteristics. For each set, the likelihoods of several yield levels were estimated. From this subjective probability distribution, the expected yield for each set of characteristics was determined. A study of 29 wheat growers in England was conducted in order to look at the range of attitudes toward risk in wheat production. From the preliminary study, seven growers representing the range of responses were chosen for further study. For each of the seven farmers utility functions were derived. It is important to note that the utility functions estimated are intended to pertain only to wheat production and not a general attitude towards risk. In the authors words, "The 105 spraying decision is made for a particular crop at a particular time. So [the grower's] utility function for yield is estimated in relation to that crop and has significance only for it. Another year and another crop would imply another utility function". It is reasonable to assume that attitude toward risk varies by crop, region, soil, etc. For each of the seven growers the utility maximizing recommendation of spray or don't spray was calculated for each of the l6 sets of field characteristics. In addition, the decisions were made for the hypothetical case of indifference to risk. In every case except one, the recommendations for each set of field characteristics are the same for the range of attitudes toward risk represented by the seven growers. In other words, if the recommendation to spray or not spray had been based solely on the assumption of risk-neutrality in only one of the ll2 cases (16 sets of field conditions x 7 growers) would the spray recommendation have been different than the utiltiy - maximizing decision. While the utility functions derived for the growers demonstrate differing attitudes toward risk, the differences were not strong enough to effect the control recommendation. It appears that risk-neutrality is an appropriate simplification for developing control guidelines. Attitude toward risk of the farmers' tests appeared to be considerably less significant. Hi the derivation of utility nmximizing control recommendations than the specification of the probability distribution of yield under alternative sets of conditions. The analysis relied on the assumption that growers' subjective probabilities are identical ix> the plant pathologists. This means that the grower 106 fully accepts the experts' opinion and that he has continuous access to that opinion. If the growers' subjective probability fUnction closely resembles that of the plant pathologist and risk-neutrality is assumed, utility maximizing control guidelines can be developed based on expected yield under various sets of field conditions. However, given the results of the Hanemann and Farnsworth study, it is heroic to assume that growers' subjective probabilities are identical. 3.2.7 ,Application to Alfalfa Weevil Pest Management The stages of the decision making process have been identified above. They are: l) problem definition, 2) information gathering, 3) interpretation of the information and 4) making the decision. Problem definition involves identification of possible action choices. The decision making process is synonymous with selecting an action choice. The probabilities of outcomes for each action choice and possible states of nature are derived through collection of information and analysis. Ideally, information gathering and analysis will continue until the marginal cost of additional information exceeds the additional value of that information. Some normative common denominator is needed to assign values to each outcome. A decision rule must be selected for comparing the values of each outcome. An action choice is selected based upon application of the decision rule. 107 The alfalfa weevil pest management problem can be defined as reducing crop loss in alfalfa production attributable to alfalfa weevil feeding using all known techniques. The action choices available are: l) harvest early, 2) spray, cn~ 3) continue with conventional harvest schedules and don't spray (Sec. 2.4). The third choice may be viewed as the do nothing approach. For the first two alternatives an infinite number of decision algorithms is possible for selecting the timing of implementation and deciding whether or not to implement control at all. A decision algorithm is a control guideline that specifies under what conditions a particular control method should be initiated. Usually a decision algorithm consists of a threshold and a control technique that should be implemented once the threshold is reached. An example is spray if there are more than 400 larvae per square meter. A routine spray also falls under the definition. The algorithm can be defined as spray on June I. Loosely speaking, June l is the threshold. The information required for choosing a decision algorithm includes knowledge of l) pest population dynamics, 2) plant growth and 3) the interaction of the two. In addition, the efficacy of alternative management practices must be studied. Implementation of each algorithm requires certain information. The information required for applying an algorithm may include the pest population, plant height, parasite population, high and low daily temperatures, or the value of alfalfa as feed. Each of these measurements may be required on an hourly basis or once a season. 108 The identification of alternative decision algorithms involves the subdecision of choosing a monitoring scheme. The cost and value of additional information for each algorithm can be evaluated. From these results, the monitoring scheme that leads to the best results for each algorithm can be selected. Any comparison of decision algorithms should be based on the best monitoring scheme. A rule for preference ordering of decision algorithms must be selected. Several methods for selecting among risky alternatives were presented in Section 3.2.4. In order to use any of the efficiency criteria described some value must be asigned to the outcome associated with each algorithm. In Michigan, alfalfa hay is usually fed to animals raised by the same unit producing the hay. Only small quantities of hay are bought and sold. Therefore, market price is not a good measure of the value of the hay produced. The value of alfalfa hay as feed ‘will be calculated in Section 4.5. There are really two levels of decision making. The first is the selection of a decision algorithm and the second is the application of the algorithm to make a specific control decision. In many cases once a decision algorithm has been selected implementation of a control strategy becomes a skill rather than decision making. 3.3 The Public Goods Nature of Information To capsulize the framework_ presented, an information system is comprised of three activities: l) data collection; 2) interpretation of the data and 3) provision of the results of the interpretation to decision nmkers. Before appropriate information can Ina produced for 109 decision makers, the following must be established: l) data needs and a method for measurement; 2) methodology for analyzing the data; and 3) a means for disseminating the information to decision makers in a timely and relevant form. This is the design aspect of an information system. Once the information systenl is designed, the implementation of the program involves Operationalizing the same three activities. When a pest management program is viewed as an information system, the discussion is fUrther complicated by nmking a distinction between defining and Operationalizing the economic threshold. Researchers collect data, analyze the data and produce information in the form of economic threshold. This 'H; the design phase. Data collection will continue only to test and refine the definition of the economic threshold. A second data system must be developed to operationalize the economic threshold for each growing season and on a regional or grower level. The information requirements for the implementation phase are determined in the design phase but need not be identical to the information requirements of the design phase. Once data has been collected in the implementation phase it is interpreted using information generated in iflwa definition phase. In other words, current field conditions are used to predict economic loss based on information already developed. A critical aspect of the design phase is establishing which individual, group or organization will carry out each activity. In particular, should information be produced by the public or private sector or some blend of the two? Before addressing this question a more general question must be asked: Which goods and services (if any) should be provided by the 110 public sector and which goods and services (if any) should be provided by the private sector? The nature of public goods will be discussed below in the context of market failure. In the next section the ideas will be applied to the provision of information for pest management. 3.3.l Private vs. Pubic Goods First a distinction must be made between public and private goods.H In the polar cases, private goods are those for which consumption by ("we person precludes consumption by' another. Public goods, on the other hand, do not have this characteristic. Consumption by one individual does not deplete the supply of the good. This phenomena is referred to as joint supply or joint impact. Public goods, then, are distinguished from private goods by the intrinsic characteristics of the goods and not by the structure of the market sytem. A fUrther distinction (uni be made between joint impact goods fOr which consumption can be avoided and those for which it cannot. An example of the former is broadcast television, an example of the latter is national defense. The issue is whether or not consumers can exclude themselves from consumption. A parallel consideration is the ability of producers to exclude consumers. For private goods market price acts as a mechanism for HPublic goods are also referred to as collective, nonrival or social goods in the public expenditure literature. The term public good is unfortunate because it falsely imples that public goods should necessarily be provided by the public sector. It is used here out of convention. 111 excluding those who do not pay from consuming the goods. However, for joint impact goods, it may or may not be feasible to exclude those who do not pay. For example, a concert is a joint impact good for which the cost; of' exclusion is low. Fireworks, on the other' hand, have 'the characteristic of jointness and high costs for exclusion. Certain goods have high exclusion costs but are not joint impact goods. These goods are often referred to as common property resources. Examples include water and air. When clean air is used for waste disposal by one industry the supply is reduced. At the same time, it is difficult to establish ownership rights and to exclude those who do not pay. Some public goods have the simultaneous characteristics of high exclusion costs and nonoptimal avoidance tn/ the consumer. For these goods it is at the same time impossible for the producer of the good to exclude individuals from consuming the good and impossible for individuals to exclude themselves from consuming the good. Four categories of public goods exist: l) joint impact—avoidance optional, high exclusion cost; 2) joint impact-avoidance optional, low exclusion cost; 3) joint impact-avoidance nonoptional, high exclusion cost; and 4) joint impact-avoidance nonoptional low exclusion cost. The last category is the empty set because it is impossible to exclude someone from consuming a good who cannot avoid consuming the good. Examples of the other three categories are pesented in Table 3.4. The nature (Hi public goods presents serious problems for decentralized markets. Only one commonly consumed quantity is produced. Regardless of whether or not it is possible to avoid consumption of the good once it is produced, the consumer cannot vary the quantity 112 Table 3.4 Interaction of Avoidance and Exclusion Costs with Respect to Joint-Impact Goods Avoidance Optional Avoidance Nonoptional —l Low exclusion cost . Cable television Empty set 2. Accees to existing electric, gas, and telephone lines up to capacity 3. Cinema seats up to theater capacity High exclusion cost I. Broadcast television 1. Defense 2. Outdoor fireworks 2. Ambient air for breathing 3. Flood control 4. Use of air waves for audible sound Source: A. Allen Schmid. Property, Power and Public Choice. New York: Praeger Publishers, l978. 113 purchased and herein lies the problem. The consumer cannot reveal his willingness to pay alternative prices for different quantities. In the polar case of private goods, the quantity demanded varies at different exclusion prices and reveals preferences. For a given exclusion price, each consumer will increase consumption up until the point where his marginal rate of substitution equals price. For public goods only one quantity is produced. Even when it is possible to exclude those who do not pay from consumption of a public good there is no reason to expect each consumer's marginal rate of substitution of the quantity produced to equal the exclusion price. For any combination of a single exclusion price and quantity, it is impossible for all consumers to equate their marginal rates of substitution with price. An obvious solution is to charge different prices for public goods for different individuals in accordance with their preferences. However, even when exclusion is possible, decentralized markets can, at best, only partially reveal preferences. The inability to vary quantity eliminates the possibility of revealing preferences in the marketplace. Prices charged to individual consumers cannot be varied unless preferences are revealed. The primary problem of provision of public goods by decentralized markets is not the inability to enforce payment but the inability of the market to reveal optimal prices. Even if preferences were known, private producers could not limit consumption to those who pay for them and therefore, could not expect to collect adequate revenue. The greater the number of people consuming the good, the greater the incentive to enjoy a free ride. The problem of enforcing market prices exists whenever exclusion is difficult 114 regardless of whether or not the good has the additional characteristic of jointness. From the above discussion, preferences are at least partially revealed when exclusion is possible. However, the jointness characteristic of public goods necessitates modification of the 12 regardless of whether or not consumers can conventional pricing rule be excluded. Assuming exclusion is possible; it then seems appropriate to lapply the standard .joint products analysis for private goods to public goods to find a quasi-competitive solution. It will be demonstrated, however, that the two cases are not perfectly analogous, and the joint product analysis cannot circumvent the inability of decentralized markets to provide joint impact goods efficiently. The contrast between private and public goods is illuminated by examining the difference between private and public joint supply. Joint supply of two private goods refers to the physical phenomenon of necessarily producing both goods wherever one of the goods is produced. The quantity produced of one good is determined once the quantity of the other is chosen. In other words, more of one cannot be produced without also producing more of the other. On the other hand, joint supply of public goods concerns an inability to adjust quantity consumed. Joint impact goods, once produced, are equally available to all individuals. The quantity consumed by one person is identical to the quantity consumed by another. 12In neoclassical economic theory, consumers maximize utility at the point where the utility of an additional unit of a product equals the market price. Producers increase output until the marginal cost of an additional unit of output equals market price. The quantity demanded equals the quantity supplied at the market equilibrium price. 115 In short, jointness is a characteristic of a good. Jointness with respect to a private good refers to the inability of a producer to adjust the quantities of two goods produced independently. Jointness with respect to a public good refers to the inability of two consumers to purchase different amounts of the same good. The classic example of private joint supply is wool and mutton. Figure 3.6 depicts the situation for' two consumers. The aggregate demand for mutton and wool is determined by horizontally summing the individual demands for mutton and wool, respectively. The aggregate demand for sheep, in turn, is found by summing the aggregate demand for mutton and the demand for wool vertically. The quantity of sheep demanded can then be determined by applying standard partial equilibrium analysis. The utility maximizing solution is to increase consumption until marginal utility equals the market price. The resulting quantity of sheep uniquely determines the quantities of mutton and wool when fixed proportions are assumed. The prices for mutton and wool are found by identifying the price corresponding to the quantities along the demand curves. It is important to note that each individual can adjust his consumption level in accordance with market price to maximize his utility. The situation is perfectly analogous to the private market for goods with 1K) jointness characteristics. Therefore, joint supply of private goods is not a source of market failure. However, when joint supply analysis is applied to collective goods the conclusion is quite different. Figure 3.7 illustrates this case. Here, the nature of the good is such that each consumer must purchase the same amount of the good. There is no possibility for variation in 116 x_aa=m peach mooom opm>wca o.m magma; cz<£mc mp¢<4 ¢<—wz_ :~x=o; aw~_~_w<¢¢¢<4 m<>c<4 ¢<_mz_ oc_=~ 32:25: A 5:3: 9:5 and ma zm___m<¢<¢ w<>¢<4 u<>¢ao «(.mz_ ozcumm au~_~_n<¢¢gmn ~w>oo3 aonaamc w:c3 :u_au_m E ma a omaum mafia coao Lou ocac :cwuoszocs .2 one Ha>oos :u_aufia o:» no :cfioofiuomcc “case 33.; .fivoczuoe ms_>uox .439. can o=_ooo. ~e< l'l '1 ¢a_>mux h420< 02—m3wur ~J=o< oz_owua ~.« . m4—>u.x p439: uz_—_moa_>o 2 L momnum “~33: :?...:= m... _ _C _ s \ 159 A set of chference equations predict the population levels for each age class over time from other state and rate variables. The difference equations are solved recursively. That is, the values of the state and rate variables at time t are used to calculate the values of the state variables at time t+l, the values at time t+l are used to calculate the values at time t+2, and so forth. Numerical analysis of this type requires the specification of initial conditions. Expressions for rate variables are solved analytically for each time period. In this model rates are defined by mathematical expressions that depend on present values of the state variables. For example, the survival rate si(t) for age class i and time period t is a function of environmental conditions and pest control decisions for time period t. The plant component of the alfalfa-alfalfa weevil model was developed by Dr. Gary Fick of Cornell University. ALSIM (ALfalfa SIMulation) is a model of material which flows between the environment and the alfalfa plants and within the plants. The state variables are expressed in grams of dry matter per square meter of field surface area as opposed to numbers of plants per square meter. Total yield is measured as the sum of the leaf and stem variables. Values of the state variables are updated in each time period based on rate equations (Figure 4.2). The objective of pest management is to reduce crop losses due to pest damage by combining the available control methods. There are several possible methods for control of alfalfa weevil in alfalfa. A means of biological control is the larval parasite described earlier. The parasite lays its eggs in the weevil larvae. The emerging 160 ALSiM I (Level I) (’1 MATS _ A LEAF ]« M M . L M O 8 OTHER) uses) \_/ DGUT (I‘LL-1 (I) _{ r71 g -‘ 4%) (a... l- k, I .1 T... l Fig.4.2 ALSIM l (LEVEL 1) is based on this model of material flow in the alfalfa crop. Rectangles represent the parts of the system modelled; arrows, the pathways of material flow; valve symbols, the rates controlling material flow; cloud symbols, parts of the system not treated in the model. Variable names are defined in the description of the model. 161 parasite larvae feed on the weevil larvae and eventually kill the weevil larvae. Timing of the first cutting is another control measure. The act of harvesting alfalfa removes or kills many of the alfalfa weevils. The number of weevils that survive a harvest is age dependent. Most of the eggs and larvae do not survive a harvest, while the survival rate for the pupae and adult stages is much higher. Alfalfa is a perrenial crop cut up to four times during a season in Michigan. Crop loss due to weevil feeding can be reduced by harvesting when most of the weevil population is in life stages vulnerable to harvesting. The method of harvesting also affects the survival rate. Mortalities due to harvest are relatively higher when the alfalfa is green chopped as Opposed to cut with a sickle bar mower. Insecticide application is the most common method of weevil control. Several insecticides are registered for use on alfalfa. One distinguishing characteristic of insecticides is their residual period. That is, the number of days they remain effectual after spraying. The toxicity of an insecticide decreases over time. Therefore, the survival rate due to insecticides is lowest on the day of applicaton and reaches 100% at the end of the residual period when the insecticide is no longer effective. Insecticide: mortality varies by age class. The egg and pupal stages of the weevil and the cocoon stages of the parasite are virtually unharmed by insecticides. The timing of the spray is critical for the best control of the weevil. Spraying too early may miss the larval stages of the weevil while spraying too late may not be in time to avoid crop damage. 162 In this study, the control variables to be manipulated in the management submodel are: (1) the timing of harvests and (2) the timing of insecticides. Parasites are present but not directly controlled. Each of the submodels is linked together. The survival rate of the weevil population is a function of weather and management. Therefore, the control variables mentioned above can be linked to the pest model by adjusting the survival rates according to the control strategy employed. Also the management model directly affects the plant model through the timing of harvest. The plant and pest models are linked through the weevil feeding on the plants. Feeding reduces the leaf, stem and bud areas of the plants. Also, if the plant population is destroyed, the insect population will decrease from lack of food. To summarize, there are three main components of the model used in this study. They are (1) the alfalfa weevil population model, (2) the alfalfa plant model and (3) the management model. Each will be described in detail below. Then the linking of each component will be discussed. 4.3.1 Alfalfa Plant Simulation — ALSIM ALSIM (ALfalfa SIMulation) is a computer program developed to simulate the growth and management of alfalfa. The modeling effort was carried out by Dr. Gary Fick of Cornell University originally as part of a project entitled "Integrated Pest Management - the Principles, Strategies and Tactics of Pest Population Regulation and Control in Major Crop Ecosystems" supported by a grant from the National Science Foundation and the Environmental Protection Agency. 163 ALSIM simulates dry Hatter yields of alfalfa for various cutting management using time steps of one day. Adequate soil moisture and fertility are assumed. The model also assumes the stand is at peak production. No adjustments are made for the age of the stand over time. Therefore, the model predicts optimal yield rather than expected yield. There are five state variables in the core of the model (Figure 4.2). All are expressed in grams of dry matter per square meter of field surface area. They are: l. MATS - material available for top growth and storage 2. LEAF - yield of leaves 3. STEM - yield of stems 4. TNC - yield of total nonstructural carbohydrates accumulated in the upper 10 cm of taproots 5. BUDS - yield of buds MATS defines the supply of fixed carbon available to produce leaves (LEAF), stems (STEM) and nonstructural carbohydrates accumulated in taproots (TNC). TNC is the source of material for bud formation. In turn, leaves and stems are generated by the elongation of basal buds (BUDS). The sections of the main program are arranged in the following order: 1. Initial section: input data aunt initialization calculations made at the start of the run 2. Crop weather section 3. MATS section 4. LEAF section 5. STEM section 6. TNC section 164 7. BUD section 8. Run control section - specifies time step between calculation of state variables, the number of days between printed output, output and format of output The values of the state variables are updated daily in the appropriate section of the program using several rate equations. The new values of the state variables are computed as the sum of the current state level and the change in the state level over one day as follows: V(t+1) = V(t) + RV (t) dt (4-3) where V(t) = yield of state variable V at time t; V(t+1) = yield of state variable V at time t+1; RV(t) = rate of change in V as computed at time t; and dt = one day. There are 14 rate variables in ALSIM. They are updated for each time period and are dimensioned in grams of dry matter per square meter of field surface per day. 1. M potential rate of top growth and storage 2. L - growth rate of leaves 3. S — growth rate of stems — storage rate of TNC 01 O --1 I other uses of MATS 6. B - growth rate of buds 7. LB - growth rate of leaves coming from bud elongation 8. SB - growth rate of stems coming from bud elongation 9. D - senescence rate of leaves 10. DS - senescence rate of stems 165 11. FL freezing rate of leaves 12. F S freezing rate of stems 13. I I harvest rate of leaves 14. HS harvest rate of stems The total rate of change for a state variable may be a function of several sources of change. For example, the rate variable for state variable STEM, is the difference between the growth rate of the stem and the maximum leaf loss attributable to harvest, freezing or senescence. It is calculated as: RVS(t) = S(t) - max (Hs(t), FS(t), DS(t)) (4-4) Where: ('1' v II the total rate of change in STEM at time t. In the original model leaves, stems and buds could be removed by three processes: (1) death because of (fut age (senescence); (2) a killing frost or; (3) harvesting. In linking ALSIM with the insect model a fourth defoliation process was added to account for insect feeding. 4.3.2 Alfalfa Weevil Model A model of the alfalfa weevil was developed under the direction of Dr. William Ruesink of the University of Illinois as part of the International Biological Program's integrated pest management subproject on alfalfa sponsored by NSF-EPA. The model simulates the life system of the alfalfa weevil and its primary parasite Bathyplectes curculinois. The alfalfa weevil life cycle is divided into 13 stages. The parasite is represented by three stages (Figure 4.1) for a total of 16 166 stages. The model assumes that the second and third instars are attacked in equal proportion and that the first and fourth instars are never attacked. The stages for the alfalfa weevil are: 1. A0 - ovipositing adult 2. E - egg 3. L1 - first instar larvae 4. L2 - second instar larvae 5. L3 - third instar larvae 6. L4 - fourth instar larvae 7. P - pupae 8. AFl - feeding adults 9. AD - diapausing adults 10. AF2 - feeding adults 11. L2P - parasitized second instar larvae 12. L3P - parasitized third instar larvae l3. L4P - parasitized fourth instar larvae The stages for the parasite are: 14. C - non-diapause cocoon stage 15. D - diapausing cocoon stage 16. A - adult Changes in alfalfa weevil population due to parasitism are accounted for by calculating the number of parasitized larvae separately from the nonparasitized larvae. The population is reduced when parasitized fourth instar larvae enter the nondiapause cocoon stage of the parasite rather than the pupal stage of the weevil. As individuals mature, they move from one life stage to the next. The number of individuals in each life stage is updated in the model 167 using a one day time step. This requires estimation of the maturation rate for each life stage on each day. The procedure used in the alfalfa model will be described in detail below. Each stage is divided into a number of cells. As an individual matures, it moves from the first cell in the stage to the last cell in that stage. From there the individual moves to the first cell of the next stage and so forth. The development of individuals can be conceptualized as moving through a train of boxcars where the first ten are painted red, the next fifteen are painted blue and the next five are painted yellow. This is analogous to three life stages. An individual must start in the first red boxcar and move to the second, third and so on. It cannot skip any boxcars to get to the end of the train. Once it has moved to the tenth boxcar it can get to the first blue boxcar. Once it has moved from the first blue boxcar to the fifteenth blue boxcar it can move to the first yellow boxcar and so forth. The laying of eggs is analogous to Inoving from the last .yellow boxcar back into the red section. The time interval used for maturation in the model is one calender day. The number of individuals in each life stage is updated each day. To determine the new’ number of individuals in each stage from the numbers in each stage on the previous day, two flows must be computed for each stage. They are (I) the number of individuals entering the stage from the previous stage, and (2) the number of individuals remaining in the stage. To accomplish this, a daily maturation rate is calculated for each stage. 168 In the alfalfa weevil model, the rate of physiological development is simulated by the number of cells that an individual advances in a day. A conceptual outline for updating the life stages will be explained, continuing the boxcar analogy. A rigorous description of the alfalfa weevil model will follow. Let's suppose that the individuals in the red section move 2 boxcars a day and that the individuals in the blue section that follows mature 3 boxcars a day. Recall that there are ten red boxcars. The individuals 'hi the first through eighth red boxcars will advance two boxcars to the third through tenth red boxcars and will remain within the red section. The individuals in cars nine and ten will move to the blue stage. As soon as the individuals in the red stage mature into the blue stage the maturation rate switches from that of the red section (2 cells a day) to the maturation rate of the blue section (3 cells a day). The individuals that mature into the blue section in a day are in a sense placed in a momentary waiting room and then distributed equally among the first three boxcars in the blue section (since three is the maturation rate of the blue section). There are fifteen boxcars in the blue section. If the daily maturation is three boxcars, then all of the individuals in the first seven boxcars on the previous day will remain in the blue section even after advancing three cars. The individuals that were in the last three cars the day before will move on to the yellow section. Therefore, the number of individuals in the blue section is the sum of the number of individuals that moved in from the red section plus the number of individuals that moved within the blue section but did not get as far as the yellow section. 169 The procedure for updating the population counts in each cell of each stage is as follows: 1. Calculate the maturation rate for each life stage as the number of cells the individuals in each stage will advance. Determine the number of individuals that will remain in each life stage. Determine the distribution of time individuals remaining in each life stage among the cells in that life stage. Determine the number of individuals entering each life stage from the previous life stage. Determine the cHstributhMi of the individuals entering each stage from the previous life stage among the cells of that stage. Calculate the population in each cell of each life stage as the sum of the individuals in step 3 and the individuals in step 5. The actual calculation of the maturation rates in the alfalfa model will now be described. Step 1 Rates of physiological development are a function of temperature. The effect of temperature on rate of development estimated by Ruesink is of the form proposed by Davidson (1944). r1(t) : (4'5) +691.[b —c. *T(t )] = instantaneous rate of development at time t for stage i; 170 __. A r.- V II instantaneous temperature at time t; and constants. Q) a U- a 0 II The instantaneous temperature is approximated from the high and low temperatures for the day using the following equation: T(t) = 1/2 TH(k) + TL(k) + 1/2 (TH(k) - TL(k)) COS2nt (4-6) where: the low centigrade temperate on day k; and —+ —1 I i— A A 7? 7? v V II II the high centigrade temperature for day k. Integrating equation (4—5) over the time interval of one day yields an average rate of development for stage i on day k, Ri(k)° It is calculated as: Ri(k) = f r1(t) dt (4-7) Let n1 be the total number of cells in stage i. Then ni*R1(k) (4-8a) is the number of cells an individual can mature during day k. This number may be different for each stage. Further, the value calculated may or may not be an integer. An individual cannot mature a fraction of a stage. A procedure was developed for handling non-integer values of equation (4-8a). The daily maturation for stage i can be represented as: ni*Ri(k) = mi+pi (4-8b) where mi is an integer and pi is a fraction less than one and greater than or equal to zero. Then the maturation rate is greater than or equal to mi and strictly less than mi+1. Let Xij represent the number of individuals in the jth cell of the ith stage. Then by convention (p*X1j) individuals 171 will move through mi+1 cells aunt the remaining (1-p)*Xij individuals will advance mi cells. For example, suppose the movement for individuals in the third life stage is calculated to be 4% on day 120. Then some of the individuals will move four cells and some five cells. By convention, one fourth will advance five cells, and three fourths will move through only four cells. Step 2 All individuals in a cell in stage i will advance m, or m1+1 cells during day k. Therefore, all individuals in cells numbered less than ni-mi will remain in stage i. And (1-p)*Xi, .individuals will ni-m1 advance m1 cells from cell ni-mi to cell ni. am; All individuals that were in stage i on day (k-I) will advance to a cell beyond m, on day k. For cell mi+1, a maximum of (1-p)*(Xij(k-1)) individuals will advance mi cells from cell one to cell mi+1. For cells greater than mi+1 and less than n, within stage i, a maximum of (I-p)*Xi,j_mi(k-1) individuals will enter: cell j fronl cell j-mi and (p*xi,j-mi-1 £2211 All individuals 111 stage i-1 WHII advance ini_ (k-I) individuals will enter cell j from cell j-mi-I. 1 or m1_1+1 cells during day k. Therefore, all individuals in cells numbered ni_1-mi_1+1 or greater will move into stage i. And (pi*Xi 1 n m ) individuals ' ’ i-l' i-l will enter stage i from cell n1._1-m1._1 of stage i-l. 172 Step 5 Individuals moving into the ith stage from the previous stage2 on day l< will advance mi in" m+1 cells. Therefore, individuals entering stage i cannot move beyond cell m1.+1 on day k. It follows that the individuals entering stage i cannot affect the number of individuals in cells beyond cell m+1. Further, cells 1 through m can only be filled by individuals moving out of the previous stage and into stage i. It is necessary to determine the distribution of the individuals entering stage i among the m+l cells they enter. Let Yi_1(k) be the number of individuals entering stage i from stage i-I on day k.2 There are Yi-l(k) individuals entering stage i. Each enters into one of the first m1+l cells. If we assume that m, *Y1_1(k) mi+pi individuals are distributed equally in the first mi cells, then 1 *Yi-l(k) individuals enter each of the first mi cells. The mi+P' . remaining p] *Yi-1(k) individuals enter cell mi+l. All of the m .+p.i individuals entering stage i are accounted for since: v. (k) + l v. (k) = Y. (k) m*1-1 w‘k 1-1 1-1 Step 6 It is clear from steps three and five that three equations are needed to update the population values in each cell of each stage; one for cells greater than mi+1, one for cell mi+1 and one for cells less than m1*1. The results of Steps 3 and Step 5 are summed formally in the following equations: 2The actual subscript will not always be i—l. For example, the stage previous to stage 1, ovipositing adult weevils is stage 10, feeding adults. For simplicity i-l will be used in this discussion. 173 ij(k) = Si(k—])*[(1-p)*xi,j-m (k’1) + p*X1,j-m _](k‘])]a mi+1 < j < n1. (4-9) _ pi ~ - x,j(k) — Si(k—l)*(l-pi)*Xi](k-l) + . p *Yi_](k), J - mi+l (4-10) X..(k) = Yi-l(k) ij mi+pi ’ 1 < j < m +1 (4-11) The survival rate, Si(k) is an adjustment for mortalities. The survival rate is decreased due to: (l) spraying; (2) harvesting; (3) starvation and other causes (Table 4.1). Survival rates due to each of these causes are determined separately and then combined to define a single survival rate incorporating all three factors to 1x3 used in updating the population of each life stage. Let 881(k) be the survival rate for life stage i at time k when no insecticides are applied and 1N) harvest takes place. 881(k) is the percentage of the population in stage i at time k that survives in the next time period, k+1. Further, let SRi(k) be the survival rate for life stage i at time k due to insecticide application at time t. Let SHi(t) be the survival rate for life stage i at time k attributable to harvesting as time k. The overall survival rate, Si(k) is expressed as: Si(k)=Ssj(k)*SRi(k)*SH1(k) (4-12) If no harvest occurs at time k then SHi(k) equals one. Similarly, if no insecticide application is made at time k then SRi(k) equals one. Equation (4—12) reduces to: Si(k) = SSi(k) If, for example, a harvest is made at time k and only half of the population in life stage i survive then SHj(k) = .5. Further assume . . . ... '3‘ ul‘c- 4a 0 ' “‘0' ‘0‘:- VW”.“‘ 'an .mua. oceanopm>mc apwmv on» we :o.pocna m m. m..>mo3 p.000 mcvamoaw>o on» so. mum. _0>w>.:m mzho .0ovcma .mavmmm. on» m0 000 pm... 0;» nmcmvwmcoo m. m:.>0cam .0 000 we. .0opmowccw m. newcon peanmmm. 0:» we met on. a .00.0_pomm:w we» as. cowcma .mauwmm. >00 m>wa 0 :0 00000 mam moon. F0>m>czm0 174 m.00. 00. 00. 00.. 0.. 00. 00. N0. 00. 0 0.00. 00.. 00.. 00.. 00.. 00.. 00.. 00.. 00.. 0 0.00. 00.. 00.. 00.. 00.. 00.. 00.. 00.. 00.. 0 00.. 00. 00. 00.. 0.. 00. 00. .0. 00. .0. 00.. 00. 0.. 00.. 0.. 00. mm. .0. 00. .0. 00.. N0. 0.. 00.. 0.. 00. 00. N0. 00. .N. 000. 00. 00. 00.. 0.. 00. 00. .0. 00. ..q 000. 00.. 00.. 00.. 00.. 00.. 00.. 00.. 00.. 00 .00. 00. 00. 00.. 0.. 00. 00. .0. 00. ..a 00. 00. 00. 00.. 00.. 00.. 00.. 00.. 00.. a 00.. .0. 00. 00.. 0.. 00. mm. .0. 00. 0. 00.. 00. 0.. 00.. 0.. 00. mm. .m. 00. 0. 00.. N0. 0.. 00.. 0.. 00. 00. .0. 00. N. 00.. 00. 00. 00.. 00. .0. 00. 00. 00. .0 00.. m0. 0.. 00.. 00.. 00.. 00.. 00.. 00.. 0 .m 00. 00. 00.. 0.. 00. mm. .0. 00. 0a momma aozu cozoz o m e m N \m mmoum .0>.>.0m cameo Lam o..o aae.x02 opxo_m mmuam .m>.>c:m mcvumo>gaz \mmouam _0>.>L:m oo_o.uommc. x..0o mmm=m<= oz< wa~u~huwmz_ ow man muh_>z:m ..v ~25 175 that no insecticide application has been made. Then equation (4-12) is calculated as: Si(k) = SSi(k)*1.0*.5 In this example, the survival rate is half of what it would have otherwise been if harvest had been postponed. The egg, pupae and diapausing stages of the alfalfa weevil and the cocoon and diapausing stages of the parasite are unaffected by insecticides. The other stages, with the exception of the first instar larvae, have an initial insecticide survival rate of .4-(Nl the day a spray is administered. The first instar larvae have a higher survival rate of .8. The model has the option of five different residual periods for the insecticide to be initialized at the start of the simulation. The insecticide survival rate increases over the residual period reaching 1 the day after the residual period ends, using the following formulas: SRi(k)=(l + SRi(k-l)*(c-r))/(c-r+l) for c—r > O, r = O (4-l3a) SRi(k)=l otherwise (4-l3b) Where: SRi(k) = insecticide survival rate on day k for stage i; SR1(k-l) = insecticide survival rate on previous day; r = number of days since insecticide application; and c = number of days in insecticide residual period. The survival rates due to harvesting depend on the type of cutting. Two options are available, green chop or sickle bar mower. In both cutting systems the diapausing adult weevils and the two cocoon stages of the parasite are unaffected by harvesting. The harvesting survival rate is significantly higher for alfalfa cut with a sickle bar mower , . . ..xdo 4‘ nu -.a. \. ("ADHQI-m .,., 176 than green chopped (Table 4.1). If a harvest occurs during the residual period of an insecticide, the effect of the insecticide is negated. The survival rate in effect on the day of harvest is simply the survival rate for harvesting. The day after the harvest all survival rates due to harvesting and insecticides are set equal to one regardless of whether or not the harvest took place during the residual period. The same harvest cannot be cut with a sickle bar mower and green chopped. Also a harvest and a spray cannot occur on the same day. Mortality due to starvation is a function of total food available and total food desired. The relationship of the starvation rate to the total survival rate will be described in detail in the discussion of linking the plant and pest models below. The survival rate due to other causes can be interpreted as the maximum survival rate. It is equal to l for the larval and egg stages of the weevil, .86 for the pupae stage and .995 for the adult stages except oviposition. The maximum survival rate for ovipositing adult weevils is a function of the daily average development rate from equation (4-7) as follows: 581(k) = l—.OOl*R](k)/n1 (4-14) Where: 551(k) = the maximum survival rate of ovipositing adult weevils on day k; R1(k) = the average development rate for ovipositing adults on day k; and the number of cells in the oviposition stage. 3 __J 11 177 To summarize, the overall survival rate is calculated by multiplying the maximum survival rate by the survival rate for insecticide and harvesting as follows: 51(k) = 351(k)*SRi(k)*SHi(k) (4-15) where: Si(k) = survival rate for stage i on day k; 351(k) = maximum survival rate for stage i on day k; SRi(k) = survival rate due to insecticides; and SHi(k) = survival rate due to harvesting. The value of Si(k) is used in equations (4-8) - (4-11) to determine the number of surviving individuals leaving each stage and updating the number of individuals in each stage. 4.3.3 Linking the Alfalfa Plant and Alfalfa Weevil Models The two models described above have been combined to simulate an alfalfa-alfalfa weevil agroecosystem "mnaged tn/ alternative harvesting and insecticide strategies under various temperature conditions. The level of alfalfa weevil feeding affects the plant while the status of the plant determines the availability of food and shelter for the weevil. The amount of food desired daily is computed for each stage separately and then summed to determine the total food desired by the weevil. With the exception of prediapausing adult weevils, all individuals within a stage are assumed to desire the same quantity of food based on the following formula: 178 Y2.(k) = C1*Rj(k)* 1 z X.. i = 8 (4-16) ..l 1:] J Where: Y21(k) = food desired by individuals in stage i on day k; Ci = a constant; Rj(k) = average rate of development for stage i on day k; xij = number of individuals in the jth cell of stage i; and n. = number of cells in stage i. Only the larval and nondiapausing adult stages feed on the plant. The number of eggs, pupae, diapausing adults and parasites does not contribute to the food desired. The constant term takes a zero value for the nonfeeding stages. The maximum rate at which the nonparasitized larvae eat increases as they age. The amount of food desired by parasitized larvae also increases as they age but not to the extent that the amount increases for nonparasitized larvae. This is reflected in the constant term. The value of C increases with the instar number. Adults emerging from the pupae stage desire more food as they age within the stage. This means that individuals in lower numbered cells desire less food than individuals in higher numbered cells. The food desired by the prediapausing adult stage is computed as: Y28(k) = J2] X8j(k)*R8(k) - j*x8,j(k)*R8(k)/n8 (4—17) The amount of food desired by the ovipositing adults is adjusted by the amount of energy they have stored, or "food reserve level" and the temperature. The higher the food reserve level the less food is desired. The upper threshold for physical development is 86°F (30°C). Therefore, no feeding occurs above this temperature. These two factors are incorporated into as follows: 179 the feeding equation (4-16) for ovipositing adults Y2](k) = C]*R1(k)*(2-F(k));=§ Xij; TH(k) < 25 (4-18) Y21(k) = C]*R1(k)*(2-F(k)*(3O-TH(k))gi] Xij/S’ 25 < TH(k) < 30 (4-19) Y2](k) = 0; 3O :_TH(k) (4-20) The food reserve level is calculated as: F(k) = F(k-l) + [.2*Y31(k-l) -.OO4*Yl](k-l) -.OO4*E(F(k-l))]/ '2' x13. (4-21) where: J=1 F(k) = food reserve level on day k; Y3](k-l) = total food eaten by individuals in the oviposition stage of the alfalfa weevil on day k-l; Y2](k-1) = total food desired by individuals in the oviposition stage of the alfalfa weevil at day k-l; Yl](k-l) = total number of eggs laid by ovipositing adult weevils; E(F(k-l)) = respiration rate on day k—l; Xij = number of individuals in the jth cell of the oviposition stage; and n. = number of cells in the ith stage. 1 The food reserve level is increased by feeding and decreased by the laying of eggs and respiration which require the expenditure of energy. The food reserve level is constrained to a value ranging from O to 2. 180 The food reserve level also affect the rate of cwiposition (the number of eggs laid) for adult weevils. The number of individuals leaving the oviposition stage equals the number of eggs laid and is computed as: Y1](k) Y3](k)*R1(k)*G[F(k),X1(k)]/Y2](k); Y2](k) > 0 (4-22) Yl](k) O; Y2](k) = 0 (4-23) The function G adjusts the oviposition rate by the food reserve level and the distribution of individuals among the cells of the oviposition stage. The value of G and, hence, of Yl1 increases as the food reserve level increases. The oviposition rate increases from the first to the second cell of the stage and then decreases at a constant rate as the cell number increases. A third way in which the status of the plant can limit weevil population is through starvation. The survival rate is adjusted for the situation in which the total food desired is greater than the total food available in the following manner: l6 l6 SM.(k) = [(a. + b.*z Y3 (k))/ z Y2.(k)]*SS.(k) (4—24) 1 l 11.:1 i i=1 1 l where: SM1(k) = the maximum survival rate adjusted for mortalities due to starvation for stage i; a., b. = constants for stage i; 2 Y3 (k) = total food eaten on day k by the weevils in stage i; z Y21(k) = total food desired by the weevil on day k; and 351(k) = the maximum survival rate for stage i on day k in stage i. The term SMi(k) can be interpreted as the survival rate of stage i on day k due to causes other than insecticides or harvesting. 181 Starvation only occurs when the total amount of febd desired is less than the total amount of food available. Of course, nonfeeding life stages cannot suffer mortalities due to starvation. The larval stages of the weevil are reduced in greater proportion due to an inadequate food source than are the feeding adult stages. Further, parasitized larvae are less affected than non-parasitized larvae (Table 4.1). The plant also provides shelter for the adult weevils during diapause. The alfalfa weevil enters diapause in late August to escape the heat and high humidity of late summer. At this time, the weevils look for a covered area in which to diapause. Therefore, the amount of cover available from the plants influences the percentage of the weevils that remain in the field and the percentage of' weevils that seek diapause sites outside the field. This phenomena is described in the equation: PY8(k) = .8*(l-er)*e-‘O]*(LEAF+STEM) (4-25) where: PY8(k) = the percent of adult weevils leaving the AFl stage and entering diapause on day k remaining in the field; r = the respiration rate of the prediapausing adults; LEAF = yield of leaves in g/mz; and STEM = yield of stems in g/m2. The percentage of weevils entering diapause and remaining in the field is positively related to the values of LEAF and STEM. The percentage of weevils that do not remain in the field are assumed to diapause elsewhere. and not to return to the field. The number of individuals entering diapause on a particular day and remaining in the system is then: 182 Y8(k) = S8(k)*PY8(k)*Y8(k) (4-26) where: Y8(k) = the number of adult weevils entering diapause and remaining in the field; 58(k) = the survival rate of prediapause adult weevils; PY8(k) = the percentage of adult weevils entering diapause and remaining in the field; and Y8(k) = the number of weevils maturing out of the prediapause adult stage. Equations (4-25) and (4—26) allow for weevils to leave the field, but not to return to the field. It should also be noted that the model does not allow for weevils from other locations to enter the system. Therefore, equations (4-25) and (4-26) determine the number of weevils that overwinter in the field the initial population for the next growing season, and hence, the populations for all subsequent growing seasons. In other words, the level of infestation in a given year is related to the status of the crop in the previous year while the adult weevils were entering diapause. This means that the model results for one year are sensitive to the timing of cuttings in late summer and fall of the previous season if the model is run for more than one season. Until this point, the discussion has focused on the impact of the plant status on weevil population. The impact of weevil feeding on plant development and crop production will now be addressed. The alfalfa weevil feeds solely on the leaves of the plants unless the food supplied by the leaves is less than the food desired by all life stages of the weevil. In this case the weevil will feed on the 183 buds. During the winter months when the plants are dormant, the only food available to the weevil is the basal buds of the plants. Reduction of the leaves by weevil feeding directly impacts each section of the plant model. The potential growth rate of top growth in the MATS section is a function of solar radiation absorbed by the plants which is positively related to the total leaf’ area. The' materials available for top growth and storage for that day are, therefore, positively related to the measure of leaves on that day. The growth rates of both leaves (GRL) and stems (GRS) are a function of materials available for growth (MATS) which is a function of the leaves remaining from the previous day. The amounts of the available materials used for leaf and stem growth respectively are also determined in part by the measure of leaves. Keeping in mind that the available materials are essentially used either for leaf growth, stem growth or storage in the roots. It follows that the rate of 'TNC accumulation in the roots (STOR) is influenced by the amount of existing leaves in several ways. When more materials are available for top growth and storage the potential rate of TNC storage in the roots is higher. Therefore, the actual change 'Hi TNC storage corresponding ixa a change 'Hl available materials will depend on the changes in stem and leaf growth as well as the materials available. The growth rate of leaves (i.e. the quantity of available materials used for leaf growth) may either increase or decrease with a reduction in the quantity of leaves depending on the day length, temperature and status of the plant. Two effects occur simultaneously when leaf area is reduced. During the growing season, a reduction in the quantity of leaves will always ... an“ 41 184 bring about an increase in the percentage of available energy the plant will put into growing leaves and a decrease in the percentage it will put into growing stems and/or root storage. The reduction in leaves will also reduce the total amount of available energy for growth. The plant will respond by increasing the portion of the shrinking energy pie allotted to leaf growing relative to stem growth and energy storage. The net result may either be an increase or decrease in the total energy allotted to leaf growth depending on the change in the size of the pie brought about by the leaf reduction. In either case the growth rate of the stems and the storage of TNC in the roots will decrease. The growth rate of buds will decrease as a result of defoliation. If the weevils also feed on the buds, the growth of the stems and leaves from bud elongation will be reduced. 4.4 Modification of the Model to Include Hay Quality Information only has value in the context of a decision. In order to determine the monetary value of information, the yield associated with each information system must also be assigned a monetary value. The value of the alfalfa yield per acre is a function of both the quantity and quality of the hay. Both are affected by the choice of management strategy. While the model presented predicts the quantity of hay under different strategies, it does not include quality considerations. The management tactics considered include timing of harvest, insecticide applications and parasite population. All are geared towards the reduction of pest numbers to decrease crop loss. Therefore, the effect 185 of management on quality must consider the effect of harvest date on quality and the effect of larval feeding on quality. It is generally assumed that the quality of alfalfa is lower at later harvest dates. This is due to both changes in the chemical composition of the leaves and stems, and a change in the leaf to stem ratio ‘with advancing maturity of plants. In the study of several forages including alfalfa by Mowart et al. (1965), in vitro digestible dry matter and percent crude protein decreased with maturity of the plant. The percentage of in vitro digestible nutrients decreased at a much greater rate for alfalfa stems than leaves. The percentage crude protein content of both leaves and stems decreased at about the same rate. One hypothesis is that larval feeding reduces the quality of alfalfa because the leaf-stem ratio is reduced (Flessel and Niemczyk, 1971). This hypothesis is based on the observation that alfalfa weevil larvae feed primarily on the leaves of alfalfa plants and that the nutrient content of leaves is higher than for stems. However, empirical work has not supported this hypothesis. The most plausible explanation is that while larvae do feed on leaves, the reduction in leaf area also retards stem growth, leaving the leaf-stem ratio unchanged. Lui and Fick (1975) measured the effect of the alfalfa weevil on yield and quality of alfalfa herbage in New York for two-cut and three-cut systems in two consecutive test years. The effect of weevil feeding on quality of total herbage, as measured by crude protein and 1p yitgp true digestibility was not statistically significant. The effect of feeding on leaf weight, as a percent of total plant weight, was also insignificant apparently because stem growth was also adversely 186 influenced. Hastings and Pepper (1953) also found percent protein to be unchanged by larval feeding. Hintz, Wilson and Armbrust (1976) estimated the yield loss attributed to one larvae per stem using regression analysis. The effect of larval feeding on in vitro dry matter digestibility and crude protein was also studied. Reduction in quality (percent in vitro digestible nutrients and percent crude protein) attributable to larval feeding was significant in only one of the three study years. For that year, quality decreased at a decreasing rate as larval density increased. Wilson, et al. (1979) also observed reductions in yield attributable to alfalfa weevil. They found larval feeding significantly reduced the percent crude protein of the first cutting. Their results are consistent with theoretical work but inconsistent with other empirical work cited above. (Lui and Fick, 1975; Hastings and Pepper, 1953; Hintz, Wilson and Armbrust, 1976). The work cited supports the claim that later cutting of alfalfa decreases quality but larval feeding does not. Data collected in Central Michigan in 1972 and 1974 was used to measure the effect of harvest date on various quality measures and test the hypothesis that larval feeding reduces quality. The experiment is described in detail in sec. 4.7. Percentages of acid detergent fiber, protein and in vitro digestible organic matter were used as measures of alfalfa quality (Table 4.2). Yield, quality and larvae population were measured for 1972 and 1974. The affect of larval population and harvest date on each quality measure was analyzed. Harvest data was measured in degree days 187 ..ooo. .c.&m oco o.._>coxmnm. a moocmou om o>ono moc30nconeo* Lo. ooamamco von+oe mum as. ac.ma ou+o.:u.ou n .n_mon co++oe >Lo o co cupcomoca ago «01.0) 0:0.cpac ..< o n.0n n... c.on o.nh v.v n.nn c.5— o.on h.~h n.n nun._ _xh n.vn «.0. o.mn v..o v.n ..nn h.m. n.0n p.05 h.N Non._ omxo o.~n m.o~ n.mo o.~o o.~ n.nn ..ow _._o v._o v.N noo.. o.\o ~.~N o.nN o.vo v.vm q.~ a.- m.NN n.no o.nm n.~ __m .nxn n.0m m.mu ..oo o.Nm 0.. n.0N —.oN 0.00 n.nm 0.. .on omxn «.m. ..ov 0.0. o.an c.0n o.n ~.on ..o. n._o n.~h ..n omv._ -\o n.nn n.~_ n.mo o.~m o.n o.on ..h. m..o n.m~ ~.N on... q.\o ~.on v.0. o.mo ..Nm o.n o.nn n.o_ n.no ..om N.N nmo nxo o.nN ..om 0.00 n.vo o.. o.- ..nw ..nn o.vo n.. are vuxn who. a a u n 96530» a a u a 30320.. 0.; 025 «motor coo» Loo. m Euro...“ mhcotgz 0.53. _o: 0.0:. Loo—u 595...". “2.3.332 02:20: so; m>oo .0 030 «comco.oo ouncu o.a.«mom_o wcomcoaoo coacu o.o_+mom.o oocmoo o.u< ocr_> c. u.u< 0L»_> c. oopnoc» unenocecn iii: I 00.00 .zmmwaa_0 »< 50 «5...... 8.3%.... oz 8.5.: 8 Ease 0.2 0.0: .0 2...... N... mg: 188 base 41°F and larval population in larvae degree days.3 There was no significant difference (P < 10%) between the sprayed and unsprayed plots for any of the quality measures. Controlling larval feeding did not influence the quality of the alfalfa appreciably. Although yields of leaves and stems were not measured separately, it is assumed that stem growth is retarded by feeding on leaves. The quality measures were significantly different for the two years. This can probably be explained by the differences in the age and variety of the stands used in the experiment. Differences in quality measures were statistically significant for the different harvest dates for each season. Percentages of acid-detergent fiber (F), crude protein (P) and in vitro digestible nutrients (INVDN) were estimated as linear ‘functions of'.accumulated degree days at the time of harvest (D) for each year (Table 4.3). Earlier cutting increased percentage of crude protein in in vitro digestible nutrients, while decreasing the percentages of fiber. Looking at both years of data, the values for crude protein ranged from 16 to 26 percent, from 20 to 37 percent for fiber and from 60 to 75 percent for in vitro digestible dry matter. The relative sensitivity of the quality measures to harvest date is not obvious from the values of the coefficients. Although the absolute change of any quality measure for a given change in growing degree days is greatest for INVDN (i.e., the coefficient of D is largest), the change is less than for 3Larvae degree days is accumulative measure of the number of larvae that have been feeding over a period of time. The procedure for calculation is described in 3.2. 189 Table 4.3 THE EFFECT OF TEMPERATURE ACCUMULATION ON QUALITY MEASURES OF ALFALFA 2 Quality Measure Year Intercept dd41 R % Crude Protein 1974 30.22 -.008 .87 (.59) (.0005) 1972 31.00 -.011 .76 (1.28) (.001) % Acid Detergent Fiber 1974 13.46 -O.16 .86 (1.18) (.001) 1972 12.74 -.O18 .77 (2.03) (.002) % in vitro Digestible 1974 72.81 -.010 .79 Nutrients (.99) (.0009) 1972 85.40 -.018 .77 (1.97) (.002) Numbers in parentheses are standard errors 190 percent fiber or percent crude protein. That is, the proportion by which INVDN changes is less for a given change in growing degree days. In order to compare the relative effects of harvest date among the quality' measures the average percent change' in the quality' measure (e.g., the percent change in the percent crude protein) associated with the average percent change in degree days between harvests was calculated for each quality measure. The ratios of the percent change in the quality measure to the percent change in degree days ranged from .42 to .62 averaging .56 for F and P. The average ratio for INVDN was .28. The results can be interpreted as follows: On the average a l pecent change in degree days is associated with a .56 percent change in F and P. (hi the other hand, a '1 percent change 'hi degree days is associated with a .28 percent change in INVDN. INVDN was found to be relatively less sensitive to changes in harvest date than either percent crude protein (N“ percent fiber. No statistically significant (Pccp to Logan: fl utwgo covumvcmseoomc ucwswomeae umoa _¢>om2 mm_oe—< m.e 6.3w» . l‘. voln.’ . a! Eloooi) .’ .o ..‘t! Isl. 4 ..¢ '- A 1599 .m:__aswm was: coo no» can tw>o m. common —_>wm3 on» .om>gm. cm can» mmop can opaecm umo>cmgotq emu. em a .o—ascmmc o» mxmulmocmmu com u.oz emu 3o» .omm mch m ems» «toe umxotam we; u_m_e was» 1_ m mmuo ano mmuo mane cfiuo cfino wfino Am utmco womv umm>cmz Logan ones to so“ \mee ccl :v mPQEammm Noumm memw ~m:m~ Renew anufi mmuxfi qumfi cu om mm mm :. opasamom mm >cmz emote oc_ AN Stags ammo uma>cmz On Cam NH-o ~_-o m~-o m~-o mfilo Nlo ~-o ~-o cc ooH c? m_;smmmm m~-m_ m~-m_ “Rue“ Ac-v~ mwucn Bmum Hmlm mmum an em c. opaEmmoz om cm mm me am mm mm mm >cmg Lmumm wees to omH NH-o 51-0 NN-o «we ooH =2 mFQEMmmm Nm-mH No-ma N~-mN at cm :2 erasamam mm mm MN pmm>ta= to >tae 0» cam mcos to oH vmmmwcocfi o“ cw;p_3 ages to oH wmwmmgooo Acuv mxmunwmtmmu Pmpoe wpasmminmp wocrm mw>gmr mo topaz: cw mmcmmo N pcwcu cowucucmeeoomm pcmsmmmcmz pmma Fw>wmz meromp< A.u:oov m.¢ mFDmP ... ..x . . o. . ..2 rulxlll..ltll.m.d;z. 201 2. Routine Sprays--Before and After the First Harvest. For maximum crop protection, an insecticide should be applied no earlier than two weeks in advance of the expected cutting date. It is possible that the spray would be unnecessary but a spray minimizes the risk of crop loss. The regrowth following the first cutting is highly vulnerable to damage by feeding larvae. It should be sprayed with an insecticide for maximum protection. The only information required for this strategy is the expected date of cutting, which is not influenced by weevil density. The first harvest is taken at 1200 degree days (base 41°F) accumulated after January 1. The first spray is applied approximately 200 degree days before the first harvest. The cost of the strategy is the cost of two spray applications. 3. Static Threshold. A spray is applied when there are more than 400 larvae per square meter. Quite often a grower will harvest early if a spray appears to be warranted within a few days of the anticipated harvest. For the purposes at hand, it is assumed that other constraints on the manager's time make prescheduled harvesting impossible. When a spray is recommended with 100 degree days of harvest, the recommendation is changed to don't spray and the harvest date is left unchanged. The cost is the cost of monitoring plus the cost of any spray applications made. 4. Harvest According to Schedule. The "do nothing" approach does not requirel monitoring of pest populations. It does require specification of a: harvest schedule. This strategy corresponds to aa control treatment. There is no cost associated with this program. . . .. ..n on: o H - -., n. flUI-JUCUIU‘ a... . . a r «...I“--‘ -I-- 202 5. Cost-Benefit Analysis. An alternative to delineating an explicit threshold is cost-benefit analysis. The default values for cutting dates are used as a base. That is, the first harvest is made after 1200 degree days (base 41°F) have accumulated after January 1 unless an earlier cutting date is recommended by the guidelines. The second and third cuttings are each 1200 degree days after the previous cutting. The control strategies considered are cut early or spray before the first harvest. The values of the first cutting for each strategy are predicted each time the field is monitored. The value of the cr0p is predicted for each possible harvest date up until the default harvest date. The value of the crop is also predicted for the default harvest date and a spray application for each day up until 100 degree days of harvest. The cost of the early harvest strategy is equal to the cost of monitoring. The cost of the spray strategy is equal to the cost of monitoring plus the cost of any spray application. On each sampling date the predicted net income is computed for each possible spray date and each possible harvest date. The predicted net income is calculated by subtracting the cost of the strategy from the predicted value of the crop. The control strategy associated with the maximum predicted net income is then identified as the best management strategy. If the best strategy is "harvest today" or "spray today" a harvest or spray will be carried out. If the best strategy is to harvest or spray (Ml a date) before the next. scheduled Inonitoring date then 'the harvest or spray date will be set in the simulation model to follow the recommendation. If the best strategy is to harvest or spray on a date 203 after the next scheduled monitoring date, the process will be repeated on the next monitoring date and the predicted profits will be updated with the additional information obtained. The algorithm for predicting crop value for alternative management strategies was developed from multiple runs of the alfalfa-alfalfa weevil simulation model. The steps to the algorithm are as follows: 1. For each monitoring date calculate: a. DD41- growing degree days base 41°F accumulated after January 1 b. 0048— growing degree days base 48°F accumulated after January 1 c. LDD- accumulated larvae degree days (defined in 3.2.3) Predict values of DD41 and DD48 for each possible cutting date. Predict LDD from the predictions for DD48 and today's observed value of LDD. Predict LDDS (larvae degree days at default harvest date) for each spray date from predictions for DD48 and today's observed value of LDD. Predict yield for each cutting date based on predictions of LDD and DD41. Predict yield for each spray date based on predictions of LDD and DD41. Predict protein value of hay for each harvest date from predictions of DD41. Calculate the value of the yield for each harvest date and each spray date from predicted yields and protein values. . .... —— at" in . . 'I' 'u ‘. IMJNQJ-V t-.. 204 9. Compare the expected values of the yields minus the cost of monitoring and determine the optimal cutting date or spray date. 10. Set harvest date or spray date if they occur before the next scheduled monitoring day. Otherwise repeat all steps on date of next monitoring. The details of each step will be discussed below. Prediction of DD41 and 0048 is based on the following equation: DDt+i = Dt + (Pt+i - P t) * DDtot (4-29) where: DDt+i = degree days i days after today; DDt = degree days today; Pt+i = percentage of the total degree days for the year usually accumulated by day t+i; P = percentage of the total degree days for the year usually accumulated by day t; and DDtot = average total number of degree days for a year. Pt+i and Pt are the average percentages from multiple runs of the simulation. The value of (Pt+i Pt) is the expected percentage increase in degree days from day until day t+i. Then (Pt+i - Pt)*DDtot is the expected increase in degree days from day t until day t+i. Notice that this increase is independent of today's degree day count. The underlying assumption is that although the temperature may have been above average today, there is no reason to believe it will be above average next week. A second assumption is that while temperature may vary throughout the year, the total number of degree days for the year 205 does not vary greatly. These assumptions were verified by the 15 years of temperature data used to run the model. On the other hand, the number of larvae degree days did vary greatly from year to year. The appraoch taken to predict larvae degree days (LDD) for day t+i was predicted from today's observation based on the following relationship: Pt = LDDt (4—30) 100 LDDtot and Pt+i = .EEELii (4-31) 100 LDDtot Solving (4-30) and (4-31) for LDDt+i yields: LDD .= Pt+i * LDD (4-32) t+i Pt t Where: Pt = the percentage of the total number of larvae degree days expected by day t; Pt+i = the percentage of the total number of larvae degree days expected by day t+i; LDDt = Larvae degree days observed today; LDDt+1 = predicted number of larvae days for i days from today; and LDDtot = total number of larvae degree days for the season. Implicit in this formulation is the assumption that if the number of larvae degree days is high (low) today it will continue to be high (low) for the rest of the season. The assumption is borne out by . a 206 multiple runs of the model. The percentages are predicted from the predicted values of DD48. The value of the hay per ton on alternative dates is based on the quality analysis presented in section 4.4. Predicted values of DD41 are used. PRO 31.0031 - .01115*DD41 (4—27) VALUE -54.3 + 7.875*PA (4-28) The effect of growing degree days and larval feeding (estimated by larvae degree days) was estimated by the following equation using results of multiple runs of the model. The yield per hectare on day t+i (YIELDt+1) is estimated as: YIELDt+i = -34.46 + 5.7* In (DD41t+i) — (7.97 * 10'6) * LDDt+1 (4-33) Finally, for each cutting date the expected value of the harvest is: NET . = VALUEt+1 * YIELDt+1 - COSTt+1 (4-34) The cutting date or spray date is selected by maximizing net income with respect to t+i. The algorithm is performed on each sampling date until the optimal t+i is found to be before the next scheduled monitoring. On each sampling date the predictions are updated using the new values of DD41, DD48 and LDD. By the nature of the construction of these variables information already obtained 'h; not discarded because DD41, DD48 and LDD are cumulative measures. 6. Early Harvest of the First Cutting. This decision rule is identical to Rule 4 except that the first cutting is made after 900 degree days (base 41°F) have accumulated after January 1 as opposed to 1200 in Rule 4. In other words, the default date for the first harvest 207 is changed. The biological time between the first and second, and second and third, is 1200 degree days, as it is 'hi all other rules. There is no cost to this strategy. 7. Routine Single Spray. This decision rule is identical to Rule 2 except that a spray is required before the first harvest but not after. The spray is applied 200 degree days before the first cut. The cost is the cost of the spray. The cost of monitoring the larvae population was assumed to be $7.00 a hectare ($2.75 per acre). The cost of spraying was assumed to be $22.00 per hectare ($9.00 per acre). These values are based on 1981 prices (Table 4.6). 4.6 Modification of the Model for Michigan Conditions The alfalfa—alfalfa weevil model can be run for any alfalfa growing region in the United States. In order to run the model for a specific location, certain input data for the model has to be specified for that location. The input data required includes the latitude, average monthly solar radiation and daily high and low temperature data. As Inentioned above, the location-specific data required by the model are latitude, average monthly solar radiation and daily high and low temperatures. Gull Lake, Michigan was chosen for running the model under Michigan conditions for several reasons. First, Gull Lake is in a major alfalfa growing region in the state. Second, there is a weather station there and the data required is available for several years. Finally, field trials on alfalfa production have been conducted at the Experiment Station at Gull Lake which makes possible verification of the model results. I I ¢ ‘ ‘ ‘ll " I ‘I. JMJMUJUQ ..ru .. v9.0 a-OQI-I" 208 .cmmvzowz .mcvmcmm .mwow>cmm cmzocw ”moczom .mmmmzpcwcmq cw was: mvmcp .mswc :oegou.l \m Acw>wmv mN.N my oo.om mo.¢_ cmmncmo A:o_;osov m_.N-Nm.N m-_ 00.4N oo.m_ _ngaEmoeac_Na Acmumczmv m©.o_m N N¢©.ov mo.qu cmczwoncmo wcom\m mcom\mpcwa N co_~mm\m pmou mwmm mpcmvvmcmcH mowed IouwowuommcH cowpmo__aa< m>wpo< \@ 4H>mm3 oNN mmczpmcmnsmp NON NNNNNNNN NNN NNNNN .NNEN NNN NNNN>meNNNV Nogams N-N New NNNN: NNNNNNNNNNN 216 NN.N N N N N NN.N N N N N NN.NNN NNN NN.N N N N N NN.N N N N N NN.NNN NNNN NN.N N N N N NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.N N N N N NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.NN Ne NN NN NN NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.NN NN NN NN NN NN.NNN . NNN NNN NNN NNN NN.NNN NNNN NN.N N N N N NN.NNN NNN NNN NNN NNN NN.NNN NNN NN.NN N NN Ne N NN.NNN NNN NNN NNN NNN NN.NNN NNN NN.NN NN NN NN NN NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.N N N N NN NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.NN NN N NN NN NN.NN NN NN NN NN NN.NNN NNNN NN.N N N N NN NN.NN NN NN NN NN NN.NNN NNNN NN.N N N N N NN.N N N N N NN.NNN NNNN NN.N N N N N NN.N N N N N NN.NNN NNNN NN.N N N N N NN. N N N N NN.NNN NNN NN.N N N N N NN.N N N N v NN.NNN NNN NN.N N N N N NN.N N N N N NN.NNN NNNN NN.N N N N N NN.N N N N N NN.NNN NNNN NN NN.N NN NN N N NN.NN NN NN NN NN NN.NNNN NNN NN.N N N N NN NN.NN NN NN NNN NNN NN.NNN NNNN NN.NN N NN NN NN NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.N N N N N NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.N N NN NN NN NN.NNN NNN NNN NNN NNN NN.NNN NNN NN.NN NN NN NN NN NN.NNNN NNN NNNN NNNN NNNN NN.NNN NNN NN.NN N NN NN NN NN.NNN NNN NNN NNN NNNN NN.NNN NNN NN.NNN NNN NNN NNN NNN NN.NNN NNN NNN NNN NNN NN.NNN NNNN NN.N N N N N NN.NN NN NN NN NN NN.NNN NNNN NN.N N N N N NN.N N N N N NN.NNN NNNN NN.N N N N N NN.N N N N N NN.NNN NNNN NN NNNLN>N N N N N NNNLN>< N N N N \m NNNN NNNN LNNN NNNNN NNNNNLN NNNNN NNNNNNNNN NNNN NNNN NNNNN 22.3.. No .89sz «Emma .58 m4¢z .m u - .. ' ’ '0 "'0 ”a. v—ndflflllflfi “on - .. .uo-.n--- an- no .-N'IU"‘6IV . .‘\. P"':~Gi$ .. ... wt 0. N, 9 v0. ..‘.l 1:] 2.. . .. N 5 ANN NN>NNN No gmaazzv NNE ANN NN>NNN No Nonezzv N mp4:mmm chcz mp42mmm chc2 0 O 0 0 O 0 U 5 S 2 n w m... N N N 4 , N .I a N ...m. F7 d NN d v 6.9 .lld \ Y Id \N V. 111.. .91: \ ‘51... 91. \\x NNNTN Ed 08 \\ .I de \\ -1 9n 0.10 2 “‘ U .1 4 \ la a a anti 7 ‘1‘ mt.- 7 \\ P: u m \\ 1U . 9 \ 1U e2 " \\ n 1|. \\ V7 \\ o ‘‘‘‘‘‘‘ a9 \‘cu‘ «II \\ 1 NT \ O 3 x S \\ St \\\ n1! \\\\ 0 U E s ..N N N \\ Sun a r. N 11 V U I U r. n e 0 J 1U 5.1: .Dt 0 .d .1 d U v- I m 9.1 ...l S CI 0 I O S v. 5v 0 n A sQIAH $.10.- ..1 .1t VII 1 ml a a] pU m w I11 1|. 0 p N 1 N N N .. C D. O 0 O O O 0 O O m 5 NCIJ :04 MG 4. 4 m NNNNENN Noozm NNNNEN emu NN>LNN No NNNE:2N ANNNENN ammzm NNNNEN Nag NN>NNN No Noaezzv u g +-§5c> IEIIIII Noam-hump + + +-c>+-c>2: + + +-c>2:u I c>+-+-§Ec>c>c> 0+2 OII >-§5 Z+OOI I I Second Degree Stochastic Dominance )- + + + c>+-z:c> + + c>c>2:| a c: + +-§5c>c3<: I I :z +-c>c>u u \JO‘IU'l-DwNH + + + c>+-c>2: + 1 EE' 1 1/ + means that R1 dominates R2 —' - menas that R2 dominates R1 0 means the rules cannot be ordered NA means it is not apprOpriate to order a rule with itself ”to ~‘ no. — n... O“‘.' -4” -v n: un-v -. .. 252 TABLE 6.5 Grouping of decision rules based on net income using FSD and SSD First Degree Stochastic Dominancei/ Decision Rule Mean Grouping 6 920 A B 5 907 A B D 4 830 C D E F 7 825 B C D E F 3 823 B C D E 1 821 C D E F 2 806 C E F 1/ Decision rules followed by the same letter cannot be ordered by FSD Second Degree Stochastic Dominanceg/ Decision Rule Mean Grouping 6 920 A 5 907 B D E 4 830 C D E F 7 825 B C D 3 823 B C E 1 821 C F 2 806 C F 3/ Decision rules followed by the same letter cannot be ordered by SSD. 253 preferred to the no control strategy (Rule 4) and the routine two sprays schedule (Rule 2) and the dynamic threshold (Rule 1). A decision maker would be indifferent among Rule 5 and the static threshold spray (Rule 3) and the routine single spray (Rule 7). The no control strategy is dominated by both early cutting schedules (Rules 5 and 6) and cannot be ordered with any of the spray schedules. The single routine spray (Rule 7) and the static threshold (Rule 3) are both preferred to the two routine sprays (Rule 2). Neither can be ordered with Rules 5, 4, 1 or each other. Both are dominated by Rule 6. Rule 1 is dominated by the early cutting rules (Rules 5 and 6). It cannot be ordered with any other rules. Rule 2 is dominated by Rules 3, 5 and 6. It cannot be ordered with any other rules. Rules 1 and 2 are not preferred to any other rules. Using second degree stochastic dominance allows for a more complete ordering of decision rules. The rankings for Rules 5 and 6 relative to all other rules are the same under SSD as for FSD. Unlike FSD, SSD allows for the ordering Of Rules 5 and 6. Rule 6 is preferred to Rule 5. They could not be ordered using FSD because Rule 5 generated a higher net income than Rule 6 at one point at the upper end of the income distributions. The early decision rules cannot be ordered for any decision makers who have a positive utility for money. When only risk averse decision makers are considered, the scheduled early harvest criteria (Rule 6) is preferred to the early harvest scheduled by monitoring information (Rule 5). The routine single spray (Rule 7) was preferred to the other spray schedules using $50. It could not be ordered with Rules 4 and 5. Rule 7 could not be ordered with Rules 1 and 3 using FSD but was preferred to 254 those spray rules using SSD. This result shows that none Of the spray rules showed the highest net income in all years. The static threshold (Rule 3) was preferred to the other spray schedules except Rule 7. It could not be ordered with Rules 4 and 5. Rules 1 and 2 were not preferred to any other rules. They could not be ordered with the no control strategy (Rule 4). Under the stochastic dominance approach the net income distributions for each decision rule generated by the simulation model are taken to be the true distributions. There is no restriction on the functional form of the distributions. It allows for an ordering of action choices according to 21 decision maker's attitude toward risk. Type I errors are not controlled. In contrast, the least significant difference tests assured that the results of the simulation model are random samples from a larger data set and are used to estimate the true distributions. The tests rely on the assumptions that the true distributions are normal and have equal variance. They do not produce an ordering that accounts for the decision maker's attitude toward risk. Type I errors are controlled. It should be noted, that in this case, the assumptions of normality and equal variance are not unreasonable if the simulation results are viewed as a random sample of observations from a larger population. The null hypothesis of normality of the distributions held was not rejected at the .10 significance level. Tests for equality Of the variances detected no differences at the .05 level for any of the pairwise comparisons. The variances of Rule 5 and Rule 2 were significantly different at the .10 level, however. 7“ a... N. a“-I—-m_-o .N , - . . . «I. an. cad _iun 255 The differences in underlying assumptions do not allow for direct comparison of results. However, under both sets of restrictions, none of the strategies is preferred to the early cutting strategies. This observation gives some stability to the results. 6.2 Value of Pest Management Programs The differences between the gross income generated under each decision algorithm and the no control strategy are given in Table 6.6. These calculations measure the value of each pest management program for each year. In other words, the value of the program is measured as the increase in gross income attributable to that program. The dollar figure represents the increased income attributable to spraying, monitoring and the information imbedded in the decision algorithm itself. For the decision rules involving the use of thresholds for spray decisions (Rules 1 and 3) the value of the program is zero in years when no spray is recommended. In those years, the decision maker would have had the same yield without monitoring. The pest management program with the highest average value was Rule 6 ($89.83 per hectare) followed by Rule 5 ($83.93). Rule 3 had the lowest average value ($10.67 per hectare). The average values of the routine-spray programs, Rules 2 and 7, were $19.33 and $17.07, respectively. This means that (N1 the average, applying two sprays annually instead of one spray increased gross income by only $2.26 per hectare. The average values of the programs utilizing threshold information for spray decisions, Rules 1 and 3, were $12.73 and $10.67, I Y H- '4': ‘_ U*-Iu-‘-‘ I". . u —.-.-.-A9_.-p Difference between gross income for each rule and the 256 TABLE 6.6 VALUE OF PEST MANAGEMENT PROGRAHS no control strategy (Rule 4) Rule 1 2 3 5 6 7 Year ---" S/hectare ~--" 1966 22 28 0 ' 75 75 23 1967 11 13 0 100 90 12 1968 11 13 0 164 164 11 1969 15 17 15 129 129 15 1970 0 9 0 38 36 8 1971 11 13 0 106 99 11 1972 0 11 10 92 87 10 1973 0 11 0 59 60 8 1974 0 11 0 119 116 10 1975 0 12 11 13 13 11 1976 14 17 14 96 115 14 1977 63 84 78 48 124 78 1978 18 20 18 41 46 18 1979 13 14 0 87 86 12 1980 13 17 14 92 108 15 0 0 AVERAGE 13 19 11 84 90 17 VARIANCE 248 342 396 1,548 1,555 299 SD 16 18 20 39 39 17 COEF. VAR. 1.236 0.957 1.865 0.469 0.439 1.014 -I 0.. con-s ~II-J“-.‘~ -1 v-n .m. «.1 .a 257 respectively. On average, the dynamic threshold used in Rule 1 generated $2.06 more income than the static threshold used in Rule 3. The average values of the programs using threshold information for early cutting decisions, Rules 5 and 6, were $83.93 per hectare and $89.83 per hectare, respectively. Using Rule 6 means $6.90 more income per acre on average than using Rule 5. 6.3 Value of Insecticide Applications and Monitoring The value of insecticide applications is shown in Table 6.7 for Rules 1, 2, 3 and 7. Rules 2 and 7 are routine schedules and there is no cost of monitoring. Rule 1 and 3 use monitoring at a cost of $7 per hectare per year. These are the only rules for which insecticide was used as a control strategy. The difference between the values in Tables 6.6 and Table 6.7 is that the cost of monitoring is taken into account in Table 6.7 but not in Table 6.6. Rules 1 and 3 involve thresholds for spray decisions and did not utilize insecticides in every .year. The value of each program is negative $7.00 for years in which no insecticide was applied. In those years, the cost of monitoring was incurred even though no insecticide was applied. Also, no benefit from spraying was derived because no spray was applied. In other words, it cost $7.00 to decide to do nothing. The two routine sprays showed an average benefit of $19.33 per hectare while one routine spray showed only 21 slightly lower average benefit of $17.07. The break even cost of an insecticide application for the two scheduled sprays is $9.66. The break even price for the one scheduled spray is $17.07. In other words, once the cost of spraying 258 TABLE 6.7 VALUE OF SPRAY APPLICATIONS Differerence between the net income above monitoring costs for each control strategy involving spraying (Rules 1,2,3 and 7) and the no control strategy (Rule 4). For Rules 2 and 7 the monitoring cost is zero. For Rules 1 and 3 the cost of monitoring is $7 per hectare. Rule 1 2 3 7 Year ---- S/hectare a--- 1966 15 28 -7 23 1967 4 13 -7 12 1968 4 13 «7 11 1969 8 17 8 15 1970 -7 9 —7 8 1971 4 13 _7 11 1972 -7 11 3 10 1973 -7 11 -7 8 1974 -7 11 -7 10 1975 -7 12 4 11 1976 7 17 7 14 1977 56 84 71 78 1978 11 20 11 13 1979 6 14 -7 12 1980 6 17 7 15 AVERAGE 6 19 4 17 VARIANCE 248 342 396 299 so 16 18 20 17 COEF. VAR. 2.745 0.957 5.425 1.014 ., . .... -‘--Qfli—' 259 goes above $9.66 per hectare it is no longer profitable on the average to apply two sprays. Once the price of a spray goes above $17.07 it is no longer profitable on the average to apply one spray. The average value of the dynamic threshold (Rule 1) was $5.73 and the average value for the static threshold (Rule 3) was $3.67. If the cost of monitoring had been zero, the average value of Rule 1 would have been $12.73 and $10.67 for Rule 3. Sprays were recommended in ten years for Rule 1 and seven years for Rule 3. 0n the average, 2/3 of a spray was made each year for Rule 1 and 7/15 of a spray was made each year for Rule 3. The breakeven cost of a spray for Rule 1 is $8.60 and for Rule 3 is $7.86 at a $7 per year cost of monitoring. With no cost of monitoring the breakeven costs become $19.10 and $22.86 for Rules 1 and 3, respectively. The average benefit of a spray for the static threshold (Rule 3) exceeded the average benefit from a spray made following the dynamic threshold (Rule 1) when no cost of monitoring was included. The average benefits from both decision rules using thresholds exeeded the average benefit from the routine sprays (Rules 2 and 7). However, when the cost of monitoring is considered, the average net benefits from the routine sprays exeeded the average net benefits from the decision rules using thresholds. At a cost of $22 per spray, the increased income from the spray applications did not cover the cost of the sprays on average for any of the decision rules. The value of monitoring above Spray costs is given in Table 6.8. It is calculated as the difference between net income above spray costs for Rules 1, 3 and 5 and the gross income from no control. Rules 1, 3 260 TABLE 6.8 VALUE or MONITORING Differerence between the net income above spray costs for each control strategy involving monitoring (Rules 1,3 and 5) and the no control strategy (Rule 4). The cost of spraying is $22 per hectare. In years when the recommended strategy is identical to Rule 4, the value of monitoring is zero. Rule 1 3 5 Year ~--- S/hectare --~- 1966 0 0 75 1967 -11 0 100 1968 ‘11 0 164 1969 -7 -7 129 1970 0 0 38 1971 -11 0 106 1972 0 -12 92 1973 0 0 59 1974 0 0 119 1975 0 -11 13 1976 -8 -8 96 1977 41 56 48 1978 "4 ~4 41 1979 -9 0 87 1980 -9 -8 92 AVERAGE —1.93 0.40 83.93 VARIANCE 163 257 1548 SD 13 16 39 COEF. VAR. -6.60 40.04 0.47 261 and 5 are the only rules that inolve monitoring for pest population levels. In years when no spray application is made, Rules 1 and 3 generate the same gross income as the no control strategy. In those years the value of monitoring is zero. The value of a monitoring program is negative when the cost of spraying exceeds the increase in revenue resulting from spraying and reducing crop loss. Similarly, the value of a monitoring program is positive when the revenue increase attributable to spraying exceeds the cost of spraying. The value of monitoring for Rules 1 and 3 was positive only in 1977. In that year the net gain for Rule 1 was $41 and for Rule 3 was $56. On the average, the value of monitoring was -$1.93 for Rule 1. At a cost of $22 per hectare per spray, monitoring did not pay on the average for Rule 1. For Rule 3 the breakeven price for monitoring was $.40 per hectare per year. Rule 5 always showed a positive benefit from monitoring. The early cutting dates recommended based (”1 larvae sampling always increased gross revenue. The breakeven cost of monitoring was $83.92 per hectare per year. At a monitoring cost of $7, the average net value of monitoring was $76.93 per hectare per year. 6.4 Sampling Freguency The simulation model was run monitoring every day, monitoring every three days and monitoring once a week. The "spray or don't spray" decision is made every time sampling occurs for Rules 1 and 3. The monitoring information is compared to the threshold criteria. A spray is applied if the threshold is reached or surpassed provided it is not 262 too close to the scheduled harvest. Similarly, the decision to cut is made on each sampling date for Rule 5. Infrequent sampling increases the chance of spraying after the threshold is reached. More frequent monitoring results in making spray applications closer to the specified threshold. Tables 6.9 and 6.10 present the effect of sampling frequency on the net incomes above spray costs and monitoring costs for each year for Rules 3 and 5, respectively. Sampling frequency is not a factor for Rule 1 because the decision algorithm dictates how often samples should be taken. For Rule 3, the average net income was reduced from $824 for daily sampling and sampling every 3 days to $821 for weekly sampling. Sampling every third day instead of every day meant at most a difference of $1 in any one year. In twelve of the fifteen years the net income was identical for the two sampling regimes. Cutting sampling back to once a week did not have much effect on net income with the exception of 1977. In 1977 net income decreased $57 from postponing sampling and consequently spraying late. Net income was unchanged in seven of the fifteen years. The value of sampling every day instead of every third was only $.14. Virtually any reduction in cost from switching to a: three-day schedule from a daily schedule would pay off. The value of sampling every 3 days instead of once a week was $3 per year. This means that if a grower could reduce the cost of monitoring from $7 per hectare to $4 per hectare, net income would be the same on average for each sampling regime. 263 TABLE 6.9 Effect of Sampling Frequency on Net Income Above Spray and Monitoring Costs for Decision Rule 3 - Static Threshold Days Between Samples Year 1 3 7 ---- 5 ...2 1966 755 755 755 1967 962 962 962 1968 923 923 923 1969 877 877 876 1970 767 767 767 1971 825 825 825 1972 862 861 860 1973 797 797 797 1974 830 830 830 1975 733 732 731 1976 878 877 880 1977 654 655 598 1978 795 795 794 1979 880 880 886 1980 817 817 825 AVERAGE 824 824 821 VARIANCE 6,143 6,118 7,790 SD A 78 78 88 COEF. VAR. 0.095 0.095 0.108 264 TABLE 6.10 Effect of Sampling Frequency on Annual Net Income Above Monitoring Costs for Decision Rule 5 - Dynamic Threshold Days Between Samples Year 1 3 7 14 "" $/hectare —-—- 1966 830 824 817 817 1967 1,062 1,045 1,025 1,025 1968 1,087 1,051 1,051 1,045 1969 1,013 995 990 975 1970 805 806 807 807 1971 931 898 865 865 1972 966 947 930 930 1973 856 850 842 842 1974 849 919 914 914 1975 757 747 749 749 1976 982 982 951 951 1977 646 646 646 646 1978 840 836 826 826 1979 967 956 950 947 1980 917 914 907 907 AVERAGE 901 894 885 883 VARIANCE 14,130 12,439 11,583 11,203 SD 119 112 108 106 COEF. VAR. 0.132 0.125 0.122 0.120 265 Net income was actually increased in three years by sampling once a week instead of daily. In those years no sample was taken on the day that the static threshold was reached and spraying was delayed. In 1977 sampling every third day resulted in a net income of $655 compared to $654 for sampling daily. In 1979, net income was $886 compared to $880 for the two sampling regimes and in 1980 it was $825 compared to $817. The failure of daily sampling to produce the highest income in every year shows that the static threshold will not always optimize net income. This could be (1) because of the uncertainty regarding weather, pest population growth, and plant growth at the time the decision is made; or (2) because other factors besides larval population should be taken into account when spray decisions are made; or (3) both. Four sampling regimes were tested for decision Rule 5; sampling every day, every three days, once a week and once every two weeks. The cost benefit analysis used in Rule 5 calculates the income from cutting hay on the day the sample is taken and predicts income for the two weeks after the sample is taken. The date which is predicted to yield the highest income is selected as the harvest date. If the date falls before the next scheduled sample, then it becomes the harvest date. If it falls after the next scheduled sample, the next sample is taken and a date is selected utilizing the new information. The process continues until the selected harvest date occurs before the next scheduled sample. This procedure makes it possible to choose any day as the day of first harvest up until the scheduled date for the conventional harvest date (Rule 4). The harvest date is selected based upon more or less information depending on the frequency of sampling which will affect the 266 decision. However, potential harvest dates are not limited to the days on which samples are taken. The average net income above monitoring costs for daily sampling for Rule 5 was $901, $894 for every three days, $885 for once a week and $883 for sampling every two weeks. The coefficients of variation were .13 for daily sampling and .12 for the other sampling regimes. The net income from sampling daily averaged $6 per hectare per year more than the net income from sampling every three days, $16 more than sampling once a week and $17 more than sampling every two weeks. The cost of daily sampling would have to be at least $16 more than sampling once a week before it paid to monitoring once a week or less. Similarly, the cost of sampling daily would have to be at least $6 more than sampling every 3 days before average net income would increase from reducing monitoring frequency. Daily sampling always resulted in a higher income than less frequent sampling with exception of 1970 when the incomes were within $2 of each other. The largest differences in net income occurred in years when income was relatively high. For example, the value of sampling every day instead of once a week was $35 in 1967 when the net income was highest at $1087. In 1980, when the net income for daily sampling was $917, the increase over sampling once a week was only $10. The timing of cutting becomes more critical as potential income increases. 6.5 Recommended Spray Dates and Harvest Dates The spray dates and harvest dates recommended for selected algorithms are presented in Tables 6.11 and 6.12. The spray dates are given for each of the single spray strategies (Rules 1, 3 and 7). The 267 TABLE 6.11 SPRAY DATES RECOMMENDED BY DECISION ALGORITHMS Rule 1 3 7 Year .— 1966 6/9 6/141 6/11 1967 6/7 6/101 6/8 1968 6/3 NS 6/4 1969 6/1 6/7 6/5 1970 NS NS 6/1 1971 6/11 6/121 6/8 1972 NS 6/6 6/5 1973 NS NS 6/3 1974 NS NS 6/5 1975 NS 6/6 6/5 1976 6/3 6/3 5/31 1977 5/17 5/20 5/20 1978 6/6 6/8 6/6 1979 6/8 NS 6/6 1980 6/3 6/10 6/7 Spray recommended wlthin 100 degree days (5 days) of harvest so no spray was applied. NS - No spray was recommended. - _4. - '- ... . .--.4..._-_~_._.__ 268 TABLE 6.12 HARVEST DATES RECOMMENDED FOR THE FIRST CUTTING BY DECISION ALGORITHMS Rule 4 5 6 Year 1966 6/19 6/7 6/7 1967 6/13 6/3 6/4 1968 6/9 5/30 5/30 1969 6/14 5/31 5/31 1970 6/11 6/1 5/30 1971 6/15 6/4 6/5 1972 6/13 6/1 6/2 1973 6/10 6/1 5/30 1974 6/13 6/2 6/1 1975 6/14 5/31 5/31 1976 6/8 5/30 5/27 1977 5/24 5/31 5/17 1978 6/14 6/3 6/1 1979 6/14 5/31 6/2 1980 6/17 6/3 6/2 269 harvest dates are given for the early cutting strategies (Rules 5 and 6) and the conventional cutting schedule (Rule 4). In two years the dynamic threshold (Rule 1) made a spray recommendation while the static threshold (Rule 3) did not. In one year the static threshold made a spray recommendation while the dynamic threshold did not. In three years no spray was recommended by either rule. The spray dates recommended by the static threshold were always later than the spray dates recommended by the dynamic threshold with the exception of one year when the dates were identical. Sprays were avoided in three years for Rule 3 because the date recommended was within 100 degree days of the scheduled harvest. A spray was never recommended within 100 degree days of harvest by Rule 1. It appears that the dynamic threshold levels developed in Illinois and used in Rule 1 are too low for Michigan conditions. The cutting dates recommended by Rules 5 and 6 were always within three days of each other with the exception of 1977 when the model failed to perform adequately. For that year, a modified data point was generated for Rule 6 (sec. 4.8). This modification did not generate a new cutting date, however. The early cuts ranged from nine to fifteen days earlier than the conventional control strategy. The cutting date recommended by Rule 6 is based solely on temperature data. In contrast, Rule 5 requires temperature data and a measure of the larvae population. The additional information required to implement Rule 5 did not generate an increase in revenue, nor did it reduce the variability in income flow. Therefore, the monitoring expense for measuring weevil population was not warranted. CHAPTER VII SUMMARY AND CONCLUSION Integrated pest management has been defined as a control system that uses all suitable techniques to repress pest populations to levels below those causing economic injury in a manner that is compatible with the environment. The concept of an economic threshold was developed by Stern et al. (1959) to define the pest level at which control strategies should be implemented. Several generic models were presented to derive the threshold population mathematically. The solutions differed depending on the variables included in the model by its designer. In particular, the inclusion of parasites, interdependencies among fields and multi-year vs. single year planning significantly altered the results. While the philosophy of pest management is intuitively appealing, implementation requires an understanding of the interactions of numerous biological and environmental factors. When pest management decisions are put in the context of all on-farm management decisions, the problem is even more complex. Pest management decisions are made under uncertainty. The grower does not have perfect knowledge of future states of nature or the effectiveness of alternative control strategies. As a result, the ideal conditions of perfect and costless knowledge are not appropriate for analysis of pest management programs. Pest management information may not be provided adequately by decentralized markets for two basic reasons: 1) the goals of pest management include non-market values sometimes referred to as collective 270 271 values and 2) information has public goods characteristics. That is, consumption by one person does not reduce the amount available to anybody else. Also it is difficult to exclude people from using information once it has been produced. Information for which exclusion is possible is likely to be provided by the private sector. But these private programs will not include regional management or the interdependencies of growers. It is unreasonable for extension workers in the area of pest management to believe that they need only demonstrate the benefits of pest management and the private sector will pick up the ball. A more viable approach has been to aid growers in providing pest management information for themselves through some form of grower organization. This alternative does not depend on the private sector response to grower needs and reduces subsidization of programs by public funds. It is clear that neither generating nor delivering pest management information is a simple matter. But developing control guidelines and providing that information along with information needed to operationalize the guidelines are not problems to be solved independently. Control guidelines should always be designed with the user in mind. If the information required is too detailed or performance is overly sensitive to sampling error, the guideline is simply an academic exercise. A paradigm for information systems was presented (Bonnen 1977). Information is the interpretation of data used in the decision making process. In pest management, information is used to make control decisions. Management can be viewed as a process by which information is the input and decisions are the output. 272 The design of a pest management program is the development of an information system. The information provided to managers is prescriptive. That is, it recommends specific pest control strategies. Often the recommendation takes the form of pest control guidelines for the timing of implementation of a strategy. These guidelines are developed from an accumulation of knowledge over time for a region. Guidelines include threshold information. The strategy should not be implemented unless the threshold is reached. A threshold can be defined in an infinite number of ways. They usually require real—time field-specific measurements of pest levels, stage of plant development and/or other factors. Information has value in the context of the decision being made. The value of the information can be evaluated by comparing the outcomes with and without the information. The outcomes are not known with certainty. Therefore, criteria for selecting among risky alternatives depend on a probability distribution of outcomes associated with each alternative management strategy. The use of simulation models to generate probability distribution was discussed in general and then applied to the alfalfa weevil problem. The simulation model presented had three submodels: 1) the alfalfa weevil model, 2) the alfalfa plant model and 3) the management model. The alfalfa weevil model developed in Illinois, and the alfalfa plant model were modified to perform reasonably under Michigan weather conditions. It was determined that the overwintering logic for the alfalfa weevil did not work adequately to run the model for consecutive years. Therefore, the model was reinitialized every fall. The plant model did not perform accurately when the temperature in early spring 273 was extremely hot or extremely cold. Changes in the model were made accordingly. The management model had seven versions. Each was an alternative decision rule for determining whether or not to inmlement a specific control strategy. The strategies were: 1) spray when a dynamic threshold is reached, 2) apply a single routine spray before harvest, 3) spray when a static threshold is reached, 4) do nothing, 5) cut early based (n1 a pest population threshold, 6) cut early regardless of pest population levels and 7) apply one routine spray before harvest and one after harvest. Rules 1, 3 and 5 involved monitoring of pest populations, the others did not. The income distributions generated by the simulation model for each decision rule were compared several ways using varying sets of assumptions. First, the simulation results were assumed to be a random sample from a larger population. Further, the underlying distributions were assumed to be normally distributed with equal variance. A comparison of means tests showed that under these assumptions, the average net incomes from the two early harvest schedules were significantly higher than for the other strategies at the .05 level. All of the strategies showed a significantly higher mean net income than the routine two sprays at the .10 level. This analysis did not take the decision maker's attitude toward risk into account. Decision analysis based on the Expected Utility Hypothesis was used to include risk-preference into the analysis. Stochastic dominance techniques assume that the income distributions generated by the simulation model are the true distributions. This assumption does not 274 control for Type I errors. No assumption is made about the functional form of the distributions. First degree stochastic dominance provides a preference ordering for all decision makers. Second degree stochastic dominance limits the ordering of action choices to risk-averse decision makers. The ordering is more complete than for FSD but the chance of Type I error increases. Using first degree stochastic dominance, the early cut rules were also preferred to the other rules and were not significantly different from each other. Using second degree stochastic dominance, Rule 6 was preferred to Rule 5. In any case, the simple cut early rule is at least as effective as cutting based on pest population counts. The value of each pest management program was calculated. The value of the spray applications did not cover the cost of the spray material on average for any of the programs including spraying. The benefit from sprays only exceeded the cost of sprays in one of the fifteen years. The results are significant at least in the Great Lake States where fall laid alfalfa weevil eggs do not survive the winter. It is important to note the limitations of the approach taken. First, the model is for a single season and single field. No in-migration of weevils is possible. Also, no long run effects of continued pesticide use such as reduced effectiveness of pesticides or reduction in parasite population are considered . The monitoring information for pest populations and weather are taken as the true values. No measurement error exists. The model also assumes that all of the acreage can be sprayed the day after the control recommendation is made. This is not unrealistic. 275 However, the model also assumes that all of the hay can be cut the day after the recommendation is made, which is not feasible. The results are appropriate if they are considered as the average of the several cuts made. The model does not allow for a reduction in hay quality due to rain on cut hay before it is baled and removed from the field. Future research needs include the following. First, Inore information is needed concerning the overwintering habits of the alfalfa weevil adults. Along these lines, the in and out migration from individual fields should be explored. At that time, multi-year strategies can be developed. Secondly, the growth rates of the alfalfa plant in early spring are not adequately understood. Thirdly, future studies should include a sampling error to test the effects of an unbiased error and an upward or downward bias. Finally, the results of this study strongly indicate that early cutting schedules are preferable to spray application for control of alfalfa weevil in alfalfa even when threshold information is available for the timing of sprays. For the early harvest strategies, the monitoring of pest population levels was not shown to improve cutting schedules over a scheduled early harvest. For the spray strategies, the dynamic threshold strategies were not preferred to static thresholds or routine single sprays. The implications are (1) that current threshold levels for spray applications are too low and (2) that more research should be concentrated on developing cutting schedules. BIBLIOGRAPHY BIBLIOGRAPHY Abu, J. F. and Ellis, C. R. "Toxicity of Five Insecticides to the Alfalfa Weevil, Hypera ,postica, and Its Parasites Bathyplectes curculionis and Microctonus aethiopoides." Environmental Entomology 6 (June l977): 385-389. Agricultural Board, Division of Biology and Agriculture, National Research Council. Pest Control Strategies for the Future. Washington, 0.0. National Academy of Sciences, l972. Alfalfa Insects Conference. Proceedings of the lSth Annual Northeast Invitational Alfalfa Insects Conference. West Lafayette, Indiana: Purdue University, Department of Entomology, l978. Anderson, J. R. "Sparse Data, Estimational Reliability, and Risk-Efficient Decisions." American Journal of Agricultural Economics 56 (August I974): 564-572. Anderson, J. R.,_etial. Agricultural Decision Analysis. Ames, Iowa: Iowa State University Press, l977. Armbrust, E. J.; Pass, B. C.; Davis, D. W.; Helgesen, R. G. Manglitz, G. R.; Pienkowski, R. L.; and Summers, C. G. "General Accomplishments Toward Better Insect Control in Alfalfa,“ New Technologies of Pest Control. Carl B. Huffaker (ed.), New Yd??? John Wiley & Sons, Inc., 1980. Arnold, C. Y. "Maximum-Minimum Temperatures as a Basis for Computing Heat Units." Proceedings of the American Society of Horticultural Science 76 (l960): 682-692. Arrow, K. J. Aspects of the Theory of Risk-Bearing. Helsinki: Yrjo Jahnsson Foundation, l965. Baquet, A. E.; Halter, A. N.; and Conklin, S. "The Value of Frost Forecasting: A Bayesian Appraisal." American Journal of Agricultural Economics 58 (August l976): STl-520. Baskerville, G. L. and Emin. P. "Rapid Estimation of Heat Accumulation from Maximum and Minimum Temperatures." Ecology 50 (Spring l969): 5l4-517. Black, J. R. and Hlubik, J. "Basis of Computerized Linear Programs for Ration Formation." Journal of' Dairy Science 63 (August l978): l366-l378. 277 Black, J.; Wandschneider, P.; and Nott, S. Alfalfa and Corn Silage Combinations to Maximize Michigan Dairy Farm Income. Agricultural Economics Staff Paper No. 74-l0, East Lansing, Michigan: Michigan State University, 1974. Bonnen, J. T. "Improving Information on Agriculture and Rural Life." American Journal of Agricultural Economics 57 (December 1975): 753-763. Bonnen, J. T. "Assessment of the Current Agricultural Data Base: An Information System Approach." A Survey of Agricultural Economics Literature. L. R. Martin (ed.), Minneapolis: University of Minnesota Press, l977. Braithwaite, J. R.; Booth, G. M.; and Robison, L. "Field Efficacy of Two Organophosphates and an Insect Growth Regulator on the Alfalfa Weevil Hypera pgstica (Gyllenhal)." Science of Biology Journal 2 (September-October, 1976): 170-179. Breimyer, H. F. Economics of the Product Markets of Agriculture. Ames, Iowa: Iowa State University Press, 1976. Brown, A. W. A. The Ecology of Pesticides. New York: John Wiley & Sons, l978. Buchanan, J. M. "Joint Supply, Externality and Optimality." Journal of Political Economy (November l966): 404-4l5. Burkhead, J. and Miner, J. Public Expenditure. New York: Aldine Publishing Company, l97l. Bush, R. R. and Mosteller, F. Stochastic Models for Learning. New York: John Wiley & Sons, Inc., 1955. Carlson, G. A. "The Microeconomics of Crop Losses." Symposium on Economic Research on Pesticides for Policy Decision Making. ERS, USDA, Washignton, D.C., I970. Carlson, G. A. "Economic and Biological Variables Affecting Demand for Publicly and Privately Provided Pest Information." American Journal of Agricultural Economics 62 (December 1980): l00l-l006. Carlson, G. A. and Castle, E. N. Economics of Pest Control. Journal paper No. 3456. Raleigh, North Carolina: North Carolina Agricultural Experiment Station, l972. Casagrande, R. A. Preliminary_Considerations on Alfalfa Weevil Management in Michigan. Interdepartmental Communication, East Lansing, Michigan: Michigan State University, Department of Entomology. December l970. 278 Casagrande, R. A. and Stehr, F. W. "Evaluating the Effects of Harvesting Alfalfa on Alfalfa Weevil (Coleoptera: Curculionidae) and Parasite Populations in Michigan." The Canadian Entomologist l05 (August l973): lll9-ll28. Chalmers, A. F. What Is This Thing Called Science? St. Lucia: University of QueenSland Press, l976. Chandler, P. T. and Martin, J. E. "Computerized Management Information Systems." Journal of Diary Science 58: 239-245. Churchman, C. W. Prediction and Optimal Decisions: Philosophic Issues of A Service of Values. New York: Prentice Hall, l96l. Cohen, K. J. and R. M. Cyert. Theory of the Firm: Resource Allocation in a Market Economy. Englewood Cliffs: Prentice Hall, Inc., l975. Coles, L. W. and Day, W. H. "The Fecundity of Hypera postica from Three Locations in the Eastern United States." Environmental Entomology 6 (April l977): 21l-2l2. Colette, W. A. and Hubbard, P. Utilization of an E-L Frontier to Evaluate Differences in Risk Preference Between Large and Small Farm Operators. Staff Paper l59, Gainesville, Florida: University of Florida Institute of Food and Agricultural Sciences, July l980. Commons, John R. The Economics of Collective Action. New York: Macmillan, l950. Cothran, W. R. and C. G. Summers. "Sampling for Egyptian Alfalfa Weevil: A Comment on the Sweep-Net Method." Journal of Econ. Entom. 65 (l972): 689—69l. Cothran, W. R.; Summers, C. G.; and Franti, C. E. "Sampling for the Egyptian Alfalfa Weevil: Comparison of' Two Standard Sweep-Net Techniques." Journal of Economic Entomology 68 (August l975): 563-564. Cumins, H. N. "The Control of Adaptable Pests." Proceedings of a Conference on Pest Management. Laxenburg, Austria: September l977. Cyert, R. M. and DeGroot, M. H. "An Analysis of Cooperation and Learning in a: Du0poly Context." The American Economic Review 63 (March l973): 24-37. Davis, G. B. Management Information Systems: Conceptual Foundations, Structure, and Development. New York: McGraw-Hill Book Company, l963. Dowdy, A. C. Alfalfa Weevil in Michigan. C00perative Economic Insect Report 16: 540. Washington, D.C.: U.S. Department of Agriculture, 1966. 279 Dumbre, R. B. and Hower, A. A. Jr. "Relative Toxicities of Insecticides to the Alfalfa Weevil Parasite Microctonus aethiops and the Influence of Parasitisnl on Host Susceptibility. Environmental Entomology 5 (April 1976): 3ll-315. Dunn, E. 5., Jr. Social Information Processing and Statistical Systems--Change and Reform. New York: John Wiley & Sons, 1974. Edwards, C. A. and G. W. Heath. The Principles of Agricultural Entomology. Springfield, Illinois: Thomas Publishers, 1964. Eisgruber, L. M. "Micro- and Macro-Analytic Potential of Agricultural Information Systems." Journal of Farm Economics 49 (December l967): l54l-l552. "Managerial Information and Decision Systems in the U.S.A.:. Historical Developments, Current Status, and Major Issues." American Journal of Agricultural Economics 55 (December l973): 930-937. "Developments in the Economic Theory of Information." American Journal of' Agricultural Economics 60 (December l978): 901-907. Feder, G. "Pesticides, Information, and Pest Management Under Uncertainty." American Journal of Agricultural Economics 61 (February l979): 98-l03. Fick, G. W. Alsim 1 (Level l) Users' Manual. Department of Agronomy, Mimeo 75-20. Ithaca, New York: Cornell University, l975. "Alfalfa Weevil Effects on Regrowth of Alfalfa." Agronomy Journal 68 (September-October l976): 809-8l2. Fick, G. W. and Liu, B. W. Y. "Alfalfa Weevil Effects on Root Reserves, Development Rate, and Canopy Structure of Alfalfa." Agronomy Journal 68 (July-August l976): 595-599. Fishburn, P. C. "Separation Theorems and Expected Utilities." Journal of Economic Theory ll (l975): l6-34. Flessel, J. K. and Niemczyk, H. 0. "Theoretical Values of Fully Grown First-Cutting Alfalfa Lost to Alfalfa Weevil Larvae." Journal of Economic Entomology 64 (February l97l): 328-329. Food and Agriculture Organization (FAO). Report of the First Session of FAO Panel of Experts on Integrated Pest Control. Rome, l967. Friedland, E. I. "Values and Environmental Modeling." Ecos stem Modeling in Theory and Practice. Charles Hall and JoEn Day, Jr. (eds.) New York: John Wiley & Sons, l977. 280 Frisbie, R. "Implementation and Economic Returns from the Systems Approach to Pest Management in Cotton." Proceedings of XV International Congress of Entomology. Washington, D.C., 1976. Frosheiser, F. I.; Munson, R. 0.; and Wilson, M. Curtis. Alfalfa Analyst. Extension Bulletin E-744, Farm Science Series, East Lansing, Michigan: Michigan State University Cooperative Extension Service, 1972. Geier, P. W. "Organizing Large-Scale Projects in Pest Management." Meeting on Cotton Pests. Rome: FAO, l970. Giese, Ronald L.; Miles, Gaines E.; Hintz, Thomas R.; and Harrington, Rodney B. "Meteorological Information Utilization 'hi Pest Management." Symposium on Weather as a Component of Pest Management Programs. Proceedings North Central Branch--Entomological Society of America 30 (1975): 20—30. Good, J. M.; Hepp, R. E.; Mohn, P. 0.; and Vogelsang, D. L. Establishing and Operating Grower-Owned Organizations for Integrated Pest Management. PA-llBO, United States Department of Agriculture, Extension Service, March 1977. Gordon, D. V. and Klein, K. K. "Determination of the Economic Threshold for Control of Horn Flies on Beef Cattle: A Whole Farm Approach." Presented to the American Agricultural Economics Association Annual Meeting, Champaign-Urbana, l980. Gutierrez, A. P.; Wang, Y.; and Jones, R. E. “Systems Analysis Applied to Crop Protection." EPPO Bulletin 9 (1979): 133-148. Gutierrez, A. P. and Wang, Y. "Applied Population Ecology: Models for Crop Production and Pest Management." Proceedings of a Conference on Pest Managment. Laxenburg, Austria: SeptemBer 1977. Hall, 0. C. "Profitability and Risk of Integrated Pest Management." California Agriculture 10 (February l978). Hall, 0. C. and Norgaard, R. B. "On the Timing and Application of Pesticides." American Journal of Agricultural Economics 55 (May l973): l98-20l. "On the Timing and Application of Pesticides: Reply." American Journal of Agricultural Econmics 56 (August l974): 644-645. Hamlin, J. C., F. V. Lieberman, R. W. Bunn, W. C. McDuffie, R. C. Newton, and L. J. Jones. Field Studies on Alfalfa Weevil and the Environment Technical Bulletin 975. Washington, D.C.: U.S. Department of Agriculture, 1949. Hanemann, W. M. and Farnsworth, R. L. "Risk Preferences and Perceptions in the Use of IPM." Presented to American Agricultural Economics Association Annual Meetings, Champaign-Urbana, July 27-30, 1980. 281 Harsh, S. B. "The Developing Technology of Computerized Information Systems." American Journal of Agricultural Economics 60 (December 1978): 908-912. Hartman, R. "Factor Demand with Output Price Uncertainty." American Economic Review 66 (September 1976): 675-681. Hastings, E. and G. Pepper. "Aerial and Ground Application of Insecticides of Pre-Season Control of Alfalfa Weevil." Journal of Economic Entomology 44 (1951): 9-l3. "Further Contributions to Alfalfa Weevil Studies. Journal of Economic Entomology 46 (1953): 785-788. Hawkins, 0. E.; Slife, F. W.; and Swanson, E. R. "Economic Analysis of Herbicide Use in Various Crop Sequences." Illinois Agricultural Economics 7 (January 1977): 8-13. Hayami, Y. and Peterson, W. "Social Returns to Public Information Services: Statistical Reporting of U.S. Farm Commodities." Ih_e_ American Economic Review 62 (May 1972): ll9—130. Head, J. G. "Public Goods and Public Policy." Public Finance (1962): 197-221. Headley, J. C. "Defining the Economic Threshold." Pest Control Strategies for the Future. Washington, D.C.: National Academy of Sciences, 1972, lOO-lO8. Headley, J. C. "The Economics of Pest Management." Introduction to Insect Pest Management. R. L. Metcalf and W. H. Luckman (eds.), New York: John Wiley and Sons, 1975. Helgesen, R. G. and Cooley, N. "Overwintering Survival of the Adult Alfalfa Weevil." Environmental Entomology 5 (February l976): l80-l82. Hepp, R. E. Alternative Delivery Systems for Farmers to Obtain Integrated Pest Management Services. Agricultural Economics Report No. 298, East Lansing, Michigan: Michigan State University, June l976. Hintz, T. R.; Wilson, M. 0.; and Armbrust, E. J. "Impact of Alfalfa Weevil Larval Feeding (Hi the Quality and Yield of First Cutting Alfalfa." Journal of Economic Entomology 69 (December l976): 749-754. Holt, 0. A.; Bula, R. J.; Miles, G. E.; Schreiber, M. M.; and Pearl, R. M. Environmental Physiology. Modeling and Simulation of Alfalfa Growth I. Conceptual Development of SIMED. Research Bulletin 907, West Lafayette, Indiana: Agricultural Experiment Station, Purdue University in cooperation with the Agricultural Research Service, U.S. Department of Agriculture, July l975. 282 Hsieh, F. and Armbrust, E. J. "Temperature Limits of Alfalfa Weevil Oviposition and Egg Density in Illinois." Journal of Economic Entomology 67 (April 1974): 203-206. Hueth, D. and Regev, U. "Optimal Agricultural Pest Management with Increasing Pest Resistance." American Journal of Agricultural Economics 56 (August 1974): 543—552. Huffman, Wallace E. "Assessing Returns to Agricultural Extension." American Journal of' Agricultural Economics 60 (December 1978): 967-975. Infanger, C.L.; Robbins, L. W.; and Debertin, D. L. "Interfacing Research and Extension in Information Delivery Systems." American Journal of Agricultural Economics 60 (December 1978): 915-920. Janes, R. L. and R. F. Ruppel. Alfalfa Weevil. Extension Bulletin E-639, East Lansing, Michigan: Michigan State University, 1969. Johnson, G. L. Some Lessons from the IMS. Agricultural Experiment Station Project 442 (Staff Paper 76-5), East Lansing, Michigan: Michigan State University, March 1977. Johnson, G. L. and C. L. Quance. The Overproduction Trap in U.S. Agriculture. Baltimore: John Hopkins Press, 1972. Just, R. E. "A Methodology for Investigating the Importance of Government Intervention in Farmers' Decisions." American Journal of Agricultural Economics 55 (August 1973): 441-452. King, R. P. and Robison, L. J. "An Interval Approach to Measuring Decision Maker Preferences." American Journal of Agricultural Economics 63 (August 1981): 510—520. Knight, F. H. Risk, Uncertainty and Profit. Boston: Houghton Mifflin Co., 1921. Koehler, C. S. and Rosenthal, S. S. "Economic Injury Levels of the Egyptian Alfalfa Weevil or the Alfalfa Weevil." Journal of Economic Entomology 68 (February 1975): 71-75. Kohls, R. L. and Downey, W. 0. Marketing of Agricultural Products. New York: Macmillan, 1972. Leslie, P. H. "On the Use of Matrices in Certain Population Mathematics.“ Biometrika 35 (June 1945): 213-245. Litsinger, J. A. and Apple, J. W. "Thermal Requirements for Embryonic and Larval Development of the Alfalfa Weevil in Wisconsin." Journal of Economic Entomology 66 (April 1973): 309-311. 283 Litsinger, J. 0.; Lumaban, M. D.; Bandong, J. P.; Pantua, P. C. Barrion, A. T.; Apostol, R. F.; and Ruhendi. A Methodology for Determining Insect Control Recommendations. IRRI Research Paper Series No. 46, Manila: The International Rice Research Institute, January 1980. Lui, B. W. Y. and G. W. Fick. "Yield and Quality Losses Due to Alfalfa Weevil. Agronomy Journal 67 (1975): 828-832. Magnusson, G. Production Under Risk. Uppsala, Sweden: Almquist & Wiksells Boktryckeri, 1969. Manetsch, T. J. and Park, G. L. Systems Analysis and Simulation with Applications to Economic and Social Systems, Part 1. East Lansing, Michigan: Michigan State University, 1974. Mathur, R. B. and R. L. Pienkowski. "Effect of Alfalfa Weevil Feeding on Alfalfa Quality. " Journal of Economic Entomology 60 (1967): 601-602. Meyer, J. "Choice Among Distributions.“ Journal of Economic Theory 14 (April 1977): 326—336. Mowart, D. N., R. S. Fulkerson, W. E. Tossell and J. E. Winch. “The jg vitro Digestibility and Protein Content of Leaf and Stem Portions of Forages." Canadian Journal of Plant Science 45 (1965): 321-331. Musgrave, R. A. "The Voluntary Exchange Theory of Public Economy." Quarterly Journal of Economics (February 1938): 213-237. National Academy of Sciences. "Insect Pest Management and Control." Principles of Plant and Animal Pest Control, vol. 3. Publication No. 1695, Washington, D. C. National Academy of Science, 1969. Newton, C. M. and Leuschner, W. A. "Recognition of Risk and Utility in Pest Management Decisions." Bulletin of the Entomological Society of America 21 (September 1975): 169-172. Nicholson, A. J. and Bailey, V. A. ”The Balance of Animal Populations." Proceedings of the Zoological Society of London, Part 1. London: 1935. Niemczyk, H. D. and Flessel, J. K. "Contact Toxicity of Eight Insecticides to Adult Bathyplectes curculionis, a Parasite of Alfalfa Weevil Larvae.” Journal of Economic Entomology 68 (October 1975): 585—586. Norgaard, R. B. "The Economics of Improving Pesticide Use." Annual Revue of Entomology 21 (1976): 45—60. "Integrating Economics and Pest Management." Integrated __“P—es—t Management. J. L. Apple and R. F. Smith (eds.), New York: Plenum Press, 1976, 17-27. 284 Norton, G. A. "Background to Agricultural Pest Management Modeling." Proceedings of a Conference on Pest Management. Laxenburg, Austria: September 1977. Odum, E. P. "The Emergence of Ecology as a New Integrative Discipline." Science 195 (March 25, 1977): 1289-1293. Office of Technology Assessment. Pest Management Strategies, vol. 1, 2. Washington, D.C., 1979. Olson, Mancur. The Logic of Collective Action: Public Goods and the Theory of Groups. Cambridge: Harvard University Press, 1971. "Pest Management Coops--The Small Grower's Answer to the IPM Puzzle?" Ag Consultant and Fieldman (February 1980): 8-11. Pimental, 0. "World Food Crisis: Energy and Food Production." Bulletin of the Entomolggical Society of America 22 (March 1976): 20-26. Pope, R. D. and Just, R. E. "On the Competitive Firm under Production Uncertainty." Australian Journal of Agricultural Economics 21 (August 1977): 111-118. Pratt, J. W. "Risk Aversion in the Small and in the Large." Econometrica 32 (January-April 1964): 122-136. Rabb, R. L. "Principles and Concepts of Pest Management." Implementing Practical Pest Management Strategies. National Extension Insect Pest Management Proceedings. West Lafayette, Indiana: Purdue University, 1972. Raiffa, H. Decision Analysis. Reading, Mass.: Adison-Wesley, 1968. Ramsey, F. P. "Truth and Probability." The Foundation of Mathematics and Other Logical Essays. R. B. Braithwaite (ed.), London: RoutTedge and Kegan Paul, 1931. Regev, U.; Butierrez, A. P.; and Feder G. "Pests as a Common Property Resource: A Case Study of Alfalfa Weevil Control." American Journal of Agricultural Economics 58 (May 1976): 186-197. Reimenschneider, C. H. and Bonnen, J. T. "National Agricultural Information Systems: Design and Assessment." Information Systems for Agriculture. M. J. Blackie and J. B. Dent (eds.), London: Applied Science Publishers, 1979. Robison, L. J. "Decision Theory--The Expected Utility Hypothesis." Presented to Workshop on Practice, Theory, and Needed Research on Capital Investment Decisions in the Energy Supply Industry, East Lansing, Michigan, November l4-15, 1977. 285 Robison, L. J. and Brake, J. R. "Application of Portfolio Theory to Farmer and Lender Behavior." American Journal of Agricultural Economics 61 (February 1979): 158-164. Robison, L. J. and King, R. P. Specification of Micro Risk Models for Farm Management and Policy Research. Agricultural Economics Report No. 349, East Lansing, Michigan: Michigan State University, 1978. Rossmiller, G. E. and Riemenschneider, C. H. Information Theory, System Simulation, and Decision Making, Agricultual Economics Staff Paper No. 77-90, East Lansing, Michigan: Michigan State University, 1977. Ruesink, W. G. "Modeling of Pest Populations in the Alfalfa Ecosystem with Special Reference to the Alfalfa Weevil." Modelingfor Pest Management: Concepts, Techniques and Applications. R. L. Tummala, D. L. Haynes and B. A. Croft (eds.), East Lansing, Michigan: Michigan State University, 1976. Ruesink, W. G.; Bartell, D. P.; and Armbrust, E. J. "Alfalfa Weevil Control: Better Results with Less Insecticide." Illinois Research (Spring 1975): 3-4. Ruesink, W. G.; Shoemaker, C. A.; Gutierrez, A. P.; and Fick, G. W. "The Systems Approach to Research and Decision Making for Alfalfa Pest Control." New Technologies of Pest Control. Carl G. Huffaker (ed.), New York: John Wiley & Sons, 1980. Ruppel, R. F. "Timing of Sprays for Alfalfa Weevil Control in Michigan." Proceedings of the Annual Meetings of the North Central Branch--Entomological Society of America 29 (February 1974): 108-112. Ruppel, Robert F. "Diurnal Sampling of the Insect Complex of Alfalfa." The Great Lakes Entomologist 7 (Winter 1974): 113-116. Ruppel, R. F. "Feeding Activity of Overwintered Adult Cereal Leaf Beetle and Alfalfa Weevil at Different Constant Temperatures." Proceedings of the Annual Meetings of the North Central Branch-- Entomological Society of America 30 (November 7975): 72-74. Ruppel, R. F. Insect Control in Hay, Forage and Pasture Crops. Extension Bulletin E-827, No. 20, East Lansing, MiChigan: Michigan State University Cooperative Extension Service, March 1977. Ruppel, R. F. and Dimoff, K. "Tabular Values for the Logistic Curve." Bulletin of the Entomological Society of America 24 (June 1978): 149-152. Ruppel, F. F. and Guyer, G. E. Infestation and Control of the Alfalfa Weevil and Cereal Leaf’ Beetle 'hi Michigan 1969-1971. Research Report 164, East Lansing, Michigan: Michigan State University Agricultural Experiment Station, 1972. 286 Ruppel, R. F. and Jennings, S. J. A Partial Phenologic Model of Alfalfa Weevil in Michigan. Report No. 2, East Lansing, M1chigan: Michigan State University, Department of Entomology, 1980. Ruppel, R. F. and F. W. Stehr. Management for Alfalfa Weevil Control. Extension Bulletin E-739, East Lansing, Michigan: Michigan State University, 1972. Ruppel, R. F.; Stehr, F. W.; and Black, J. R. Management for Alfalfa Weevil Control. Extension Bulletin E-739, No. 11, East Lansing, Michigan: Michigan State University Cooperative Extension Service, April 1976. Saksena, V. N. “Statistical Risk Analysis in Project Appraisal." Indian Journal of Agricultural Economics 33 (October-December 1978): 210-215. Samuels, W. J. "Conceptual Problems of Regulatory Theory and Testing." Presented to American Political Science Association, Washington, D.C., l977. Samuelson, P. A. "The Pure Theory of Public Expenditures." Review of Economics and Statistics (November 1954): 387-389. Sarhan, M. E.: Howitt, R. E.; and Moore, C. V. "Pesticide Resistance Externalities and Optimal Mosquito Management." Journal of Environmental Economics and Management 6 (March 1979): 69-84. Savage, L. J. "The Foundations of Statistics Revisited." Studies in Subjective Probability. H. E. Kyburg and H. E. Smokler (eds.), New York: Wiley & Sons, 1964. Scott, A. "The Economic Goals of Federal Finance." Public Finance 19 (1964): 241-288. Schmid, A. A. Property, Power and Public Choice. New York: Praeger Publishers, 1978. Shade, Richard E.; Axtell, John D.; and Wilson, M. Curtis. "A Relationship Beteen Plant Height of Alfalfa and the Rate of Alfalfa Weevil Larval Development." Journal of Economic Entomology 64 (April 1971): 437-438. Shaffer, R. E. "The Developing Technology of Computerized Information Systems: Discussion." American Journal of Agricultural Economics 60 (December 1978): 913-914. Shoemaker, C. A. "Mathematical Construction of Ecological Models." Ecosystem Modeling in Theory and Practice. Charles Hall and John Day, Jr., (eds.), New York: John Wiley & Sons, 1977. "Optimal Management of an Alfalfa Ecosystem." Proceedings of a Conference on Pest Management. Laxenburg, Austria: September, 1977. 287 "Optimal Timing of Multiple Applications of Pesticides with Residual Toxicity." Biometrics 35 (December 1979): 803-812. . "Pest Management Models of Crop Ecosystems." Ecosystem Modeling in Theory and Practice: An Introduction with Case Histories. Charles A. S. Hall and John W. Day, Jr., (eds.), New York: John Wiley & Sons, 1980. Shoemaker, C. A.; Huffaker, C. B.; and Kennett, C. E. "A Systems Approach to the Integrated Management of a Complex of Olive Pests." Environmental Entomology 8 (February 1979): 182-189. Smith, R. F.; Apple, J. L.; and Bottrell, D. G. "The Origins of Integrated Pest Management Concepts for Agricultural Crops." Integrated Pest Management. J. Lawrence Apple and Ray F. Smith, (eds.), New York: Plenum Press, 1976. Smith, R. F. and Allen, W. W. "Insect Control and the Balance of Nature." Scientific American 190 (June 1954): 38-42. Smith, R. F. and Reynolds, H. T. "Principles, Definitions and Scope of Integrated Pest Control." Proceedings. of' the FAO Symposiunl on Integrated Pest Control, vol. 1. Rome: FAO,71965. Stern, V. M.; Smith, R. F.; van den Bosch, R.; and Hagen, K. S. "The Integrated Control Concept." Hilgardia 29 (October 1959): 81-101. Stigler, G. J. "The Economics of Information." Journal of Political Economics 69 (June 1961): 213-225. Surgeoner, G. A. and Ellis, C. R. "Effect of Field Applications of Carbofuran on Hypera postica (Coleoptera: Curculionidae) and Its Parasitoids." The Canadian Entomologist 108 (June 1976): 649-654. Talpaz, H. and Borosh, I. "On the Timing and Application of Pesticides: Comment." American Journal of Agricultural Economics 56 (August 1974): 642-643. Talpaz, H. and Borosh, 1. "Strategy for Pesticide Use: Frequency and Applications." American Journal of Agricultural Economics 56 (November 1974): 769-775. Tesar, M. B. Good Stands for Top Alfalfa Production. Extension Bulletin E-lOl7, No. 11, East Lansing, Michigan: Michigan State University C00perative Extension Service, September 1978. . Recommended Alfalfa Varieties for Michigan. Extension Bulletin E-1098, No. 131, East Lansing, Michigan: Michigan State University Cooperative Extension Service, March 1978. 288 Tesar, M. B., Z. R. Helsel, R. Leep and J. W. Thomas. Producing High Quality, High Yielding Alfalfa for Michigan. Extension BuTletin E41413, East Lansing, Michigan: MiChigan State University, 1980. Tesar, M. B. and R. F. Ruppel. Five to Seven Tons of Alfalfa with Weevil Control. Department of Crops and Soils Science Mimeo 653. East Lansing, Michigan: Michigan State University, 1968. Trocke, J. K. Articles of Incorporation and Bylaws for Southeastern Michigan Crop Management Association, Inc. East Lansing, Michigan: MiChigan State University Cooperative Extension Service, May 11, 1978. U.S. Department of Agriculture, Economics and Statistics Service, Farm Pesticide Economic Evaluation, 1981. by T. R. Eichers, Agricultural Economic Report No. 464, March 1981. University of California, "Estimates of Crop Losses and Disease-Control Costs in California, 1963." Berkeley: Division of Agricultural Sciences, 1965. Varian, H. R. Microeconomic Analysis. New York: W. W. Norton and Company, Inc., 1978. von Neumann, J. and Morgenstern, O. The Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944. Wald, A. Seqyential Analysis. New York: John Wiley and Sons, 1947. Walker, 0. L. and Nelson, A. G. Dealingywith Risks in the Management of Agricultural Firms: An Extension/Teaching Viewpoint. Professional Paper 831, Stillwater, Oklahoma: Oklahoma Agricultural Experiment Station, 1980. Ware, G. W. The Pesticide Book. San Francisco: W. H. Freeman and Company, 1978. Webster, J. P. G. "The Anlaysis of Risky Farm Management Decisions: Advising Farmers About the Use of Pesticides." Journal of Agricultural Economics 28 (1977): 243-259. Wedberg, J. L.; Ruesink, W. G.; Armbrust, E. J.; and Bartell, D.P. Alfalfa Weevil Pest Management Program. Circular 1136, Urbana-Champaign, Illinois: University of Illinois Cooperative ExtenSion Service, April 1977. White, G. B. The Economics of New York's Pest Management Program for Tree Fruit. Agricultural Economics Staff Paper, No. 80-9, Ithaca, New York: Cornell University, 1980. Wilson, M. C.; Stewart, J. K.; and Vail, H. D. "Full Season Impact of the Alfalfa Weevil, Meadow Spittlebug, and Potato Leafhopper in an Alfalfa Field." Journal of Economic Entomology 72 (December 1979): 830-834. 289 Witz, J. A. "Farm-Agricultural Computer Modeling Information System." Agricultural Engineering 59 (August 1978): 30-31. Wolf, 0. D.; Buss, G. R.; and Pienkowski, R. L. "Growth and Physiological Response of' Alfalfa to Diazinon and Methoxychlor Insecticides." Crop Science 16 (March-April 1976): 190-192. Yeargan, K.V.; Parr, J. C.; and Pass, B. C. "Fecundity and Longevity of Bathyplectes circulionis Under Constant and Flucturating Temperatures." Environmental Entomology 7 (February 1978): 36-38. Yound, 0. "Risk Preferences of Agricultural Procedures: Their Measurement and Use." Risk Management in Agriculture: Behavioral Managerial and Policy Issues. AE-4478, Champaign-Urbana, Illinois: Department of Agricultural Economics, University of Illinois, 1979. Zavaleta, L. R. and Ruesink, W. G. "Expected Benefits-from Nonchemical Methods of' Alfalfa Weevil Control." American Journal of Agricultural Economics 62 (November 1980): 801-805. Zusman, Pinhas and Amiad, Amotz. "Simulation: A Tool for Farm Planning Under Conditions of Weather Uncertainty." Journal of Farm Economics 47 (August 1965): 574-594. 290 MICHIGAN STATE | 1 1111 312930 V . LIBRARIES IIIIIIIIIIIII 8076 I I II 617