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University Microfilms International 300 N. Zeeb Road Ann Arbor, Ml 48106 8315443 Cochran, Mark James SELECTION OF OPTIMAL PEST MANAGEMENT STRATEGIES UNDER UNCERTAINTY: A CASE STUDY IN MICHIGAN APPLE PRODUCTION Michigan State University University Microfilms International PH.D. 1982 300 N. Zeeb Road, Ann Arbor, MI 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1. Glossy photographs or p ag es______ 2. Colored illustrations, paper or print_____ 3. Photographs with dark background_____ 4. Illustrations are poor copy______ 5. Pages with black marks, not original copy______ 6. Print shows through as there is text on both sides of page______ 7. Indistinct, broken or small print on severalpages 8. Print exceeds margin requirem ents_____ 9. Tightly bound copy with print lost in spine______ 10. Computer printout pages with indistinct print 11. Page(s)___________ lacking when material received, and not available from school or author. 12. P age(s)___________ seem to be missing in numbering only a s text follows. 13. Two pages num bered___________ . Text follows. 14. Curling and wrinkled p ag es______ 15. Other____________________________________________________________________ ^ University Microfilms International \ SELECTION OF OPTIMAL PEST MANAGEMENT STRATEGIES UNDER UNCERTAINTY: A CASE STUDY IN MICHIGAN APPLE PRODUCTION By Mark J . Cochran A DISSERTATION S ubmitted t o Michigan S t a t e U n i v e r s i t y i n p a r t i a l f u l f i l l m e n t o f t h e re qu ir e m en t s f o r th e d eg r ee o f DOCTOR OF PHILOSOPHY Department o f A g r i c u l t u r a l Economics 1982 ABSTRACT SELECTION OF OPTIMAL PEST MANAGEMENT STRATEGIES UNDER UNCERTAINTY: A CASE STUDY IN MICHIGAN APPLE PRODUCTION By Mark J . Cochran T hi s s tu dy focus ed on t h e problems o f op timal p e s t management s t r a t e g i e s used i n Michigan a p p l e o r c h a r d s . A ca s e stu d y a n a l y s i s of t h r e e common p e s t s was performed which allowed t h e exam ina ti on o f the i n t e r r e l a t i o n s h i p s between t h e c o n t r o l s o f each p e s t . p e s t s s e l e c t e d were s c a b , c o d l i n g moth and m i t e s . The t h r e e In a d d i t i o n t o t h e p e s t s , a n a t u r a l p r e d a t o r o f t h e p l a n t f e e d i n g m i te s was i n c lu d e d as w e l l . A l a r g e systems s i m u l a t i o n model was c o n s t r u c t e d t o ana ly ze t h e i m p l i c a t i o n s o f v a r i o u s a l t e r n a t i v e p e s t management s t r a t e g i e s . A number o f s o u r c e s o f u n c e r t a i n t y were in t r o d u c e d and t h e performan­ ces o f th e s t r a t e g i e s were s im u l a te d f o r twenty d i f f e r e n t s i n g l e s ea s on s o r s t a t e s o f n a t u r e . Cumulative p r o b a b i l i t y f u n c t i o n s o f n e t revenue were c a l c u l a t e d f o r each c o n t r o l s t r a t e g y . S t r a t e g i e s which a r e r i s k e f f i c i e n t ( h i g h e s t ex pe c te d u t i l i t i e s ) f o r d i f f e r e n t r i s k p r e f e r e n c e s were i d e n t i f i e d . Rankings o f th e s t r a t e g i e s c o n s is te n t with the preferences of several c la ss e s of d e c i s i o n makers were performed u s in g v a r i o u s s t o c h a s t i c dominance techniques. The s u p e r i o r i t y o f S t o c h a s t i c Dominance With Res pec t t o a F un ct io n was de m on str ate d over Second Degree S t o c h a s t i c Dominance s i n c e t h e l a t t e r r e s u l t s in both Type I and Type I I e r r o r s . When a r i s k p r e f e r e n c e i n t e r v a l f o r SDWRF was d e f i n e d t o i n c l u d e t h e r i s k a t t i t u d e s o f a l l a g r i c u l t u r a l d e c i s i o n makers, t h e r e s u l t i n g e f f i c i e n c y Mark J . Cochran s e t s remained r e l a t i v e l y l a r g e . Convex S e t S t o c h a s t i c Dominance coul d be employed t o reduce t h e e f f i c i e n c y s e t w i t h o u t imposing f u r t h e r r e s t r i c t i o n s on t h e a l r e a d y s p e c i f i e d r i s k p r e f e r e n c e i n t e r v a l . CSD p r o v i d e s a more complete r a n k in g o f t h e a c t i o n c h o i c e s w i t h o u t i n c r e a s i n g t h e p r o b a b i l i t y o f e i t h e r a Type I o r Type I I e r r o r . The a n a l y s i s us in g t h e s i m u l a t i o n model and t h e s t o c h a s t i c dominance te c h n i q u e s was used t o make a s e r i e s o f n i n e p r e d i c t i o n s abo ut p e s t management i n t h e s p e c i f i e d p r o d u c t i o n system. The model p r e d i c t s t h a t th e ex p ec te d n e t r ev enu es and th e ex p ec te d u t i l i t i e s in gene ra l a r e h i g h e r f o r t h e IPM s t r a t e g i e s when compared w i t h c o n v en ti o n al c a l e n d a r s p r a y programs. Two n o t a b l e e x c e p t i o n s o c c u r r e d in t h e scab and c o d l i n g moth s c e n a r i o s . For r i s k a v e r s e d e c i s i o n makers, the co n v e n t io n a l scab c o n t r o l s t r a t e g y may be r i s k e f f i c i e n t . When t h e c o d l i n g moth p o p u l a t i o n i s h i g h , th e c o n v e n t i o n a l c a l e n d a r sp ray program r e s u l t s in a comparable expec ted n e t revenue and a h i g h e r e x pe c te d u t i l i t y f o r some d e c i s i o n makers. FOR ALICIA ACKNOWLEDGEMENTS This s tu d y has b e n e f i t e d from th e e f f o r t s o f a g r e a t many peop le . F i r s t and f o r e m o s t , Dr. Lindon J . Robison who se rv ed as T he s is Super­ v i s o r must be c r e d i t e d with th e guidance o f t h e development o f n o t only th e t h e s i s b u t th e a u t h o r as w e l l . His p r o f e s s i o n a l con duct and uncompromising adherence t o t h e p r i n c i p l e s o f s c i e n t i f i c r e a s o n in g s e t an exemplary s t a n d a r d f o r anyone f o r t u n a t e enough t o work w ith him. G r a t i t u d e should a l s o be e x p re s s e d f o r t h e r o l e t h a t Dr. Don Ricks and Dr. A1 Shapley played a s committee members. Their in s ig h tfu l comments prompted a c l e a r e r p r e s e n t a t i o n o f th e p r a c t i c a l u t i l i t y o f t h e s tu dy and i t s r e s u l t s . Others worthy o f s p e c i a l r e c o g n i t i o n a r e Drs. Brian C r o f t and Alan Jones who took th e time t o t r y t o e d u ca te an economist in t h e b io l o g y o f a p p l e p e s t management. Their patience and s k i l l a t communication have been g r e a t l y a p p r e c i a t e d . Steve Wagner helped immensely in t h e c o n s t r u c t i o n o f t h e computer s i m u l a t i o n model and had primary r e s p o n s i b i l i t y f o r th e entomo logi cal components o f t h e m i te and c o d l i n g moth subsy st ems . The programming a s s i s t a n c e o f Paul Winder i s a l s o g r e a t l y a p p r e c i a t e d . The work and c o l l a b o r a t i o n o f Weldon Lodwick on th e computer a l g o r i t h m t o perform th e a n a l y s i s u s in g Convex Set S t o c h a s t i c Dominance d e s e r v e s an e x p r e s s i o n o f g r a t i t u d e as w e l l . The guidance and a d vi ce o f Dr. James B. Johnson t h r o u g h o u t our many y e a r s o f a s s o c i a t i o n should be r e c o g n i z e d f o r th e b e n e f i c i a l i n f l u e n c e t h a t he has had on t h i s r e s e a r c h . A s p e c i a l mention i s deser ved f o r t h e r o l e t h a t Dr. Lar ry Libby has played in my d o c t o r a l program. He has s er v ed as Major P r o f e s s o r th r ou gh ou t my long g r a d u a t e s t u d e n t c a r e e r and an e x p r e s s i o n o f g r a ­ t i tu d e is merited f o r his s e rv ic e . While n o t a c t i v e l y invol ved in t h e t h e s i s i t s e l f , h i s i n f l u e n c e was s t i l l p r e s e n t through h i s pers on al impact on th e a u t h o r . A p p r e c i a t i o n must be e x p r e s s e d t o t h e P e s t Control Branch o f t h e Economic Research S e r v i c e o f t h e U.S.D.A. f o r p r o v id i n g t h e funding n s ^ s s a r y t o complete t h e e n t i r e p r o j e c t . The d i s s e r t a t i o n i s a r e s u l t V o f a l a r ^ r v m u l t i - d i s c i p l i n a r y r e s e a r c h p r o j e c t which was funded under C o o p e r a f o ^ R e s e a r c h Agreement 58-319V-9-02699 between t h e Economic Research Se i^ s ce and Michigan S t a t e U n i v e r s i t y . The t h e s i s p r e s e n t s th e id e a s o f onljNiJie a u t h o r and does n o t n e c e s s a r i l y r e p ­ r e s e n t th e views o f t h e f u nd in g agency. The e f f o r t s o f Kim Payne who d i l i g e n t l y typ ed and pr ep ar ed th e f i n a l d r a f t o f t h e m a n u sc r i p t sh ould be acknowledged f o r t h e f i n e work accomplished. Barbara Dickhaut and Donnavieve T a y l o r need t o be thanked as well f o r t h e i r ty p i n g on e a r l y d r a f t s o f th e d i s s e r t a t i o n . An immeasureable amount o f g r a t i t u d e sh ould be e x p r e s s e d t o my w if e A l i c i a f o r h e r p a t i e n c e and u n d e r s t a n d i n g w i t h o u t which t h i s p r o j e c t co ul d nev er have been completed. The c o s t s o f w r i t i n g a d i s s e r t a t i o n a r e pr ob abl y borne more by th e f a m i l y than by the research e r himself. F i n a l l y , I would l i k e t o thank John H a ll o ra n f o r h i s r o l e in my pers ona l r e c o g n i t i o n o f t h e d i f f i c u l t y in c o n t r o l l i n g s c a b s . iv TABLE OF CONTENTS Page LIST OF TABLES................................................................................................... vii LIST OF FIGURES................................................................................................. x CHAPTER 1.1 1..2 1.3 1.4 1. 5 1.6 I. INTRODUCTION............................................................................. Problem S e t t i n g ............................................................................... Concerns o f P e s t Management.................................................... Experience i n Apple P e s t Management.................................. Need f o r t h e R e s e a r c h .................................................................. O b j e c t i v e s .......................................................................................... O r g a n i z a t i o n o f t h e S t u d y ........................................................ 1 1 4 5 8 10 10 CHAPTER 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 II. PROBLEM REVIEW...................................................................... I n t r o d u c t i o n ...................................................................................... E f f i c i e n t Inpu t Usage.................................................................. Theory o f Firm Under U n c e r t a i n t y ......................................... D eci si on A n a ly s is Under U n c e r t a i n t y .................................. Implementation E f f o r t s o f EUH................................................ Economic T h r e s h o l d s ...................................................................... The Economic Th res hol d as an Investment P r o b l e m . . . . Risk and t h e Economic T h r e s h o l d ........................................... Optimal P e s t Management S t r a t e g y S e l e c t i o n Under U n c e r t a i n t y ...................................................................................... 13 13 14 18 19 24 48 56 70 CHAPTER I I I . RESEARCH PROCEDURES ....................................... 3.1 Use o f S im u l a ti o n Models and P hi los op hy o f R es e a rc h ............................................................................................. 3 .2 D e s c r i p t i o n o f t h e Actual System............................................. 3.3 D e s c r i p t i o n o f th e S im u l a ti o n Model..................................... 3. 4 The T e s t s o f Model H yp ot h es es ................................................ 3 . 5 Comparison o f Model P r e d i c t i o n s With A P r i o r i S ta te m en ts o f A n t i c i p a t e d System B e h a v i o r .................. 77 77 83 94 103 CHAPTER 4.1 4.2 4.3 IV. The The Risk MITE MODEL RESULTS............................................................. S im u l a ti o n Model..................................................................... Mite Model R e s u l t s ................................................................ A n a l y s i s ........................................ 110 110 125 144 CHAPTER 5.1 5 .2 5.3 V. SCAB MODELRESULTS................................................................ The S im u la ti o n Model..................................................................... Apple Scab Model R e s u l t s ........................................................... Risk A n a l y s i s .................................................................................... 158 158 173 181 CHAPTER 6.1 6.2 6.3 VI. CODLING MOTH MODEL RESULTS........................................... The S im u l a ti o n Model.................................................................... Model R e s u l t s .................................................................................... Risk A n a l y s i s .................................................................................... 190 190 202 212 v 74 107 Page CHAPTER VII. CHAPTER 8.1 8.2 8.3 COMPREHENSIVE MODEL RESULTS......................................... 219 V I I I . SUMMARY OF RESULTS........................................................... P r e d i c t e d and A n t i c i p a t e d System Behavior Compared.. I m p l i c a t i o n s o f Model P r e d i c t i o n s ......................................... F u r t h e r Research and E x t e n s i o n s ............................................. 225 225 245 251 BIBLIOGRAPHY............................................................................ 253 APPENDIX I ................................ 264 APPENDIX I I ........................................................................................................... 283 APPENDIX I I I ......................................................................................................... 286 APPENDIX IV........................................................................................................... 310 vi LIST OF TABLES Page CHAPTER I . I n t r o d u c t i o n Tabl e 1. I n s e c t i c i d e Usage in P ro d u c ti o n o f S e l e c t e d A g r i c u l t u r a l Commodities.................................................. Tabl e 2. Average Crop Value p e r Pound o f P e s t i c i d e - 1 9 6 6 . CHAPTER I I . Table 1. Tab le 2. CHAPTER I I I . CHAPTER IV. Ta bl e 1. Tabl e 2. Table 3. Ta bl e 4. Tabl e 5. Table 6. Table 7. Table 8. Tabl e 9. Table 10. Table 11. Table 1? Tabl e 13. Table 14. PROBLEM REVIEW The EUH Decis ion M a t r i x ..................................................... Performance I n d i c a t o r s f o r A l t e r n a t i v e P r e f e r e n c e Measures ...................................................................................... 6 6 22 44 RESEARCH PROCEDURES MITE MODEL RESULTS Age C la s s e s f o r Mite and P r e d a t o r P o p u l a t i o n s . . Mite Model S t r a t e g i e s .......................................................... Spray Costs f o r Mite Control S t r a t e g i e s ................. Mite Model R e s u l t s w it h Medium Yield and Weekly S c o u t i n g ...................................................................................... Mite Model R e s u l t s w it h Medium Y i e l d , Weekly Scouti ng and Revised D eci sio n Rules Which Always Apply a H a lf Dose on F i r s t S p r a y ................ Mite Model R e s u l t s with Low Yiel d and Weekly S c o u t i n g .......................................................... ........................... Mite Model R e s u l t s w i t h Low Y i e l d , Weekly Scouti ng and Revised 7 Decision R u l e s ..................... The I n f l u e n c e o f t h e Sco utin g I n t e r v a l on Net Revenue........................................................................................ Mite Model R e s u l t s w ith Medium Yiel d and Grower P e r c e p t i o n a t 5 M ites p e r L e a f .................................... Mite Model R e s u l t s with Medium Y i e l d s , Grower P e r c e p t i o n a t 5 Mites p e r Leaf and th e Revised Deci sio n Rules which Always Apply a H al f Dose on t h e F i r s t S p r a y ................................................................ Mite Model R e s u l t s w i t h Medium Yiel d and Grower Problem P e r c e p t i o n a t 9 Mites p e r L e a f .................. Mite Model R e s u l t s w ith Medium Y i e l d , Grower Problem P e r c e p t i o n a t 9 Mites p e r Leaf and Revised Decis ion Rules which Always Apply a H a l f Dose on th e F i r s t S p ra y ......................................... R e l a t i v e Comparisons o f C la s s e s o f S t r a t e g i e s by D i f f e r e n c e s from t h e Expected Net Revenue o f t h e Simple P l i c t r a n I PM S t r a t e g y ................................ Risk A n a ly s is R e s u l t s f o r Mite Control S t r a t e g i e s .................................................................................. Ill 121 126 128 130 132 134 135 137 139 140 142 143 152 Page CHAPTER V. SCAB MODEL RESULTS Table 1. Chemical A t t e n u a t i o n R a t e s ............................................... 162 Table 2. Cumulative P r o b a b i l i t y F u nc ti o ns o f % Ascospore D e p l e t i o n .................................................................................... 165 Table 3. Spray Costs f o r t h e Chemical A p p l i c a t i o n s C o n s id e r e d ................................................................................. ' 166 Table 4. D e s c r i p t i o n o f Scab Control S t r a t e g i e s .................... 169 Table 5. Adjustment F a c t o r s f o r Late Season I n f e c t i o n s . . 172 Table 6. Scab Model R e s u l t s w it h Medium Y i e l d ....................... 175 Table 7. Scab Model R e s u l t s w i t h Medium Yiel d and an I n c r e a s e in t h e P r i c e o f Benomyl o f 36.7%........... 176 Table 8. Scab Model R e s u l t s w i t h Medium Yiel d and No Damage Assumed......................................................................... 178 Table 9. Scab Model R e s u l t s w ith Low Y i e l d .............................. 179 Table 10. Scab Model R e s u l t s w it h High Y i e l d ............................ 180 Table 11. Rankings o f Scab Control S t r a t e g i e s by Size o f Expected Net Revenues.................................................. 182 Table 12. Risk A n a ly s is R e s u l t s f o r Scab Control S t r a t e g i e s ................................................................................. 187 CHAPTER VI. Table 1. Table 2. Table 3. Table 4. Table 5. Table 6. Table 7. Table 8. CODLING MOTH MODEL RESULTS The C h a r a c t e r i s t i c s o f t h e Erlang D i s t r i b u t i o n s R ep re s e n t in g Delay Times f o r th e L i f e S tag es o f t h e Codling Moth............................................................. Codling Moth Model S t r a t e g i e s ........................................ Spray Costs f o r Moth Control S t r a t e g i e s .................. Moth Model R e s u l t s w i t h Medium Y ie ld and a High D en s ity f o r t h e I n i t i a l Moth P o p u l a t i o n . . . Moth Model R e s u l t s w it h Medium Yield and Low D e n s it y f o r I n i t i a l Moth P o p u l a t i o n ......................... Moth Model R e s u l t s w i t h Medium Yiel d and Medium D en s ity f o r I n i t i a l Moth P o p u l a t i o n s ....................... R e l a t i v e Comparisons o f C la s s e s o f S t r a t e g i e s by D i f f e r e n c e s from t h e Expected Net Revenue o f t h e Cal end ar Spray Program f o r Codling M o t h s . . . Risk A n a ly s is R e s u l t s f o r Moth Control S t r a t e g i e s ................................................................................. 195 200 205 206 208 210 211 215 CHAPTER V II. COMPREHENSIVE MODEL RESULTS Table 1. Comprehensive Model R e s u l t s f o r Medium Yield and Medium I n i t i a l Moth P o p u l a t i o n D e n s i t y .................. Table 2. Comparison o f Q u a n t i t i e s o f P e s t i c i d e s Applied by S e l e c t e d Control S t r a t e g i e s .................................... 220 CHAPTER V I I I . SUMMARY OF Table 1. Comparison o f Conventional Table 2. Comparison o f Conventional 225 RESULTS Expected Net Revenues: IPM and S t r a t e g i e s .................................................... Control C o s ts : IPM and S t r a t e g i e s .................................................... v iii 223 226 Table 3. Table 4. Table 5. Table 6. Tabl e 7. Table 8. Table 9. Table 10. Table 11. Table 12. Table 13. Table 14. Table 15. Table 16. Table 17. Table 18. Table 19. Page Comparison o f Expected Net Revenues f o r IPM and Conventional Moth Control S t r a t e g i e s : Medium P o p u la t io n D e n s i t y ............................................... 226 Comparison o f Expected Net Revenues f o r IPM and Conventional Moth Control S t r a t e g i e s : Low P o p u la t io n D e n s i t y ...................................................... 227 Comparison o f Scab Control S t r a t e g i e s : IPM and C o n v e n t i o n a l .................................................................... 227 Comparison o f Mite Control S t r a t e g i e s : IPM and C o n v e n t i o n a l r . T T r r r r r . .................................. 227 The R e l a t i o n Between t h e Sco utin g I n t e r v a l and t h e Economic Th r es h o ld : A Comparison o f Expected Net Revenues............................................................................. 231 Impact on Yiel d on R e l a t i v e Performances o f IPM and Conventional Scab Control S t r a t e g i e s . . . 232 Impact on Yield on Mite Control S t r a t e g i e s 232 Comparisons o f E f f i c i e n c y S et s f o r SSD and SDWRF............................................................................................ 237 Comparison o f Chemical Usage: IPM and Conventional S t r a t e g i e s .................................................... 238 Expected P e s t Damage f o r Scab Control S t r a t e ­ g i e s ............................................................................................... 239 Expected P e s t Damage f o r Mite Control S t r a t e ­ g i e s (Weekly S c o u t i n g ) ...................................................... 239 Expected P e s t Damage f o r Codling Moth Control S t r a t e g i e s (Medium Y i e l d ) ................................................ 240 Expected P e s t Damage f o r Comprehensive Control S t r a t e g i e s ................................................................................. 240 Comparison o f Expected Net Revenues: S o p h i s t i ­ c a t e d and Simple Moth IPM S t r a t e g i e s 242 Comparison o f Expected Net Revenues: Simple and S o p h i s t i c a t e d Mite Control S t r a t e g i e s 243 Impact on Expected Net Revenues o f a Random Sampling E r r o r f o r IPM Mite Control S t r a t e g i e s . 244 Impact on Expected Net Revenues o f a Random Sampling E r r o r f o r IPM Moth Control S t r a t e g i e s . 244 ix LIST OF FIGURES Page CHAPTER I . INTRODUCTION CHAPTER I I . PROBLEM REVIEW Fig u re 1. Total P hy s ic al P r o d u c t , Average Ph y s ic al P ro du ct and Marginal P h ys ic al P r o d u c t ......... 15 F igu re 2. Total Value P r o d u c t , Average Value P r o du ct and Value o f t h e Marginal P r o d u c t .................. 17 F igu re 3. Risk Premium and C e r t a i n t y E q u i v a l e n t .......... 30 F ig ur e 4. Second Degree S t o c h a s t i c Dominance and Cumula­ t i v e P r o b a b i l i t y F u n c t i o n s ................................. 38 F ig u r e 5. Risk P r e f e r e n c e I n t e r v a l s f o r Various S t o c h a s ­ 43 t i c Dominance Te c h n iq u e s ...................................... Fig ur e 6. The Envelope o f Curves f o r Convex S e t S t o c h a s ­ t i c Dominance............................................................... 47 CHAPTER I I I . Fig u re 1. RESEARCH PROCEDURES Model Components......................................................... 96 CHAPTER IV. MITE MODEL RESULTS Fi g u r e 1. S u b r o u ti n e AFPOP: The P o p u la t io n Dynamics o f th e P r e d a t o r ................................................................. 112 Fig u re 2. S u b r o u ti n e ERPOP: The P o p u l a t i o n Dynamics o f M i t e s ................................................................................. 114 Figu re 3. Decis ion Framework f o r IPM Mite Control S t r a t e g i e s ...................................................................... 119 CHAPTER V. SCAB MODEL RESULTS CHAPTER VI. CHAPTER VII . CHAPTER V I I I . CODLING MOTH MODEL RESULTS COMPREHENSIVE MODEL RESULTS SUMMARY OF RESULTS x I. 1.1 INTRODUCTION Problem S e t t i n g In r e c e n t y e a r s th e i n t e n s i v e use o f chemical p e s t i c i d e s has become q u e s t i o n e d more and more. I t i s o f g r e a t i n t e r e s t t o th o s e who a r e concerned abo ut th e environmental damage t h a t can r e s u l t when r e s i d u e s s u r f a c e in organisms o t h e r than t h e t a r g e t s p e c i e s and t o t h o s e who f e a r t h e long term r e p e r c u s i o n s o f th e c o n ti nu ed consumption o f commodities t h a t have been sprayed d u r in g t h e p r o d u c t i o n o r m a rk e ti n g p r o c e s s e s . Water q u a l i t y i s being i n c r e a s i n g l y a f f e c t e d by chemical p e s t i c i d e s and r a i s e s concerns about t h e i r uses as w e l l . However, even t h e t r a d i t i o n a l u s e r s a r e revie wing t h e i r u t i l i t y and a r e s e a r c h i n g f o r a l t e r n a t i v e s as p e s t r e s i s t a n c e and t h e r i s i n g c o s t s o f chem icals become a problem a t t h e farm l e v e l . In th e l a s t deca de, mounting concerns about t h e consequences o f pr olonged use o f chemical p e s t i c i d e s have b ro ugh t t h e e n t i r e a r e a o f p e s t management under c l o s e s c r u t i n y . Both a g r i c u l t u r a l p r o d u c e r s and e n v i r o n m e n t a l i s t s a r e concerned abo ut e f f i c i e n t use o f c h e m i c a l s , alt hou gh n o t always f o r t h e same r e a s o n s . E n v i r o n m e n t a l i s t s a r e concerned about t h e d i s r u p t i o n o f l o c a l e c o l o g i e s by chemical p e s t i c i d e s and t h e p r e ­ sence o f p o t e n t i a l l y ( o r in some ca s e s a c t u a l l y ) harmful r e s i d u e s in a v a r i e t y o f l i v i n g organisms n o t in t e n d e d as t a r g e t s o f t h e s p r a y s . These conce rns have r e s u l t e d in governmental r e g u l a t i o n s t o c o n t r o l i n d i s c r e e t us es and p r e v e n t abuses o f p e s t i c i d e s . However, f u r t h e r r e d u c t i o n s in p e s t i c i d e uses a r e d e s i r e d by many e n v i r o n m e n t a l i s t s and th e y a r e i n t e r e s t e d in ways t o minimize t h e i r usage. 1 Prolonged chemical usage has produced consequences which concern f ar me rs as w e l l . Increased i n c i d e n c e s o f r e s i s t a n c e in both t a r g e t s p e c i e s and s eco nd ary p e s t s have g e n e r a t e d o u tb r e a k s o f t r a d i t i o n a l p e s t s and emergence o f minor i n s e c t s and d i s e a s e s a t p o p u l a t i o n l e v e l s which pose ma jor t h r e a t s to a g r ic u ltu r a l production. The r e s i s t a n c e r ed u ce s th e e f f i c i e n c y o f t h e p e s t i c i d e s and when coupled w i t h t h e o u t b r e a k s , o f t e n r e s u l t s in i n c r e a s e s in t h e t o t a l amounts o f chem icals t h a t a r e in t r o d u c e d i n t o t h e env iro n m en t, w h i l e lowering t h e p r o f i t a b i l i t y o f t h e crop p r o d u c t i o n t o t h e fa rm e r s in v o l v e d ( 2 ) . For many c r o p s , p e s t management ac c o u n ts f o r a s i z a b l e s h a r e o f the costs of production. I t has been e s t i m a t e d t h a t well ov er one t h i r d o f t h e v a r i a b l e c o s t s o f prod ucin g ap p l e s in Michigan a r e p e s t management r e la te d (70,71). While co n v e n t io n a l c o n t r o l p r a c t i c e s , w ith some excep­ t i o n s , have been f a i r l y s u c c e s s f u l in p r o t e c t i n g p l a n t s from p e s t damage, t h e r e a r e a number o f f a c t o r s which a r e m o t i v a t i n g i n t e r e s t i n a l t e r n a t i v e methods o f c o n t r o l which may re du ce chemical us age . I n c r e a s e s in p r i c e s o f chem ica ls have s u b s t a n t i a l l y r a i s e d t h e c o s t s o f th e co n v en t io n al s p r a y programs. R e s i s t a n c e has become a problem as p e s t p o p u l a t i o n s have been exposed more and more t o ch em ica ls t h a t a r e s t r u c t u r a l l y s i m i l a r ( 2 ) . I n d i s c r i m i n a t e s u p p r e s s i o n o f n a t u r a l p r e d a t o r s by c o n v e n t io n a l s p r a y programs enhances th e d i f f i c u l t i e s o f c o n t r o l l i n g major p e s t s and may r e s u l t in s i g n i f i c a n t i n f e s t a t i o n s o f s ec on dar y p e s t s which a r e u s u a l l y of l i t t l e i n t e r e s t (2). Conventional s p r ay programs which have been used h i s t o r i c a l l y , a r e f r e q u e n t l y based on a c a l e n d a r sc h ed ul e where a chemical t r e a t m e n t i s apDlied a t a f i x e d time i n t e r v a l w i t h o u t r e g a r d t o t h e p r o b a b i l i t y t h a t t h e p e s t p o p u l a t i o n s a r e l i k e l y t o be high enough t o w a r r a n t such app­ lications. Conventional programs have been d es ign ed t o minimize t h e r i s k 3 o f p e s t damage by app ly in g dos es o f chem ica ls s t r o n g enough t o c o n t r o l major p e s t i n f e s t a t i o n s w i t h o u t r e g a r d t o t h e a c t u a l p o p u l a t i o n d e n s i t y in t h a t y e a r. As a r e s u l t , some chemical a p p l i c a t i o n s can o n ly be j u s t i f i e d as i n s u r a n c e a g a i n s t t h e u n c e r t a i n occure nce o f s i g n i f i c a n t p e s t pop­ ulations. Apparent o v e r - a p p l i c a t i o n s a r i s e from t h e s e r i s k c o n s i d e r a t i o n s o r from u n a v a i l a b l e and i n a d e q u a t e i n f o r m a t i o n a t t h e time c o n t r o l d e c i s i o n s a r e made. Oth er problems a r i s e from f a u l t y c a l i b r a t i o n p r o ­ c e d u re s and e s t i m a t e s o f t h e s e l o s s e s run i n t o t h e m i l l i o n s o f d o l l a r s a n n u a l l y (137). An a l t e r n a t i v e s e t o f c o n t r o l p r a c t i c e s known under th e ge ne ra l t i t l e o f I n t e g r a t e d P e s t Management (IPM) te c h n i q u e s began t o evo lv e i n t h e 1 9 5 0 ' s (135) b u t r e a l l y became p o p u l a r in t h e l a s t decade. IPM i s a co n ce pt u al approach t o crop p r o t e c t i o n based upon e c o l o g i c a l p r i n ­ ciples. Management s t r a t e g i e s i n c l u d e an i n t e g r a t i o n o f w e l l - t i m e d chemical a p p l i c a t i o n s , b i o l o g i c a l c o n t r o l s , r e s i s t a n t p l a n t v a r i e t i e s and c u l ­ tural practices. Re duc ti ons in p e s t i c i d e usage o f t e n r e s u l t from f o ll o w i n g IPM s t r a t e g i e s as i n f o r m a t i o n , n a t u r a l and i n t r o d u c e d p r e d a t o r s , and c u l t u r a l p r a c t i c e s a r e s u b s t i t u t e d f o r chemical t r e a t m e n t s . An improved u n d e r s t a n d i n g o f t h e p l a n t / p e s t system i s t h e c o r n e r s t o n e o f IPM s t r a t e g i e s which use t h i s knowledge t o i n c r e a s e t h e e f f i c i e n c y o f a wide a r r a y o f i n p u t s . While in f o r m a ti o n can i n c r e a s e t h e e f f i c i e n c y o f p e s t i c i d e s (and in some c a s e s a c t u a l l y s u b s t i t u t e d i r e c t l y f o r them in t h e p r o d u c t i o n p r o ­ c e s s ) , t i m e l y in f o r m a ti o n i s n o t c o s t f r e e . I t i s f r e q u e n t l y th e a c q u i ­ s i t i o n c o s t s o f up t o d a t e i n f o r m a t i o n t h a t f o r c e s f a r m e r s t o a c c e p t s t r a t e g i e s which in a p e r f e c t knowledge s i t u a t i o n would y i e l d i n a p p r o p r i a t e rate s of application. C o l l e c t i v e a c t i o n in th e form o f government 4 programs, the e x t e n s i o n s e r v i c e , o r p e s t management c o o p e r a t i v e s i s a common way t o pr o v id e groups o f i n d i v i d u a l s i n f o r m a t i o n which i n d i v i d u a l l y t h e y co u ld n o t a f f o r d t o a c q u i r e . 1.2 Concerns o f P e s t Management The problems inv ol ved in p e s t management can be c a t e g o r i z e d i n t o two b a s i c co nc e rn s. The f i r s t concern l i e s a t t h e farm l e v e l and f o cu s es on d e t e r m in i n g t h e nirst a p p r o p r i a t e c o n t r o l s t r a t e g y f o r a g iv e n far me r w ith a p a r t i c u l a r r i s k p r e f e r e n c e . I t considers the e ffic ie n c y of the c o n t r o l s t r a t e g i e s in g e n e r a t i n g outcomes f a v o r a b l e t o th e f ar m e r . It i n v o l v e s t h e e v a l u a t i o n o f c o n t r o l s t r a t e g i e s u sin g d i f f e r e n t d e c i s i o n r u l e s , d i f f e r e n t ty p e s o f c h e m i c a l s , d i f f e r e n t r a t e s o f s p r a y , d i f f e r e n t t i m i n g s o f s p r a y s , t h e use o f m o n i to r in g and t h e use o f b i o l o g i c a l c o n t r o l . The second concern ensues from a group o f consequences t h a t r e s u l t from t h e s t r a t e g y s e l e c t i o n d e c i s i o n s a t t h e farm l e v e l b u t do n o t n e c e s s a r i l y in fluence these d ecisions. This concern i n c l u d e s such m a t t e r s as e n v i r o n ­ mental d e g r a d a t i o n , h e a l t h h az a r d s and th e impacts t h a t one f a r m e r ' s c o n t r o l d e c i s i o n s have on th e p e s t management d e c i s i o n environment o f a second far me r or group o f f ar me rs ( i . e . , m i g r a t i o n o f p e s t s from an uns prayed f i e l d o f one f ar m e r t o a f i e l d o f a second f a n n e r ) . A b a s i c r e q u ir e m e n t t o a d d r e s s i n g t h e problems o f t h e two concerns w i l l be an u n d e r s t a n d i n g o f t h e d e c i s i o n p r o c e s s e s by which i n d i v i d u a l f a r m e r s s e l e c t p e s t management s t r a t e g i e s . The i n t e r r e l a t i o n s h i p s o f t h e ma rket c o n d i t i o n s , th e f a r m e r ' s p e r s p e c t i v e on r i s k and t h e b i o l o g i c a l dynamics o f t h e p e s t p o p u l a t i o n s , t h e p r e d a t o r p o p u l a t i o n s and t h e crop w i l l need t o be un d er s to o d b e f o r e u s e f u l p r e s c r i p t i o n s t o t h e problems o f e i t h e r concern can be made. Th is r e s e a r c h s h a l l a d d r e s s t h e s e f a c t o r s and t h e i r r o l e in p e s t management s t r a t e g y s e l e c t i o n . 5 Although p e s t management has v a r y in g importance in d i f f e r e n t c r o p s , t h e b a s i c s e l e c t i o n and d e c i s i o n p r o c e s s e s sh oul d be common t o th e p r o d u c t i o n o f a l m o s t a l l a g r i c u l t u r a l commodities. In f a c t , i t w i l l be shown t h a t much o f t h e knowledge a b o u t d e c i s i o n making under r i s k t h a t developed in a r e a s co m p le te ly d i s t i n c t from p e s t management has r e l e v a n t a p p lic a tio n s f o r p est control fo r a ll a g r ic u ltu r a l crops. O bv iously, thou gh , t h e l a r g e s t c o n t r i b u t i o n s t h a t t h e r e s e a r c h can make t o a l l e v i a t i n g e i t h e r o f th e concerns w i l l be found in i n v e s t i g a t i o n s with d i r e c t a p p l i c a t i o n s t o t h o s e crops which have r e c e i v e d th e most i n t e n s i v e t r e a t m e n t s o f chemical p e s t i c i d e s , o r which c o n t r i b u t e s i g n i f i c a n t l y t o a r e g io n 's a g r i c u l t u r a l production. 1. 3 Experience i n Apple P e s t Management Apples have h i s t o r i c a l l y been one o f t h e most h e a v i l y sp rayed o f a l l a g r ic u ltu r a l crops. In a s tu d y done by E i ch er s in 1970, (17) i t was found t h a t in t h e f o r t y - e i g h t c o n t i n e n t a l s t a t e s , a p p l e s have more pounds o f a c t i v e i n s e c t i c i d e i n g r e d i e n t a p p l i e d t o them th a n any o t h e r crop (Tables 1 and 2 ) . The same s tu d y concluded t h a t a p p l e s have one o f the lo w es t r a t i o s o f av era ge va lu e o f commodity t o pounds o f p e s t i c i d e applied. This i l l u s t r a t e s th e p o i n t t h a t more pounds o f p e s t i c i d e s a r e used t o produce one d o l l a r ' s worth o f a p p l e s than i s used in t h e p r o d u c t i o n o f one d o l l a r o f most o t h e r commodities. In Michigan, p e s t management a c c o un ts f o r about 45% o f th e v a r i a b l e c o s t s and a l m o s t 20% o f th e t o t a l c o s t s o f t h e o p e r a t i o n o f an ap p l e o r c h a r d ( 7 1 , 7 2 ) . The i n t e n s i v e use of p e s t i c i d e s in a p pl e p r o d u c t i o n would seem t o c r e a t e a l a r g e p o t e n t i a l f o r IPM s t r a t e g i e s t o c o n t r i b u t e t o th e a m e l i o r a t i o n o f t h e conce rns a r i s i n g from t r a d i t i o n a l p e s t management 6 Table 1. Crop I n s e c t i c i d e Usage in P r od uc ti o n o f S e l e c t e d A g r i c u l t u r a l Commodi t i e s . Pounds o f A ct iv e I n s e c t i c i d e I n g r e d i e n t p e r Acre* Cotton 6.27 Corn 0.36 Soybeans 0.0 9 A lfalfa 0.1 2 P o ta t o e s 1.99 Apples 12.58 *As p r e s e n t e d in Carlson and C a s t l e ( 17) . Table 2. Crop Average Crop Value p e r Pound o f P e s t i c i d e —1966* Insecticide Fung ici de Cotton 19.25 896.98 Apples 23.16 19.00 Peanuts 49.14 16.44 Potatoes 208.54 175.52 Corn 215.19 NA A lfalfa 502.84 NA Soybeans 683.27 NA 2, 32 2. 13 NA Wheat *As p r e s e n t e d in Carlson and C a s t l e ( 17 ). 7 controls. In o t h e r s t a t e s , e x p e r i e n c e s w it h IPM programs a r e i n d i c a t i n g t h a t i n f a c t n e t revenues can be i n c r e a s e d and p e s t i c i d e usage de c r e a se d by adop ti ng IPM s t r a t e g i e s i n ap p le p r o d u c t i o n syst ems . In M a s s a c h u s e t t s , a s t u d y was conducted comparing th e performance o f IPM programs in s i x t e e n b loc ks o f el ev en o r c h a r d s t o c o n v e n t io n a l s t r a t e g i e s a p p l i e d in n i n e b lo ck s ( 2 8) . All b lo c k s were in commercial o r c h a r d s and th e av era ge p e r a c r e y i e l d was 550 b u s h e l s . p e s t s were monitored in t h e IPM b l o c k s . A v arie ty of They i n c l u d e d t h e t a r n i s h e d p l a n t bug, European a p p l e s a w f l y , a p p l e maggot, c o d l i n g moth, l e a f r o l l e r s , plum c u r c u l i o , green ap pl e a p h i d s , woolly a pp l e a p h i d s , f r u i t w o r m s , t e n t i f o r m l e a f m i n e r , s p i d e r and r u s t m i t e s and a pp l e s c a b . a r e from 1979 and a r e in nominal d o l l a r s . All f i g u r e s I t was d i s c o v e r e d t h a t th e i n c r e a s e in n e t revenue p e r a c r e was $122.83 w it h a $82.37 p e r a c r e s av in g s r e s u l t i n g from lowered p e s t management c o s t s and $40.96 p e r a c r e a r i s i n g from l e s s i n s e c t damage. service. No ch arg e was in c lu d ed f o r t h e m o ni to r in g The f u l l does e q u i v a l e n t s o f i n s e c t i c i d e s were 42% l e s s with th e IPM bl oc ks and a p h i c i d e use was reduced 60%. F u r t h e r r e d u c t i o n s were e x p e r i e n c e d w ith m i t i c i d e s (76%) and f u n g i c i d e s (12%). In North C a r o l i n a , 45 ap p le o r c h a r d b lo ck s were p a r t o f a r e s e a r c h e f f o r t which e x t e n s i v e l y moni tor ed t h e o r c h a r d s from 1976 t o 1980 (2 0) . In th e f i r s t f o u r y e a r s , no a d v i c e was given and c o n v e n t i o n a l s p r a y programs were fo ll o w ed . In 1980, IPM programs were i n t r o d u c e d . In t h e l a s t y e a r i n s e c t i c i d e e x p e n d i t u r e s were reduced 25% b u t f u n g i c i d e e x p e n d i t u r e s were up 30% due t o a l a r g e scab i n f e c t i o n . Using t h e 1980 f r e s h f r u i t u t i l i z a t i o n p e r c e n t a g e and t h e 5 - y e a r av era ge p r i c e f o r f r e s h and p r o c e s s e d f r u i t , t h e IPM programs produced g r o s s and n e t revenu es 35% h i g h e r th a n t h e avera ge co n ve nt io n al s p r a y programs. These b lo c ks had an av er a ge y i e l d o f 8 ap p r o x im a te ly 775 b u s h e l s p e r a c r e . In New York, a st u d y was conducted examining 1978 r e c o r d s o f 33 commercial bloc ks us in g IPM s t r a t e g i e s and 23 commercial b lo c k s which foll owe d non-IPM programs ( 14 3) . The av er a ge s p r a y m a t e r i a l s c o s t s were $25 p e r a c r e l e s s f o r th e IPM bl oc ks than t h e o r c h a r d s u s i n g co nv e n t io n a l techniques. av e r a g e . The IPM s t r a t e g i e s used one few er s p r a y p e r se as on on t h e When machinery and l a b o r c o s t s and a $12.00 p a r t i c i p a t i o n charge f o r IPM o r c h a r d s were c o n s i d e r e d , t h e s a v i n g s p e r a c r e were c a l ­ c u l a t e d t o be about $16. I t was found t h a t no d i s c e r n a b l e d i f f e r e n c e in f r u i t q u a l i t y e x i s t e d between th e IPM group and t h e c o n t r o l group. P r i c e s a r e in terms of 1978 d o l l a r s . I t s h ou ld be n o te d t h a t most p e s t damage in a p p l e s r e s u l t s in a lower q u a l i t y n o t a lower q u a n t i t y . These r e s u l t s do i n d i c a t e t h a t t h e a d o p t io n o f IPM s t r a t e g i e s does have a p o t e n t i a l f o r r e d u c i n g t h e concerns s u r f a c i n g ab out co n v e n t io n a l p e s t management b u t th e y deal w i t h l i m i t e d o b s e r v a t i o n s , d i f f e r e n t p r o ­ duction systems and l a r g e l y i g n o r e t h e c o n s i d e r a t i o n s t h a t r i s k may have on t h e s e l e c t i o n o f c o n t r o l p r a c t i c e s . To more t h o r o u g h l y i n v e s t i g a t e t h e p o t e n t i a l o f IPM, a more complete u n d e r s t a n d i n g o f t h e d e c i s i o n p r o c e s s is necessary. 1.4 Need f o r t h e Research There a r e a t l e a s t t h r e e ma jor a r e a s which w a r r a n t f u r t h e r r e s e a r c h in t h e f i e l d o f p e s t management. There has been a g e n e r a l n e g l e c t o f t h e d e c i s i o n making p r o ce s s a t t h e farm l e v e l in t h e s e l e c t i o n o f c o n t r o l strategies. The n e g l e c t o f t h i s s e l e c t i o n p r o c e s s h i n d e r s recommendations o f a problem s o l v i n g n a t u r e t h a t a r e p ro v id ed f o r a s p e c i f i c f a r m e r and t h e u n d e r s t a n d i n g o f more a g g r e g a t e problems such as enviro nm ent al damage, h e a l t h h az a r d s and p r o d u c t i o n e x t e r n a l i t i e s . There i s a d e f i n i t e need 9 t o app ly t h e r e l e v a n t d e c i s i o n th e o r y developed i n o t h e r f i e l d s to farm le v e l p e s t management t o p r o v i d e a c l e a r e r u n d e r s ta n d i n g o f t h e p r o ce s s by which control s t r a t e g i e s are se le c te d . The m a j o r i t y o f a n a l y s e s o f farm l e v e l p e s t management problems f oc us on one p e s t a t a ti m e . I n t e r r e l a t i o n s h i p s between t h e p o p u l a t i o n dynamics o f v a r i o u s p e s t s and t h e i r c o n t r o l s a r e o f t e n n o t a d d r e s s e d . The sim u l ta n e o u s management o f more than one p p s t d e s e r v e s more a t t e n t i o n th a n what i t has a c q u i r e d in t h e p a s t . Optimal s t r a t e g y s e l e c t i o n could e a s i l y be a f f e c t e d by t h e s e i n t e r r e l a t i o n s h i p s . Therefore, th e re is a r e a l c o n t r i b u t i o n t o i n t e g r a t e d p e s t management t h a t a m u l t i - p e s t systems s t u d y would p r o v i d e by e n a b l i n g t h e a n a l y s i s o f t h e i n t e r r e l a t i o n s h i p s between p e s t s and c o n t r o l s . Apple p r o d u c t i o n i n Michigan s u f f e r s from p e s t damage caused by a number o f d i f f e r e n t s p e c i e s . Three predominant a p p l e p e s t s in Michigan a r e a p p l e s c a b , m i t e s and c o d l i n g moth. They c o u l d s e r v e as a b a s i s f o r a ca s e s t u d y in such a systems p r o j e c t . These p e s t s a r e s u i t a b l e f o r a case st u d y s i n c e t h e r e e x i s t s an a de qu a te d a t a b as e on each and t h e c o n t r o l s f o r scab and c o d l i n g moth can impact on t h e m i t e s and m i te p r e d a t o r s . There i s ev id en ce t h a t recommendations based on economic t h r e s h o l d s d e r i v e d from margi nal a n a l y s i s may be m i s l e a d i n g due t o t h e omi ssi on o f risk. Economic l i t e r a t u r e s u g g e s t s t h a t th e p r e s e n c e o f r i s k adds an a d d i t i o n a l c o s t which sh ou ld be c o n s i d e r e d in d e t e r m i n i n g optimal in p u t use p a t t e r n s . There i s a need t o develop a t h e o r e t i c a l p r oc ed ur e by which th e economic t h r e s h o l d could be d e f i n e d w i t h r i s k i n c l u d e d . The p r o c e d u r e s h o ul d be a p p l i e d t o an a c t u a l problem with r e a l d a t a t o d e m o n s t r a te i t s u t i l i t y . While i t i s proposed t h a t a ca se s tu d y o f t h r e e a p p l e p e s t s s e r v e as 10 t h e b a s i s o f th e r e s e a r c h , th e r e s u l t i n g t h e o r e t i c a l c o n s t r a i n t s , th e r e s e a r c h framework and t h e a n a l y t i c a l p r o c e d u r e s sh oul d be a p p l i c a b l e t o a v a r i e t y o f uses w i t h i n t h e g en era l a r e a o f p e s t management. The r e s e a r c h sh oul d be u s e f u l t o e x t e n s i o n pe rs on ne l in recommending p r e s c r i p t i o n s t o s p e c i f i c problems o f s p e c i f i c f a r m e r s . By p r e d i c t i n g system b e h a v i o r , i t s h ou ld a l s o produce v a l u a b l e s u b j e c t m a t t e r i n f o r m a t i o n t o r e s e a r c h e r s in v ol ve d in t h e more a g g r e g a t e problems o f p e s t management l i k e environmental damage, h e a l t h h a z a r d s , impact a n a l y s i s o f r e g u l a t i o n s and p r o d u c t i o n externalities. 1.5 Objectives The s p e c i f i c o b j e c t i v e s o f t h e s tu d y a r e : A. I d e n t i f y t h e im p o r t a n t d e t e r m i n a n t s which i n f l u e n c e a p p l e p r o d u c e r s ' d e c i s i o n s in t h e s e l e c t i o n o f p e s t management s t r a t e g i e s used t o c o n t r o l s c a b , c o d l i n g moth and m i t e s . B. I d e n t i f y t h e im p o r ta n t a l t e r n a t i v e s t r a t e g i e s which a r e a v a i l a b l e f o r a p p l e p e s t c o n t r o l r e l e v a n t t o ap p l e s c a b , m i t e s and co d l in g moth. C. I n t e g r a t e th e b i o l o g i c a l and economic i m p l i c a t i o n s o f pest management s t r a t e g i e s i n t o a n a l y t i c a l and s i m u l a t i o n models which can s i m u l a t e th e d e c i s i o n making environment and e v a l u a t e t h e s e management a l t e r n a t i v e s and develop p r o b a b i l i t y J e n s i t y f u n c t i o n s f o r th e outcomes a s s o c i a t e d w it h each s t r a t e g y . D. P r e d i c t which p e s t management s t r a t e g i e s and economic t h r e s h o l d s may be p r e f e r r e d f o r d e c i s i o n makers w i t h v a r i o u s r i s k p r e f e r e n c e s . 1.6 O r g a n i z a t i o n o f t h e Study The s t u d y i s or g a n iz e d i n t o seven re ma ini ng c h a p t e r s . Due t o the 11 m u l t i - d i s c i p l i n a r y n a t u r e o f th e work, t h e r e a r e s e c t i o n s which may be more r e l e v a n t t o some th an o t h e r s . Some d i s c u s s i o n may be r ed u nd an t b u t a r e r e p e a t e d t o f a c i l i t a t e t h e use o f th e st u d y by no n-economists who may be i n t e r e s t e d in only s e l e c t e d t o p i c s . Redundant d i s c u s s i o n s w i l l be i d e n t i f i e d so r e a d e r s may proceed t o o t h e r s e c t i o n s . Chapter I I p r e s e n t s a ge n era l d i s c u s s i o n o f t h e problem and reviews p r e v i o u s work r e l a t e d t o th e t o p i c . I t begi ns w it h a b a s i c d i s c u s s i o n o f e f f i c i e n t i n p u t usage under c o n d i t i o n s of c e r t a i n t y , which should be a r ev ie w f o r eco n o m is ts . Next, i t d e m o n s t r a te s t h a t t h e importance o f r i s k and shows how optimal i n p u t use p a t t e r n s can be changed when i t i s c o n s i d e r e d . This i s fo ll ow ed by a d i s c u s s i o n o f how optimal d e c i s i o n s can be made under u n c e r t a i n t y us ing t h e Expected U t i l i t y Hypothesis (EUH) and revie ws a number o f te c h n iq u e s t o implement EUH. The d i s c u s s i o n o f d e c i s i o n a n a l y s i s i s then d i r e c t e d towards d e f i n i n g th e economic t h r e s h o l d and optimal p e s t management s t r a t e g y s e l e c t i o n under u n c e r t a i n t y . In Chapter I I I , t h e r e s e a r c h p r o ce du re s a r e d e s c r i b e d . There i s a d i s c u s s i o n on t h e a p p r o p r i a t e r o l e o f s i m u l a t i o n models in s c i e n t i f i c research. A d e s c r i p t i o n o f th e a c t u a l system and an overview o f t h e computer model a r e p r e s e n t e d . The j u s t i f i c a t i o n and c r e d i b i l i t y o f t h e model and r e s u l t s a r e d i s c u s s e d as w e l l . A l i s t o f s t a t e m e n t s about t h e a n t i c i p a t e d system b e h a v i o r a r e c o n s t r u c t e d from c u r r e n t knowledge a v a i l a b l e abo ut th e system. They w i l l be compared with model p r e d i c t i o n s l a t e r in t h e s tu d y . In Chap ters IV, V and VI, t h e r e s u l t s from th e t h r e e p e s t s s t u d i e d are described. These c h a p t e r s have been w r i t t e n t o i n c l u d e s h o r t d e s ­ c r i p t i o n s o f t h e i r model components and a sy n o p si s o f t h e r i s k a n a l y s i s methodology. There may be red un d an t m a t e r i a l in t h e s e d i s c u s s i o n s , but i t i s hoped t h a t i n d i v i d u a l s i n t e r e s t e d only in t h e c o n t r o l o f one p e s t may 12 rea d t h e s e c h a p t e r s w i t h o u t r e f e r r i n g in d e t a i l t o th e remainder o f the text. Chapt er VII i s a summary of t h e comprehensive model r e s u l t s which i n v e s t i g a t e t h e i n t e r r e l a t i o n s h i p s between t h e c o n t r o l o f each o f th e three pests. In Chapter VIII th e model p r e d i c t i o n s a r e compared with the s t a t e m e n t s on t h e a n t i c i p a t e d system b e h a v i o r . Discrepancies are a t t r i b u t e d t o model e r r o r s f o r improvements t o t h e u n d e r s t a n d i n g o f t h e system. The i m p l i c a t i o n s o f th e model p r e d i c t i o n s f o r e x t e n s i o n , r e s e a r c h and p o l i c y a r e d i s c u s s e d as w e l l . a r e posed. F i n a l l y , f u t u r e r e s e a r c h and e x t e n s i o n s II. 2.1 PROBLEM REVIEW Introduction The problem o f s e l e c t i n g p e s t management s t r a t e g i e s r e a l l y fo c u s e s on e f f i c i e n t i n p u t usage. The de s ig n o f both c o n v en ti on al and IPM c o n t r o l s t r a t e g i e s a t t e m p t s t o combine v a r i o u s i n p u t s i n t o c o n c i s e d e c i s i o n r u l e s . These d e c i s i o n r u l e s guide t h e a p p l i c a t i o n o f t h e i n p u t s i n t o what should be a p a t t e r n o f e f f i c i e n t i n p u t usage. The s e l e c t i o n o f t h e c o n t r o l s t r a t e g y t o be foll owe d i s then a ch o i ce between d i f f e r e n t d e c i s i o n r u l e s which may use d i f f e r e n t i n p u t s . Conventional c a l e n d a r sp ray programs g e n e r a l l y develop a p a t t e r n o f use which w i l l pro vi d e crop p r o t e c t i o n in a " t y p i c a l bad y e a r . " The sp ray s c h e d u le i s desig ned t o ap p ly p e s t i c i d e s in a manner which w il l i n s u r e p r o t e c t i o n even i f c o n d i t i o n s a r e s u i t a b l e f o r l a r g e p e s t i n f e s ­ t a t i o n s to oc cu r. In t r a d i t i o n a l u s e s , l i t t l e e f f o r t i s made t o i n ­ c o r p o r a t e i n fo rm a ti o n on t h e c u r r e n t c o n d i t i o n s i n t o t h e s e s t r a t e g i e s . A l t e r n a t i v e l y , one o f t h e major i n p u t s o f IPM programs i s i n f o r m a ti o n on t h e c u r r e n t c o n d i t i o n s . The d e c i s i o n r u l e s o f t h e s e s t r a t e g i e s a r e f l e x i b l e so t h a t t h e a p p l i c a t i o n o f t h e o t h e r i n p u t s can o f t e n be a d j u s t e d t o meet t h e c u r r e n t c o n d i t i o n s o f t h e o r c h a r d s . I t w i l l be u s e f u l f o r d i s c u s s i o n purpos es t o b r i e f l y h i g h l i g h t some o f t h e f o u n d a t i o n s o f optimal i n p u t usage. review can s k ip s e c t i o n s 2 . 2 and 2 . 3 . Readers n o t r e q u i r i n g t h i s One o f t h e d e c i s i o n r u l e s mrst commonly used in IPM programs i s th e economic t h r e s h o l d . This concept s h a l l be d i s c u s s e d , followed by a s e c t i o n on d e f i n i n g th e economic t h r e s h o l d under u n c e r t a i n t y . 13 14 2.2 E f f i c i e n t Inp ut Usage A s e r i e s o f s e q u e n t i a l c h o i c e s between two hypotheses^ a r e made t o d et erm in e t h e optimal amount of a c o n t r o l (perha ps a chemical p e s t i c i d e ) t h a t w i l l be in t h e b e n e f i t o f t h e f a r m e r . Typically, choices are c o n c e p t u a l i z e d as a p ro d u c ti o n f u n c t i o n r e l a t i o n s h i p where t h e h o r i z o n t a l a x i s measures t h e amount o f t h e i n p u t a p p l i e d and t h e v e r t i c a l a x i s i s t h e amount o f o u t p u t ( f r u i t o r c r o p ) produced f o r each l e v e l o f input. This a n a l y s i s , of c o u r s e , holds a l l o t h e r i n p u t s h e l d c o n s t a n t a t some s p e c i f i c l e v e l ( s ) . In p e s t c o n t r o l a n a l y s i s , however, t h e p e s t s a r e a n e g a t i v e i n p u t only i n d i r e c t l y under t h e c o n t r o l o f a d e c i s i o n maker. The i n p u t can be d e f i n e d as th e p o s t - a p p l i c a t i o n p e s t p o p u l a t i o n which o f c o ur s e c o n t a i n s as a component th e amount o f c o n t r o l a p p l i e d . a p p l i c a t i o n p e s t i s dependent on t h e c o n t r o l . Thus, t h e p o s t ­ I t should be noted t h a t t h e r e w i l l be a d i s t i n c t p r o d u c ti o n f u n c t i o n f o r each l e v e l o f t h e p r e ­ a p p licatio n pest population. So t h e r e e x i s t s a s e r i e s o f p r o d u c ti o n f u n c t i o n s d i s p l a y i n g th e r e l a t i o n s h i p between th e o u t p u t and th e p o s t ­ a p p l i c a t i o n p e s t p o p u l a t i o n which may d i f f e r by p a r a l l e l o r n o n - p a r a l l e l s h i f t s depending upon t h e i n t e r r e l a t i o n s h i p s between t h e c o n t r o l , th e "pre" and " p o s t " a p p l i c a t i o n p e s t p o p u l a t i o n and t h e growth p r o c e s s o f the p l a n t . In Figur e 1, th e t o t a l ph y s ic a l p r o d u c t i o n f u n c t i o n (TPP) i s d i s ­ p la y e d , i l l u s t r a t i n g t h a t under many c i r c u m s ta n c e s i t can be ex pe ct ed t o i n c r e a s e f i r s t a t an i n c r e a s i n g r a t e , th en i n c r e a s e a t a d e c r e a s i n g r a t e and f i n a l l y r eac h a maximum b e f o r e i t b eg in s t o d e c r e a s e . The ^The hypotheses could be f o rm ul at ed a s : H0 : The amounts o f n e t revenue a s s o c i a t e d with two d i f f e r e n t l e v e l s o f in p u t usage a r e e q u a l . H/\: The amount o f n e t revenue a s s o c i a t e d w ith one l e v e l o f i n p u t usage i s s i g n i f i c a n t l y g r e a t e r th a n t h e n e t revenue a s s o c i a t e d with an a l t e r n a t i v e l e v e l o f i n p u t usage. 15 Q TPP APP MPP Fig ur e 1. Tot al Ph ys ic al P r o d u c t , Average Ph y sic al P r o d u c t and Marginal Ph ys ic al P r o d u c t. 16 avera ge p h y s ic a l p r o d u c t i o n f u n c t i o n (APP) i s d e r i v e d by d i v i d i n g th e t o t a l p h y s ic a l p r o d u c ti o n by t h e number o f u n i t s o f i n p u t a p p l i e d . The marginal p h y s ic al p r o d u c ti o n f u n c t i o n (MPP) i s det ermined by c a l c u l a t i n g th e d i f f e r e n c e in t h e t o t a l p h y s ic a l p r o d u c ti o n by a p p l y in g one a d d i t i o n a l u n it of the input. In t h i s example, no p r i c e s o r c o s t s have been i n c l u s i o n does n o t a l t e r t h e pr o c e d u r e s t o f i n d introduced, but their an optimum. Whenp r i c e s do n o t vary with o u t p u t o r i n p u t u s a g e , v a l u e p r o d u c t i v i t y f u n c t i o n s can be det erm ine d by m u l t i p l y i n g t h e p h y s ic a l p r o d u c t i o n f u n c t i o n s by th e p r i c e o f t h e o u t p u t (Py). I f p r i c e s vary w it h o u t p u t o r i n p u t u s a g e , t h e v al u e p r o d u c t i v i t y f u n c t i o n s must c o n s i d e r t h e f u n c t i o n a l r e l a t i o n s h i p between th e o u t p u t and th e p r i c e . I f t h e p r o d u c t p r i c e i s a f u n c t i o n of o u t p u t (P = f ( Y)) , th e n t h e va lu e p r o d u c t i v i t y f u n c t i o n s can be d e f i n e d •J as : 2.1 2.2 VTP = Y * f(Y) VAP = Y * f(Y) X1 2. 3 MVP = f(Y)3Y/3X1 + y | ^ - The l a s t f u n c t i o n has been renamed t h e margi nal v a l u e p r o d u c t (MVP). The MVP i s used t o d e s c r i b e t h e change in t h e v a l u e o f t h e o u t p u t by changing th e i n p u t w hi le t h e VMP i s t h e v a l u e o f t h e change in t o t a l p h y s ic a l p r o d u c t a r i s i n g from an in c re m en t al change i n t h e i n p u t . a r e c o n s t a n t , o f c o u r s e , t h e two terms a r e i d e n t i c a l . When p r o d u c t p r i c e s These f u n c t i o n s ap p e a r in Figur e 2. In t h e case o f complete knowledge, an optimum ca s e may be found he r e by e q u a t i n g th e marginal v al u e p ro d u ct t o th e p r i c e o f th e i n p u t . This p o i n t w i l l i d e n t i f y t h e amount o f t h e i n p u t which s ho uld be u t i l i z e d and th e c o r r e s p o n d in g amount (and v a l u e ) o f t h e o u t p u t t h a t can be 17 P*Q TVP AVP VMP Figure 2. Total Value P r o d u c t , Average Value P ro d uc t and Value o f t h e Marginal P r od uc t. 18 expec ted t o be produced. The c o n t r i b u t i o n t h a t t h e a g r i c u l t u r a l econom ist can make i s in the a r e a o f i d e n t i f y i n g th e a p p r o p r i a t e v a l u e s ( p r i c e s and c o s t s ) t o c o n v e r t th e p h y s ic a l p r o d u c t i v i t y cu rv es i n t o va lu e p r o d u c t i v i t y cu rv es which p e r m i t o p t i m i z a t i o n o f income. Although t h i s t a s k i s q u i t e im p o r t a n t , i t i s no t t h e only c o n t r i b u t i o n t h a t t h e economist has t o o f f e r in d e t er m in in g t h e most e f f i c i e n t c o n t r o l s t r a t e g y f o r a given d e c i s i o n maker. Marginal a n a l y s i s i s q u i t e u s e f u l f o r s i t u a t i o n s o f s u b j e c t i v e c e r t a i n t y , b u t economics can p r o v id e many i n s i g h t s i n t o d e c i s i o n making in t h e u n c e r t a i n t y s i t u a t i o n s as w e l l . Decision c r i t e r i a a r e changed and t h e r e s u l t i n g d e c i s i o n r u l e s f o r o p t i m i z a t i o n o f t e n produce d i f f e r e n t s o l u t i o n s f o r t h e same problem ad d r e s s e d in a c e r t a i n t y c o n t e x t . Under t h e s e ci rc u m s ta n c es th e r o l e o f t h e economist in t h e m u l t i - d i s c i p l i n a r y a n a l y s i s o f management i s g r e a t l y expanded. The d e c i s i o n p r o ce s s under u n c e r t a i n t y has been s t u d i e d by economic and management e x p e r t s f o r a number o f y e a r s and s e v e r a l i n s i g h t f u l a n a l y t i c a l t e c h n i q u e s have been developed. A p p l i c a t i o n o f some o f t h e s e t e c h n i q u e s sh oul d prove t o be h e l p f u l in the ca se o f p e s t management. 2.3 Theory o f Firm Under U n c e r t a i n t y Risk imposes an a d d i t i o n a l c o s t on th e o p e r a t i o n o f a producing f ir m which depending upon i t s s o u r ce and t h e p r o d u c ti o n f u n c t i o n , changes s u b s t a n t i a l l y t h e optimal p r o d u c ti o n d e c i s i o n s . Sandmo (120) has i n ­ v e s t i g a t e d t h e impact o f r i s k on p r o d u c t i o n d e c i s i o n s when t h e o u t p u t price is uncertain. He concl ud es t h a t f o r a r i s k a v e r s e f i r m under p e r ­ f e c t c o m p e t i t i o n th e optimal o u t p u t l e v e l i s c h a r a c t e r i z e d by marginal c o s t being l e s s than th e ex p ec te d p r i c e . This im pl ie s t h a t th e r i s k o f u n c e r t a i n pr od uc t p r i c e s adds a d d i t i o n a l c o s t s t o th e conve nt ion al 19 p r o d u c ti o n c o s t s . S i m i l a r r e s u l t s have been o b t a i n e d by d i f f e r e n t a u t h o r s examining o t h e r s o u r c e s o f u n c e r t a i n t y . B l a i r (12) e x p l o r e d t h e ca se with i n p u t p r i c e u n c e r t a i n t y and Lei and (76) anal yze d t h e s i t u a t i o n o f a f i r m f ace d by u n c e r t a i n t y in t h e demand f o r i t s o u t p u t . Tec hnological u n c e r t a i n t y has drawn a t t e n t i o n from s e v e r a l a u t h o r s such as R a t t i and Ullah (10 6), Robison and Black (114) and Pope and J u s t ( 9 9 ) , who have reac hed s i m i l a r c o n c l u s i o n s . These r e s u l t s s u g g e s t t h a t t h e optimal i n p u t p a t t e r n s determined by marginal a n a l y s i s under c e r t a i n t y may not be a p p r o p r i a t e i n d i c a t o r s o f optimal i n p u t usage under u n c e r t a i n t y . 2.4 Decis ion A n al ys is Under U n c e r t a i n t y In the 1 9 2 0 ' s , Frank Knight (75) d i s t i n g u i s h e d between r i s k and u n c e r t a i n t y by d e s i g n a t i n g th e former as a c o n d i t i o n where outcomes o f an a c t i o n cho ic e can be a s s i g n e d a p r o b a b i l i t y o f o c c u r r i n g w h i l e in th e l a t t e r ca se i n s u f f i c i e n t i n f o r m a t i o n e x i s t s t o c o n s t r u c t such a p r o b a b i l i t y function. The Knightian d e f i n i t i o n s o f r i s k and u n c e r t a i n t y have o f t e n been i n t e r p r e t e d t o imply t h a t r i s k i s t h e s i t u a t i o n where o b j e c t i v e (mea sur ab le) p r o b a b i l i t y d i s t r i b u t i o n s can be a s s i g n e d and u n c e r t a i n t y i s t h e ca s e where th e p r o b a b i l i t y d i s t r i b u t i o n s a r e s u b j e c t i v e (unmeasur­ able). About te n y e a r s a f t e r Knight, F.P. Ramsey (105) deduced t h a t p r o b a b i l i t i e s were pers on al and s u b j e c t i v e s i n c e th e y a r e in r e a l i t y " d eg ree s o f b e l i e f " r a t h e r than o b j e c t i v e f a c t s . The terms r i s k and u n c e r t a i n t y a r e now commonly used i n t e r c h a n g e a b l y in a c o n t e x t t h a t d e s c r i b e s a d e c i s i o n s i t u a t i o n where each ch o i ce may r e s u l t in more than one outcome. One o f t h e e a s i e s t ways t o e v a l u a t e t h e a l t e r n a t i v e c h o i c e s under u n c e r t a i n t y i s t o c a l c u l a t e t h e ex pe c te d v a l u e o f each ch o i ce by w ei g h t in g t h e outcomes e xp r es s ed in monetary terms by t h e i r a s s o c i a t e d p r o b a b i l i t i e s . 20 However, t h i s com ple te ly ig n o r e s d i f f e r e n c e s in v a r i a n c e s in t h e d i s ­ t r i b u t i o n s o f th e outcomes and r e l i e s on the mean as t h e only c r i t e r i o n for selection. The v a r i a n c e in t h e d i s t r i b u t i o n o f outcomes i s o f t e n used a s an i n d i c a t o r o f t h e amount o f r i s k invol ved with a p a r t i c u l a r alternative.^ Only i f d e c i s i o n makers a r e r i s k n e u t r a l w i l l t h e ran k in g o f th e a c t i o n c h o i c e s determined by t h e s i z e o f th e ex p ec te d v a l u e be c o n s i s t e n t with a c t u a l p r e f e r e n c e s . Risk a v e r s i o n , a common r e a c t i o n to u n c e r t a i n t y , may g e n e r a t e a d i f f e r e n t ra n k in g . The e x p e c te d v a l u e o r ex pec ted n e t r e t u r n s i s t h e r e f o r e l i m i t e d in a d d r e s s i n g q u e s t i o n s o f s e l e c t i n g amongst a l t e r n a t i v e ch oi ce s under u n c e r t a i n t y . I f under u n c e r t a i n t y , t h e expec ted n e t revenues c a n n o t be used t o rank a l t e r n a t i v e c o u r s es o f a c t i o n c o n s i s t e n t w it h r i s k p r e f e r e n c e s , t h e problem a r i s e s as t o what i s an a p p r o p r i a t e p r o c e d u r e . For ca s e s where a d e c i s i o n maker i s f ace d w it h a s i t u a t i o n where he must s e l e c t from s e v e r a l a c t i o n c h o i c e s w it h v ar y in g outcomes, t h e expec ted u t i l i t y h y p o t h e s i s (EUH) can be used t o p e r m i t e v a l u a t i o n s beyond t h e s i m p l i s t i c maximum expected n e t revenue r u l e . The EUH can be implemented by f o ll o w i n g a s i x s t e p p r o c e s s which w i l l i n s u r e t h a t c o n s i d e r a t i o n o f both t h e ex2 p ec t ed n e t r e t u r n s and th e u n c e r t a i n t y o r r i s k . These s t e p s a r e : 1. Id e n tify the possible a ctio n choices. 2. I d e n t i f y t h e p o s s i b l e outcomes f o r each o f t h e a c t i o n c h o i c e s . The v a r i a n c e i s an a p p r o p r i a t e measure o f r i s k only when t h e d i s ­ t r i b u t i o n s a r e normal. Otherwise o t h e r moments o f t h e d i s t r i b u t i o n a r e im p o r t a n t as w e l l . 2 The EUH l e g i t i m a c y i s o f t e n based on th e ax io ns o f th e vonNeumann and Morgenstern (131) u t i l i t y f u n c t i o n . These axioms i n c l u d e : 1) Ordering - i f a d e c i s i o n maker i s i n d i f f e r e n t between d i s t r i b u t i o n s h.| and h2 , and h 1 i s p r e f e r r e d t o h 3 th e n h2 i s p r e f e r r e d t o h 3 as w e l l ; 2) C o n t i n u i t y - i f an i n d i v i d u a l p r e f e r s t h e p r o b a b i l i t y d i s t r i b u t i o n h, t o h? to h 3 , then t h e r e e x i s t s a unique p r o b a b i l i t y , p , such t h a t he w i l l b£ i n d i f f e r e n t between h 2 and a l o t t e r y o f p*h^ and ( l - p ) ^ ; 3) Independence - i f hi i s p r e f e r r e d t o h 2 , the n a l o t t e r y w ith hi and (13 w i l l be p r e f e r r e d t o t h e same l o t t e r y w it h outcomes h 2 and h 3 (113). 21 3. I d e n t i f y a p r o b a b i l i t y d e n s i t y f u n c t i o n f o r t h e outcomes. 4. Derive u t i l i t y measures f o r t h e outcome*. 5. Determine th e expec ted u t i l i t y f o r each a c t i o n ch o i ce by summing th e u t i l i t y measures f o r t h e outcomes which a r e weighted by th e a s s o c i a t e d p r o b a b i l i t y t h a t each outcome w i l l o cc u r . 6. S e l e c t t h e a c t i o n c h o i c e which produces t h e h i g h e s t expec ted u tility . The B e r n o u l li s i x s t e p EUH p r o c e s s can be c o n s o l i d a t e d i n t o a d e c i s i o n m a t r i x as d i s p l a y e d in Table The outcomes e x p r e s s e d in terms o f u t i l i t y v a l u e s ap pe a r in a m x n matrix. The a c t i o n c h o i c e s w i t h th e h i g h e s t ex pe c te d u t i l i t y determined by summing th e columns weighted by t h e r e l e v a n t p r o b a b i l i t y w i l l be s e l e c t e d as th e b e s t a l t e r n a t i v e by t h i s method. The q u e s t i o n a r i s e s a s t o w he th er o r n o t d e c i s i o n makers a c t u a l l y f o ll o w th e EUH and i f n o t , sh ould t h e y . Two e x c e l l e n t reviews o f the v a l i d i t y o f t h e EUH have r e c e n t l y ap p e a re d . Schoemaker (123) has i d e n t i f i e d f o u r gener al uses f o r th e EUH and examines t h e uses from t h e p e r s p e c t i v e of f o u r c l a s s e s o f e v i d e n c e . The uses o f th e EUH t h a t a r e i d e n t i f i e d a r e d e s c r i p t i v e , p r e d i c t i v e , p o s t d i c t i v e and p r e s c r i p t i v e w h ile ev id enc e i s summarized in t h e f o u r c a t e g o r i e s o f : a) t e s t s on axioms, b) f i e l d r e s e a r c h , c) i n f o r m a t i o n p r o c e s s i n g s t u d i e s and d) c o n t e x t e f f e c t s . Schoemaker arg ue s t h a t t h e d e s c r i p t i v e and p r e s c r i p t i v e uses may be e v a l u a t e d with a l l f o u r t y p e s o f e v id en ce b u t th e p o s t d i c t i v e and p r e ­ d i c t i v e uses a r e more concerned w ith t h e r e s u l t s o f f i e l d r e s e a r c h . He co n cl ude s t h a t as a d e s c r i p t i v e model, t h e EUH f a i l s t o s e r v e e x c e p t f o r " w e l l - s t r u c t u r e d r e p e t i t i v e t a s k s , with im p o r t a n t s t a k e s , and w e l l t r a i n e d d e c i s i o n makers " (123, p. 552). As a p r e d i c t i v e model, al th o u g h he concedes t h a t i n t e r p r e t a t i o n o f t h e e vi de nc e i s c o m p l i c a t e d , Schoemaker s u g g e s t s t h a t th e EUH i s more t h e e x c e p t i o n than t h e r u l e . The p o s t d i c t i v e 22 Table 1. The EUH Decision M at ri x. S t a t e s o f Nature Probability A.j N1 P1 °11 °12 °13 * * * °ln N2 P2 °21 °22 °23 # * * °2n m Pm m 0m mll Ag 0 nm2 ,9 A^ 0 m3 m9 An 0 mn mn 23 use i s d is m i ss e d l a r g e l y on t h e b a s i s o f problems t h a t i t e n c o u n t e r s with th e f o u n d a t i o n s o f s c i e n t i f i c r e a s o n i n g . model i s a l s o d i f f i c u l t t o a p p r a i s e . Evidence t o e v a l u a t e t h i s F i n a l l y , t h e p r e s c r i p t i v e use s u f f e r s from d i f f i c u l t i e s in o p e r a t i o n a l i z i n g t h e e l i c i t a t i o n o f p r e f e r e n c e s c o n s i s t e n t with t h e axioms and from th e la ck o f ev id en ce on whether o r n o t b a s i c p r e f e r e n c e s a r e r e a l l y co m pa tib le with t h e EUH axioms. D es p it e t h e somewhat p e s s i m i s t i c a p p r a i s a l o f th e EUH, Schoemaker conc lu des t h e review w ith th e f o ll o w i n g s t a t e m e n t : "nevertheless, until r i c h e r models o f r a t i o n a l i t y emerge, EU max imiza tion may well remain a worthwhile benchmark a g a i n s t which t o compare, and towards which t o d i r e c t b e h a v i o r " (123, p. 556). The second review o f t h e EUH a r r i v e s a t abo ut th e same c o n c l u s i o n , bu t expends more e f f o r t on t h e e v a l u a t i o n o f t h e t e s t s o f t h e EUH. Robison (116) o u t l i n e s t h e c h a r a c t e r i s t i c s o f a good t e s t and then p r o ­ ceeds t o review t h e l i t e r a t u r e t o a p p r a i s e i f t h e r e i s j u s t i f i c a t i o n f o r t h e use o f t h e EUH as a d e s c r i p t i v e , p r e d i c t i v e o r p r e s c r i p t i v e model. He c o nc lu de s t h a t a l th ou gh t h e r e has been i n a d e q u a te t e s t i n g o f th e EUH, i t can be surmised t h a t , based on t h e a v a i l a b l e e v i d e n c e , t h e model i s a u s e f u l bu t f a r from p e r f e c t p r e d i c t o r o f ch o i ce b e h a v i o r . Under ex p er i m en t al c o n d i t i o n s , t h e Type I ac c u r a c y o f t h e EUH i s a bo ut 65% when based on a s i n g l e argument. Refinements in th e b a s i c model can i n c r e a s e t h e Type I ac c u r a c y b u t u s u a l l y a t t h e expense o f i n c r e a s e d Type I I e r r o r s . Robison i m p l i e s t h a t t h e d e f i c i e n c i e s o f t h e EUH should be r e c o g n i z e d , b u t t h a t i t i s t h e b e s t o f a v a i l a b l e models and can s t i l l provide i n s i g h t s in d e s c r i p t i v e , p r e d i c t i v e and p r e s c r i p t i v e u s e s . I t can be concluded on th e b a s i s o f t h e s e reviews t h a t t h e EUH i s an i m p e r f e c t model b u t p r o v i d e s a u s e f u l f u n c t i o n i n appro xim atin g how d e c i s i o n makers o r d e r r i s k y a l t e r n a t i v e s ; in p r e d i c t i n g what th e ra n k in g s 24 o f th e a l t e r n a t i v e s in a cho ic e s e t a r e ; and in p r e s c r i b i n g what a l t e r ­ n a t i v e s w i l l be p r e f e r r e d given in f o r m a ti o n about t h e r i s k a t t i t u d e s o f d e c i s i o n makers. 2. 5 Implementation E f f o r t s o f EUH Three ma jor problems a r i s e in t h e a p p l i c a t i o n o f t h e EUH a n a l y s i s : t h e measurement o f r i s k p r e f e r e n c e s ; t h e e s t i m a t i o n o f p r o b a b i l i t y den­ sity f u n c t i o n s a s s o c i a t e d w ith t h e oc c u r r e n c e o f t h e outcomes; and v i o l a t i o n s o f the axioms. The f i r s t concern has by f a r r e c e i v e d t h e most a t t e n t i o n in r e s e a r c h conducted in th e l a s t 40 y e a r s . no e x c e p ti o n o f t h a t t r e n d . This d i s c u s s i o n w i l l be The l a t t e r two problems can be reviewed i n Robison ( 11 6) , Schoemaker (123) and S p e t z l e r and S t a e l von H ols tei n (134). However, b e f o r e procee ding i n t o t h e d i s c u s s i o n on e l i c i t a t i o n o f r i s k p r e f e r e n c e s , i t w i l l be us ef u l t o make some b r i e f comments about these othe r concerns. The problem o f e s t i m a t i n g t h e p r o b a b i l i t y d e n s i t y f u n c t i o n have been p r a c t i c a l l y a d d r e s s e d by such a u t h o r s as Ramsey ( 10 5 ), Anderson (3) and King ( 7 3 ) , who fo l l o w t h e s u b j e c t i v i s t ' s school o f th o u g h t . As King (73) d e s c r i b e s , th e d e c i s i o n makers use p r o b a b i l i t y d i s t r i b u t i o n s based on t h e i r e x p e c t a t i o n s o f what i s l i k e l y t o o cc u r . These e x p e c t a t i o n s a r e s u b j e c t i v e (105) and can be drawn on l o g i c a l d e d u c t i o n s , on i n f e r e n c e s from e m p ir ic a l d a t a , on pe rs on al i n t u i t i o n s o r on some combination o f t h e t h r e e . A f t e r th e s t o c h a s t i c exogenous v a r i a b l e s have been d i s t i n g u i s h e d from the endogenous c o n t r o l v a r i a b l e s , in f o r m a ti o n can be c o l l e c t e d from th e d e c i s i o n maker t h a t w i l l .allow t h e r e p r e s e n t a t i o n o f a cu m ul ati v e p r o b a b i l i t y f u n c t i o n . Three b a s i c c l a s s e s o f encoding p r o c e d u r e s f r e q u e n t l y used t o e l i c i t i n f o r m a ti o n t h a t can be c o n ve r te d i n t o a cum ula ti ve p r o b a b i l i t y f u n c t i o n have been i d e n t i f i e d by S p e t z l e r 25 and S t a e l vonH ols tei n (1 34) . These c l a s s e s a r e : 1) Procedures which f i x t h e val ue o f s t o c h a s t i c v a r i a b l e ( s ) and th e d e c i s i o n maker i s asked t o s p e c i f y t h e p r o b a b i l i t y l e v e l : what i s th e p r o b a b i l i t y t h a t t h e v a r i a b l e X w i l l be l e s s than X*? 2) P rocedu res which f i x t h e p r o b a b i l i t y and t h e d e c i s i o n maker i s asked t o s p e c i f i c a v a l u e f o r t h e v a r i a b l e X which w i l l be l e s s than X*: What i s t h e va lu e o f v a r i a b l e X t h a t w i l l be l e s s than X* w ith t h e given p r o b a b i l i t y ? 3) P rocedu res which f i x both th e v a l u e o f t h e s t o c h a s t i c v a r i a b l e and a p r o b a b i l i t y va lu e a s s o c i a t e d w it h i t by examining h i s ­ to ric a l data. With t h e completion o f th e encoding p r o c e s s , s e v e r a l p o i n t s on the cu m u lati v e d i s t r i b u t i o n f u n c t i o n should have been i d e n t i f i e d . Following t h e pr ocedure d e s c r i b e d by S c h l a i f f e r ( 1 2 2 ) , th e o b s e r v a t i o n s can be ar r an g ed in o r d e r o f th e s i z e and t h e k - t h o b s e r v a t i o n can be c o n s i d e r e d a reasonable estim ate o f the k /(n + l) f r a c t i l e o f the d i s t r i b u t i o n . A smooth curve can then be drawn through th e s e l e c t e d p o i n t s o r r e g r e s s i o n t e c h n i q u e s can be used t o f i t a s p e c i f i c form i f i t i s s u s p e c t e d t h a t t h e d i s t r i b u t i o n o f t h e s t o c h a s t i c v a r i a b l e i s from a known f a m i ly o f d istributions. Of c o u r s e , th e more d a t a p o i n t s t h a t a r e a v a i l a b l e , th e more r e l i a b l e w i l l be th e r e p r e s e n t a t i o n o f th e p r o b a b i l i t y d i s t r i b u t i o n . Anderson (3) has examined t h i s r e l a t i o n s h i p and concl udes t h a t wh ile e s t i m a t i o n a l r e l i a b i l i t y i n c r e a s e s w it h t h e number o f o b s e r v a t i o n s , in many ca s e s good e s t i m a t e s o f t h e d i s t r i b u t i o n can be ach ie ve d with as few as t h r e e t o f i v e o b s e r v a t i o n s . When more than one so u rc e o f u n c e r t a i n t y i s p r e s e n t in th e d e c i s i o n en vi ronm ent , th e encoding p r o c e s s w i l l have t o be accomplished f o r each stochastic variable. However, ca r e must be ta ke n t o r e c o g n i z e any depen­ d e n c i e s o r i n f l u e n c e s t h a t may e x i s t between v a r i o u s s t o c h a s t i c v a r i a b l e s . When t h e s t o c h a s t i c v a r i a b l e s a r e c o r r e l a t e d , a m u l t i v a r i a t e d i s t r i b u t i o n 26 sho uld be e s t i m a t e d from th e c o r r e l a t i o n s and t h e a p p r o p r i a t e marginal distributions. The v i o l a t i o n o f t h e axioms o f t h e EUH and t h e r e c e n t advances in th e p r o o f s o f t h e EUH a r e d i s c u s s e d in Schoemaker (123). I t s ho uld be p o i n t e d o u t t h a t t h e axioms a r e in t e n d e d t o d e m o n s t ra te t h e e x i s t e n c e o f numerical u t i l i t i e s f o r outcomes whose e x p e c t a t i o n s f o r t h e r i s k y a c t i o n ch o i ce p r e s e r v e th e o r d e r i n g o f a l t e r n a t i v e s . Recent advances have reduced t h e n e c e s s i t y o f i n c l u d i n g t h e independence and t r a n s i v i t y axioms, two o f t h e most f r e q u e n t l y v i o l a t e d axioms (123). In t h e y e a r s o f r e s e a r c h t h a t have been conducted in a t t e m p t s t o measure r i s k a t t i t u d e s , s e v e r a l approaches have been developed w ith v ar y in g d eg r ee s o f s u c c e s s . Young (150) has i d e n t i f i e d f o u r c l a s s e s o f approaches t o measuring r i s k p r e f e r e n c e s . They a r e : 1) d i r e c t e l i c i t a t i o n o f u t i l i t y f u n c t i o n s ( D .E . U .) ; 2) exp er im en ta l methods (E. M.); 3) observed economic b e h a v i o r ( O . E . B . ) ; and o t h e r methods. The d i r e c t e l i c i t a t i o n approach i s commonly a s s o c i a t e d w ith th e t h r e e most p o p u la r i n t e r v i e w methods which O f f i c e r and H a l t e r (93) r e f e r t o as t h e von Neumann-Morgenstern; th e mo d if ie d von Neumann-Morgenstern; and th e Ramsey methods. These t h r e e models may a l s o be r e f e r r e d t o r e s p e c t i v e l y as t h e s t a n d a r d r e f e r e n c e c o n t r a c t , t h e e q u a l l y l i k e l y / c e r t a i n t y method and t h e e q u a l l y l i k e l y b u t r i s k y outcome method (1 13) . C r i t i c i s m s o f t h e s e te c h n i q u e s i n c l u d e b i a s in t r o d u c e d by d i f f e r e n t i n t e r v i e w e r s , p r e f e r e n c e s f o r o r a g a i n s t gambling, th e e x c l u s i o n o f o t h e r i m p o rt a n t v a r i a b l e s in a d d i t i o n t o monetary g a i n s and l o s s e s , and th e a c c u r a c y o f a " p a r l o r game" in r e f l e c t i n g a c t u a l r i s k p r e f e r e n c e s when outcomes w i l l r e a l l y be e x p e r i e n c e d . The ex pe ri me n ta l approach used by Binswanger (150) in r u r a l I n d ia in v o l v e s t h e a c t u a l f i n a n c i a l compensation o f s u r v e y p a r t i c i p a n t s . The 27 compensation i s th e outcome o f ch oi ce s amongst e i g h t gambles and the s e l e c t i o n s a r e an i n d i c a t i o n o f th e r i s k p r e f e r e n c e s o f th e p a r t i c i p a n t s . Binswanger a r gu es t h a t t h e approach more r e a l i s t i c a l l y ap pr oxi m ate s a f a n n e r ' s normal d e c i s i o n environment and th u s i s s u p e r i o r t o t h e D.E.U. techniques. O b s e r v a ti o n s on a c t u a l economic b e h a v i o r (O.E.B.) i n s i t u a t i o n s under u n c e r t a i n t y can be used t o i n d i r e c t l y measure r i s k p r e f e r e n c e s . The f i r s t o r d e r c o n d i t i o n s in th e ca s e o f ex p ec te d u t i l i t y ma ximizatio n under r i s k can be d e f i n e d f o ll o w i n g Magnusson (150) as 2.4 E(MVPi ) = MFC. + Ra I r , i = l f . . . n Where E(MVP.) = ex p e c te d marginal v a l u e p r o d u c t o f i n p u t i MFC.. = n o n s t o c h a s t i c marginal f a c t o r c o s t o f i n p u t i Rg I r = a r i s k ad j u st m e n t 2 R3 = l o c a l r i s k a v e r s i o n c o e f f i c i e n t ( d u /d a ) EU = c o n s t a n t a I r = marginal c o n t r i b u t i o n t o r i s k o f a d d i t i o n a l i n p u t use or> With o b s e r v a t i o n s on th e i n p u t usage and I r , t h e MVP., can be c a l ­ c u l a t e d and Rg coul d be s o lv ed f o r . Moscardi and deJ anv ry (150) have used s im i la r techniques. While th e obs erved economic b e h a v i o r approach t o measu rin g r i s k p r e f e r e n c e s can be acknowledged as having s o lv e d t h e problem t h a t p r e ­ f e r e n c e s r e v e a l e d d u r i n g th e su rv ey p r o c e s s a r e not r e p r e s e n t a t i v e o f a c t u a l b e h a v i o r , i t does s u f f e r from t h e d i f f i c u l t y o f measuring t h e s to c h a s tic influences ( I r ). G e n e r a l l y , t h i s i s accomplished o n ly by th e a d o p t i o n o f v e r y r e s t r i c t i v e assu mpti on s on t h e s o u r c e s and f u n c t i o n a l forms o f u n c e r t a i n t y . I t a l s o d e s i g n a t e s t h e e n t i r e d is c r e p a n c y between t h e c e r t a i n t y p r o f i t maximizing e q u i l i b r i u m c o n d i t i o n s (MVP^ = MFC^) and th e ob served b e h a v i o r as bei ng a t t r i b u t a b l e t o r i s k w h i l e o t h e r 28 f a c t o r s such as inc omp lete market i n f o r m a t i o n , d i f f e r e n t r e s o u r c e endowments, c a p i t a l c o n s t r a i n t s , d i f f e r e n t o b j e c t i v e f u n c t i o n s , d i f f e r e n t s u b j e c t i v e p r o b a b i l i t y a s s e s s m e n t s , e x - p o s t u n c e r t a i n t y a d j u s t m e n t s and measurement e r r o r s cou ld e a s i l y a cc ou nt f o r some p a r t o f th e d i f f e r e n c e . O ther app roaches t o r i s k p r e f e r e n c e measurement a r e o f t e n focused on c o n s t r u c t i n g r i s k a v e r s i o n i n d i c e s based on a d op t io n o f r i s k management s t r a t e g i e s o r on p s y c h o lo g i c a l o r s o c i o l o g i c a l c r i t e r i a assumed t o be r e la te d to w illin g n ess to bear r is k . As Young, e t a l . (150) d i s c u s s e s , t h e s e measures a r e d i f f i c u l t t o i n c o r p o r a t e i n t o p r e d i c t i v e models s i n c e t h e y do n o t g e n e r a t e c o e f f i c i e n t s o f r i s k p r e f e r e n c e d e r i v a b l e from e x p l i c i t t h e o r i e s o f d e c i s i o n making and a r e even l e s s r e l e v a n t f o r p r e ­ s c r i p t i v e uses. More complete reviews o f th e methods used t o implement t h e EUH and th e g e n e r a l v a l i d i t y o f th e h y p o t h e s i s ap p ea r in Robison (113) and Schoemaker (123). S i n g l e Valued U t i l i t y F unctions The D.E.U. and ex p e r i m e n t a l approac hes produce e s t i m a t i o n s o f s i n g l e v al ue d u t i l i t y f u n c t i o n s . Be sides from th e e s t i m a t i o n problems a l r e a d y d i s c u s s e d , s i n g l e valued u t i l i t y f u n c t i o n s i n h e r e n e t l y have a high p ro b ­ ability o f a Type I e r r o r . That i s t o say t h a t t h e r e i s a tendency t o r e j e c t t h e n u l l h y p o t h e s i s t h a t t h e e x p e c te d u t i l i t y o f an a l t e r n a t i v e f o r any p e r c e i v e d d i f f e r e n c e , whe ther i t r e s u l t s from an a c t u a l d i f f e r e n c e o r from some measurement e r r o r (113). The c o n c e p t o f t h e s i n g l e v al ued u t i l i t y f u n c t i o n i s r o o te d i n the c l a s s i c a l d e s c r i p t i o n o f th e problem (4 3 ) . can be i l l u s t r a t e d g r a p h i c a l l y . function is displayed. The l o g i c o f t h e argument In F ig ur e 3 , t h e c l a s s i c a l u t i l i t y In t h i s c a s e , t h e u t i l i t y i s a f u n c t i o n o f income and t h e f i r s t d e r i v a t i v e (marginal u t i l i t y o f income) i s p o s i t i v e w h il e t h e second d e r i v a t i v e i s n e g a t i v e . This i n d i c a t e s t h a t ma rginal u t i l i t y o f income i s i n c r e a s i n g a t a d e c r e a s i n g r a t e J a r i s k a v e r s e d e c i s i o n maker. Thi s ca s e would r e p r e s e n t The concave c u r v a t u r e o f th e f u n c t i o n w i l l i n d i c a t e t h e d eg ree o f r i s k a v e r s i o n . Risk a v e r s i o n can be d e s c r i b e d as t h e w i l l i n g n e s s t o pay a premium t o avoid an a c t u a r i a l l y f a i r l o t t e r y . A s t r a i g h t l i n e would r e p r e s e n t a r i s k n e u t r a l i n d i v i d u a l . A convex c u r v a t u r e i n d i c a t e s r i s k p r e f e r r i n g o r r i s k lo v i n g b e h a v i o r . I f a decision maker w ith t h i s u t i l i t y f u n c t i o n i s f a c e d w it h a l o t t e r y o f r e c e i v i n g (x+a) 50% o f t h e time and r e c e i v i n g ( x - a ) 50% o f t h e t i m e , th e e xp ec te d u t i l i t y o f t h e l o t t e r y , [ . 5 * u ( x - a ) + .5 * u ( x + a ) ] would be l e s s than u t i l i t y o f t h e ex p ec te d v a l u e o f t h e l o t t e r y ( U ( x ) ) . A r is k neutral i n d i v i d u a l would r e c e i v e th e same u t i l i t y from t h e l o t t e r y and t h e ex p ec te d v a l u e o f th e l o t t e r y w h il e f o r a r i s k - l o v i n g d e c i s i o n maker, t h e expec ted u t i l i t y would be g r e a t e r th a n th e u t i l i t y o f t h e ex p ec ted v a l u e o f the lottery. Most r i s k a v e r s e d e c i s i o n makers would be w i l l i n g t o pay an i n ­ su ra n ce premium t o e l i m i n a t e t h e u n c e r t a i n t y . The amount o f premium depends on the d egr ee o f t h e d e c i s i o n m a k er 's r i s k a v e r s i o n , r e f l e c t e d by t h e c u r v a t u r e o f t h e u t i l i t y f u n c t i o n . The premium, ir, t h a t could be p ai d and l e a v e t h e d e c i s i o n maker i n d i f f e r e n t between th e s u r e outcome (x-tt) 3. and t h e l o t t e r y with outcomex x- a and x+a i s i n d i c a t e d in Figure I t i s t h e d i f f e r e n c e between t h e ex p ec te d v a l u e o f th e l o t t e r y , x , and th e income l e v e l (x-tt) which produces a u t i l i t y i d e n t i c a l t o t h e expe ct ed u t i l i t y o f t h e l o t t e r y . c e rta in ty equivalent. This s u r e outcome l e v e l The s i z e o f t h e (x -tt) i s th e c e r t a i n t y e q u i v a l e n t and the r is k premium w i l l depend on th e c u r v a t u r e o f t h e u t i l i t y f u n c t i o n s and the c h a r a c te r i s t ic s of the lo t t e r y . More r i s k a v e r s e d e c i s i o n makers w i l l have V h e a b s t r a c t i o n o f u t i l i t y h e r e may n o t always be an al ago us t o t h e co nce pt o f u t i l i t y d e r i v e d under c e r t a i n t y . See Schoemaker (123, p. 535) f o r d i s c u s s i o n o f d i f f e r e n c e . 30 U t i 1i t y U(x+a) U(x) U(x-a) Income (x-a) Fig u re 3. CE X Risk Premium and C e r t a i n t y E q u i v a le n t . (x+a) 31 lower c e r t a i n t y e q u i v a l e n t s than l e s s r i s k a v e r s e d e c i s i o n makers wh ile f o r a given d e c i s i o n maker, l e s s r i s k y l o t t e r i e s w i l l have h i g h e r c e r ­ t a i n t y e q u i v a l e n t s than more r i s k y l o t t e r i e s . A l t e r n a t i v e a c t i o n c h o i c e s can then be ranked by th e s i z e o f the c e r t a i n t y e q u i v a l e n t s and t h e r a n k i n g s w i l l be c o n s i s t e n t w ith th e EUH when a s i n g l e valued u t i l i t y f u n c t i o n has been p r o p e r l y measured. However, measurement e r r o r s may l e a d t o i n a c c u r a t e ra n k in g s s i n c e the c e r t a i n t y e q u i v a l e n t s w i l l be d e r i v e d e r r o n e o u s l y . Since th e s i n g l e value u t i l i t y f u n c t i o n i m p li e s an e x a c t measurement, a tendency f o r a Type I e r r o r i s q u i t e h ig h . This has l e a d t o th e development o f more f l e x i b l e te c h n i q u e s . A l t e r n a t i v e s t o t h e S in g le Valued U t i l i t y Function The O.E.B. approach g e n e r a t e s a r i s k a v e r s i o n c o e f f i c i e n t r a t h e r than attempting to d i r e c t l y estim ate a u t i l i t y function. The r i s k a v e r s i o n c o e f f i c i e n t g e n e r a te d in t h i s manner belongs t o an a l t e r n a t i v e c l a s s o f methods t o t h e s i n g l e valued u t i l i t y f u n c t i o n s which can a l s o be used to evaluate action choices. This second c l a s s o f e v a l u a t i o n methods ar e r e f e r r e d t o as e f f i c i e n c y c r i t e r i a s i n c e th e y reduce th e o p p o r t u n i t y s e t of a l t e r n a t i v e a c t i o n c h o i c e s t o a s m a l l e r s u b s e t in a manner t h a t i n s u r e s t h a t th e expec ted u t i l i t y maximizing a c t i o n c h oi ce i s i n c lu d e d in t h e reduced s u b s e t . These e f f i c i e n c y c r i t e r i a a r e c o n t r a r y t o th e s i n g l e val ued u t i l i t y f u n c t i o n s in t h a t th ey have a tendency towards a high p r o b a b i l i t y o f making a Type I I e r r o r . E f f i c i e n c y c r i t e r i a may f a i l t o r e c o g n i z e a d i f f e r e n c e between t h e ex pec ted u t i l i t i e s o f two a l t e r n a t i v e a c t i o n c h o i c e s l e a d i n g t o th e a c c e p t a n c e o f t h e n u ll h y p o t h e s i s t h a t the two a l t e r n a t i v e s a r e o f equal u t i l i t y t o th e d e c i s i o n maker. The O.E.B. g e n e r a t e d r i s k a v e r s i o n c o e f f i c i e n t i s o nl y one o f s e v e r a l 32 efficiency c r i t e r i a . Jock Anderson (5) has i d e n t i f i e d f o u r t e e n a d d i t i o n a l efficiency c r i t e r i a . He groups them i n t o t h r e e c a t e g o r i e s : dominance; 2) u t i l i t y f a m i l y - s p e c i f i c and 3) o t h e r s . 1) s t o c h a s t i c The f i r s t c a t e g o r y c o n s i s t s o f c r i t e r i a which employ r u l e s t o o r d e r a c t i o n c h o i c e s on th e b a s i s o f c h a r a c t e r i s t i c s o f t h e c um ul at iv e p r o b a b i l i t y d i s t r i b u t i o n s . The second group adopt r u l e s which a r e based on v er y g e n e r a l assumptions abo ut th e n a t u r e o f u t i l i t y f u n c t i o n s . The f i n a l c a t e g o r y i s a m i s c e l l a n e o u s gro up in g c o n t a i n i n g E-V c r i t e r i a , i t s o f f s h o o t s and such a l t e r n a t i v e s as Baumol's E-L s a f e t y c r i t e r i a . A nd er s o n' s c l a s s i f i c a t i o n i s somewhat s u p e r f i c i a l s i n c e a l l e f f i c i e n c y c r i t e r i a a r e based upon u t i l i t y f u n c t i o n c h a r a c t e r i s t i c s . E-V c r i t e r i a a r e a s p e c i a l ca s e o f Second Degree S t o c h a s t i c Dominance, where t h e u t i l i t y f u n c t i o n i s q u a d r a t i c o r a l l d i s t r i b u t i o n s a r e n o rm al .- S t o c h a s t i c Dominance te c h n i q u e s a l l impose c o n s t r a i n t s on t h e form o f t h e u t i l i t y f u n c t i o n which al lo w t h e o r d e r i n g o f a l t e r n a t i v e s by comparing th e cu m ul ati v e probability d istrib u tio n s. While t h e c l a s s i f i c a t i o n i s s u p e r f i c i a l , i t i s u s e f u l to d i s t i n g u i s h between some o f t h e more common c r i t e r i a . G e n e r a l l y , e f f i c i e n c y c r i t e r i a a r e c o n s t r u c t e d by l i m i t i n g th e ty p e s o f u t i l i t y f u n c t i o n s t h a t w i l l be c o n s i d e r e d o r by t h e a d op t io n o f some a s s es sm en t r u l e s on t h e c h a r a c t e r i s t i c s o f t h e p r o b a b i l i t y d e n s i t y f u n c t i o n s . Examples o f th e ty p e s o f u t i l i t y f u n c t i o n s o f t e n used as e f f i c i e n c y c r i t e r i a a r e t h e log u t i l i t y f u n c t i o n , t h e n e g a t i v e e x p o n e n t i a l u t i l i t y f u n c t i o n and t h e q u a d r a t i c u t i l i t y f u n c t i o n . The l a t t e r f u n c t i o n i s f r e q u e n t l y used t o g e n e r a t e an ex p e c te d v a l u e - - v a r i a n c e (EV) s e t s us in g q u a d r a t i c programming. Thi s EV e f f i c i e n c y s e t i n c l u d e s a l l a c t i o n c h o i c e s which f o r i d e n t i c a l ex pe ct ed r e t u r n s have t h e s m a l l e s t v a r i a n c e . i s , f o r an ex p e c te d r e t u r n t h e v a r i a n c e i s minimized. That 33 Tobin (144) and Samuelson (118) have r e s p e c t i v e l y shown t h a t EV c r i t e r i a can be c o n s i s t e n t with t h e p o s t u l a t e s o f e x pe c te d u t i l i t y t h e o r y only when t h e u t i l i t y f u n c t i o n i s q u a d r a t i c o r when outcomes a r e d i s t r i b u t e d n or ma ll y . As s u c h , EV a n a l y s i s i s a s p e c i a l c a s e o f Second Degree S t o c h a s t i c Dominance. Examples o f e f f i c i e n c y c r i t e r i a t h a t a r e based on c h a r a c t e r i s t i c s of the p ro b a b ility d ensity functions are s to c h a s tic dominance t e c h n i q u e s . These e f f i c i e n c y c r i t e r i a have d e f i n i t e r u l e s used t o compare t h e c um u la ti ve p r o b a b i l i t y d i s t r i b u t i o n s o f each a c t i o n c h o i c e ' s s e t o f outcomes. They can have d i f f e r i n g u n d e r l y i n g as sumptions and v a r i o u s d eg re e s of r e s t r i c t i v e n e s s . The S t o c h a s t i c Dominance t e c h n i q u e s a r e by f a r t h e most u s e f u l as t h e o t h e r e f f i c i e n c y c r i t e r i a s u f f e r from more r e s t r i c t i v e as su mp ti o ns . E f f i c i e n c y c r i t e r i a developed due t o two d e f i c i e n c i e s in th e EUH a n a l y s i s conducted w it h s i n g l e va lu ed u t i l i t y f u n c t i o n s . F i r s t , i t is d i f f i c u l t t o make s t a t e m e n t s abo ut t h e p r e f e r e n c e s o f c l a s s e s o f d e c i s i o n makers w ith t h e former method u n l e s s each i n d i v i d u a l ' s r i s k a t t i t u d e has been measured o r i t i s assumed t h a t everyone has an i d e n t i c a l u t i l i t y function. Second, due t o th e measurement problems i n h e r e n t in t h e e l i c i t a t i o n o f s i n g l e va l u e d u t i l i t y f u n c t i o n s , r e l a t i v e l y i n a c c u r a t e p r e d i c t i o n s r e s u l t from implementing t h e EUH i n t h i s f a s h i o n . Most e f f i c i e n c y c r i t e r i a , b u t n o t a l l , a r e desig ned t o ci rcu mv ent t h e s e pr ob ­ lems. They a r e c o n s t r u c t e d t o r e p r e s e n t the p r e f e r e n c e s o f a c l a s s o f d e c i s i o n makers and do n o t use an e x a c t measure f o r t h e s e r i s k a t t i t u d e s . The two p o i n t s a r e r e l a t e d . Ra th er th an u s i n g a s i n g l e v al u ed u t i l i t y f u n c t i o n , a c l a s s o f u t i l i t y f u n c t i o n s ( o r d e c i s i o n makers) a r e d e f i n e d by s e t t i n g an i n t e r v a l around p o s s i b l e v a l u e s . Th is i s done in a manner which r ed u ce s the ch o i ce s e t o f a l l a l t e r n a t i v e s i n t o a s m a l l e r s u b s e t 34 in a f a s h i o n t h a t i n s u r e s t h a t t h e a c t i o n ch o i ce w ith th e h i g h e s t ex pe c te d u t i l i t y i s a member o f t h e s u b s e t . The remaining s u b s e t i s denoted as t h e e f f i c i e n c y s e t s i n c e i t s members a r e r i s k e f f i c i e n t . The a l t e r n a t i v e s t h a t a r e r e j e c t e d from t h e s u b s e t a r e r i s k i n e f f i c i e n t and have a lower ex pec ted u t i l i t y f o r t h e e n t i r e c l a s s o f d e c i s i o n makers. E f f i c i e n c y c r i t e r i a , in g e n e r a l , d e c r e a s e t h e p r o b a b i l i t y o f a Type I e r r o r b u t i n c r e a s e t h e p r o b a b i l i t y o f a Type I I e r r o r . The l a r g e r th e e f f i c i e n c y s e t , t h e g r e a t e r w i l l be t h e Type I I e r r o r . There i s a p o s i t i v e r e l a t i o n s h i p between th e s i z e o f t h e e f f i c i e n c y s e t and t h e s i z e o f th e c l a s s o f d e c i s i o n makers r e p r e s e n t e d by th e c r i t e r i a . With t h e e x c e p ti o n o f Convex S e t S t o c h a s t i c Dominance, e f f i c i e n c y c r i t e r i a r e q u i r e t h a t a consensus among a l l i n d i v i d u a l s in t h e c l a s s o f d e c i s i o n makers be reached b e f o r e an a c t i o n c h o i c e can be r e j e c t e d as i n e f f i c i e n t . Since th e y o p e r a t e by making p a i r w i s e co m par iso ns, t h e s e e f f i c i e n c y c r i t e r i a r e q u i r e t h a t everyone a g r e e on which s i n g l e a c t i o n c h o i ce i s p r e f e r r e d t o some a l t e r ­ n a t i v e b e f o r e th e a l t e r n a t i v e can be removed from t h e e f f i c i e n c y s e t . So i f i n d i v i d u a l A p r e f e r s a c t i o n cho ic e 2 t o 1 and i n d i v i d u a l B p r e f e r s 3 t o 1 but n o t 2 t o 1, then a c t i o n cho ic e 1 c an n ot be d e c l a r e d r i s k i n e f f i c i e n t f o r most e f f i c i e n c y c r i t e r i a . E f f i c i e n c y c r i t e r i a o f t e n r e f o r m u l a t e t h e t r a d i t i o n a l EUH problem us in g cum ula ti ve p r o b a b i l i t y f u n c t i o n s r a t h e r than p r o b a b i l i t y d e n s i t y functions. The c o n s t r u c t i o n o f cum ula ti ve p r o b a b i l i t y f u n c t i o n s has been previously discussed. I t i s a p r o c e s s where t h e outcomes a r e or d er ed f r o m s m a l l e s t t o l a r g e s t and a p r o b a b i l i t y o f r e c e i v i n g each outcome l e v e l o r l e s s i s e s t a b l i s h e d (pp. 24 -2 6 ). These f u n c t i o n s can be d e f i n e d as: 2.5 F(x) = p(y < x) V y e R. They a l s o have t h e f o l l o w i n g c h a r a c t e r i s t i c s : 35 2.6 F(x) = 0 as x 2.7 F(x) = 1 as x -*■ °° and F(x) i s n on de cr e as in g and r i g h t co n t in u o u s . The p r o b a b i l i t y d e n s i t y f u n c t i o n a s s o c i a t e d with F(x) i s denoted f ( x ) and s a t i s f i e s t h e f o l l o w i n g : 2.8 F(x) = ) x f(y)dy —00 2.9 f ( x ) = dF(x) F i r s t Degree S t o c h a s t i c Dominance The e a r l i e s t o f t h e s t o c h a s t i c dominance t e c h n i q u e s t o s u r f a c e was F i r s t Degree S t o c h a s t i c Dominance, FSD (104). I t imposes r a t h e r mild r e s t r i c t i o n s on t h e u t i l i t y f u n c t i o n and does i t in a f a s h i o n which should n o t e xc lu de any p o s s i b l e p r e f e r e n c e s from t h e i n t e r v a l . p la c e d on t h e u t i l i t y f u n c t i o n p o s i t i v e , U '( x ) > 0. i s t h a t th e f i r s t d e r i v a t i v e Thi s d e f i n e s th e c l a s s o f a l l The r e s t r i c t i o n must be d e c i s i o n makers who p r e f e r more income t o l e s s . The e f f i c i e n c y c r i t e r i a o f FSD can d em on st ra te t h a t one a c t i o n ch o i ce has a h i g h e r expec ted u t i l i t y th a n a n o t h e r i f i t o f f e r s a g r e a t e r outcome in a t l e a s t one l e v e l o f t h e cu m u lati v e p r o b a b i l i t y and a t no p r o b a b i l i t y l e v e l i s th e outcome l e s s th a n th e outcome o f t h e o t h e r . The cu m u la ti v e p r o b a b i l i t y f u n c t i o n o f th e p r e f e r r e d a c t i o n ch o i ce must n e v e r be t o t h e l e f t o f t h e dominated ch o i ce and must l i e t o th e r i g h t o f i t in a t l e a s t one p r o b a b i l i t y l e v e l . This i n s u r e s t h a t t h e ra n k in g s w i l l be c o n s i s t e n t w it h t h e only c h a r a c t e r i s t i c known about p r e f e r e n c e s — t h a t d e c i s i o n makers p r e f e r more t o l e s s . I t sh ou ld be obvious t h a t FSD i s l i m i t e d in i t s a b i l i t y t o o r d e r a c t i o n c h o i c e s s i n c e most c h o i c e s e t s w i l l have few a l t e r n a t i v e s whose c u m ul at iv e p r o b a b i l i t y f u n c t i o n s do n o t c r o s s . I n t u i t i v e l y , t h i s makes s e n s e because FSD r e p r e s e n t s t h e c l a s s o f a l l d e c i s i o n makers ( a l l 36 p o s s i b l e i n c r e a s i n g u t i l i t y f u n c t i o n s ) and can r e j e c t an a c t i o n ch o i ce as having a lower ex pe ct ed u t i l i t y only i f a l l i n d i v i d u a l s a g r e e . M a th e m a ti c a ll y , t h e d e c i s i o n r u l e s f o r FSD can be s t a t e d as Cumulative p r o b a b i l i t y f u n c t i o n F(x) s t o c h a s t i c a l l y dominates cu m ul ati ve d i s t r i b u t i o n G(x) in t h e f i r s t de gr ee i f 2 .10 G{x) - F(x) > 0 V x e [ 0 , 1 ] . Second Degree S t o c h a s t i c Dominance The i n a b i l i t y o f FSD t o d i s c r i m i n a t e between a l t e r n a t i v e a c t i o n c h o i c e s r e s u l t e d in l a r g e e f f i c i e n c y s e t s and high Type II e r r o r s . To improve on t h i s e f f i c i e n c y c r i t e r i a , Second Degree S t o c h a s t i c Dominance, SSD was devel oped. I t imposes t h e same r e s t r i c t i o n on th e f i r s t d e r i ­ v a t i v e o f th e u t i l i t y f u n c t i o n as FSD, U '( x ) > 0. a l s o p l a c e s a r e s t r i c t i o n on t h e second d e r i v a t i v e : the c l a s s o f a l l r i s k a v e r s e d e c i s i o n makers. In a d d i t i o n , i t U"(x) < 0. It identifies On one ex tre m e, i t in c l u d e s t h e d e c i s i o n maker f o l l o w i n g th e maxi-min d e c i s i o n r u l e w h il e on th e o t h e r ex tre m e, i t i n c l u d e s th e r i s k n e u t r a l i n d i v i d u a l as w e l l . However, no convex u t i l i t y f u n c t i o n s (U"(x) > 0) which i n d i c a t e r i s k lovi ng be h a v i o r a r e in c lu d e d in t h i s i n t e r v a l . This c r i t e r i a i s ex pe c te d t o produce l a r g e e f f i c i e n c y s e t s alth ou gh t h e y should be s m a l l e r than t h e s e t s i d e n t i f i e d f o r FSD. The p r o b a b i l i t y o f Type I I e r r o r remains l a r g e because o f t h e d i f f i c u l t i e s o f r e a c h i n g a consensus in th e comparisons o f e x pe c te d u t i l i t i e s o f a c t i o n ch o ic es f o r a d i v e r s e group o f d e c i s i o n makers. The p r e f e r e n c e s r e p r e s e n t e d by t h i s i n t e r v a l range from t h e maxi-min i n d i v i d u a l on one extreme t o t h e d e c i s i o n maker who approaches r i s k n e u t r a l i t y on t h e o t h e r . I t sh ould be d i f f i c u l t t o g e t t h e s e i n d i v i d u a l s t o concur on r a n k i n g s . In a d d i t i o n t o th e high p r o b a b i l i t y o f a Type I I e r r o r , t h e r e i s 37 a p o s s i b i l i t y o f a Type I e r r o r as well with t h i s e f f i c i e n c y c r i t e r i a . Since i t exc lu de s th e p o s s i b i l i t y o f any r i s k lo v i n g b e h a v i o r , i t may r e j e c t an e f f i c i e n t a c t i o n cho ic e f o r any d e c i s i o n maker w it h a convex portion of the u t i l i t y function. The p r o b a b i l i t y o f a Type I e r r o r w i l l depend on t h e cho ic e s e t and th e a c t u a l r i s k a t t i t u d e s o f t h e d e c i s i o n makers in t h e s tu d y. With SSD i t can be demo nst rated t h a t one a c t i o n c h o i c e (F) has a h i g h e r ex p ec ted u t i l i t y than a n o t h e r (G) i f t h e a r e a under th e cum­ u l a t i v e p r o b a b i l i t y d i s t r i b u t i o n of F n ev er exceeds t h e a r e a under cum ulative p r o b a b i l i t y d i s t r i b u t i o n o f G and f o r a t l e a s t some income l e v e l , G i s above F. All a c t i o n c h o i ce s which a r e r i s k e f f i c i e n t f o r SSD a r e a l s o r i s k e f f i c i e n t f o r FSD b u t n o t n e c e s s a r i l y v i c e - v e r s a . An example i s p r e s e n t e d in Figure 4. In 4 a , F does n o t dominate G because a r e a A i s n o t g r e a t e r than a r e a B. r e s u l t i s obse rve d. than th e a r e a B. In 4b, F j u s t the o p p o s i t e F i s p r e f e r r e d t o G s i n c e th e a r e a A i s g r e a t e r I n t u i t i v e l y i t sh oul d be obvious t h a t A must be equal t o o r g r e a t e r than B f o r F t o dominate G because we know t h a t t h e marginal u t i l i t y i s d e c l i n i n g ( U '( x ) > 0; U"(x) < 0 ) . I f A and B were e q u a l , th e u t i l i t y o f each u n i t o f income i n A i s g r e a t e r th a n t h e u t i l i t y o f each u n i t o f B and t h e expec ted u t i l i t y o f F i s g r e a t e r th a n t h a t o f G. On th e o t h e r hand, i f A were l e s s than B, th e two r e s t r i c t i o n s imposed on t h e u t i l i t y f u n c t i o n by SSD a r e in a d eq u at e t o prove t h a t F has a l a r g e r expec ted u t i l i t y than G. One a d d i t i o n a l p o i n t i s made about SSD. For F t o be p r e f e r r e d t o G, a t t h e lo w es t income l e v e l where th e two c um ul at iv e p r o b a b i l i t y d i s t r i b u t i o n s a r e not e q u a l , F must l i e below G. I f th is condition is n o t met, SSD cannot d em on str ate t h a t F i s p r e f e r r e d t o G r e g a r d l e s s o f t h e a r e a s under t h e cum ulative p r o b a b i l i t y f u n c t i o n s . Thi s i s r e f e r r e d 38 1. 0 Cumulative P r o b a b il it y 0 Income a 0 Cumulative Probability 0 Income b F ig ur e 4. Second Degree S t o c h a s t i c Dominance P r o b a b i l i t y F u n c ti o n s . and Cumulative 39 t o as th e l e f t hand t a i l problem and r e s u l t s from t h e i n c l u s i o n o f the maxi-min i n d i v i d u a l i n t h e c l a s s o f d e c i s i o n makers. Since SSD r e q u i r e s a consensus amongst a l l d e c i s i o n makers i n t h e c l a s s f o r F t o be d e c l a r e d as p r e f e r r e d t o G, any a c t i o n ch oi ce which does n o t meet t h i s c o n d i t i o n w i l l n o t be p r e f e r r e d by t h e maxi-miner and hence ca nno t be r e j e c t e d from t h e e f f i c i e n c y s e t . The mathematical d e s c r i p t i o n o f th e d e c i s i o n r u l e o f SSD i s as f o l 1ows: F(x) s t o c h a s t i c a l l y dominates G(x) in t h e second d egr ee i f 2.11 [G(x) - F{x)3 dx >_ 0 f o r a l l y e [ 0 , 1 ] . T hi rd Degree S t o c h a s t i c Dominance The n ext e f f i c i e n c y c r i t e r i a t o s u r f a c e was Thi rd Degree S t o c h a s t i c Dominance, TSD (135). I t r e f i n e s t h e e f f i c i e n c y s e t i d e n t i f i e d by SSD as imposing a t h i r d r e s t r i c t i o n on th e u t i l i t y f u n c t i o n . In a d d i t i o n t o t h e p r e v i o u s r e s t r i c t i o n s ( U '( x ) > 0; U"(x) < 0 ) , TSD r e q u i r e s t h a t t h e t h i r d d e r i v a t e be p o s i t i v e U '" ( x ) > 0. Thi s i n t e r v a l r e p r e s e n t s th e t h e c l a s s o f r i s k a v e r s e d e c i s i o n makers whose r i s k a v e r s i o n i s d i m in is h in g as income i n c r e a s e s . I t r ed u ce s th e p r o b a b i l i t y o f t h e Type I I e r r o r b u t m a i n t a i n s th e same p o s s i b i l i t y o f a Type I e r r o r as SSD. TSD i s n o t f r e q u e n t l y used because o f t h e la ck o f a t h e o r e t i c a l j u s t i f i c a t i o n f o r i t s assumptions on t h e shape o f t h e u t i l i t y f u n c t i o n . There i s no c o n c l u s i v e e vi de nc e t o s u g g e s t t h a t most d e c i s i o n makers in f a c t , e x h i b i t d im in is h in g r i s k a v e r s i o n (81, 113). F ur th er m o re , f o r many c h o i c e s e t s , TSD may produce th e same e f f i c i e n c y s e t as SSD. S t o c h a s t i c Dominance with Respect t o a Function The n e x t development in th e S t o c h a s t i c Dominance e f f i c i e n c y c r i t e r i a produced a more f l e x i b l e pr oce dur e where t h e r e s t r i c t i o n s on t h e u t i l i t y 40 f u n c t i o n a r e n o t n e c e s s a r i l y r i g i d l y s e t by as s u m p ti o n , b u t can be s e t t o r e f l e c t a c t u a l p r e f e r e n c e measurements as w e l l . S t o c h a s t i c Dominance w ith Respect t o a F u n c t i o n , 1 SDWRF (85, 87) al low s t h e s e t t i n g o f t h e upper and lower bounds t h a t d e f i n e t h e r i s k p r e f e r e n c e i n t e r v a l a t any level. Rat her tha n e x p r e s s i n g t h e r e s t r i c t i o n s i n terms o f t h e d e r i ­ v a t i v e s o f the u t i l i t y f u n c t i o n , i t uses t h e P r a t t a b s o l u t e r i s k a v e r s i o n c o e f f i c i e n t , R(x). The P r a t t a b s o l u t e r i s k a v e r s i o n c o e f f i c i e n t was developed as a measure o f r i s k p r e f e r e n c e s which i s u n a f f e c t e d by p o s i t i v e l i n e a r transform ations. As s t a t e d e a r l i e r , s i n c e u t i l i t y f u n c t i o n s a r e c o n s t r u c t e d u s i n g an a r b i t r a r y o r i g i n and u n i t o f s c a l e , i t i s n o t v a l i d t o make comparisons o f u t i l i t y v a l u e s between d e c i s i o n makers. To c a t e g o r i z e d e c i s i o n makers by t h e i r r i s k p r e f e r e n c e s r e q u i r e s a measure which i s n o t i n f l u e n c e d by th e a r b i t r a r y o r i g i n and u n i t o f s c a l e o r by p o s i t i v e l i n e a r t r a n s f o r m a t i o n s . r i s k premium. A p o s s i b l e measure i s t h e s i z e o f th e A more ge n era l measure which i s c o n s i s t e n t w it h th e r i s k premium measure i s t h e P r a t t a b s o l u t e r i s k a v e r s i o n c o e f f i c i e n t defined as: 2 .1 2 R(X) = where U(X) i s t h e u t i l i t y f u n c t i o n o f income X (1 01) . Th is measure c o n t a i n s a l l t h e u s e f u l i n f o r m a t i o n a b ou t t h e r i s k p r e f e r e n c e s b u t e l i m i n a t e s e v e r y t h i n g a r b i t r a r y a bo ut t h e u t i l i t y f u n c t i o n . I t can be c o n s i d e r e d a measure o f c o n c a v i t y o f th e u t i l i t y f u n c t i o n a t X (and hence i s c o n s i s t e n t w i t h t h e r i s k premium measure) b u t i s unchanged— ^There a r e two v e r s i o n s t o t h i s problem, a c l o s e d form s o l u t i o n and an optimal c o n t r o l a l g o r i t h m . Meyer o r i g i n a l l y d e s i g n a t e d t h e for mer as S t o c h a s t i c Dominance w it h Respect t o a Function and t h e l a t t e r as Choice Between D i s t r i b u t i o n s . The optimal c o n t r o l f o r m u l a t i o n i s now commonly known as S t o c h a s t i c Dominance w i t h R espect t o a Fu nc ti o n. 41 l i k e b e h a v i o r —when t h e u t i l i t y f u n c t i o n i s m u l t i p l i e d by a p o s i t i v e constant. The l a t t e r f e a t u r e i s n o t o b t a i n e d i f a l t e r n a t i v e measures l i k e U"(X) o r th e c u r v a t u r e o f t h e f u n c t i o n , U"(X) (1 + [U‘ ( x ) ] 2 ) " 3^ 2 a r e used. The P r a t t r i s k a v e r s i o n c o e f f i c i e n t can be used f o r r i s k n e u t r a l , risk a v e r s e and r i s k lo v i n g a t t i t u d e s . Positive co e ffic ie n ts indicate r i s k a v e r s i o n w h i l e n e g a t i v e c o e f f i c i e n t s r e p r e s e n t r i s k lo v i n g be­ havior. A c o e f f i c i e n t equal t o z e r o de no te s r i s k n e u t r a l i t y . I t can be e x p r e s s e d as a f u n c t i o n o f income and h and le d i v e r s e p r e f e r e n c e s l i k e the Friedman-Savage u t i l i t y , i . e . , i t can c a p t u r e t h e d e c i s i o n maker which i s sometimes r i s k a v e r s e , r i s k n e u t r a l and r i s k p r e f e r r i n g over t h e domain o f v a l u e s . I t should be remembered t h a t th e measure i s a c t u a l l y a f u n c t i o n o f income as in t h e ca se o f u t i l i t y f u n c t i o n s . SDWRF i s a p ro ced u re where t h e u t i l i t y f u n c t i o n s ( d e c i s i o n makers) r e p r e s e n t e d by th e r i s k p r e f e r e n c e i n t e r v a l a r e bounded by an upper and a lower r i s k a v e r s i o n , r-j(x) and r 2 (x) r e s p e c t i v e l y . The ex pec ted u t i l i t i e s a r e compared in a p a i r w i s e f a s h i o n which n e c e s s i t a t e s th e consensus by a l l d e c i s i o n makers. SDWRF i s a s y s t e m a t i c s e a r c h pr oce ss where t h e u t i l i t y f u n c t i o n w i t h i n t h e i n t e r v a l t h a t i s most not to p re fe r F to G i s i d e n t i f i e d . likely I f i t can be s a i d t h a t f o r t h i s u t i l i t y f u n c t i o n t h e e x pe c te d u t i l i t y o f F i s s t i l l g r e a t e r tha n the ex p e c te d u t i l i t y o f G, then i t i s known t h a t F i s p r e f e r r e d by t h e e n t i r e c l a s s o f d e c i s i o n makers. This pr o ce du r e i s i n e s s e n c e used by FSD, SSD and TSD as well and i s th e rea so n t h a t a l l s t o c h a s t i c dominance t e c h n i q u e s d i s c u s s e d so f a r r e q u i r e t h a t a consensus on t h e r a n k i n g o f a c t i o n c h o i ce s be met b e f o r e any a l t e r n a t i v e i s r e j e c t e d from th e e f f i c i e n c y s e t . SDWRF i s r e a l l y a g en era l v e r s i o n o f t h e e a r l i e r s t o c h a s t i c dom­ ina n ce e f f i c i e n c y c r i t e r i a . I f r ^ ( x ) and r 2 (x) a r e s e t equal t o p o s i t i v e 42 and n e g a t i v e i n f i n i t y r e s p e c t i v e l y , SDWRF becomes FSD and i t s i n t e r v a l w i l l r e p r e s e n t th e c l a s s o f a l l d e c i s i o n m a k e r s J i f r ^ ( x ) and r 2 (x) a r e s e t a t z e r o and p o s i t i v e i n f i n i t y r e s p e c t i v e l y , SDWRF w i l l i d e n t i f y th e same e f f i c i e n c y s e t as SSD. F ig u re 5. These r e l a t i o n s h i p s a r e d i s p l a y e d i n I t sh ou ld be remembered t h a t SDWRF can use v a l u e s f o r r ^ ( x ) and r 2 (x) t h a t can v ar y with income and t h a t can d e f i n e i n t e r v a l s o f d i f f ­ e r e n t w id th s . The r e l a t i v e p r o b a b i l i t i e s o f Type I and Type I I e r r o r s a r e r e l a t e d t o th e width o f t h e r i s k p r e f e r e n c e i n t e r v a l . a l a r g e r Type I I e r r o r would be e x p e c te d . The wid er t h e i n t e r v a l The nar row er t h e i n t e r v a l i s , t h e l a r g e r w i l l be th e ex pe c te d Type I e r r o r . SDWRF i s f l e x i b l e in r e g a r d t o th e Type I and Type I I e r r o r s s i n c e t h e i n t e r v a l can be a d j u s t e d t o meet t h e needs o f t h e r e s e a r c h e r . E f f o r t s t o document th e s i z e o f th e r e l a t i v e Type I and Type I I e r r o r s o f t h e v a r i o u s u t i l i t y measures have de m on st ra te d t h a t , as e x p e c t e d , th e s i z e o f th e e r r o r s i s r e l a t e d t o t h e width o f the i n t e r v a l ( 74) . The s i n g l e val ued u t i l i t y f u n c t i o n a c c u r a t e l y p r e d i c t e d t h e r an k in g s o f a c t i o n c h o i c e s 65% o f t h e time w h i l e SSD was a c c u r a t e 98% b u t only was a b l e t o o r d e r 7% o f th e a c t i o n c h o i c e s . SDWRF with i n t e r v a l s o f v a r i o u s w id th s produced a range o f a c c u r a c y from 98% t o 72% and a p e r c e n t a g e o f c h o i c e s o r d e r e d t h a t ranged from 9% t o 91%. An i n a c c u r a t e p r e d i c t i o n o f o r d e r i n g s r e f l e c t s a Type I e r r o r and an i n a b i l i t y t o o r d e r t h e a c t i o n c h o i c e s r e p r e s e n t s a Type I I e r r o r . These r e s u l t s a r e p r e s e n t e d in Table 2. The ma thematical r e p r e s e n t a t i o n o f SDWRF i s c o n t a i n e d in Meyer's theorem ( 8 5) : H h i s can be seen by r ev ie w in g t h e r e s t r i c t i o n s o f FSD: Since U '( x ) > 0 and U"(x) i s u n r e s t r i c t e d , r ( x ) = U " ( x ) / l l ' ( x ) could be p o s i t i v e o r n e g a t i v e i n f i n i t y depending on U"(x). 43 00 Second Degree .0015 .0008 .0004 SDWRF Income 0 -.001 F i r s t Degree S.D. •00 Fig ur e 5. Risk P r e f e r e n c e I n t e r v a l s f o r Various S t o c h a s t i c Dominance Techniques. 44 Table 2. Performance I n d i c a t o r s f o r A l t e r n a t i v e P r e f e r e n c e Measures. Interval Measurement 3 4 Single-Valued Utility Function Performance Number of Questions Indicator 1 1. 2. Percentage of choices predicted cotT cctiy Percentage o f choices ordered SOURCE: 2 First-Degree Stochastic Dominance Second-Degree Stochastic Dominance 98 88 78 72 65 100 98 9 50 83 91 100 0 7 King and Robison. "Measuring Decis ion Maker P r e f e r e n c e s . " American J . Agr. Econ, Vol. 63, No. 3, p. 519. 45 An optimal c o n t r o l -U ^(y)/U^ (y) which minimized 2 .1 3 2 .1 4 J1 o [G(y) - F ( Y ) ] u ' ( y ) d y 1 s u b j e c t to r ^ y ) < [ u ; ( y ) / u ; ( y ) ] < r 2 (y) U"(y) 2. 15 - - 2 ------- = U '( y ) 0 r,(y) i f ,1 ' [G(x) - F (x)]U' (x) dx < 0 r 2 (y) i f f 1 CG(x) - F (x ) ] U ; (x) dx > 0 ' y Convex S e t S t o c h a s t i c Dominance A most r e c e n t advance in t h e a r e a o f S t o c h a s t i c Dominance e f f i c i e n c y c r i t e r i a r e l a x e s even f u r t h e r t h e n e c e s s i t y o f o b t a i n i n g p r e c i s e measures or r i s k preferences (or the u t i l i t y fu n c tio n ). Convex S e t S t o c h a s t i c Dominance, CSD, (39, 86, 80) can be used t o r e f i n e t h e e f f i c i e n c y s e t s i d e n t i f i e d by FSD, SSD, TSD o r SDWRF. I t can be used t o f u r t h e r d i s c r i m i n a t e between t h e e x pe c te d u t i l i t i e s o f t h e a c t i o n c h o i c e s w i t h o u t imposing f u r t h e r r e s t r i c t i o n s on t h e u t i l i t y f u n c t i o n (narrowing t h e r i s k p r e f e r e n c e interval). I t can accomplish t h i s by r e l a x i n g t h e p re v io u s re q u ir e m e n t t h a t a concensus o f a l l t h e d e c i s i o n makers i s n e c e s s a r y t o r e j e c t an action choice as being r i s k i n e f f i c i e n t . With FSD, SSD, TSD and SDWRF, i f t h e i n t e r v a l i d e n t i f i e d a c l a s s o f two d e c i s i o n makers, A and B, and A p re fe rre d action choice2 to ch oi ce 3 t o 1 b u t n o t 1 b u t n o t 3 t o 1 w h il e Bp r e f e r r e d a c t i o n 2 t o 1, i t 1 from th e e f f i c i e n c y s e t . was i m p o s s i b l e t o r e j e c t a c t i o n choi ce Sin ce e v e r y d e c i s i o n maker does n o t p r e f e r some a l t e r n a t i v e t o 1, even though t h e r e i s no con ce n su s , w ith CSD i t coul d be r e j e c t e d a s r i s k i n e f f i c i e n t s i n c e i t does indeed have a lower 1This r e s u l t can be from comparisons o f expec ted u t i l i t i e s : K ' f(y)u(y)dy - "’I < o by p a r t s , [F (y ) - G(y)] u(y ) / I g(y)u(y)dy = \ [ f ( y ) - g ( y ) ] u(g)dy and i n t e g r a t i n g o n ,-i \} S [F (y ) - G ( y ) ] U ' ( y ) d y = ( ] [G(y) - F f y ) ] u ' (y)dy o s i n c e [F(0) - G(0)] and [ F ( l ) - G ( l ) ] = 0. 46 expec ted u t i l i t y than some a l t e r n a t i v e f o r everyone in t h e c l a s s . is CSD unique o f th e e f f i c i e n c y c r i t e r i a in t h a t i t i d e n t i f i e s an e f f i c i e n c y s e t which c o n t a i n s only th e a c t i o n c h o i c e s t h a t a t l e a s t one d e c i s i o n maker would a c t u a l l y p r e f e r from t h e ch o i ce s e t and removes a l l a l t e r ­ n a t i v e s t h a t no one would s e l e c t . CSD i s a b l e t o r e l a x th e consensus re q u ir e m e n t because r a t h e r than comparing two a c t i o n a c h o i c e s (F and G) in a p a i r w i s e f a s h i o n , i t com­ pa re s one a c t i o n c ho i ce G, t o a convex combination o f s e v e r a l o t h e r , F .. Each F. t h a t remains i n CSD e f f i c i e n c y s e t w i l l be th e a c t i o n c h o i c e with t h e h i g h e s t ex p ec te d u t i l i t y f o r some u t i l i t y f u n c t i o n in the in t e r v a l . The use o f CSD i s a two s t a g e p r o c e s s where an e f f i c i e n c y s e t i s i d e n t i f i e d f o r t h e r e l e v a n t r i s k p r e f e r e n c e i n t e r v a l ( u s in g e i t h e r FSD, SSD, TSD o r SDWRF) and then CSD i s a p p l i e d t o f u r t h e r reduce the number o f e f f i c i e n t c h o i c e s . Thi s can be dona s i n c e no a c t i o n c h oi ce which i s i n f e r i o r t o the e n t i r e group would be p r e f e r r e d by any s i n g l e d e c i s i o n maker in t h e c l a s s so any F r e j e c t e d i n t h e f i r s t s t a g e w i l l not a p p e a r in th e optimal F . . G r a p h i c a l l y , CSD can be d e p i c t e d as a p r o c e s s which c o n s t r u c t s a convex combination o f t h e F. d i s t r i b u t i o n s weighted by a X t h a t w i l l dominate G. The ide a i s t o d i s c o v e r t h e X which w i l l produce t h e -com­ b i n a t i o n t h a t i s as f a r t o t h e r i g h t as p o s s i b l e f o r each p r o b a b i l i t y level. That i s t o say t h a t th e i d e a l com bination i s t h e t h e h i g h e s t p o s s i b l e income f o r each p r o b a b i l i t y l e v e l . one t h a t has I t s h ou ld be remembered t h a t X i s a c o n s t a n t and c an n ot vary in income. In Fig u re 6 i t can be seen t h a t no combination co ul d l i e t o t h e r i g h t o f th e bottom o f t h e OABC o f th e env el op e OABCDO. Feasible values f o r X w i l l depend upon t h e r i s k p r e f e r e n c e i n t e r v a l be in g used. For FSD, t h e s e l e c t e d X w i l l have t o produce a combination o f F.. which n e v e r l i e s 47 .0 Cumulative Probability 0 F ig ur e 6. Income The Envelope o f Curves f o r Convex S et S t o c h a s t i c Dominance. 48 above th e d i s t r i b u t i o n G and f o r some income l e v e l t h e combination must be below G. For SSD, th e s e l e c t e d A w i l l need t o r e s u l t in a cum ula ti ve p r o b a b i l i t y f u n c t i o n whose a r e a i s l e s s than t h e a r e a o f G and which has no l e f t hand t a i l problem. The d i f f i c u l t y in implementing CSD i s i d e n t i f y i n g th e s m a l l e s t s e t o f F.j and d ev el o p in g a s y s t e m a t i c s e a r c h i n g p r o c e s s f o r d i s c o v e r i n g a f e a s i b l e A ou t o f t h e s e t Ap . An i t e r a t i v e p r o c e s s o f r ed uc i n g t h e f i r s t s t a g e e f f i c i e n c y s e t i s n e c e s s a r y t o t e s t w het her th e s e t o f F. e x c l u d i n g F. can dominate F .( G ) . I J J A d i s c u s s i o n o f an o p e r a t i o n a l a l g o r i t h m t o perform CSD can be found in Cochran, Lodwick and Robison ( 25) . In summary, t h e im ple m ent at ion o f th e EUH has been f a c i l i t a t e d g r e a t l y by the r e c e n t advances in p r e f e r e n c e measurement (74) and o f efficiency c r ite r ia . These developments e n a b l e t h e p r e d i c t i o n o f r an k in g s o f a l t e r n a t i v e a c t i o n ch o i c e s f o r c l a s s e s o f d e c i s i o n makers w i t h o u t r e q u i r i n g e x a c t measurements o f t h e u t i l i t y f u n c t i o n s . This g r e a t l y enhances t h e ac c ur ac y o f t h e EUH and i n c r e a s e s i t s u s e f u l n e s s f o r p r e ­ d i c t i v e and p r e s c r i p t i v e p u r po s es . 2.6 Economic Th res ho ld s A key component o f many IPM programs a r e d e c i s i o n r u l e s employing th e co n ce p t o f th e economic t h r e s h o l d . Thi s co n ce p t i s a p r o c e s s where i n f o r m a t i o n on th e p e s t p o p u l a t i o n l e v e l s i s used as an i n d i c a t o r o f the need f o r some c o n t r o l and t h e a p p r o p r i a t e time t o begin t h a t c o n t r o l . The i d e n t i f i c a t i o n o f such t h r e s h o l d p o p u l a t i o n l e v e l s has been t h e fo cus o f r e s e a r c h from a v a r i e t y o f d i s c i p l i n e s such as entomology, b o ta n y , p l a n t p a t h o l o g y , animal s c i e n c e and a g r i c u l t u r a l eocnomics. o f t h i s r e s e a r c h spans some twenty t o t h i r t y e a r s . The development 49 Vernon S te r n in h i s a r t i c l e "Economic Th re sh ol d s" (135) c r e d i t s Sho rtw ell as being the f i r s t t o e s t a b l i s h a r e l a t i o n s h i p between t h e pop­ u l a t i o n d e n s i t y o f a p e s t and p o t e n t i a l crop damage. S t e r n , e t a l . (135) o r i g i n a l l y c o n s o l i d a t e d th e b i o l o g i c a l and economic v a r i a b l e s i n t o a conc ep t known as th e economic t h r e s h o l d . These a u t h o r s begin by d e f i n i n g economic damage as t h e amount o f i n j u r y t h a t w i l l j u s t i f y a r t i f i c i a l c o n t r o l me asures. The economic i n j u r y l e v e l i s t h e " lo w e s t p o p u l a t i o n d e n s i t y t h a t w i l l cause economic damage," and f i n a l l y , t h e economic t h r e s h o l d i s d e f i n e d as " the d e n s i t y a t which c o n t r o l measures sh ould be dete rmin ed t o p r e v e n t an i n c r e a s i n g p e s t p o p u l a t i o n from r e a c h i n g th e economic i n j u r y l e v e l . " Edward and Hueth (36) r e f i n e d t h e co nce pt t o a r r i v e a t t h e i r d e f ­ i n i t i o n o f t h e economic t h r e s h o l d as th e p e s t p o p u a l t i o n l a r g e enough t o cause damages val ued a t th e c o s t o f p r a c t i c a l c o n t r o l . The concept was pu t i n t o t h e framework o f marginal economic th e o r y by Headley (5 1 ) . He developed a simple model w it h a p e s t p o p u l a t i o n growth f u n c t i o n , a p e s t damage f u n c t i o n , a crop y i e l d f u n c t i o n and a control cost function. The model d et er m in e s th e economic t h r e s h o l d a t th e p o p u l a t i o n l e v e l where t h e marginal b e n e f i t d e r i v e d from t h e p e s t c o n t r o l program i s equal t o th e marginal c o s t o f r e a l i z i n g t h a t p o p u l a t i o n through t h e p e s t c o n t r o l program. T h i s , o f c o u r s e , i s th e t r a d i t i o n a l o p t i m i z i n g c r i t e r i a f o r t h e use o f any in p u t . F u r t h e r r e f in e m e n t s were made t o t h e b a s i c Headley model by a number o f a u t h o r s such as Hall and Norgaard ( 4 8 ) , CArlson and Main ( 1 9 ) , Hueth and Regev ( 6 2 ) , Regev, G u t i e r r e z and Feder ( 1 0 7 ) , Talpaz and Borosh ( 1 3 8 ) , and Talpaz and F r i s b i e (140). Most o f t h e s e improvements r e s u l t from i n c l u d i n g more v a r i a b l e s in the b a s i c Headley framework a n d / o r a p p l i c a t i o n o f more s o p h i s t i c a t e d method olog ica l p r o c e d u r e s . Hueth and Regev 50 m e r i t s p e c i a l mention he re s i n c e t h e i r d e f i n i t i o n o f th e economic t h r e s h o l d i s the most complete. I t i s d ef in e d a s t h e l e v e l o f i n p u t ( c o n t r o l ) usage t h a t e q u a t e s t h e sum o f th e marginal b e n e f i t from i n c r e a s i n g t h e p o t e n t i a l p l a n t p r o d u c t in th e f u t u r e , t h e marginal b e n e f i t from d e c r e a s i n g t h e p e s t p o p u l a t i o n d e n s i t y now, and t h e marginal b e n e f i t from d e c r e a s i n g th e p e s t p o p u l a t i o n d e n s i t y in th e f u t u r e w it h th e sum o f th e marginal c o s t s o f m a t e r i a l s , t h e marginal c o s t s o f i n c r e a s i n g p e s t r e s i s t a n c e t o chemical in p u t and th e marginal c o s t s o f a d d i t i o n a l in p u t s needed in th e f u t u r e due t o r e s i s t a n c e t o m a i n t a i n some l e v e l o f control. Headley (52) p r e s e n t e d th e importance o f c o n s i d e r a t i o n of ris k and i n t e r t e m p o r a l cum ula ti ve e f f e c t s in t h e d e t e r m i n a t i o n o f t h e economic threshold. He c o n s t r u c t s a te c h n i q u e which p e r m i ts t h e d e r i v a t i o n o f t h e ex p ec te d b e n e f i t s from a p e s t c o n t r o l in a dynamic, d e c i s i o n t r e e framework. Newton and Lueschner (91) a l s o i n c o r p o r a t e th e p r o b a b i l i t y o f v a r i o u s outcomes o c c u r r i n g f o r d i f f e r e n t a c t i o n s and w h i l e th ey p r o ­ pose t h e use o f an u t i l i t y s c a l e f o r c a s e s where monetary v a l u e s a r e d i f f i c u l t t o o b t a i n , t h e y r e a l l y do n o t ext end t h e i r a n a l y s i s beyond a maximum e x pe c te d r e t u r n s d e c i s i o n r u l e . E x p l i c i t r e c o g n i t i o n t h a t in a d d i t i o n t o ex p ec te d r e t u r n s , r i s k can a l s o i n f l u e n c e farm l e v e l p e s t management d e c i s i o n s d a t e s a t l e a s t t o Carlso n (16) and H e l l e b r a n t (5 6 ). Although Ca rlson d id n o t d i r e c t l y examine t h e impact t h a t t h e c o n s i d e r a t i o n o f r i s k has on t h e economic t h r e s h o l d , he d id i n t r o d u c e s e v e r a l f i r m o b j e c t i v e f u n c t i o n s t h a t i n ­ c o r p o r a t e r i s k i n t o a d e c i s i o n m a k e r ' s u t i l i t y f u n c t i o n used t o e v a l u a t e a l t e r n a t i v e s p r a y i n g s t r a t e g i e s t o c o n t r o l br o w n- ro t o f peac hes . By r e f i n i n g h i s d e f i n i t i o n o f c o n t r o l s t r a t e g i e s t o focus on th e economic 51 t h r e s h o l d , Carlson could have determined t h e impact t h a t r i s k could have on t h e t h r e s h o l d ^or each o f t h e given o b j e c t i v e f u n c t i o n s . He did r e c o g n i z e though t h a t t h e expec ted r e t u r n s a n a l y s i s i s s i m p l i s t i c and ig n o r e s th e i n s u r a n c e a s p e c t s o f p e s t c o n t r o l s and th e r i s k a v e r s i o n o f d e c i s i o n makers. Two o t h e r a t t e m p t s t o i n c o r p o r a t e r i s k i n t o t h e p e s t management d e c i s i o n framework a r e t h e works o f Carlso n (18) and Feder ( 38 ). C arl son p r e s e n t s a p r o d u c t i o n f u n c t i o n t h a t could be used t o maximize e x pe c te d income o r e xp ec te d u t i l i t y when u t i l i t y i s e x p r e s s e d in terms o f th e mean and v a r i a n c e of th e p e s t damage f u n c t i o n . This p r o d u c ti o n function is : 2.16 Y = Py Q * ( l- q ) - PxX -P-jL - F Where: Y = firm 's net returns Q* = p o t e n t i a l crop y i e l d w i t h o u t p e s t damage X = q u a n t i t y o f chemical p e s t c o n t r o l s L = q u a n t i t y o f non-chemical p e s t management r e s o u r c e s used P A = price per u n it of X Py = p r i c e p e r u n i t o f Y P-| = p r i c e p e r u n i t o f L F = fixed costs q = p e r c e n t o f p o t e n t i a l crop lo s t to pests and ( 1- q ) = S = S(X,L,R,0) where 0 and r a r e random v a r i a b l e s d e no t in g r e s p e c t i v e l y p e s t numbers and p e s t t y p e s . 3S/3X > 0 9 s 2 /ax2 < 0 9S/9L > 0 9s2/gL2 < 0 52 and E(Y) = Py Q * [ l - E ( q ) ] - PXS - P-|L - F a 2y = [PyQ*]2 aq2 Using t h i s p r o d u c t i o n f u n c t i o n and a g en er a l u t i l i t y f u n c t i o n where 2 3U/3y > 0 a n d 3 U / 3 a y < 0 , Carlson co n cl ud es t h a t such i n p u t s as m o n i t o r ­ ing and i n f o r m a t i o n a l s e r v i c e s s ho uld reduce t h e v a r i a b i l i t y i n Y and hence i n c r e a s e th e u t i l i t y . Feder (38) u se s a p r o d u c t i o n f u n c t i o n s i m i l a r t o t h a t o f C ar l so n. His f u n c t i o n i s : 2 .1 7 n = (nQ - CQ) - Where: n = profits SN[1 - k ( x ) ] - cx CQ = f i x e d c o s t s 6 = damage p e r p e s t N = s iz e of p e s t population k(x ) = k i l l f u n c t i o n x = pesticide cx = c o s t o f p e s t i c i d e t r e a t m e n t Feder assumes a concave u t i l i t y f u n c t i o n , ^ d e p i c t i n g r i s k a v e r s i o n on t h e p a r t o f th e fa rm er s and con cludes t h a t t h e o b j e c t i v e i s t h e maxi­ m i z a t i o n o f expec ted u t i l i t y as f o l l o w s : 2 .1 8 Max EU (nQ - CQ) He th en s e q u e n t i a l l y 6N[1 - k ( x ) ] - cx c o n s i d e r s t h e impact o f a l lo w in g 6, N and k t o be s t o c h a s t i c v a r i a b l e s . He shows t h a t i n c r e a s e s in t h e v a r i a n c e s o f N and 6 w hil e m a i n t a i n i n g t h e i r means a t i n i t i a l l e v e l s w i l l i n c r e a s e p e s t i c i d e use and lower t h e economic t h r e s h o l d . The c a s e o f t h e e f f e c t ­ i v e n e s s o f t h e p e s t i c i d e i s more d i f f i c u l t s i n c e t h e v a r i a n c e i s l i k e l y t o be h e t e r o s k e d a s t i c . _ 3U / 3 y Feder i d e n t i f i e s two s i t u a t i o n s : concave u t i l i t y f u n c t i o n i s d e f i n e d by < 0 and im p l i e s r i s k a v e r s i o n . 3U/3y a) t h e v a r i a n c e > 0 and 53 i n p e s t res p on se t o th e p e s t i c i d e d e c l i n e s f o r h i g h e r d o s a g e s ; and b) t h e v a r i a n c e i n c r e a s e s with t h e dosage. For t h e f i r s t s i t u a t i o n , t h e i n c r e a s e in u n c e r t a i n t y i n c r e a s e s t h e p e s t i c i d e usage and d e c r e a s e s t h e economic t h r e s h o l d . In t h e second c a s e , t h e use o f t h e p e s t i c i d e w i l l d e c r e a s e and t h e economic t h r e s h o l d w i l l i n c r e a s e as t h e v a r i a n c e in k i n c r e a s e s . Most a t t e m p t s t o measure t h e economic t h r e s h o l d e i t h e r do so under t h e assumption o f c e r t a i n t y o r r e l y on t h e e x pe c te d r e t u r n s c r i t e r i a t o handle r i s k . Con se qu en tl y , th e y s i m p l i f y t h e d e c i s i o n making p r o c e s s t o such an e x t e n t t h a t th e y l i k e l y d e r i v e m i s l e a d i n g r e s u l t s i n many c a s e s . Feder and Carlso n have extended t h e d i s c u s s i o n i n t o th e realm o f ex pe c te d u t i l i t y a n a l y s i s bu t have imposed o n ly g en er a l c o n d i t i o n s ( r i s k a v e r s i o n ) on t h e u t i l i t y f u n c t i o n . In t h e f i e l d s o f economics and management s c i e n c e , r e c e n t advances in im plem entation te c h n i q u e s o f EUH have evolved which sh oul d have a g r e a t p o t e n t i a l t o s t r e n g t h e n th e e x i s t i n g work n o t o n ly i n t h e d e t e r m i n a t i o n o f th e economic t h r e s h o l d bu t in t h e o v e r a l l realm o f p e s t management d e c i s i o n s . Combining t h e i n s i g h t s o f t h e work o f Pope and J u s t (99) on th e ap pr op­ r i a t e form o f th e p r o d u c t i o n f u n c t i o n with t h e Feder p e s t management model, t h e i n f l u e n c e t h a t r i s k and r i s k p r e f e r e n c e s w i l l have on th e economic t h r e s h o l d can be c l e a r l y de m o n st r at ed . F u rt h er m o re , th e i n f l u e n c e t h a t changes in t h e i n p u t p r i c e and t h e o u t p u t p r i c e w i l l have on r i s k e f f i c i e n t t h r e s h o l d s can be e x p l o re d as w e l l . A p r o f i t f u n c t i o n can be f o r m u l a te d t o i n c l u d e t h e r i s k o f p e s t damage as f o l l o w s : 2.1 9 ir = p ( f ( x ) - dN e ( l - k ( z ) ) - pxx - p£z - B where tt = p r o f i t 54 p = profit x = v a ria b le inputs d = damage p e r p e s t N = p e st population density e = random element k(z) * k i l l function z = pesticide Px = p r i c e o f v a r i a b l e i n p u t s Pz = p r i c e o f p e s t i c i d e B = fixed costs 2 and e i s assumed t o have a d i s t r i b u t i o n o f 1 and a . This model conforms t o t h e form o f t h e Pope and J u s t (99) p r o d u c t i o n function since f = f ( x ) and h = - d N e ( l - k ( z ) ) . The e x pe c te d p r o f i t s f o r th e f u n c t i o n can be ex p r e s s e d as 2 .2 0 E(u) = p ( f ( x ) - d N ( l - k ( z ) ) - Pvx - P z - B. A Z The c e r t a i n t y e q u i v a l e n t can be d e r i v e d u s in g A/2 a s t h e expec ted profit-variance 2.21 of p r o f it tra d e -o ff a t equilibrium . It is: CE = p ( f ( x ) - d N ( l - k ( z ) ) - P x - P z - B A b (A/2) [ p d N ( l - k ( z ) ) ] 2a 2 . The model now has two c o n t r o l v a r i a b l e s x and z , w i t h t h e l a t t e r bei ng t h e r i s k r ed u ci ng i n p u t which in t h i s c a s e i s the p e s tic id e . The f i r s t o r d e r c o n d i t i o n s w i t h r e s p e c t t o x and z a r e : 2.22 3CE/3X = p ’ (x) - px = 0 2.23 3CE/3z = t p d N k ^ z ) - ?z + A p d N (l - k (z ) J k 1 ( z ) o 2 = 0. The o u t p u t d e c i s i o n i s inde p en de n t The p e s t i c i d e i s of the p est control decision. a p p l i e d u n t i l t h e c o s t o f t h e p e s t i c i d e i s equal t o t h e v a l u e o f t h e r e d u c t i o n i n p r o f i t v a r i a b i l i t y and t h e r e d u c t i o n in ex p e c te d p r o f i t . I t s h ou ld be note d t h a t t h i s p o i n t w i l l depend 55 upon t h e r i s k p r e f e r e n c e s o f th e d e c i s i o n maker. This can be c l e a r l y de m o ns tr at ed by r e w r i t i n g t h e f i r s t o r d e r c o n d i t i o n a s : 2.24 XpdN{l-k(z)) k' ( z ) o 2 + pdNk' (z) = P . The g r e a t e r X, t h e more r i s k a v e r s e t h e d e c i s i o n maker w i l l be and more v a l u e w i l l be plac ed on t h e r i s k r e d u c i n g c a p a b i l i t i e s o f t h e p e s t i c i d e . So dz/dX sh ould be p o s i t i v e and t o t a l l y d i f f e r e n t i a t i n g t h e above f i r s t o r d e r c o n d i t i o n proves t h i s h y p o t h e s i s . This r e s u l t ap pe ar s below. o dz _ - p d N O - k ( z ) ) k ' ( z ) a 2 „ „ „ 2 ‘ 25 d l " LUpdN (1-k fz')) V ' ( z ) a 2 - XpdNk'tz)2^2— pdNk-’T z ) ] > 0 where k" ( z) < 0 pdN(l-k(z)) > 0 k ' (z ) > 0 2 a > 0 X> 0 The economic t h r e s h o l d can be dete rmin ed by s e a r c h i n g f o r th e p o i n t when th e a p p l i c a t i o n s ho ul d begi n — where t h e m arg in al c o s t s a r e equal t o t h e marginal b e n e f i t s . This p o i n t i s found by s e t t i n g z equal t o ze r o and r e s o l v i n g t h e f i r s t o r d e r c o n d i t i o n s . 2 .2 6 dNk"(0) - ?z + X p dN ( l - k( 0 ) ) k ' ( 0 ) a 2 = 0 2.27 d k '( O ) + X p d ( l - k ( 0 ) ) k ' ( 0 ) o2~ = N I t i s h y p o th e si ze d t h a t as t h e c o s t o f t h e p e s t i c i d e i n c r e a s e s , t h e economic t h r e s h o l d w i l l d e c r e a s e . The d i f f e r e n t i a t i o n o f t h e e q u a t i o n d e f i n i n g th e economic t h r e s h o l d s u p p o r t s t h i s c l a im . s i g n o f dN/dPz i s n e g a t i v e . 2.28 ^ = 2 3 V 8 E ( 7 r ) * m ^ - p d ( l - k ( 0 ) ) k '(0) a2 ---dk '( O) + Xpd(1- k ( 0 )) k ' ( 0 ) o 2 -P z ^ ^ The 56 A s i m i l a r pr o ced ur e can be used t o d e r i v e th e impact o f product p r i c e changes on t h e economic t h r e s h o l d . The r e l a t i o n s h i p between th e l a t t e r and th e former w i l l be p o s i t i v e . 2. 29 - pz * d ( l - k ( 0 ) ) k ' ( 0 ) a 2 dp [dk'(O) + ApdTT-k(O) FT0')'J2 These a n a l y t i c a l r e s u l t s w i l l be e xt re m el y u s e f u l i n g u id i n g th e e m p i r i c a l ex p er i m en t s de s ig ne d t o t e s t t h e co rr es p on d en ce t o r e a l i t y of the hypothesis. 2.7 The Economic Thres ho ld as an In vestm ent Problem The t h e o r e t i c a l b a s i s o f t h e d e f i n i t i o n o f th e economic t h r e s h o l d needs t o be ext en de d f o r o t h e r r e a s o n s as w e l l . A discussion of the d e f i c i e n c i e s and a s u gg es te d improvement i s p r e s e n t e d h e r e based on r e f o r m u l a t i n g t h e q u e s t i o n as an in v e st m en t problem. The new t h e o r e t i c a l f o u n d a t i o n should a l s o be u s e f u l in h a n d l in g m u l t i - p e s t economic t h r e s h o l d s and d e c i s i o n r u l e s g u id i n g r e s i s t a n c e management s t r a t e g i e s . The economic t h r e s h o l d i s an approach t o d ev el op in g d e c i s i o n r u l e s f o r p e s t i c i d e a p p l i c a t i o n s based on t h e observed p e s t p o p u l a t i o n , the c h o i c e c r i t e r i o n u s u a l l y bei ng t o maximize p r o f i t s . I t attempts to d et er m in e th e d e n s i t y l e v e l when ch em ica ls sh ould be a p p l i e d t h a t p r o f i t has been maxin ize d. The co nce pt c f t h e economic t h r e s h o l d has been used i n a p r e ­ s c r i p t i v e manner t o gui de t h e development o f IPM s t r a t e g i e s . I t has been based on a maximization p r i n c i p l e t h a t may n o t be v a l i d a t e d f o r th is application. T h e r e f o r e , t h e p r e d i c t i o n s which a r e g e n e r a te d from t h i s model may n o t be c r e d i b l e . Refinements in t h e d e f i n i t i o n o f th e t r a d i t i o n a l co n c e p t may be n e c e s s a r y t o i n c r e a s e th e c r e d i b i l i t y o f th e models t h a t implement i t . 57 S t e r n (122) was th e f i r s t t o o p e r a t i o n a l i z e t h i s c o n c e p t. His system d e f i n e d t h e economic i n j u r y l e v e l t o be t h e p o p u l a t i o n d e n s i t y l e v e l a t which damage caused by t h e p e s t exceeds t h e c o s t o f c o n t r o l l i n g it. The economic t h r e s h o l d i s t h e p o p u l a t i o n d e n s i t y l e v e l a t which th e p e s t must be c o n t r o l l e d t o p r e v e n t i t from r e a c h i n g t h e economic injury level. Since t h e H i l l e b r a n d t (49) a r t i c l e on p e s t i c i d e u s a g e , economists have t y p i c a l l y approached t h e problem o f optimal p e s t c o n t r o l with marginal a n a l y s i s . Headley (44) co n v e r t e d th e te rm in o l o g y o f t h e e n t o ­ m o l o g i s t i n t o t h e framework o f marginal a n a l y s i s when he d e f i n e d th e economic t h r e s h o l d as t h a t p e s t p o p u l a t i o n d e n s i t y l e v e l where t h e mar­ g i n a l b e n e f i t s a r e equat ed w i t h t h e marginal c o s t s o f t h e p e s t c o n t r o l program. Subsequent a u t h o r s such a s Hall and Norgaard (41) and Hueth and Regev (53) have d e f i n e d t h e c o s t s and b e n e f i t s more r i g o r o u s l y w h il e s t i l l a p p l y in g marginal a n a l y s i s t o det erm ine t h e economic threshold. Other a u t h o r s have moved i n t o t h e realm o f s i m u l a t i o n models t h a t s e a r c h f o r economic t h r e s h o l d s which maximize an o b j e c t i v e f u n c t i o n in terms o f p r o f i t s . While t h e s e models r e c o g n i z e t h e dynamic n a t u r e o f th e problem, t h e y do n o t d i r e c t l y ad d r e s s th e a n a l y t i c s o f how t o d et e r m in e t h e economic t h r e s h o l d , i n s t e a d th e y r e l y i m p l i c i t l y on t h e r e s u l t s o f marginal a n a l y s i s . Talpaz and Borosh ( 1 2 5 ) , Ta l p a z , Curr y, Sharpe, DeMichele and F r i s b i e (126) and Shoemaker (115, 116, 117) a l l ex em pli fy t h i s approach. The l o g i c o f marginal a n a l y s i s i s n o t something t h a t can be u n iv e rsally applied. I t i s an a n a l y t i c a l p r oc ed ur e t h a t i s a p p r o p r i a t e when i n p u t s a r e d i v i s i b l e in a c q u i s i t i o n and use and where time i s n o t an im p o r t a n t c o n s i d e r a t i o n . 58 Most i n p u t s a r e a c q u i r e d and used in one time p e r i o d ; and, th e y can o f t e n be a c q u i r e d and used in d i v i s i b l e amounts. There a r e o t h e r i n p u t s t h a t p r o v id e s e r v i c e s f o r more th a n one time p e r i o d and may only be o b t a i n e d in lumpy q u a n t i t i e s , b u t whose s e r v i c e s a r e a v a i l a b l e in d i v i s i b l e amounts. Those a s s e t s which p r o v id e s e r v i c e s in more th an one p e r i o d we d e f i n e as d u r a b l e s . The d i s t i n g u i s h i n g f e a t u r e o f d u r a b l e s i s n o t t h e i r i n d i v i s i b i l i t y in e i t h e r a c q u i s i t i o n o r use but t h a t th e y a r e no t "used up" in one ti m e p e r i o d . c o s t s t h a t change with time as well as with u s e. As such t h e y c a r r y I t sh ould be obvious t h e n , t h a t t h e d i s t i n c t i o n between d u r a b l e s and n o n - d u r a b le s depends upon t h e l e n g t h o f t h e time p e r i o d . The l o n g e r th e time p e r i o d , t h e fewer w i l l be th e i n p u t s t h a t a r e d u r a b l e s . The d e f i n i t i o n o f t h e time p e r i o d i s not a r b i t r a r y b u t sh ou ld r e f l e c t t h e r a t e o f change of im p o r ta n t v a r i a b l e s in t h e d e c i s i o n envi ron me nt. Often ec ono m ist s d e f i n e time p e r i o d s on t h e b a s i s o f how f r e q u e n t l y p r i c e s change. While t h i s i s c o n v e n i e n t f o r many c a s e s , t h e r e a r e o t h e r i m p o r t a n t f a c t o r changes t h a t sh ould a l s o be c o n s i d e r e d . In p e s t management, t h e s c o u t i n g i n t e r v a l , o r th e ti m e between p e s t m o n i to r s may be an a p p r o p r i a t e ti m e p e r i o d . T r a d i t i o n a l marginal economic a n a l y s i s c o n s i d e r s o n ly t h e c o s t s and b e n e f i t s t h a t change d i r e c t l y w it h i n p u t usage and bec au se i t c o n s i d e r s only c o s t s and b e n e f i t s in a s i n g l e p e r i o d , c o s t s a s s o c i a t e d w ith time do n o t e n t e r i n . I f a s i t u a t i o n a r i s e s t h a t f o r an i n p u t whose s e r v i c e s l a s t more th an one time p e r i o d , t h e r e a r e changes in c o s t s a n d / o r b e n e f i t s t h a t r e s u l t from t h e p ass age o f t i m e , r a t h e r th a n i n p u t u s a g e , t r a d i t i o n a l marginal economic a n a l y s i s w i l l be an i n a p p r o p r i a t e way t o f i n d optimal i n p u t us age. Marginal a n a l y s i s a l s o 59 assumes t h a t a l l i n p u t s a r e d i v i s i b l e in a c q u i s i t i o n when f o r many inputs t h a t is not the case. A n al y s is o f i n p u t s which a r e n o t d i v i s i b l e i n a c q u i s i t i o n i s n o t e a s i l y handled by t r a d i t i o n a l marginal economics. Costs and b e n e f i t s may change w ith th e passage o f time i n two ways - - throug h t h e time v a l u e o f money^ and thr ough any changes in v a l u e s and d u r a b l e i n p u t p r o d u c t i v e c a p a c i t y t h a t f o l l o w a time r e l a t e d p a t t e r n and i n f l u e n c e such d e c i s i o n s as optimal r a t e s o f use and r e p l a c e ­ ment s c h e d u l e s . There a r e a number o f c o s t s t h a t must be i d e n t i f i e d t o s o l v e an i n v e s t m e n t / d i s i n v e s t m e n t d e c i s i o n which may n o t s u r f a c e i n a r e c o g n i z a b l e f a s h i o n w i t h a t r a d i t i o n a l marginal economic a n a l y s i s . These c o s t s can be c a t e g o r i z e d as t h e i n v e n t o r y c o n t r o l c o s t s , d i r e c t u s e r c o s t s , c a p a c i t y time c o s t s , time d e p r e c i a t i o n c o s t s , i n d i r e c t u s e r c o s t s and re p la c e m e n t o p p o r t u n i t y c o s t s (102). The c a p a c i t y o f a d u r a b l e t o p r o v i d e s e r v i c e s i s o f t e n ex h aus te d a s t h e d u r a b l e i s used and as time p a s s e s . o r each f a c t o r i s c o n s i d e r e d a c o s t . The v a l u e o f l o s t c a p a c i t y Losses t h a t r e s u l t from use a r e d i r e c t u s e r c o s t w h i l e t h o s e l o s s e s a s s o c i a t e d w it h t h e p as s ag e o f t im e a r e c a p a c i t y ti m e c o s t s . Since a d u r a b l e l a s t s more tha n one p e r i o d , t h e r e a r e r e s o u r c e s committed t o i t t h a t co u ld have been used i n an a l t e r n a t i v e a c t i v i t y . The v al ue o f t h e s e r e s o u r c e s ( t h e remaining c a p a c i t y ) need t o be charged an o p p o r t u n i t y c o s t equal t o t h e r a t e o f r e t u r n p o s s i b l e in t h e most p r o d u c t i v e a l t e r n a t i v e . Thi s o p p o r t u n i t y c o s t i s th e i n v e n t o r y control c o s t . A f t e r a c q u i s i t i o n , t h e v a l u e o f t h e d u r a b l e t h a t s h ou ld be used in c o s t c a l c u l a t i o n s i s t h e m ark et o r s a l v a g e v a l u e , s i n c e i t s h ou ld ^Since each t i m e p e r i o d i s a f r a c t i o n o f a s e a s o n , t h e time v a l u e o f money w i l l n o t be t o o r e l e v a n t in t h e d e f i n i t i o n o f t h e economic t h r e s h o l d . 60 r e f l e c t t h e ex pe ct ed p r e s e n t v a l u e o f t h e remaining s e r v i c e s . Changes in t h e s a l v a g e v al ue can be a t t r i b u t e d t o two s o u r c e s —changes in i t s p r o d u c t i v e c a p a c i t y and changes in th e p r i c e p e r u n i t o f t h e p r o d u c t i v e c a p a c i t y which may r e s u l t from t h e i r r e v e r s i b l e n a t u r e o f th e in v e s t m e n t , t h e ma rket s t r u c t u r e o r changes i n th e demand f o r t h e s e r v i c e s g e n e r a t e d by t h e a s s e t . The l o s s o f c a p a c i t y due t o use and time have been a t t r i b u t e d t o d i r e c t u s e r c o s t s and c a p a c i t y time c o s t s , b u t changes in t h e p e r u n i t p r i c e o f th e c a p a c i t y a r e n o t in c l u d e d i n t h e s e c o s t s . These c o s t s which r e f l e c t changes in market p r i c e s due t o d i f f e r e n c e s between a c q u i s i t i o n and s a l v a g e v a l u e s and due t o changes in th e demand f o r the a s s e t ' s s e rv ic e s a re time d e p re c ia tio n c o s t s . When t h e a s s e t in q u e s t i o n i s one o f a s e r i e s t h a t may be r e p l a c e d t o p r o v id e a s tr ea m o f s e r v i c e s beyond t h e l i f e t i m e o f any one d u r a b l e , t h e r e a r e two a d d i t i o n a l c o s t s t h a t have i m p o r t a n t time components, f i r s t , t h e a c q u i s i t i o n d a t e and t h e s i z e o f th e f i r s t d u r a b l e can i n f l u e n c e t h e c o s t s and b e n e f i t s o f t h e s u b s e q u e n t d u r a b l e s i n t h e series. Secondl y, t h e o p t i o n o f r e p l a c i n g t h e f i r s t d u r a b l e when i t s p r o d u c t i v e c a p a c i t y has been reduced by time and use with a new second d u r a b l e , imposes an o p p o r t u n i t y c o s t o f r e t u r n s foregone t h a t should be c o n s i d e r e d in management d e c i s i o n s o f t h e f i r s t d u r a b l e . The d e c i s i o n s abo ut t h e s i z e , r a t e o f use and i f c a p a c i t y d e c l i n e s with ti m e , t h e d a t e o f e s t a b l i s h m e n t o f t h e f i r s t d u r a b l e can impact on t h e c o s t s and b e n e f i t s o f f u t u r e d u r a b l e s . These impacts become more and more r e l e v a n t when t h e f u t u r e c o s t s and b e n e f i t s a r e changing with ti m e . As t h e economic l i f e o f t h e f i r s t d u r a b l e i s le n g th e n e d o r s h o r t e n e d and s i n c e th e c o s t s and b e n e f i t s o f t h e f u t u r e durables are a function o f tim e, th e l i f e (s iz e ) of the f i r s t durable 61 i n f l u e n c e s th e n e t r e t u r n s o f f u t u r e d u r a b l e s . The management d e c i s i o n s o f t h e f i r s t d u r a b l e should i n c l u d e t h e s e im p a c ts . I f the influences on th e b e n e f i t s and c o s t s o f f u t u r e d u r a b l e s can be viewed as being f a v o r a b l e , t h e s e impacts can be c a l l e d i n d i r e c t u s e r b e n e f i t s w h il e i f t h e y a r e u n f a v o r a b l e th e y a r e i n d i r e c t u s e r c o s t s . The r ep la ce m e nt o p p o r t u n i t y c o s t i s a measure o f t h e p o t e n t i a l l o s s t h a t might r e s u l t when a d u r a b l e i s r e t a i n e d t o o lo n g . Even though one d u r a b l e may s t i l l have some p r o d u c t i v e c a p a c i t y re m a in in g , t h e r e t u r n s from us ing t h e remaining c a p a c i t y may be s m a l l e r than t h e r e t u r n s e x pe c te d from the r e p la c e m e n t. The postponement o f r e c e i v i n g th e r e t u r n s from th e new d u r a b l e i s r e f e r r e d t o as t h e r ep la ce m e n t opportunity c o s t . The d e c i s i o n r u l e t o d et er m in e t h e optimal r ep la ce m e n t d a t e i s r e p l a c e t h e f i r s t d u r a b l e when t h e n e t r e t u r n s in t h e l a s t time p e r i o d a r e l e s s than t h e a n n u a l i z e d av e r a g e r e t u r n s ov er th e l i f e o f t h e second d u r a b l e (87). The Durable A ss e t Nature o f P e s t Control In t h e c a s e o f p e s t management, i t i s n o t c l e a r t h a t t h e d e t e r m i n a t i o n o f the economic t h r e s h o l d i s a problem t h a t can be s o l v e d by t r a d i t i o n a l marginal economic a n a l y s i s . R at he r tha n c o n s i d e r i n g th e e n t i r e seas on as a s i n g l e p e r i o d and s p r a y s as v a r i a b l e i n p u t s w i t h i n t h a t p e r i o d , i t a p p e a r s t h a t t h e r e ar e enough i n t e r a c t i o n s between s p r a y s and p o p u l a t i o n dynamics from one p a r t o f th e s eas on t o a n o t h e r t h a t i t becomes j u s t ­ i f i e d t o c o n s i d e r t h e season as a s e r i e s o f d e c i s i o n p e r i o d s and t h a t th e s p r a y s a r e r e a l l y d u r a b l e a s s e t s t h a t g e n e r a t e s e r v i c e s which l a s t lo n g e r th a n one p e r i o d . Assuming t h a t t h e s c o u t i n g i n t e r v a l has a l r e a d y been o p t i m a l l y d e t e r m in e d , t h e p o i n t s i n time when a fa rm e r i s f ac e d with i n f o r m a t i o n a b o u t t h e p e s t p o p u l a t i o n and he must make a s p r a y / n o 62 s p r a y d e c i s i o n can d e f i n e t h e time p e r i o d s . So f o r a 25 week season w ith a s c o u t i n g i n t e r v a l o f once a week, a season would c o n s i s t o f 25 time p e r i o d s . The problem a l s o e x h i b i t s some o f t h e o t h e r c h a r a c t e r i s t i c s o f in v e stm en t problems in t h a t some b e n e f i t s and c o s t s change as a f u n c t i o n of time. The p e s t p o p u l a t i o n , th e p l a n t c o n d i t i o n and th e a t t e n u a t i o n o f t h e ch em ica ls a r e a l l a f u n c t i o n o f time and w ea th e r (which has a time r e l a t e d p a t t e r n ) . So t h e v a l u e o f t h e s p r a y i s going t o be dep endent on t i m e , th ro ugh i t s i n f l u e n c e on th e p e s t p o p u l a t i o n , th e p l a n t c o n d i t i o n and th e r a t e a t which t h e chemical a t t e n u a t e s . Further­ more, s i n c e th r o u g h o u t t h e season u s u a l l y some s e r v i c e s ( p r o t e c t i o n ) a r e r e q u i r e d and very r a r e l y w i l l one s p r a y g e n e r a t e enough s e r v i c e s f o r t h e e n t i r e s e a s o n , t h e s p a r y s c h e d u le i s a d u r a b l e r ep la ce m e n t problem. The d e c i s i o n c r i t e r i a should fo cus on t h e a p p l i c a t i o n (o r investment) p a tte r n of the s e r i e s o f sprays needed d u r in g th e se as on n o t t h e optimal use o f any one s p r a y in de p en de nt o f i t s r e l a t i o n with o t h e r s . T r a d i t i o n a l marginal economic a n a l y s i s p r o v i d e s a s y n t h e t i c s o l u t i o n t o t h e problem o f d e t e rm in i n g optimal i n p u t use p a t t e r n s . However, t h e problem o f d e t e r m i n i n g t h e economic t h r e s h o l d i s in r e a l i t y n o t a q u e s t i o n o f t h e optimal r a t e o f use o f a v a r i a b l e i n p u t b u t one o f d e t e r m in i n g t h e optimal s i z e o f a d u r a b l e i n p u t and t h e opti mal time t o r e p l a c e one d u r a b l e w it h a n o t h e r . A dynamic in ve st m en t t h e o r y i s n e c e s s a r y t o a d e q u a t e l y a d d r e s s t h e problem. The r a t e o f use o f t h e s p r a y i s n o t under t h e c o n t r o l o f t h e farm manager. I t is t h e chemical a t t e n u a t i o n r a t e which i s b a s i c a l l y a f u n c t i o n o f time and w ea th e r . The manager i s in a c t u a l i t y concerned w it h when i t i s he 63 s hould s pr ay and t h e dosage he should app ly . Ret urns from Sprays The r e t u r n s from t h e use o f th e d u r a b l e ( s p r a y ) a r e d i r e c t l y asso ciated with the value of the se rv ic e s e x tra c te d . In t h e case o f a p e s t i c i d e , th e s e r v i c e s a r e t h e avoidance o f damage t h a t would have been caused i f t h e c o n t r o l had n o t been a p p l i e d . g e n e r a t e d through time in two ways. The s e r v i c e s a r e F i r s t , in t h e a p p l i c a t i o n p e r i o d t h e r e i s an a c t u a l r e d u c t i o n i n th e p e s t p o p u l a t i o n . Depending upon t h e chemical a t t e n u a t i o n r a t e , th e a c t i v e i n g r e d i e n t s o f t h e p e s t i c i d e may a l s o r edu ce th e p o p u l a t i o n in some p e r i o d s s u bs e q ue nt t o th e application. The damage avoided by t h e a c t u a l number o f p e s t s k i l l e d by t h e chemical i s t h e f i r s t way s e r v i c e s a r e g e n e r a t e d by s p r a y s . The second way in which s e r v i c e s a r e g e n e r a t e d i s by changing t h e growth pat h o f p e s t p o p u l a t i o n . By r ed uc i n g t h e p e s t p o p u l a t i o n in t h e p e r io d o f th e a p p l i c a t i o n , th e p o p u l a t i o n w i l l be reduced in th e f o ll o w i n g p e r i o d s u n t i l i t has grown t o t h e l e v e l t h a t i t would have o b ta in e d w i t h o u t th e s p a r y . Simply s t a t e d , t h e r e t u r n s o f t h e i - t h s p r ay can be r e p r e s e n t e d as t h e sum over time o f th e d i f f e r e n c e between t h e value o f t h e p r o d u c t w i t h o u t t h e c o n t r o l and t h e v a l u e o f t h e p r o d u c t w ith th e control. Ob vi o us ly , t h e o u t p u t w i t h and w i t h o u t th e c o n t r o l w i l l depend on t h e p e s t p o p u l a t i o n i n t h e c u r r e n t time p e r i o d , i t s growth r a t e and t h e use o f a l l o t h e r i n p u t s l i k e f e r t i l i z e r , d r a i n a g e , l a n d , etc. Moreover, th e p e s t p o p u l a t i o n i n th e c u r r e n t time p e r i o d depends on t h e p o p u l a t i o n l e v e l i n th e p r e v i o u s time p e r i o d , th e w e a th e r and th e k i l l i n g c a p a c i t y o f t h e s p r a y under c o n s i d e r a t i o n . The l a r g e r t h e p e s t p o p u l a t i o n in t h e c u r r e n t time p e r i o d , t h e f a s t e r t h e growth r a t e and th e l a r g e r th e k i l l i n g c a p a c i t y o f t h e s p r ay th e g r e a t e r w i l l 64 be t h e b e n e f i t s from th e chemical a p p l i c a t i o n . Cost o f Sprays As d i s c u s s e d e a r l i e r , t h e r e a r e a number o f c o s t s t h a t may change w ith t h e use o f th e d u r a b l e ( s p r a y ) and t h e pa s s ag e o f ti m e. These c o s t s a r e i n v e n t o r y c o n t r o l c o s t s , i n d i r e c t u s e r c o s t s , time d e p r e c i a t i o n c o s t s and r ep la ce m e n t o p p o r t u n i t y c o s t s . Many o f t h e s e c o s t s a r e c a l ­ c u l a t e d by c o n s i d e r i n g both th e amount o f c a p a c i t y rema ining and t h e per u n it salvage value of t h a t c ap a city . Sin ce t h e s p r a y s a r e i r r e v e r s i b l e d u r a b l e s w ith ze r o o r n e g a t i v e s a l v a g e v a l u e , t h e r e a r e no d i r e c t u s e r c o s t s o r c a p a c i t y ti m e c o s t s . The v al u e change from t h e a c q u i s i t i o n p r i c e t o a s a l v a g e p r i c e o f ze r o i s c a p t u r e d by t h e ti m e d e p r e c i a t i o n c o s t s i n c e i t i s n o t r e l a t e d t o changes in t h e p h y s i c a l c a p a c i t y o f th e d u r a b l e t o g e n e r a t e s e r v i c e s b u t i t i s due t o t h e i r r e v e r s i b l e n a t u r e of spray. The i n v e n t o r y c o s t s a r e t h e c o s t s o f m a i n t a i n i n g r e s o u r c e s in th e d u r a b l e (s p r a y ) when th e y co ul d have been employed in some a l t e r n a t i v e . By a s s e s s i n g an o p p o r t u n i t y c o s t equal t o t h e r e t u r n in t h e b e s t a l t e r n a t i v e , i t i s a s s u r e d t h a t t h o s e r e s o u r c e s a r e i n v e s t e d in th e most p r o f i t a b l e o p t i o n a v a i l a b l e . The a c q u i s i t i o n p r i c e o f t h e s p r a y i s t h e c o s t o f o b t a i n i n g t h e m a t e r i a l , and t h e v a l u e o f t h e l a b o r and machinery time used in a p p l y i n g i t . The i n v e n t o r y o f s e r v i c e s h e l d d u r i n g t h e l i f e o f t h e s pr ay i s t h e rema ining l i f e t i m e c a p a c i t y o f t h e chemical t o g e n e r a t e s e r v i c e s , th e "av oidan ce" o f p e s t damage. Th is c a p a c i t y , o f c o u r s e , w i l l depend upon t h e chemical a t t e n u a t i o n r a t e , th e do sa g e, t h e p e s t p o p u l a t i o n , t h e p e s t p o p u l a t i o n growth r a t e and t h e s t a g e a n d / o r c o n d i t i o n o f t h e p l a n t . The i n v e n t o r y c o n t r o l c o s t i s c a l c u l a t e d by m u l t i p l y i n g t h e v a l u e o f t h e i n v e n t o r y h e l d i n each 65 time p e r i o d by t h e r a t e o f r e t u r n p o s s i b l e from th e n e x t b e s t a l t e r n a t i v e . Since a f t e r a s p r a y i s a p p l i e d i t s s a l v a g e v a l u e i s equal t o z e r o , th e value o f th e i n v e n t o r y i s z e r o a f t e r t h e f i r s t time p e r i o d r e g a r d ­ l e s s o f t h e rema ining l i f e t i m e c a p a c i t y . So, t h e r e o c c u r s an i n v e n t o r y c o n t r o l c o s t only i n th e f i r s t p e r i o d . I t can be r e p r e s e n t e d as th e p r o d u c t o f t h e f o l l o w i n g t h r e e te rm s : t h e number o f u n i t s o f c a p a c i t y r e m a in in g , th e v a l u e p e r u n i t o f t h a t c a p a c i t y and t h e r a t e o f r e t u r n in t h e b e s t a l t e r n a t i v e . The m a j o r i t y o f t h e c o s t s o f a chemical c o n t r o l t h a t f u n c t i o n s as a d u r a b l e a r e i n c u r r e d as time d e p r e c i a t i o n c o s t s . This c o s t c a p t u r e s changes in t h e v a l u e o f t h e d u r a b l e due t o d i f f e r e n c e s between a c q u i s i t i o n and s a l v a g e p r i c e s which a r e caused by f a c t o r s u n r e l a t e d t o t h e p h y s i c a l cap acity of the durable to generate s e r v ic e s . In t h i s c a s e , th e major cau se o f t h e d e c l i n e in v a l u e from a p o s i t i v e a c q u i s i t i o n p r i c e t o a zero salvage valu e, i s the i r r e v e r s i b l e nature of the spray. Sin ce i t i s im p o s s i b l e t o a l t e r e i t h e r t h e l o c a t i o n o r time o f use o f t h e chemical once i t has been a p p l i e d , t h e ma rket v a l u e o f t h e a p p l i e d chemical c o n t r o l i s z e r o even though t h e chemical may r e t a i n th e m ajority of i t s serv ices. Whereas t h i s d e c l i n e in v a l u e i s n o t g ra du al b u t immediate, in a d i s c r e t e ca se t h e time d e p r e c i a t i o n c o s t s can be c o n s i d e r e d t o o c c u r a t t h e b e g i n n in g o f t h e second time period. They w i l l be equal t o t h e a c q u i s i t i o n p r i c e o f t h e chemical ( t h e c o s t o f th e m a t e r i a l s , and t h e c o s t o f t h e l a b o r and machinery used t o a p p l y them) s i n c e t h e d e c l i n e in v a l u e i s equal t o t h e drop to the zero salvage value. Another f a c t o r o f i n v e s t i n g in i n p u t s t h a t l a s t m o r e th a n one p e r i o d o r i n d e t e r m i n i n g t h e optimal ti m in g and s i z e d e c i s i o n s f o r a s e r i e s o f d u r a b l e s t o be used in sequence i s t h e i n d i r e c t u s e r c o s t / 66 benefit. This c o s t r e s u l t s from t h e r e l a t i o n s h i p between the number o f s p r a y s t h a t may be needed and t h e d e c i s i o n on each s p r a y as t o i t s optimal s i z e (dosage) and time o f a p p l i c a t i o n . I f t h e timin g ( d a t e o f e s t a b l i s h m e n t ) and t h e dosage ( s i z e o f t h e d u r a b l e ) o f th e f i r s t sp r a y in a s e r i e s o f s p r a y s i n c r e a s e f u t u r e a c q u i s i t i o n c o s t s by i n c r e a s i n g t h e number o f su b se qu en t s p r a y s neede d, t h e r e i s an i n d i r e c t user cost. However, i f t h e s e d e c i s i o n s r e s u l t in a d e c r e a s e o f th e f u t u r e time d e p r e c i a t i o n and i n v e n t o r y c o n t r o l c o s t s , t h e r e i s an in d ire c t user benefit. To measure t h e i n d i r e c t u s e r c o s t ( b e n e f i t ) i t i s n e c e s s a r y t o use some a r b i t r a r y s t a n d a r d from which i n c r e a s e s and d e c r e a s e s in f u t u r e c o s t s can be gauged. P e r h a p s , i t would be b e s t t o s e l e c t a c o n v en ti o na l c a l e n d a r based s p r a y s c h e d u l e from t h e myriad o f a l t e r n a t i v e s t o s e r v e as t h i s s t a n d a r d . A c o n v e n t io n a l c a l e n d a r based s p r a y sc h ed u le o f an e x a c t number o f s p r a y s o f an e x a c t dosage^ could be used as a bas e t o measure how th e dosage and time o f a p p l i c a t i o n o f one s p r a y (wit h i n f o r m a t i o n on t h e p e s t p o p u l a t i o n , t h e p o p u l a t i o n growth r a t e , t h e k i l l i n g c a p a c i t y o f t h e chemical and t h e s t a g e a n d / o r c o n d i t i o n o f t h e p l a n t ) i s l i k e l y t o a f f e c t t h e optimal number ( o r d o s a g e s ) o f su b se q u en t s p r a y s . I f th is cost (benefit) i s c a l c u l a t e d in t h i s manner, i t i s l i k e l y t h a t most m o n i to r in g based s t r a t e g i e s w i l l have an i n d i r e c t u s e r b e n e f i t r a t h e r th an th e c o s t b u t d i f f e r e n t s t r a t e g i e s w i l l p r o b a b ly have d i f f e r e n t l e v e l s o f b e n e f i t s . The i n d i r e c t u s e r b e n e f i t ( c o s t ) o f s p r a y s^ w i l l be d e r i v e d from th e p r o d u c t o f two t e r m s - - t h e change in th e optimal number of s p r a y s in t h e s eas on due t o changes i n the ti m e o f a p p l i c a t i o n o r dosage of s p r a y s.. and t h e av era ge a c q u i s i t i o n p r i c e o f th e s ub se qu en t s p r a y s . ^ I . e . , 10 sp ra ys in t h e s e a s o n , one e v e r y 14 days w it h a dosage o f 2 lbs/acre. 67 Unlike most d u r a b l e s , t h e chemical p e s t i c i d e s p r a y s w i l l n o t i n c u r a l l o f th e c o s t s no rmally a s s o c i a t e d w i t h t h e i n v e s t m e n t / d i s i n v e s t m e n t problem. Sin ce t h e s a l v a g e v a l u e o f t h e s p r a y s i s ze r o a f t e r th e y have been a p p l i e d , t h e c a p a c i t y ti m e c o s t s and t h e d i r e c t u s e r c o s t s become z e r o (changes i n p h y s i c a l c a p a c i t y val ued a t z e r o a r e z e r o ) . The r e l e v a n t c o s t s i n t h i s ca se a r e t h e i n v e n t o r y c o n t r o l c o s t s ( i n the f i r s t p e r i o d ) , t h e time d e p r e c i a t i o n c o s t s ( i n t h e second p e r i o d ) and th e i n d i r e c t u s e r b e n e f i t ( c o s t s ) . Net R eturns in Each Time P eri od Using t h e d e f i n i t i o n s o f r e t u r n s and c o s t s p r e s e n t e d e a r l i e r , i t i s now p o s s i b l e t o c a l c u l a t e t h e n e t r e t u r n s from a d u r a b l e a s s e t and d e t e r m in e optimal u s e , s i z e and r ep la ce m e n t d e c i s i o n s . The d e t e r ­ m i n a ti o n o f t h e economic t h r e s h o l d i s r e a l l y an optimal re pl a ce m e nt problem s i n c e i t d e a l s w i t h a d e c i s i o n r u l e t h a t g ui de s when a new d u r a b l e should be a c q u i r e d . I t i s an a t t e m p t t o use an o b s e r v a b l e p e s t p o p u l a t i o n l e v e l as an i n d i c a t i o n o f t h e p o i n t i n ti m e when i t i s more p r o f i t a b l e t o i n s t a l l a new d u r a b l e ( s p r a y ) tha n t o co n t in u e t o e x t r a c t s e r v i c e s from th e e x i s t i n g one. When p e r c e i v e d as an i n v e s t m e n t problem, t h e p r o c e s s f o r d e f i n i n g t h e economic t h r e s h o l d i s q u i t e d i s t i n c t from t h e p r o c e d u r e s d e s c r i b e d and used i n th e e x i s t i n g literature. R at he r th a n f o ll o w i n g th e t r a d i t i o n a l ma rginal economic a n a l y s i s o f f i n d i n g t h e economic t h r e s h o l d by e q u a t i n g t h e change in b e n e f i t s due t o changes i n i n p u t ( s p r a y ) usage w it h t h e changes in c o s t s due t o changes in i n p u t u s a g e , a new p ro ce du r e i s n e c e s s a r y s i n c e c o s t s and b e n e f i t s change w i t h both t h e i n p u t usage and th e pas s ag e o f ti m e. In t h i s ca se th e economic t h r e s h o l d i s t h e d e n s i t y 68 l e v e l t h a t t h e p e s t p o p u l a t i o n r e a c h e s in t h e time p e r i o d when i t becomes economical t o r e p l a c e ( s pr ay a g a i n ) . Replacement o f one s p r a y with a n o t h e r w i l l occ ur in th e time p e r i o d when th e n e t r e t u r n s from t h e f i r s t s p r a y a r e l e s s th a n t h e av era ge n e t r e t u r n s over t h e l i f e o f t h e second s p r a y . The c a l c u l a t i o n s o f t h e n e t r e t u r n s in each time p e r i o d in v o l v e several step s. F i r s t , i t i s n e c e s s a r y t o i d e n t i f y t h e l i f e o f t h e s pra y by a n a l y z i n g how many p e r i o d s a f t e r i t s a p p l i c a t i o n i t can co n t in u e t o g e n e r a t e s e r v i c e s ( t h e avoida nce o f damage). This r e q u i r e s i n f o r ­ mation on th e w e a t h e r , th e p e s t p o p u l a t i o n and i t s growth r a t e , and t h e chemical attenuation rate. For each p e r i o d i t w i l l be n e c e s s a r y t o e s t i m a t e t h e b e n e f i t s o r t h e v a l u e o f damage t h a t would have o c c u r r e d i f t h e s pr ay had n o t been a p p l i e d . In c o n j u n c t i o n w it h t h e c a l c u l a t i o n of the b e n e f i t s , i t i s necessary to estim ate the per period costs o f the s pr ay as w e l l . The m a j o r i t y o f t h e c o s t s a r e l i k e l y t o ap p e a r in t h e f i r s t two time p e r i o d s s i n c e i n v e n t o r y c o n t r o l c o s t s a r e i n c u r r e d in t h e f i r s t p e r i o d only and t h e time d e p r e c i a t i o n c o s t s a r e charged a t t h e b eg in n in g o f t h e second p e r i o d . There w i l l be no d i r e c t u s e r c o s t s o r c a p a c i t y time c o s t s , b u t i n d i r e c t u s e r c o s t s ( b e n e f i t s ) could o cc ur t h r o u g h o u t t h e l i f e o f t h e d u r a b l e . In each p e r i o d , t h e d i f f e r e n c e between t h e b e n e f i t s o f t h e s p r a y and i t s c o s t s w i l l de te rm in e th e n e t r e t u r n s . A f t e r t h e n e t r e t u r n s in each time p e r i o d have been d e t e r m i n e d , i t i s n e c e s s a r y t o d et erm in e t h e time p e r i o d in which i t i s optimal t o d i s i n v e s t in t h e f i r s t sp ray and appl y a second. This optimal d i s i n v e s t m e n t p e r io d w i l l be dete rmin ed when t h e n e t r e t u r n s in t h e l a s t p e r i o d o f t h e f i r s t s p ra y a r e l e s s th a n t h e average r e t u r n s o f 69 th e second s p r a y . This w i l l r e q u i r e t h e s o l u t i o n o f t h e problem in a f a s h i o n s i m i l a r t o a dynamic programming model in t h a t t h e n e t r e t u r n s o f t h e l a s t d u r a b l e must be assumed t o det erm ine when t o d i s ­ i n v e s t in th e n e x t t o l a s t s p r a y . The economic t h r e s h o l d f o r t h e s ^ s p r a y w i l l be t h e l e v e l o f th p e s t p o p u l a t i o n in t h e time p e r i o d when i t i s optimal t o d i s i n v e s t in t h e s^ s p r a y . The economic t h r e s h o l d w i l l then be de te rm ine d by t h e p a t t e r n s o f w e a t h e r , chemical a t t e n u a t i o n , p e s t p o p u l a t i o n s , th e s t a g e , c o n d i t i o n a n d / o r s t r e s s o f t h e p l a n t and t h e r e l a t e d p r i c e s o f t h e p r o d u c t , t h e chemical and t h e l a b o r and machinery used in th e application. S t r a t e g i e s us ing d i f f e r e n t combinations o f s p r a y s o f va ry in g dosages could be e v a l u a t e d by pr o cee d in g in t h e same manner t o i d e n t i f y th e economic t h r e s h o l d f o r each s p ra y and t h e p a t t e r n o f p e s t i c i d e use t h a t maximizes each s t r a t e g y ' s n e t r e t u r n s a c r o s s a l l s p r a y s w it h i n t h e s e as on . The s t r a t e g i e s could th en be compared on t h e b a s i s o f the lev els seasonal net r e tu r n s . Approaching t h e d e t e r m i n a t i o n o f t h e economic t h r e s h o l d as an inv es tme nt problem r a t h e r th an throug h marginal a n a l y s i s p r o v id e s a more complete a n a l y t i c a l bas e f o r r e s e a r c h . The l o g i c o f t h i s d e f i n i t i o n i s more c o n s i s t e n t with economic t h e o r y d e a l i n g with p r o­ d u c t io n s i t u a t i o n s where time i s im p o r t a n t . As s u ch , i t p a s s e s t h e t e s t o f i n t e r n a l c o n s i s t e n c y w hi le t h e t r a d i t i o n a l f o r m u l a t i o n o f th e problem w i l l n o t . I t s c o n trib u tio n to the i d e n t i f i c a t i o n of the el em ent s o f t h e argument o f t h e t h e o r e t i c a l h y p o t h e s i s l i e s in th e e x p l i c i t r e c o g n i t i o n t h a t i t p r o v id e s t o th e importance o f t h e p as sa ge o f ti me . I t s h ou ld i n c r e a s e t h e c r e d i b i l i t y o f s i m u l a t i o n models by increasing t h e i r validation. I t should f a c i l i t a t e t h e j u s t i f i c a t i o n 70 o f th e t h e o r e t i c a l hypotheses by e x p l i c i t l y i d e n t i f y i n g t h e maximization p r i n c i p l e t o be used. I t sh ould c l a r i f y t h e d e d u c t io n p r o c e s s in a n a l y t i c a l problems w h il e i l l u m i n a t i n g both t h e r e c o g n i t i o n o f which hypotheses a r e being t e s t e d in s y n t h e t i c ( s i m u l a t i o n and optimal c o n t r o l ) and t h e i n d u c t i v e p r o c e s s o f i n f e r e n c e abo ut t h o s e hyp oth ese s tests. 2.8 Risk and t h e Economic Th re s ho ld The c o s t o f r i s k i s r e l a t e d t o makers. I t can be p e r c e i v e d as t h e the u t i l i t y function ofdecision way in which i n d i v i d u a l v al u e t h e t r a d e - o f f between ex pe ct ed v a l u e s and v a r i a n c e . The c o s t o f r i s k can be d e f i n e d as t h e amount t h e d e c i s i o n makers would pay t o e l i m i n a t e th e r i s k . This i s a r i s k premium and i s c o n c e p t u a l l y analo go us t o an in s u r a n c e premium. P ra tt's coefficient (101) app roxim ates t h i s premium and 2 .3 0 of absolute r is k aversion can be d e p i c t e d a s : -ft' P r a t t ' s a b s o l u t e r i s k c o e f f i c i e n t ap pr oxi m ate s t h e r i s k premium s i n c e t h e s i z e o f t h e premium an i n d i v i d u a l i s w i l l i n g t o pay depends on t h e d egree o f c o n c a v i t y i n h i s u t i l i t y f u n c t i o n . The more concave t h e u t i l i t y f u n c t i o n , t h e h i g h e r a premium he i s w i l l i n g t o pay and th e h i g h e r t h e a b s o l u t e r i s k c o e f f i c i e n t . Sin ce t h e r i s k premium i s th e amount th e d e c i s i o n maker i s w i l l i n g t o pay t o be i n d i f f e r e n t between t h e ex p ec te d v a l u e o f an u n c e r t a i n outcome and t h e c e r t a i n v a l u e o f a c e r t a i n outcome, i t can a l s o be d e f i n e d a s : 2.31 n = E(y) - CE(y) where E(y) i s t h e ex p ec ted v al u e o f y and t h e CE(y) i s t h e c e r t a i n t y equivalent. Since t h e d e t e r m i n a t i o n o f t h e economic t h r e s h o l d r e q u i r e s a 71 p r o d u c t i o n d e c i s i o n t h a t o p t i m i z e s i n p u t usage and i t has been shown t h a t r i s k adds a d d i t i o n a l c o s t s t h a t must be co n s id e r e d in optimal p r o d u c t i o n d e c i s i o n s , c a l c u l a t i o n o f t h e economic t h r e s h o l d in a c e r t a i n t y c a s e may be m i s l e a d i n g i n t h a t i t i s b i a s e d from t h e n e g l e c t of the c o s t o f r i s k . The ca s e o f p e s t c o n t r o l i n p u t s demands more a t t e n t i o n t o r i s k th a n many o t h e r c l a s s e s o f i n p u t s due t o th e environment o f u n c e r t a i n t y in which th e y a r e a p p l i e d . The u n c e r t a i n t y a r i s e s from two b a s i c s o u r c e s a l th o ug h i n p u t p r i c e u n c e r t a i n t y co ul d a l s o be in c l u d e d i n some c a s e s . the production fu nction. These s o u r c e s a r e t h e p r o d u c t p r i c e and As Sandmo (120) d e s c r i b e s , p r o d u c t p r i c e u n c e r t a i n t y produces optimal c o n d i t i o n s where o u t p u t i s l e s s th an t h e p r o d u c t i o n under c e r t a i n t y . The impact o f t e c h n o l o g i c a l u n c e r t a i n t y i s i n d e t e r m i n a t e w i t h o u t ex am ina ti on o f t h e p r o d u c t i o n f u n c t i o n . When both s o u r c e s o f u n c e r t a i n t y a r e co n s id e r e d s i m u l t a n e o u s l y , t h e i r impact i s s t i l l a p r i o r i i n d e t e r m i n a t e w i t h o u t some o b s e r v a t i o n o r s i m u l a t i o n o f th e p r o d u c t i o n p r o c e s s . A t r a d i t i o n a l approach t o e s t i m a t i n g a g g r e g a t e l e v e l marginal v al u e p r o d u c t s f o r p e s t c o n t r o l i n p u t s i s t o d e r i v e them from p r o ­ d u c t i o n f u n c t i o n s s t a t i s t i c a l l y f i t t e d from h i s t o r i c a l o r c r o s s sectional data. Two examples o f t h i s t y p e o f a n a l y s i s a r e Headley (50) and F i s h e r (4 0 ) . Both a u t h o r s have f i t t e d t h e d a t a us ing Cobb-Douglas p r o d u c t i o n f u n c t i o n s . F i s h e r e s t i m a t e d marginal p r o ­ d u c t i v i t i e s f o r t h e p e s t c o n t r o l i n p u t and t h e n o n - p e s t c o n t r o l i n p u t v a r i a b l e s in each o f t h r e e ge og r ap hi c a r e a s . For t h e p e s t c o n t r o l i n p u t s , h i s e s t i m a t e s a r e $5 .7 1 / $ 1 .00 f o r Quebec, $ 2 . 3 4 / $ l .00 f o r O n t a r i o and $ 1 2 . 8 0 / $ ! . 0 0 f o r Nova S c o t i a . These e s t i m a t e s " i n d i c a t e t h e r e t u r n s which on t h e av e r a g e a r e ex p ec ted from th e 72 a d d i t i o n o f one more u n i t ( i . e . , $ 1 . 0 0 ) " o f t h e i n p u t s . C a l c u l a t i o n s o f marginal b e n e f i t s in t h i s manner assumes t h a t t h e p e s t c o n t r o l i n p u t s c o n t r i b u t e t o t h e p r o d u c t i o n o f t h e o u t p u t in much t h e same way t h a t o t h e r t y p e s o f i n p u t s do, such as c a p i t a l , labor, f e r t i l i z e r , e tc . With p e s t c o n t r o l i n p u t s , t h e r e a pp ea r s t o be two s i t u a t i o n s i n which t h e y a r e used. The f i r s t s i t u a t i o n i s where p e s t s and p e s t damage have become a r e g u l a r o c c u r r e n c e and need t o be c o n s id e r e d as a c o n t i n u a l f a c t o r o f t h e c r o p ' s growing environment. The second s i t u a t i o n r e s u l t s when p e s t i n f e s t a t i o n s and damage a r e an i n f r e q u e n t b u t perhaps d i s a s t e r o u s even when t h e y o cc u r . In t h e f i r s t s i t u a t i o n , t h e p e s t c o n t r o l i n p u t s can be assumed t o impact on both t h e ex p ec te d v a l u e o f t h e o u t p u t and i t s v a r i a n c e w h ile in t h e second ca se i t can be argued t h a t o n ly t h e v a r i a n c e i s a f f e c t e d s i n c e t h e s e i n p u t s do n o t d i r e c t l y hel p g e n e r a t e o u t p u t —th e y only p r e v e n t o c c a s s i o n a l r e d u c t i o n s under i n f r e q u e n t c o n d i t i o n s . In both s i t u a t i o n s a s p e c i a l form o f t h e p r o d u c t i o n f u n c t i o n must be used. As Pope and J u s t (99) have d e s c r i b e d , i t i s i n a p p r o p r i a t e t o use any o f t h e p o p u l a r forms which employ a m u l t i p l i c a t i v e d i s ­ t u r b a n c e term. This i n c l u d e s such p r o d u c t i o n f u n c t i o n s as th e Cobb- Douglas, th e t r a n s l o g , t h e t r a n s c e n d e n t a l and t h e g e n e r a l i z e d power function. Pope and J u s t (99) s u g g e s t t h a t in t h e ca s e o f an i n p u t whose use d e c r e a s e s r i s k r a t h e r th a n i n c r e a s i n g i t , a p r o d u c t i o n f u n c t i o n which i s t h e sum o f two s u b - f u n c t i o n s , one o f which i s r e l a t e d t o o r m u l t i p l i e d by t h e e r r o r term and t h e o t h e r one inde pendent of i t , i s ap p ro p ria te . 2.32 One example o f t h a t form might be: Qt = F(x) = f ( x t ) + h ( x t )e where E(e) = 0 , f A > 0, h A < 0. 73 This form o f a p r o d u c t i o n f u n c t i o n al low s t h e use o f an i n p u t t o both impact on t h e expec ted v a l u e o f t h e o u t p u t and d e c r e a s e s i t s v a r i a n c e . The above p r o d u c ti o n f u n c t i o n i s a c c e p t a b l e f o r t h e f i r s t s i t u a t i o n s i n c e p e s t i n f e s t a t i o n can be c o n s i d e r e d a normal p a r t o f t h e c r o p ' s environment and p e s t c o n t r o l would be a n t i c i p a t e d t o a f f e c t both the ex p e c te d v a l u e o f t h e o u t p u t and t h e a s s o c i a t e d v a r i a n c e . However, i f p e s t i n f e s t a t i o n s a r e so i n f r e q u e n t t h a t t h e use o f p e s t c o n t r o l has a r e l a t i v e l y i n s i g n i f i c a n t e f f e c t on t h e e xp ec te d o u t p u t b u t can r ed uc e t h e v a r i a n c e , then t h e p e s t c o n t r o l i n p u t s s h o u ld n o t ap pea r i n t h e f i r s t s u b - f u n c t i o n ( f ) b u t remain in t h e s u b - f u n c t i o n (h) which i s m u l t i p l i e d by t h e e r r o r term. This second c a s e i s r a r e f o r most commercial c r o p s . A p r o d u c t i o n f u n c t i o n which pe;.„ s the c a lc u la tio n of the e f f e c t which an i n p u t can have on t h e ex p ec te d o u t p u t and on t h e t e c h n o l o g i c a l u n c e r t a i n t y o f p r o d u c t i o n w i l l be u s e f u l i n t h e d e t e r m i n a t i o n o f th e economic t h r e s h o l d . Such a f u n c t i o n w i l l be u s e f u l in d e t e r m in i n g t h e margi nal b e n e f i t s g e n e r a t e d by t h e p e s t c o n t r o l —b e n e f i t s which can a r i s e from i n c r e a s e d crop y i e l d s o r d e c r e a s e d r i s k s . The d e c r e a s e i n r i s k s coul d not be d e r i v e d us in g t h e more c o n v e n t i o n a l f u n c t i o n s w it h m u l t i p l i c a t i v e e r r o r te rms. Sinc e th e b e n e f i t s now i n c l u d e r i s k , some u t i l i t y c o n s i d e r a t i o n must be used t o measure t h e r e l a t i v e v a l u e t h a t a d e c i s i o n maker p l a c e s on d i f f e r e n t l e v e l s o f ex p ec te d o u t p u t w i t h v a r y i n g l e v e l s o f risk. The c o n s i d e r a t i o n o f r i s k i n t r o d u c e s t h e u t i l i t y f u n c t i o n i n t o t h e d e t e r m i n a t i o n o f t h e economic t h r e s h o l d . While each d e c i s i o n maker may have an unique u t i l i t y f u n c t i o n , an unique v a l u a t i o n o f th e p e s t c o n t r o l b e n e f i t s and hence an unique economic t h r e s h o l d , t h e r e a r e enough s i m i l a r i t i e s between u t i l i t y f u n c t i o n s t h a t appr oxim ate 74 s o l u t i o n s can be d e r i v e d f o r groups o f d e c i s i o n makers. c r i t e r i a o f d i f f e r i n g degrees of r e s t r i c t i v e n e s s measures o f t h e u t i l i t y f u n c t i o n s . Various can even be used as King ( 7 2 ) , King (73) and Robison and King (112) d e s c r i b e p r o c e d u r e s t o accomplish such an a n a l y s i s . Using th e common p r o c e d u r e s t o e s t i m a t e t h e economic t h r e s h o l d i n a c e r t a i n t y c o n t e x t , t h e t h r e s h o l d under r i s k can be c a l c u l a t e d in t h e same way. Of c o u r s e , t h e r e w i l l be a d d i t i o n a l d a t a demands. H i s t o r i c a l d a t a could s t i l l be used t o e s t i m a t e t h e t h r e s h o l d in a " p o s i t i v i stic" s en s e by s t a t i s t i c a l l y f i t t i n g an a p p r o p r i a t e p r o d u c ti o n f u n c t i o n and d e r i v i n g t h e n e c e s s a r y i n f o r m a t i o n f o r t h e c a l c u l a t i o n i n much t h e same way t h a t Talpaz and F r i s b i e (140) used f o r t h e c e r ­ ta in ty case. However, th e p h y s i c a l p r o d u c t i v i t i e s measured i n terms o f changes in ex p ec ted o u t p u t and in th e v a r i a n c e would need t o be co n v e r t e d t o a s t a n d a r d denominator t o a l lo w comparison. This could be accomplished by employing a u t i l i t y f u n c t i o n s p e c i f i c t o a given d e c i s i o n maker o r by comparing t h e outcomes o f a l t e r n a t i v e p e s t c o n t r o l measures w i t h one ( o r more) o f t h e e f f i c i e n c y c r i t e r i a . I t should be note d t h a t as Robison (113) i l l u s t r a t e s , t h e p r o b a b i l i t y o f making a Type I as opposed t o a Type I I e r r o r i s d i f f e r e n t f o r a s i n g l e v a l u e u t i l i t y f u n c t i o n and an e f f i c i e n c y c r i t e r i a ( o r amongst th e various e f f ic ie n c y c r i t e r i a ) . 2.9 Optimal P e s t Management S t r a t e g y S e l e c t i o n Under U n c e r t a i n t y Rat her than o p t i m i z i n g ahd viewing th e s e l e c t i o n o f p e s t management c o n t r o l s as a ca s e s i m i l a r t o o t h e r t r a d i t i o n a l i n p u t s t h a t can be a p p l i e d i n c o n t in u o u s manners, thfese i n p u t s a r e o f t e n combined i n t o now-continuous packages b u i l t around v a r i o u s d e c i s i o n r u l e s . The p e s t management d e c i s i o n th en becomes a ch o i ce between t h e c o n t r o l s t r a t e g i e s t h a t implement t h e d e c i s i o n r u l e s . An a l t e r n a t i v e t o an 75 o p t i m i z i n g model i s a Monte Carlo s i m u l a t i o n model which may be mathematically simpler to solv e. These models have t h e ad va n ta ge s t h a t i t s use i s no t as r e s t r i c t e d by burdensome assu mpti on s and th e y e a s i l y a n a l y z e t h e com plex ity o f t h e c o n t r o l s t r a t e g i e s . The use o f Monte Carl o s i m u l a t i o n models t o produce t h e prob­ a b i l i t y d i s t r i b u t i o n s n e c e s s a r y t o ap p ly th e s t o c h a s t i c dominance te c h n i q u e s in an e v a l u a t i o n o f th e a l t e r n a t i v e c o n t r o l s t r a t e g i e s i s a l s o recommended. With t h e SDWRF and CSD, r i s k e f f i c i e n t s t r a t e g i e s which a r e p r e f e r r e d by a l l members o f t h e c l a s s o f d e c i s i o n makers can be i d e n t i f i e d . Monte Car lo s i m u l a t i o n can approximate t h e economic t h r e s h o l d by comparing d i f f e r e n t run s which have v a r i e d t h e d e c i s i o n r u l e s r e g a r d ­ in g t h e ti m in g a n d / o r dosage o f the p e s t c o n t r o l . Using s t o c h a s t i c dominance t e c h n i q u e s as an e f f i c i e n c y c r i t e r i a , th e a l t e r n a t i v e s t r a t e g i e s coul d be e v a l u a t e d f o r a given c l a s s o f d e c i s i o n makers. Depending upon t h e r e f in e m e n t o f t h e r i s k p r e f e r e n c e i n t e r v a l , t h e a l t e r n a t i v e s t r a t e g i e s can be o r de re d f o r a c l a s s o f d e c i s i o n makers c o n s i s t e n t w ith t h e p r e f e r e n c e s o f each member o f t h e c l a s s . The p r e f e r r e d s t r a t e g i e s can then be i n t e r p r e t e d as having t h e "o pti m al" economic t h r e s h o l d s ( d e c i s i o n r u l e s ) . I f enough ru n s a r e g e n e r a t e d , an approx imati on o f t h e t r u e economic t h r e s h o l d w i l l be g e n e r a t e d . The economic t h r e s h o l d does n o t a d d r e s s problems o f d e c i d i n g between a l te r n a t iv e c o n tro ls , but i t i s r e la te d . S t r a t e g i e s which a r e r i s k e f f i c i e n t a r e p r e f e r r e d because t h e i r d e c i s i o n r u l e s (economic t h r e s h o l d s ) perform b e t t e r th an t h e a l t e r n a t i v e s . B e t t e r performi ng d e c i s i o n r u l e s imply a p r e f e r r e d p a t t e r n o f i n p u t us age. In summary, Monte Carlo s i m u l a t i o n can be used t o d et e r m in e n o t only t h e economic t h r e s h o l d under u n c e r t a i n t y b u t can e v a l u a t e t h e e n t i r e s e t o f c o n t r o l s t r a t e g i e s a t th e same t i III. 3.1 RESEARCH PROCEDURES Use o f Sim ul at io n Models and Philos op hy o f Research The c o m p il a t io n o f t h e i n f o r m a t i o n n e c e s s a r y t o c o n s t r u c t th e d e c i s i o n m a t r i c e s used in t h e s e l e c t i o n o f "o p ti m al " p e s t management s t r a t e g i e s i s a complex p r o c e s s . There a r e many f a c t o r s which may i n f l u e n c e th e s t a t e s o f n a t u r e , t h e i r p r o b a b i l i t y o f o c c u r r i n g and the outcomes a s s o c i a t e d w ith each s t a t e . Problems o f g r e a t com plexity a r e o f t e n an al yz ed u s in g a systems approach. A systems approach t o p e s t management sh ou ld c o n t r i b u t e t o both the e v a l u a t i o n o f t h e farm management a l t e r n a t i v e s and t h e a n a l y s i s o f th e b r o a d e r problems o f p ro d u c ti o n e x t e r n a l i t i e s , en vi ron m ent al damage and health hazards. I t p r o v id e s a p e r s p e c t i v e which f a c i l i t a t e s t h e c l a s s ­ i f i c a t i o n o f t h e problem i n t o more manageable components. The systems approach i s e x t re m e l y u s e f u l in t h e problem f o r m u l a t i o n because i t f o r c e s th e i d e n t i f i c a t i o n o f bou nd ar ie s o f t h e problem, th e e s s e n t i a l elements o f th e problem, t h e i n t e r a c t i o n s between t h e elements and t h e performance c r i t e r i a f o r t h e system. The bo un da rie s o f t h e problem w i l l d e f i n e th e system and d i s t i n g u i s h i t from i t s env ironm ent. t o be pla ce d on t h e problem. be c l a s s i f i e d as environmental They i d e n t i f y th e l i m i t s The e s s e n t i a l eleme nts o f th e system can (uncontrollable) inputs, the co n tro lla b le i n p u t s (management v a r i a b l e s ) , th e system o u t p u t s ( d e s i r e d and u n d e s i r e d ) , and system and de sig n p a r a m e te r s . The o r g a n i z a t i o n o f t h e e s s e n t i a l el em ent s i n t o components and t h e i n t e r a c t i o n s among t h e components comprise t h e s t r u c t u r e o f t h e system. The o u t p u t s o f t h e components can be d e s c r i b e d as s t a t e v a r i a b l e s which may i n d i c a t e t h e c o n d i t i o n o f th e 77 73 system a t a p a r t i c u l a r time o r s t a g e . The system can be s t r u c t u r e d in a d e t e r m i n i s t i c f a s h i o n where a l l c o n v e r s i o n s o f i n p u t s t o o u t p u t s a r e e x a c t r e l a t i o n s h i p s o r the s t r u c t u r e may be a s t o c h a s t i c one where t h e s e c o n v e r s i o n s may c o n t a i n random e r r o r te rm s. L i ke w is e, t h e environmental i n p u t s may be s t o c h a s t i c o r n o n - s t o c h a s t i c . The s t r u c t u r e o f a system can be p e r c e i v e d as b e i n g h i e r a r c h i c a l as each component could be c o n s i d e r e d as a subsystem. The more d e t a i l t h a t i s m a in ta i n e d in th e s t r u c t u r e and th e more components t h e system c o n t a i n s , th e system w i l l be more p r o c e s s o r i e n t e d and app roaches a m e c h a n i s t i c model. The l e s s d e t a i l in th e s t r u c t u r e and t h e fewer components t h e system h a s , th e system i s more opaque and i s d e s c r i b e d as a "black box" model. The systems approach can be used t o perform t h r e e b a s i c f u n c t i o n s o f research. 1) These f u n c t i o n s a r e : an a n a l y s i s f u n c t i o n where t h e system s t r u c t u r e and th e i n p u t v a r i a b l e s a r e s p e c i f i e d and t h e system o u t p u t i s t o be d et er m in e d; 2) a c o n t r o l o r management f u n c t i o n where given t h e system s t r u c t u r e , t h e i n p u t s a r e det ermined which w i l l produce th e s p e c i f i e d o u t p u t s ; and 3) a d es ig n f u n c t i o n where the a v a i l a b l e system i n p u t s and the d e s i r e d system o u t p u t s a r e s p e c i f i e d w hi le t h e system s t r u c t u r e t h a t w i l l c o n v e r t th e i n p u t s i n t o t h e d e s i r e d o u t p u t s i s t o be d et erm ine d ( 8 3) . While n o t a l l r e s e a r c h u s in g a systems approach needs t o c o n s t r u c t a computer s i m u l a t i o n model, i t i s o f t e n c o n v e n i e n t t o do s o . t h e comi p u t e r can be an ai d in p r o c e s s i n g t h e i n f o r m a t i o n about a complex system where such an a c t i v i t y may be t o o t e d i o u s o r to o inv ol ved f o r most mental processes. I t i s o f t e n s a i d t h a t a computer model does n o t produce any new i n f o r m a t i o n b u t simply o r g a n i z e s e x i s t i n g i n f o r m a t i o n i n t o a format more e a s i l y un d e r s to o d . 79 Besides from t h e b e n e f i t s of o r g a n i z i n g complex d a t a b a s e s , o t h e r ad v an ta g es o f using computer system s i m u l a t i o n models have been s t r e s s e d . Dent and Bla ck ie (33) i d e n t i f y f o u r adv antag es o f t h e s e models. They are: 1) They allo w th e s tu d y o f systems where t h e r e a l - l i f e e x p e r i m e n t a t i o n would be e i t h e r i m p o s s i b l e , i n o r d i n a t e l y c o s t l y o r d i s r u p t i v e ; 2) The s y n t h e s i s o f systems in a model-form p e r m i ts t h e st u d y o f systems t h a t do n o t c u r r e n t l y e x i s t ; 3) They al lo w th e stu dy o f lo n g - t e r m e f f e c t s s i n c e th e time ho riz o n over which a model i s run i s w i t h i n t h e c o n t r o l o f t h e r e s e a r c h e r wh ile t h a t o f t h e a c t u a l system may n o t meet t h e demands o f r e s e a r c h s c h e d u l e ; and 4) The mode lling p r o c e s s f o r c e s t h o s e concerned with b u i l d i n g the s i m u l a t i o n model t o examine t h e system o b j e c t i v e l y and c o n s e q u e n t ly u n d e r t a k e a thorough and c r i t i c a l review o f knowledge con ce rn in g th e system (3 3) . These ad va nt ag es o f computer s i m u l a t i o n models have le d t o t h e i r w id es pr ea d a p p l i c a t i o n i n a v a r i e t y o f ty p e s o f r e s e a r c h . Glenn Johnson (65) has c a t e g o r i z e d r e s e a r c h i n t o t h r e e b a s i c t y p e s : s u b j e c t m a t t e r and problem s o l v i n g . disciplinary, The purpose o f d i s c i p l i n a r y r e s e a r c h i s t o ex te n d t h e t h e o r e t i c a l knowledge a n d / o r methodology o f a p a r t i c u l a r discipline. S u b j e c t m a t t e r r e s e a r c h i s concerned w it h p r o v i d i n g knowledge a b o u t a r e l a t e d s e r i e s o f problems t h a t deal w ith a p a r t i c u l a r t o p i c . I t i s m u l t i - d i s c i p l i n a r y in n a t u r e and i s u n l i k e l y t o p r o v i d e enough information on a s i n g l e problem t o s o l v e i t b u t i t emphasizes t h e i n t e r ­ r e l a t i o n s h i p between problems. Problem s o l v i n g r e s e a r c h i s problem s p e c i f i c , g e n e r a l l y m u l t i - d i s c i p l i n a r y and i f s u c c e s s f u l , s ho uld p r o v id e a s o l u t i o n t o th e i d e n t i f i e d problem. System s i m u l a t i o n models can be 80 used as a framework f o r a l l t h r e e ty p e s o f r e s e a r c h . R e g a r d l e s s , which type o f r e s e a r c h i s bei ng conducted o r th e reason f o r which a system s i m u l a t i o n model i s s e l e c t e d , t h e r e a r e some u n i v e r s a l g u i d e l i n e s o f s c i e n t i f i c r e a s o n i n g which must be adhered t o . The use o f a computer model t o conduct ex p eri me n ts does not r e q u i r e a unique ph il osophy of research. I t i s i m p e r a t i v e , however, t h a t a t t e n t i o n be p a i d t o the b a s i c pr o c e d u r e s o f s c i e n t i f i c r e a s o n in g o r th e c o n c l u s i o n s d e r i v e d from t h e model w i l l be s p u r i o u s . Since th e o b j e c t o f r e s e a r c h i s t o g e n e r a t e knowledge, i t should be r e c a l l e d t h a t t h e r e e x i s t s t h r e e typ e s o f knowledge: and p r e s c r i p t i v e . p o s i t i v e , normative P o s i t i v e knowledge i s i n f o r m a t i o n d e s c r i b i n g th e c h a r a c t e r i s t i c s o f a c o n d i t i o n , s i t u a t i o n o r t h i n g w i t h o u t r e g a r d t o th e v a l u e s a s s o c i a t e d to th o s e c h a r a c t e r i s t i c s . Normative knowledge, by c o n t r a s t , i s i n f o r m a ti o n about v a l u e s ( t h e goodness and badness o f the characteristics). P r e s c r i p t i v e knowledge i s th e s o l u t i o n t o a given problem and r e l a t e s th e normative t o t h e p o s i t i v e ( 6 5 ) . Although o f t e n f o r g o t t e n , i t should be re c o g n i z e d t h a t i t i s p o s s i b l e (and n e c e s s a r y ) t o g e n e r a t e a l l t h r e e kinds o f knowledge in an o b j e c t i v e fashion. The b a s i c p r oc ed ur es o f s c i e n t i f i c r e a s o n i n g i n s u r e t h a t knowledge i s o b t a i n e d o b j e c t i v e l y . proposed by Glenn Johnson (6 5 ) . Four t e s t s o f o b j e c t i v i t y have been The f i r s t t e s t t h a t a model must pass is a t e s t o f l o g i c a l c o n s i s t e n c y . This t e s t i n s u r e s t h a t t h e g e n e r a t i o n o f knowledge from th e r e s e a r c h i s done in a manner c o n s i s t e n t w ith b a s i c l o g i c and t h e t h e o r i e s o f t h e d i s c i p l i n e s in v o l v e d . known as v a l i d a t i o n . It is alternatively The second t e s t i s one o f cor res pondence t o r e a l i t y . The model must be a b l e t o s i m u l a t e t h e b e h a v i o r o f th e r e a l system and make a c c u r a t e p r e d i c t i o n s . Johnson d e s c r i b e s t h i s as v e r i f i c a t i o n . The 81 t h i r d t e s t i s one o f c l a r i t y which i n s u r e s t h a t t h e model and i t s t h e o r i e s a r e u n d e r s ta n d a b le and unambiguous. W o r k a b i li t y i s t h e f i n a l t e s t . This t e s t i s concerned w ith t h e p r e s c r i p t i v e c a p a b i l i t y o f th e model and mea­ s u r e s i t s a b i l i t y t o s o lv e r e a l world problems. While t h e s e gene ra l g u i d e l i n e s may s e r v e as a framework f o r the r e a s o n i n g pr oc es s and i d e n t i f y th e i m p o r ta n t components r e q u i r e d t o o b t a i n c r e d i b i l i t y f o r t h e r e s u l t s , more d e t a i l e d guides a r e n e c e s s a r y t o a c t u a l l y d i r e c t the research. Gie re (45) p r e s e n t s a proc edu re which w i l l i n s u r e t h a t th e f o u r t e s t s o f o b j e c t i v i t y a r e f u l f i l l e d when us ing a computer s i m u l a t i o n model as a r e s e a r c h t o o l . Giere p e r c e i v e s a model as bei ng a t h e o r y o r a d e f i n i t i o n o f a system. A t h e o r e t i c a l h y p o th e s i s i s a c o n t i n g e n t s t a t e m e n t a s s e r t i n g t h a t some d e s i g n a t e d r e a l system f i t s th e d e f i n i t i o n o f th e system d e s c r i b e d by t h e th e o r y (model). The c o n s t r u c t i o n and t e s t i n g o f t h e o r e t i c a l hypo­ t h e s e s i s o f t e n t h e purpose o f u sin g a system s i m u l a t i o n model f o r once t h e t h e o r e t i c a l h y p o th e s i s i s j u s t i f i e d , t h e model can be used t o p r e ­ d i c t o r e x p l a i n how a system behaves. However, t h i s s t e p i s f r e q u e n t l y n o t e x p l i c i t l y r e co gn iz ed and t h e elements o f t h e argument used t o j u s t i f y t h e h y p o th e s i s a r e n o t c l e a r l y d e s c r i b e d . The argument w i l l c o n t a i n the c o n c l u s i o n and premises t h a t r e l a t e both t o t h e exper im ent and t o i t s results. The c o n c l u s i o n w i l l be t h e j u s t i f i c a t i o n o f th e h y p o t h e s i s o r i t s negation. The b a s i c elements o f t h e argument a r e t h e h y p o t h e s i s , t h e p r e d i c t i o n , t h e i n i t i a l c o n d i t i o n s and th e a u x i l i a r y as s um pt io ns . The t h a t some r e a l system f o ll o w s t h e d e f i n i t i o n o f t h e model. hypothesis is The p r e d i c t i o n d e s c r i b e s t h e o cc u rr en c e o f a p o s s i b l e s t a t e o f th e system a t an i n i d c a t e d ti m e . The i n i t i a l c o n d i t i o n s d e s c r i b e t h e s t a t e o f t h e system a t th e be gi nn ing o f t h e expe ri me nt . A u x i l i a r y as sumptions a r e a d d i t i o n a l 82 c h a r a c t e r i s t i c s o f t h e system o r i t s environment t h a t may be n e c e s s a r y t o conduct t h e expe rime nt. These elements a r e a l l n e c e s s a r y components t o t h e c o n s t r u c t i o n o f t h e argument. Giere d e s c r i b e s th e need t o form two arguments o r t o have two c o n d i t i o n s o f a good t e s t . Condit ion 1 t e s t s t o s e e i f t h e r e i s a c o n d i t i o n a l r e l a t i o n s h i p between t h e h y p o t h e s i s and t h e p r e d i c t i o n . I t in fe rs t h a t i f the a u x ilia ry a s s u m p ti o n s, i n i t i a l c o n d i t i o n s and h y p o t h e s i s a r e t r u e ( p r e m i s e ) , then a c o r r e c t p r e d i c t i o n w i l l l i k e l y follow (conclusion). The second c o n d i t i o n i n s u r e s t h a t an a l t e r n a t i v e t h e o r y would y i e l d a co m pl ete ly d i f f e r e n t p r e d i c t i o n with t h e same i n i t i a l c o n d i t i o n s and a u x i l i a r y as su mp ti on s. The two c o n d i t i o n s can be d e p i c t e d by th e f o l l o w i n g s t a t e m e n t s : Condi ti on 1: I f [H and IC and AA], then P. C on dit ion 2: I f [Not H and IC and AA], th en p ro ba bl y n o t P. P and IC and AA. Thus, H. where H = t h e o r e t i c a l h y p o th e s i s IC = i n i t i a l c o n d i t i o n s AA = a u x i l i a r y assumptions P * prediction The Giere g u i d e l i n e s o f a good t e s t should be u s e f u l t o model b u i l d e r s and u s e r s in t h a t t h e y w i l l f o r c e an e x p l i c i t s t a t e m e n t o f t h e h y p o t h e s i s b e i n g t e s t e d w ith th e model and i n s u r e t h a t t h e f o u r g e n e r a l t e s t s o f o b j e c t i v i t y are addressed. The j u s t i f i c a t i o n of t h e h y p o t h e s i s u s in g t h i s p r o c e d u r e w i l l r e q u i r e t h e p as sa ge o f t h e t e s t o f co rr es pon den ce t o 83 r e a l i t y through th e ex per im ent d e a l i n g w ith th e p r e d i c t i o n . The c l e a r d e f i n i t i o n o f t h e elements o f t h e argument and c o n d i t i o n I I w i l l meet th e r eq ui r e m en t s o f t h e t e s t o f c l a r i t y . The r i g o r o f t h e pro ced ur e w i l l f o r c e t h e r e s e a r c h t o ad d r e s s t h e t e s t o f i n t e r n a l c o n s i s t e n c y . 3.2 D e s c r i p t i o n o f t h e Actual System The system can be p e r c e iv e d t o c o n s i s t o f s e v e r a l major p a r t s o r com­ p o ne nt s. Such c h a r a c t e r i s t i c s as t h e l o c a t i o n o f p r o d u c t i o n , market p r i c e s , c o s t s o f p r o d u c t i o n , y i e l d s , t r e e growth and p e s t management problems a r e a l l v i t a l components o f th e system which sh ould be r e l e v a n t t o a model building e x erc ise. Before th e model can be c o n s t r u c t e d t h e s e components needed t o be unde rs too d and p r e c i s e l y d e s c r i b e d . P r o du ct io n System The p r o d u c ti o n system o f Michigan a p p l e o r c h a r d s i s a complex one. Apple p ro d u c ti o n in Michigan i s most h e a v i l y c o n c e n t r a t e d in t h r e e c o u n t i e s , Kent, B e r r ie n and Van Buren, a l th o u g h o r c h a r d s a r e common th r o u g h ­ o u t t h e o t h e r c o u n t i e s b o r d e r in g Lake Michigan. The v a r i e t i e s which have t h e h i g h e s t number o f t r e e s in t h e s t a t e a r e Red D e l i c i o u s w it h 27.4 p e r c e n t o f th e s t a t e ' s t o t a l , Jona tha n w it h 18.1 p e r c e n t , Golden D e li c io u s w ith 9 . 8 p e r c e n t and McIntosh with 9 . 6 p e r c e n t . However, when t h e p e r ­ centage of the s t a t e ' s t o t a l production i s considered, the v a r i e t a l ran k in g i s q u i t e d i f f e r e n t because o f t h e i n f l u e n c e o f y i e l d s . McIntosh e n jo ys a high p r o d u c t i v i t y in Michigan w h i l e Red D e l i c i o u s s u f f e r s from e rra tic yields. The l a r g e s t p e r c e n t a g e o f t h e s t a t e ' s p r o d u c t i o n i s ac co unt ed f o r by J o na th an s (24.3%), foll owe d by D e l i c i o u s (20.7%), McIntosh (17.5%) and Northern Spy (8.6%) ( 2 4) . H i s t o r i c a l l y , about 40 p e r c e n t o f t h e Michigan crop goes f o r f r e s h 84 uses and th e r e s t i s p ro c e s s e d . Of t h e amount p r o c e s s e d , a p pr o xi m at e ly 30 p e r c e n t i s canned, 40 t o 50 p e r c e n t goes t o j u i c e and 20 t o 25 p e r c e n t ends up in f r o z e n p r o c e s s i n g . In t h e l a s t few y e a r s , j u i c e has become more and more i m p o r ta n t (2 4 ) . During t h e te n y e a r p e r i o d from 1969 t o 1978, t h e Michigan season av era ge p r i c e f o r a l l a p p l e s a l e s averaged 6.01 c e n t s p e r pound w ith a standard d eviation o f 2.24. For t h e same time p e r i o d , th e f r e s h con­ sumption s a l e s p r i c e averaged 8 .7 0 c e n t s p e r pound w i t h a s t a n d a r d d e v i a t i o n o f 2.40 w h i l e th e a l l p r o c e s s i n g p r i c e had a mean o f 4 .2 5 c e n t s p e r pound and a s t a n d a r d d e v i a t i o n o f 2 . 1 9 . R e l a t i v e l y , th e a g g r e g a t e d a t a i n d i c a t e t h a t t h e f r e s h ma rket e x p e r i e n c e s much more p r i c e v a r i a t i o n than does th e p r o c e s s i n g market (2 4 ) . The farm v al ue o f t h e Michigan ap p le crop was $67,640,000 in 1978. Of t h a t t h e f r e s h ma rket s a l e s accounted f o r 56. 9 p e r c e n t . Ju ice pro­ c e s s i n g c o n t r i b u t e d 15. 8 p e r c e n t o f th e s t a t e ' s t o t a l v al u e w h il e canned and f ro z e n p r o c e s s i n g r e s p e c t i v e l y g e n e r a t e d 15.5 p e r c e n t and 12.5 p e r c e n t o f t o t a l v a l u e ( 24 ). The b e s t a v a i l a b l e i n f o r m a t i o n on t h e c o s t s o f pr od uci ng one a c r e o f a p p l e s in Michigan e s t i m a t e s t h a t t o t a l c o s t s p e r a c r e a r e ab out $1,040. Of t h a t , about 30 p e r c e n t a r e i n overhead c h a r g e s , 40 p e r c e n t in th e growing o p e r a t i o n and 30 p e r c e n t in h a r v e s t i n g a c t i v i t i e s . These e s t i m a t e s a r e f o r a semi-dwarf o r c h a r d w it h a d e n s i t y o f 108 t r e e s p e r a c r e and an a v er a g e y i e l d o f 400 b u s h el s p e r a c r e . The p r i c e s a r e l i s t e d in 1978 d o l l a r s (2 4 ). There a r e a number o f p e s t s which a r e p r e s e n t in commercial o r c h a r d s where p e s t s a r e d e f i n e d t o be i n s e c t s , d i s e a s e s and m i t e s . The most common p e s t s which cause problems a r e European red m i t e s , c li m bi ng cutworms, 85 San J o s e s c a l e a p h i d s , t a r n i s h e d p l a n t bu gs , o b li q u e - b a n d e d l e a f r o l l e r , g r e e n f r u i t w o r m , plum c u r c u l i o , red -banded l e a f r o l l e r , w h i t e ap p le l e a f h o p p e r , c o d l i n g moth, t e n t i f o r m l e a f m i n e r , a p p l e maggot, powdery mildew, f i r e b l i g h t , and scab (66). Conventional c a l e n d a r c o n t r o l programs can app ly from 12 t o 15 s p r a y s a y e a r and p e r a c r e p e s t management c o s t s can r ea c h extremes o f $600 p e r a c r e . Control c o s t s may be h i g h e r in Michigan th an in o t h e r r e g i o n s due t o t h e c l i m a t e and problems w i t h abandoned o r c h a r d s . Chemicals de sig ne d t o c o n t r o l s p e c i f i c p e s t s a r e o f t e n a p p l i e d t o g e t h e r i n "cock­ t a i l " s p r a y s which d e c r e a s e machinery and l a b o r c o s t s b u t which might e x a c e r b a t e problems by im pacting on n a t u r a l p r e d a t o r s and s eco nd ary p e s t s o r by promoting t h e development o f r e s i s t a n c e . Three o f t h e most i m p o rt a n t p e s t s o f t h e e n t i r e complex a r e s c a b , c o d l in g moth and European red m i t e s . ca se s tu d y . These p e s t s w i l l s e r v e f o r th e Scab i s a fungus and i s an e a r l y season problem. Codling moth i s an i n s e c t w ith high m i g r a t i o n p o t e n t i a l and u s u a l l y i s a l a t e s eason problem. somewhat Mites u s u a l l y s u r f a c e in t h e pre-bloom s t a g e and a r e unique due t o t h e complex o f n a t u r a l p r e d a t o r s which can p ro v id e e f fe c tiv e biological control. Both t h e m i te s and t h e m i te p r e d a t o r s can be a f f e c t e d by some f u n g i c i d e s a p p l i e d f o r scab c o n t r o l and by some i n s e c t i c i d e s used t o p r e v e n t i n f e s t a t i o n s o f c o d l i n g moth. Mites In Michigan a p pl e o r c h a r d s , one common p e s t t h a t has c o n s i d e r a b l e p o t e n t i a l f o r t h e a p p l i c a t i o n o f I n t e g r a t e d P e s t Management (IPM) s t r a t e g i e s i s t h e European red m i t e , Panonychus u l m i . Mites a r e common and d e s t r u c t i v e p e s t s o f a v a r i e t y o f p l a n t s i n c l u d i n g most deciduous fr u it trees. They use s ha r p mouth p a r t s t o p i e r c e p l a n t t i s s u e , suck up 86 sap and d e s t r o y t h e c h l o r o p h y l l . This r e s u l t s in a gray o r brown m o t t l i n g o f t h e f o l i a g e o r in t h e f o r m a t io n o f g a l l s o r growths. Plants or t h e i r f r u i t s a r e s t u n t e d , b u t in extreme c a s e s , d e f o l i a t i o n can o c c u r . In a p p l e s , m it e damage u s u a l l y r e s u l t s in s m a l l e r and d i s c o l o r e d f r u i t which can impact on both t h e q u a l i t y and t h e q u a n t i t y o f t h e h a r v e s t . The l i f e c y c l e o f t h e m i te can be completed in 15 o r 20 days under f a v o r a b l e c o n d i t i o n s and s i n c e a c t i v e females may l a y a few eggs each day f o r abo ut 2 weeks, p o p u l a t i o n s can i n c r e a s e q u i t e r a p i d l y . Mites f l o u r i s h d ur in g warm, dry we at h e r and do n o t g e n e r a l l y reach s e r i o u s l e v e l s d u r in g c o o l , wet seasons (103, pp. 6 6 - 70 ) . The m i te s o v e r w i n t e r in eggs l a i d on th e u n d e r s i d e o f tw ig s and small b r a n c h e s. At bloom immature m i t e s emerge from th e w i n t e r eggs and a d u l t s soon become a c t i v e on t h e a p pl e l e a v e s . There can be as many as 6 t o 8 g e n e r a t i o n s a se as on and p o p u l a t i o n s can r ea c h as high a s 100 m i t e s p e r l e a f in June t o August. In th e f a l l , th e m i te s r e t u r n t o t h e t r e e base o r ground l i t t e r t o o v e r w i n t e r ( 31 ). The p o t e n t i a l f o r IPM programs in mite c o n t r o l e x i s t s s i n c e a number o f n a t u r a l p r e d a t o r s a r e common in commercial o r c h a r d s . These in c lu d e a predaceous black l a d y b i r d b e e t l e , S t e t h o r u s punctum, and predaceous m i t e s such as Amblyseius f a l l a c i s , Agistemus f l e s c h n e r i and Z e t z e l l i s mali (3 1 ) . Of t h e s e t h e most i m p o r ta n t i s Amblyseius f a l l a c i s . These p r e d a t o r s have the c a p a b i l i t y o f co m pl ete ly c o n t r o l l i n g th e p l a n t f e e d i n g m i t e s in some y e a r s and s i n c e the y may r e a c t d i f f e r e n t l y th a n th e m it e p e s t s t o c e r t a i n p e s t i c i d e d o s a g e s , th ey may complement a s p r a y program des ig ne d t o ta k e advant age o f t h e i r p r e d a t i o n . The com­ b i n a t i o n o f reduced dosages and n a t u r a l p r e d a t i o n may r e s u l t in s u b s t a n t i a l savings. 87 While m i t i c i d e a p p l i c a t i o n s may only be made two o r t h r e e times a s e a s o n , t h e i r m a t e r i a l s c o s t a r e q u i t e high and can acc ount f o r as much as 20-30% o f t h e annual c o s t f o r p e s t control (31). Two f u l l dose a p p l i c a t i o n s o f c a r z o l (2 l b s / a c r e ) would c o s t a p p r o x im a te ly $ 6 5 / a c r e i f carzol could be purchased f o r about $16.50 p e r pound. Some m i t i c i d e s a p p l i e d a t reduced dosages w i l l be l e s s t o x i c t o the p r e d a t o r s tha n t o t h e mite p e s t s . Th is d i f f e r e n t i a l impact can be e xt re m el y b e n e f i c i a l s i n c e f u l l dose a p p l i c a t i o n s d i s r u p t t h e b i o l o g i c a l c o n t r o l because t h e p e s t p o p u l a t i o n s w i l l r e c o v e r much f a s t e r from most chemical t r e a t m e n t s than th e p r e d a t o r p o p u l a t i o n s . I t s h ou ld be p o s s i b l e t o ta k e advant age o f t h i s d i f f e r e n t i a l impact and t o promote a p r e d a t o r / p r e y r a t i o t h a t w i l l allo w more b i o l o g i c a l c o n t r o l t o oc cu r than what would r e s u l t when both p o p u l a t i o n s a r e s u b s t a n t i a l l y reduced from a f u l l strength application. The use o f t h e s e m i t i c i d e s a t reduced dosages pla y an im p o r ta n t r o l e in IPM s t r a t e g i e s desig ned t o c o n t r o l s p i d e r m i t e s . While m i t i c i d e s u s u a l l y do n o t e f f e c t i v e l y c o n t r o l o t h e r p e s t s , t h e p e s t i c i d e s a p p l i e d t o c o n t r o l such p e s t s as a p pl e s c a b , powdery mildew, c o d l i n g moth, plum c u r c u l i o , ap p l e maggot and redbanded l e a f r o l l e r can d i s r u p t the p o p u l a t i o n s o f t h e m i te p e s t s a n d / o r t h e i r p r e d a t o r s . Once a g a i n , th e p e s t s and p r e d a t o r s may r e a c t d i f f e r e n t l y t o c e r t a i n c h e m ic a ls , so t h a t i t i s e s s e n t i a l f o r t h e s u c c e s s o f IPM s t r a t e g i e s t h a t a l l p e s t i c i d e s be s e l e c t e d w i t h a r e c o g n i t i o n o f t h e i r both th e m it e p e s t s and th e mite p r e d a t o r s . impact on Those chem icals which a r e l e s s t o x i c on th e p r e d a t o r s a r e g e n e r a l l y encouraged f o r use in IPM spray s c h e d u le s (31). Scab The most im p or ta n t d i s e a s e o f a p p l e s in th e humid-temperate c l i m a t e s 88 i s ap pl e s c a b , a fungus caused by V en tu ria i n a e q u a l i s . The fungus o v e r ­ w i n t e r s in f a l l e n i n f e c t e d l e a v e s w ith p e r i t h e c i a being produced d u r in g t h e w i n t e r in t h e s e l e a v e s . By s p r i n g , th e p e r i t h e c i a c o n t a i n mature a s c o s p o r e s which a r e th e primary s ou rc e o f inoculum f o r th e d i s e a s e each year. Rain i s e s s e n t i a l f o r t h e d i s c h a r g e o f t h e s p o r e s which once d i s c h a r g e d , a r e c a r r i e d by a i r c u r r e n t s t o a d j a c e n t t r e e s , b r a n c h e s , and fruit. Within a few hours upon l a n d i n g , th e s p o r e s g erm in ate and cause i n f e c t i o n s i f th e y s t a y wet. The r a t e a t which th e s p o r e s g erm in ate and r e s u l t in i n f e c t i o n s i s p a r t i a l l y det ermined by t h e te m p e r a t u r e and th e length of the wetting period. Dis cha rge s o f primary as c o s p o r e s may c o n t i n u e two t o f o u r weeks a f t e r p e t a l f a l l bu t th e y u s u a l l y a r e a l l gone by the f i r s t co v er s t a g e o f t h e development. Primary scab i n f e c t i o n can a l s o r e s u l t in t h e p r o d u c t i o n o f secondary spores. Secondary s p o r e s , o r con id i a , can o c c u r from 7 t o 18 days a f t e r a primary scab i n f e c t i o n , depending upon t h e te m p e r a t u r e range in t h e time p e r i o d f o ll o w i n g th e i n i t i a l i n f e c t i o n . Conidia a r e u s u a l l y s p r e a d by dropping o r s p l a s h i n g w at er b u t can be wind borne as w e l l . c o n i d i a do have a l e s s e r im pa ct , though. i n f e c t nearby f r u i t and f o l i a g e . Wind borne C o n id i a , t h e r e f o r e , g e n e r a l l y I t i s a m a t t e r o f d i s c u s s i o n as t o whe ther o r n o t c o n i d i a r e q u i r e a s h o r t e r w e t t i n g p e r i o d f o r an i n f e c t i o n t o o c c u r (21). Apple scab can r e s u l t in i n f e c t e d f r u i t which u s u a l l y must be c u l l e d o r s o ld f o r j u i c e (no scab i s p e r m i t t e d i n U.S. U t i l i t y w hi le i n t e r m e d i a t e g r a d e s pe rm i t a d e f e c t a r e a o f 1/4 inch in d i a m e t e r ) . I t can a l s o cause e a r l y f r u i t and l e a f drop t h a t may s e r i o u s l y a f f e c t y i e l d s . Trees s e r ­ i o u s l y d e f o l i a t e d f o r two o r t h r e e c o n s e c u t i v e y e a r s a r e weakened and s u s c e p t i b l e t o low te m p e r a t u r e damage. I f th e scab i n f e c t i o n i s s e v e r e i n e a r l y summer, f l o w e r bud p ro d u c ti o n i s o f t e n poor t h e f o l l o w i n g season 89 and t h e crop can be l o s t f o r two y e a r s . In a d d i t i o n t o th e l o s s e s i n c u r r e d from q u a l i t y damage and r e d u c t i o n s in y i e l d s , in many i n s t a n c e s growers who s u f f e r a g r e a t e r th a n 10% i n f e c t i o n r a t e must pay th e c o s t s o f s o r t i n g t h e undamaged f r u i t from th e damaged. Common c o n t r o l p r a c t i c e s f o r a p p l e scab in v o l v e t h e use o f f u n g i c i d e s p r a y s d u r in g t h e p e r i o d o f primary as c o s p o r e p r o d u c t i o n i n s p r i n g and e a r l y summer. Spray programs a r e o f t e n s e l e c t e d from one o f t h r e e d i s t i n c t approac hes t o c o n t r o l l i n g ap pl e scab: single application treatm ent, a c a l e n d a r based p r o t e c t i v e s pr ay program and a p o s t - i n f e c t i o n IPM program. The t h r e e g e n e r a l approac hes a r i s e from d i f f e r e n c e s i n t h e p e r ­ formances o f c l a s s e s o f ch e m ic a ls . The s i n g l e a p p l i c a t i o n t r e a t m e n t employs a chemical t r e a t m e n t e a r l y in t h e se ason ( gre en t i p ) t h a t p r o t e c t s new growth from scab i n f e c t i o n f o r s e v e r a l weeks. Late s eas on c o n t r o l can then be o b t a i n e d from a p r o t e c t i v e c a l e n d a r s pr ay program o r a p o s t - i n ­ f e c t i o n IPM program. The p r o t e c t i v e c a l e n d a r s p r a y program in v o l v e s t h e use o f ch em ic a ls which must be a p p l i e d in 5 t o 14 day i n t e r v a l s to i n s u r e ad eq ua te c o n t r o l o f a p p l e sca b. This time i n t e r v a l w i l l depend upon t h e chemical compound u s e d , t h e dosage a p p l i e d and t h e p a r t o f the season t h a t i t i s in t e n d e d t o p r o t e c t . The p o s t - i n f e c t i o n IPM program employs ch em ic a ls which have t h e c a p a c i t y t o e r a d i c a t e any i n f e c t i o n which s t a r t e d 2 to 3 days e a r l i e r . These c h e m i c a l s , r a t h e r th a n being a p p l i e d a t a p r ed et er m i ne d time o r a f i x e d time i n t e r v a l t o p r o t e c t th e o rc h ar d regard less of the in fe c tio n p o te n tia l (like ^ f i r s t two approa ch es d o ) , a r e s p ray ed on ly when i n d i c a t i o n s o f d i s e a s e oevclopment have been ob­ se rv ed o r th e w ea th e r c o n d i t i o n s s u i t a b l e f o r an i n f e c t i o n p e r i o d have been e x p e r i e n c e d . I t s ho ul d be noted however, i f i t r a i n s 2 days in a row, i t may n o t be p o s s i b l e t o c o v e r th e o r c h a r d in time t o i n s u r e t h a t t h e ch em ic a ls e r a d i c a t e t h e s p o r e s . 90 In g e n e r a l , t h e c o n t r o l measures f o r a p p l e scab a r e aimed a t d i s ­ r u p t i n g th e development o f t h e a s c o s p o r e s i n t o scab i n f e c t i o n s . I t i s known t h a t l e a f w e t t i n g by r a i n i s an a b s o l u t e r e q u ir e m e n t f o r s i g n i f i c a n t ascospore re le a s e . The l e n g t h o f l e a f wetn es s (number o f h o u r s ) , th e te m p e r a t u r e d u r i n g t h e w e t t i n g p e r i o d , t h e r e l a t i v e humidity and t h e l e v e l o f incoculum p r e s e n t a r e key d e t e r m i n a n t s o f i n f e c t i o n p e r i o d s . Infor­ mation on th e r e l a t i o n s h i p between scab i n f e c t i o n , t h e l e n g t h o f t h e w e t t i n g p e r i o d and t h e t e m p e r a t u r e has been i n c o r p o r a t e d i n t o t h e M i ll s t a b l e which can be used t o i d e n t i f y when w ea th e r c o n d i t i o n s have been s u i t a b l e f o r t h e completion o f t h e i n n o c u l a t i o n and i n c u b a t i o n s t a g e s o f t h e fungus and an i n f e c t i o n might o cc u r . The M i l l s t a b l e has been used in many sp ray programs t o p r e d i c t when scab i n f e c t i o n p e r i o d s have occurred. However, t h e M i l l s t a b l e assumes t h a t a high l e v e l o f inoculum a r e p r e s e n t which pro ba bl y does n o t r e p r e s e n t t h e s i t u a t i o n in most commercial o r c h a rd s (67). In fo r m at io n i s a l s o a v a i l a b l e on t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f a s co s p or e p r o d u c t i v i t y . Knowledge on t h e g en er a l p a t t e r n o f t h e p e r c e n t a g e d e p l e t i o n o f a s c o s p o r e s from o v e r w in te r e d l e a v e s can be used t o d i r e c t when p r o t e c t i v e s p r a y s s hou ld be a p p l i e d t o av o id any dangers o f scab i n f e c t i o n s . However, complete e p i d e m i o l o g i c a l u n d e r s t a n d i n g o f t h e d i s e a s e i s s t i l l lacking. The development o f economic c o n t r o l programs has r e s u l t e d more from t h e emergence o f e f f i c i e n t f u n g i c i d e s than from e p i d e m i o l o g i c a l advances (67). G i l p a t r i c k and S zko lni k have concluded a r e c e n t a r t i c l e with th e following note: In fo r m at io n on t h e r e a l impact o f measured incoclum p o t e n t i a l ( s p o r e d i s c h a r g e and dose in a i r ) in r e l a t i o n t o scab p o t e n t i a l , dosage r es p o n s es o f f u n g i c i d e s , c h o i c e o f f u n g i c i d e s , and ti m in g o f sp ra y s i s v i r t u a l l y n o n - e x i s t e n t . Thus, i t i s i m p o s s ib l e and, 91 inde ed , hazardous a t t h i s time t o i n t e r p r e t inoculum p o t e n t i a l e s t i m a t e s in terms of p r a c t i c a l s p r a y recommendations e x c e p t in broad and c o n s e r v a t i v e ways (67). Codling Moth The c o d l i n g moth, L a s p e y r e s i a po mo n el la, i s a p e s t common t o wherever a p p l e s a r e grown in t h e world. I t was in t r o d u c e d t o t h e United S t a t e s from s o u t h e a s t e r n Europe be gi nn in g in t h e middle o f t h e 18th c e n t u r y . By th e 1 8 8 0 ' s , th e co d l in g moth had become a major p e s t c a us in g n e a r l y t o t a l l o s s in some a r e a s w h il e d e s t r o y i n g some 20% o f th e f r u i t in t h e n o r t h e r n a p p l e and p e a r prod ucin g a r e a s . Codling moths f r e q u e n t l y a t t a c k a p p l e , p e a r , En g li sh w a ln u t , q u i n c e , c r a b a p p l e , hawthorn and w il d a p p l e . Codling moths o v e r w i n t e r under t h e b ar k o r in t h e ground in w a t e r ­ p r o o f cocoons. i n t o pupae. In Apr il o r May, t h e l a r v a e which have o v e r w i n t e r e d change A f t e r about f o u r t o s i x weeks o f c o o l , s p r i n g w e a t h e r , th e pupae s t a g e comes t o a c l o s e and an a d u l t moth emerges from t h e cocoon. U su a lly male moths emerge f i r s t , abo ut a week e a r l i e r tha n t h e fe m a le s . In Michigan, emergence commences in l a t e May and ex te n ds u n t i l e a r l y July. O v i p o s i t i o n be gi ns when t h e te m p e r a t u r e s a r e above 60° in the a f t e r n o o n s and e a r l y e v e n i n g s . fruit itself. Eggs can be l a i d on l e a v e s , twigs and the In t h e f i r s t g e n e r a t i o n , eggs normally ta ke 12 t o 14 days t o ha tc h but w it h warmer we at he r i t may be q u i c k e r . F i r s t generation l a r v a e e n t e r th e f r u i t ov er a p e r i o d o f t h e n e x t f i v e t o s i x weeks. The l a r v a e u s u a l l y e n t e r t h e f r u i t th ro ugh t h e ca l y x end and e a t t h e i r way t o t h e c e n t e r o f th e f r u i t t o f e e d on t h e se eds and c o r e . S t i n g s can oc cu r on t h e f r u i t when a l a r v a b i t e s i n t o a f r u i t t r e a t e d w it h an i n s e c t ­ i c i d e and d i e s . A f t e r th e l a r v a e have ha t c h e d and b e f o r e th e y have e n t e r e d th e f r u i t , t h e young l a r v a e a r e e x t re m e l y v u l n e r a b l e and s u f f e r high l o s s e s due t o wind, r a i n and p r e d a t i o n . This i s one c r i t i c a l p o i n t in th e 92 l i f e c y c l e f o r c o n t r o l measures because th e l a r v a e must be stopped from r e a c h i n g t h e f r u i t and ca u s in g i n j u r y . The c a t e r p i l l a r s w i l l fe e d in th e f r u i t f o r a bo ut t h r e e weeks and th e n tu n n e l o u t t o f i n d a p l a c e t o s p in t h e i r cocoons. Around 25% o f t h e c a t e r p i l l a r s w i l l remain in t h e i r cocoons u n t i l t h e f o l l o w i n g s p r i n g . The rem ai nde r w i l l become pupae w i t h i n f o u r t o s i x days. In about two weeks t h e pupae s t a g e e n d s , t h e new a d u l t s w i l l emerge and and the process continues. can o c c u r ( 9 8 ) . In some warm c l i m a t e s , as many as f i v e g e n e r a t i o n s In Michigan, i t i s n o t uncommon f o r a second and a p a r t i a l t h i r d g e n e r a t i o n t o be observed (111). In Michigan th e p o t e n t i a l f o r b i o l o g i c a l c o n t r o l o f th e c o l d i n g moth i s not h ig h . There a r e a number o f n a t u r a l enemies such as a b ar co n i d wasp, A s c o g a s t e r e a r p o c a p s a e , bu t th e y a r e i n c a p a b l e o f p r e v e n t i n g t h e p e s t p o p u l a t i o n from r ea c h in g i n t o l e r a b l e l e v e l s . I t i s r a r e t h a t in unsprayed o r c h a r d s t h e r a t e o f p a r a s i t i z a t i o n would exceed 10% t o 20%. I t i s n e c e s s a r y t o r e l y on some form o f chemical t r e a t m e n t s t o i n s u r e c o n t r o l o f the c o d l i n g moth (111). P r e v e n t i v e s pr ay programs o f t e n i n v o l v e around a h a l f dozen co ve r s p r a y s spaced about two weeks a p a r t d ur in g t h e summer months when th e c o d l i n g moth i s u s u a l l y most a c t i v e . A high q u a l i t y f r u i t i s u s u a l l y in s u r e d w i t h t h e s e programs b u t th e y do i n t r o d u c e some a d d i t i o n a l problems. By n o t m o n i to r in g o r a t t e m p t i n g t o p r e d i c t th e phenology o f t h e p e s t , the p r e v e n t i v e s p r a y programs o f t e n r e s u l t in more s p r a y a p p l i c a t i o n s tha n a r e i n c u r r e d in IPM programs. This can i n c r e a s e c o n t r o l c o s t s and by i n t r o d u c i n g more chemicals in t h e o r c h a r d , the ra te of re s is ta n c e b u ild ­ up i s f a s t e r and t h e p r o b a b i l i t y t h a t t h e n a t u r a l p r e d a t o r complex o f o t h e r f r u i t p e s t s w i l l be d i s r u p t e d i s i n c r e a s e d . 93 By combining b i o l o g i c a l and environmental m o n i t o r i n g , p r e d i c t i o n s can be made about th e phenology o f t h e co d l in g moth and s p r a y s can be timed t o be most e f f e c t i v e . The number o f s p r a y s can p o t e n t i a l l y be reduced in most s eas on s by b e t t e r ti m i n g . The b i o l o g i c a l m o n i to r in g performed with t h e use o f pheromone t r a p s w i l l i n d i c a t e the p o p u l a t i o n d e n s i t y o f a d u l t s which a r e a c t i v e . I t i s known t h a t 210 d egree days (base 50°) a f t e r th e emergence o f th e a d u l t s , t h e t a r g e t l a r v a e p o p u la ti o n w i l l be o bs er v ed . I t i s then p o s s i b l e t o develop economic t h r e s h o l d s f o r th e number o f c a p t u r e d a d u l t s t h a t w i l l i n d i c a t e when a s p r a y should be a p p l i e d t o e f f e c t i v e l y time t h e chemical t r e a t m e n t . The economic t h r e s h o l d s can be a d j u s t e d by t h e number o f degree days t h a t have accumulated t o match th e r e l a t i o n s h i p between t h e number o f g e n e r a t i o n s ex p ec te d and t h e amount o f damage a n t i c i p a t e d . The economic t h r e s h o l d s should be s e t a t a l e v e l t h a t w i l l bal an ce t h e c o s t s o f t h e s p ra y with the val ue o f th e damage avoided by th e t r e a t m e n t . Phe nolo gic al Stage s o f Apple Trees The i m p o r ta n t s t a g e s o f t r e e growth and f r u i t development can be d e s c r i b e d by s e v e r a l benchmark e v e n t s . Common benchmarks a r e green t i p , t i g h t c l u s t e r , p i n k , bloom, p e t a l f a l l , and f r u i t s e t . Green t i p occur s when t h e f i r s t green t i s s u e b eg in s t o push th ro ugh th e bud s c a l e s w hi le t i g h t c l u s t e r i s observed when t h e sp u r l e a v e s a r e showing b u t n o t f u l l y expanded, and t h e f lo w e r buds a r e exposed b u t s t i l l t i g h t l y clustered. In p i n k , th e f l o w e r buds have s e p a r a t e d in th e c l u s t e r and th e pink u n d e r s i d e s o f th e p e t a l s a r e showing. has a r r i v e d . fallen. When th e f l o w e r s open, bloom In p e t a l f a l l , a b o u t t h r e e - f o u r t h s o f t h e p e t a l s have F i n a l l y , f r u i t s e t t r a n s p i r e s when t h e r e c e p t a c l e s o f th e s u c c e s s - f u l l y p o l l e n a t e d f lo w er s have begun t o swell and t h e u n p o l l e n a t e d flo w er s 94 have begun t o ye l lo w and drop ( 8 ) . The t r e e s w i l l pass from one s t a g e t o t h e o t h e r depending on th e passa ge o f p h y s i o l o g i c a l time u s u a l l y r e l a t e d t o t h e acc umulation o f degree days. 3.3 D e s c r i p t i o n o f th e Sim u la ti on Model To a n a l y z e t h e problem i d e n t i f i e d in a manner which would pe r m i t th e achievement o f t h e s t a t e d o b j e c t i v e s , a s t o c h a s t i c Monte Carlo s i m u l a t i o n model was s e l e c t e d as t h e a p p r o p r i a t e a n a l y t i c a l approach. The a n a l y s i s o f t h e problem n e c e s s i t a t e s th e g e n e r a t i o n o f i n f o r m a t i o n on th e c um u la ti ve p r o b a b i l i t y d i s t r i b u t i o n s o f n e t revenue a s s o c i a t e d with each p e s t management s t r a t e g y . This r e q u i r e s t h a t t h e performance o f t h e v a r i o u s s t r a t e g i e s be mo nitored over a number o f d i f f e r e n t s t a t e s o f nature. U n f o r t u n a t e l y t h i s d a t a i s not a v a i l a b l e from f i e l d o b s e r v a t i o n s nor i s i t l i k e l y t h a t an ex pe ri m en t could be de si gne d t o econo mic ally p r ov id e i t . F u rth erm ore , even i f t h e expenses and t h e time ho riz o n were n o t a problem, i t would be d i f f i c u l t t o perform v a l u a b l e s e n s i t i v i t y a n a l y s i s w i t h f i e l d ex p e r i m e n t s. A s i m u l a t i o n model can be used t o conduct t h e expe ri men ts n e c e s s a r y t o pr ov id e t h i s in f o r m a ti o n w hi le s u b s t a n t i a l l y r ed uc i n g both t h e time and t h e c o s t s i n v o l v e d . In t h i s c a s e , o f t h e f o u r adva nt age s o f systems s i m u l a t i o n models i d e n t i f i e d by Dent and B l a c k i e , o nl y t h e second one i s irrelevant. There ap p ea rs to be no need t o s tu dy any systems t h a t do not c u r r e n t l y e x i s t . However, a model can be used t o pr o v id e i n f o r m a ti o n in a ti m e l y and economical f a s h i o n and t h e c o n s t r u c t i o n o f t h e model w i l l f o r c e a c r i t i c a l review o f th e c u r r e n t knowledge o f t h e system. System Bounds The system t o be modelled i s one which must have some l i m i t s imposed 95 upon i t . I t w i l l c o n s i s t o f a t e n a c r e o r c h a r d block w it h semi-dwarf r o o t s t o c k p l a n t e d a t a d e n s i t y o f about 100 t r e e s p e r a c r e . The geo­ g r a p h i c a l l o c a t i o n o f t h e or ch ar d w i l l be s p e c i f i e d t o be Ea st Lansi ng, Michigan. moth. The system w i l l i n c l u d e t h r e e p e s t s : s c a b , red m i te s and co d l in g The n a t u r a l p r e d a t o r s o f th e m i te s w i l l be p r e s e n t in t h e system as w e l l . The remaining complex o f p e s t s and p r e d a t o r s a r e n o t c o n s i d e r e d . The f r u i t produced in th e o rc h ar d w i l l be a s s i g n e d t o t h r e e p o s s i b l e u s e s : f r e s h m a rk e t, p r o ce s s ed market and th e j u i c e mark et . The p r o p o r t i o n going t o each use i s s e t equal t o t h e s t a t e w i d e te n y e a r a v e r a g e . However, as p e s t damage o c c u r s , t h e f r u i t can be r e a s s i g n e d . Significant damage from t h e c o d l i n g moth i s assumed t o r e s u l t i n t h e i n f e c t e d f r u i t being c u l l e d . Three y i e l d l e v e l s w i l l be anal yze d with t h e model: 900 b u s h el s p e r a c r e , 500 b u s h el s p e r a c r e and 250 b u s h el s p e r a c r e . With th e e x c e p t i o n o f t h e market p r i c e s and t h e p o s s i b l e i n - m i g r a t i o n o f a d u l t c o d l i n g moth the model w i l l c o n s i d e r th e system as b ei ng c l o s e d . No e x t e r n a l i t i e s w i l l be in c lu d ed in t h e a n a l y s i s . Model Components This model can be d e s c r i b e d in terms o f i t s major components. s t r u c t u r e o f t h e model i s d i s p l a y e d in Figur e 1. be c l a s s i f i e d i n t o seven c a t e g o r i e s . The The components can There a r e components which a r e des ig n ed t o f a c i l i t a t e th e i n t r o d u c t i o n o f t h e u s e r s u p p l i e d environmental inputs. These i n p u t s a r e t h e mean o f y i e l d d i s t r i b u t i o n s ^ and t h e i n i t i a l c o d l i n g moth p o p u l a t i o n d e n s i t y . There a r e components des ig n ed t o g e n e r a t e t h e s t o c h a s t i c environmental in p u t s which in c lu d e p r i c e s , y i e l d s , w e a t h e r , m it e emergence d a t e s and t h e m it e i n i t i a l p o p u l a t i o n d e n s i t y . One s e r i e s ^Yields a r e randomly g e n e r a te d us ing p r o b a b i l i t y d i s t r i b u t i o n s based on h i s t o r i c a l da ta b u t us in g the mean s u p p l i e d by t h e model u s e s . Figu re 1 . Model Components. Strategies Generation of Stochastic Variables Mite Population Initial Mite and Mite Predator Populations User Supplied Initial Moth Population Density: High 1/100; Medium 1/1000; Low Emergence Dates for Mites and Predators Control Control Control Predator Population Mite Kill Function 1 / 10,000 Larvae/ Apples Avg. Daily Temperature Codling Moth Population Function Daily Pre­ cipitation User Supplied Mean for Pro­ bability Dis­ tribution for Per Acre Yields: High900 bu; Med­ ium-500 bu; Low-250 bu Degree Days Accumulated Prior to 3/31 Yield Fresh Market Price-Proc. Market Price Juice Market Priee ii Surviving Populations Phenologlcal Development of Trees Damage Function Market Market Production Costs 97 of components s i m u l a t e s th e ph en o lo g ic al development and p o p u l a t i o n dynamics f o r t h e system. A f o u r t h c l a s s o f components implements th e d e c i s i o n r u l e s o f t h e management s t r a t e g i e s . There i s a n o t h e r group o f components which h an d le s t h e m o r t a l i t y f u n c t i o n s o f th e p e s t s and p r e d a t o r s when t he y a r e exposed t o th e chemical p e s t i c i d e s . The remaining two c l a s s e s deal w it h t h e e s t i m a t i o n o f p e s t damage and t h e c a l c u l a t i o n o f t h e n e t revenue. The season begi ns a t th e r i g h t supplied inputs. se as o n. o f F igu re 1 w ith t h e u s e r The s t o c h a s t i c el em en ts ar e then g e n e r a t e d f o r th e e n t i r e Each day, t h e growth o f p e s t s , p r e d a t o r s and t r e e s a r e s im u l a t e d . The d e c i s i o n r u l e s of th e c o n t r o l s t r a t e g i e s a r e implemented and when s p r a y s a r e a p p l i e d then th e p o p u la ti o n d e n s i t i e s a r e a d j u s t e d t o r e f l e c t th e m o r t a l i t y r a t e s . At t h e end o f t h e s e a s o n , damage, g r o s s revenue and n e t revenue a r e a l l c a l c u l a t e d . System Inp uts The i n p u t s in t h e system can be c a t e g o r i z e d i n t o enviro nm ent al and controllable. The env ironm ental i n p u t s , in t u r n , a r e e i t h e r s t o c h a s t i c or d eterm inistic. The s t o c h a s t i c enviro nm ent al i n p u t s a r e t h e i n i t i a l m it e and m it e p r e d a t o r p o p u l a t i o n d e n s i t i e s , t h e emergence d a t e s f o r t h e m it es and m i te p r e d a t o r s , t h e av era ge d a i l y te m p e r a t u r e and t h e d a i l y p r e c i p i t a t i o n , th e de gre e days accumulated p r i o r t o t h e end o f March f o r each s e a s o n , t h e y i e l d s , the ap pl e market p r i c e s and t h e random sampling error. The d e t e r m i n i s t i c environmental i n p u t s a r e t h e p r o d u c t i o n c o s t s , p r i c e s o f chemical i n p u t s , s c o u t i n g f e e s and t h e i n i t i a l p o p u l a t i o n d e n s i t y f o r t h e co d l in g moth. The l a t t e r i s u s e r s u p p l i e d as i s t h e mean o f t h e p r o b a b i l i t y d i s t r i b u t i o n f o r th e y i e l d s . The c o n t r o l l a b l e i n p u t s a r e t h e d e c i s i o n r u l e s o f t h e a l t e r n a t i v e p e s t management s t r a t e g i e s . The v a r i o u s r u l e s w i l l m on i to r d i f f e r e n t s t a g e v a r i a b l e s ( d e g r e e d a y s , 98 p e s t p o p u l a t i o n d e n s i t i e s , growth s t a g e s o f t r e e s , c a l e n d a r d a y s , p r e ­ c i p i t a t i o n , e t c . ) and a t d e s i g n a t e d v a l u e s f o r t h e s e v a r i a b l e s , a l t e r n a t i v e a c t i o n s w i l l be implemented. System Outputs The o u t p u t s o f t h e system can be d i v i d e d i n t o d e s i r a b l e and un­ d esirab le categories. The former a r e th e v a r i a b l e s which sh ou ld be maxi­ mized w h il e t h e l a t t e r a r e ones t h a t sh ou ld be minimized. The d e s i r a b l e o u t p u t s a r e th e n e t revenue w hi le examples o f th e u n d e s i r a b l e a r e the c o n t r o l c o s t s , t h e p e s t damage, th e q u a n t i t i e s o f chem icals a p p l i e d and t h e number o f t r i p s through th e o r c h a r d t o ap pl y s p r a y s . S t o c h a s t i c Elements The s t o c h a s t i c eleme nts o f t h e model have been g e n e r a t e d by t h e use o f a random p r o c e s s o r developed by King ( 72 ). In many c a s e s , t h e v a r i a b l e s have been g e n e r a t e d from m u l t i v a r i a t e p r o b a b i l i t y d i s t r i b u t i o n s which a l l o w t h e p r e s e r v a t i o n o f th e c o r r e l a t i o n s between t h e v a r i o u s e l e m e n t s. Such m u l t i v a r i a t e p r o b a b i l i t y d i s t r i b u t i o n s a r e c o n s t r u c t e d by f i r s t d e r i v i n g t h e marginal d i s t r i b u t i o n s f o r each v a r i a b l e from h i s t o r i c a l data. The c o r r e l a t i o n c o e f f i c i e n t s and t h e marginal d i s t r i b u t i o n s a r e the n merged t o c o n s t r u c t th e m u l t i v a r i a t e d i s t r i b u t i o n s . Two s e t s o f m u l t i v a r i a t e d i s t r i b u t i o n s were c o n s t r u c t e d f o r t h i s model. They a r e : 1) a d i s t r i b u t i o n g e n e r a t i n g v a l u e s f o r t h e appl e market p r i c e s and t h e p e r a c r e y i e l d ; and 2) a s e r i e s o f e i g h t d i s t r i b u t i o n s t o g e n e r a t e v a l u e s o f t h e avera ge d a i l y p r e c i p i t a t i o n and t h e d a i l y precipitation. There a r e e i g h t w ea th e r d i s t r i b u t i o n s , each one c o v e r i n g 21 days t o al lo w f o r seas on al v a r i a t i o n s i n t h e d i s t r i b u t i o n s and t o red ucce t h e number o f c o r r e l a t i o n s t o a manageable number. Each d a y ' s t e m p e r a t u r e 99 and p r e c i p i t a t i o n i s c o r r e l a t e d with t h e te m p e r a t u r e and p r e c i p i t a t i o n o f t h e day immediately pr e c e d in g i t . The Yield and F r o s t Components. The model has th e o p t i o n o f c a l c u l a t i n g t h e y i e l d in two manners. I t can be randomly g e n e r a t e d from a m u l t i v a r i a t e d i s t r i b u t i o n w ith the f r e s h and p r o c e s s e d a p p l e p r i c e s o r a c a l c u l a t i o n o f t h e f r o s t damage can be used t o reduce a p o t e n t i a l y i e l d t o t h e end o f season f i n a l e s t i m a t e . The former pro ced ur e m a i n t a i n s th e r e l a t i o n s h i p between the y i e l d and th e p r i c e s w h i l e i g n o r i n g th e r e l a t i o n between t h e f r o s t damage and the p e s t damage. The l a t t e r pr oc ed ur e i g n o r e s t h e c o r r e l a t i o n between the y i e l d and p r i c e s w h i l e i t p r e s e r v e s t h e r e l a t i o n s h i p between th e p e s t and f r o s t damage. The a l g o r i t h m used t o c a l c u l a t e th e f r o s t damage has no t been v a l i d a t e d o r v e r i f i e d . The random g e n e r a t i o n o f the y i e l d in v o l v e s th e use o f an h i s t o r i c a l s e r i e s o f p e r a c r e y i e l d s in th e S t a t e o f Michigan from t h e y e a r s 1970 t o 1979. The shape o f th e cum ula ti ve p r o b a b i l i t y d i s t r i b u t i o n d i s c e r n e d from t h e h i s t o r i c a l d a t a i s always p r e s e r v e d b u t can be s h i f t e d t o allow th e model t o s i m u l a t e t h e o r c h a r d a t t h r e e d i s t i n c t y i e l d l e v e l s . The mean o f th e d i s t r i b u t i o n can be s e t equal t o 250 b u s h el s p e r a c r e , 500 b u s h e l s p e r a c r e o r 900 b u s h e l s p e r a c r e . To e x e r c i s e t h e o p t i o n o f employing t h e a l g o r i t h m t o c a l c u a l t e the f r o s t damage, t h e s u b r o u t i n e FROST must be c a l l e d on a d a i l y b a s i s from th e main program. The a l g o r i t h m has been adapt ed from an o r i g i n a l v e r s i o n developed by Arneson (8 pp. A34-A35). The v e r s i o n c u r r e n t l y used in t h e model was adapted t o produce a d i s t r i b u t i o n o f y i e l d s t h a t matched t h e v a r i a n c e o f t h e d i s t r i b u t i o n c a l c u l a t e d from d a t a c o l l e c t e d f o r t h e y e a r s 1975-1979 ( 2 4 ) . To d e r i v e a d i s t r i b u t i o n with a mean o f about TOO 400 b u s h el s per a c r e , th e p o t e n t i a l y i e l d sh ould be s e t a t th e begi nning o f each season t o a v a l u e o f 500. The a l g o r i t h m c a l c u l a t e s t h e amount o f f r o s t damage t h a t occur s each day by examining th e s t a g e of t h e p l a n t and t h e av era ge d a i l y temperature. A d a i l y low i s i n f e r r e d from t h e av era ge te m p e r a t u r e by assuming t h a t t h e low i s always a c o n s t a n t number o f d eg re e s below t h e a v e ra g e . The o r i g i n a l a l g o r i t h m deducted 10° F from th e av era ge t o produce the d a i l y low t e m p e r a t u r e b u t i t has been a d j u s t e d t o 7° F in t h e c u r r e n t model. The model s t a r t s th e season with a p o t e n t i a l y i e l d o f 500 b u / a c r e and d ed uc t s th e f r o s t damage from t h a t f i g u r e on a d a i l y b a s i s . The r o u t i n e produces an a f t e r f r o s t d i s t r i b u t i o n o f t h e y i e l d with a mean of 403 b u / a c r e and a s t a n d a r d d e v i a t i o n o f 104. Due t o t h e la c k o f v a l i d a t i o n o f t h e f r o s t r o u t i n e and t h e d e s i r e to m a in ta i n t h e r e l a t i o n s h i p between th e p r i c e s and th e y i e l d , t h e a n a l y s i s has been performed us in g t h e randomly g e n e r a t e d y i e l d e s t i m a t e s . Model Hier arc hy The model i s c o n s t r u c t e d in a h i e r a r c h i a l manner so t h a t each p e s t could be anal yze d in d e p e n d e n tl y of th e o t h e r two o r i n combination as an e n t i r e system. The s t o c h a s t i c envi ronm ental i n p u t s and th e c o n t r o l l a b l e in p u t s have been i n t r o d u c e d in a f a s h i o n t o i n s u r e t h a t each a c t i o n choi ce i s exposed t o t h e same twenty s t a t e s o f n a t u r e . The ma jor l i n k a g e s o f th e t h r e e p e s t subsystems a r e through t h e impacts t h a t th e v a r i o u s chemical p e s t i c i d e s have on t h e n o n - t a r g e t s p e c i e s . t h e model, t h e r e a r e two such c a s e s . In t h e system d e f i n e d by The p y r e t h r o i d i n s e c t i c i d e s a p p l i e d t o c o n t r o l the c o d l i n g moth a r e a l s o l e t h a l t o both th e m i t e s and th e m it e p r e d a t o r s . The f u n g i c i d e , benomyl w i l l a f f e c t t h e m i t e s as w e l l . However, i t s e f f e c t i s l e s s on th e mite p r e d a t o r than i t i s on t h e m i te s 101 th e m s e lv e s . The model does assume t h a t th e damage r e s u l t i n g from each p e s t oc cu rs on f r u i t p r e v i o u s l y undamaged by e i t h e r o f th e o t h e r two pests. The model components w i l l be d i s c u s s e d in more d e t a i l in t h e c h a p t e r s d e s c r i b i n g th e a n a l y s i s o f each o f th e p e s t s in de pen den t o f th e o t h e r s . The p e s t s were s t u d i e d i n d e p e n d e n tl y f i r s t t o reduce th e number o f s t r a t e g i e s t o be examined t o a s m a l l , manageable s u b s e t . The complete system was th e n an al yz ed u s in g combinations o f t h e s t r a t e g i e s a p p ea r in g in th e s u b s e t s . In t h i s manner, p r e d i c i t o n s on th e e x t e n t o f th e b e n e f i t s t h a t could be gai ned by i n t e g r a t i n g th e s i n g l e p e s t s t r a t e g i e s i n t o a comprehensive system s t r a t e g y could be examined. Ev al u at i o n o f th e Desired Outputs The s t o c h a s t i c Monte Carlo s i m u l a t i o n model w i l l produce an e s t i m a t e o f th e n e t revenue f o r each p e s t management s t r a t e g y examined f o r each s e as o n. In t h i s c a s e , t h e r e a r e twenty s eas o ns and each season has been c o n s t r u c t e d t o s e r v e as a s t a t e o f n a t u r e . The n e t revenue observed f o r each season w i l l thus be a s s i g n e d a p r o b a b i l i t y o f .05 (1 /2 0 ) and cum ula ti ve p r o b a b i l i t y d i s t r i b u t i o n s can be e s t i m a t e d f o r each p e s t management strategy. So the s i m u l a t i o n model can be used t o g e n e r a t e two o f th e t h r e e components o f t h e d e c i s i o n m a t r i x n e c e s s a r y f o r th e implementation o f the EUH. I t i d e n t i f i e s t h e outcomes o f t h e a c t i o n c h o i c e s and a s s i g n s th e p r o b a b il it ie s of t h e i r occurrence. The remaining component i s an e s t i m a t e o f th e r i s k p r e f e r e n c e s o r a u t i l i t y measure t h a t can be used t o e v a l u a t e t h e a l t e r n a t i v e s . As d e s c r i b e d e a r l i e r , t h e r e a r e d e f i n i t e ad va nt ag es t o u s i n g an i n t e r v a l approach t o u t i l i t y measures r a t h e r than a s i n g l e v al ued f u n c t i o n . For t h i s s t u d y , f i v e d i f f e r e n t i n t e r v a l s w i l l be used t o measure r i s k p r e f e r e n c e s . 102 Four o f t h e i n t e r v a l s w i l l be d e f i n e d by assumption and w i l l f u n c t i o n f o r com par ati ve p ur p os es . The remaining i n t e r v a l has been i n f e r r e d from s ur ve y d a t a o f 30 f ar me rs a c r o s s t h e s t a t e o f Michigan ( 8 1) . A small su rv ey o f a group o f f r u i t growers from B e l d i n g , Michigan was conducted as p a r t o f t h i s r e s e a r c h t o conf irm th e v a l i d i t y o f t h e r e s u l t s o f t h e l a r g e r s u rv ey f o r ap pl e p r o d u c e r s . The r e s u l t s o f t h i s s m a l l e r survey o f f r u i t growers a r e p r e s e n t e d in Appendix I I I . This i n t e r v a l i s d e f i n e d t o r e p r e s e n t t h e p r e f e r e n c e s o f 80% t o 90% o f t h e growers i n t h e s t a t e o f Michigan. The i n t e r v a l s can be used t o rank t h e a l t e r n a t i v e s t r a t e g i e s and comparisons between t h e ra n k i n g s can then be made. D i f f e r e n c e s in th e r an k in g s w i l l i n d i c a t e t h e importance t h a t t h e r i s k p r e f e r e n c e can make on p o s s i b l e s t r a t e g y s e l e c t i o n . S i m i l a r i t i e s in th e r a n k in g s w i l l i n d i c a t e how s e n s i t i v e t h e ex pec ted u t i l i t i e s a r e t o changes in t h e c o n t r o l practices. By v a ry in g t h e y i e l d s , p r i c e s , w ea th e r p r o b a b i l i t i e s o r i n i t i a l p e s t p o p u l a t i o n d e n s i t i e s , t h e r a n k i n g s can be checked f o r s t a b i l i t y a c r o s s d i f f e r e n t p r o d u c ti o n s i t u a t i o n s . The r a n k i n g s o f t h e s t r a t e g i e s w i l l be conducted in a two s t a g e process. F i r s t , SDWRF w i l l be used t o i d e n t i f y an e f f i c i e n c y s e t f o r each r i s k i n t e r v a l and each p r o d u c t i o n s c e n a r i o . These e f f i c i e n c y s e t s can be f u r t h e r r e f i n e d i n t h e second s t a g e t o i n s u r e t h a t o n ly s t r a t e g i e s which w i l l a c t u a l l y be s e l e c t e d by members o f each c l a s s o f d e c i s i o n makers a r e d e c l a r e d as being r i s k e f f i c i e n t . This w i l l be accomplished by t h e a p p l i c a t i o n o f CSD r u l e s . Form o f t h e R e s u l t s o f t h e A n al ys is The f i n a l r e s u l t s o f t h e a n a l y s i s w i l l be in t h e form o f d i s t r i b u t i o n s o f t h e d e s i r e d and u n d e s i r e d o u t p u t s . The d i s t r i b u t i o n s can be d e s c r i b e d by 1 03 t h e means, v a r i a n c e s , s t a n d a r d d e v i a t i o n s o r t h e c u m u la ti ve p r o b a b i l i t y functions. The r e s u l t s w i l l a l s o i n c l u d e t h e e f f i c i e n c y s e t s i d e n t i f i e d f o r each p e s t management s t r a t e g y under each p r o d u c t i o n s c e n a r i o . E f f i c i e n c y s e t s w i l l be d e r i v e d u s in g both SDWRF and CSD. The p ro d u c ti o n s c e n a r i o s w i l l vary due t o changes i n th e number o f p e s t s c o n s i d e r e d , th e mean o f t h e marginal p r o b a b i l i t y d i s t r i b u t i o n f o r t h e p e r a c r e y i e l d s and t h e i n i t i a l p e s t p o p u l a t i o n d e n s i t i e s . 3.4 The T e s t s o f Model Hypotheses Following the G ie r e g u i d e l i n e s ( 4 5 ) , th e model d e f i n e d f o r t h e a c t u a l sy stem i s in r e a l i t y a t h e o r y . The t h e o r e t i c a l h y p o t h e s i s proposed by t h e r e s e a r c h i s t h a t t h e a c t u a l system i s a c c u r a t e l y d e s c r i b e d by th e model. The model can be used t o make p r e d i c t i o n s a b ou t t h e performance and b e h a v i o r o f t h e system. I f th e t h e o r e t i c a l h y p o t h e s i s i s j u s t i f i e d , th e n t h e r e i s r ea s o n t o have a g r e a t deal o f c o n f id e n c e in t h e p r e d i c t i o n s o f th e model. I f i t c a n no t be f u l l y j u s t i f i e d , then th e p r e d i c t i o n s s e r v e t h e v a l u a b l e f u n c t i o n o f i d e n t i f y i n g one o f t h e p o s s i b i l i t i e s t h a t could o cc u r and the s i t u a t i o n from which t h e p o s s i b i l i t y w i l l a r i s e . I t sh ou ld be remembered t h a t t h e r e a r e s e v e r a l eleme nts t o a good argument. These i n c l u d e t h e h y p o t h e s i s , a u x i l i a r y a s s u m p ti o n s , i n i t i a l c o n d i t i o n s and th e p r e d i c t i o n s . In r e a l i t y , s i n c e t h e r e a r e a number o f d i f f e r e n t uses o f t h e model because o f th e t r e a t m e n t o f subsystems as in de pen den t systems f o r some a n a l y s e s and t h e g e n e r a t i o n o f s e v e r a l forms o f th e o u t p u t s , t h e r e i s more tha n one t h e o r e t i c a l h y p o t h e s i s i n h e r e n t i n t h e r e s e a r c h . a t h e o r e t i c a l h y p o th e s i s f o r each s i n g l e p e s t subsystem. There w i l l be There w i l l be a n o t h e r h y p o t h e s i s d e a l i n g w i t h th e comprehensive t h r e e p e s t model. F i n a l l y , t h e r e w i l l be a n o t h e r t h e o r e t i c a l h y p o t h e s i s f o r t h e use o f th e 104 EUH t o e v a l u a t e t h e performances o f th e a l t e r n a t i v e c o n t r o l s t r a t e g i e s . Each t h e o r e t i c a l h y p o t h e s i s needs t o be t e s t e d . Ju stific a tio n for one w i l l n o t n e c e s s a r i l y imply j u s t i f i c a t i o n f o r t h e o t h e r s . However, due t o t h e h i e r a r c h i a l n a t u r e o f th e r e s e a r c h a p p r oa c h, i f one o f th e e a r l y hy po th es es i s n o t j u s t i f i e d , i t i s u n l i k e l y t h a t s ub se q ue nt hypotheses which a r e based on models u s in g the subsystems as components w i l l be ju s tifie d either. For each t h e o r e t i c a l h y p o t h e s i s , i t i s n e c e s s a r y t o c l e a r l y i d e n t i f y t h e el em ent s o f t h e agreement. The ca se o f th e m it e model(s) w i l l be used as an example t o d em o ns tr at e t h e p r oc ed u r e. The f i r s t t h e o r e t i c a l h y p o t h e s i s t h a t sh ou ld be d i s c u s s e d s i n c e i t i s p a r t o f t h e f o u n d a t i o n o f t h e l a r g e r sy ste m , i s t h e b i o l o g i c a l model o f t h e mite system. In t h i s c a s e , t h e h y p o th e s i s i s t h a t t h e a c t u a l mite system i s a c c u r a t e l y d e s c r i b e d by t h e model t h a t s i m u l a t e s t h e p o p u l a t i o n growth, p r e d a t o r consumption, chemical m o r t a l i t y r a t e s and damage. e l s o f f i n a l season periods. The p r e d i c t i o n s o f t h e model a r e l e v ­ damage and p o p u l a t i o n d e n s i t i e s a t v a r i o u s time The a u x i l i a r y assumption of t h e argument a r e t h a t : o t h e r p e s t s and p r e d a t o r s p r e s e n t in t h e o r c h a r d do n o t a f f e c t 1) th e the m i t e s ; 2) th e e x t e n t o f damage caused by t h e m i t e s i s a f u n c t i o n o f only th e m it e p o p u l a t i o n d e n s i t y ; 3) m it e damage can be measured in a lower q u a l i t y f r u i t r e p r e s e n t e d by a d e c r e a s e in t h e v al u e o f th e h a r v e s t ; and 4) t h a t m u l t i - s e a s o n a l e f f e c t s a r e marginal a l lo w in g t h e system t o be accurately d e s c r i b e d by a s e r i e s o f in de pen den t s i n g l e s e a s o n s . The i n i t i a l c o n d i t i o n s can be d e s c r i b e d in terms o f both s t o c h a s t i c and determ inistic variables. For t h e s t o c h a s t i c v a r i a b l e s , t h e i n i t i a l c o n d i t i o n s a r e c o n t a i n e d i n th e p r o b a b i l i t y d i s t r i b u t i o n s d e f i n e d f o r each v a r i a b l e . They d e s c r i b e t h e l i k e l i h o o d o f occure nce f o r t h e p o s s i b l e 105 v a l u e s o f th e s t o c h a s t i c v a r i a b l e s . The d e t e r m i n i s t i c v a r i a b l e s with i n i t i a l c o n d i t i o n s o f import a r e t h e a g e, h e a l t h and p r o d u c t i v i t y o f the t r e e s in t h e o r c h a r d . The t r e e s a r e from a h e a l t h y , m a tu r e, b e a r i n g o r c h a r d and t h e p r o d u c t i v i t y i s u s e r s u p p l i e d a t a low y i e l d o f 250 b u s h e l s p e r a c r e ; a medium y i e l d o f 500 b u s h e ls p e r a c r e ; o r a high y i e l d o f 900 b u s h e ls p e r a c r e . The j u s t i f i c a t i o n o f t h e model i s d i s c u s s e d in two a r t i c l e s . e t al. Dover (35) d i s c u s s e s t h e p r e d i c t i o n s r e l a t e d t o p o p u l a t i o n growth p a t t e r n s , p o p u l a t i o n d e n s i t i e s and p r e d a t o r / p r e y r a t i o s . Hoyt e t a l . (61) d i s ­ c u s s e s th e p r e d i c t i o n r e l a t i n g t h e f r u i t damage t o m i te p o p u l a t i o n den­ sities. From t h e r e s u l t s o f t h e s e d i s c u s s i o n s , i t can be seen t h a t t h e r e e x i s t s reason t o b e l i e v e t h a t t h e model a c c u r a t e l y d e f i n e s t h e a c t u a l system. When p r i c e s a r e in t r o d u c e d i n t o t h e sub syste m, u s in g G i e r e ' s s t r i c t d e f i n i t i o n , a new model i s c o n s t r u c t e d . In t h i s c a s e , a l l th e p r ev io u s components o f t h e argument a r e s t i l l p r e s e n t b u t an a d d i t i o n a l p r e ­ d i c t i o n and two a d d i t i o n a l a u x i l i a r y assumptions a r e in c l u d e d as w e l l . The new p r e d i c t i o n i s based on th e n e t income a s s o c i a t e d w it h each c o n t r o l s t r a t e g y examined. The a u x i l i a r y as sumpti ons a r e : 1) t h a t t h e h i s t o r i c a l p r o b a b i l i t y d i s t r i b u t i o n s o f t h e ma rke t a r e a c c u r a t e i n d i c a t o r s o f what can be ex pe ct ed o f t h e p r e s e n t syst em ; 2) t h a t t h e n o n - p r i c e terms o f market t r a n s a c t i o n s a r e i n c i d e n t a l ; and 3) t h e c o s t s o f p r o d u c t i o n vary only with y i e l d s and p e s t management d e c i s i o n s . The i n i t i a l c o n d i t i o n s r e q u i r e t h a t t h e system i s d e s c r i b e d by th e l e v e l s o f c o s t s f o r t h e n o n - p e s t management a c t i v i t i e s . The j u s t i f i c a t i o n o f th e t h e o r e t i c a l h y p o t h e s i s o f t h i s model i s d i f f i c u l t t o e s t a b l i s h because t h e r e a r e few a c c u r a t e r e c o r d s o f t h e performance o f t h e a c t u a l system w ith which d i s t r i b u t i o n s 106 o f n e t revenue could be c o n s t r u c t e d . l e s s than f u l l y j u s t i f i e d . In t h i s c a s e , t h e h y p o t h e s i s i s In t h e terms o f J o h n s o n ' s f o u r t e s t s o f o b j e c t i v i t y ( 6 5 ) , th e model has been v a l i d a t e d but n o t v e r i f i e d . It t he n becomes a m a t t e r t h a t t h e r e e x i s t s some evi dence t o b e l i e v e th e model and i t s p r e d i c t i o n s b u t t h e e v i d en ce i s no t overwhelming. The l o g i c o f t h e p r o c e s s o f v a l i d a t i o n may even s u g g e s t t h a t f o r r e l a t i v e com­ p a r i s o n s between s t r a t e g i e s , t h e p r e d i c t i o n s have more b a s i s f o r c r e d i ­ b i l i t y tha n f o r uses r e q u i r i n g t h e a b s o l u t e v a l u e s o f th e n e t income estim ates. I f an o r d e r i n g o f th e s t r a t e g i e s as t o t h e p r e f e r e n c e s o f th e appl e growers i s made, a new model i s c o n s t r u c t e d by adding th e EUH t o th e p r e v i o u s l y d i s c u s s e d model. The p r e d i c t i o n o f th e model i s now th e r a n k in g s o f t h e a l t e r n a t i v e s t r a t e g i e s . c e n t e r on t h e v a l i d i t y o f t h e EUH. The new a u x i l i a r y assumptions The i n i t i a l c o n d i t i o n s now must i n c l u d e both t h e c u r r e n t we alt h p o s i t i o n o f t h e d e c i s i o n makers and some s t a t e m e n t about t h e ch o i ce s e t o f growers with r e s p e c t t o th e s t r a t e g i e s . U n f o r t u n a t e l y , t h e r e i s n o t enough evid enc e t o j u s t i f y t h e EUH (116). Fu rtherm ore, t h e i n i t i a l c o n d i t i o n s ca nno t be j u s t i f i e d e i t h e r . However, d e s p i t e t h e f a c t t h a t t h e t h e o r e t i c a l h y p o t h e s i s cannot be f u l l y j u s t i f e d , i t produces th e b e s t p r e d i c t i o n s ab out t h e b e h a v i o r o f th e system t h a t a r e currently available. The EUH based model i s p r ob ab ly c l o s e r t o being j u s t i f i e d than any o f i t s a l t e r n a t i v e s (116). As an u n j u s t i f i e d model, t h e p r e d i c t i o n s a r e s t i l l u s e f u l s i n c e th e y uncover r e l a t i o n s h i p s between s i t u a t i o n s and p o s s i b l e outcomes. B e s id e s , t h e a c t u a l system i s one t h a t i s n o t p a r t i c u l a r l y conducive t o th e t e s t i n g o f t h e o r e t i c a l models. It may be t h a t no model, r e g a r d l e s s o f i t s m e r i t s , w i l l e v e r be f u l l y j u s ­ t i f i e d f o r t h i s system. The need f o r p r e d i c t i o n s i s n o t l e s s e n e d , b u t 107 c a r e must be e x e r c i s e d t h a t th e ac c ur ac y o f th e p r e d i c t i o n s can a t b e s t be d i s c u s s e d in p r o b a b i l i s t i c terms. The r i s k p r e f e r e n c e i n t e r v a l s were t e s t e d f o r a small group o f ap p l e growers in a h y p o t h e t i c a l d e c i s i o n s e t t i n g and in t h i s s e t t i n g th e EUH p r e d i c t e d w e l l . The r e l e v a n c e o f t h e r e s u l t s in t h i s s e t t i n g f o r a c t u a l d e c i s i o n s has y e t t o be d et er m in e d . The o t h e r subsystems a l l w i l l have s i m i l a r h i e r a r c h i c a l t h e o r e t i c a l h y p ot h e se s . A review o f th e e n t i r e s e t o f p r e d i c t i o n s produced by th e s t u d y w i l l ap pe a r in Chapter V I I I . 3.5 Comparison o f Model P r e d i c t i o n s With A P r i o r i S ta te m en ts o f A n t i c i p a t e d System Behavior Since t h e t h e o r e t i c a l h y p o t h e s i s o f t h e comprehensive model w i l l not be f u l l y j u s t i f i e d , t h e p r e d i c t i o n s o f t h e model should be used in a c a u t i o u s manner. P r i o r t o g e n e r a t i n g th e p r e d i c t i o n s w ith t h e model, i t w i l l be b e n e f i c i a l t o make some s t a t e m e n t s about t h e b e h a v i o r o f the system which can be a n t i c i p a t e d based on t h e c u r r e n t u n d e r s ta n d i n g of i t s operation. D is c r e p a n c i e s between t h e p r e d i c t e d and a n t i c i p a t e d b e h a v i o r can then be anal yze d f o r : 1) improvements in t h e u nd e r s ta n d i n g o f t h e system pro vi d ed by th e mo de lli n g p r o c e s s ; a n d / o r 2) problems with th e model due t o o v e r s i m p l i f i c a t i o n o r m i s s p e c i f i c a t i o n . A s e r i e s o f te n s t a t e m e n t s can be r a i s e d w it h r e g a r d t o system b e h a v i o r t h a t i s a n t i c i p a t e d from e x i s t i n g i n f o r m a t i o n on th e system. They a r e : 1) The expec ted n e t revenue from th e IPM s t r a t e g i e s s ho ul d exceed t h e n e t revenue from c o n v en ti on al c o n t r o l s t r a t e g i e s . 2) The expec ted u t i l i t y o f t h e co n v en t io n al c o n t r o l s t r a t e g i e s sh ould be g r e a t e r th a n t h e ex pec ted u t i l i t y o f th e IPM s t r a t e g i e s f o r a t l e a s t some d e c i s i o n makers w ith s t r o n g r i s k a v e r s i o n . 108 This r e s u l t coul d e x p l a i n why some d e c i s i o n makers do n o t adopt IPM s t r a t e g i e s . 3) By changing t h e l e v e l o f th e economic t h r e s h o l d in d i f f e r e n t IPM programs, t h e amount o f r i s k a s s o c i a t e d w i t h each program w i l l be d i f f e r e n t . More r i s k a v e r s e d e c i s i o n makers sh ould p r e f e r IPM s t r a t e g i e s w ith lower economic t h r e s h o l d s . Less r i s k a v e r s e d e c i s i o n makers w i l l p r e f e r IPM s t r a t e g i e s with h i g h e r economic t h r e s h o l d s . 4) I f p e s t p o p u l a t i o n d e n s i t i e s a r e e s t i m a t e d a t d i s c r e t e time i n t e r v a l s , th e e f f i c i e n c y o f a given economic t h r e s h o l d w i l l depend in p a r t in t h e amount o f p o p u l a t i o n growth between e s t i m a t e s and t h e r e should e x i s t a r e l a t i o n s h i p between t h e economic t h r e s h o l d and t h e s c o u t i n g i n t e r v a l . a) The ex p ec ted n e t revenue o f IPM s t r a t e g i e s with low economic t h r e s h o l d s w i l l be h i g h e r w ith l o n g e r s c o u t i n g i n t e r v a l s . b) With s h o r t e r s c o u t i n g i n t e r v a l s , IPM s t r a t e g i e s w ith h i g h e r economic t h r e s h o l d s w i l l have l a r g e r ex p e c te d n e t rev en u e s. c) With l o n g e r s c o u t i n g i n t e r v a l s t h e ex pe c te d u t i l i t i e s o f th e IPM s t r a t e g i e s with lower economic t h r e s h o l d s w i l l be l a r g e r tha n th e ex p e c te d u t i l i t i e s o f t h e IPM s t r a t e g i e s w ith h i g h e r economic t h r e s h o l d s . d) With s h o r t e r s c o u t i n g i n t e r v a l s , th e ex p ec te d u t i l i t i e s o f the IPM s t r a t e g i e s w i t h h i g h e r economic t h r e s h o l d s w i l l be l a r g e r tha n th e ex p ec te d u t i l i t i e s o f t h e IPM s t r a t e g i e s w it h th e lower economic t h r e s h o l d s . 5) With l a r g e r y i e l d s ( o r h i g h e r v al u e o f th e crop due t o h i g h e r p r i c e s ) , t h e d i f f e r e n c e s in t h e ex pe ct ed n e t revenues (and e x pe c te d u t i l i t i e s ) o f t h e co nv e n t io n a l c o n t r o l programs and t h e 109 IPM s t r a t e g i e s w i l l be lower. L i k ew is e, as y i e l d s i n c r e a s e , t h e ex pe c te d n e t revenues (and e x p e c t e d u t i l i t i e s ) o f th e IPM s t r a t e g i e s with low economic t h r e s h o l d s w i l l i n c r e a s e r e l a t i v e t o t h e e xp ec te d n e t revenues (and e x p e c te d u t i l i t i e s ) o f t h e IPM s t r a t e g i e s w i t h high economic t h r e s h o l d s . 6) By i g n o r i n g any p o s s i b i l i t y o f Friedman-Savage u t i l i t y f u n c t i o n s , Second Degree S t o c h a s t i c Dominance s h ou ld i d e n t i f y an e f f i c i e n c y s e t which i s b i a s e d . The b i a s in t r o d u c e d by u s in g t h e c l a s s of a l l ris k averse individual to re p re se n t a g ric u ltu ra l decision makers could r e s u l t in both Type I and Type I I e r r o r s . 7) The ex p e c te d v al u e o f t h e amounts o f c h em ic a ls in t r o d u c e d i n t o t h e environment by c o n v en ti o na l s p r a y programs w i l l exceed th e e x pe c te d v a l u e o f t h e amount o f ch em ic a ls in t r o d u c e d by IPM strategies. 8) The e xp ec te d crop damage under th e IPM s t r a t e g i e s s ho ul d be l a r g e r than t h e e x pe c te d damage o f t h e c o n v e n t io n a l s p r a y programs. The ex pe c te d damage o f t h e IPM programs w i t h t h e low economic t h r e s h o l d s sh ould be lower th a n t h e ex p ec te d damage o f t h e IPM programs w it h h i g h e r economic t h r e s h o l d s . 9) There a r e s i g n i f i c a n t g a i n s t o be r e a l i z e d by r e f i n i n g t h e IPM d e c i s i o n r u l e s and a c c u r a t e l y d e f i n i n g t h e economic t h r e s h o l d . Sampling e r r o r s i n c u r r e d i n t h e m o n i t o r i n g p r o c e s s sh ould d e t r a c t c o n s i d e r a b l y from th e e f f i c i e n c y o f IPM programs. 10) The e f f i c i e n c y s e t s i d e n t i f i e d by SDWRF can be f u r t h e r r e f i n e d by CSD as s t r a t e g i e s which would n o t be s e l e c t e d by any d e c i s i o n maker a r e r e j e c t e d from t h e e f f i c i e n c y s e t . These s t a t e m e n t s w i l l be compared w it h t h e p r e d i c t i o n s on t h e model in Chapter V I I I . IV. 4.1 MITE MODEL RESULTS The S im u l a ti o n Model The m i te model i s an a d a p t a t i o n o f a model t h a t was o r i g i n a l l y w r i t t e n by Dover, C r o f t , Welch and Tummala ( 3 5 ) . The model uses a time i n t e r v a l o f one day and i s d r i v e n by t h e av er a g e d a i l y t e m p e r a t u r e . The model has a number o f components bu t t h e main t h r e e s u b r o u t i n e s a r e t h o s e which s i m u l a t e t h e p o p u l a t i o n dynamics o f t h e European red m i t e , Panonychus u l m i , and i t s p r i n c i p a l p r e d a t o r , Amblysesius f a l l a c i s . These s u b r o u t i n e s a r e PRED, ERPOP and AFPOP. They a r e d es ig n ed t o be c a l l e d each day and r e s p e c t i v e l y c a l c u l a t e t h e p r e d a t i o n , t h e red mite p o p u l a t i o n growth and th e p r e d a t o r m i te p o p u l a t i o n growth. r o u t i n e s o p e r a t e u s i n g t h e d a i l y av era ge t e m p e r a t u r e . The sub­ The te m p e r a t u r e i n f l u e n c e s t h e r a t e of development in t h e p o p u l a t i o n and t h e p r e d a t i o n rate. Below 50° F p r e d a t i o n , growth and r e p r o d u c t i o n s t o p . For ave rage t e m p e r a t u r e s above 80° F, th e f e e d i n g and growth r a t e s may n o t be a c c u r a t e . The s u b r o u t i n e AFPOP advances t h e p r e d a t o r p o p u l a t i o n each day by c a l c u l a t i n g t h e f r a c t i o n o f i n d i v i d u a l s in each o f 10 age c l a s s e s which sh ou ld mature in t h e n e x t c l a s s and by d e t e r m i n i n g t h e number o f eggs oviposited. The t e n age c l a s s e s ap p e a r in Table 1. The p o p u l a t i o n can be d e c r e a se d by n a t u r a l m o r t a l i t y , s t a r v a t i o n o r exp osure t o t o x i c che m ic a ls . The s u b r o u t i n e i s d e p i c t e d in a flow c h a r t a p p e a r i n g in F igu re 1. The s u b r o u t i n e ERPOP f u n c t i o n s in much t h e same way and uses th e same age c l a s s e s . I t procee ds each day by c a l c u l a t i n g t h e o v i p o s i t i o n , t h e f r a c t i o n o f i n d i v i d u a l s n o t e a t e n and t h e f r a c t i o n o f i n d i v i d u a l s no Ill Table 1. Age C la s s e s f o r Mite and P r e d a t o r P o p u l a t i o n s . Age C la ss Description 1 egg 2 larva 3 protonymph 4 deutonymph 5 preoviposition 6 oviposition, f i r s t q u in tile 7 o v i p o s i t i o n , second q u i n t i l e 8 oviposition, th ird q u in tile 9 o viposition, fourth q u in tile 10 oviposition, f i f t h q u in tile 112 F igu re 1 . S u b ro u tin e AFPOP: YES I n itia liz a tio n o f d e n s it y f o r each s t a g e The P o p u la tio n Dynamics o f th e P r e d a to r . -''F ir s t X Entry INTO SUBROUTINE COMPUTE OVIPOSITION FOR THE DAY COMPUTE RATE o f d evelopm en t f o r each p r e d a to r s t a g e f o r th e day YES d ecr ea se a d u lt pop. by 5% d eterm in e f r a c t i o n o f p o p u la tio n o f each a c t i v e s t a g e w hich m atures t o th e n ex t s t a g e , advance t h o s e w hich m ature YES ✓ 'p o p u la tio n \ .v e r y ^ Advance E g g s, f r a c t io n o f eg g s w hich d i d n ' t h atch + eg g s j u s t la id YES p o p u la tio n ^ low / decrease a ll a c t iv e s t a g e s by 20% INCREASE AF pop. t o minimum le v e l com pute f e e d in g p o t e n t ia l o f AF pop. a s a d u lt e q u iv a le n t s RETURN 113 in each of th e te n c l a s s e s which should mature and g r a d u a t e t o th e ne x t class. I t i s assumed t h a t food i s u n l i m i t e d f o r t h e red m i te s a t den­ s i t i e s below 35 m i t e s / l e a f and t h a t a t d e n s i t i e s above 70 m i t e s / l e a f o v ip osition ceases. u l a t i o n i s reduced At d e n s i t i e s g r e a t e r than 35 m i t e s / l e a f , th e pop­ a t a r a t e o f 3% p e r day. The s u b r o u t i n e i s depicted i n a flow c h a r t in Fig ur e 2. The s p e c i e s p o p u l a t i o n s a r e both measured in terms o f th e female population. I t i s assumed t h a t t h e male p o p u l a t i o n i s 1/3 t h e s i z e o f th e female p o p u l a t i o n f o r th e red m i t e s and t h a t t h e r e a r e 4 fema les f o r each one o f th e male m it e p r e d a t o r s . The males a r e in c lu d ed in t h e model where t h e food v al ue o f t h e prey i s c a l c u l a t e d , when th e p r e d a t i o n r a t e o f Amblyesius f a l l a c i s i s dete rmin ed and when t h e t o t a l number o f members in th e a c t i v e s t a g e s a r e e s t i m a t e d f o r e i t h e r s p e c i e s . The food val ue o f t h e prey i s c o nv er te d i n t o Tet ranychus u r t i c a e egg e q u i v a l e n t s (EPY). A more complete d e s c r i p t i o n o f t h e model and a d i s c u s s i o n o f i t s v a l i d a t i o n ap p e a r in Environmental Entomology (3 5 ) . The ma jor d i f f e r e n c e s between t h e o r i g i n a l model and t h e ad apt ed v e r s i o n l i e in s e v e r a l sim­ p l i f y i n g as s um pt io n s. F i r s t , t h e c o h o r t s a r e n o t m a in ta i n e d b u t r a t h e r , a f r a c t i o n from each o f t h e 10 age c l a s s e s i s matured each day. The n e g a t i v e binomial d i s t r i b u t i o n i s n o t used t o compute t h e p r e d a t i o n and t h e red mite p o p u l a t i o n i s co n v e r t e d i n t o prey e q u i v a l e n t s which i s then used t o compute p r e d a t i o n . assumption t h a t a t The f i n a l change i s t h e im p o s i t i o n o f the d e n s i t i e s o f g r e a t e r than 70 m i t e s / l e a f o v i p o s i t i o n ceases e n t i r e l y . Using t h e s e t h r e e s u b r o u t i n e s as a base from which t h e p o p u l a t i o n dynamiics can be s i m u l a t e d , t h e complete model can be c o n s t r u c t e d t o i n c o r p o r a t e m o r t a l i t y caused by p e s t i c i d e s t r e a t m e n t s , th e a p p l i c a t i o n o f d i f f e r e n t p e s t management s t r a t e g i e s , t h e random g e n e r a t i o n o f i n i t i a l 114 F ig u re 2 . S u b rou tin e ERPOP: The P o p u la tio n Dynamics o f M ite s. F ir s t Entry In to S u b ro u tin e I n itia liz a tio n of d e n s it y f o r each s t a g e COMPUTE OVIPOSITION FOR THE DAY COMPUTE % PREY NOT EATEN COMPUTE RATE o f D evelopm ent f o r each prey s t a g e DETERMINE THE FRACTION OF PREY WHICH MATURE FROM ONE STAGE TO ANOTHER ER p o p u la tio n t o o h igh Advance e g g s , s u b t r a c t h atch and add o v ip o s it io n t o y e s te r d a y s t o t a l p o p u la tl In c r e a se pop. t o . 2 / 1 e a f COMPUTE FOOD VALUE OF PREY t o P red a to r RETURN 115 p o p u l a t i o n d e n s i t i e s and emergence d a t e s and th e e s t i m a t e o f f r u i t damage t h a t would be caused each season by m i t e s . The s u b r o u t i n e MMORT d e te rm in e s m o r t a l i t y o f both t h e p l a n t f e e d i n g m i t e s and t h e p r e d a t o r m i t e s when th e y a r e exposed t o d i f f e r e n t dosages o f two m i t i c i d e s ( p l i c t r a n and c a r z o l ) , one f u n g i c i d e (benomyl a n d / o r an i n s e c t i c i d e p y r e t h r o i d ) . The m o r t a l i t y r a t e s a r e a f u n c t i o n o f th e time t h a t has e l a p s e d s i n c e t h e a p p l i c a t i o n . The i n i t i a l p o p u l a t i o n d e n s i t i e s f o r t h e two s p e c i e s a r e randomly g e n e r a t e d by a s u b r o u t i n e e n t i t l e d INTMITE. This model component uses a uniform d i s t r i b u t i o n t o randomly s e l e c t one o f twenty d i f f e r e n t s t a r t i n g population le v e ls . The twenty l e v e l s o c c u r a t i r r e g u l a r i n t e r v a l s and have been de s ig ne d t o s i m u l a t e t h e h i s t o r i c a l d i s t r i b u t i o n on i n i t i a l densities. Both s p e c i e s use th e same pr oc ed ur e b u t t h e p r e d a t o r p o p u l a t i o n i s dete rmin ed by an inde pendent draw from th e un ifo rm d i s ­ t r i b u t i o n and i s s e t equal t o 1/10 o f t h e s t a r t i n g l e v e l s e l e c t e d by t h a t draw. This s u b r o u t i n e s e l e c t s t h e emergence d a t e s f o r t h e p o p u l a t i o n s in much t h e same f a s h i o n . I t uses a uniform d i s t r i b u t i o n t o randomly s e l e c t from a number o f emergence d a t e s d e s i g n a t e d t o rep ro du ce t h e o bs erv ed h isto rical pattern. In t h i s c a s e , t h e two s p e c i e s do n o t use t h e same d a t a on th e emergence d a t e s . The p r e d a t o r p o p u l a t i o n u s e s an ind ep en de nt draw from th e uniform d i s t r i b u t i o n t o s e l e c t from t e n d a t e s p e c u l i a r t o i t s own emergence p a t t e r n wh ile th e m it e p o p u l a t i o n i s randomly s e l e c t e d from 20 p o s s i b l e d a t e s . The p r o b a b i l i t y i s high t h a t t h e m i te p o p u l a t i o n s hould emerge much s oo ne r than i t s p r e d a t o r s . Each season w i l l have a u n iq u e , random com bination o f two emergence d a t e s and two i n i t i a l p o p u l a t i o n d e n s i t i e s . The mite i n j u r y and su b se q u en t f r u i t damage a r e handled i n two 116 subroutines. F i r s t , i n th e component e n t i t l e d MITEINJ t h e number o f m i te days f o r each o f t h r e e p a r t s o f t h e se ason a r e computed. A m it e day i s a measure o f t h e number o f m i t e s p r e s e n t and t h e l e n g t h o f time t h a t th e y f e e d . In t h i s c a s e , i t i s t h e sum o f t h e number o f m i t e s p e r l e a f by which t h e p o p u l a t i o n exceeds t h e s p e c i f i e d t h r e s h o l d each day. The t h r e s h o l d i s s e t a t 15 m i t e s / l e a f s i n c e i t i s b e l i e v e d t h a t European red m it e p o p u l a t i o n s can be t o l e r a t e d a t t h i s l e v e l w i t h o u t th e f e e d i n g a d v e r s e l y a f f e c t i n g f r u i t p r o d u c t i o n o r t r e e v i g o r (31, p. 4 ) . se as o n . The m it e days a r e accumulated f o r each o f t h r e e p a r t s o f th e The f i r s t t h i r d o f t h e season ends a t June 15, t h e mid dle p a r t ru n s from June 16 t o August 15 and th e f i n a l t h i r d be gi ns on August 16 and e x t e n d s t o t h e end o f t h e s e a s o n . The number o f m i te days i s c o n v e r t e d t o a damage f i g u r e u s in g i n ­ fo r m a t io n from a s tu d y ap p e a r in g in Recent Advances in Acarology (61) and from unpublished d a t a c o l l e c t e d by C r o f t . Hoyt e t . al concluded t h a t "an e s t i m a t e d 3,000 m i t e - d a y (peak o f abo ut 120 m i t e s p e r l e a f ) was r e q u i r e d t o produce a l o s s o f one box s i z e o r ap p r o x im a te ly 12% l o s s in y i e l d " (61, p. 11). i n Michigan by C r o f t . This c o n c l u s i o n has been ad ap te d t o t h e s i t u a t i o n The peak has been a d j u s t e d t o 2000 m i t e - d a y s and a c u r v i l i n e a r f u n c t i o n i s used t o e s t i m a t e damage a t lower d e n s i t i e s . Since t h e damage r e s u l t s i n both d i s c o l o r e d and small s i z e d f r u i t , i t was f e l t c o n v e r t i n g t h e e x p r e s s i o n o f p e r c e n t a g e l o s s t o terms o f v al u e o f th e h a r v e s t r a t h e r tha n number o f b u s h e l s would more c l o s e l y c a p t u r e t h e damage o f both q u a l i t y and q u a n t i t y . The e a r l i e r i n t h e season t h a t t h e m i te i n j u r y o c c u r s , t h e more a f f e c t e d w i l l be t h e f r u i t p r o d u c t i o n and t r e e v i g o r . T h e r e f o r e , t h e maximum damage ex p ec te d in each p a r t o f th e season w i l l be p r o g r e s s i v e l y s m a l l e r . On t h e f i r s t p a r t , a sum o f 117 2000 m i t e - d a y s w i l l reduce t h e v al ue o f t h e crop by 12% w hi le t h e same p o p u l a t i o n d e n s i t y in t h e middle t h i r d o f th e season w i l l o n ly r e s u l t i n an 8% d e c l i n e . In t h e f i n a l time i n t e r v a l , t h e peak p o p u l a t i o n o f 2000 m i te days would produce a 3.432% r e d u c t i o n in t h e v a l u e o f t h e f r u i t . Under t h e w o r s t p o s s i b l e c o n d i t i o n s t h e maximum amount o f damage could a cc ou nt f o r j u s t under 24% o f t h e v a l u e o f t h e p o t e n t i a l , non -m it e damaged yield. These c a l c u l a t i o n s a r e performed in t h e s u b r o u t i n e ESMITES which i s desig ned t o be c a l l e d once a y e a r , a t t h e end o f each s e as o n. The model implements t h e d e c i s i o n r u l e s which a r e d i c t a t e d by the v a r i o u s s t r a t e g i e s in t h e s u b r o u t i n e MSCOUT. This s u b r o u t i n e has been de s ig n e d t o handle s t r a t e g i e s which a r e based on c a l e n d a r s p r a y s c h e d u le s o r IPM programs o f v a r y in g d eg ree s o f s o p h i s t i c a t i o n . In t h e ca s e o f a s t r a t e g y which f o ll o w s a s t r i c t l y b i o l o g i c a l c o n t r o l program, t h i s s u b ­ r o u t i n e would no t be c a l l e d . In t h e c a s e o f c a l e n d a r based s t r a t e g i e s , t h e s u b r o u t i n e i s c a l l e d on t h e days d e s i g n a t e d f o r s p r a y s by t h e s p e c i f i e d time i n t e r v a l s . I t i s c a l l e d whenever t h e o r c h a r d i s t o be mo nitored by a p r o f e s s i o n a l s c o u t when any o f t h e IPM s t r a t e g i e s a r e being examined. There a r e t h r e e c l a s s e s o f s t r a t e g i e s examined by th e model. a r e b i o l o g i c a l c o n t r o l , c a l e n d a r and IPM. They The b i o l o g i c a l c o n t r o l r e l i e s e n t i r e l y on t h e e f f i c a c y o f t h e n a t u r a l p r e d a t o r s t o c o n t r o l t h e p l a n t f e e d i n g m i te s and a p p l i e s no chemical m i t i c d e s r e g a r d l e s s o f t h e p o p u l a t i o n d e n s it ie s experienced. The c a l e n d a r programs in c l u d e d in t h e model a r e t h e f u l l dose a p p l i c a t i o n s o f two d i f f e r e n t chem icals ( p l i c t r a n and carzol) a t specified dates. In t h i s c a s e , s p r a y s a r e a p p l i e d a t th e end o f June and a g ai n a t th e be gi nn ing o f August. The IPM s t r a t e g i e s have v a ry in g d eg ree s o f s o p h i s t i c a t i o n and can ap p l y f u l l o r reduced dosages depending upon t h e d e c i s i o n r u l e e x e r c i s e d and th e r a t i o o f 118 p o p u l a t i o n d e n s i t i e s o f th e m i te s and th e m it e p r e d a t o r s . Reduced dosages a r e d e s ig n e d t o minimize t h e impact o f t h e chem ica ls on th e p r e d a t o r s and promote t h e b i o l o g i c a l c o n t r o l o f p e s t s . Whent h e chemical ca rz o l i s employed, t h e p o t e n t i a l f o r reduced dosages i s n o t g r e a t s i n c e even a t l e s s th an f u l l s t r e n g t h i t remains ve ry t o x i c t o th e p r e d a t o r s . The IPM s t r a t e g i e s which do n o t have t h e o p t i o n o f ap p l y in g reduced dosages a r e f a i r l y s im p l e. Whenever t h e m it e p o p u l a t i o n i s monitored and i t exceeds t h e economic t h r e s h o l d , a f u l l dose o f t h e m i t i c i d e i s applied. However, when a more s o p h i s t i c a t e d s t r a t e g y i s employed, th e d e c i s i o n r u l e becomes more complex. These s t r a t e g i e s have a t l e a s t two key management v a r i a b l e s - - t h e economic t h r e s h o l d f o r a f u l l dosage (FET) and th e economic t h r e s h o l d f o r a lower dosage (HET). I f th e r e d m it e p o p u l a t i o n i s l e s s than HET, no s p r a y i s a p p l i e d , w h il e i f i t exceeds FET, a f u l l dosage i s recommended. I f t h e red m i te p o p u l a t i o n l i e s between HET and FET, t h e r a t i o o f t h e p re y t o th e p r e d a t o r becomes i m p o r t a n t . I f t h e p r e d a t o r p o p u l a t i o n i s g r e a t e r than TRP1, then no sp ray i s a p p l i e d . I f i t f a l l s between TRP1 and TRP2, a t h i r d dosage i s recommended wh ile f o r l e v e l s between .08 p r e d a t o r m i t e s / l e a f and TRP2, a h a l f dosage i s required. TRP1 and TRP2 a r e d e f i n e d as f o l l o w s : 1) TRP1 - .099 * AER - .3 2) TRP2 = .08267 * AER- .34 AER = red m i te p o p u l a t i o n d e n s i t y ( mi tes p e r l e a f ) This d e c i s i o n framework i s d i s p l a y e d in F ig u r e 3. The b a s i c framework can be s l i g h t l y r e v i s e d t o promote even more biological control. I f the decision ru le is adjusted to d ic ta te a h alf dosage f o r t h e f i r s t s p r a y r e g a r d l e s s o f t h e p r e d a t o r prey r a t i o , t h e p o s s i b i l i t y o f sav ing some chem icals would e x i s t . S t r a t e g i e s based on F ig u re 3. D e c i s i o n F ra m e w o rk f o r IPM M i t e C o n t r o l S t r a t e g i e s . PREDATOR MITES PER LEAF NO SPRAY NO SPRAY FULL DOSAGE TRP 1 / 3 DOSAGE TRP 1 / 2 DOSAGE FULL DOSAGE FULL DOSAGE HET FULL DOSAGE FET MITES PER LEAF 120 t h i s r e v i s e d r u l e a r e dependent upon t h e sub se qu ent m o n i t o r i n g , b i o l o g i c a l c o n t r o l and f u t u r e s p r a y s t o avoi d l o s s e s i f a f u l l dosage s ho ul d have been a p p l i e d f i r s t . T h e r e f o r e , even with th e p o s s i b i l i t y o f some sa vi n gs on t h e chemical c o s t s , i t might r e s u l t t h a t th e r i s k o f employing one o f t h e s e s t r a t e g i e s may be i n c r e a s e d by t h e danger o f i n c r e a s e d mite damage. The model compares th e s o p h i s t i c a t e d IPM s t r a t e g i e s both w ith the a u t o m a t i c h a l f d o s a g e - f i r s t s p r a y r u l e and w i t h o u t i t . The s t r a t e g i e s examined by t h e model a r e p r e s e n t e d and d e s c r i b e d in Table 2. The performance o f t h e IPM s t r a t e g i e s have been s i m u l a t e d under two assu mpti on s a bo u t th e s i z e o f sampling e r r o r a s s o c i a t e d w ith s c o u t ' s e s t i m a t e o f m it e p o p u l a t i o n . F i r s t , t h e model o p e r a t e d as i f th e sampling e r r o r was z e r o — t h a t th e s c o u t ' s e s t i m a t e was e x a c t l y a c c u r a t e . Then, t h e model r e p e a t e d t h e s i m u l a t i o n s b u t w it h t h e assumption t h a t 95% o f t h e time th e s c o u t ' s e s t i m a t e was w i t h i n 50% o f th e t r u e pop­ ulation. Another f a c t o r which can i n f l u e n c e t h e performance o f th e s t r a t e g i e s i s th e s c o u t i n g i n t e r v a l . The model c u r r e n t l y has two o p t i o n s by which th e s c o u t i n g i n t e r v a l can be d e f i n e d . t a in circumstances. request b asis. Each has i t s advantages f o r c e r ­ The f i r s t o p t i o n can be d e f i n e d as s c o u t i n g on a With t h i s o p t i o n , whenever t h e growers p e r c e i v e t h a t t h e r e i s a problem in t h e o r c h a r d w it h m i t e s , th e y r e q u e s t a v i s i t from a p r o f e s s i o n a l s c o u t who th e n e s t i m a t e s t h e p o p u l a t i o n d e n s i t i e s . This in f o r m a ti o n i s then used by th e d e c i s i o n r u l e o f t h e a p p r o p r i a t e IPM s t r a t e g y and some a c t i o n i s implemented. I t i s assumed t h a t t h e r e i s a t h r e e day d e l a y between when t h e s c o u t i s r e q u e s t e d and when th e v i s i t i s a c t u a l l y made. The s c o u t w i l l v i s i t t h e o r ch ar d tw ic e f o r each r e q u e s t an i n i t i a l v i s i t and a check t h r e e days l a t e r . For t h i s s e r v i c e a charge 121 T ab le 2 . S trittjji M ite Model S t r a t e g i e s . Chemical 1 t. P llctran (1 1/7 lbs/acre i Carzol (2 Ibi/ecro] 4 P ltctran-F ull Dote (1 1/7 lbs/acre) 5 P llctren-F ull Dote 0 1/2 lbs/acre) Typ* Pf Control Program Decision Rule Monitoring Srror •lo lo g lc tl control No chemicals are applied, but control r e lie s on natural predators Calendar Apply fu ll dose a t the end of June and a t the. end of July Hone Apply fu ll dote a t the and of June and. a* the end of July None Full dotage Economic threshold-15 m ites/ lo af. No reduced dosages applied None IPM Full dosage Economic threshold-28 m ites/ le a f. Reduced dosage economic threshold-22 m ites/ leaf None Full dosage economic threshold 28 n lte V le a f Reduced dosage economic threshold 7 aittes/1eaf Calendar IPM 8 P lfctran-F ull Dose (1 1/2 Ibs/acrel IPM 7 P llctran-F ull Dose 0 1/2 lbs/acre) IPM 8 Carzol-(? Ibs/acre] IPM Full dosage economic threshold 28 arites/leaf No'reduced dosages applied None 9 Carzol (2 Ibs/acrel IPM Full dosage economic threshold 15 m ites/leaf No reduced dosages applied None 10 Carzol (21bs/acre) IPM Full dosage economic threshold 35 m ites/leaf No reduced dosages applied None II PHctran-Full dose 0 1/2 Ibs/acrel ?** Full dotage economic threshold 15 a lte s /le a f No reduced dosages applied P5t of time estimated popula­ tio n 1s within SOI of true population 1Z P11ctran-Ful1 dose (1 1/2 lbs/acrel IPM Full dosage economic threshold 2B m llet/leaf Reduced dotage economic threshhold. 22 a lte s /le a f 951 of time estim ated popula­ tion is within SOX of true population IJ P llctran-F ull dose (1 1/2 lbs/acrel ,PH Full dosage economic threshold 38 a lte s /le a f Reduced dotage economic threshhold. 7 m ites/leaf 951 of time estim ated popula­ tio n is within SOI of true population 14 P lletran -F u ll dose (1 1/2 Ibs/acre) IPM Full dosage economic threshold ' 35 a lte s /le a f Reduced dosage economic threshhold. 25 a lte s /le a f 951 o f time estimated popula­ tio n Is within SOX of true population 15 Corzol (2 Ibs/acre) IPM Full dosage economic threshold 28 a lte s /le a f No reduced dosage applied 95X of time estim ated popula­ tio n is within 50* of true population 18 Carzol (2 lb s /a c re )' IPM Full dosage economic threshold IS a lte s /le a f No reduced dosage applied 95t of time estim ated popula­ tio n Is within SOX of true population 17 Carzol (2 lbs/acre) 1PM Full dosage economic threshold35 m ites/leaf Reduced dosage economic threshold 25 a lte s /le a f Full dosage economic threshold 35 a lte s /le a f No reduced dosage applied None None 951 of linn, estim ntrd popula­ tion is within 50* of true population 122 i s a s s e s s e d a t t h e r a t e o f $5.00 p e r te n a c r e block p e r r e q u e s t . The model has been s im u l a te d w it h growers p e r c e i v i n g a m i te problem a t two d iffere n t densities. F i r s t , i t was assumed t h a t th e y r e c o g n i z e d a problem a t 5 m i te s p e r l e a f and then l a t e r i s was a d j u s t e d t o 9 m i t e s p e r l e a f . I t has been d et erm ine d from h i s t o r i c a l r e c o r d a n a l y s i s t h a t growers f i r s t d e t e c t m i t e s a t d e n s i t i e s between 3 and 10 p e r l e a f (148, pp. 46 -4 8) . When t h e e r r o r terms a r e in t r o d u c e d f o r t h e sampling o f t h e mite p o p u l a t i o n th e y a r e a l s o in c l u d e d in t h e growers d e t e c t i o n o f mite problems. The e r r o r s would be t h e same f o r both v a r i a b l e s - - t h e sampling and th e problem p e r c e p t i o n . The second o p ti o n i s t h e s t a n d a r d weekly i n t e r v a l where ev er y seven days a p r o f e s s i o n a l s c o u t v i s i t s th e o rc h a r d and samples t h e p e s t populations.^ The charg e f o r t h i s s e r v i c e i s $12 . 0 0 / a c r e , b u t i t i s assumed t h a t th e sampling o f more than j u s t t h e m it e p o p u l a t i o n o c c u rs . This o p ti o n i s more r e l e v a n t when more tha n one p e s t i s being m oni tor ed. When a s i n g l e p e s t i s c o n s i d e r e d in d e p e n d e n tl y from t h e complex o f p e s t s whose c o n t r o l would l i k e l y b e n e f i t from t h e weekly s c o u t i n g , i t i s d i f f i c u l t t o a s s e s s th e a p p r o p r i a t e ch arg e t o c o n t r o l o f th e s i n g l e pest f o r the scouting se rv ic e . The S t o c h a s t i c Elements o f t h e Model The model i s a Monte Carlo s i m u l a t i o n o f twen ty in de pen den t seas ons f o r each s t r a t e g y . 15. Each season b eg i ns on A pr il 1 and ends on September For each s t r a t e g y , t h e model s i m u l a t e s twenty s ea s o ns so t h a t the performance o f t h e v a r i o u s c o n t r o l programs can be e v a l u a t e d under d i f f e r e n t circumstances. As t h e c o n d i t i o n s in t h e o r c h a r d and th e market change, i t i s u n l i k e l y t h a t s t r a t e g i e s w i l l produce t h e same outcomes. ^In some a n a l y s e s th e i n t e r v a l was changed t o one v i s i t eve ry 14 days. 123 The u n c e r t a i n t y about which c o n d i t i o n s w i l l oc cu r i n f l u e n c e s th e v a r i a b i l i t y in t h e outcomes and hence t h e amount o f r i s k a s s o c i a t e d with eac h s t r a t e g y . The change in c o n d i t i o n s in t h e model i s governed by the random g e n e r a t i o n o f t h e v a l u e s f o r t h e s t o c h a s t i c v a r i a b l e s . The random g e n e r a t i o n o f v a l u e s i s , in t u r n , dete rmin ed by t h e u n d e r l y i n g p r o b a b i l i t y d i s t r i b u t i o n s f o r t h e v a r i a b l e s which a r e u s u a l l y based on h i s t o r i c a l data records. The m i te model has s i x m a jo r s o u r c e s o f u n c e r t a i n t y . 1) They a r e : t h e p r o d u c t p r i c e s ; 2) t h e av era ge d a i l y t e m p e r a t u r e ; 3) t h e number o f d egree days accumulated p r i o r t o A p ril 1; 4) t h e emergence d a t e s of t h e p o p u l a t i o n s ; 5) th e i n i t i a l p o p u l a t i o n d e n s i t i e s ; and 6) th e random sampling e r r o r f o r m o n i to r in g and t h e d e t e c t i o n o f m i t e problems by growers. The p r o d u c t p r i c e s a r e randomly g e n e r a t e d f o r both th e f r e s h and p r o ­ c es s ed ma rkets us ing a m u l t i v a r i a t e random p r o c e s s o r ( 6 3 ) . These s t o ­ c h a s t i c v a r i a b l e s a r e drawn from a m u l t i v a r i a t e d i s t r i b u t i o n which has i n c o r p o r a t e d t h e c o r r e l a t i o n c o e f f i c i e n t s between th e two ma rket p r i c e s and th e y i e l d . Thi s m a i n t a i n s t h e obs erved r e l a t i o n s h i p s o f the v a r i a b l e in t h e random draws. The y i e l d can be drawn f r : m t h r e e a l t e r n a t i v e marginal d i s t r i b u t i o n s which each have a d i f f e r e n t mean v a l u e . The m u l t i v a r i a t e d i s t r i b u t i o n was c o n s t r u c t e d from h i s t o r i c a l d a t a from 1970 t o 1979. This m u l t i v a r i a t e random p r o c e s s o r i s a l s o used i n t h e g e n e r a t i o n o f t h e random we at h e r v a r i a b l e s . Although t h e m i te model does n o t d i r e c t l y use d a i l y p r e c i p i t a t i o n , i t i s drawn from a m u l t i v a r i a t e d i s t r i b u t i o n w ith t h e av er a ge d a i l y te m p e r a t u r e which t h e model does u s e . The c o r r e ­ l a t i o n s which a r e im p o r t a n t in t h e s e d i s t r i b u t i o n s a r e t h e c o r r e l a t i o n c o e f f i c i e n t s between t h e t e m p e r a t u r e and p r e c i p i t a t i o n f o r each day 124 w i t h i n t h e time i n t e r v a l , t h e a u t o c o r r e l a t i o n between t h e p r e c i p i t a t i o n f o r each day and t h e p r e v io u s day. Since t h e season was d i v i d e d i n t o 8 p a r t s o f 21 days e a c h , t h e r e a r e 8 d i s t i n c t m u l t i v a r i a t e d i s t r i b u t i o n s . The p r o b a b i l i t y o f a given te m p e r a t u r e being drawn i s d i f f e r e n t in th e 8 p a r t s o f th e season b u t i t i s i d e n t i c a l f o r a l l 21 days w i t h i n any p a r t o f t h e s e a s o n . The d i s t r i b u t i o n s were developed from h i s t o r i c a l w e a th e r r e c o r d s from t h e E a s t Lansing w ea th e r ex p er im en t s t a t i o n f o r t h e y e a r s between 1910 and 1979. An a l t e r n a t i v e s e t o f d i s t r i b u t i o n s was a l s o developed from d a t a from Grand Rapids (1944-1979). As was p r e v i o u s l y d i s c u s s e d , th e number o f d eg r ee days (base 43° F) t h a t have accumulated p r i o r t o April 1 i s randomly g e n e r a t e d from a normal d i s t r i b u t i o n w it h a mean o f 580 and a s t a n d a r d d e v i a t i o n o f 80. The d egree day cou nt i n f l u e n c e s the p h e n o l o g ic a l s t a g e o f th e t r e e s , t h e amount o f f r o s t damage and c e r t a i n components o f t h e c o d l i n g moth model. The random g e n e r a t i o n o f t h e emergence d a t e s o f t h e p o p u l a t i o n s and th e i n i t i a l p o p u l a t i o n d e n s i t i e s has been p r e v i o u s l y d i s c u s s e d i n t h i s c h a p t e r . The p r o b a b i l i t y d i s t r i b u t i o n s o f t h e s e v a r i a b l e s a r e based on h i s t o r i c a l data. The random sampling e r r o r i s an o p t i o n which can be used i n con­ j u n c t i o n w ith two p r o c e s s e s i n t h e model. I t can a d j u s t t h e ac c u ra cy o f t h e e s t i m a t e o f t h e mite p o p u l a t i o n t h a t i s pr ovi ded by th e p r o f e s s i o n a l scout. I t can a l s o i n f l u e n c e t h e a cc u r ac y o f t h e p e r c e p t i o n o f the grower as t o when t h e p o t e n t i a l o f a m i te problem e x i s t s and a r e q u e s t f o r a p r o f e s s i o n a l s c o u t should be made. The random e r r o r i s drawn from a normal d i s t r i b u t i o n w it h a mean equal t o t h e a c t u a l p o p u l a t i o n d e n s i t y and a s t a n d a r d d e v i a t i o n i n f e r r e d by t h e co n fid e nc e i n t e r v a l d e f i n e d by t h e u s e r o f t h e model. In t h i s ca s e t h e e r r o r i n s u r e s t h a t t h e 125 e s t i m a t e w i l l be w i t h i n 50% o f t h e t r u e p o p u l a t i o n 95% o f th e time. 4.2 The Mite Model R e s u l t s The performance o f a p e s t management s t r a t e g y could be measured in s e v e r a l d i f f e r e n t ways. The ex p ec te d n e t revenue would o b v i o u s l y be an im p o r ta n t one s i n c e i t i n d i c a t e s how on th e a v e r a g e , t h e far me r who adopted a s t r a t e g y would do f i n a n c i a l l y . However, i t i s n o t a complete measure o f t h e val ue t h a t t h e income would have f o r t h e f ar m e r s i n c e i t ig n o r e s any v al u e t h a t may be p la ce d on t h e r i s k a s s o c i a t e d with the strategy. The v a r i a n c e in n e t revenue could be used as a measure o f the i n h e r e n t r i s k o f t h e s t r a t e g y b u t o f t e n i t i s n e c e s s a r y t o examine o t h e r moments o f th e d i s t r i b u t i o n as well t o t r u l y e s t i m a t e th e impact t h a t r i s k can have on optimal d e c i s i o n s . The model r e p o r t s th e ex p ec ted v a l u e and v a r i a n c e in t h e p e r a c r e n e t revenue and p r o v id e s enough i n f o r ­ mation t h a t a l l o t h e r im p o r t a n t moments o f th e d i s t r i b u t i o n can be e s t i m a t e d i f needed. The number o f s p r a y s a p p l i e d and t h e amounts o f t h e chem icals used a r e o f i n t e r e s t n o t only f o r a n a l y s i s o f th e on-farm impact t h a t t h e ad o p t io n o f s t r a t e g i e s could have b u t because o f th e i m p l i c a t i o n s f o r environmental q u a l i t y as w e l l . The model r e p o r t s th e use o f chemicals in terms o f f u l l dose e q u i v a l e n t s . For c a r z o l , a f u l l dose i s an app­ l i c a t i o n o f 2 l b s . p e r a c r e w h i l e f o r p l i c t r a n i t i s a r a t e o f 1 1/2 l b s . per acre. The p r i c e p e r pound f o r t h e two ch em ica ls which th e model c u r r e n t l y uses i s $ 1 6 . 5 0 / l b . f o r c a r z o l and $ 1 8 . 5 0 / l b . f o r p l i c t r a n . The s p r a y c o s t s app ea r i n Table 3. Another i m p o rt a n t performance v a r i a b l e i s t h e e s t i m a t e o f mite damage. Mite damage i s a s s e s s e d i n terms o f d o l l a r s p e r a c r e s i n c e i t i s c a l c u l a t e d as a p e r c e n t a g e r e d u c t i o n i n th e v a l u e o f t h e p o t e n t i a l non- T able 3 . S pray C o sts f o r H ite C o n tro l S t r a te g i e s . Labor C o s t Per A p p lica tio n Machinery C o st Per A p p lication Cost P er A p p lica tion $3 3 .0 0 /a cre $ . 70 /a c re $ . 7 0 /a c r e $ 3 4 .4 0 /a cre $ 2 7 .7 5 /a cre $ . 70 /a c re $ . 7 0 /a c r e $ 29.15 /a c r e $ 1 3 .875/acre $ . 70 /a c re $ . 70/acre $ 1 5 .275/acre $ 9 .2 5 /a cre $ . 7 0 /a cre $ . 70 /a cre $ 1 0 .6 5 /a cr e Spray Chemical . Price P er U n it Chemical C o st Per A p p lic a t i o n C arzol (2 l b s / a c r e ) S16. 5 0 / l b P l i c t r a n (1 1 / 2 I b s / a c r e ) $ i s . 5 0 / l b P lic tr a n (3 /4 lb /a c r e ) $ 1 8 .5 0 /1 b P lic tr a n 1/2 lb /a c r e ) $ 1 8 .5 0 /lb SOURCE: P e s t Control Branch, NREO, ERS, USDA. 127 m it e damaged h a r v e s t , Since t h e f i g u r e s f o r mite damage a r e h e a v i l y i n f l u e n ­ ced by t h e assumptions t h a t d i r e c t l y i n f l u e n c e th e d e t e r m i n a t i o n o f th e y i e l d , c a u t i o n must be e x e r c i s e d in u s in g th e numbers as an a b s o l u t e e s t i ­ mate. They were d es ign ed more f o r r e l a t i v e comparisons with each o t h e r . Another v i t a l s t a t i s t i c i s one which a t t e m p t s t o b a l a n c e t h e e x p e n d i t u r e s on p e s t c o n t r o l with the amount o f p e s t damage t h a t i s experienced. I f t h e two measures a r e c o n s i d e r e d in d e p e n d e n tl y t h e p o t e n ­ t i a l f o r some s p u r i o u s c o n c l u s i o n s i s h i g h . I t would n o t be a t a l l i n f e a s i b l e t o imagine c a s e s where small amounts o f damage a r e observed b u t l a r g e expenses f o r p e s t c o n t r o l have been i n c u r r e d , o r v i c e v e r s a . The v a r i a b l e , "Control C o s t s , " t r i e s t o a cc ou nt f o r t h i s measure. I t is t h e sum o f t h e m it e damage, and t h e c o s t s o f t h e ch em ica ls a p p l i e d , and t h e l a b o r and machinery used i n t h e s p r a y a p p l i c a t i o n s . For each o f t h e s t r a t e g i e s , t h e ex pe ct ed v a l u e s and s t a n d a r d d e v i a t i o n s ap pea r f o r each performance v a r i a b l e i n Table 4. I t should be noted t h a t t h e s e r e s u l t s a r e f o r a weekly s c o u t i n g program where a m o n i to r in g charge o f $12 / a c r e has been a s s e s s e d t o t h e IPM s t r a t e g i e s f o r the control mites. The performance o f s t r a t e g i e s w it h th e o p t i o n which p r o v i d e s a s c o u t on r e q u e s t from t h e grower w i l l be discussed l a t e r . I t s h o u ld a l s o be remembered t h a t s t r a t e g i e s 4-10 have no sampling e r r o r w h ile s t r a t e g i e s 11-17 have a random e r r o r in th e e s t i m a t e s o f th e p o p u l a t i o n d e n s i t i e s provided by th e p r o f e s s i o n a l scout. The s t r a t e g i e s were s i m u l a t e d w i t h t h e medium o r low y i e l d levels. Medium Yiel d and Weekly Sco utin g At t h e medium y i e l d l e v e l , o f t h o s e s t r a t e g i e s w i t h th e zero sampling e r r o r , s t r a t e g y 6 has t h e h i g h e s t expec ted n e t reven ue . I t has a very low reduced dosage economic t h r e s h o l d (HET-7 m i te s p e r l e a f ) 128 Table 4. Mite Model R e s u l t s w ith Medium Yiel d and Weekly Sco uti ng . S trategy P o te n tia l Yield (bu/acre) Mite Damage (S /acre) 1 502.1 (47.5) 112.0 (115.2) 2 502.1 (47.5) 26.1 (64.2) 2 (0 .0 ) 3 502.1 (47.5) 27.7 (65.5) 2 (0.0) 4 502.1 (47.5) 1.4 (5.1) 2 (1.8) 5 502.1 (47.5) 3.6 (6.8) 6 502.1 (47.5) 7 Humber Of 5prays P lic tra n (F.D .E.*) »»» Cftrzol (F.D .E.*) Total Control Costs (5 /a c re ) Net Revenue (5 /a c re ) . . . 482.7 (48.0) 296.4 (618.3) • •• 369.3 (128.4) 323.9 (689.9) 2:0 (0 .0 ) 383.0 (131.1) 311.8 (690.3) 2.0 (1.8) « ... 319.8 (51.8) 348.7 (685.9) 2 (1.6) 1.7 (1.6) mmm 314.9 (53.1) 355.8 (685.7) 1.1 (5.1) 2 (1.8) 1.6 (1 .5 ) 308.0 (44.8) 360.2 (692.1) 502.1 (47.5) 4.5 (8.5) 2 (1 .5) 1.5 (1 .5 ) mmm 311.7 (55.2) 359.9 (687.7) 502.1 (47.5) 7.2 (9.2) 2 (1.7) *->- 2 .0 (1 .7 ) 340.2 (73.1) 334.1 (681.1) 9 502.1 (47.5) 1.4 (5.1) 2 (1.9) 2 .2 (1 .9 ) 337.2 (64.5) 331.3 (680.9) 10 502.1 (47.5) 13.5 (14.2) 2 (1 .7 ) 1.8 (1 .7 ) 347.7 (8 1 .2 ) 332.9 (679.5) 11 502.1 (47.5) 1.8 (5.1) 2 (1 .8 ) 2.0 (1.8) mmm 319.1 (5 3 .1 ) 349.7 (687.8) 12 502.1 (47.5) 3.2 (6.5) 2 (1.8) 1.8 (1 .8 ) mmm 317.0 (57.7) 353.3 (688.7) 13 502.1 (47.5) 1.1 (5.1) 2 (1.6) 1.6 (1 .5 ) mmm 307.5 (43.7) 360.7 (692.8) 14 502.1 (47.5) 4.5 (6 .8 ) 2 (1 .7 ) 1.7 (1 .6 ) mmm 317.5 (55.3) 354.2 (688.5) 15 502.1 (47.5) 7.2 (9.5) 2 (1.7) 1.9 (1 .7 ) 338.5 (69.9) 335.8 (683.9) 16 502.1 (47.5) 1.7 (5 .0 ) 2 (1.9) 2.1 (1 .9 ) 334.5 (6 5 .7 ) 334.3 (679.1) 17 502.1 (47.5) 13.0 (13.0) 2 (1 .7 ) 1.9 (1 .7 ) 348.5 (80.0) 331.6 (681.9) 8 • * F ull Dose E qu iva le n ts 2 .0 (0 .0 ) • •• mmm 129 and a moderate f u l l dose economic t h r e s h o l d (FET-22 m i te s p e r l e a f ) . The s t r a t e g y w it h the h i g h e s t economic t h r e s h o l d s , s t r a t e g y 7 (FET-35, and HET-25), has an ex p ec te d n e t revenue o f only $ . 3 0 / a c r e l e s s than s t r a t e g y 6. There i s more damage e x p e r i e n c e d w it h s t r a t e g y 7 b u t s t r a t e g y 6 u ses s l i g h t l y more o f t h e m i t i c i d e . All o f t h e IPM s t r a t e g i e s have ex pe ct ed n e t r ev enu es g r e a t e r than th e co n v en t io n al c a l e n d a r s p r a y program. The c o n v e n t i o n a l programs s u f f e r c o n s i d e r a b l y more damage and use more chem icals th a n t h e IPM strategies. The c a r z o l s t r a t e g i e s produced n e t r ev enu es from $26 t o $13 an a c r e below t h e i r p l i c t r a n c o u n t e r p a r t s . These d i f f e r e n c e s r e f l e c t t h e h i g h e r s p r a y c o s t s and t h e d i s r u p t i o n o f t h e n a t u r a l p r e ­ dation. The b i o l o g i c a l c o n t r o l s t r a t e g y has an avera ge n e t r e t u r n below th e c a l e n d a r s p r a y programs b u t t h e n a t u r a l p r e d a t i o n c o m pl et e ly p r e v e n t s t h e m i te s from c a us in g damage i n 7 of t h e 20 s e a s o n s . The i n t r o d u c t i o n o f t h e random sampling e r r o r has a g r e a t e r impact on th e IPM s t r a t e g i e s w i t h t h e high economic t h r e s h o l d s th a n on th e ones w it h t h e lower t h r e s h o l d s . In f a c t , s t r a t e g i e s 4 and 6 d i s p l a y a marginal improvement w h il e s t r a t e g i e s 5 and 7 e x p e r i e n c e d e c l i n e s in t h e i r e x pe c te d n e t r e v e n u e s. o f over $ 5 / a c r e . S t r a t e g y 7 has a r e d u c t i o n i n n e t income A s i m i l a r p a t t e r n i s e x h i b i t e d by th e c a r z o l s t r a t e g i e s . When t h e d e c i s i o n r u l e s a r e r e v i s e d t o always ap p ly a h a l f dose on t h e f i r s t s p r a y r e g a r d l e s s o f th e p r e d a t o r / p r e y r a t i o , t h e p l i c t r a n IPM s t r a t e g i e s a l l un v ei l h i g h e r ex p ec ted n e t rev enue e s t i m a t e s . r e s u l t s o f t h e s i m u l a t i o n ap p e a r in Table 5. The With t h e e x c e p t i o n o f s t r a t e g y 7, t h e i n c r e a s e in t h e n e t revenue i s a b ou t $ 8 / a c r e . Strategy 7 e x p e r i e n c e s o n ly a $ 2 / a c r e i n c r e a s e which i s p r o b a b ly bec ause i t s reduced dose economic t h r e s h o l d i s so high t h a t i t p r e v i o u s l y a p p l i e d a T ab le 5 . M ite Model R e s u l t s w it h Medium Y i e l d , Weekly S c o u tin g and R e v is e d D e c i s i o n R u les Which Always Apply a H a lf Dose on F i r s t Spray. P o te n tia l Y ie ld (b u /acre) M ite Damaqe ($ /a cre) •lumber of Snr-.'.ys P lic tr a n (F .D .E .)* Carzol ( F . D .E .* ) T ota l Control C o sts ($ /ec re ) Net Revenue ( 5 /2 C - 0 ) 4 502.1 (4 7 .5 ) 1 .5 (5 .0 ) 2 (1 .8 ) 1.7 (1 .7 ) 3 1 2 .4 (4 8 .4 ) 356.1 (6 8 4 .0 ) 5 502.1 (4 7 .5 ) 3 .5 (5 .4 ) 2 (1 .6 ) 1.4 (1 .4 ) 3 0 7 .8 (4 4 .1 ) 362 .8 (6 8 8 .5 ) 6 502.1 (4 7 .5 ) 1.1 (5 .1 ) 2 (1 .6 ) 1.3 (1 .3 ) 3 0 0 .2 (3 8 .4 ) 368.1 (6 9 4 .6 ) 7 502.1 (4 7 .5 ) 5 .8 (1 0 .2 ) 2 (1 .6 ) 1 .4 (1 .4 ) 3 1 1 .0 ( 5 5 .5 ) 3 6 1 .8 ( 6 8 9 .1 ) 11 502.1 (4 7 .5 ) 1 .8 (5 .1 ) 2 (1 .9 ) 1.8 (1 .7 ) 3 1 4 .5 ( 5 0 .2 ) 3 5 4 .3 (6 8 4 .2 ) 12 5 02.1 (4 7 .5 ) 2 .8 (5 .3 ) 2 (1 .6 ) 1.5 (1 .4 ) 3 07.1 ( 4 4 .0 ) 362.8 (6 9 1 .3 ) 13 502.1 (4 7 .5 ) 1 .1 (5 .1 ) 2 (1 .6 ) 1 .3 (1 .3 ) 299 .5 (3 7 .9 ) 3 6 8 .7 (6 9 5 .1 ) 14 502.1 (4 7 .5 ) 4 .3 (6 .1 ) 2 (1 .7 ) 1 .3 (1 .4 ) 3 0 6 .6 (4 8 .3 3 6 4 .8 (6 8 9 .4 ) *Ful1 Dose E q u iv a le n t ' 131 h a l f dose on t h e f i r s t s pr ay on a r e g u l a r b a s i s . In most c a s e s , t h e amount o f chemical a p p l i e d i s reduced w h il e t h e amount of damage remains alm os t unchanged. S t r a t e g y 7 does have i t s damage i n c r e a s e over $ l / a c r e b u t th e s av in g s from t h e reduced m i t i c i d e usage exceed t h i s amount by $2/acre. The i n t r o d u c t i o n o f t h e random sampling e r r o r has a marginal impact on th e expected n e t r e v en ue s. The l a r g e s t change i s observed in S t r a t e g y 7 and i t i s an i n c r e a s e i n t h e av era ge n e t income o f $ 3 / a c r e . Low Yiel d and Weekly Scouting The low y i e l d s c e n a r i o produces model r e s u l t s s l i g h t l y d i f f e r e n t than the p r e v i o u s s c e n a r i o . The r e s u l t s a r e shown in Table 6. s t r a t e g y with th e h i g h e s t ex pe ct ed n e t revenue i s s t r a t e g y 7. income i s $15 h i g h e r th a n th e n e t income o f s t r a t e g y 6. The I ts net The IPM s t r a t e g i e s have average n e t revenues $14 t o $27 p e r a c r e h i g h e r th an t h e c o n v en ti o na l c a l e n d a r s p r ay programs. All s t r a t e g i e s ap p ly the same amount o f chemicals as with t h e p r e v i o u s s c e n a r i o b u t th e damage e s t i m a t e s a r e lower r e f l e c t i n g the change in t h e y i e l d . The s t r a t e g y u s i n g e x c l u s i v e l y b i o l o g i c a l c o n t r o l g e n e r a t e s an ex p e c te d n e t revenue h i g h e r than t h e c o n v e n t io n a l c a l e n d a r s p r a y programs, t h e sim pl e p l i c t r a n IPM s t r a t e g y and a l l o f th e ca r z o l IPM s t r a t e g i e s . The co n v e n t io n a l program a p p l y in g p l i c t r a n i s s l i g h t l y more p r o f i t a b l e tha n th e c a r z o l IPM s t r a t e g y w it h th e lo w es t eocnomic t h r e s h o l d . The l a t t e r s t r a t e g y a p p l i e s t h e most s p r a y s on average o f any o f th e s t r a t e g i e s examined. The pr es en ce o f t h e random sampling e r r o r i n f l u e n c e s th e r e l a t i v e performances o f t h e s t r a t e g i e s in much t h e same way as was uncovered earlier. The changes i n ex p e c te d n e t revenue a r e small e x c e p t f o r th o s e s t r a t e g i e s w it h l a r g e economic t h r e s h o l d s . The p l i c t r a n IPM s t r a t e g y with th e h i g h e s t economic t h r e s h o l d s s u f f e r s alm os t a $ 6 /a c r e d e c l i n e in 132 Table 6. tra te g y Mite Model R e s u l t s with Low Yield and Weekly Sco uti ng. P o te n tia l Yield (b u /acre) Mite Damage (S /acre) Nianber of Sprays P lic tra n (F.D .E.)* 1 248.0 (50.8) 52.1 (55.2) z 248.0 (50.8) 14.5 (36.1) 2 (0.0) 3 248.0 (50.8) 15.4 (36.8) 2 (0.0) -- 4 248.0 (50.8) .6 (2.2) 2 (1.8) 5 248.0 (50.8) 1.7 (3.4) 6 248.0 (50.6) 7 Carzol (F.D .E.*) T otal C ontrol Costs (S /a c re ) Net Revenue (S/acre! 362.9 (110.4) -346.6 (301.3) 346.1 (72.1) -367.4 (321.3) 358.3 (73.5) -378.7 (321.3) 2.0 (1.8) 318.3 (51.6) -353.5 (324.1) 2 (1.6) 1.7 (1.6) 311.1 (49.3) -345.2 (321.6) 0.5 (2 .3 ) 2 (1.8) 1.6 (1.5) 306.8 (44.4) -342.1 (324.1) 248.0 (50.8) 2.2 (4.4) 2 (1.5) 1.5 (1.5) 307.0 (49.6) -340.6 (322.8) 8 248.0 (50.8) 3.5 (4.9) 2 (1.7) 2 .0 <1.7) 332.9 (66.5) -365.2 (321.3) 9 248.0 (50.8) 0.6 (2.2) 2 (1.9) !■ 2.2 (1 .9 ) 335.7 (64.4) -370.9 (319.6) 10 248.0 (50.8 6.6 (7.4) 2' (1.7) .. 1.8 (1 .7 ) 333.9 (69.5) -363.1 (318.6) 11 248.0 (50.8) 0.8 (2.2) 2 (1.8) 2.0 (1.8) 317.2 (52.4) -352.2 (324.7) 12 248.0 (50.8) 1.6 (3.2) 2 (1.8) 1.8 (1.8) 313.7 (54.4) -348.0 (322.2) T3 248.0 (50.8) 0.5 (2 .3 ) 2 (1.6) 1.6 (1.5) 306.2 (4 3 .3 ) -341.5 (325.0) 14 248.0 (50.8) 2.2 (3 .3 ) 2 (1 .7 ) 1.7 (1.6) 312.8 (5 1 .7 ) -346.4 (321.3) 15 248.0 (50.8) 3.5 (4.9) 2 (1 .7 ) .. 1.9 (1 .7 ) 331.1 (64.1) -363.4 (322.9) 16 248.0 (50.8) .8 (2.3) 2 (1.9) — 2.1 (1 .9 ) 332.6 (6 5 .2 ) -367.6 (319.5) 17 248.0 (50.8) 6.4 (6.8) 2 (1.7) •• 1.9 (1 .7 ) 335.1 (6 9 .3 ) -364.6 (321.4) ♦ F u ll Dose E q u iv a le n ts 2 (0.0) 2.0 (0 .0 ) • _ 133 n e t income when th e sampling e r r o r i s c o n s i d e r e d . The m a j o r i t y o f s t r a t e g i e s e x p e r i e n c e a change in n e t revenue o f $ 2 / a c r e o r l e s s which ca nno t be viewed a s v er y l a r g e when t h e s i z e o f th e sampling e r r o r i s considered. The ex p e c te d n e t revenues o f most o f th e p l i c t r a n IPM s t r a t e g i e s can be i n c r e a s e d by $7 t o $8 p e r a c r e by r e v i s i n g t h e d e c i s i o n r u l e s t o ap p ly a h a l f dose on th e f i r s t s p r a y r e g a r d l e s s o f th e p r e d a t o r / p r e y ratio. This p r o v id e s t h e p r e d a t o r s more o f a chance t o become e s t a b l i s h e d before a fu ll strength treatm ent is applied. The e x c e p t i o n t o t h i s o b s e r v a t i o n i s s t r a t e g y 7 which p r e v i o u s l y a p p l i e d a h a l f dose f i r s t s p r a y due t o i t s high reduced dose economic t h r e s h o l d . p e r a c r e i n c r e a s e i n n e t income of $2. I t displays a These r e s u l t s a r e p r e s e n t e d in Table 7. Medium Yiel d and Biweekly Sco utin g When t h e s c o u t i n g i n t e r v a l i s changed from e v e r y seven days t o ev ery 14 d ay s , th e expec ted n e t r eve nue s o f t h e p l i c t r a n IPM s t r a t e g i e s with t h e high economic t h r e s h o l d s d e c l i n e s u b s t a n t i a l l y . r e s u l t s a r e d i s p l a y e d in Table 8. These The s t r a t e g i e s examined used the r e v i s e d d e c i s i o n r u l e s which a u t o m a t i c a l l y appl y a h a l f dose on the f i r s t spray. S t r a t e g y 7 s u f f e r s a d e c r e a s e in i t s avera ge n e t income o f over $ l l / a c r e w h i l e s t r a t e g y 6 e n j o ys a s l i g h t i n c r e a s e in i t s n e t revenue. I t a p p e a r s t h a t t h e lo n g e r th e s c o u t i n g i n t e r v a l , t h e l e s s e f f i c i e n t a r e t h e s t r a t e g i e s w i t h t h e high economic t h r e s h o l d s . Medium Yield and Sco utin g on Request w ith a Grower Problem P e r c e p t i o n a t 5 Mites Per Leaf In t h i s s c e n a r i o t h e s c o u t i n g program i s changed t o a system where t h e s c o u t v i s i t s t h e o r c h a r d on ly when a grower p e r c e i v e s a m i te problem T ab le 7 . S trategy H i t e Model R e s u l t s w it h Low Y i e l d . Weekly S c o u t in g and R ev is ed 7 D e c i s i o n R u l e s . P o te n tia l Y ie l d (b u /a cr e) M ite Damage ($ /a cr e) Number of S pra ys P lictra n (F .D .E .)* C arzol (F .D .E .* ) Total C o n tro l C o sts ($ /a cr e) Net Revenue ($ /a cr e) 4 2 48 .0 (5 0 .8 )' .7 ( 2 .2 ) 2 (1 .8 ) 1.7 (1 .7 ) 310 .8 ( 4 8 .2 ) -3 4 6 .0 ( 3 2 1 .3 ) 5 248 .0 (5 0 .8 ) 1 .6 (2 .3 ) 2 (1 .6 ) 1 .4 (1 .4 1 3 0 4 .0 (4 1 .9 ) - 3 3 8 .2 (3 2 2 .7 ) 6 248 .0 (5 0 .8 ) .5 (2 .3 ) 2 (1 .6 ) 1.3 (1 .3 ) 298 .9 (3 8 .1 ) -3 3 4 .2 (3 2 6 .8 ) 7 248.0 (5 0 .8 ) 2 .8 (5 .5 ) 2 (1 .6 ) 1 .4 (1 .4 ) 3 0 5 .1 (4 8 .2 ) -3 3 8 .1 (3 2 4 .3 ) 11 248 .0 (5 0 .8 ) .8 (2 .3 ) 2 (1 .9 ) 1 .8 (1 .7 ) 3 12.6 ( 4 9 .6 ) -3 4 7 .6 (3 2 1 .5 ) 12 2 48.0 (5 0 .8 ) 1 .3 (2 .4 ) 2 (1 .6 ) 1.5 (1 .4 ) 3 04.2 (4 2 .7 ) -3 3 8 .7 (3 2 5 .2 ) 13 248.0 (5 0 .8 ) .5 (2 .3 ) 2 (1 .6 ) 1 .3 (1 .3 ) 298 .2 (3 7 .6 ) -3 3 3 .5 (3 2 6 .8 ) 14 248.0 (5 0 .8 ) 2 .0 (2 .9 ) 2 (1 .7 ) 1 .3 (1 .4 ) 302 .1 (4 4 .9 ) -3 3 5 .8 (3 2 2 .4 ) * F u l l Dose E q u i v a le n t s 135 Table 8. Strategy The I n f l u e n c e o f th e Scou ting I n t e r v a l on Net Revenue. Expected Net Revenues 7 day 14 day 4 356.1 353.0 5 362.8 355.8 6 368.1 369.6 7 361.8 350.3 136 d ev e l o p in g . The grower o f t h e t y p i c a l o r c h a r d p e r c e i v e s a problem when th e p o p u l a t i o n d e n s i t y i s a t 5 m i t e s p e r l e a f . There i s a 3 day l a g between t h e time t h a t r e q u e s t f o r t h e s c o u t i s made and t h e v i s i t t o th e o r c h a r d i s a c t u a l l y p a i d . The s c o u t e s t i m a t e s the m i te and p r e ­ d a t o r p o p u l a t i o n s and an a c t i o n i s implemented f o l l o w i n g t h e d e c i s i o n ru les o f the control s t r a t e g i e s . Three days a f t e r t h e f i r s t v i s i t the s c o u t r e t u r n s f o r a second v i s i t . v i s i t s i s $5.00 p e r 10 a c r e b lo c k . The ch arg e f o r t h e s e r i e s o f two The model r e s u l t s from t h i s s c e n a r i o a r e p r e s e n t e d in Table 9. In t h i s s c e n a r i o t h e p l i c t r a n IPM s t r a t e g i e s w ith th e h ig h e r economic t h r e s h o l d s produce t h e h i g h e s t ex pe c te d n e t r e v e n u e s . S t r a t e g i e s 5 and 7 a r e on t h e av e r a g e $1.5 t o $4.5 p e r a c r e more p r o f i t a b i l i t y than s t r a t e g y 6. They apply l e s s m i t i c d e but s u f f e r more damage. All o f t h e IPM s t r a t e g i e s have expec ted n e t r ev enu es h i g h e r th an th e b i o l o g i c a l c o n t r o l and t h e co n v en t io n al c a l e n d a r based programs. The av er a g e n e t incomes o f th e c a r z o l s t r a t e g i e s a r e $12 t o $28 lower th a n t h e i r p l i c t r a n c o u n t e r ­ parts. The i n t r o d u c t i o n o f th e random sampling e r r o r has t h e s u r p r i s i n g result o f i n c r e a s i n g t h e e xp ec te d n e t revenue o f t h e m a j o r i t y o f the strategies. Of th e seven IPM s t r a t e g i e s examined, o n ly t h r e e s t r a t e g i e s had a d e c l i n e in n e t revenue w i t h t h e sampling e r r o r . The sampling e r r o r i s p r e s e n t in both t h e s c o u t ' s e s t i m a t e o f t h e m it e p o p u l a t i o n s and in th e d e n s i t y a t which t h e grower p e r c e i v e s a probelm d e v el o pi n g. The i n c r e a s e s i n n e t revenues may be i n d i c a t i n g t h a t t h e r e e x i s t s a p o t e n t i a l t o f u r t h e r r e f i n e t h e d e c i s i o n r u l e s o f th e s t r a t e g i e s . All o f t h e changes i n t h e revenue e s t i m a t e s due t o t h e sampling e r r o r s ar e l e s s than $ 2 / a c r e . 137 Table 9. Mite Model R e s u l t s w ith Medium Yiel d and Grower Problem P e r c e p t io n a t 5 Mites p e r Leaf. Total Control Costs (S /a c re ) Net Revenue (S /a c re ) 470.7 (230.4) 308.4 (618.3) 357.3 (128.4) 335.9 (689.9) 371.0 (131.1) 323.8 (690.3) mmm 308.2 (51.2) 359.9 (687.2) mmm 296.1 (46.2) 372.4 (690.6) 297.4 (45.4) 370.7 (686.4) ••• 294.0 (46.8) 375.2 (685.9) 2 .0 (1 .8 ) 322.6 (66.1) 347.3 (684.2) . .. 2.2 (1 .8 ) 325.3 (63.7) 342.9 (678.9) 2 (1 .7 ) • •• 1.9 (1 .7 ) 325.0 (70.2) 347.8 (680.5) 1.1 (4.8) 2 (1 .7 ) 1.9 (1 .7 ) ••• 306.8 (51.7) 361.3 (686.1) 502.1 (47.5) 1.6 (5.3) 2 (1.6) 1.4 (1 .5 ) ... 294.5 (4 6 .7 ) 13 502.1 (47.5) 1.1 (4.8) 2 (1.7) 1.5 (1 .5 ) 14 502.1 (47.5) 2.1 (4.7) 2 (1 .5 ) 1.4 (1 .4 ) 502.1 44 7 .5 ) 3.8 (5.8) 2 (1-7) 16 502.1 (47.5) 1.2 (4.7) 2 (1.8) 17 502.1 (47.5) 7.4 (3.9) 2 (1 .7 ) P otential Yield (b u /acre) H ite Damage (S /acre) 1 502.1 (47.5) 112.0 (115.2) 2 502.1 (47.5) 26.1 (64.2) 2 (0.0) 2.0 (0.0) 3 502.1 (47.5) 27.7 (65.5) 2 (0.0) *•* 2.0 (0 .0 ) 4 502.1 (47.5) 1.1 (4.8) 2 (1 .7 ) 2.0 (1 .7 ) 5 502.1 (47.5) 1.5 (4.7) 2 0 .6 ) 1.5 (1.5) 6 502.1 (47.5) 1.1 (4.8) 2 (1.7) 7 502.1 (47.5) 2.1 (4.8) 2 (1.5) 8 502.1 (47.5) 2.9 (4.9) 2 (1 .8 ) 9 502.1 (47.5) 1.1 (4.8) 2 (1 .8 ) 10 502.1 (47.5) 5.8 (6.2) 11 502.1 (47.5) 12 tra te g y 15 1 * F u ll Dose E q uiv a le nt Number of Sprays P lic tra n (F.D .E.*) Carzol (F.D .E.*) . .. ' 1.6 (1 .5 ) 1.4 (1 .4 ) ■ 374.2 (688.3) 295.4 (46.7) 372.2 (691.2) ••• 294.1 (46.4) 375.1 (687.6) 2 .0 (1 .7 ) 324.5 (65.8) 346.4 (676.2) ... 2.2 (1 .8 ) 325.7 (6 4 .0 ) 342.6 (678.9) . .. 1.8 (1 .7 ) 324.9 (72.8) 349.6 (677.0) 138 R evi sin g t h e d e c i s i o n r u l e s t o always app ly a h a l f dose on th e f i r s t s p r a y , i n c r e a s e s t h e ex pec ted n e t revenue by between $8 t o $10 an a c r e f o r each o f th e p l i c t r a n IPM s t r a t e g i e s . Table 10 c o n t a i n s t h e s e r e s u l t s . The amounts o f m i t i c i d e a p p l i e d in t h i s ca se a r e th e lo w es t f o r a l l o f the s c e n a r i o s examined. The damage e s t i m a t e s a r e equal t o o r s l i g h t l y lower than t h e o t h e r r e s u l t s as w e l l . S t r a t e g y 7 , whose expected n e t revenue was r e l a t i v e l y unimproved by t h e r e v i s e d d e c i s i o n r u l e s in th e p re v io u s s c e n a r i o s , r e g i s t e r s one o f t h e l a r g e s t i n c r e a s e s i n t h i s s c e n a r i o . However, when t h e random sampling e r r o r i s c o n s i d e r e d , th e i n c r e a s e i s reduced by h a l f . Three o f the f o u r s t r a t e g i e s e x p e r i e n c e d e c l i n e s in t h e i r ex p ec ted n e t revenues o f al m os t $ 5 / a c r e due t o t h e sampling error. This i s t h e f i r s t time when a p a t t e r n o f a s i g n i f i c a n t de c r e a se in income has been enc o un te re d when t h e sampling e r r o r was i n t r o d u c e d . Medium Yield and Scou ting on Request Grower Problem P e r c e p t i o n a t 9 Mites p e r Leaf In t h i s s c e n a r i o , th e s c o u t i n g program i s v e r y s i m i l a r t o th e system o f t h e p re v io u s s c e n a r i o e x c e p t t h a t t h e growers re c o g n i z e a problem dev el o pi n g when th e m it e p o p u l a t i o n r e a c h e s a d e n s i t y o f 9 m i te s per leaf. At t h i s l e v e l , a r e q u e s t i s made f o r a s c o u t t o v i s i t t h e orc ha rd i n t h r e e days and measure th e p o p u l a t i o n . The s c o u t ' s p o p u l a t i o n e s t i m a t e s a r e then used in t h e d e c i s i o n r u l e s o f t h e IPM s t r a t e g i e s . r e s u l t s f o r t h i s s c e n a r i o ap p ea r in Table 11. The model I t can be seen t h a t l i t t l e has changed by a d j u s t i n g t h e l e v e l a t which growers i d e n t i f y a mite problem d ev e l o p in g . S t r a t e g y 7 s t i l l produces t h e h i g h e s t ex p ec ted n e t revenue by a p pl yi n g t h e l e a s t amount o f mi t i c i d e . experience S t r a t e g i e s 4 and 6 t h e low es t damage but as e x pe c te d w i t h t h e i r low economic t h r e s h o l d s , the y appl y more chem icals than s t r a t e g y 7. The ca rz o l Tab le 1 0. M ite Model R e s u l t s w i t h Medium Y i e l d s , Grower Problem P e r c e p t io n a t 5 M ite s p e r L e a f and t h e R evised D e c i s i o n R u les which Always Apply a H a lf Dose on t h e F i r s t Spray. P o ten tia l Y ie ld (b u /a cre) 4 M ite Damage T o ta l Control C osts ($ /a cr e) Net Revenue ($ /a cr e) Number of Sprays P lictra n ( F . D .E .* ) 502 .1 (4 7 .5 ) 1.1 (4 .8 ) 2 (1 .7 ) 1.6 (1 .5 ) 2 97 .7 (4 5 .9 ) 3 7 0 .5 ( 6 7 9 .7 ) 5 502.1 (4 7 .5 ) 1 .6 (4 .7 ) 2 (1 .6 ) 1.2 (1 .3 ) 288 .4 (4 1 .0 ) 3 8 0 .3 (6 9 3 .7 ) 6 502.1 (4 7 .5 ) 1.1 (4 .8 ) 2 (1 .7 ) 1 .3 (1 .4 ) 2 8 9 .9 (4 0 .6 ) 3 78.3 (6 9 0 .1 ) 7 5 02.1 (4 7 .5 ) 2 .0 (4 .8 ) 2 (1 .5 ) 1.0 (1 .2 ) 2 83.9 (3 9 .3 ) 385.1 ( 6 9 1 .0 ) 11 502.1 (4 7 .5 ) 1 .1 (4 .8 ) 2 (1 .8 ) 1.7 (1 .7 ) 3 0 2 .2 (4 9 .6 ) 3 6 6 .0 (6 8 0 .8 ) 12 5 02.1 (4 7 .5 ) 1.7 (4 .7 ) 2 (1 .7 ) 1.3 (1 .4 ) 292.2 (4 5 .1 ) 3 7 6 .6 ( 6 9 4 .1 ) 13 502.1 ( 4 7 .5 ) 1.1 (4 .8 ) 2 (1 .6 ) 1.3 (1 .3 ) 2 8 7 .3 ( 3 8 .6 ) 3 8 0 .8 (6 9 4 .0 ) 14 502.1 (4 7 .5 ) 2.9 (4 .9 ) 2 (1 .6 ) 1.2 (1 .4 ) 289 .4 (4 4 .7 ) 3 8 0 .6 (6 9 0 .9 ) S trategy * F u ll Dose E q u i v a le n t s Carzol ( F . D .E .* ) ($ /a cre) Table 11. Mite Model R e s u l t s with Medium Yield and Grower Problem P e r c e p t i o n a t 9 Mites p e r Leaf. Total Control Costs (5 /a c re ) Net Revenue ($ /a c re 470.7 (230.4) 308.4 (618.3) 357.3 (128.4) 335.9 (689.9) 371.0 (131.1) 323.8 (690.3) 306.9 (5 1 .1 ) 361.2 (691.1) 295.7 (45.1) 372.9 (691.9) 294.5 (4 4 .9 ) 373.6 (690.7) 292.5 (43.8) 376.5 (689.2) 1.9 (1 .7 ) 319.9 (6 3 .6 ) 350.0 (683.7) 2.1 (1.8) 320.6 (61.0) 347.6 (686.7) 1.8 (1 .7 ) 322.1 (6 7 .6 ) 350.4 (681.1) 1.9 (1 .7 ) 306.2 (52.3) 362.1 (688.3) 2 (1.7) 1.6 (1 .6 ) 299.7 (50.1) 369.1 (684.8) 1.1 (4.8) 2 (1.7) 1.5 (1.5) 293.7 (44.8) 374.4 (691.8) 502.1 (47.5) 2.8 (5.3) 2 (1.7) 1.5 (1.5) 296.8 (5 0 .2 ) 373.0 (6S6.7) IS 502.1 (47.5) 3.5 (5.5) 2 (1 .8 ) 1.9 (1 .8 ) 321.5 (67.0) 349.1 (693.1) 16 502.1 (47.5) 1.2 (4.7) 2 (1.9) 2.2 (1 .9 ) 326.5 (65.6) 341.8 (679.3) 17 502.1 (47.5) 7.4 (8.7) 2 (1.7) 1.8 (1 .7 ) 324.3 (7 2 .4 ) 350.2 (674.2) P o te n tia l Yield (b u /acre) Mite Damage (J/a c re ) 1 502. T (47.5) 112.0 (115.2) 2 502.1 (47.5) 26.1 (64.2) 2 (0.0) 3 502.1 (47.5) 27.7 (65.5) 2 (0.0) 4 502.1 (47.5) 1.1 (4.8) 2 (1 .7) 2.0 (1.7) 5 502.1 (47.5) 1.6 (4.7) 2 (1 .6 ) 1.5 (1 4) 6 502.1 (47.5) 1.1 (4.8) 2 (1 .7 ) 7 502.1 (47.5) 1.9 (4.7) 2 (1 .5 ) 8 502.1 (47.5) 2.8 (4.7) 2 (1 .7) 9 502.1 (47.5) 1.1 (4.8) 2 (1.8) 10 502.1 (47.5) 5.5 (6.3) 2 (1.7) n 502.1 (47.5) 1.2 (4.7) 2 (1.7) 12 502.1 (47.5) 1.7 (4.7) 13 502.1 (47.5) 14 •trateg y - F u l l Dose E q u iv a le n t Number of Sprays P lic tra n (F.D.E.)*. 2.0 (0.0) Carzol (F .D .E .-) mm 2 .0 (0 .0 ) ■ 1.5 (1.5) mm , mm 1.4 (1.4) mm mm „ 141 s t r a t e g i e s a r e once a g a i n l e s s p r o f i t a b l e tha n t h e p l i c t r a n s t r a t e g i e s and a l l of t h e IPM s t r a t e g i e s g e n e r a t e more income on th e av era ge th a n th e co nv en ti o na l c a l e n d a r programs. The i n t r o d u c t i o n o f the random sampling e r r o r once a g a i n has a l a r g e r , d e t r i m e n t a l e f f e c t on t h e s t r a t e g i e s w it h t h e high economic thresholds. S t r a t e g i e s 5 and 7 both have t h e r e d u c t i o n s i n n e t revenue o f more tha n $ 3 / a c r e w h il e s t r a t e g i e s 4 and 6 d i s p l a y marginal improvements in t h e i r av era ge income. The sampling e r r o r can change t h e amount o f m i t i c i d e s a p p l i e d and t h e amount o f damage i n c u r r e d . The r e v i s i o n o f t h e d e c i s i o n r u l e s t o a u t o m a t i c a l l y appl y th e f i r s t s p r a y a t h a l f dose enhances th e p r o f i t a b i l i t y o f t h e p l i c t r a n IPM s t r a t e g i e s by $5 t o $10 p e r a c r e . S t r a t e g y 5 has t h e h i g h e s t expec ted n e t revenue because i t a p p l i e s th e l e a s t amount o f m i t i c i d e s a p p l i e d and s u f f e r s l e s s damage than s t r a t e g y 6. With th e e x c e p t i o n o f s t r a t e g y 7, a l l o f th e s t r a t e g i e s e x p e r i e n c e t h e same amount o f damage as b e f o r e b u t app ly c o n s i d e r a b l y l e s s p e s t i c i d e . S t r a t e g i e s 5 , 6 and 7 have ex p ec te d n e t revenu es a l l w i t h i n $ 0 . 8 0 / a c r e o f each o t h e r even though t h e r e i s s u b s t a n t i a l d i f f e r e n c e between t h e i r economic t h r e s h o l d s . Consistent w it h t h i s r e s u l t i s th e o b s e r v a t i o n t h a t t h e random sampling e r r o r changes t h e n e t revenue o f none o f t h e s t r a t e g i e s by more th an $ 2 / a c r e . These r e s u l t s a r e e x h i b i t e d i n Table 12. The r e s u l t s from t h e v a r i o u s s c e n a r i o s a r e compared f o r c l a s s e s o f s t r a t e g i e s i n Table 13. There a r e some b a s i c p a t t e r n s which can be d i s c e r n e d from t h e comparisons. With t h e e x c e p t i o n o f t h e low y i e l d s c e n a r i o , th e b i o l o g i c a l c o n t r o l s t r a t e g y has t h e lo w e s t e x p e c te d n e t re ven ue . The c a l e n d a r programs and t h e c a r z o l IPM s t r a t e g i e s a r e l e s s p r o f i t a b l e th an t h e simpl e p l i c t r a n IPM s t r a t e g y . All o t h e r IPM s t r a t e g i e s produce more income on t h e av e r a g e th a n t h i s s t r a t e g y , e x c e p t Table 12. Strategy Mite Model R e s u l t s w it h Medium Y i e l d , Grower Problem P e r c e p t i o n a t 9 Mites p e r Leaf and Revised D e c is io n Rules which Always Apply a H a l f Dose on t h e F i r s t Spray. Total Potential Mite Number Co n tr o l Y ie l d Damage of Plictran Carzol Co s ts (bu/acre) ($/acre) Spra ys (F.D.E.)* (F.D.E.*) ($/acre) 4 502.1 ( 4 7 .5 ) 1.1 (4.8) 2 (1-7) 1. 6 (1.5) 5 502.1 (47.5) 1.6 (4.7) 2 (1.5) 6 502.1 (47.5) 1.1 (4.7) 7 502.1 ( 4 7 .5 ) 11 __ Net Revenue ($/acre) 296.4 ( 4 5 .0 ) 371.7 (6 88 .9 ) 1. 2 (1.3) 286.7 (40.8) 382.0 ( 6 9 0 .8 ) 2 (1.7) 1. 3 (1.3) 287 .0 ( 3 9 .1 ) 381.2 (6 94 .4 ) 2.0 (4.7) 2 (1.5) 1.2 . ( 1- 3 ) *_ 287 .5 (40.8) 381.6 (6 9 0 .4 ) 502.1 (47.5) 1.1 (4.8) ,2 (1.7) 1. 6 (1-5) __ 296.7 ( 4 6 .2 ) 371.4 (6 8 4 .1 ) 12 502.1 ( 4 7 .5 ) 1. 6 (4.7) 2 (1.6) 1. 2 (1.2) 286.7 ( 3 8 .7 ) 382.0 ( 69 3. 6) 13 502.1 ( 4 7 .5 ) 1.1 (4.8) 2 (1.7) 1.3 (1.5) 288 .8 ( 4 4 .9 ) 379.3 (69 0.8 ) 14 502.1 ( 4 7 .5 ) 2.2 (4.9) 2 (1.5) 1.1 (1-2) 286.5 (41.3) 382.7 (6 90 .1 ) * F u ll Dose E q u i v a l e n t s __ g Table 13. R e l a t i v e Comparisons o f C l a s s e s o f S t r a t e g i e s by D i f f e r e n c e s from t h e Expected Net Revenue o f t h e Simple P l i c t r a n IPM S t r a t e g y . B io lo g ic a l ■ Control S cen a rio s Weekly S cou tin g P lic tr a n Calendar 0 ) __________ C arzol C alendar ill __________ ( 3 ) Carzol IPM Carzol IPM w /E rror (8 -1 0 ) (1 5 -1 7 ) Sim ple P lic tr a n IPM (4 ) Sim ple P lic tr a n S o p h is tic a te d S o p h is tic a te d IPM P lic tr a n IPM P lic tr a n IPM w /E rror w /E rror (1 1 ) (5 -7 ) (1 2 -1 4 ) -5 2 /a c r e -2 5 /a c r e -3 7 /a c r e -1 7 /a c r e to -1 5 /a c r e -1 7 /a c r e to -1 3 /a c r e Weekly S cou tin g Low Y ield + 7 /a cre -1 4 /a c r e -2 5 /a c r e -1 7 a cre - 1 4 /a c r e to -1 0 /a c r e B iw eekly S cou tin g -4 9 /a c r e -2 2 /a c r e - 3 4 /a c r e -5 2 /a c r e -2 4 /a c r e -3 6 /a c r e -1 7 /a c r e to -1 2 /a c r e - 1 7 /a c r e to -1 0 /a c r e — + l/a c r e +11 /a c r e to • +15 /a c r e -5 3 /a c r e - 2 5 /a c r e -3 7 /a c r e -1 4 /a c r e to -ll/a c r e -2 0 /a c r e to -1 1 /a c r e — + l/a c r e to +12 /a c r e to +15 /a c r e Request S cou tin g: Grower Per­ c e p tio n 0 5 m ites per le a f Request S cou tin g: Grower P er­ c e p tio n § per l e a f U n a v a ila b le to -1 0 a c r e a a — — R evised R evised P lic tr a n P lic tr a n IPM w/ IPM Error (H4-H71 (H11-H141 + l/a c r e + 7 /a cre to ♦ 1 2 /a c r e + 5 /a cre to ♦ 1 2 /a c r e + 7 /a cre to + 19 /a crc + 6 /a cre to ♦ 2 0 /a cre + l/a c r e + 8 /a cre to +13 /a c r e + 6 /a cre to ♦ 1 2 /a c r e + 8 /a cre to ♦ 1 9 /a c r e + 6 /a c r e to ♦ 2 0 /a c r e a a a ♦ 1 2 /a c r e to ♦ 1 5 /a c r e + 8 /a c r e to ♦ 1 3 /a c r e -3 /a c r e to ♦ 1 7 /a c r e ♦ ll/a c r e to ♦ 2 5 /a c r e ♦ ll/a c r e to ♦ 2 1 /a c r e a + 6 /a c r e to +21/a c r e ♦ 10/acre to ♦ 22/acre OJ 144 f o r one r e v i s e d p l i c t r a n IPM s t r a t e g y i n t h e biweekly s c e n a r i o . The r e v i s e d d e c i s i o n r u l e s g e n e r a l l y improve expec ted n e t revenue by $5 to $10/acre. 4.3 Risk A n al y s is The f o l l o w i n g s e c t i o n i s d i v i d e d i n t o two p a r t s . The f i r s t p a r t d e s c r i b e s t h e a n a l y t i c a l p r o ce du re s w hi le t h e second p r e s e n t s th e model results. Readers f a m i l i a r w ith t h e r i s k a n a l y s i s s h ou ld s k i p t h e d i s c u s s i o n o f t h e a n a l y s i s proc edu re and proceed t o th e p a r t d e s c r i b i n g th e r e s u l t s . A n a ly s is Procedure E v a l u a ti n g mite management s t r a t e g i e s by th e s i n g l e c r i t e r i a o f the e x p e c te d n e t revenue may ig n or e some o t h e r i m p o r t a n t performance v a r i a b l e s . The amounts o f chem icals in t r o d u c e d i n t o t h e environment i s c e r t a i n l y o f i n t e r e s t t o more i n d i v i d u a l s th a n j u s t t h e i n d i v i d u a l grower who s e l e c t s which s t r a t e g y t o implement. However, t h e r e a r e s t i l l some p e r ­ formance v a r i a b l e s which a r e o f concern t o only t h e grower making t h e decision. These i n v o l v e t h e amount o f r i s k which he i s w i l l i n g t o b e a r . The w i l l i n g n e s s t o b e a r r i s k i s a co nce pt which a t t e m p t s t o measure how w ill in g in d iv id u a ls are to experience a higher p ro b a b il it y of a loss i n o r d e r t o have a h i g h e r p r o b a b i l i t y o f a g a i n . I n d i v i d u a l s who f or eg o h i g h e r p r o b a b i l i t i e s o f more income t o avoid h i g h e r p r o b a b i l i t i e s o f a l o s s a r e l e s s w i l l i n g t o b e a r r i s k and a r e r e f e r r e d t o as r i s k a v e r s e . On th e o t h e r ext rem e, a r e t h e i n d i v i d u a l s who d e c i d e t o e x p e r i e n c e h i g h e r p r o b a b i l i t i e s o f l e s s income i f th e y can i n c r e a s e th e p r o b a b i l i t i e s of e a r n i n g a h i g h e r income. These i n d i v i d u a l s a r e r i s k l o v e r s . I t is r e co gn iz ed t h a t th e w i l l i n g n e s s t o b e a r r i s k i s g r e a t l y i n f l u e n c e d by t h e amount o f income inv ol ved and t h a t t h e r e c u r r e n t l y does n o t e x i s t a 145 g r e a t enough u n d e r s t a n d i n g t o i d e n t i f y r e l a t i o n s h i p s between r i s k p r e f e r e n c e s - a n d per so nal a t t r i b u t e s such as a g e , e d u c a t i o n , f i n a n c i a l d e b t , etc. However, i t i s a p p a r e n t t h a t r i s k p r e f e r e n c e s a r e a f u n c t i o n o f p e r s o n a l i t y and t h a t they a r e l i k e l y t o vary c o n s i d e r a b l y from i n d i v i d u a l to individual. I f i n d i v i d u a l s a r e e i t h e r r i s k a v e r s e o r r i s k lo v i n g f o r t h e range o f income r e l e v a n t t o a p a r t i c u l a r d e c i s i o n , t h e c r i t e r i a o f th e expected v a l u e f o r th e n e t revenue w i l l n o t be an ad eq ua te r e p r e s e n t a t i o n o f t h e i r preferences. S i m p l i s t i c a l l y , t h e s i t u a t i o n i s o f t e n d e s c r i b e d as a t r a d e - o f f between the mean and th e v a r i a n c e o f the d i s t r i b u t i o n s o f income. Of two d i s t r i b u t i o n s w ith t h e same mean and d i f f e r e n t v a r i a n c e s , r i s k a v e r s e d e c i s i o n makers w i l l p r e f e r th e d i s t r i b u t i o n w it h t h e s m a l l e r variance. Thi s a n a l y s i s assumes t h a t th e v a r i a n c e s i s th e only r e l e v a n t measure f o r r i s k ( o r t h a t a l l d i s t r i b u t i o n s a r e normal) b u t i t i s na iv e s i n c e o t h e r moments o f t h e d i s t r i b u t i o n can be as im p o r ta n t as w e l l . The skewness o f t h e d i s t r i b u t i o n can i n f l u e n c e t h e d e c i s i o n s o f some i n d i v d u a l s j u s t l i k e the v a r i a n c e . The p r e f e r e n c e s t h a t i n d i v i d u a l s hold f o r the amount o f r i s k t h a t th e y a r e w i l l i n g t o b e a r vary from i n d i v i d u a l t o i n d i v i d u a l . Furthe rmo re, th e p r e f e r e n c e s o f a s i n g l e i n d i v i d u a l u s u a l l y change f o r d e c i s i o n s t h a t in v o l v e d i f f e r e n t amounts o f money. The w i l l i n g n e s s t o b e a r t h e r i s k of an in ve st me nt which has a 50% chance o f winning and a 50% chance of l o s i n g i s l i k e l y t o be d i f f e r e n t i f th e p o s s i b l e g a i n s and l o s s e s a r e $10 r a t h e r tha n $10,000. The manner in which the i n d i v i d u a l s va lu e t h e u n c e r t a i n t y o f which o f t h e p o s s i b l e outcomes w i l l r e s u l t from s e l e c t i n g an a l t e r n a t i v e i s d if f e r e n t fo r d iffe re n t individuals. I t i s p o s s i b l e t h a t f o r some i n d i v i d u a l s , the w o r s t p o s s i b l e outcome o f each a l t e r n a t i v e i s so im p o r ta n t 146 t h a t l i t t l e a t t e n t i o n i s pai d t o th e o t h e r p o s s i b l e outcomes. These i n d i v i d u a l s a r e some o f t h e most r i s k a v e r s e t h a t a r e p o s s i b l e . They a r e so concerned abo ut minimizing t h e p r o b a b i l i t y o f a ma jor l o s s t h a t they do n o t even c o n s i d e r t h e p r o b a b i l i t i e s o f e a r n i n g th e h i g h e r incomes ( t h e b e s t outcomes). They compare t h e minimums o f t h e d i s ­ t r i b u t i o n s o f th e a l t e r n a t i v e s and s e l e c t t h e a l t e r n a t i v e which has th e b e s t "worst" outcome. These i n d i v i d u a l s f o l l o w a d e c i s i o n r u l e known as maxi-min. The o t h e r extreme i s t h e d e c i s i o n r u l e c a l l e d maxi-max. This d e c i s i o n r u l e i s fo ll ow ed by i n d i v i d u a l s who a r e t h e most r i s k lo vi ng th a t is possible. In t h i s c a s e , th e o nl y outcomes which concern th e d e c i s i o n makers a r e t h e outcomes w it h t h e h i g h e s t incomes. They a r e so e a g e r t o ea r n t h e high incomes t h a t th ey w i l l b e a r any amount o f r i s k t o i n c r e a s e t h e p r o b a b i l i t y o f r e c e i v i n g t h e b e s t outcome. They examine the maximums o f t h e d i s t r i b u t i o n s and s e l e c t th e a l t e r n a t i v e w it h th e b e s t " b e s t " outcome. Between t h e s e extremes i s a n o t h e r c l a s s i c a l b e h a v i o r model which i s t h e maximization o f t h e e xp ec te d p r o f i t . This d e c i s i o n r u l e p l a c e s no v al ue on t h e r i s k in t h e d i s t r i b u t i o n s b u t a ve r a ge s th e p o s s i b l e outcomes weighted by t h e i r p r o b a b i l i t y o f o c c u r r i n g and s e l e c t s t h e a l t e r n a t i v e with the h i g h e s t e x pe c te d v a l u e . Survey r e s u l t s (81) would i n d i c a t e t h a t i t i s u n l i k e l y t h a t nay i n d i v i d u a l s would e x h i b i t any one o f th e t h r e e o f t h e s e c l a s s i c a l b e h a v i o r models, b u t ov er c e r t a i n income range s t h e y may approach one. Some i n d i v i d u a l s may even approach d i f f e r e n t models i n d i f f e r e n t income r a n g e s . I t i s expec ted however, t h a t most i n d i v i d u a l s w i l l d i s p l a y a lower deg ree o f r i s k a v e r s i o n tha n th e maxi-min o v e r some p a r t o f t h e income range and t h a t th e y w i l l be r i s k lo v i n g a t some d eg r ee f o r 147 a t l e a s t some o t h e r s e c t i o n o f t h e i r income r an g e. The c l a s s i c a l models a r e i m p o r ta n t because th ey a i d in th e i n t e r p r e t a t i o n o f many o f the a n a l y t i c a l te c h n i q u e s developed t o e v a l u a t e c h o i c e s between v a r i o u s alternatives. E a r l y a t t e m p t s t o e v a l u a t e t h e s e d e c i s i o n s f oc us ed on t h e s p e c i ­ f i c a t i o n o f s i n g l e - v a l u e d u t i l i t y f u n c t i o n s from which r i s k p r e f e r e n c e s coul d be i n f e r r e d . The u t i l i t y f u n c t i o n i s a co n c e p t d e s ig n e d t o measure th e amount o f s a t i s f a c t i o n t h a t an i n d i v i d u a l r e c e i v e s from such items as income, r i s k , l e i s u r e , consumption, e t c . However, i t i s im po ss ib le t o c o n s t r u c t a s i n g l e va lu ed u t i l i t y f u n c t i o n which can r e p r e s e n t th e p r e f e r e n c e s o f more than one i n d i v i d u a l and i t i s d i f f i c u l t t o avoid measurement e r r o r s i n s p e c i f y i n g th e f u n c t i o n f o r even one d e c i s i o n maker. To circ umv ent t h e s e problems, a s e r i e s o f t e c h n q i e u s commonly r e f e r r e d t o as e f f i c i e n c y c r i t e r i a have been dev eloped. E f f i c i e n c y c r i t e r i a do n o t a t t e m p t t o d i r e c t l y measure u t i l i t y f u n c t i o n s b u t i n s t e a d c o n s t r u c t i n t e r v a l s , s i m i l a r t o s t a t i s t i c a l c o n f i d e n c e i n t e r v a l s , around t h e p o s s i b l e u t i l i t y f u n c t i o n s f o r a c l a s s o f d e c i s i o n makers a n d / o r t h e p o s s i b l e shape o f t h e u t i l i t y f u n c t i o n f o r a s p e c i f i c d e c i s i o n maker. The s i z e o f t h e i n t e r v a l i s r e l a t e d t o t h e r e l a t i v e p r o b a b i l i t y o f making a Type I o r Type I I e r r o r on th e h y p o t h e s i s t h a t t h e ex p ec te d u t i l i t i e s o f two d i s t r i b u t i o n s a r e e q u a l . The narrow er t h e i n t e r v a l i s , t h e g r e a t e r w i l l be th e p r o b a b i l i t y o f a Type I e r r o r w h il e t h e w id e r t h e i n t e r v a l i s , t h e h i g h e r w i l l be t h e p r o b a b i l i t y o f a Type I I e r r o r . The more d e c i s i o n makers t h a t a r e i n c lu d e d in t h e c l a s s r e p r e s e n t e d by t h e i n t e r v a l , t h e more d i f f i c u l t w i l l i t be t o i d e n t i f y which s t r a t e g y i s preferred. E f f i c i e n c y c r i t e r i o n examine t h e d i s t r i b u t i o n s o f th e a l t e r n a t i v e s and r e j e c t as i n e f f i c i e n t any d i s t r i b u t i o n abo ut which i t can be s a i d 148 t h a t f o r ev er y d e c i s i o n maker (e v er y u t i l i t y f u n c t i o n ) w i t h i n t h e c l a s s d e f i n e d by t h e i n t e r v a l , t h e r e i s a t l e a s t one o t h e r d i s t r i b u t i o n which is preferred. A f t e r a l l d i s t r i b u t i o n s t h a t can be p o s s i b l y r e j e c t e d as bei ng i n e f f i c i e n t a r e e l i m i n a t e d , t h e r em ai nd er a r e d e s i g n a t e d a s t h e efficiency set. The e f f i c i e n c y s e t w i l l n o t always be reduced t o one s t r a t e g y , in f a c t f o r l a r g e i n t e r v a l s i t may be as l a r g e as 50% o f t h e t o t a l number o f t h e a l t e r n a t i v e s examined. A g e n e ra l c l a s s o f e f f i c i e n c y c r i t e r i o n i s t h e f a m i l y o f te c h n i q u e s known as S t o c h a s t i c Dominance. There a r e f o u r ty p e s o f S t o c h a s t i c Domin­ ance which a r e r e l e v a n t t o t h i s s t u d y . They a r e F i r s t Degree, Second Degree, S t o c h a s t i c Dominance w it h Respect t o a Function and Convex Se t S t o c h a s t i c Dominance. F i r s t Degree S t o c h a s t i c Dominance has t h e w i d e s t p o s s i b l e i n t e r v a l and i s in t e n d e d t o i n c l u d e e v e r y i n d i v i d u a l . I t suffers from l a r g e Type I I e r r o r s and u s u a l l y produces v er y l a r g e e f f i c i e n c y s e t s . Second Degree S t o c h a s t i c Dominance narrows t h e i n t e r v a l by ex c l u d in g from t h e c l a s s o f d e c i s i o n makers any i n d i v i d u a l s who a r e r i s k lo v in g o v e r any p a r t o f t h e income ran ge . I t i s bounded on t h e one extreme by t h e maxi-min i n d i v i d u a l and on t h e o t h e r by t h e r i s k n e u t r a l d e c i s i o n maker. I t i s more d i s c r i m i n a t i n g th a n F i r s t Degree S t o c h a s t i c Dominance b u t s t i l l can produce l a r g e e f f i c i e n c y s e t s . S t o c h a s t i c Dominance w ith Respect t o a Fun ction i s more f l e x i b l e tha n th e o t h e r two. I t a l lo w s t h e r e s e a r c h e r t o d e f i n e t h e s i z e o f t h e i n t e r v a l and t h e c l a s s o f d e c i s i o n makers t o be r e p r e s e n t e d . F i r s t and Second Degree S t o c h a s t i c Dominance a r e r e a l l y s p e c i a l c a s e s o f t h e more g en er a l S t o c h a s t i c Dominance w it h Respect t o F u n c ti o n . The i n t e r v a l does not need t o be c o n s t a n t a c r o s s a l l income v a l u e s and i t can be s e t t o i n ­ c l u d e ( e x c l u d e ) th e maxi-min, t h e maxi-max, t h e r i s k n e u t r a l o r any o t h e r preferences. Convex Set S t o c h a s t i c Dominance i s a te c h n i q u e which can be used with 149 any o f th e o t h e r e f f i c i e n c y c r i t e r i a t o examine t h e p o s s i b i l i t y o f whether some combination o f two a l t e r n a t i v e s can dominate (be p r e f e r r e d t o ) some other a lte rn a tiv e . I t can be used t o reduce l a r g e e f f i c i e n c y s e t s w i t h o u t having t o narrow t h e r i s k i n t e r v a l o r reduce t h e c l a s s o f d e c i s i o n makers. The v a r i o u s s t r a t e g i e s f o r c o n t r o l l i n g t h e European red m i te have been examined by t h e S t o c h a s t i c Dominance e f f i c i e n c y c r i t e r i a . From t h e i n f i n i t e number o f p o s s i b l e i n t e r v a l s , f i v e were s e l e c t e d f o r th e a n a l y s i s . The f i r s t i n t e r v a l s a p p e a r in Table 14. They a r e b r i e f l y d e s c r i b e d in th e t a b l e and a r e l i s t e d i n o r d e r o f t h e r i s k a v e r s i o n o f t h e lower l i m i t on the in t e r v a l. The c o e f f i c i e n t s o f th e i n t e r v a l s r e f e r t o t h e lower and upper bounds and a r e i n terms o f t h e P r a t t Risk Aversion C o e f f i c i e n t which i s d e f i n e d as t h e n e g a t i v e r a t i o o f t h e second d e r i v a t i v e o f t h e u t i l i t y f u n c t i o n t o f i r s t d e r i v a t i v e o f th e u t i l i t y f u n c t i o n ( - u " ( x ) / u ' ( x ) ). The v a l u e s o f t h e c o e f f i c i e n t s can be i n t e r p r e t e d a s t o t h e r i s k p r e ­ f e r e n c e s which t h e y r e p r e s e n t . aversion c o e f f ic ie n t of 0.0. Risk n e u t r a l i t y i s i n d i c a t e d by a r i s k The most r i s k a v e r s e i n d i v i d u a l would be r e p r e s e n t e d by a r i s k a v e r s i o n c o e f f i c i e n t o f + » wh ile on t h e o t h e r e x ­ t r em e, t h e most r i s k lo v i n g i n d i v i d u a l would be d e p i c t e d by a c o e f f i c i e n t o f - ». P o s i t i v e c o e f f i c i e n t s i n d i c a t e some l e v e l o f r i s k a v e r s i o n and n e g a t i v e c o e f f i c i e n t s d i s p l a y a p r e f e r e n c e towards r i s k . The f i r s t i n t e r v a l i s t h e w i d e s t one c o n s i d e r e d . I t a p pr o xi m at e s Second Degree S t o c h a s t i c Dominance s i n c e i t ran g es from 0 t o . 1 . I t i s an a p p r o x i ­ mation because i t does n o t i n c l u d e t h e ra n g es from .1 t o ® bu t i t assumed t h a t t h e .1 i s of a l a r g e r e l a t i v e magnitude and t h e e f f i c i e n c y s e t i d e n t i ­ f i e d w i l l be i d e n t i c a l t o t h e one w it h Second Degree S t o c h a s t i c Dominance. Since t h e i n t e r v a l r e p r e s e n t s a c l a s s o f d e c i s i o n makers i n c l u d i n g t h e maximin and t h e r i s k n e u t r a l i n d i v i d u a l , i t i s e x p e c te d t h a t t h e e f f i c i e n c y s e t 150 f o r t h i s i n t e r v a l would c o n t a i n a t l e a s t t h e a l t e r n a t i v e w ith th e l a r g e s t minimum v al ue and t h e a l t e r n a t i v e w i t h t h e g r e a t e s t expec ted v a l u e . The ne x t i n t e r v a l i s alm ost i d e n t i c a l t o t h e f i r s t e x c e p t t h a t th e lower bound has been a d j u s t e d t o ex cl ude t h e r i s k n e u t r a l and s l i g h t l y r is k averse individuals. The upper bound remains unchanged. It r e p r e s e n t s a c l a s s of d e c i s i o n makers which in c l u d e s th e i n d i v i d u a l who f o l l o w s th e maxi-min d e c i s i o n r u l e and t h o s e i n d i v i d u a l s who a r e n o t l e s s r i s k a v e r s e than t h e l e v e l imp lie d by t h e .0003 r i s k a v e r s i o n c o e f f i c i e n t . In th e t h i r d i n t e r v a l , t h e e x t re m e l y r i s k a v e r s e i n d i v i d u a l s have been e l i m i n a t e d from t h e c l a s s o f d e c i s i o n makers and th e lower bound has been a d j u s t e d t o i n c l u d e i n d i v i d u a l s who a r e more than s l i g h t l y risk averse. The maxi-min d e c i s i o n r u l e has been removed from c o n s i d e r a t i o n . The f o u r t h i n t e r v a l i n c l u d e s i n d i v i d u a l s who a r e s l i g h t l y r i s k l o v i n g t o th o s e who a r e s l i g h t l y r i s k a v e r s e . I t does i n c l u d e t h e r i s k n e u t r a l case b u t e x c l u d e s both e x t r e m e s - - t h e maxi-min and th e maxi-max. I t should have an e f f i c i e n c y s e t c o n s i s t i n g o f a t l e a s t th e s t r a t e g y t h a t produces t h e g r e a t e s t ex p ec te d n e t revenue. The f i n a l i n t e r v a l i s an a t t e m p t t o d e f i n e an i n t e r v a l which would r e p r e s e n t a c l a s s o f d e c i s i o n makers t h a t s h o ul d i n c l u d e 80-90% o f th e f ar me rs in Michigan. I t i s an i n t e r v a l which has been i n f e r r e d from s ur ve y r e s u l t s (81) measuring th e r i s k p r e f e r e n c e s o f a group o f Michigan farmers. The width o f th e i n t e r v a l v a r i e s by t h e income l e v e l alt hou gh t h e lower bound i s c o n s t a n t a t - . 0 0 0 1 . The upper bound a d j u s t s t o th e s i z e o f the income invo lv ed i n a d e c i s i o n and i s r e p r e s e n t e d by t h r e e p o i n t s from an e s t i m a t e d f u n c t i o n . At z e r o income, t h e upper bound i s .0008 w hil e a t $10,000 i t i n c r e a s e s t o .0015 and a t $25,000 i t d e c r e a s e s t o i t s lo w es t l e v e l .0004. The t h r e e l e v e l s on t h e upper 151 bound r e p r e s e n t v a r i o u s d eg ree s o f mo de ra te ly s t r o n g r i s k a v e r s i o n . The lower bound i m p li e s a mo de ra te ly s t r o n g r i s k lo v i n g p o s i t i o n . The i n t e r v a l does i n c l u d e t h e r i s k n e u t r a l ca se b u t does n o t i n c l u d e the extreme ca s e s o f maxi-min o r maxi-mum. I t i s a f a i r l y wide i n t e r v a l s i n c e i t i s i n t e n d e d t o r e p r e s e n t a l a r g e c l a s s o f d e c i s i o n makers and i t i s expected t o produce a l a r g e e f f i c i e n c y s e t . The o t h e r i n t e r v a l s , w it h th e e x c e p ti o n o f t h e f i r s t one sh oul d have e f f i c i e n c y s e t s con­ s i s t i n g o f 1 t o 3 members. R e s u lt s The v a r i o u s i n t e r v a l s were used t o examine d i f f e r e n t groups o f s t r a t e g i e s and i d e n t i f y which s t r a t e g i e s a r e r i s k e f f i c i e n t f o r the c l a s s e s o f d e c i s i o n makers r e p r e s e n t e d by each i n t e r v a l . The s t r a t e g i e s have been grouped by the type o f s c o u t i n g program, t h e l e v e l a t which growers d e t e c t a mite problem d e v e l o p i n g , t h e p r e s e n c e o r absence o f the random sampling e r r o r and t h e i n c l u s i o n o r e x c l u s i o n o f t h e r e v i s e d d e c i s i o n r u l e s which a u t o m a t i c a l l y apply t h e f i r s t s p r a y a t h a l f s t r e n g t h . The e f f i c i e n c y s e t s f o r each o f t h e s c e n a r i o s a r e p r e s e n t e d in Table 14. The e f f i c i e n c y s e t s i d e n t i f i e d f o r t h e s c e n a r i o us in g th e weekly s c o u t ­ ing program and th e medium y i e l d as dominated by t h e p r es en ce o f th e IPM s t r a t e g i e s w ith th e r e v i s e d d e c i s i o n r u l e s . t h e r e v i s e d d ec i so n r u l e s a r e r i s k e f f i c i e n t . Only two s t r a t e g i e s w i t h o u t They a r e s t r a t e g i e s 7 and 13 and th e y appear in t h e e f f i c i e n c y s e t i d e n t i f i e d f o r t h e l a s t i n t e r v a l , t h e one r e p r e s e n t i n g t h e p r e f e r e n c e s o f t h e c l a s s o f Michigan a g r i c u l t u r a l d e c i s i o n makers. There a r e 8 s t r a t e g i e s which a r e r i s k e f f i c i e n t f o r the i n t e r v a l , i n c l u d i n g f o u r w it h t h e random sampling e r r o r . I t a pp ea r s t h a t th e s im pl e p l i c t r a n IPM s t r a t e g y and th e one w ith t h e h i g h e s t economic t h r e s h o l d s (H4, HI 1 and H7) may only be p r e f e r r e d by t h e more r i s k a v e r s e * Table 14. R isk A n a ly s is R e s u lts f o r M ite C o n tro l S tr a te g ie s . Risk In te rv a l 1) 0 .0 to 0.1 General D escription Approximates Second Degree S to c h a stic Dominance: Ineludes r is k n e u tra l and maxi-min 2} .0003 to 0.1 Ranges from maxi-min to m oderately stro n g ris k aversion 3) .0001 to .0003 Ranges from s l i g h t ris k 'a v e rsio n to m oderately stro n g aversion Meekly Scouting and Medium Y ields excluding Revised S tra te g ie s Meekly Scouting and Low Yield H4, MS, H7, H ll, H12, H13, Hid 5 , 7 , 10. 12, 13 1 . H4, H5, H ll. H12, H13 H4 H5 Hll H12 * * ’ 10, 13 Meekly Scouting and Medium Yield 1 Meekly Scouting and low Y ield excluding Revised S tra te g ie s 1. 5 , 7. 13 1 Grower Perception a t 9 M ites/L eaf and Medium Yield H5. H7 H14, 7 H7, H14, 7 cn 4) -.0001 to .0001 5) -.001 to .0008 a t SO -.001 to .0015 a t S10.000 -.001 to .0004 a t S25.000 Ranges from s li g h tl y ris k loving to s l i g h tl y r is k a v erse ; includes r is k n e u tr a lity In te rv a l changes as income in c re a s e s ; ranges from m oderately stro n g r is k loving to v a rio u s le v e ls o f m oderately stro n g r is k a v ersio n ; includes r i s k n e u tr a lity ; re p re se n ts p referen ces o f 85X of Michigan farm ers - S tra te g ie s denoted w ith an H in d ic a te re v ise d d e cisio n ru le s which always apply a h a lf dose f i r s t spray. no 7 . 13 H5, H13, H14 7 .13 H13 7 , 13, H4, H5, H12. H13. H14 H7, 7 , 12, 13. 14 1 , HI 3 HI 3 1, H5, H7. HI3, 1114 1, 7 H14 7. 13 H5, H6, H12, HI4 1, 5 , 7 , 13 H5, H6, H7, HI2, HI 3, HI 4 Table 14. C ontinued. Grower Perception a t 9 m ite s /le a f and Medium Y ield excluding Revised S tra te g ie s 7. 14 7 7 Grower P erception a t S H ites/L e af and Medium Yield 1 . H4, H5, H7, H ll, H12, H13, H14 1, HS, H7, HI2 H7 Grower Perception a t 5 m ite s /le a f and Medium Y ield excluding Revised S tra te g ie s 1, 5 , 7, 12, 15, 17 1, 5 . 12, 15. 17 7, 12 cn Ca J 7, 13 5 . 6 . 7 . 11, 13, 14 H7 H5, H6. H7, P12 H13. H14 7, 12, 13, 14 5 , 6 . 7 . 12, 13 14 154 d e c i s i o n makers s i n c e the y a r e n o t r i s k e f f i c i e n t f o r i n t e r v a l s 3 and 4. These i n t e r v a l s do n o t in c l u d e t h e p r e f e r e n c e s o f s t r o n g l y r i s k a v e r s e d e c i s i o n makers. I f t h e r e v i s e d d e c i s i o n r i s k s t r a t e g i e s a r e ex cl ude d from c o n s i d e r a t i o n , t h e e f f i c i e n c y s e t s a r e changed. S t r a t e g y 7 , t h e p l i c t r a n IPM s t r a t e g y w it h t h e h i g h e s t economic t h r e s h o l d s , may be r i s k e f f i c i e n t f o r d e c i s i o n makers who a r e l e s s th a n m o d e ra te l y r i s k a v e r s e . I t a p p e a r s in th e e f f i c i e n c y s e t s o f a l l i n t e r v a l s e x c e p t t h e second one. S t r a t e g y 10 which i s th e c a r z o l IPM program w i t h t h e h i g h e s t economic t h r e s h o l d s may be r i s k e f f i c i e n t f o r very r i s k a v e r s e i n d i v i u d a l s , b u t i s no t p r e f e r r e d by any o f t h e d e c i s i o n makers r e p r e s e n t e d by t h e l a s t i n t e r v a l . There a r e f o u r s t r a t e g i e s which appea r i n th e e f f i c i e n c y s e t i d e n t i f i e d f o r t h e c l a s s o f Michigan d e c i s i o n makers. 13 and 14. They a r e s t r a t e g i e s 7, 12, Three o f t h e f o u r have t h e random sampling e r r o r which may i n d i c a t e t h a t t h e d e c i s i o n r u l e s o f t h e s t r a t e g i e s w i t h o u t t h e sampling e r r o r could be improved. The n e x t s c e n a r i o c o n s i d e r e d i s t h e one c o n s i s t i n g o f th e weekly s c o u t i n g program and t h e low y i e l d . The e f f i c i e n c y s e t s c o n t a i n th e s t r a t e g i e s w it h t h e r e v i s e d d e c i s i o n r u l e s and t h e b i o l o g i c a l c o n t r o l option. In f a c t , t h e b i o l o g i c a l c o n t r o l s t r a t e g y i s t h e unique member o f t h e e f f i c i e n c y s e t g e n e r a t e d f o r t h e second i n t e r v a l , i n d i c a t i n g t h a t i t i s p r e f e r r e d by the most r i s k a v e r s e d e c i s i o n makers - p ro ba bl y because in t h e w o rs t y e a r s , t h e r i s k o f a p p l y i n g t o o much p e s t i c i d e i s g r e a t e r than th e r i s k o f m it e damage w i t h u n i n t e r r u p t e d n a t u r a l p r e d a t i o n . 1 The s t r a t e g i e s which would be p r e f e r r e d by Michigan f a r m e r s ap p ea r in th e e f f ic ie n c y s e t fo r the l a s t i n t e r v a l. They a r e t h e b i o l o g i c a l c o n t r o l 1This r e s u l t , o f c o u r s e , i s p r e d i c a t e d on th e ass ump ti on no o t h e r p e s ­ t i c i d e s t a r g e t e d f o r o t h e r p e s t s a r e a p p l i e d which may impact t h e n a t u r a l predators. 155 o p t i o n (1) and t h e s o p h i s t i c a t e d p l i c t r a n IPM s t r a t e g i e s (H5, H7, H13, HI4 ) . None o f t h e c a r z o l IPM s t r a t e g i e s o r t h e p l i c t r a n s t r a t e g i e s w i t h o u t t h e r e v i s e d d e c i s i o n r u l e s a r e r i s k e f f i c i e n t f o r any o f th e i n t e r ­ vals. F ur th er m o re , even a t t h i s low y i e l d l e v e l , th e c o n v e n t io n a l c a l e n d a r programs a r e dominated by a t l e a s t one o f th e IPM s t r a t e g i e s . The most predominant s t r a t e g y i s HI3 which i s t h e s o p h i s t i c a t e d p l i c t r a n IPM program w it h t h e lo w es t economic t h r e s h o l d s . I t us es t h e r e v i s e d d e c i s i o n r u l e s and has t h e random sampling e r r o r . When th e s t r a t e g i e s w it h th e r e v i s e d d e c i s i o n r u l e s a r e excluded from c o n s i d e r a t i o n , s t r a t e g i e s 7 and 1 become t h e s t r a t e g i e s which app ea r i n th e most e f f i c i e n c y s e t s . The i n d i v i d u a l s in t h e c l a s s o f Michigan f a r m e r s would p r e f e r one o f f o u r s t r a t e g i e s : 1, 5 , 7 o r 13. I t ap p ea r s t h a t more r i s k a v e r s e i n d i v i d u a l s would p r e f e r 1 o r 5 w h il e l e s s r i s k a v e r s e ones may s e l e c t 13. S t r a t e g y 7 may be p r e f e r r e d by t h e w i d e s t group o f i n d i v i d u a l s as i t o n ly can be s a i d t h a t i t s i n o t p r e f e r r e d by anyone whose r i s k a v e r s i o n c o e f f i c i e n t i s .0003 o r g r e a t e r . The s c e n a r i o us in g a medium y i e l d and an o n - r e q u e s t s c o u t i n g program w it h growers d e t e c t i n g a problem d e v e l o p in g a t m i te d e n s i t i e s o f 9 m i t e s p e r l e a f produces an e f f i c i e n c y s e t f o r t h e l a s t i n t e r v a l which i s more as e x p e c te d . This e f f i c i e n c y s e t c o n s i s t s o f s i x s t r a t e g i e s - t h e t h r e e s o p h i s t i c a t e d p l i c t r a n IPM s t r a t e g i e s w i t h no sampling e r r o r and t h e i r c o u n t e r p a r t s w i t h t h e random sampling e r r o r s . use th e r e v i s e d d e c i s i o n r u l e s . All s i x s t r a t e g i e s This was somewhat as ex p ec te d s i n c e t h e s e s t r a t e g i e s had t h e h i g h e s t ex p e c te d n e t r ev enu es and t h e i n t r o d u c t i o n o f t h e random sampling e r r o r d i d n o t g r e a t l y change t h e i r perf or ma nce s. The o n ly s t r a t e g y which i s r i s k e f f i c i e n t t h a t does n o t use t h e r e v i s e d d e c i s i o n r u l e s i s s t r a t e g y 7 b u t i t a pp ea r s t o be p r e f e r r e d by 156 only e x t re m e l y r i s k a v e r s e d e c i s i o n makers and i t i s n o t l i k e l y t h a t any Michigan fa rm er s would be so r i s k a v e r s e t h a t th e y may s e l e c t i t above th e a l t e r n a t i v e s on t h e b a s i s o f i t s r i s k e f f i c i e n c y . However, i f t h e r e v i s e d d e c i s i o n r i s k s t r a t e g i e s a r e i g n o r e d , s t r a t e g y 7 becomes th e predominant c o n t r o l program, ap p e a r in g in ev er y efficiency set. There a r e f i v e o t h e r s t r a t e g i e s which a r e r i s k e f f i c i e n t f o r th e l a s t i n t e r v a l so growers may p r e f e r any one o f s e v e r a l a l t e r n a t i v e s dependent upon t h e i r r i s k a t t i t u d e s . e f f i c i e n t a r e 5, 6, 7, 11, 13 and 14. The s t r a t e g i e s which a r e r i s k Half o f t h e s e s t r a t e g i e s have th e random sampling e r r o r - once ag ai n i n d i c a t i n g how l i t t l e o f a d e t r i m e n t a l e f f e c t i t e x e r t s on th e IPM programs. The l a s t s c e n a r i o t o be d i s c u s s e d i s t h e one us in g a medium y i e l d and s c o u t i n g system where growers r e q u e s t a v i s i t when th e m i te pop­ u l a t i o n r e a c h e s a d e n s i t y o f 5 m i te s p e r l e a f . The s t r a t e g i e s p r e f e r r e d by i n d i v i d u a l s i n th e c l a s s o f Michigan a g r i c u l t u r a l d e c i s i o n makers a r e a l l examples o f t h e s o p h i s t i c a t e d p l i c t r a n IPM s t r a t e g i e s w ith t h e r e v i s e d d e c s io n r u l e s . T he-efficiency s e t id e n t i f i e d f o r the c la s s o f decision makers i n c l u d e s th e t h r e e s t r a t e g i e s w i t h o u t t h e sampling e r r o r s and the same t h r e e s t r a t e g i e s w it h t h e sampling e r r o r . This r e s u l t d e m o ns tr at es th e i n s e n s i t i v i t y o f t h e system t o changes i n t h e economic t h r e s h o l d , e i t h e r by d e s ig n or by way o f th e sampling e r r o r . The b i o l o g i c a l c o n t r o l program i s r i s k e f f i c i e n t f o r some p r e ­ f e r e n c e s b u t t h e y a r e more r i s k a v e r s e than what can be expec ted o f any a c t u a l d e c i s i o n maker. This program produces a minimum v a l u e in th e w o r s t y e a r , h i g h e r tha n th e o t h e r a l t e r n a t i v e s and would be p r e f e r r e d by i n d i v i d u a l s app roaching t h e extreme a t t i t u d e o f t h e maxi-min d e c i s i o n criteria. 157 I g n o r in g t h e r e v i s e d de ci so n r i s k s t r a t e g i e s produces an e f f i c i e n c y s e t f o r t h e l a s t i n t e r v a l o f a l l t h e c o u n t e r p a r t s t r a t e g i e s which do not use t h e r e v i s e d d e c i s i o n r u l e s . That i s t o say t h a t each r e v i s e d s t r a t ­ egy which was r i s k e f f i c i e n t i s r e p l a c e d by th e o r i g i n a l v e r s i o n o f the strategy. Thi s r e s u l t i s observed o n ly f o r th e l a s t i n t e r v a l . The e f f i c i e n c y s e t f o r th e f o u r i n t e r v a l s which r e p r e s e n t s t h e c l a s s o f d e c i s i o n makers who approach r i s k n e u t r a l i t y i s i n t e r e s t i n g because i t c o n t a i n s f o u r members. U sua lly t h i s s e t has a s i n g l e member b u t in t h i s c a s e , th e f o u r s t r a t e g i e s have ex pe ct ed n e t revenu es so s i m i l a r t h a t s l i g h t d i v e r s i o n s in th e r i s k a t t i t u d e from r i s k n e u t r a l i t y may i n f l u e n c e t h e rank ing o f the a l t e r n a t i v e s . Some gener al c o n c l u s i o n s can be r ea ch ed a bo ut th e s t r a t e g i e s which may be c o n s i s t e n t w ith gr ow ers ' r i s k p r e f e r e n c e s . F i r s t , i n none o f the s c e n a r i o s were e i t h e r th e co nv e n t io n a l o r th e c a r z o l IPM s t r a t e g i e s r i s k e f f i c i e n t f o r th e c l a s s o f Michigan a g r i c u l t u r a l d e c i s i o n makers. The b i o l o g i c a l c o n t r o l program may be p r e f e r r e d by some d e c i s i o n makers b u t only a t low y i e l d l e v e l s and w it h weekly s c o u t i n g syst ems . The r e v i s e d d e c i s i o n r u l e s t r a t e g i e s a r e g e n e r a l l y p r e f e r r e d t o th e o r i g i n a l v e r s i o n s o f th o s e same s t r a t e g i e s . The s o p h i s t i c a t e d p l i c t r a n IPM s t r a t e g i e s ar e t h e most f r e q u e n t members o f th e e f f i c i e n c y s e t s and t h e i r r i s k e f f i c i e n c y f o r th e c l a s s o f d e c i s i o n makers as a whole appears t o be somewhat i n s e n s i t i v e t o the l e v e l o f t h e economic t h r e s h o l d o r th e pr es enc e o f t h e random sampling e r r o r . F i n a l l y , t h e changes in the p r o d u c t i o n system r e p r e s e n t e d by th e v a r i o u s s c e n a r i o s examined can i n f l u e n c e t h e ra nk in g s o f th e s t r a t e g i e s . V. 5.1 SCAB MODEL RESULTS The S im u la ti on Model The ap pl e scab model has been c o n s t r u c t e d by employing a number o f assum pti on s t h a t f a c i l i t a t e th e s i m u l a t i o n o f a v er y complex b i o l o g i c a l p r o c e s s by a s i m p l i f i e d model t h a t s t i l l c a p t u r e s th e e s s e n t i a l elements o f th e p r o c e s s . The model has s e v e r a l components o r s u b r o u t i n e s which perform t h e i m p o r ta n t f u n c t i o n s o f th e b i o l o g i c a l and chemical p r o c e s s e s t h a t d i r e c t t h e development o f a p pl e scab i n commercial o r c h a r d s . The model has been c o n s t r u c t e d i n a Monte Carl o framework which p e r m i ts t h e a n a l y s i s o f th e performance o f each o f t h e s t r a t e g i e s und er a v a r i e t y of d if f e r e n t conditions. In t h i s ca s e th e model s i m u l a t e s t h e performance of t h e s t r a t e g i e s und er twenty d i f f e r e n t s t a t e s o f n a t u r e . In each s t a t e o f n a t u r e , t h e s t o c h a s t i c v a r i a b l e s a l l have d i f f e r e n t v a l u e s drawn a t random from t h e a p p r o p r i a t e m u l t i v a r i a t e p r o b a b i l i t y d i s t r i b u t i o n s . The major s t o c h a s t i c v a r i a b l e s a r e t h e p r o d u c t p r i c e s , t h e t e m p e r a t u r e , the p r e c i p i t a t i o n , t h e i n f e c t i o n p e r i o d s and t h e damage c o e f f i c i e n t s . The tw en ty s t a t e s o f n a t u r e can be viewed as twen ty in de pen den t se a s o n s . The model in i t s c u r r e n t v e r s i o n does n o t i n c o r p o r a t e any m u l t i - s e a s o n a l relationships. The model o p e r a t e s on a d a i l y b a s i s and u s e s randomly g e n e r a t e d o b s e r v a t i o n s f o r t h e average d a i l y t e m p e r a t u r e and th e amount o f p r e c i p i t a ­ tion. variate The te m p e r a t u r e and p r e c i p i t a t i o n a r e randomly drawn by a m u l t i ­ random g e n e r a t o r from d i s t r i b u t i o n s c o n s t r u c t e d from h i s t o r i c a l d a t a from t h e Ea st Lansing w e a th e r s t a t i o n . The o b s e r v a t i o n s a r e g e n e r a t e d wh ile m a i n t a i n i n g t h r e e c r i t i c a l s e t s o f c o r r e l a t i o n s . 158 The c o r r e l a t i o n 159 between th e te m p e r a t u re and p r e c i p i t a t i o n f o r each day i s p r e s e r v e d in th e random draws. Like wis e, t h e c o r r e l a t i o n s between t h e te m p e r a t u r e on one day and t h e p r e v io u s day and between t h e p r e c i p i t a t i o n on a given day and on t h e p r e c e e d in g day a r e a l s o p r e s e r v e d . The season i s d i v i d e d i n t o e i g h t 21-day p a r t s so t h a t se as o na l i n f l u e n c e s can be c a p t u r e d . There i s , t h e r e f o r e , one m u l t i v a r i a t e d i s t r i b u t i o n f o r each p a r t o f t h e s e as o n. The p r o d u c t p r i c e s , both f r e s h market and a l l p r o c e s s i n g p r i c e s a r e randomly g e n e r a t e d i n a s i m i l a r f a s h i o n w i t h a m u l t i - v a r i a t e random generator. The d i s t r i b u t i o n s used by th e random g e n e r a t o r have been c o n s t r u c t e d from h i s t o r i c a l p r i c e s e r i e s f o r t h e s t a t e o f Michigan d u r in g th e y e a r s 1969 t o 1979. They a r e ex p r e s s e d i n c o n s t a n t 1979 d o l l a r s . The c o r r e l a t i o n s between t h e f r e s h and p r o c e s s e d mark et s a r e p r e s e r v e d in t h e random g e n e r a t i o n . The g e n e r a t o r can a l s o produce y i e l d e s t i m a t e s which a r e c o r r e l a t e d t o t h e randomly drawn p r i c e s . The y i e l d e s t i m a t e s a r e drawn from a s e r i e s o f d i s t r i b u t i o n s based on h i s t o r i c a l Michigan d a t a from th e y e a r s 1969 t o 1979. The s e r i e s o f y i e l d d i s t r i b u t i o n s a r e d e r i v e d by m a i n t a i n i n g t h e shape o f t h e h i s t o r i c a l d i s t r i b u t i o n b u t s e t t i n g the mean a t t h r e e d i s t i n c t l e v e l s . There i s a low l e v e l y i e l d which has a mean o f 250 b u / a c r e and a medium l e v e l which c o r r es p on ds t o an ave rage y i e l d o f 500 b y / a c r e . The high l e v e l has a mean o f 900 b u / a c r e . u s e r can s e l e c t t h e y i e l d The level th a t is desired. A ju ic e p rice is inferred from th e random p r o ce s s ed p r i c e through t h e use o f t h e te n y e a r av era ge r a t i o o f th e two p r i c e s . The j u i c e p r i c e in each y e a r i s s e t a t a l e v e l which i s 72.5% o f t h e a l l processed p r ic e . At t h e begi nn ing o f each y e a r , i n a d d i t i o n t o t h e random w ea th e r p a t t e r n and p r o d u c t p r i c e s , t h e number o f d egr ee days t h a t have accumulated p r e v i o u s t o April 1 a r e randomly g e n e r a t e d from a normal d i s t r i b u t i o n with 160 a mean o f 580 and a s t a n d a r d d e v i a t i o n o f 80. Each season i s assumed t o begin on April 1 w ith t h e random s t a r t i n g d egr ee days and proceeds t o September 15. The randomly g e n e r a t e d v a r i a b l e s a r e a l l e n t e r e d i n t o t h e model in t h e s u b r o u t i n e GETWET. Those v a r i a b l e s which must be i n i t i a l i z e d a t t h e b eg in ni n g o f each y e a r a r e i n i t i a l i z e d in a s u b r o u t i n e INIT w h il e th e s u b r o u t i n e DDAYS c a l c u l a t e s t h e accumulated de gr ee days each day on a base o f 43° F. The s u b r o u t i n e STAGE d et e r m in e s th e p r o g r e s s i o n o f t h e a p p l e t r e e s in t h e i r various physiological stages. The a l g o r i t h m i s t a k en from a pedagogic model developed by Arneson ( 8 ) . The number o f accumulated degree days d e te r m in e s t h e s t a g e which t h e t r e e s w i l l be i n . de g r ee days i t i s assumed t h a t t h e t r e e s a r e a t g ree n t i p . At 700 When 750 d eg r ee days a r e r e a c h e d , th e y a r e a t 1/2 inch g ree n w h i l e 800 deg ree days i s t h e t r a n s i t i o n p o i n t t o t i g h t c l u s t e r . r e s p e c t i v e l y a t 900 and 1,000 de gr ee days. a l l i s assumed t o o c c u r . Pink and bloom occur At 1,100 d egr ee d a y s , etal Seven c a l e n d a r days f o l l o w i n g p e t a l f a l l , t h e model has f r u i t s e t o c c u r r i n g . F u n gi ci de s l o s e t h e i r e f f e c t i v e n e s s as a f u n c t i o n o f t h e amount o f time t h a t has e l a p s e d s i n c e a p p l i c a t i o n , t h e i r exposure t o t h e w ea th e r and t h e r a t e o f growth in t h e t r e e . s i m p l i f i e d due t o two r e a s o n s . However, t h e model has been g r e a t l y F i r s t , t h e a t t e n u a t i o n p r o c e s s o f th e d i f f e r e n t chem ica ls and t h e i r a s s o c i a t e d impact on t h e fungus i s l i t t l e u n d e r s to o d . Secondl y, t h e model could become q u i t e l a r g e , u nw iel dly and e x t r e m e l y e x pe ns iv e t o o p e r a t e i f a l l t h e d e t a i l was i n c o r p o r a t e d . T h e r e f o r e , some s i m p l i f y i n g assu mpti ons have been made a b o u t t h e r a t e a t which t h e ch em ica ls l o s e t h e i r e f f e c t i v e n e s s . Following t h e recommendations 161 which ap pea r in t h e 1979 F r u i t P e s t i c i d e Handbook (66, pp. 38-47) the time f o r which each chemical remains a c t i v e and w i l l e f f e c t i v e l y c o n t r o l a p p l e scab i s c a l c u l a t e d . The model r e a c t s as i f t h e chem ica ls e i t h e r c o n t r o l t h e d i s e a s e o r th e y do n o t . in t h e e f f e c t i v e n e s s c o n s i d e r e d . rates of attenuation. There i s no c o nt in uo us d e c r e a s e However, d i f f e r e n t dosages have d i f f e r e n t The a t t e n u a t i o n r a t e s w i l l a l s o change by t h e time o f t h e season t o r e f l e c t changes in scab a c t i v i t y , t r e e and f r u i t growth and o t h e r f a c t o r s . There a r e t h r e e ch em ic a ls w ith two dosages f o r each chemical in th e c u r r e n t model. captafol. The chemicals a r e : c a p t a n , benomyl and The l e n g t h s o f p r o t e c t i v e and e r a d i c a n t a c t i o n s f o r each chemical and dosage ap p e a r in Table 1. Scab i n f e c t i o n p e r i o d s a r e c a l c u l a t e d by c o n s i d e r i n g t h e p r o b a b i l i t y t h a t given a combination o f p r e c i p i t a t i o n , t h e av era ge d a i l y t e m p e r a t u r e , th e p a r t o f t h e se as on and t h e p r e v i o u s i n f e c t i o n s , t h a t an i n f e c t i o n o f a l i g h t , moderate or heavy l e v e l w i l l oc cu r. The p r o b a b i l i t i e s were c o n s t r u c t e d from d a t a on f i e l d o b s e r v a t i o n s from a number o f d i f f e r e n t s i t e s a c r o s s t h e s t a t e o f Michigan. The o r i g i n a l d a t a c o n t a i n e d t h e l e v e l o f i n f e c t i o n , and t h e w e a th e r ex p e r i e n c e d du r in g th e w e t t i n g p e r i o d . How­ e v e r , t h e model s i m u l a t e s on a d a i l y b a s i s , n o t on an h o u r ly o ne, so t h e i n f e c t i o n l e v e l s f o r each day were matched w i t h w e a th e r r e c o r d s on a d a i l y p r e c i p i t a t i o n and av era ge t e m p e r a t u r e . To s i m u l a t e t h e a p pl e season on an h o u r l y o r even a t h r e e hour b a s i s f o r a Monte Carl o model which w i l l be run f o r a minimum o f 20 y e a r s f o r each s t r a t e g y to be e v a l u a t e d would be e x t re m e l y e x p e n s iv e . I t i s e s p e c i a l l y e xp en s iv e when t h e a p p l e scab model i s coupled w it h a d d i t o n a l p e s t models t o al lo w t h e e v a l u a t i o n o f IPM s t r a t e g i e s . T h e r e f o r e , t h e b io l o g y was s i m p l i f i e d , but h o p e f u l l y n o t compromised, t o a l lo w t h e model t o fo cu s on t h e c e n t r a l o b j e c t i v e o f t h e s t u d y — t h e e v a l u a t i o n o f p e s t management s t r a t e g i e s under u n c e r t a i n t y . 162 Table 1. Chemical Chemical A t t e n u a t i o n R at es . Dosage Protective Action Before Petal Fall Protective Action Petal Fall to 6/15 Protective Action After 6/15 Captan 8 lbs/acre 7 days 7 days 1A days Captan 6 lbs/acre 5 days 7 days 1A days Captan A lbs/acre 5 days 5 days 1A days Captafol 5 gal/acre Green Tip to Petal Fall Captafol 3 gal/acre Green Tip to Pink Benomyl 16 oz/acre 7 days 7 days 1A days Benomyl* 12 oz/acre 7 days 7 days *When applied with Captan 0 A lbs/acre. Eradicant Action 1 day 2 days 163 The p r o b a b i l i t i e s d e r i v e d from th e f i e l d d a t a were th en a d j u s t e d t o produce a d i s t r i b u t i o n o f i n f e c t i o n p e r i o d s s i m i l a r t o th e d i s t r i b u t i o n o f a s c o s p o r e d e p l e t i o n r e p o r t e d from New York S t a t e (6 7 , p. 4 ) . This assumes, perhap s h e r o i c a l l y , t h a t t h e r e i s a d i r e c t r e l a t i o n s h i p between th e a s c o s p o r e p ro d u c ti o n and t h e number o f i n f e c t i o n p e r i o d s , b u t i t does p r o v id e a guide t o i n t r o d u c i n g t h e s ea s o na l n a t u r e o f th e l i f e c y c l e o f t h e fungus t o t h e model. I t i s known t h a t 15% o f t h e as c o s p o r e s which have o v er w in te r ed a r e d e p l e t e d by th e end o f A p r i l , 70% by th e middle o f J u n e , and 99% by J u l y 31. The p r o b a b i l i t i e s o f a scab i n f e c t i o n p e r i o d were a d j u s t e d f o r t h e model by f i r s t d i v i d i n g th e season i n t o f o u r p a r t s as f o l l o w s : A p r il 1 t o A p ril 31, May 1 t o June 15, June 16 t o J u l y 31 and t h e remain­ der o f t h e season a f t e r t h e end o f J u l y . Thus, i t was assumed t h a t t h e f i e l d d a t a r e p r e s e n t e d most c l o s e l y t h e second p a r t o f t h e s e a s o n , so t h e p r o b a b i l i t i e s i n p a r t s 1 and 3 were a d j u s t e d t o conform t o th e documented p a t t e r n o f a s c o s p o r e p r o d u c t i o n . This was accomplished by m u l t i p l y i n g t h e observed p r o b a b i l i t i e s by t h e r a t i o o f t h e p e r c e n ta g e d e p l e t i o n o f a s c o s p o r e s in t h a t time p e r i o d t o t h e p e r c e n t a g e d e p l e t i o n o f a s c o s p o r e s in th e second p a r t o f t h e s e a s o n . p r o b a b i l i t y t h a t any scab i n f e c t i o n might o cc u r This r e s u l t e d in the in th e f i r s t time p e r i o d a s being about one f o u r t h o f t h e p r o b a b i l i t y o f an i n f e c t i o n i n t h e second p a r t o f th e se as o n. The l a s t p a r t o f t h e seas on was assumed t o be f r e e o f any primary s p o r e s and, hence, any i n f e c t i o n must r e s u l t from c o n id i a produced by a pr im ar y i n f e c t i o n . I f t h e c o n t r o l s a r e co m p le te ly s u c c e s s f u l and no s i g n i f i c a n t primary i n f e c t i o n o c c u r s , t h e p r o b a b i l i t y o f i n f e c t i o n du rin g t h i s time p e r i o d i s z e r o . However, i f two o r more i n f e c t i o n s o f moderate 164 o r heavy l e v e l s o c c u r , th e p r o b a b i l i t y o f a secondary i n f e c t i o n i s e x a c t l y equal t o th e p r o b a b i l i t y o f a prim ary i n f e c t i o n d ur in g th e secfcnd p a r t o f t h e s e as on . The cu m ul ati v e p r o b a b i l i t i e s o f scab i n f e c t i o n s s i m u l a t e d by the model a r e compared t o t h e p a t t e r n ob se rv ed f o r as c o s p o r e p r o d u c t i o n in Table 2. I t should be no te d t h a t by assumption a l l s i m u l a t e d primary scab i n f e c t i o n s have o c c u rr e d by th e end o f J u l y . With t h e e x c e p t i o n o f th e f i r s t time i n t e r v a l , t h e s i m u l a t e d p a t t e r n f o r a l l y e a r s i s w i t h i n 5 percentage p o in ts of the p a t te r n of ascospore d e p letio n . The d e t e r m i n a t i o n o f t h e scab i n f e c t i o n p e r i o d s i s handled w i t h i n th e s u b r o u t i n e SCABINF. This s u b r o u t i n e a l s o d et er m in e s when w e a th e r con­ d i t i o n s have been r i g h t f o r an i n f e c t i o n t o o c c u r . The i n f o r m a t i o n i s used by s t r a t e g i e s which a t t e m p t t o e r a d i c a t e any e x i s t i n g i n f e c t i o n s r a t h e r than p r o t e c t i n g t h e o r c h a r d from f u t u r e a t t a c k s . An i n f e c t i o n does n o t always r e s u l t when t h e w e a t h e r c o n d i t i o n s have been s u i t a b l e s i n c e t h e r e i s almos t always some p r o b a b i l i t y t h a t no i n f e c t i o n w i l l oc cu r. The l e v e l o f i n f e c t i o n (none, l i g h t , moderate o r heavy) w i l l depend upon t h e random draw and t h e p r o b a b i l i t i e s o f each e v e n t . The c u r r e n t model examines t h e performance o f el eve n c o n t r o l strategies. The s t r a t e g i e s c o n s i s t o f d i f f e r e n t d e c i s i o n r u l e s as to when c e r t a i n chem ica ls a t s p e c i f i c dosages should be a p p l i e d . As men­ t i o n e d b e f o r e , t h e r e a r e t h r e e ch em ica ls which were employed i n the model: benomyl, c a p t a n and c a p t a f o l . The a p p l i c a t i o n c o s t s f o r th e chem ica ls a t d i f f e r e n t dosages a r e p r e s e n t e d in Table 3. The f i r s t s t r a t e g y a p p l i e s no chemical c o n t r o l a t a l l and i s used a s a b a s e l i n e f o r comparison. The second s t r a t e g y c o n s i s t s o f a p p l y i n g c a p t a f o l (5 g a l / a c r e ) a t g r e e n t i p fo ll ow ed by weekly a p p l i c a t i o n o f c a p t a n (8 l b s / a c r e ) s t a r t i n g a t P e t a l f a l l and l a s t i n g u n t i l the middle o f June. A f t e r t h a t , a biweekly Table 2. C um ulative P r o b a b ilit y F u n ctio n s o f G ilpatrick & Date 4/6 4/30 5/14 5/31 6/7 6 /3 0 7/31 S z k o ln i k All Years 0 .15 .30 .55 .667 .90 .99 Ascospore D e p le tio n . S im u l a te d Years 1 0 .084 % .038 0 ' .059 0 .125 0 .136 .143 0 8 9 10 0 0 0 .017 .067 .15 CTY cn .323 .605 .701 .8 9 2 1.00 .192 .235 .50 .429 .318 .357 .20 .385 .333 .35 .423 .529 .625 .714 .636 .643 .7 0 462 .667 .75 .517 .588 .625 .786 .727 .643 .90 692 .8 0 .80 .923 .765 .813 .929 .818 .786 .90 00 1.00 1.00 1.00 00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 166 Table 3 . Spray C osts f o r Chemical A p p l i c a t i o n s C onsidered. Spray Chemical Price per U n it Chemical C ost per A p p lica tion C aptafol ( 5 g a l / a c r e ) $ 2 4 .00/gal $ 1 2 0 .0 0/acre C aptafol ( 3 g a l / a c r e ) $ 2 4 .0 0 / g a l Captan ( 8 1 b s / a c r e ) Labor Cost per A p p lic a t i o n Machinery C ost per A p p lic a t i o n Cost per A p p lic a t i o n $ . 70 /a cre $ . 7 0 /a c r e $121 .4 /a c re $ 7 2 .0 0 /a cr e $ . 7 0 /a cre $ . 7 0 /a c r e $ 7 3 .4 /a cr e $ 1 . 8 5 /lb $ 1 4 .8 /a cr e $ . 7 0 /a c r e $ . 7 0 /a c r e $ 1 6 .2 /a cr e Captan ( 6 1 b s / a c r e ) $ 1 .8 5 /lb $ 1 1 .1 /a cr e $ . 70 /a cre $ . 7 0 /a cre $ 1 2 .5 /a cr e Captan $ 1 .8 5 /lb $ $ . 7 0 /a c r e $ . 7 0 /a c r e $ Benomyl (16o z / a c r e ) $ .6 5 9 /o z $ 1 0 .5 4 /a cr e $ . 70/acre $ . 7 0 /a c r e $ 1 1 .9 4 /a cr e Benomyl (12o z / a c r e ) $ .6 5 9 /o z $ $ . 7 0 /a c r e $ . 7 0 /a c r e $ Benomyl (T6 o z / a c r e ) $ .9 /o z $ 1 4 .4 /a cr e $ . 70 /a cre $. 7 0 /a c r e $ 1 5 .8 /a cr e Benomyl (12 o z / a c r e ) $ .9 /o z $ 1 0 .8 /a cr e $ . 7 0 /a c r e $ . 70 /a cre $ 1 2 .2 /a cr e Source: (4 l b s /a c r e ) 7 .4 /a cr e 7 .91/a c r e 8 .8 /a cre 9 .3 1 /a c re Pest Control Branch, Natural Resource Economics Division, Economic Research Service, USDA. 167 program o f c a p t a n (4 l b s / a c r e ) i s p ur s ue d. The t h i r d s t r a t e g y a p p l i e s c a p t a n (8 l b s / a c r e ) e v e r y 7 days u n t i l t h e 15th o f June and the n t h e f u l l dosage o f c a p t a n i s a p p l i e d e v e r y 14 d ay s . The f o u r t h s t r a t e g y i s s i m i l a r i n t h a t i t f o l l o w s t h e same s p r a y s c h e d u le b u t a h a l f dosage o f captan (4 l b s / a c r e ) i s a p p l i e d i n s t e a d o f th e f u l l do sa g e. The n e x t s t r a t e g y i s . a p o s t i n f e c t i o n program which a p p l i e s benoniyl (16 o z / a c r e ) whenever o b s e r v a t i o n s o f average d a i l y t e m p e r a t u r e and d a i l y p r e c i p i t a t i o n i n d i c a t e t h a t we at h e r c o n d i t i o n s have been s u i t a b l e f o r an i n f e c t i o n . In t h i s s t r a t e g y w e a th e r c o n d i t i o n s s u i t a b l e f o r an i n f e c t i o n t o o cc u r a r e assumed to be whenever t h e av era ge d a i l y t e m p e r a t u r e exce eds 34° F and th e p r e c i p i t a t i o n i s g r e a t e r tha n .01 i n c h e s . An a p p l i c a t i o n w i l l n o t be made i f t h e o r c h a r d has been t r e a t e d by benomyl w i t h i n t h e l a s t week. The s i x t h s t r a t e g y i s an example o f th e use o f benorryl in combination w ith c ap t an in a p r o t e c t i v e mode. I t a p p l i e s benomyl (12 o z / a c r e ) and cap ta n (1 l b / a c r e ) on a weekly b a s i s . The co nv e n t io n a l s p r a y program commonly used i n Michigan i s r e p r e s e n t e d by s t r a t e g y 7. Th is s t r a t e g y in v o l v e s t h e a p p l i c a t i o n o f a f u l l dosage o f cap ta n (8 l b s / a c r e ) ev er y 7 days u n t i l p e t a l f a l l , a f t e r which a lower dosage i s a p p l i e d . Between p e t a l f a l l and June 15, c ap t an (6 l b s / a c r e ) i s a p p l i e d ev er y 10 days. A f t e r June 15, cap ta n (4 l b s / a c r e ) i s a p p l i e d ev er y 14 days. The ne x t t h r e e s t r a t e g i e s use c a p t a f o l f o r t h e f i r s t p a r t o f t h e season and e i t h e r e r a d i c a t e w ith benomyl o r p r o t e c t w it h c a p t a n f o r t h e rem a in de r o f th e year. Capt afo l i s a p p l i e d w it h a l l t h r e e s t r a t e g i e s a t gr een t i p . When s t r a t e g y 8 i s f o l l o w e d , a f t e r pink c a p t a n (8 l b s / a c r e ) i s a p p l i e d weekly u n t i l June 16 and then a h a l f dosage o f c a p t a n (4 l b s / a c r e ) i s a p p l i e d on a biweekly b a s i s . c a p t a f o l (3 g a l / a c r e ) . This s t r a t e g y b e g i n s t h e se ason w i t h a t r e a t m e n t o f With s t r a t e g y 9 , c a p t a f o l (5 g a l / a c r e ) i s a p p l i e d a t green t i p and a f t e r p e t a l f a l l , benomyl (16 o z / a c r e ) i s a p p l i e d every 168 time t h a t t h e we at he r c o n d i t i o n s have been s u i t a b l e f o r an i n f e c t i o n ( e x c e p t when benomyl has been a p p l i e d w i t h i n t h e l a s t 6 d a y s ) . The t e n t h s t r a t e g y i s i d e n t i c a l t o t h e p r e v i o u s one e x c e p t t h e dosage o f c a p t a f o l i s reduced (3 g a l / a c r e ) and t h e p o s t - i n f e c t i o n program comnences a t pink. The f i n a l s t r a t e g y i s a h y p o t h e t i c a l one used f o r d e m o n s t r a t i v e pu rp os es . I t i s an example o f a p o s t - i n f e c t i o n program w it h p e r f e c t knowledge about the incidence of in f e c tio n s . Since t h e a c c u r a c y o f t h e i n f e c t i o n p r e d i c ­ t i o n s based on we at he r c o n d i t i o n s i s l i k e l y t o i n f l u e n c e t h e e f f i c i e n c y o f p o s t - i n f e c t i o n c o n t r o l programs, t h i s s t r a t e g y d e m o n s t r a te s t h e p o t e n ­ t i a l t h a t t h i s t y p e o f p o s t - i n f e c t i o n can have. Thi s s t r a t e g y a p p l i e s benomyl (16 o z / a c r e ) whenever an i n f e c t i o n a c t u a l l y o c c u r s r a t h e r tha n j u s t whenever t h e w ea th e r c o n d i t i o n s have been s u i t a b l e f o r an i n f e c t i o n . The s t r a t e g i e s a r e more f u l l y d e s c r i b e d i n Table 4. For a l l t h e c o n t r o l s t r a t e g i e s , t h e r e a r e two a d j u s t m e n t s t o t h e normal s pr ay s c h e d u le . I f th e r a i n f a l l exceeds .02 in c h e s on t h e day d e s i g n a t e d f o r a s p r a y , t h e a p p l i c a t i o n i s postponed u n t i l t h e n e x t day. The second a d j u s t m e n t i n v o l v e s t h e s p e c i a l s p r a y s which a r e n e c e s s a r y i f an i n f e c t i o n o c c u r s . Two benomyl s p r a y s (16 o z / a c r e ) 7 days a p a r t a r e n e c e s s a r y t o e r a d i c a t e scab l e s i o n s t h a t have d ev el op ed. The s p e c i a l s p r a y s e l i m i n a t e l i g h t i n f e c t i o n s and s u b s t a n t i a l l y r ed uce t h e s p r ea d o f moderate o r heavy i n f e c t i o n s . I f t h e s e e r a d i c a n t s p ra y s a r e r e q u i r e d , normal a p p l i c a t i o n s a r e postponed. The normal s p r a y s a r e handled in t h e s u b r o u t i n e APPLY w h ile a l l o f t h e s p e c i a l s p r a y s a r e a d m i n i s t e r e d in a n o t h e r s u b r o u t i n e c a l l e d SPSPRAY. The l a s t o f t h e major components o f t h e s i m u l a t i o n model i s th e s u b r o u t i n e SCABDAM. Thi s s u b r o u t i n e e s t i m a t e s t h e amount o f damage t h a t S ir a t e g y Pink to Petal Fall Orivn Tip tu Pink Do Nothing Do Nothing Captafol (5 gal/ acre) at green tip or 4/9 Petal Tall to 6/15 6/15 to ?/7 6/7 6/1 Do Nothing Do Nothing Do N o t h i n g At petal f a l l , apply captan (8 lbs/acre) every 7 days (for 3 cover sprays) After 3 weekly fu ll dose captan cover sprays, apply captan (4 lbs/acre) every 14 days Do nothing unless at le a st 2 inlections have developed previously then apply captan (4 lb s/ac re) every 14 days Captan (8 lbs/acre) every 7 days s t a r t ­ ing on 4/10 Captan (8 lbs/ acre) every 7 days Captan (8 lbs/acre) every 7 days Captan (8 lbs/ acre) every 14 days Do nothing unless a t le a st 2 infections have developed pre­ viously; then apply captan (8 lb s/ac re) every 14 days Captan (4 lb s/ac re) every 7 days s t a r t ­ ing on 4/10 Captan (4 lbs/ acre) every 7 days Captan (4 lbs/acre) every 7 days Captan (4 lb s/ acre) every 14 days Do nothing unless a t le a s t 2 Infections have developed pre­ viously, then apply captan (4 lb s/acre) every 14 days Benomyl (16 oz/acre) when weather condi­ tions have been suitable* for an Infection—unless benomyl has been applied within the la s t week Benomyl (16 oz/acre) when weather condi­ tions* have been suitable fo r an 1nfectlon—unless benomyl has been applied within the la s t week Benomyl (16 o il acre) when weather conditions* have been suitable for an Infection— unless benomyl has been applied within the la s t week Do nothing unless at Benomyl (16 o il le a s t 2 Infections acre) when weather conditions* have developed have been su itab le previously, then for an Infection- apply benomyl (16 0 1 / unless benomyl acre when weather has been applied conditions* have been suitable for an Infec­ withln the la s t tion unless benomyl week has been applied within the l a s t week Benomyl (12 oz/acre) and captan (4 lbs/ acre) every 7 days sta rtin g on 4/10 Benomyl (12 02/ acre) and captan (4 lb s/acre) every 7 days Benomyl (12 oz/ acre) and captan (4 lbs/acre) every 7 days Benomyl (12 oz/ acre) and captan (4 lbs/acre) every 14 days Do nothing unless a t le a s t 2 Infections have previously developed; then apply benomyl (12 oz/acre) and captan (4 lb s/a c re ) every 7 days Captan (8 lb s/acre) every 7 days s t a r t ­ ing on 4/10 Captan (8 lb s/ acre) every 7 days Captan (6 lb s/ acre) every 10 days Captan (4 lbs/ acre) every 14 days Do nothing unless at le a s t 2 Infections have previously developed; then apply captan (4 lb s/acre) every 14 days Captafol 3 gal/acre) a t green tip or 4/9 Captan (8 lb s/ acre) every 7 days (fo r 5 cover sprays) Captan (8 lb s/ acre) every 7 days for 5 cover sprays After 5 cover snrays, apply captan (4 lb s/ acre) every 14 days Do nothing unless a t le a st 2 Infections have previously developed; then apply captan (4 lb s/acre) every 14 days Benomyl (16 oz/ acre) when weather conditions have been suitable for an 1nfection*--unlcss benomyl has been applied within the la s t week Benomyl (16 oz/ Do nothing unless a t acre) when weather le a st 2 infections have conditions have previously developed; been suitable for then apply benomyl (16 an Infection*— oz/acre) when weather unless benomyl conditions have been has been applied su itab le for an Infection*—unless within the la s t week benomyl has been applied within the la s t week Captafol (5 gal/acre) a t green tip or 4/9 10 Captafol (3 gal/acre) a t green t ip or 4/9 Benomyl (16 o il acre) when weather conditions have been su itab le for an Infection*— unless benomyl has been applied within the la s t week Benomyl (16 oz/ acre) when weather conditions have been suitable for an Infection*— unless benomy) has been applied within the la s t week Benomyl (16 oz/ acre) when weather condi­ tions have been suitable for an Infection*—un­ less benomyl has been applied within the la s t week Do nothing unless a t le a st 2 Infections have previously developed; then apply benomyl (16 oz/acre) when weather conditions have been su itab le for an Infection*—unless benomyl has been applied within the la s t week 11 Hhen an Infection actually occurs, benomyl (16 oz/ acre) When an Infection actually occurs, benomyl (16 or/ acre) When an Infection actually occurs, benomyl (16 0 1 / acre) When an Infection actually occurs, benomyl (16 o il acre) When an infection a ctually occurs, benomyl (16 oz/ acre) * Weather conditions suitable for an Infection arc assumed to be when the average dally temperature has exceeded 35"F and preclpatation is g reater than .01 inruns. Table U. D e s c r i p t i o n of Scah Control S t r a t e g i e s 169 170 r e s u l t s from each i n f e c t i o n . Thi s c a l c u l a t i o n i s guide d by t h e assumption t h a t t h e scab i s e x p e r i e n c e d i n t h e f r u i t in t en d ed f o r t h e f r e s h m a rk e t. Following t h e h i s t o r i c a l s t a t e w i d e av e r a g e use p a t t e r n , 40% o f t h e y i e l d i s d e s i g n a t e d as being i n t e n d e d f o r t h e f r e s h ma rke t a t t h e begi nn ing o f each season with t h e rema inde r going t o p r oc es s ed u s e s . f r u i t i s s o ld o nl y in t h e j u i c e ma rk e t. Scab damaged In s e v e r e scab s e a s o n s , t h e e n t i r e f r e s h market crop can be damaged and some o f t h e f r u i t t o be mar­ ket ed f o r pr oc es se d u s es can be i n f e c t e d a s w e l l . s u l t s in 5% o f t h e f r u i t damaged. A lig h t infection r e ­ The moderate and heavy i n f e c t i o n s p r o ­ duce damages t h a t a r e randomly drawn from uniform d i s t r i b u t i o n s . The d i s t r i b u t i o n f o r moderate i n f e c t i o n s has a range o f .05 t o .10 w hi le t h e range f o r t h e d i s t r i b u t i o n o f heavy i n f e c t i o n damage i s from .05 t o .70. The damage s u f f e r e d a t each i n f e c t i o n i s summed a t t h e end o f each y e a r and ca nn ot exceed 100%. S t o c h a s t i c Elements o f t h e Apple Scab Model The model was used t o s i m u l a t e t h e performance o f 11 d i f f e r e n t s t r a t e g i e s under twen ty d i f f e r e n t c o n d i t i o n s . Each c o n d i t i o n can be p e r ­ c e i v e d a s a s t a t e o f n a t u r e w it h a random v a l u e f o r each o f t h e s t o c h a s ­ tic variables. scab model. variable. There a r e a number o f s o u r c e s o f u n c e r t a i n t y in t h e a p p l e Each s o u r ce o f u n c e r t a i n t y i s r e p r e s e n t e d by a s t o c h a s t i c As p r e v i o u s l y d i s c u s s e d t h e f r e s h and p r o c e s s e d ma rket p r i c e s a r e a l s o random v a r i a b l e s . The av era ge d a i l y t e m p e r a t u r e and t h e d a i l y p r e c i p i t a t i o n a r e a l s o randomly drawn from m u l t i v a r i a t e d i s t r i b u t i o n s based on h i s t o r i c a l d a t a . The number o f d eg ree days t h a t have accumulated p r e v i o u s t o April 1 when t h e s im u l a te d season i s assumed t o commence 171 i s a random v a r i a b l e from a normal d i s t r i b u t i o n with a mean o f 580 and a s t a n d a r d d e v i a t i o n o f 80. The d e t e r m i n a t i o n o f scab i n f e c t i o n p e r i o d s i s a l s o based upon a random v a r i a b l e . Each day a random v a r i a b l e between 0 and 1 i s drawn from a uniform d i s t r i b u t i o n . This random v a r i a b l e i s compared t o t h e p r o b a b i l i t i e s o f no i n f e c t i o n , l i g h t i n f e c t i o n , moderate i n f e c t i o n o r heavy i n f e c t i o n det ermined by t h e combination o f av er a g e p r e c i p i t a t i o n , average d a i l y te m p e r a t u r e and t h e p a r t o f t h e se as on . Hence, f o r a given s e t o f we at h e r c o n d i t i o n s , t h e development o f an in f e c tio n is not d e te rm in istic but a s to c h a s t ic process. The c a l c u l a t i o n o f t h e p e r c e n t a g e o f f r u i t damaged by moderate and heavy i n f e c t i o n s i s handled in a s i m i l a r f a s h i o n . A u n if o rm ly d i s t r i b u t e d v a r i a b l e between 0 and 1 i s randomly drawn each day. I f an i n f e c t i o n o cc u r s on t h a t given d ay, t h e random v a r i a b l e i s used t o c a l c u l a t e t h e amount o f damage t h a t w ill r e s u lt. The damage o f l i g h t i n f e c t i o n s i s d e t e r m i n i s t i c and always s e t equal t o 5%. However, t h e damage r e s u l t i n g from moderate and heavy i n f e c t i o n s i s s t o c h a s t i c and i s c a l c u l a t e d a t f o l l o w s : For Moderate I n f e c t i o n s : Damage = 0.1 0 - R *0.05 For Heavy I n f e c t i o n s ' Damage = 0.75 - R *0.70 Where R = random v a r i a b l e The l a t e season damage e s t i m a t e s f o r moderate and heavy i n f e c t i o n s a r e a d j u s t e d t o ac c o u n t f o r t h e l e n g t h o f time e a r l y in t h e se as on t h a t no scab i s allowed t o deve lop . I f no i n f e c t i o n s have o c c u r r e d , t h e e s t i m a t e s a r e a d j u s t e d by t h e p e r c e n t a g e s a p pe a r in g in Table 5. The a d j u s t m e n t f a c t o r s a r e d e r i v e d from th e p e r c e n t a g e d e p l e t i o n o f a s c o s p o r e s i n each s t a g e o f t h e development (58, p. 4 ) . The damage e s t i m a t e s f o r s e l e c t e d s t r a t e g i e s a r e s t a t i s t i c a l l y compared t o r e s u l t s ob se rv ed i n e x pe r im en ta l o r c h a r d s in Appendix I . 172 Table 5. Adjustment F a c t o r s f o r Late Season I n f e c t i o n s . Stage When I n f e c t i o n Occurs Damage Adjustment Tight C luster 78% o f O r ig in a l Es ti ma te Pink 70% o f O r ig in al Es ti ma te B1 oom 58% o f O r i g i n a l Esti mat e P e t a l Fall 45% o f O r ig in a l Es ti ma te F r u i t S e t t o H arvest 35% o f O r ig in a l Es ti ma te 173 5. 2 Apple Scab Model R e s u l t s The model produces a number o f performance v a r i a b l e s which coul d be used to ev alu ate th e various s t r a t e g i e s . The performance v a r i a b l e s r ange from t h o s e which measure n e t revenue t o t h o s e which m o n i to r t h e amounts o f t h e chem icals a p p l i e d . Some performance v a r i a b l e s may be more r e l e v a n t t o p o t e n t i a l u s e r s o f t h e model th a n o t h e r s , b u t t h e model t r i e s t o r e p o r t a l l t h a t may be o f i n t e r e s t . For th e p r i v a t e f i r m , t h e avera ge n e t revenue o v e r t h e twenty s im u l a te d s eas o ns could o f t e n be used as a p r i n c i p a l c r i t e r i a , b u t i t i g n o r e s th e v a l u e which might be a t t r i b u t e d to r is k . The v a r i a n c e in t h e n e t revenue can be used t o c a p t u r e some of t h e c o s t s o f r i s k but f r e q u e n t l y o t h e r moments o f t h e d i s t r i b u t i o n must be c o n s id e r e d t o t r u l y r e f l e c t t h e e n t i r e realm o f t h e e f f e c t s t h a t r i s k can have on optimal d e c i s i o n s . The model r e p o r t s both t h e ex p ec te d v al ue and th e v a r i a n c e o f th e n e t revenue and t h e d i s t r i b u t i o n i t s e l f can be c o n s t r u c t e d from t h e twenty y e a r s o f d a t a . The number o f s p r a y s a p p l i e d could be o f i n t e r e s t i n some c a s e s wh ile t h e amount o f t h e chemicals a p p l i e d should be im p o r t a n t in al m os t a l l cases. Captan i s measured i n pounds p e r a c r e and d e f o l a t a n i s re co rd ed i n g a l l o n s p e r a c r e w hi le benomyl ap pe a r s in terms o f ounces p e r a c r e . The p r i c e p e r pound o f ca p t an used in t h e model i s $1.85 w h ile t h e p r i c e s f o r th e o t h e r two chemicals a r e $ 2 4 /g a ll o n f o r d i f o l a t a n and $ . 659/ounce for benlate. The number o f b u s h e ls l o s t each y e a r t o ap p l e scab i s o f im p or ta nc e , b u t given t h e s t r u c t u r e o f t h e model t h e more r e l e v a n t v a r i a b l e i s p r o ba bl y th e p e r c e n t a g e o f t h e p o t e n t i a l h a r v e s t which becomes i n f e c t e d s i n c e t h e a c t u a l y i e l d i s i n f l u e n c e d g r e a t l y by t h e as sumpti ons i n h e r e n t in t h e f r o s t damage c a l c u l a t i o n . The f i g u r e s s h ou ld no t be used as an a b s o l u t e 174 e s t i m a t e but r a t h e r were d es ig ne d more f o r r e l a t i v e comparison w ith each other. A v a r i a b l e which b a l a n c e s t h e c o s t s i n c u r r e d in a c o n t r o l program w ith the value of the f r u i t l o s t is the v aria b le "control c o s t s . " I t is t h e sum o f a) t h e c o s t s o f t h e ch em ica ls a p p l i e d ; b) t h e c o s t o f t h e l a b o r and machinery used in t h e s p r a y a p p l i c a t i o n s ; and c) t h e v a l u e o f t h e f r u i t damaged by t h e fu ngus. For each o f t h e el ev en s t r a t e g i e s t h e v a l u e s f o r t h e v a r i o u s performance v a r i a b l e s ap p e a r in Table 6. The s t a n d a r d d e v i a t i o n s ap p e a r in p a r e n ­ t h e s i s below t h e ex p ec ted v a l u e s . These r e s u l t s were o b t a i n e d when the y i e l d l e v e l was s e t w ith a mean o f 500 b u s h e ls p e r a c r e . The t h r e e s t r a t e g i e s with t h e h i g h e s t ex pe c te d revenue p e r a c r e a r e d i f f e r e n t forms o f t h e p o s t i n f e c t i o n , IPM program. S t r a t e g y 11 which a p p l i e d benomyl only a f t e r an i n f e c t i o n a c t u a l l y oc cu rr ed produced t h e h i g h e s t n e t revenue o f $ 4 3 0 /a c r e . I t was fo llowed by s t r a t e g y 5 which p r e d i c t s i n f e c t i o n p e r i o d s by o b s er v in g t h e d a i l y te m p e r a t u r e and p r e c i p i t a t i o n . When an i n f e c t i o n p e r i o d has been p r e d i c t e d , benoniyl i s a p p l i e d . This s t r a t e g y a p p l i e d more chem ica ls b u t s u f f e r e d l e s s damage th a n s t r a t e g y 11. The s t r a t e g y w it h t h e t h i r d h i g h e s t n e t r e t u r n was number 10. It f o ll o w s a Reduced S i n g l e A p p l i c a t i o n Treatment (RSAT) e a r l y and a p o s t ­ i n f e c t i o n IPM program s i m i l a r t o s t r a t e g y 5 l a t e in t h e s e a s o n . I t is a p p r o x im a te ly $20 p e r a c r e l e s s e f f e c t i v e th an s t r a t e g y 5. The c o n v en ti on al s p r ay program r e p r e s e n t e d by s t r a t e g y 7 has th e f o u r t h h i g h e s t expec ted n e t r ev enu e. As d i s p l a y e d in Table 7 , h o ld i ng e v e r y t h i n g e l s e c o n s t a n t , i t would t a k e a 36.7% i n c r e a s e in t h e p r i c e o f benomyl t o make th e co n v en t io n al program as e f f e c t i v e on an ex p ec te d n e t revenue b a s i s as t h e p o s t - i n f e c t i o n IPM program o f s t r a t e g y 5. Table 6. S trategy Scab Model Results with Medium Yield. P o t e n t l al Scab Damage Y ie ld ( b u )' (b u .) Scab Damage (*) Net Undamaged Y ie ld Nuiriber of Sprays Benbiwl (oz) — iptan jt>s) C aptafol (g a ls) — — C ontrol C o sts ($) P rod u c tion Net C o sts Revenue (S) ($) 1 1 0 7 .6 (1 6 8 .3 ) 1302.8 (4 8 .0 ) -4 4 0 .5 (5 9 2 .1 ) 5 ,0 (0 .0 ) 2 93 .3 (8 .4 ) 1 5 0 4 .3 ( 5 0 .5 ) 3 73.8 (7 0 1 .0 ) 1 0 7 .6 (5 .5 ) — 317.1 ( 2 3 .5 ) 1523 (4 7 .8 ) 3 4 9 .9 (6 9 2 .4 ) 6 7 .2 (2 5 .2 ) 45 .0 (4 .1 ) — 341.1 ( 2 1 2 .0 ) 1 4 5 1 .9 (4 7 .2 ) 326 .0 (7 0 2 .0 ) 11 (.9 ) 1 7 5 .2 (1 4 .2 ) — — 2 47.2 (5 3 .5 ) 1 4 3 3 .6 (4 4 .6 ) 419.8 (7 0 5 .5 ) 4 99.5 ( 4 7 .0 ) 14 (.5 ) 1 6 4 .6 (6 .9 ) 53 .8 (2 .7 ) — 3 24.0 (2 3 .4 ) 1 5 2 9 .9 (4 7 .8 ) 3 43.1 (6 9 2 .5 ) 0 .5 4 99.5 (4 7 .0 ) 14 (-7) 1 7 .6 (1 9 .4 ) 8 2 .1 (6 .3 ) -- 2 85.7 (3 9 .7 ) 1 4 8 5 .3 ( 4 7 .0 ) 3 8 1 .4 (6 9 0 .3 ) 2.6 (8 .1 ) 0 .5 4 99.5 10 (1 .5 ) 1 1 .2 (1 5 .7 ) 5 0 .2 (7 .0 ) 3 .0 (0 .0 ) 2 8 8 .2 (4 1 .3 ) 1 4 8 8 .5 ( 4 8 .9 ) 3 7 8 .9 (6 9 2 .9 ) 502.1 (4 7 .5 ) 7.0 (3 1 .3 ) 1 .4 4 9 5 .1 (5 6 .5 ) 6 (.7 ) 8 5 .6 (1 0 .7 ) — 5 .0 (0 .0 ) 3 0 9 .2 ( 1 4 2 .7 ) 148 8.1 ( 4 9 .4 ) 3 5 7 .9 (7 1 9 .0 ) 10 5 02.1 (4 7 .5 ) 5 .4 (1 4 .1 ) 1.1 4 96 .7 (4 5 .5 ) 8 (1 .0 ) 1 1 0 .4 (1 6 .3 ) — 3 .0 (0 .0 ) 2 6 6 .5 (5 1 .0 ) 1 4 5 8 .6 (4 8 .0 ) 4 0 0 .6 ( 7 0 4 .0 ) 11 502.1 (4 7 .5 ) 16.1 (2 7 .4 ) 3.2 486 .0 (4 4 .3 ) 1 1 0 .4 (1 6 .3 ) — (1 .0 ) 237 .2 (1 0 9 .2 ) 1 3 8 5 .2 (4 7 .5 ) 4 2 9 .9 (6 9 4 .6 ) 1 502.1 ( 4 7 .5 ) 502.1 ( 4 7 .5 ) 1 00.0 — — 2 502.1 (4 7 .5 ) 0 .0 ( 0 .0 ) 0 .0 0 5 02.1 (4 7 .5 ) 8 (.8 ) 4 .8 (1 1 .7 ) 36 .6 (5 .4 ) 3 5 02.1 (4 7 .5 ) 1 .3 (5 .8 ) 0 .3 5 00.8 (4 7 .4 ) 14 (.5 ) 3.2 (9 .8 ) 4 5 02.1 (4 7 .5 ) 26 .7 (6 0 .7 ) 5 .3 4 9 5 .5 (4 5 .6 ) 15 (1 .1 ) 5 5 02.1 (4 7 .5 ) 6 .6 (1 4 .7 ) 1 .3 500.8 (4 7 .4 ) 6 5 02.1 ( 4 7 .5 ) 1 .3 (5 .8 ) 0 .3 7 5 02.1 (4 7 .5 ) 2 .6 (8 .0 ) 8 5 02.1 (4 7 .5 ) 9 • Scab Model Results with Medium Yield and an-Increase 1n the Price o f Benomyl o f 3 6 . It. j t e n t i a l Scab Y ie ld Damage (b u .) (b u .) Scab Damage (*) N et Undamaged Y ie l d ( b u .) Number of Sprays Benomyl (oz) Captan (lb s .) 2 502 .1 ( 4 7 .5 ) 0 .0 (0 .0 ) 0 .0 5 02.1 (4 7 .5 ) 8 (.8 ) 4 .8 (1 1 .7 ) 3 6 .6 (5 .4 ) 3 502.1 (4 7 .5 ) 1.3 (5 .8 ) 0 .3 500.8 (4 7 .4 ) 14 (.5 ) 3.2 (9 .8 ) 1 0 7 .6 (5 .5 ) 4 502.1 (4 7 .5 ) 2 6 .7 (6 0 .7 ) 5 .3 4 7 5 .4 (7 6 .3 ) 15 (1 .1 ) 6 7.2 (2 5 .2 ) 4 5 .0 (4 .1 ) 5 502.1 (4 7 .5 ) 6 .6 (1 4 .7 ) 1.3 4 95.5 (4 5 .6 ) 11 (.9 ) 1 7 5 .2 (1 4 .2 ) 6 5 0 2 .1 (4 7 .5 ) 1 .3 (5 .8 ) 0 .3 5 0 0 .8 (4 7 .4 ) 14 (.5 ) 1 6 4 .6 (6 .9 ) 7 5 02.1 ( 4 7 .5 ) 2 .6 ( 8 .0 ) 0 .5 4 99.5 (4 7 .0 ) 14 (.7 ) 8 5 02.1 (4 7 .5 ) 2 .6 (8 .1 ) 0 .5 4 9 9 .5 (4 6 .8 ) 9 5 02.1 (4 7 .5 ) 7 .0 (3 1 .3 ) 1 .4 10 5 02.1 ( 4 7 .5 ) 5 .4 ( 1 4 .1 ) 11 5 02.1 ( 4 7 .5 ) 16.1 (2 7 .4 ) C a p ta fo l (g a ls.) C ontrol C o sts ($) Production C osts ($) 5 .0 (0 .0 ) 294 .5 (9 .2 ) 1 5 0 5 .4 (5 0 .8 ) • 3 1 7 .9 (2 5 .1 ) 1 5 2 3 .8 (4 8 .0 ) 357 .3 (2 0 9 .6 ) 1 468.1 (4 9 .3 ) 289.5 (5 3 .8 ) 1 4 7 5 .8 (4 4 .0 ) 5 3.8 (2 .7 ) 363 .6 (2 4 .5 ) 1 5 6 9 .6 (4 8 .0 ) 1 7 .6 (1 9 .4 ) 8 2 .1 (6 .3 ) 2 89.9 (4 2 .6 ) 1 4 8 9 .5 (4 6 .1 ) 10 (1 .5 ) 1 1 .2 (1 5 .7 ) 5 0 .2 (7 .0 ) 3 .0 (0 .0 ) 2 9 0 .9 (4 3 .4 ) 1 4 9 1 .2 (4 9 .7 ) 4 9 5 .1 (5 6 .5 ) 6 (.7 ) 8 5 .6 (1 0 .7 ) 5 .0 (0 .0 ) 329.8 (1 4 2 .6 ) 1 5 0 8 .7 ( 5 0 .2 ) 1 .1 496 .7 (4 5 .5 ) 8 (1 .0 ) 110 .4 (1 6 .3 ) 3 .0 (o .o ) 2 9 3.1 (5 2 .0 ) 1 4 8 5 .2 (4 8 .7 ) 3 .2 486 .0 (4 4 .8 ) 7 (1 .0 ) 1 1 0 .4 (1 6 .3 ) 263 .8 ( 1 1 0 .9 ) 1 4 1 1 .8 (4 8 .1 ) • a. 177 I t s ho uld be noted t h a t benomyl i s used in eve ry c o n t r o l program even though i t i s n o t a p r i n c i p a l chemical o f many. Thi s i s because a t l e a s t d u r in g some season each s t r a t e g y allowed an i n f e c t i o n t o develop t h a t required the special e ra d ic a n t sprays. sp ra y s w i l l appl y 32 ounces o f benomyl. One s e r i e s o f e r a d i c a n t So f o r example, s t r a t e g y 3 w i l l a l lo w one i n f e c t i o n t o develop eve ry t e n y e a r s ( 3 . 2 / 3 2 ) . I f i t i s assumed t h a t a l l s t r a t e g i e s p r o v id e complete c o n t r o l o f th e d i s e a s e and the damage e s t i m a t e s a r e i g n o r e d , t h e s t r a t e g i e s coul d be ranked on t h e b a s i s o f t h e i r s p r ay c o s t s . 8. These r e s u l t s a r e p r e s e n t e d in Table The same t h r e e s t r a t e g i e s (11, 5 , 10) a r e s t i l l t h e most e f f e c t i v e . When t h e y i e l d l e v e l i s lowered t o a mean o f 250 b u s h e l s p e r t h e p o s t - i n f e c t i o n IPM programs a r e r e l a t i v e l y more e f f e c t i v e . r e s u l t s a r e p r e s e n t e d in Table 9. acre, These The IPM programs a r e r e l a t i v e l y more e f f e c t i v e s i n c e th e y g e n e r a l l y i n c u r h i g h e r p e r c e n t a g e damage l o s s e s than co n ve nt io n al programs and s i n c e y i e l d s a r e l e s s , th e v a l u e o f th e damage i s lower r e s u l t i n g in a more f a v o r a b l e comparison between t h e s p r a y c o s t s and va lu e o f damage avoided f o r t h e IPM programs. When y i e l d s a r e r a i s e d t o an av er a g e l e v e l o f 900 bus hes ! p e r a c r e , an o p p o s i t e r e s u l t i s obse rve d. The c o n v e n t io n a l programs become r e l a t i v e l y more e f f e c t i v e than b e f o r e . However, th e p o s t - i n f e c t i o n IPM programs, s t r a t e g i e s 5 , 10 and 11 a r e s t i l l producing t h e h i g h e s t expected n e t r ev en u e s. These r e s u l t s a p p e a r in Table 10. The performances o f th e s t r a t e g i e s were s i m u l a t e d un der f i v e d i f f e r e n t scenarios: mediumyield, low y i e l d , high y i e l d , medium y i e l d and high benomyl p r i c e , and medium y i e l d and no damage assumed. The r a n k in g s o f t h e s t r a t e g i e s by t h e s i z e o f ex p ec ted n e t revenues remains f a i r l y s t a b l e a c r o s s th e s c e n a r i o s with two i m p o r ta n t e x c e p t i o n s . When no damage i s Table 8. ir a te g y Scab Model Results with Medium Yield and No Damage Assumed. Scab P o ten tia l Damage Y ie ld (b u .) (b u .) Scab Damaoe (X) Net Ondamaoed Y ie l d Number of Sorays Ben’ a t e (oz) Captan (lb s) C aptafol (gals) Control C o sts (*) P rod u c tio n Not C o sts Revenue (S) (5) 2 5 02.1 (4 7 .5 ) — — — 8 (.8 ) 4 .8 (1 1 .7 ) 36 .4 (5 .4 ) 5.0 (0 .0 ) 2 9 3 .3 ( 8 .4 ) 1 5 0 4 .3 (5 0 .3 ) 3 73.8 (7 0 1 .0 ) 3 502.1 (4 7 .5 ) — — — 14 (.5 ) 3.2 (9 .8 ) 1 0 7 .6 (5 .5 ) -- 312.1 (7 .7 ) 1 5 2 3 .0 (4 7 .8 ) 3 5 5 .0 (7 0 2 .1 ) 4 572.1 (4 7 .5 ) — — — 15 o .n 6 7 .2 ( 2 5 .2 ) 4 5 .0 (4 .1 ) — 2 4 1 .0 ( 1 3 .4 ) 1 4 5 1 .9 (4 7 .2 ) 4 26.1 (6 3 9 .3 ) 5 502.1 ( 4 7 .5 ) — — — 11 (.9 ) 1 7 5 .2 ( 1 4 .2 ) — — 2 2 2 .6 (1 0 .6 ) 1 4 3 3 .6 (4 4 .6 ) 4 4 4 .5 ( 6 9 8 .2 ) 6 502.1 (4 7 .5 ) — — — 14 (.5 ) 1 6 4 .6 (6 .9 ) 5 3 .8 (2 .7 ) — 3 1 8 .9 (8-0) 1 5 2 9 .9 (4 7 .8 ) 3 4 8 .2 (7 0 2 .2 ) 7 5 02.1 (4 7 .5 ) — — — 14 (.7 ) 1 7 .5 (1 9 .4 ) — 2 74.3 (1 0 .2 ) 1 4 8 5 .3 (4 7 .0 ) 392 .8 (7 0 2 .3 ) 8 502.1 ( 4 7 .5 ) — — — 10 0 .5 ) 1 1 .2 0 5 .7 ) 5 0 .2 (7 .0 ) 3 .0 (0 .0 ) 2 7 7 .5 (1 5 .4 ) 1 4 8 8 .5 (4 8 .9 ) 3 8 9 .6 (6 3 9 .5 ) 9 5 02.1 (4 7 .5 ) — -- — 6 (.7 ) 85 .6 0 0 .7 ) — 5 .0 (0 .0 ) 2 77.1 (8 .0 ) 1488.1 (4 9 .4 ) 3 9 0 .0 (7 3 1 .9 ) 10 51)2.1 (4 7 .5 ) -- — — 8 1 1 0 .4 0 6 .3 ) — 3.0 (0 .0 ) 247.6 (1 2 .2 ) 1 4 5 8 .6 (4 8 .0 ) 419.5 (6 9 7 .5 ) 5 9 2 .1 — 1 1 0 .4 (1 6 .3 ) — — 1 7 4 .2 ( 1 2 .2 ) 1 3 8 5 .2 (4 7 .6 ) 4 9 2 .0 ( 6 9 9 .9 ) 11 (4 7 .5 ) 0 .0 ) — — 7 O .o ) 8 2 .1 (6 .3 ) Table 9. Strategy Scab Model Results with Low Yield. P o t e n t i a l Scab Y ie l d Damage ( B u .) (b u .) Scab Damage (1) N et Undamaged Y ie ld Number of Sprays Benomyl (oz) C ontrol C o sts ($) P rod u c tion N et Revenue C osts ($) ($) Captan (lb s) C a p ta fo l (g a ls) - - — 5 9 3 .3 (1 1 8 .9 ) 1 046.1 ( 5 1 .3 ) - 6 2 9 .1 (2 7 8 .8 ) 1 248 .0 (5 0 .8 ) 2 48.0 (5 0 .8 ) 1 0 0 .0 2 248.0 ( 5 0 .8 ) 0 .0 (0 .0 ) 0 .0 2 4 8 .0 (5 0 .8 ) 8 (.8 ) 4 .8 (1 1 .7 ) 3 6 .6 (5 .4 ) 5.0 (0 .0 ) 293.3 (8 .4 ) 1 2 4 7 .6 (5 3 .1 ) - 3 2 9 .1 (3 3 2 .3 ) 3 248.0 ( 5 0 .8 ) .4 (1 .8 ) 0 .2 247 .6 (5 1 .6 ) 14 (.5 ) 3.2 ( 9 .8 ) 1 0 7 .6 (5 .5 ) — 313 .6 (1 0 .1 ) 1 2 6 6 .4 (5 0 .9 ) -3 4 9 .4 (3 3 3 .8 ) 4 2 4 8 .0 (5 0 .8 ) 1 2 .0 (2 6 .6 ) 4 .8 2 3 6 .0 (6 0 .7 ) 15 (1 .1 ) 6 7 .2 (2 5 .2 ) 4 5.0 ( 4 .1 ) — 2 8 6 .4 (8 9 .9 ) 1 1 9 5 .3 ( 5 3 .3 ) -3 2 2 .2 (3 3 9 .6 ) 5 2 4 8 .0 (5 0 .8 ) 2 .7 (5 .7 ) 1.1 2 4 5 .3 (5 1 .6 ) 11 (.9 ) 1 7 5 .2 (1 4 .2 ) — — 2 32.6 (2 1 .1 ) 1 1 7 6 .9 ( 4 7 .2 ) -2 6 8 .4 ( 3 3 7 .2 ) 6 2 4 8 .0 (5 0 .8 ) .4 (1 .8 ) 0 .2 2 47.6 (5 1 .6 ) 14 (.5 ) 1 6 4 .6 (6 .9 ) 53 .8 (2 .7 ) — 3 2 0 .5 (1 0 .2 ) 1 2 7 3 .2 ( 5 0 .9 ) -3 5 6 .3 (3 3 3 .9 ) 7 2 4 8 .0 (5 0 .8 ) 1.0 (3 .1 ) 0 .4 2 4 7 .0 (5 1 .9 ) 14 (.7 ) 1 7 .6 (1 9 .4 ) 8 2.1 (6 .3 ) -- 2 7 8 .6 (1 9 .6 ) 1 2 2 8 .7 (4 9 .6 ) -3 1 4 .4 (3 3 4 .9 ) 8 24 8.0 (5 0 .8 ) 1 .1 (3 .7 ) 0 .4 2 4 6 .9 (5 1 .0 ) 10 (1.5) 1 1 .2 (1 5 .7 ) 5 0 .2 (7 .0 ) 3 .0 (0 .0 ) 2 82.1 (2 6 .3 ) 1 2 3 1 .8 (5 6 .0 ) -3 1 7 .9 (3 2 9 .6 ) 9 248.0 (5 0 .8 ) 3 .7 (1 6 .6 ) 1.5 2 4 4 .3 (5 2 .0 ) 6 (.7 ) 8 5.6 (1 0 .7 ) — 5 .0 (0 .0 ) 2 9 4 .1 (7 5 .6 ) 1 2 3 1 .4 ( 5 2 .3 ) -3 2 9 .9 (3 3 9 .8 ) 10 248.0 (5 0 .8 ) 2 .0 (5 .2 ) 0 .8 2 4 6 .0 (5 1 .8 ) 8 (1 .0 ) 110.4 (1 6 .3 ) — 3 .0 (0 .0 ) 254.5 (1 9 .5 ) 1 2 0 1 .9 (5 0 .6 ) -2 9 0 .3 (3 3 6 .3 ) 11 24 8.0 (5 0 .8 ) 6.4 (1 0 .0 ) 2.6 2 41.6 (5 4 .8 ) 1 1 0 .4 (1 6 .3 ) — — (i!o) 1 9 9 .3 ( 4 2 .7 ) 1 1 2 8 .5 (5 0 .2 ) -2 3 5 .2 ( 3 4 3 .2 ) - - Table 10. Scab Model Results with High Yield. S trategy P o t e n t i a l Scab Scab Net Y ie l d Damage Damage Undamaged ( B u .) (b u .) { %) yi ld 1 89 8 .7 ( 5 0 .3 ) 2 898 .7 (5 0 .3 ) 0 .0 (0 .0 ) 3 8 9 8 .7 (5 0 .3 ) 2 .2 (1 0 .0 ) 4 898.7 ( 5 0 .3 ) 4 8 .1 (1 1 4 .1 ) 5 8 9 8 .7 (5 0 .3 ) 6 Number of Sprays Benomyl (o z .) Captan (lb s) C a p ta fo l (g a ls) 8 9 8 .7 1 00.0 (5 0 .3 ) C ontrol C o sts w . P rod u c tion C osts ($) Net Revenue ($) 19 2 0 .6 (3 2 6 .8 ) 1703.4 (5 0 .8 ) -1 0 5 .9 (1 1 7 9 ) 2 9 3 .3 (8 .4 ) 1 9 0 4 .9 (4 9 .8 ) 1 5 2 1 .4 (1 4 4 3 .8 ) 3 2 0 .9 (3 9 .7 ) 1 9 2 3 .7 (5 1 .9 ) 1 4 9 3 .8 (1 4 3 0 .9 ) 421 .2 (4 0 3 .7 ) 1 8 5 2 .6 (5 2 .8 ) 1 3 9 3 .5 ( 1 4 4 5 .8 ) 2 6 3 .4 (8 7 .1 ) 1 8 3 4 .2 (5 3 .5 ) 1 5 5 1 .3 (1 4 5 4 .0 ) 8 98.7 (5 0 .3 ) 8 (.8 ) 4 .8 (1 1 .7 ) 3 6 .6 (5 .4 ) 8 9 6.5 (5 1 .4 ) 14 (.5 ) 3.2 (9 .8 ) 1 0 7 .6 (5 .5 ) 5 .4 8 5 0 .6 (1 2 1 .3 ) 15 (1 .1 ) 6 7.2 (2 5 .2 ) 10.9 (2 2 .8 ) 1.2 887.8 (6 0 .5 ) 11 (.9 ) 1 7 5 .2 (1 4 .2 ) 8 9 8.7 (5 0 .3 ) 2 .2 (1 0 .0 ) 0 .2 8 9 6 .5 (5 1 .4 ) 14 (.5 ) 1 6 4 .6 (6 .9 ) 5 3.8 (2 .7 ) 3 2 7 .7 ( 3 9 .5 ) 1 9 3 0 .5 (5 2 .1 ) 1 4 8 7 .0 (1 4 3 1 .0 ) 7 8 9 8 .7 (5 0 .3 ) 4 .4 (1 3 .6 ) 0 .5 8 94.3 (5 3 .5 ) 14 (.7 ) 1 7 .6 (1 9 .4 ) 8 2 .1 (6 .3 ) 293.4 (6 3 .2 ) 1 8 8 5 .9 (5 0 .7 ) 1 5 2 1 .3 (1 4 3 0 .2 ) 8 8 9 8.7 (5 0 .3 ) 4 .5 (1 4 .0 ) 0 .5 8 9 4 .2 (5 1 .3 ) 10 (1 .5 ) 1 1 .2 (1 5 .7 ) 50.2 (7 .0 ) 3 .0 (0 .0 ) 2 95.9 (6 4 .3 ) 1 889.1 (5 2 .1 ) 1 5 1 8 .8 (1 4 3 3 .4 ) 9 8 9 8 .7 (5 0 .3 ) 1 2 .3 (5 4 .9 ) 1 .4 886.5 (7 6 .5 ) 6 (.7 ) 85 .6 (1 0 .7 ) 5.0 (o .o ) 3 3 3 .4 (2 5 1 .2 ) 1 8 8 8 .7 (5 0 .5 ) 1 4 8 1 .3 (1 4 7 4 .5 ) 10 8 9 8 .7 (5 0 .3 ) 8 .7 (2 2 .5 ) 1.0 890.0 (5 9 .5 ) 8 (1 .0 ) 1 1 0 .4 (1 6 .3 ) 3.0 (0 .0 ) 2 7 8 .2 (8 0 .4 ) 1 8 5 9 .2 (8 0 .4 ) 1 5 3 6 .5 (1 4 5 1 .7 ) 11 898 .7 (5 0 .3 ) 2 7 .1 (4 6 .7 ) 3 .0 8 7 1 .6 (7 0 .3 ) 7 (1 .0 ) 1 1 0 .4 (1 6 .3 ) 280 .2 (1 8 2 .6 ) 1 7 8 5 .8 (5 5 .5 ) 1 5 3 4 .5 (1 4 4 6 .4 ) 0 .0 0 .2 5 .0 (0 .0 ) 45 .0 (4 .1 ) __ 181 assumed, t h e program which a p p l i e s a h a l f dosage o f cap ta n t h r o u g h o u t th e s e a s o n , s t r a t e g y 4 , becomes one o f t h e t h r e e most e f f e c t i v e programs. Thi s oc cu rs because s t r a t e g y 4 has a r e l a t i v e low t o t a l s p r a y c o s t b u t s u f f e r s th e most damage o f any o f t h e c o n t r o l programs examined. The o t h e r e x c e p t i o n i s t h a t a t high y i e l d s t h e h y p o t h e t i c a l p o s t - i n f e c t i o n program, s t r a t e g y 11 s l i p s from bei ng t h e most e f f e c t i v e s t r a t e g y t o th e t h i r d most e f f e c t i v e s t r a t e g y . This r e s u l t p ro b a b ly i s observed s i n c e s t r a t e g i e s 5 and 10 by i n a c c u r a t e l y p r e d i c t i n g i n f e c t i o n p e r i o d s and ap p l y in g more s p r a y s a r e b e n e f i t i n g from some o f t h e c a p a c i t y o f each o f th e benomyl a p p l i c a t i o n s . protective The r a n k i n g s a r e compared f o r t h e v a r i o u s s c e n a r i o s in Table 11. 5.3 Risk A n al ys is The f o l l o w i n g d i s c u s s i o n i s d i v i d e d i n t o two s e c t i o n s - - a d e s c r i p t i o n o f t h e a n a l y t i c a l p ro ce du r es and t h e p r e s e n t a t i o n o f t h e r e s u l t s o f t h e analysis. The f i r s t s e c t i o n may be r ed un da nt t o most r e a d e r s and th ey s hould proceed d i r e c t l y t o th e s e c t i o n p r e s e n t i n g t h e r e s u l t s . For r e a d e r s i n t e r e s t e d only in t h e scab model, t h i s d i s c u s s i o n may be p e r ­ tinent. A n a l y t i c a l Pr ocedures The very n a t u r e o f crop p r o t e c t i o n i m p li e s t h a t d e c i s i o n s about p e s t management a r e n o t always made on t h e b a s i s o f th e e x p ec te d v a l u e s o f n e t income bu t t h a t t h e avoidance o f r i s k i s im p o r ta n t as w e l l . Sim- p l i s t i c a l l y , th e s i t u a t i o n can be d e p i c t e d as be in g a t r a d e - o f f between t h e mean and th e v a r i a n c e o f t h e d i s t r i b u t i o n o f n e t income where t h e v a r i a n c e i s o f t e n used as a measure o f r i s k . However, t h i s can be n ai v e s i n c e o t h e r moments in t h e d i s t r i b u t i o n can be i m p o r t a n t as w e l l . The 182 Table 11. Rankings o f Scab Control S t r a t e g i e s by S iz e o f Expected Net Revenues. High Benomyl P r i c e and Medium Yield Medium Yield and No Damage Strategy Medium Yield Low Yield High Yie ld 1 11 11 11 11 11 2 6 7 4 6 8 3 8 9 7 7 9 4 9 6 10 9 3 5 2 2 1 2 2 6 10 10 8 10 10 7 4 4 4 3 5 8 5 5 6 4 7 9 7 8 9 8 6 10 3 3 2 5 4 11 1 1 3 1 1 183 skewness o f t h e d i s t r i b u t i o n can i n f l u e n c e t h e d e c i s i o n s o f some i n ­ d ividuals j u s t lik e the variance. The t r a d e - o f f between t h e e xp ec te d v a l u e , t h e v a r i a n c e a n d / o r o t h e r measures o f r i s k i s l i k e l y t o be r a t h e r p e r s o n a l . D ifferent individuals have d i f f e r e n t p e r s p e c t i v e s about how much r i s k th e y a r e w i l l i n g t o b e a r and each i n d i v i d u a l i s l i k e l y t o a l t e r h i s / h e r r i s k p r e f e r e n c e as th e amount o f money in v ol ve d in t h e d e c i s i o n changes. The w i l l i n g n e s s t o p a r t i c i p a t e in an inv e stm en t t h a t has a 50% chance o f e a r n i n g $10 and 50% chance o f l o s i n g $10 i s l i k e l y t o change i f th e outcomes were t h e chance t o win o r l o s e $10,000,000 r a t h e r th an j u s t $10. However, t h e a d j u s t m e n t o f t h e r i s k p r e f e r e n c e t o changes in income i s n o t expected t o be i d e n t i c a l f o r a l l i n d i v i d u a l s . Many i n d i v i d u a l s w i l l d i s p l a y r i s k a v e r s i o n , r i s k p r e f e r e n c e and r i s k n e u t r a l i t y over a t l e a s t some s e c t i o n s o f t h e i r r e l e v a n t income ran g e. The manner in which i n d i v i d u a l s v al u e t h e u n c e r t a i n t y in t h e outcomes which r e s u l t from t h e i r d e c i s i o n s i s an a r e a t h a t i s s t i l l stood. l i t t l e und er­ I t i s hy p ot h e siz ed t h a t f o r some i n d i v i d u a l s t h e w o r s t p o s s i b l e outcomes o f e a c h p o s s i b l e a c t i o n ch o i ce a r e t h e most i m p o r t a n t . i n d i v i d u a l s a r e t h e most r i s k a v e r s e t h a t i s p o s s i b l e . These They compare the minimums o f t h e cu m u lati v e p r o b a b i l i t y f u n c t i o n s a s s o c i a t e d w ith each a c t i o n c h oi ce and s e l e c t t h a t a c t i o n c h o i c e which has th e h i g h e s t minimum value. In e s s e n c e th e y compare t h e w o r st p o s s i b l e outcomes and choose the a l t e r n a t i v e which has th e b e s t " w o r s t 1' outcome. They ig n o r e th e r e s t o f t h e outcomes and t h e e x pe c te d v a l u e s s i n c e the y a r e i n t e r e s t e d o n l y in minimizing t h e impacts o f any p o s s i b l e d i s a s t e r s . These i n d i v i d u a l s f o l l o w a d e c i s i o n r u l e known a s maxi-min. Another c l a s s i c a l b e h a v i o r model i s t h a t o f ma ximization o f expec ted 184 profit. The i n d i v i d u a l s who f o l l o w t h i s d e c i s i o n r u l e ig n o r e any r i s k o r u n c e r t a i n t y a s s o c i a t e d w it h t h e a c t i o n c h o i c e s and s e l e c t o nl y on t h e b a s i s o f th e ex p ec ted v a l u e s . The a l t e r n a t i v e w ith th e l a r g e s t ex­ pec te d v a l u e i s chosen as t h e b e s t . These two extreme c a s e s a r e i m p o r ta n t because o f t h e way which some a n a l y t i c a l t o o l s t h a t a r e commonly used t o e v a l u a t e a l t e r n a t i v e a c t i o n c h o i c e s f o r c l a s s e s o f d e c i s i o n makers o p e r a t e . Sin ce i t i s i m p o ss ib l e t o c o n s t r u c t a s i n g l e f u n c t i o n which can r e p r e s e n t th e r i s k p r e f e r e n c e s o f more than one i n d i v i d u a l , a s e r i e s o f a n a l y t i c a l te c h n i q u e s r e f e r r e d t o as S t o c h a s t i c Dominance has devel op ed. These e f f i c i e n c y c r i t e r i a s e t upper and lower bounds on th e r i s k p r e f e r e n c e s o f a c l a s s o f d e c i s i o n makers. The wide r th e i n t e r v a l d ef in e d by t h e bounds, th e l a r g e r th e c l a s s o f d e c i s i o n makers w i l l be. However, t h e l a r g e r t h a t t h e c l a s s o f the d e c i s i o n makers i s , th e more d i f f i c u l t i t w i l l be t o d i s c a r d a l t e r n a t i v e a c t i o n ch o ic es as i n e f f i c i e n t . The pro ced ur e examines a l l o f th e p o s s i b l e a l t e r n a t i v e s and r e j e c t s any a l t e r n a t i v e f o r which i t can be s a i d t h a t f o r ev er y member o f th e c l a s s o f d e c i s i o n ma kers, t h e r e e x i s t s a t l e a s t some o t h e r a l t e r n a t i v e t h a t i s p r e f e r r e d . a r e r e f e r r e d t o as t h e e f f i c i e n c y s e t . The remaining a l t e r n a t i v e s The e f f i c i e n c y s e t i s n o t always narrowed down t o one a l t e r n a t i v e , in f a c t f o r wide i n t e r v a l s ( l a r g e c l a s s e s o f d e c i s i o n makers) i t may be as l a r g e as 50% o f t h e t o t a l number o f a l t e r n a t i v e s examined. For t h i s r e a s o n , t h e i n t e r v a l o f r i s k p r e ­ f e r e n c e s i s much l i k e a s t a t i s t i c a l co n f id e n c e i n t e r v a l . A wide i n t e r v a l has a high p r o b a b i l i t y o f a Type I I e r r o r (c l a i m i n g no d i f f e r e n c e between t h e expec ted u t i l i t i e s o f t h e a l t e r n a t i v e s when one a c t u a l l y e x i s t s ) w h il e a narrow i n t e r v a l has a tendency f o r a Type I e r r o r ( c l a i m i n g t h e r e i s a d i f f e r e n c e between t h e ex p ec ted u t i l i t i e s o f t h e a l t e r n a t i v e s when 185 none a c t u a l l y e x i s t s ) . There a r e f o u r typ e s o f S t o c h a s t i c Dominance which a r e r e l e v a n t f o r t h i s study. They a r e : F i r s t Degree, Second Degree, S t o c h a s t i c Dom­ in a n ce w ith Respect t o a F u n c ti o n , and Convex S e t S t o c h a s t i c Dominance. F i r s t Degree S t o c h a s t i c Dominance s e t s th e bounds on t h e r i s k p r e f e r e n c e s in such a way t h a t i t s c l a s s o f d e c i s i o n makers i n c l u d e s ev er y p o s s i b l e d e c i s i o n maker. I t s u f f e r s from t h e l a c k o f d i s c r i m i n a t i n g power and prod uces l a r g e e f f i c i e n c y s e t s . Second Degree S t o c h a s t i c Dominance narrows t h e i n t e r v a l somewhat bu t i t s t i l l o f a Type I I e r r o r . preferring. s u f f e r s from a high p r o b a b i l i t y I t ex cl ud es a l l r i s k p r e f e r e n c e s which a r e r i s k I t s c l a s s o f d e c i s i o n makers i s bounded on t h e one extreme by t h e maxi-min i n d i v i d u a l and on t h e o t h e r by th e r i s k n e u t r a l d e c i s i o n maker. S t o c h a s t i c Dominance with Respect t o a Function i s a much more f l e x i b l e a n a l y t i c a l t o o l than t h e f i r s t two t y p e s . R a t h e r th an having a f i x e d i n t e r v a l l i k e F i r s t and Second Degree S t o c h a s t i c Dominance, i t s i n t e r v a l can be s e t by t h e r e s e a r c h e r . The i n t e r v a l does n o t need to be c o n s t a n t a c r o s s t h e e n t i r e income ran ge and i t can be s e t t o i n c l u d e r i s k preferences t h a t are r i s k av erse, r i s k n e u tra l o r r i s k loving. The s i z e o f t h e c l a s s o f d e c i s i o n makers and t h e r e l a t i v e p r o b a b i l i t i e s o f t h e Type I and Type I I e r r o r s w i l l be det erm ine d by t h e s i z e o f the interval. F i r s t and Second Degree S t o c h a s t i c Dominance a r e r e a l l y s u b s e t s o f t h e more gener al S t o c h a s t i c Dominance w ith Respect t o a Fu n ct io n , Convex S e t S t o c h a s t i c Dominance i s a te c h n i q u e which when a p p l i e d w it h one o f t h e o t h e r S t o c h a s t i c Dominance p r o c e d u r e s w i l l de te rm in e i f t h e e f f i c i e n c y s e t can be f u r t h e r reduced by e l i m i n a t i n g any a l t e r n a t i v e s f o r which t h e r e e x i s t s a convex combination o f two o r more o t h e r a l t e r ­ n a t i v e s which i s p r e f e r r e d by ev er y d e c i s i o n maker w i t h i n t h e c l a s s . 186 I t removes from t h e e f f i c i e n c y s e t s t r a t e g i e s which a r e not the most p r e ­ f e r r e d a l t e r n a t i v e f o r a t l e a s t one d e c i s i o n maker in t h e c l a s s . The 11 s t r a t e g i e s f o r c o n t r o l l i n g a pp l e scab which were s im u l a te d by t h e model were examined by t h e S t o c h a s t i c Dominance p r o c e d u r e s . Of the i n f i n i t e number o f i n t e r v a l s t h a t would be p o s s i b l e , f i v e were selected for th is analysis. 12. The f i v e i n t e r v a l s a r e d i s p l a y e d in Table The c o e f f i c i e n t s f o r t h e i n t e r v a l s a r e in terms o f th e P r a t t Risk Aversion C o e f f i c i e n t which i s d e f i n e d as t h e n e g a t i v e o f t h e r a t i o o f t h e second d e r i v a t i v e o f t h e u t i l i t y f u n c t i o n t o th e f i r s t d e r i v a t i v e o f th e u t i l i t y f u n c t i o n { - u " ( x ) / u ' ( x ) ). The u t i l i t y f u n c t i o n i s a con­ c e p t which ec ono m ist s use t o r e p r e s e n t t h e amount o f s a t i s f a c t i o n o r v a l u e t h a t i n d i v i d u a l s r e c e i v e from such items as income, l e i s u r e , consumption, e t c . Risk n e u t r a l i t y i s r e p r e s e n t e d as having a r i s k a v e r s i o n c o e f f i c i e n t of 0.0. The most r i s k a v e r s e i n d i v i d u a l would be r e p r e s e n t e d w ith a c o e f f i c i e n t o f +°° w h il e on t h e o t h e r ex t re m e, t h e most r i s k lo v i n g i n ­ d i v i d u a l would be d e p i c t e d by a c o e f f i c i e n t o f - » . The f i r s t i n t e r v a l ap pr ox im ate s Second Degree S t o c h a s t i c s i n c e i t ran g es from 0 t o . 1 . Dominance I t i s an ap p rox im ati on s i n c e i t does n o t e x t e n d c o m p le te ly t o +« b u t i t i s o f a l a r g e enough magnitude t o produce an i d e n t i c a l e f f i c i e n c y s e t t o t h e one i d e n t i f i e d f o r Second Degree S t o c h a s t i c Dominance. I t would be ex p e c te d t h a t t h i s i n t e r v a l would r e t a i n as r i s k e f f i c i e n t a t l e a s t both t h e a l t e r n a t i v e w it h t h e h i g h e s t e x p e c te d v al u e and t h e one with th e l a r g e s t minimum v a l u e . The n e x t i n t e r v a l i s s i m i l a r t o t h e f i r s t e x c e p t t h a t t h e r i s k n e u t r a l and s l i g h t l y r i s k a v e r s e p r e f e r e n c e s . i t ex c l u d e s I t s lower bound b e g i n s a t .0003 which co r r e s p o n d s t o a m o d e ra te l y high l e v e l o f r i s k aversion. Table 12. R isk A n a ly s is R e su lts f o r Scab C o n tro l S tr a te g ie s . Risk In te rv a l 1) O.C to 0.1 General D is c r e tio n Approximates Second Degree S to c h astic Dominance: Ineludes r is k n e u tra l and maxi-m1n Medium Y ield (All S tra te g ie s ) 7 , 8 . 11 2) .0003 to 0.1 Ranges from maxi-min to m oderately strong ris k aversion 11 3) .0001 to .0003 Ranges from s lig h t r is k aversion to m oderately stro n g aversion 11 Medium Y ield (Excluding u ) Low Y ield (All S tra te g ie s ) Low Yield (Excluding 11 ' 5 ,7 ,8 .9 11 5, 7. 8 5. 7. 8 11 5, 7, 8 11 5 5 High Y ield (All S tra te g ie s ) High Y ield (Excluding 11) Medium Medium Yield High Yield Hirn Benomyl P ric e Benomyl " n r e (All S tra te g ie s ) ( E x c lu d ' : n ' Z. 7, 8 . 11 2 ,5 ,7 ,8 .9 ,1 1 8 , 11 7, 8 , 11 2 . 5 . 7, 8 2 ,5 .7 ,8 ,9 2 . 7. 9* 7, 8 7, 8 . 11 11 7. 8 7.8 CO 4) -.0001 to .0001 5) Ranges from s l i g h tl y ris k loving to s lig h tly ris k a v e rse ; in rlu d e s ris k n e u tr a lity ■ 5, 11 -.001 to .0008 In terv a l changes as income a t SO in c re a se s; ranges from -.001 to .0015 m oderately s tr o ig r is k 9 7 x 7 0 a t $10, 000 loving to v a rijn s le v e ls *0 , 0 il -.001 to .0004 o f m oderately strong " • ,u> " a t $25,000 ris k a v e rsio n ; includes ris k n e u tr a lity ‘ Excludes S trateg y 8 a s w ell as S trateg y 11 • ‘ Excludes S tra te g y 5 but Includes S tra te g y 11 5 9 7 x 7 ■ a TA ’ *• *» 10 H n 5 5 5. 7 2 ,7,8,10,11** 5 , 7, C 9 , 10, 11 2, E, 7 , 6 . S. 10 11 2 , 3, 4 . 5 . 7 . 8 , 9 . 10. 11 2 , 5, 7, 8 2 , 3. 4, 5, 7. 8 . 9 . 10 188 The n e x t two i n t e r v a l s r e p r e s e n t a much s m a l l e r c l a s s o f d e c i s i o n makers. The t h i r d i n t e r v a l ex c l u d e s the d e c i s i o n makers who have more tha n m od e ra te l y s t r o n g r i s k a v e r s e a t t i t u d e s and t h o s e who a r e l e s s than s l i g h t l y ris k averse. The f o u r t h i n t e r v a l i n c l u d e s th e r i s k n e u t r a l i n d i v i d u a l and t h o s e whose p r e f e r e n c e s approach r i s k n e u t r a l i t y . It does r e p r e s e n t d e c i s i o n makers who a r e s l i g h t l y r i s k a v e r s e and t h o s e who a r e s l i g h t l y r i s k lo v i n g. The f i n a l i n t e r v a l i s t h e most complex. I t i s an a t t e m p t t o use s u rv ey d a t a on r i s k p r e f e r e n c e s (81) t o c o n s t r u c t an i n t e r v a l which would i n c l u d e th e 80 t o 90% o f t h e Michigan f a r m e r s . I t s upper bound v a r i e s by t h e income l e v e l and i t s lower bound i s s e t t o i n c l u d e t h e s t r o n g l y r i s k lo v i n g i n d i v i d u a l s . At z e r o income, t h e upper bound i s .0008 which re p re sen ts a strong r is k aversion. At $10,000 i t i n c r e a s e s t o .0015 wh ile a t $25,000 i t drops t o .0004 which i s s t i l l a m o de ra te l y s t r o n g r i s k averse p o sitio n . Since t h i s i s a wide i n t e r v a l , i t i s e xp ec te d t h a t th e e f f i c i e n c y s e t w i l l be r e l a t i v e l y l a r g e . R e s u lt s E f f i c i e n c y s e t s have been i d e n t i f i e d f o r each o f th e f i v e i n t e r v a l s u s i n g t h e d i s t r i b u t i o n s o f n e t revenue g e n e r a t e d by th e s i m u l a t i o n model under t h e v a r i o u s s c e n a r i o s . s e t s were i d e n t i f i e d . t h e second s e r i e s For each s c e n a r i o , two s e r i e s o f e f f i c i e n c y The f i r s t s e r i e s in c lu d ed a l l 11 s t r a t e g i e s wh ile exc lu de s from c o n s i d e r a t i o n s t r a t e g y 11. Strategy 11 i s a h y p o t h e t i c a l p o s t - i n f e c t i o n IPM program which assumes t h a t t h e r e i s no e r r o r in p r e d i c t i n g t h e i n f e c t i o n p e r i o d s . The e f f i c i e n c y s e t s a r e compared in Table 12. There a r e t h r e e major p o i n t s t h a t s u r f a c e from th e comparison o f the e f f ic ie n c y s e t s . The f i r s t p o i n t i s t h a t s t r a t e g y 11 i s r i s k e f f i c i e n t 139 f o r a l l i n t e r v a l s under each s c e n a r i o with th e e x c e p ti o n o f th e f o u r t h i n t e r v a l f o r t h e high y i e l d s c e n a r i o . The second p o i n t i s t h a t th e co n v e n t i o n a l program r e p r e s e n t e d by s t r a t e g y 7 i s r i s k e f f i c i e n t in th e f i f t h i n t e r v a l f o r each s c e n a r i o e x c e p t f o r th e low y i e l d one. The f i n a l p o i n t i s t h a t t h e e f f i c i e n c y s e t i d e n t i f i e d f o r th e l a s t i n t e r v a l is g e n e r a l l y q u i t e l a r g e . In some c a s e s , only two o r t h r e e s t r a t e g i e s can be d e c l a r e d a s bei ng i n c o n s i s t e n t w ith t h e r i s k p r e f e r e n c e s o f the m a j o r i t y o f t h e Michigan f a r m e r s. I f a s m a l l e r c l a s s o f d e c i s i o n makers were used ( i . e . , 50-60% o f t h e f a r m e rs ) o r i f a t t i t u d e s t o r i s k were more homogenous, i t i s l i k e l y t h a t more s t r a t e g i e s could be removed as being risk inefficient. I t sh ould be n o t e d , however, t h a t t h e r e a r e growers in Michigan who f o l l o w programs which a r e v er y s i m i l a r t o each o f the s t r a t e g i e s w it h t h e e x c e p t i o n o f s t r a t e g y 3. VI . CODLING MOTH MODEL RESULTS 6.1 The S im u la ti on Model The c o d l i n g moth model u t i l i z e s a time va r y in g d i s t r i b u t e d d e l a y . I t was developed by s l i g h t l y modifying t h e PETE phenology model which i s w id el y used t o p r e d i c t c o l d i n g moth oc c u r r e n c e on a p p l e s (148). The r a t e s a t which th e i n s e c t p o p u l a t i o n ma tur es from one age c l a s s t o a n o t h e r i s time v a r y in g and dependent upon th e accumulated deg ree days. The avera ge time t h a t i t t a k e s f o r t h e i n s e c t s t o p ass from one s t a g e to a n o t h e r i s d i r e c t l y r e l a t e d t o the ambient te m p e r a t u r e . In t h i s c a s e , t h e ambient te m p e r a t u r e i s measured in d egree days accumulated from a b i o - f i x , a p o i n t in time f i x e d by t h e o c c u rr e n c e o f an e a s i l y observed b i o l o g i c a l e v e n t . o f f r u i t s e t in t h e a p p l e t r e e s . The b i o - f i x used he re i s th e o cc u r re n c e The model produces a s e r i e s o f phen­ ol o g ic a l s t a g e s in t h e sea so na l development o f t h e t r e e s based upon th e number o f deg ree days (bas e 43°F) t h a t have accumulated s i n c e J an uar y 1 each y e a r . The w ea th e r p a t t e r n f o r each se ason i s randomly g e n e r a te d f r o m a d i s t r i b u t i o n developed from h i s t o r i c a l r e c o r d s from th e East Lansing w ea th e r exper im ent s t a t i o n d u r i n g t h e y e a r s 1910 t o 1979. The model commences each se ason on Apr il 1 so t h e number o f d eg ree days t h a t ha ve accumulated d u r in g th e months o f J a n u a r y , February and March a r e randomly g e n e r a t e d from a normal d i s t r i b u t i o n w ith a mean o f 580 and a s t a n d a r d d e v i a t i o n of 80. The f i r s t s t a g e dete rmin ed by t h e model i s green t i p which o cc u r s a t 700 deg ree days . At 750 de gr ee days 1/2 inch green i s reached w h i l e 800 deg ree days i s t h e t r a n s i t i o n p o i n t t o t i g h t cluster. At 900 and 1,000 d egree d a y s , pink and bloom r e s p e c t i v e l y oc cu r. 190 191 P e t a l f a l l i s assumed t o oc cur a t 1,100 deg ree days and f r u i t s e t i s o b s e r v e d seven c a l e n d a r days a f t e r p e t a l f a l l ( 8 , pp. A34-A35). It s h o u l d be noted t h a t t h e r e i s a d i f f e r e n c e between th e de gr ee days used t o c a l c u l a t e t h e p h e n ol o gi ca l s t a g e s o f t h e t r e e s and t h e days used to s i m u l a t e t h e p o p u l a t i o n dynamics o f th e c o d l i n g moth. They have d i f f e r e n t s t a r t i n g p o i n t s and employ d i f f e r e n t b a s e s . The model b eg in s each s eas on a t f r u i t s e t by s i m u l a t i n g th e p o p u l a t i o n dynamics o f t h e c o d l i n g moth by a l l o w i n g a time v a r y in g d i s t r i b u t e d d e l a y t o c a l c u l a t e t h e r a t e s a t which t h e i n s e c t s mature from one s t a g e to the other. The model has f i v e l i f e s t a g e s : the eggs, the la rv a e , th e pupae, th e p r e - o v i p o s i t i o n a d u l t s and t h e o v i p o s i t i n g a d u l t s . While t h e same r o u t i n e i s used f o r a l l f i v e l i f e s t a g e s , t h e r e a r e a number o f c a l c u l a t i o n s which a r e unique t o t h e m a t u r a t i o n p r o c e s s o f each stage. The s u b r o u t i n e DELAY i s an exte mel y f l e x i b l e a l g o r i t h m t h a t can be u s e d t o c a l c u l a t e time v ar y in g d i s t r i b u t e d d e l a y s w it h p r o p o r t i o n a l losses. I t f u n c t i o n s by d i v i d i n g each d e l a y i n t o K c a s c a d i n g s t a g e s . The s t a g e s o f t h e d e l a y a r e d i s t i n c t from t h e l i f e s t a g e s o f p o p u l a t i o n s i n c e each l i f e s t a g e i s r e p r e s e n t e d by a d i f f e r e n t d e l a y . The d e l a y i s p r e d i c t a t e d upon a s e r i e s o f d i f f e r e n t i a l e q u a t i o n s which d e s c r i b e s the p r o c e s s and can be s o lv e d by E u l e r ' s i n t e g r a t i o n . The e q u a t i o n s can be r e p r e s e n t e d by: 1) ^ ( t ) = R - ( t - D t ) + Dt* g f t *Dt) * [Ri+1 ( t - D t ) - where = r a t e o f t h e i t h ca s c a d in g s t a g e D = t h e mean time d e l a y K = t h e o r d e r o f t h e d e l a y p r o c e s s (number o f ca s c a d in g s t a g e s ) PLR = p r o p o r t i o n a l l o s s r a t e o u t o f each s t a g e Dt = i n t e g r a t i o n s t e p s i z e ( 1 , pp. 3-6) 192 The amount o f time t h a t i t t a k e s f o r an i n d i v i d u a l t o pass co m pl ete ly throu gh a d e l a y p r o c e s s ( l i f e s t a g e ) depends upon t h r e e f a c t o r s . As has been p r e v i o u s l y d i s c u s s e d , t h e r a t e a t which de gr ee days a r e accumulated i s one f a c t o r . The o t h e r two f a c t o r s a r e t h e v a l u e s which a r e used f o r t h e v a r i a b l e s D and K in t h e e q u a t i o n s r e p r e s e n t e d by Equation 1. The d e l a y p r o c e s s o p e r a t e s with a Erlang d i s t r i b u t i o n r e p r e s e n t i n g t h e amount o f time n e c e s s a r y t o complete t h e d e l a y . The v a r i a b l e DEL i s s e t equal to t h e d e s i r e d mean wh ile th e v a r i a n c e i s equal t o th e f o l l o w i n g e x p r e s s i o n : 2) a 2 = DEL2/K The v a r i a b l e D i s equa l t o DEL/K and i s t h e time n e c e s s a r y t o complete each cas ca di n g s t a g e . There a r e a number o f i n t e r e s t i n g c h a r a c t e r i s t i c s o f t h e Erlang f a m i ly o f d i s t r i b u t i o n s . Where K i s equal t o 1 , t h e d i s t r i b u t i o n i s th e f a m i l i a r ex p o n e n t ia l d e n s i t y f u n c t i o n . As K becomes a s y m p t o t i c a l l y l a r g e , t h e d i s t r i b u t i o n app roxim ates a normal d e n s i t y f u n c t i o n . With K e q u a l t o 00 t h e d i s t r i b u t i o n qpproaches a normal d i s t r i b u t i o n w it h a mean o f D and a v a r i a n c e o f z e r o - - o r a d i s c r e t e d e l a y . By s e l e c t i n g t h e a p p r o p r i a t e v a l u e s f o r D and K, t h e a l g o r i t h m can a c c u r a t e l y s i m u l a t e th e p a t t e r n o f m a t u r a t i o n obs erved in t h e r e a l population. D i f f e r e n c e s in t h e l e n g t h o f time n e c e s s a r y t o mature from t h e d i f f e r e n t l i f e s t a g e s can be handled by a s s i g n i n g d i f f e r e n t v a l u e s f o r D, a n d / o r K in each d e l a y p r o c e s s ( 82) . Another v a r i a b l e which i n f l u e n c e s t h e number o f i n d i v i d u a l s t h a t a c t u a l l y emerge from each d e l a y ( l i f e s t a g e ) i s t h e v a r i a b l e PLR. This v a r i a b l e c a l c u l a t e s a p r o p o r t i o n a l l o s s from each o f th e K ca s c a d in g stag es o f the delay. I t r ed uc e s th e number o f i n d i v i d u a l s in ea c h 193 c a s c a d i n g s t a g e by t h e avera ge amount t h a t w i l l be l o s t in each d e l a y . U s u a l l y th e d e l a y p r o ce s s w i l l co ns erv e flow— t h a t i s t o say t h a t th e number o f i n d i v i d u a l s who e n t e r t h e d e l a y w i l l be e x a c t l y equal t o t h e nimber which emerge when t h e d e l a y has been completed. However, in some c a s e s t h e r e may o c c u r a l o s s d u r i n g t h e m a t u r a t i o n p r o c e s s and n o t a l l o f th o s e who e n t e r e d w i l l f i n i s h th e p r o c e s s . This phenomena can be s i m u l a t e d by th e i n t r o d u c t i o n o f t h e p r o p o r t i o n a l l o s s r a t e v a r i a b l e . Each time t h e a l g o r i t h m i s c a l l e d , a r e d u c t i o n o cc urs i n th e p o p u l a t i o n s o f each c a s c a d in g s t a g e in d i r e c t p r o p o r t i o n t o t h e number o f i n d i v i d u a l s t h a t i t has. Losses in th e d e l a y p r o c e s s e s in th e p o p u l a t i o n dynamics o f i n s e c t s can be a c c r e d i t e d t o n a t u r a l d e a t h s from r a i n , wind and parasites. The l o s s r a t e can be s e t a t d i f f e r e n t l e v e l s f o r th e v a r i o u s l i f e s t a g e s (8 2) . The model b eg i n s a t f r u i t s e t by i n i t i a l i z i n g t h e v a l u e s f o r a number o f v a r i a b l e s which must be r e s e t a t t h e b eg in nin g o f each s e a s o n . i s performed in t h e s u b r o u t i n e CMINIT. This In t h i s s u b r o u t i n e , t h e v a r i a b l e s t h a t a r e i n i t i a l i z e d which a r e i m p o r t a n t f o r t h i s d i s c u s s i o n a r e DEL, K, R and STRG, PLR, and SCMPOP. There a r e o f c o u r s e , o t h e r i n i t i a l i z a t i o n s o c c u r r i n g b u t t h e y a r e f a i r l y s t a n d a r d and do n o t m e r i t mention h e r e . The v a r i a b l e DEL i s th e av er a g e ti m e t h a t i t t a k e s f o r an i n d i v i d u a l t o co m p le te ly mature from one l i f e s t a g e t o t h e n e x t . I t is the to ta l time t o complete t h e e n t i r e d e l a y p r o c e s s w h ile D i n e q u a t i o n 1 i s th e time n e c e s s a r y t o complete one s t a g e o f th e d e l a y . I t i s equal t o DEL/K. I t i s e x p r e s s e d in terms o f d eg ree days (base 50°F) t h a t have accumulated since f r u i t s e t . a d i f f e r e n t value. For each d e l a y ( l i f e s t a g e ) t h e v a r i a b l e i s a s s i g n e d For t h e f i r s t l i f e s t a g e , th e egg s t a g e , i t t a k e s a n av er a ge o f 145 degree days t o h a t c h i n t o a l a r v a . The l a r v a l s t a g e 194 i s ex p e c te d t o l a s t 587 degree days and t h e pupal s t a g e a n o t h e r 265 d ay s . The p r e - o v i p o s i t i o n a d u l t s t a g e i s by f a r t h e s h o r t e s t . l a s t s an av era ge o f 50 degree days. It The o v i p o s i t i n g a d u l t s t a g e has an expec ted d u r a t i o n o f 175 days. In each d e l a y , t h e number val ue o f K f o r a l l distributions o f ca s c a d in g s t a g e s i s t h e same. The l i f e s t a g e s i s 15. The c h a r a c t e r i s t i c s o f th e Erlang gover ning t h e m a t u r a t i o n r a t e s from each l i f e s t a g e can now be i n f e r r e d . The means and v a r i a n c e s o f each delay are presented in Table 1. The n e x t two v a r i a b l e s , R and STRG a r e r e l a t e d t o t h e r a t e s o f movement from one c a s c a d i n g s t a g e t o t h e ne x t and th e number o f i n ­ d i v i d u a l s t h a t may be found in any one d e l a y ( l i f e s t a g e ) a t a given p o i n t in ti me . i s commonly assumed t h a t when T= 0 and t h e s i m u l a t i o n It i s j u s t be gi nni ng t h a t most i n i t i a l va lu es f o r R and STRG w i l l be z e r o . However, i t i s t o be remembered t h a t in th e p o p u l a t i o n dynamics o f the c o d l i n g moth, t h e i n s e c t o v e r w i n t e r s a s l a r v a and t h a t a t f r u i t s e t th e o v e r w i n t e r i n g p o p u l a t i o n s ho ul d have advanced t o t h e l a t e r l a r v a l s t a g e s . I t i s t h e r e f o r e n e c e s s a r y t o i n i t i a l i z e some o f th e v a l u e s o f R and STRG f o r t h e l a r v a l s t a g e a t n on - ze ro l e v e l s . The r a t e s o f movement o u t o f th e l a s t t e n c a s c a d in g s t a g e s o f t h e d e l a y r e p r e s e n t i n g the pupal s t a g e a r e a s s i g n e d no n -z er o v a l u e s . All o t h e r r a t e s w i t h i n t h i s d el ay and t h e o t h e r d e l a y s as well a r e s e t equal t o ze r o a t t h e b eg in ni n g of each s e a s o n . At f r u i t s e t s i n c e only i n d i v i d u a l s t h a t have o v er w in te r ed as l a r v a e can be fou nd, a l l i n i t i a l v a l u e s f o r STRG a r e s e t equal t o ze ro e x c e p t f o r th e STRG v a r i a b l e r e l a t e d t o t h e d e l a y f o r t h e l a r v a l stage. The p r o p o r t i o n a l l o s s r a t e s a s s i g n e d t o each o f t h e d e l a y s a r e different. For th e two a d u l t l i f e s t a g e s , t h e r e i s no l o s s w hi le f o r the 195 Table 1. The C h a r a c t e r i s t i c s o f t h e Erlang D i s t r i b u t i o n s R e p r es en ti ng Delay Times f o r th e L i f e S ta g e s o f t h e Codling Moth. Standard Delay Life Stage Me a n Variance Deviation 1 Eggs 145 1402 37.4 2 Larvae 587 22971 151.6 3 Pupae 265 4682 68.4 4 Pre-ovlposition Adults 50 167 12.9 5 Ovipositing Adults 175 2038 45.1 196 e g g s , l a r v a e and pupae a small l o s s e x i s t s . The l o s s e s f o r t h e t h r e e s t a g e s a r e r e s p e c t i v e l y .00103, .00140 and .00023 p e r deg ree day i n t h a t l i f e s t a g e o r .149, .822^ and .061. The t o t a l n a t u r a l m o r t a l i t y would thus be 85.8$. The f i n a l v a r i a b l e whose i n i t i a l i z a t i o n needs t o be d i s c u s s e d i s th e s t a r t i n g p o p u l a t i o n d e n s i t y , SCMP0P. I t can be s e t a t t h r e e l e v e l s which approximate a h i g h , medium and low p o p u l a t i o n d e n s i t y . A high le v el can be a s s i g n e d by s e t t i n g t h e value f o SCMP0P equal t o 10.0 while a medium d e n s i t y i s d e f in e d by a v al u e o f 1 . 0 . The low p o p u l a t i o n den­ s i t y i s determined by i n i t i a l i z i n g SCMP0P w ith a v al u e o f 0 . 1 . The high p o p u l a t i o n co rr es pon ds t o d e n s i t y o f one l a r v a p e r 100 ap p l e s w h ile t h e medium l e v e l i s equal t o a d e n s i t y o f one l a r v a p e r 1000 a p p l e s . The low p o p u l a t i o n r e p r e s e n t s a d e n s i t y o f one l a r v a p e r 10,000 a p p l e s . I t i s assumed t h a t t h e o r c h a r d produces 100 ap p l e s t o t h e bushel and t h a t t h e r e a r e 100 t r e e s p e r a c r e . A f t e r th e i n i t i a l i z a t i o n has been com ple te d, t h e model commences with t h e s i m u l a t i o n . is called. Each day a f t e r f r u i t s e t , th e s u b r o u t i n e C0DM0TH This s u b r o u t i n e performs seven b a s i c f u n c t i o n s . I t calculates t h e number o f degree days from t h e av era ge d a i l y te m p e r a t u r e and u p da te s t h e movement o f th e p o p u l a t i o n through t h e v a r i o u s l i f e s t a g e s . Every two d eg ree days an i t e r a t i o n of t h e d e l a y p r o c e s s e s o cc ur s so i t i s q u i t e c o n c e i v a b l e t h a t in most days t h e number o f ti m es t h e m a t u r a t i o n p r o c e s s i s updated w i l l g r e a t l y exceed one. C0DM0TH a l s o c a l c u l a t e s th e i n - m i g r a t i o n o f th e i n s e c t i n t o t h e o r c h a r d and th e amount o f o v i p o s i t i o n t h a t occurs. 3) The i n - m i g r a t i o n i s det ermined by e q u a t i o n 3. R ( J , 2 ) = R ( J ,2 ) + .002555 * Apples * .0022 1A f t e r f r u i t damage. 197 where R = r a t e of movement ou t o f th e J t h c a s ca di ng s t a g e in d e l a y representing the larval l i f e stage Apples = t h e number o f a p p l e s p e r t r e e I t i s now p o s s i b l e t h a t th e number o f l a r v a e l e a v i n g a give n c a s ca di n g s t a g e may a c u t a l l y exceed t h e number which e n t e r e d due t o t h e i n - m i g r a t i o n . The o v i p o s i t i o n i s det ermined by t h e number o f a d u l t s which ap pe a r in each o f th e 15 c a s c a d in g s t a g e s o f th e l a s t d e l a y p r o c e s s . i n t h e f o l l o w i n g c a s ca d in g s t a g e s a c t u a l l y l a y eggs: and 7. Only i n d i v i d u a l s 2 , 3, 4 , 5, 6 , The o v i p o s i t i o n r a t e s d i f f e r f o r each o f t h e ca s c a d in g s t a g e s . The s u b r o u t i n e c a l c u l a t e s th e m o r t a l i t y t o t h e newly hat ched l a r v a e t o t h e chemical s p r a y s a f t e r t h e o v i p o s i t i o n and i n - m i g r a t i o n a r e dete rm ine d. The s p r a y m o r t a l i t y t o t h e a d u l t s t a g e s and t h e eggs a r e c a l c u l a t e d in t h e s u b r o u t i n e CMMORT which i s c a l l e d once by CODMOTH a t t h e b eg in ni n g o f each day. The m o r t a l i t y t o t h e newly hatch ed l a r v a e , as well as t h e o v i p o s i t i o n and i n - m i g r a t i o n a r e updat ed w it h th e d e l a y p r o c e s s ev er y two de gr ee days. The r a t e o f movement o u t o f t h e f i r s t ca s c a d in g s t a g e o f t h e l a r v a l d el ay i s t h e only r a t e a d j u s t e d f o r the s p r a y m o r t a l i t y by CODMOTH. A f t e r th e s p r a y m o r t a l i t y i s c a l c u l a t e d f o r t h e newly hatch ed l a r v a e , t h e number o f a p p l e s t h a t a r e i n f e s t e d by worms i s d e r i v e d u s in g t h e r a t e o f movement o u t o f t h e f i r s t ca s c a d in g s t a g e o f th e l a r v a l delay. viosly This c a l c u l a t i o n i s updated ev er y two d egree days w it h th e p r e discussed o p eratio n s. At th e end o f t h e day, th e p r o p o r t i o n ■ofapples t h a t a r e i n f e s t e d w ith t h e c o d l i n g moth l a r v a e i s computed. The . l a s t f u n c t i o n t h a t i s performed by th e s u b r o u t i n e i s t h e e s t i ­ mation o f t h e numbers i n each o f t h e v a r i o u s l i f e s t a g e s . They a r e r e p r e s e n t e d by th e STRG v a r i a b l e s f o r t h e f i v e d e l a y s and a r e c a l c u l a t e d 198 by summing t h e r a t e s o f movement o u t o f th e ca s c a d in g s t a g e s f o r each d el ay and d i v i d i n g by K/DEL. The v a r i a b l e CMLEVEL i s s e t equal t o the number o f eggs e s t i m a t e d d i v i d e d by t h e number o f a p p l e s p e r t r e e . These c a l c u l a t i o n s a r e performed once a day a t th e end o f t h e CODMOTH s u b r o u t i n e . Thi s model was ad apt ed with few r e v i s i o n s from a wid ely used PETE phenology model which has been v a l i d a t e d f o r a number o f d i f f e r e n t r e g i o n s ( 1 1 0 ; 148; and 63 ). The rema ining s u b r o u t i n e o f t h e c o d l i n g moth model i s t h e one which implements t h e d e c i s i o n r u l e s o f t h e v a r i o u s s t r a t e g i e s examined. It i s r e f e r r e d t o as CMSCOUT and i s c a l l e d on a weekly b a s i s from t h e sub­ r o u t i n e SCOUT. I t e x e c u t e s t h e d e c i s i o n r u l e s f o r both c o n v e n t io n a l c a l e n d a r s p r a y s c h e d u le s and I n t e g r a t e d P e s t Management (IPM) programs. There a r e 19 d i f f e r e n t s t r a t e g i e s which a r e examined by t h e model. The f i r s t s t r a t e g y c o n s i s t s o f app ly in g no c o n t r o l and i t i s used as a b a s e l i n e f o r comparison p u r p o s e s . The n e x t two s t r a t e g i e s a r e co n ve nt io n al c a l e n d a r sc h ed u le s which ap p l y r e s p e c t i v e l y azinphosmethyl and p y r e t h r o i d . The s p r a y s a r e a p p l i e d on a b i- w e e k l y b a s i s from f r u i t s e t u n t i l 1700 de gr ee days (base 50°F) have accumulated s i n c e f r u i t s e t . The remaining s t r a t e g i e s a r e v a r i a t i o n s o f IPM programs with d i f f e r e n t l e v e l s f o r t h r e e economic t h r e s h o l d s . For each o f t h e two chem ica ls c o n s i d e r e d , t h e r e a r e f o u r d i s t i n c t IPM programs. Each program i s examined t w i c e , f i r s t w it h no sampling e r r o r assumed in t h e s c o u t ' s e s t i m a t e o f th e p o p u l a t i o n and th e n l a t e r w i t h a random sampling e r r o r t h a t 95% o f t h e time o f th e s c o u t ' s e s t i m a t e i s w i t h i n 50% o f t h e t r u e p o p u l a t i o n density. The sampling e r r o r i s randomly drawn from a normal d i s t r i b u t i o n u s i n g th e s u b r o u t i n e RAN. 199 The IPM programs use t h r e e economic t h r e s h o l d s ( o r per haps more c o r r e c t l y one dynamic economic t h r e s h o l d a d j u s t e d by t h e observed w e a th e r p a t t e r n ) . A maximum o f two s p ra y s a r e a p p l i e d f o r c o n t r o l o f f i r s t g e n e r a t i o n eggs and l a r v a e . Which economic t h r e s h o l d t h a t i s t o be used i s dependent upon th e number o f d egr ee days (b as e 50°) e x p e r i e n c e d s i n c e f r u i t s e t and t h e number o f s p r a y s a p p l i e d . I f no s p r a y s have been a p p l i e d , t h e r e l e v a n t economic t h r e s h o l d i s d e f i n e d by t h e v al u e f o r th e v a r i a b l e ECM1. I f one s p r a y has been p r e v i o u s l y a p p l i e d and l e s s th an 800 deg ree days have accumulated s i n c e f r u i t s e t , t h e v al ue o f ECM2 i s t h e t h r e s h o l d l e v e l t o be us ed. I f more than 1200 de gr ee days have been o b s e r v e d , t h e t h r e s h o l d v a l u e o f concern i s ECM3. These programs w i l l n e v e r a p p l y more th an 3 s p r a y s p e r s e a s o n . The p o p u l a t i o n e s t i m a t e s a r e made i n terms o f e g g s / a p p l e s / t r e e (CMLEVEL). The s t r a t e g i e s a r e more c o m pl et e ly d e s c r i b e d in Table 2. S t o c h a s t i c Elements o f t h e Model The model was c o n s t r u c t e d t o perform a s t o c h a s t i c Monte Carlo analysis. For each s t r a t e g y a s i m u l a t i o n was made f o r twenty in de pen den t seasons. The purpose o f t h e Monte Carlo a n a l y s i s was t o g e n e r a t e enough i n f o r m a t i o n abo ut th e performance o f t h e s t r a t e g i e s under d i f f e r e n t , p o s s i b l e c o n d i t i o n s t h a t t h e s t r a t e g i e s could be e v a l u a t e d i n a s t o c h a s t i c manner. Each seas on can be viewed as a d i s t i n c t s e t o f c o n d i t i o n s be cause th e y a r e randomly g e n e r a t e d from a s e r i e s o f m u l t i v a r i a t e d i s ­ t r i b u t i o n s , u s u a l l y based on h i s t o r i c a l r e c o r d s . The per formances o f a l l o f t h e s t r a t e g i e s ar e examined under t h e same twenty s e a s o n s . The d i f f e r e n c e s in t h e v a r i o u s s e a s o n s l i e in t h e random draws from t h e m u l t i v a r i a t e p r o b a b i l i t y d i s t r i b u t i o n s . Each s t o c h a s t i c v a r i a b l e T a b le .2 . C odling Moth Model S t r a te g i e s . Strategy Chemical Never Spray Baseline 1 Calendar 2 3 IPM 4 — Yes Biweekly Spray.#1 Sprays Until When Pop>EMCl 1700 Degree Days (Value of EMC1) Spray #2 When Pop>EMCl and DD <800 (Value of EMC2) Spray #3 When Pop>ZMC3 Sampling and DD >1200 Error (Value of EMC3)___________ No No — — — — — No No Azinphosmethy1 No No Pyrethroid Yes Yes Azinphosmethyl No No .001 003 .005 No 5 Pyrethroid No No .001 ' 003 .005 No 6 Axinphosmethyl No No .001 001 .001 No 7 Pyrethroid No No .001 ,001 .001 No 8 Az inphosmethy1 No No .002 ,006 .01 No 9 Pyrethroid No No .002 .006 .01 No 10 Az inphosmethy1 No No .0015 .0045 .0075 No 11 Pyrethroid No No .0015 .0045 .0075 No Yes — 12 Az inphosme thyl No No .001 .003 .005 13 Pyrethroid No No .001 .003 .005 Yes 14 Azinphosmethyl No No .001 .001 .001 Yes 15 Pyrethroid No No .001 .001 .001 Yes 16 Az inphosmethy1 No No .002 .006 .01 Yes 17 Pyrethroid No No .002 .006 .01 Yes 18 Azinphosmethyl No No .0015 .0045 .0075 Yes 19 Pyrethroid No No .0015 .0045 .0075 Yes 201 r e p r e s e n t s a so u rc e o f u n c e r t a i n t y and i t i s the u n c e r t a i n t y w i t h i n the system t h a t n e c e s s i t a t e s t h e e v a l u a t i o n o f t h e s t r a t e g y performances under different conditions. I f t h e r e were no u n c e r t a i n t y in t h e system, i n f o r m a t i o n from a s i n g l e s i m u l a t i o n would be s u f f i c i e n t t o rank the s t r a t e g i e s as t o t h e i r d e s i r a b i l i t y . The so ur ce o f u n c e r t a i n t y i n t h e inde pe nd en t c o d l i n g moth model a r e th e f r e s h market p r i c e , t h e p r o ce s s ed ma rke t p r i c e , th e av er a ge d a i l y t e m p e r a t u r e , th e number o f deg ree days (b as e 43°F) accumulated in J a n u a r y , F eb r ua ry , and March, and in some c a s e s t h e random sampling e r r o r . The ap p le p r i c e s a r e randomly g e n e r a t e d from a m u l t i v a r i a t e d i s ­ t r i b u t i o n which was i n f e r r e d from a h i s t o r i c a l time s e r i e s o f d a t a from t h e y e a r s 1969 t o 1978. The f r e s h market and t h e a l l - p r o c e s s e d market p r i c e s a r e randomly drawn from t h e d i s t r i b u t i o n in a f a s h i o n t h a t should p r e s e r v e t h e observed c o r r e l a t i o n between th e two. This p r o c e s s i s performed by an a l g o r i t h m developed by King and i s c a l l e d MVGEN (6 3 ) . The av era ge d a i l y t e m p e r a t u r e i s g e n e r a te d from a m u l t i v a r i a t e random p r o c e s s o r which a l s o in c l u d e s p r o b a b i l i s t i c i n f o r m a t i o n on d a i l y precipitation. There a r e a number o f i m p o r ta n t c o r r e l a t i o n s which a r e incorporated into th is processor. The c o r r e l a t i o n c o e f f i c i e n t s between t h e t e m p e r a t u r e and t h e p r e c i p i t a t i o n f o r each day a r e used by t h e a l g o r i t h m , as a r e t h e a u t o c o r r e l a t i o n s f o r t h e p r e c i p i t a t i o n and t h e average te m p e r a t u r e f o r a given day and t h e day immediately p r e c e d in g i t . S in ce t h e se ason was d i v i d e d i n t o 8 p a r t s o f 21 days e a c h , t h e r e a r e 8 d i s t i n c t m u l t i v a r i a t e d i s t r i b u t i o n s w it h t h r e e s e t s o f c o r r e l a t i o n c o e f f i c i e n t s i n c o r p o r a t e d t o p r e s e r v e i m p o r ta n t r e l a t i o n s h i p s in the randomly g e n e r a t e d d i s t r i b u t i o n s . The p r o b a b i l i t y o f a given t e m p e r a t u r e being drawn i s d i f f e r e n t in th e 8 p a r t s o f t h e season b u t i t 202 i s i d e n t i c a l f o r a l l 21 days w i t h i n any one p a r t o f t h e s e a s o n . The m u l t i v a r i a t e d i s t r i b u t i o n s were developed from h i s t o r i c a l w e a th e r r e c o r d s from t h e East Lansing weather exper im ent s t a t i o n f o r t h e y e a r s 1910 t o 1979. The number o f d egr ee days (b as e 43°F) t h a t have accumulated p r i o r t o Apr il 1 i s n e c e s s a r y t o c a l c u l a t e th e p h y s i o l o g i c a l p r o g r e s s i o n o f the a p p l e t r e e s through th e s e as o n. b eg in n in g of April. The model b eg i ns each se ason a t th e The d eg ree day t o t a l p r e v i o u s t o t h e s e a s o n ' s b eg in ni n g i s randomly g e n e r a t e d from an u n i v a r i a t e normal d i s t r i b u t i o n w ith a mean o f 580 and a s t a n d a r d d e v i a t i o n o f 80. The random sampling e r r o r t h a t can be imposed on t h e s c o u t ' s e s t i m a t e o f t h e p o p u l a t i o n used in t h e IPM programs i s a l s o drawn from a normal d i s t r i b u t i o n . The a l g o r i t h m t h a t d i r e c t s t h i s random g e n e r a t i o n uses a mean t h a t i s s e t equal t o th e a c t u a l p o p u l a t i o n d e n s i t y and the s t a n d a r d d e v i a t i o n i s i n f e r r e d by t h e s i z e o f t h e c o n f id e n c e i n t e r v a l d e f i n e d by t h e u s e r o f t h e model. In t h i s c a s e , t h e random e r r o r t h a t i s g e n e r a t e d w i l l e n s u r e t h a t th e e s t i m a t e o f t h e s c o u t i s w i t h i n 50% o f t h e t r u e p o p u l a t i o n 95% o f th e ti m e . Sin ce i t i s drawn from a normal d i s tr i b u t io n , the p r o b a b ility t h a t scout overestim ates the population is equal t o t h e p r o b a b i l i t y o f an u n d e r - e s t i m a t i o n . 6.2 Model R e s u lt s There a r e a number o f performance v a r i a b l e s which a r e s i m u l a t e d by t h e model and which coul d be used to e v a l u a t e t h e v a r i o u s s t r a t e g i e s . More th a n one performance v a r i a b l e may be n e c e s s a r y t o t h o r o u g h l y e v a l u a t e a s t r a t e g y s i n c e i t i s u n l i k e l y t h a t a s i n g l e v a r i a b l e can c a p t u r e a l l o f t h e p ar am et er s which may be o f i n t e r e s t t o someone concerned w it h p e s t 203 management. Of a l l th e v a r i a b l e s , pr o b ab ly th e f o u r most r e l e v a n t a r e p e r a c r e ex p ec ted n e t r ev en u e , t h e d i s t r i b u t i o n o f n e t re v e n u e , the amount o f moth damage and th e q u a n t i t y o f p e s t i c i d e s in t r o d u c e d i n t o t h e environment. The expec ted n e t revenue can be used as an i n d i c a t i o n , on t h e a v e r a g e , o f th e r e l a t i v e p r o f i t a b i l i t y o f f o l l o w i n g one s t r a t e g y ove r a n o t h e r , b u t i t i s n e c e s s a r y t o c o n s i d e r t h e d i s t r i b u t i o n o f n e t revenue t o e v a l u a t e t h e r i s k e f f i c i e n c y o f t h e s t r a t e g i e s . The amount o f moth damage and th e q u a n t i t y o f p e s t i c i d e s employed a r e u s e f u l measures o f t h e g en era l e f f i c a c y o f t h e s t r a t e g i e s . O ther performance v a r i a b l e s prov ide d by t h e model s p r a y s a p p l i e d and a measure which a t t e m p t s t o b al an ce and t h e c o s t s i n c u r r e d t o c o n t r o l i t . a r e t h e number o f th e p e s t damage This v a r i a b l e i s " c o n t r o l c o s t " and i s t h e sum o f t h e p e s t damage, th e p e s t i c i d e c o s t , t h e s c o u t i n g c o s t , and t h e c o s t o f l a b o r and machinery used in t h e a p p l i c a t i o n . In many c a s e s t h e r e w i l l e x i s t a t r a d e - o f f between t h e damage and t h e o t h e r c o s t s —t h a t i s t o say t h a t i f t h e a p p l i c a t i o n and p e s t i c i d e c o s t s a r e r ed u ce d , th e damage i s l i k e l y to i n c r e a s e . However, i t may be p o s s i b l e t o s u b s t i t u t e i n f o r m a t i o n pr ov ide d by s c o u t i n g ( a t a lower c o s t ) f o r some p e s t i c i d e w i t h o u t g r e a t l y a f f e c t i n g t h e amount o f damage e x p e r i e n c e d . This i s p a r t o f t h e b a s i s f o r many IPM s t r a t e g i e s . For each o f th e 19 s t r a t e g i e s th e model was s i m u l a t e d a number o f times. Following t h e Monte Carlo f o r m a t , t h e model was run once f o r each s t a t e o f n a t u r e f o r each s t r a t e g y f o r each i n i t i a l p o p u l a t i o n l e v e l . There a r e t h r e e p o p u l a t i o n l e v e l s and 20 s t a t e s o f n a t u r e so a t o t a l o f s i x t y s eas on s were s im u l a te d f o r each s t r a t e g y . All s t r a t e g i e s were s i m u l a t e d f o r t h e same 20 s t a t e s o f n a t u r e . The s t r a t e g i e s a r e a l l desig ned t o use one o f two c h e m i c a l s —azinphosmethyl 204 or a p y rethroid. A f u l l dose a p p l i c a t i o n f o r azinphosmethyl i s assumed t o be 32 ounces p e r a c r e w hi le t h e f u l l s t r e n g t h s p r a y o f the p y r e t h r o i d c o n s i s t s o f a r a t e o f 26 ounces p e r a c r e . azinphosmethyl used by t h e model i s $5. 25. The p r i c e p e r pound o f The p y r e t h r o i d i s assumed t o be a v a i l a b l e a t a p r i c e of $10.50 p e r pound. As seen i n Table 3, t h e c o s t p e r a p p l i c a t i o n i s c o n s i d e r a b l y l e s s in t h e use o f a z i n ­ phosmethyl. The two chem icals have i d e n t i c a l m o r t a l i t y r a t e s f o r c o d l in g moth b u t th e p y r e t h r o i d impacts on t h e m it e p r e d a t i o n which azinphosmethyl does n o t. The ex pe c te d v a l u e s and s t a n d a r d d e v i a t i o n s produced by t h e s i m u l a t i o n o f t h e model f o r t h e high i n i t i a l p o p u l a t i o n d e n s i t y ap p ea r in Table 4. The high i n i t i a l p o p u a l t i o n d e n s i t y r e f e r s t o a l e v e l o f l a r v a e p e r a p p l e s p e r t r e e o f 10/1000. The s t r a t e g y with t h e h i g h e s t expec ted n e t revenue i s s t r a t e g y 8 , t h e IPM s t r a t e g y w ith t h e h i g h e s t economic thresholds. The co n ve nt io n al c a l e n d a r program based on t h e use o f azinphosmethyl has th e second h i g h e s t avera ge income. I t i s a bo ut $4 p e r a c r e lower b u t i t sh ou ld be noted t h a t i t p r e v e n t s alm os t a l l damage w h il e s t r a t e g y 8 s u f f e r s ap p r o x im a te ly 3% damage. I t should a l s o be remembered t h a t th e c a l e n d a r s p r a y s a r e de sig ned t o c o n t r o l more p e s t s than j u s t t h e c o d l i n g moth and t h e a c t i v i t y o f t h e s e p e s t s i s igno red in th e model. The IPM s t r a t e g i e s only apply h a l f t h e s p r a y s t h a t th e c a l e n d a r c o n t r o l program do, but th e y r e s u l t in more damage. Of a l l th e IPM s t r a t e g i e s , only s t r a t e g y 8 e n j o ys an ex pe c te d n e t revenue h i g h e r than th e c a l e n d a r program. The IPM s t r a t e g i e s w i t h e i t h e r the s t a t i c economic t h r e s h o l d s o r t h e low and medium l e v e l dynamic t h r e s h o l d s perform i d e n t i c a l l y . This s u g g e s t t h a t n e t revenue i s n o t to o s e n s i t i v e t o t h e economic t h r e s h o l d . The chemical p r i c e d i f f e r e n t i a l between T ab le 3 . S pray C o sts f o r Moth C o n tro l S t r a te g i e s . Spray Chemical P rice P er U n it Chemical C o st p e r A p p lica tio n Labor C o st p er A p p lic a tio n Machinery C o st p er A p p lic a tio n C o st p er A p p lic a tio n A zinphosm ethyl 50UP 32 o z / a c r e $ .0 3 2 8 /o z $ 1 0 .5 0 /a cre $ . 70 /a c re $ . 7 0 /a cre $ 11.9 0 /a c re P y r e t h r o i d 3EC 26 o z / a c r e $ .8 0 8 /o z $21.0 0 /a c r e $ . 70 /a c re $ . 7 0 /a cre $22.4 0 /a c re Spurce: Pest Control Branch, NRED, ERS, USDA. 206 Tible 4. Moth Model Results with Medium Yield end a High Density fo r the I n i ti a l Moth Population. Potential Yield .(bu/acre) Moth Damage (bu/acre) 1 502.1 <47.5) 308.0 (79.3) 194.1 (88.9) 13 4 (IPM-Low E.T.) -354 5 (IPM-High E.T.) -345 6 (IPM-Low E. T. ) -342 7 (IPM-High E.T.) -341 > 25 349 > 9 > 7 > 4 > 0 356 > 9 360 > 1 360 The d i f f e r e n c e s in t h e expected n e t revenues app ea r t o th e r i g h t o f th e revenue f i g u r e s . In t h e comparison o f th e IPM program with the 233 c o nv ent ion al one, t h e d i f f e r e n c e s in t h e e xp ec te d n e t revenues i s j u s t o p p o s i t e o f what t h e h y p o th e s i s would s u g g e s t . As y i e l d s i n c r e a s e d , the d iffe re n c e increased as well. In two o f th e t h r e e comparisons o f t h e IPM s t r a t e g i e s with v a r i o u s l e v e l s o f t h e economic t h r e s h o l d , t h e d i f f e r e n c e between t h e ex p ec ted n e t revenues d ec r e as e d as th e y i e l d s i n c r e a s e d , as t h e h y p o t h e s i s would suggest. However, in the t h i r d c a s e , t h e d i f f e r e n c e i n c r e a s e d . At l e a s t , t h i s i s marginal s u p p o r t f o r th e h y p o t h e s i s . A p o ssible explanation of the d is p a r i ty of the t e s t r e s u lt s between t h e scab and mite model might be t h e i n f l u e n c e o f th e b i o l o g i c a l c o n t r o l provi ded by t h e mite p r e d a t o r s . By red u ci ng t h e amount o f th e m i t i c i d e a p p l i e d , th e b i o l o g i c a l c o n t r o l i s enhanced s i n c e f u l l dose m i t i c i d e t r e a t m e n t s can impact on t h e p r e d a t o r s as well as t h e m i t e s . There i s no b i o l o g i c a l c o n t r o l a c t i v e f o r ap p le sc ab . The t h r e a t o f m it e damage i s dampended by t h e e x i s t e n c e o f t h e n a t u r a l mite p r e d a t o r s . B. Comparison o f Expected U t i l i t i e s The e f f i c i e n c y s e t s f o r t h e v a r i o u s i n t e r v a l s can be examined a c r o s s t h e t h r e e y i e l d s c e n a r i o s t o uncover how t h e ex p ec ted u t i l i t i e s o f t h e s t r a t e g i e s w i l l l i k e l y change as t h e v a l u e o f t h e crop changes. The co n v en t io n al s p r ay program f o r ap pl e scab i s r i s k e f f i c i e n t f o r th e f i f t h i n t e r v a l f o r a l l o f t h e y i e l d s c e n a r i o s e x c e p t f o r t h e low one. So a t l e a s t some farme rs w i l l p r e f e r t h e c o n v e n t io n a l c o n t r o l program a t th e low y i e l d l e v e l . This s u p p o r t s t h e s t a t e m e n t on th e a n t i c i p a t e d system b e h a v i o r . Another approach t o de t e r m in i n g t h e changes in t h e expec ted u t i l i t i e s o f th e s t r a t e g i e s i s t o look f o r changes in th e e f f i c i e n c y s e t s o f a l l f i v e r i s k p r e f e r e n c e i n t e r v a l s as t h e s c e n a r i o s change. These e f f i c i e n c y s e t s a r e d i s p l a y e d in Table 12 o f Ch ap te r V. The 234 r i s k p r e f e r e n c e i n t e r v a l s r e p r e s e n t d i f f e r e n t d eg r ee s o f r i s k a v e r s i o n and d i f f e r e n c e s in t h e i r e f f i c i e n c y s e t s have i m p l i c a t i o n s as t o which i n d i v i d u a l s w i l l p r e f e r which s t r a t e g i e s . At th e medium y i e l d l e v e l , when t h e h y p o t h e t i c a l IPM s t r a t e g y i s i g n o r e d , t h e c o n v en ti o na l s p ra y program, s t r a t e g y 7 , a p p e a rs i n the e f f i c i e n c y s e t s f o r a l l e xc e pt th e t h i r d and f o u r t h i n t e r v a l s . From t h i s i t can be i n f e r r e d t h a t a t t h i s y i e l d l e v e l , th e c o n v e n t io n a l program i s c o n s i s t e n t w ith farme rs who have more th a n mo de ra te ly strong ris k aversion (.0003). At t h e low y i e l d l e v e l , th e c o n v e n t io n a l s t r a t e g y i s r i s k e f f i c i e n t on ly f o r t h e f i r s t two i n t e r v a l s . Since i t does n o t ap p e a r in th e e f f i c i e n c y s e t o f t h e l a s t i n t e r v a l , i t can be concluded t h a t i t i s p r e f e r r e d only by d e c i s i o n makers more r i s k a v e r s e than .0004, s l i g h t l y h i g h e r tha n a t t h e medium y i e l d l e v e l . With th e high y i e l d s c e n a r i o , t h e r e i s no e vi d en ce t o assume t h a t t h e ex p ec ted u t i l i t y o f t h e c o n v en ti on al program i s l e s s th a n any a l t e r ­ n a t i v e f o r any o f t h e d e c i s i o n makers in c l u d e d in t h e a n a l y s i s ( e x c e p t f o r th e r i s k n e u t r a l i n d i v i d u a l ) . I t a p p e a r s in a l l o f t h e e f f i c i e n c y sets. The e vi de nc e from t h i s approach s u p p o r t s th e s t a t e m e n t s i n c e as th e y i e l d i n c r e a s e s , t h e co nv e n t io n a l program i s r i s k e f f i c i e n t f o r more r i s k p r e f e r e n c e s . I t should be r e c a l l e d t h a t a s t r a t e g y i s r i s k i n e f f i c i e n t o nl y i f a l l i n d i v i d u a l s p r e f e r one o t h e r s t r a t e g y t o i t . With S t o c h a s t i c Dominance With Respect t o a F u n c ti o n , t h e r e must be co ncu rr enc e among a l l d e c i s i o n makers as t o which a l t e r n a t i v e i s preferred. When more tha n one s t r a t e g y a p pe a rs in t h e e f f i c i e n c y s e t , i t may be t h a t some i n d i v i d u a l s in t h e group p r e f e r one s t r a t e g y w h i l e t h e o t h e r s p r e f e r t h e second. However, u n l e s s a s t r a t e g y i s r e j e c t e d from th e e f f i c i e n c y s e t , t h e r e i s no ev id en ce t h a t i t s 235 exp ec ted u t i l i t y i s l e s s than t h e expec ted u t i l i t y o f t h e members o f th e e f f i c i e n c y s e t . In t h e ca s e o f t h e m i t e s , t h e evidence i s i n c o n c l u s i v e . With th e weekly s c o u t i n g program, n e i t h e r t h e co nv en ti o na l nor t h e IPM program w ith th e lo w es t economic t h r e s h o l d e v e r ap pea r in th e e f f i c i e n c y s e t s . The o t h e r t h r e e IPM s t r a t e g i e s a r e a l l r i s k e f f i c i e n t f o r t h e f i f t h i n t e r v a l in both the low and medium y i e l d s c e n a r i o s . The e n t i r e s e t o f e f f i c i e n c y s e t s a r e d i s p l a y e d in Table 14 o f Chapter I I I . SSD vs . SDWRF Often i n f e r e n c e s a r e made about t h e p r e f e r e n c e s o f a g r i c u l t u r a l d e c i s i o n makers w it h an u n d e r ly i n g assumption t h a t a l l i n d i v i d u a l s a r e always r i s k a v e r s e . No a t t e m p t i s made t o r e s t r i c t t h e de g r ee o f r i s k a v e r s i o n and t h e c o n c l u s i o n s reach ed about t h e r a n k in g s o f th e a l t e r ­ n a t i v e s must be a c c u r a t e f o r t h e most r i s k a v e r s e d e c i s i o n maker (maxi-min) and t h e i n d i v i d u a l approaching r i s k n e u t r a l i t y . These a n a l y s e s a r e f r e q u e n t l y done w it h Second Degree S t o c h a s t i c Dominance. I t i s h y p o th e s i z e d t h a t two problems w i l l a r i s e with t h i s te c h n i q u e . Since t h e group o f d e c i s i o n makers i s so l a r g e , i t w i l l be d i f f i c u l t t o d i s c r i m i n a t e among a l t e r n a t i v e s so l a r g e Type II e r r o r s w i l l l i k e l y be e n c o u n t e r e d . errors. The second problem i s r e l a t e d t o Type I By e x c l u d i n g any p o s s i b i l i t y f o r r i s k lo v i n g b e h a v i o r , t h i s te c h n i q u e ig n o r e s th e p r e f e r e n c e s o f a l a r g e m a j o r i t y o f a g r i c u l t u r a l d e c i s i o n makers ( 81) . The r e s u l t s may be b ia s e d from t h i s l a c k o f c o n s i d e r a t i o n t o t h e p o s s i b l e n e g a t i v e ranges o f t h e r i s k p r e f e r e n c e functions. The s i z e o f t h e Type I and Type I I e r r o r s can be e s t i m a t e d by comparing t h e e f f i c i e n c y s e t s o f i n t e r v a l 1 and 5. I n t e r v a l 1 approximates 236 Second Degree S t o c h a s t i c Dominance w hil e i n t e r v a l 5 has been desig ned t o r e p r e s e n t th e p r e f e r e n c e s o f 80 t o 90% o f Michigan f a r m e r s . The s i z e o f t h e e r r o r s w i l l depend upon t h e cho ic e s e t o f t h e problem and t h e width o f t h e i n t e r v a l which i n c l u d e s th e p r e f e r e n c e s o f a l l members o f th e c l a s s o f d e c i s i o n makers. The exam ina ti on o f t h e e f f i c i e n c y s e t s produces t h e r e s u l t s d i s p l a y e d in Table 10. In only two o f t h e n i n e t e e n ca s e s a r e t h e e f f i c i e n c y s e t s e q u a l . By u s in g Second Degree S t o c h a s t i c Dominance only s l i g h t l y more than 10% o f t h e time did t h e te c h n i q u e a c c u r a t e l y r e f l e c t t h e p r e f e r e n c e s o f Michigan a g r i c u l t u r a l d e c i s i o n makers (as measured by i n t e r v a l 5 ) . In f i v e o f t h e n i n e t e e n s c e n a r i o s , Second Degree S t o c h a s t i c Dominance i d e n t i f i e d some s t r a t e g i e s as e f f i c i e n t when in a c t u a l i t y th e y were i n e f f i c i e n t (Type I I e r r o r ) . Over 60% o f t h e time (12 o f 1 9 ) , Second Degree S t o c h a s t i c Dominance d e c l a r e d some s t r a t e g i e s as being r i s k i n e f f i c i e n t when the y s ho ul d r e a l l y have appeared in t h e e f f i c i e n c y s e t (Type I e r r o r ) . There i s c o n s i d e r a b l e s u p p o r t from t h i s a n a l y s i s t h a t t h e r e e x i s t s a g r e a t p o t e n t i a l f o r both Type I and Type I I e r r o r s in t h e use o f Second Degree S t o c h a s t i c Dominance ( o r o t h e r te c h n i q u e s t h a t ig n o r e r i s k lo v i n g b eh a v i o r ) t o r e p r e s e n t th e c l a s s o f a l l a g r i c u l t u r a l d e c i s i o n makers. Chemical Usage Often one o f t h e r e s u l t s o f ado pt in g a t IPM s t r a t e g y i s a lower r a t e o f use o f chemical p e s t i c i d e s . Two comparisons a r e p r e s e n t e d in Table 11 t o t e s t t h e h y p o t h e s i s t h a t t h e expec ted amount o f chemicals used in an IPM program w i l l be l e s s than t h e ex p ec ted amount o f chem ica ls used in c o n v e n t io n a l c a l e n d a r s p r a y programs. 237 Table 10. Comparisons o f E ffic ie n c y Sets f o r SSD and SDWRF. Mites Total Number 8 Number o f Cases where E f f i c i e n c y S e t o f Second Degree S t o c h a s t i c Dominance i s l a r g e r than 5th i n t e r v a l * 4 Number o f c a s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s t h e same as t h e 5th i n t e r v a l 1 Number o f c a s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s s m a l l e r th a n t h e 5th i n t e r v a l 3 * F i f t h i n t e r v a l i s i n f e r r e d from su rv ey d a t a and sh oul d r e p r e s e n t th e p r e f e r e n c e s o f 80-90% o f M ic h i g a n ' s f a r m e r s . Apple Scab Tot al Number o f Cases Number o f ca s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s l a r g e r than 5th i n t e r v a l Number o f c a s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s equal t o th e 5th i n t e r v a l Number o f c a s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s s m a l l e r than t h e 5th i n t e r v a l Codling Moth Total Number o f Cases 3 Number o f c a s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s l a r g e r than 5th i n t e r v a l 0 Number o f c a s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s equal t o th e 5th i n t e r v a l 0 Number o f c a s e s where e f f i c i e n c y s e t o f Second Degree S t o c h a s t i c Dominance i s s m a l l e r th an t h e 5th i n t e r v a l 3 238 Tabl e 11. Comparison o f Chemical Usage: IPM and Conventional S t r a t e g i e s . Codling Moth (Medium Y ie l d ) - Azinphosmethyl Low I n i t i a l P o p u la t io n Conventional IPM 204.8 60.8 oz. oz. Medium I n i t i a l P o p u la t io n 204.8 9 2. 8 oz. oz. High I n i t i a l P o p u la t io n 204 .8 92.8 oz. oz. Mite (Medium Y ie ld ) - P l i c t r a n Weekly S co u ti n g Conventional IPM IPM w it h Revised De cision Rule 3 lbs/acre 2. 25 l b s / a c r e 1.95 l b s / a c r e GPP5* 3 2.1 1.5 lbs/acre lbs/acre lbs/acre GPP9** 3 lbs/acre *2.1 l b s / a c r e 1.65 l b s / a c r e *Sco utin g on r e q u e s t when grower p e r c e i v e s a m i te problem dev el o pi n g a t 5 mites per le a f . **Scouting on r e q u e s t when grower p e r c e i v e s a m it e problem deve lo pin g a t 9 m i t e s per l e a f . 239 In a l l c a s e s , t h e IPM s t r a t e g i e s apply l e s s chemicals than t h e c o u n t e r p a r t c a l e n d a r s p ra y programs. I t range s from a low o f 30% o f co n v en t io n al s t r a t e g y ' s usage t o a high o f 75%. The s t a t e m e n t i s d e f i n i t e l y su p po rte d by t h e s e comparisons. P e s t Damage I t i s o f t e n p e r c e i v e d t h a t IPM programs r e s u l t in h i g h e r p e s t damages than co nv e n t io n a l programs. Conventional programs by a p p l y in g more chem icals sh ould b e n e f i t from more p l a n t p r o t e c t i o n . However, t h e i n f l u e n c e on t h e damage o f t h e ti m in g o f s p r a y s and th e impacts on n o n - t a r g e t p e s t s and p r e d a t o r s may d i s p r o v e t h i s c o n t e n t i o n . The expec ted damages can be compared from v a r i o u s s c e n a r i o s f o r the scab model, the mite model, th e c o d l i n g moth model and t h e comprehensive model. The model r e s u l t s a r e p r e s e n t e d in Tabl es 12 through 15. Table 12. Expected P e s t Damage f o r Scab Control S t r a t e g i e s . Strategy Expected Damage (%) Yield S c e n a r i o Low Medium 8 (RSAT/Conventional) 0.4 0.4 1.1 Table 13. 1.2 0.5 0.5 1. 3 0.5 0. 5 Expected P e s t Damage f o r Mite Control S t r a t e g i e s (Weekly Scouting). Strategy 2 4 5 6 7 High ( P l i c t r a n Conventional (IPM Low E . T . ) (IPM High E . T . ) (IPM Low E. T. ) (IPM High E .T .) Expected Damage ( $ / a c r e ) Yiel d S ce na r i o Low Medium 14.5 0.6 1. 7 0.5 2.2 26.1 1.4 3. 6 1.1 4.5 240 Table 14. Expected P e s t Damage f o r Codling Moth Control S t r a t e g i e s (Medium Y i e l d ) . Expected Damage (%) I n i t i a l P e s t P op u la t io n High Low Medium Strategy 2 4 6 8 (Con ven tion al) (IPM Medium Dynamic E .T .) (IPM Low Cons tan t E. T. ) (IPM High Dynamic E .T .) 0.0 0 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.0 0 3.53 3.53 3.15 f o r Comprehensive Control S t r a t e g i e s . Strategy 7-2-2 ( C o n v en ti o na lAzinphosmethyl) 7 -2- 3 (C o n v en t io n al Pyrethroid) 5-13-12 (IPM-benomyl & a z i n p h o s m e th y l) 5-13-13 (IPM-benomyl & pyrethroid) Scab (%) Mite ($) 0.05 4.2 0.00 0.05 17.4 0.00 0.0 0.0 6 0.0 0.06 1.31 1.31 - Codling 1 In t h e ca s e o f a p p l e scab c o n t r o l s , th e IPM s t r a t e g y s u f f e r s more damage, almost tw ic e as much as the co nv e n t io n a l s t r a t e g i e s . With low and medium i n i t i a l p o p u l a t i o n d e n s i t i e s , t h e IPM c o d l i n g moth s t r a t e g i e s e x p e r i e n c e damage o n ly s l i g h t l y d i f f e r e n t th a n th e conven­ t i o n a l , bu t a t high p o p u l a t i o n d e n s i t i e s t h e d i f f e r e n c e i s s i g n i f i c a n t . Mite c o n t r o l w it h t h e p o s s i b i l i t y o f b i o l o g i c a l c o n t r o l by n a t u r a l p r e d a t i o n t h a t can be d i s r u p t e d by f u l l dose m i t i c i d e t r e a t m e n t s d i s ­ p la y s a d i f f e r e n t p a t t e r n . In t h i s c a s e , t h e IPM s t r a t e g y r e s u l t s in c o n s i d e r a b l y l e s s damage s i n c e i t has th e o p t i o n s o f a p p l y in g reduced dosages and n o t sp r a y in g a t a l l when th e p r e d a t o r - p r e y r a t i o i s in b al a n c e . In t h e comprehensive model r e s u l t s , two im p o r ta n t r e s u l t s a r e th e impacts t h a t th e p y r e t h r o i d i n s e c t i c i d e and t h e f u n g i c i d e benomyl have on m it e c o n t r o l . The damage e s t i m a t e s f o r c o d l i n g moth and scab a r e 241 s i m i l a r t o th e r e s u l t s o f th e in de pen den t model r u n s . Certainly a major component o f IPM programs sh ould be t h e c o o r d i n a t i o n o f c o n t r o l s f o r t h e v a r i o u s p e s t s p r e s e n t in th e system. The use o f p y r e t h r o i d i n s e c t i c i d e s in appl e p r o d u c ti o n systems would n o t be an example o f t h i s coordination. The m it e damage f o r th e " c o n v e n t i o n a l " program which employs azinphosmethyl i s about one f o u r t h o f t h e damage o f th e s i m i l a r program using t h e p y r e t h r o i d . The model r e s u l t s i n d i c a t e t h a t t h e benomyl o f t h e IPM programs w i l l co m p le te ly su p p r es s th e mites. However, i t should be remembered t h a t t h e model s i m u l a t e s a s i n g l e season and i t i s l i k e l y t h a t m it e problems w i l l be enhanced in t h e second season w i t h t h e benomyl program. The d a t a from t h e c o n t r o l o f appl e scab and c o d l i n g moth su p p o r t t h e e x p e c t a t i o n s on system b eh av i or b u t t h e i n t r o d u c t i o n o f th e n a t u r a l p r e d a t o r s in t h e c o n t r o l o f m i te s c o m p li c a te s t h e i s s u e . I t appea rs t h a t IPM programs r e s u l t in l e s s m it e damage tha n co nv e n t io n a l t r e a t ­ ments. The argument t h a t as th e economic t h r e s h o l d i n c r e a s e s , th e p e s t damage sh oul d i n c r e a s e as well appea rs n o t t o hold f o r t h e ca se o f t h e c o d l i n g moth c o n t r o l . The ex pe ct ed damage e s t i m a t e s f o r th e t h r e e IPM programs a r e ex tre me ly s i m i l a r . J u s t t h e o p p o s i t e i s observed in t h e r e s u l t s from t h e m i te model. There i s a v er y d e f i n i t e r e l a t i o n s h i p between th e economic t h r e s h o l d and t h e ex pe ct ed damage. The m it e d a t a do s u p p o r t t h i s c o n t e n t i o n . Economics o f Decision Rule Refinements The o b s e r v a t i o n t h a t t h e r e f i n e m e n t s t o t h e economic t h r e s h o l d s w i l l improve th e b e n e f i t s t h a t a r e gained by a d o p t in g a cru de IPM program i s c e r t a i n l y no t s u pp or te d by t h e r e s u l t s from t h e c o d l i n g 242 moth model. Table 16. These r e s u lts appear in Table 16. Comparison of Expected Net Revenues: Simple Moth IPM S t r a t e g i e s . Strategy 2 (C o nv en ti o na l) 6 (IPM-low s t a t i c E . T . ) 8 (IPM-high dynamic E . T . ) S o p h i s t i c a t e d and Expected Net Revenues I n i t i a l Moth D e n s it y Level Low Medium High 317.4 370.1 375.6 317.4 355.7 356.2 317.4 315.3 320.9 In t h e low i n i t i a l p o p u l a t i o n d e n s i t y s c e n a r i o , 90% o f th e d i f f e r ­ ence in n e t revenues between t h e IPM s t r a t e g y w ith th e h i g h e s t r e t u r n and t h e co n v en t io n al program could be c a p t u r e d by a d o p t in g a simple IPM program w it h a s t a t i c economic t h r e s h o l d . p o p u l a t i o n l e v e l , t h e p e r c e n t a g e i s al mo st 99%. At t h e medium i n i t i a l In th e s c e n a r i o using th e high i n i t i a l moth d e n s i t y , t h e crude IPM s t r a t e g y has a n e t revenue below t h a t o f t h e co nv e n t io n a l program w h ile t h e s o p h i s t i c a t e d IPM s t r a t e g y i s above t h a t f i g u r e . However, a l l t h r e e a r e w i t h i n $ 5 / a c r e o f each o t h e r . The c o n t r o l o f m i te s i s somewhat more complex due t o t h e n a t u r a l p r e d a t i o n and th e marginal r e t u r n s t o t h e more s o p h i s t i c a t e d d e c i s i o n r u l e s i s r e l a t i v e l y much h i g h e r . The IPM s t r a t e g y w it h th e h i g h e s t e x pe c te d n e t revenue f o r t h e medium y i e l d and weekly s c o u t i n g s c e n a r i o i s s t r a t e g y 6 w it h t h e r e v i s e d d e c i s i o n r u l e which a u t o m a t i c a l l y a p p l i e s a h a l f dose on th e f i r s t s p r a y . The IPM s t r a t e g y w ith th e simpl e d e c i s i o n r u l e s and no o p t i o n f o r a p p l y in g reduced dosages can ac c o u n t f o r 56% o f t h e d i f f e r e n c e in ex p ec ted n e t revenue o f t h e " b e s t" IPM s t r a t e g y and t h e co n v en t io n al program. The IPM s t r a t e g y with the d e c i s i o n r u l e s guided by p r e d a t o r / p r e y r a t i o s w i l l produce abo ut 82% o f t h e maximum b e n e f i t s uncovered by t h e model. There i s a bo ut a $8 t o $12 p e r a c r e r e t u r n t o th e a d o p t io n o f d e c i s i o n r u l e s o f each 243 stage of s o p h is tic a tio n . Table 17. Comparison o f Expected Net Revenues: Mite Control S t r a t e g i e s . Strategy 2 4 6 H6 Simple and S o p h i s t i c a t e d Expected Net Revenues Medium Yield and Weekly S cou ti ng Conventional Simple IPM S o p h i s t i c a t e d IPM S o p h i s t i c a t e d IPM with r e v i s e d decision rules 324 349 360 368 I f r e f in e m e n t s in th e economic t h r e s h o l d s do n o t s i g n i f i c a n t l y im­ prove th e ex pe ct ed n e t r e v e n u e s , i t can be assumed t h a t sampling e r r o r s a s s o c i a t e d w i t h t h e p o p u l a t i o n e s t i m a t e s g e n e r a t e d by the s c o u t i n g program should n o t d r a s t i c a l l y reduce th e e xp ec te d n e t r e v e n u e s. The model was used t o re-examine th e performance o f t h e IPM s t r a t e g i e s when a sampling e r r o r was i n t r o d u c e d . The sampling e r r o r was drawn from a normal d i s t r i b u t i o n w i t h t h e p r o p e r t i e s t h a t 95% o f t h e t r u e population. The r e s u l t s from th e m i te model a r e p r e s e n t e d below f o r t h r e e s c e n a r i o s (Table 18). With t h e e x c e p t i o n o f t h e s t r a t e g y w ith th e high economic t h r e s h o l d s t h e random sampling e r r o r does n o t app ea r t o s i g n i f i c a n t l y change t h e revenue f i g u r e s . In f a c t , in some ca s es th e ex p ec te d n e t revenue i n c r e a s e d s l i g h t l y . The s t r a t e g y with th e high economic t h r e s h o l d s e x p e r i e n c e d a d e c l i n e o f from $3 t o $6 p e r a c r e when th e e r r o r was i n t r o d u c e d . The same p a t t e r n i s en co un te r ed in t h e ca se o f t h e c o d l i n g moth. The ex pe c te d n e t revenues do n o t change a p p r e c i a b l y e x c e p t a t th e high i n i t i a l p o p u l a t i o n d e n s i t y . However, t h e d e c l i n e in income even a t t h i s l e v e l i s l e s s th a n ]% o f t h e e x pe c te d n e t revenue w it h no random sampling e r r o r . These r e s u l t s ap p e a r in Table 19. 244 Table 18. Impact on Expected Net Revenues o f a Random Sampling E rro r f o r IPM M ite C o n tro l S tra te g ie s . Expected Net Revenue Strategy Low Yield 4 (Simple IPM-no e r r o r ) 6 (IPM low E . T . -n o e r r o r ) 7 (IPM high E . T . -n o e r r o r ) 11 (IPM low E.T. w ith e r r o r ) 13 (IPM low E.T. w i t h e r r o r ) 14 (IPM high E.T. with e r r o r ) -354 -342 -341 -352 -342 -346 Table 19. Medium Yield 349 360 360 350 361 354 Medium Yield 353 370 350 353 369 347 Impact on Expected Net Revenues o f a Random Sampling E r ro r f o r IPM Codling Moth Control S t r a t e g i e s . Expected Net Revenue I n i t i a l P o p u l a t i o n Den sity Low Medium High Strategy 4 (IPM medium dynamic E. T. ) 6 (IPM low s t a t i c E. T. ) 8 (IPM high dynamic E. T. ) 12 (IPM medium dynamic E.T. with e r r o r ) 14 (IPM low s t a t i c E.T. w ith e r r o r ) 16 (IPM high dynamic E.T. w ith e r r o r ) 370 370 376 356 356 356 315 315 321 370 355 313 370 355 313 373 356 321 The ex pe c te d u t i l i t i e s o f t h e s t r a t e g i e s a r e n o t changed d r a ­ m atically e ith e r. As can be seen in Table 14 Chap te r IV, some s t r a t e g i e s w ith t h e random sampling e r r o r s ap pe a r i n al mo st e v e r y e f f i c i e n c y s e t . I t does n o t a p p e a r t h a t t h e p re s en ce o f th e sampling e r r o r g r e a t l y changes t h e r i s k e f f i c i e n c y o f t h e s t r a t i g i e s . P o t e n t i a l o f CSD In t h e s c e n a r i o examining t h e scab c o n t r o l s t r a t e g i e s a l o n e with a medium y i e l d , t h e e f f i c i e n c y s e t s o f two i n t e r v a l s ap p e a r in g in Table 12, Chapter V were f u r t h e r r e f i n e d through t h e a p p l i c a t i o n o f CSD. These were i n t e r v a l s 1 and 5. In th e ca s e o f i n t e r v a l 1 , s t r a t e g y 9 245 was r e j e c t e d as i n e f f i c i e n t wh ile in i n t e r v a l 5 , s t r a t e g i e s 2 , 3 , 9 and 10 were a l l r e j e c t e d as n o t being th e most p r e f e r r e d s t r a t e g y o f any d e c i s i o n maker in th e c l a s s . The e f f i c i e n c y s e t s i d e n t i f i e d f o r t h e m i te s t r a t e g i e s in Table 14, Chapter V f o r t h e weekly s c o u t i n g and medium y i e l d s c e n a r i o were not p a r t i c u l a r l y reduced by CSD. Of t h e s t r a t e g i e s r i s k e f f i c i e n t f o r the f i r s t and l a s t i n t e r v a l s , on ly H4 coul d be r e j e c t e d with CSD. The c o d l i n g moth e f f i c i e n c y s e t s may ap pe a r l a r g e a t f i r s t g l a n c e b u t due t o th e f a c t t h a t t h e d i s t r i b u t i o n s o f n e t revenue were i n s e n s i t i v e t o changes in t h e economic t h r e s h o l d , th e cu m u la ti v e p r o b a b i l i t y f u n c t i o n s a r e alm os t i d e n t i c a l f o r most o f t h e IPM programs. CSD was n o t a p p l i e d t o t h e s e e f f i c i e n c y s e t s . 8.2 I m p l i c a t i o n s of Model P r e d i c t i o n s Extension There a r e f o u r major r e s u l t s which s hou ld be r e l e v a n t f o r e x t e n ­ s i o n e f f o r t s in a p p l e p e s t management. areas: The r e s u l t s a r e in th e fo ll o w i n g t h e comparisons o f t h e avera ge n e t revenues between s t r a t ­ e g i e s , t h e comparison o f th e r i s k e f f i c i e n c i e s o f t h e s t r a t e g i e s , the r e l a t i o n s h i p between t h e s i z e o f th e economic t h r e s h o l d and t h e l e n g th o f t h e s c o u t i n g i n t e r v a l , and th e s e l e c t i o n o f optimal economic t h r e s h o l d s . The model p r e d i c t i o n s can be u s e f u l in an e x t e n s i o n c o n t e x t by p r o v i d i n g a d d i t i o n a l ev id en ce t h a t th e ex p ec ted n e t revenu es o f IPM programs w i l l be g r e a t e r than t h e ex p e c te d n e t revenues o f co nv e n t io n a l c a l e n d a r s t r a t e g i e s . In some c a s e s , t h e s a v i n g s in con­ t r o l c o s t s can amount t o as much as 30% t o 40%. The s a v i n g s w i l l l i k e l y i n c r e a s e as t h e r a t i o o f a pp l e p r i c e s t o p e s t i c i d e p r i c e s d e c r e a s e s s i n c e t h e IPM programs use l e s s chem ica ls and may r e s u l t in 246 more damage. I n c r e a s e s in ap p l e p r i c e s o r y i e l d s may f a v o r t h e s e l e c t i o n o f co nv en ti o n al s t r a t e g i e s by s t r o n g l y r i s k a v e r s e growers s i n c e with a h i g h e r v al u e o f th e h a r v e s t , growers can a f f o r d to ap p ly more chemic al s t o avoi d p e s t damage. Furth erm ore , p r od uc er s w ith lower y i e l d i n g o r c h a r d s pro ba bl y have more t o ga i n from IPM s t r a t e g i e s on a p e r a c r e b a s i s than growers w it h more p r o d u c t i v e farms because t h e i r r a t i o o f crop v al u e t o p e s t i c i d e p r i c e s i s low er. The p e r a c r e v al u e o f t h e damage avoided i s lower w ith s m a l l e r y i e l d s so l e s s chemicals can be e f f i c i e n t l y a p p l i e d . I t a pp ea r s t h a t r i s k p r e f e r e n c e s w i l l be an i m p o r ta n t c o n s i d e r ­ a t i o n in t h e a d o pt io n of scab c o n t r o l s t r a t e g i e s . For some r i s k a v e r s e d e c i s i o n makers, t h e co nv en ti o na l c a l e n d a r program ( s t r a t e g y 7) w i l l be p r e f e r r e d because i t produces h i g h e r n e t revenu es i n th e bad years. Other d e c i s i o n makers who a r e l e s s r i s k a v e r s e w i l l p r e f e r a l t e r n a t i v e s t r a t e g i e s such as t h e p o s t - i n f e c t i o n IPM program (5) o r t h e reduced s i n g l e a p p l i c a t i o n t r e a t m e n t followed by a p r o t e c t i v e c a l e n d a r s c h e d u le ( 8 ) . These s t r a t e g i e s on av er a ge produce h i g h e r n e t revenu es . In t h e ca se o f t h e c o n t r o l o f m i te s and c o d l i n g moth, i t i s g e n e r a l l y t r u e t h a t even very r i s k a v e r s e d e c i s i o n makers w i l l p r e f e r th e IPM programs. The model p r e d i c t s t h a t t h e r i s k o f most IPM s t r a t e g i e s , even w it h a l a r g e e r r o r i n t h e s c o u t i n g e s t i m a t e s , i s l e s s than t h e r i s k o f th e co nv en ti o na l c a l e n d a r programs. Perhaps th e t h r e a t o f p e s t damage i s l e s s th a n th e t h r e a t o f a p p l y in g to o much pesticide. I t should be noted t h a t t h e r e were in g e n e r a l , s e v e r a l IPM s t r a t e g i e s which were r i s k e f f i c i e n t so d e c i s i o n makers with d i f f e r e n t r i s k p r e f e r e n c e s may p r e f e r d i f f e r e n t IPM programs. However, 247 t h e r e d i d not app ea r t o be a s t r o n g r e l a t i o n s h i p between t h e p r e ­ f e r r e d le ve l o f th e economic t h r e s h o l d and th e r i s k p r e f e r e n c e . There i s a r e l a t i o n s h i p between th e l e n g th o f th e s c o u t i n g i n t e r v a l and t h e performance of t h e IPM s t r a t e g i e s with d i f f e r e n t economic thresholds. S t r a t e g i e s with high economic t h r e s h o l d s performed con­ s i d e r a b l y worse when th e s c o u t i n g i n t e r v a l was i n c r e a s e d from one week t o two weeks. S t r a t e g i e s w ith lower economic t h r e s h o l d s were n o t so d r a s t i c a l l y a f f e c t e d . This r e s u l t i s observed s i n c e t h e p e s t p o p u l a t i o n s should be h i g h e r w it h t h e s t r a t e g i e s w ith high economic t h r e s h o l d s and l e s s f r e q u e n t m on it o r in g sh ou ld enhance th e p r o b a b i l i t y t h a t t h e d e n s i t y r e a c h e s an i n j u r y l e v e l between v i s i t s o f th e s c o u t . The s u b s t i t u t i o n o f i n f o r m a t i o n f o r chem icals w i l l be a f f e c t e d by th e t i m e l i n e s s o f t h e i n f o r m a t i o n and l e s s f r e q u e n t s c o u t i n g does no t p ro v id e as t i m e l y i n f o r m a t i o n . The model p r e d i c t s t h a t i n t h e ca s e o f t h e c o d l i n g moth c o n t r o l s t r a t e g i e s , t h e r e a r e a wide range o f p o s s i b l e economic t h r e s h o l d s t h a t produce s i m i l a r r e s u l t s . The i n t r o d u c t i o n o f l a r g e sampling e r r o r s in t h e s c o u t i n g program did n o t p a r t i c u l a r l y change th e ra n ki n gs o f t h e s t r a t e g i e s by e i t h e r th e s i z e o f t h e expec ted n e t revenue o r by th e ex p ec ted u t i l i t y . S i m i l a r , bu t n o t as dr am a tic r e s u l t s were observ ed f o r th e m i te c o n t r o l s t r a t e g i e s . However, in t h e case o f m i te s t h e r e may be as much as a $10 p e r a c r e sa vi n gs by always app ly in g a h a l f dose o r l e s s on t h e f i r s t s p r a y . The economic t h r e s h o l d s f o r m i t e s which produced t h e h i g h e s t expec ted n e t revenues were in the range o f 25 t o 30 m i te s p e r l e a f . The l a c k o f impact t h a t th e random sampling e r r o r had on th e r a n k in g s o f th e s t r a t e g i e s i m p l i e s t h a t e l a b o r a t e s c o u t i n g programs which i n c r e a s e th e ac c u ra cy o f p o p u l a t i o n e s t i m a t e s may be producing 248 in f o r m a ti o n whose v a l u e i s l e s s than i t s c o s t . I t does n o t ap p ea r t h a t e i t h e r th e m i t i c i d e c a r z o l o r t h e p y r e ­ t h r o i d i n s e c t i c i d e s sh oul d e v e r be used a t c u r r e n t p r i c e s . Their impact on n o n - t a r g e t s p e c i e s f u r t h e r d e t r a c t from t h e i r o v e r a l l p e r f o r ­ mance. Research The p r e d i c t i o n s o f t h e model a r e r e l e v a n t f o r r e s e a r c h because th e y de m o n st r at e t h e p o t e n t i a l f o r a number o f r e c e n t advances. F irst, by c o n s i d e r i n g t h r e e p e s t s s i m u l t a n e o u s l y r a t h e r tha n i n d e p e n d e n tl y a f u r t h e r u n d e r s t a n d i n g o f t h e system i s enhanced and p r e d i c t i o n s can be r e f i n e d . Second, t h e p r e d i c t i o n s d e a l i n g w ith t h e s e n s i t i v i t y o f th e s t r a t e g y ra nk in g s t o r e f i n e m e n t s in d e c i s i o n r u l e s and sampling e r r o r s should help gu ide f u t u r e r e s e a r c h t o a r e a s where i n f o r m a t i o n can be ec on o m ic a lly g e n e r a t e d . T h i r d , th e i n c r e a s e d ac c u r a c y o f ra nk in g s based on SDWRF should d is s u a d e f u t u r e use o f SSD and E-V a n a l y s e s . The use o f CSD de m o n s t r a te s i t s c a p a b i l i t y t o f u r t h e r d i s c r i m i n a t e between a l t e r n a t i v e s w i t h o u t i n c r e a s i n g th e Type I e r r o r . The adven t o f CSD should d im in is h t h e need t o a t t e m p t t o a c c u r a t e l y measure r i s k p r e f e r e n c e s f o r many p u r p o s e s . F i n a l l y , t h e r e s u l t t h a t only in t h e c a s e o f scab c o n t r o l and high moth p o p u l a t i o n s c e n a r i o s i s th e ev id en ce t o s u g g e s t t h a t r i s k p r e f e r e n c e s could ac co un t f o r th e l a c k o f ad o p t io n o f IPM s t r a t e g i e s , should encourage f u r t h e r r e s e a r c h i n t o th e a r e a o f s u b j e c t i v e p r o b a b i l i t y as se ssm ent s t o e x p l a i n c o n ti nu ed use o f c o n v en ti o na l s pr ay programs. P e r h a p s , th e p e r c e p t i o n s by growers o f th e r e l a t i v e performance o f th e s t r a t e g i e s i s a v i t a l key to u n d e rs ta n d i n g t h e a d o p t io n p r o c e s s . 249 Policy The IPM programs a l l r e s u l t e d in th e i n t r o d u c t i o n o f fewer p e s t i c i d e s i n t o t h e envi ron me nt. F ur th er m ore , i t a p pe a r s t h a t t h e r e a r e a number o f f i r m l e v e l b e n e f i t s from a d o p t i n g t h e s e s t r a t e g i e s . In a l m o s t a l l c a s e s , th e expec ted n e t revenu es were h i g h e r f o r t h e IPM s t r a t e g i e s b u t f o r some d e c i s i o n makers t h e c o n v e n t io n a l scab and moth s t r a t e g i e s were s t i l l p r e f e r r e d . As t h e r a t i o o f ap p l e p r i c e s t o p e s t i c i d e p r i c e s i n c r e a s e s , th e c o n ve nt io na l s t r a t e g i e s w i l l r e l a t i v e l y improve in t h e comparison. When t h e v a l u e o f t h e h a r v e s t i s high in r e l a t i o n t o th e chemical c o s t s , more p e s t i c i d e s can be e f f i c i e n t l y applied. This may r e s u l t in IPM s t r a t e g i e s bei ng s l i g h t l y l e s s a t t r a c t i v e t o r i s k a v e r s e growers w it h h i g h l y p r o d u c t i v e o r c h a r d s . The v al u e o f t h e h a r v e s t i s dete rmin ed by a p p l e p r i c e s and t h e y i e l d . However, i f a p p l e p r i c e s d e c l i n e , IPM programs may become more r e a d i l y adopted s i n c e g r o s s revenues w i l l d e c r e a s e and t o remain p r o f i t a b l e f ir m s w i l l need t o d e c r e a s e t h e i r c o s t s o f p r o d u c t i o n . A m a jo r com­ ponen t o f t h e v a r i a b l e p r o d u c t i o n c o s t s a r e r e l a t e d t o p e s t management and s i n c e IPM s t r a t e g i e s can reduce t h e s e c o n t r o l c o s t s by 30 t o 40%, t h e y should be more w id el y adopted in t h i s s i t u a t i o n . At t h e farm l e v e l , i t a p p e a r s t h a t t h e promotion o f IPM s t r a t e g y ad o p t io n may be a c o s t e f f e c t i v e p o l i c y i n s t r u m e n t i n d e a l i n g w ith th e e x t e r n a l i t y problems c r e a t e d by e x c e s s i v e p e s t i c i d e u s e. At c u r r e n t p r i c e s , t h e r e a r e s u b s t a n t i a l b e n e f i t s t o a d o p t i n g most IPM s t r a t e g i e s . P u b l i c s u b s i d i e s o f t h e i n f o r m a t i o n ( s c o u t s and w e a th e r r e p o r t s ) n e c e s s a r y t o implement IPM programs sh ould enhance t h e b e n e f i t s and i n c r e a s e th e r a t e o f a d o p t i o n . P u b l i c e x p e n d i t u r e s in t h e form o f s u p p o r t r e q u i r e d t o perform t h e te c h n o lo g y t r a n s f e r o f t h e n e c e s s a r y 250 ma nag eri al s k i l l s should be a v i a b l e o p t i o n as w e l l . These i n s t r u m e n t s a r e a t t r a c t i v e s i n c e th e y encourage v o l u n t a r y ac c e p ta n c e o f reduced p e s t i c i d e u s ag es . The s u b s i d i e s may be n e c e s s a r y t o conv ince r i s k a v e r s e d e c i s i o n makers t o adopt t h e IPM s t r a t e g i e s . c e i v e d a s s u b s i d y t o t h e r i s k premium. I t can be p e r ­ There sh ould be lower admin­ i s t r a t i o n c o s t s and l e s s en fo rce m ent problems th a n with programs u s in g regulations o r d ire c t incentives. I t sh ou ld be noted t h a t th e p o s s i b i l i t y e x i s t s t h a t wides prea d ad o p t io n o f IPM programs may a c t u a l l y l e a d t o a h i g h e r t o t a l p e s t i c i d e u se. I f t h e ad o p t io n o f t h e IPM s t r a t e g i e s r ed uc es p r o d u c t i o n c o s t s t o an e x t e n t t h a t p r o f i t s a r e i n c r e a s e d , o r c h a r d s may be expanded and even though t h e i n t e n s i t y o f use has been d i m i n i s h e d , t h e o v e r a l l q u a n t i t y o f p e s t i c i d e s in t r o d u c e d i n t o t h e environment may i n c r e a s e (1 41) . The r e l e v a n t q u e s t i o n th e n becomes th e importance t h a t the c o n c e n t r a t i o n o f the p e s t i c i d e has on t h e s e v e r i t y o f t h e e x t e r n a l i t i e s . Th is w i l l v a r y w ith th e chem ica ls inv ol ve d and sh ould be examined b e f o r e any p o l i c y i n s t r u m e n t s a r e s e l e c t e d . The model p r e d i c t i o n s may be r e l e v a n t f o r t h e review o f t h e r e g i s t r a t i o n of the fungicide captan. Captan has produced c a n c e r in i s o l a t e d c e l l s b u t n o t in c e l l s or g a n iz e d i n t o t i s s u e s . The model p r e d i c t s t h a t two scab c o n t r o l s t r a t e g i e s which use ca p t an ar e p r e f e r r e d t o some r i s k a v e r s e d e c i s i o n makers t o t h e a l t e r n a t i v e s examined. The s t r a t e g i e s u s in g cap ta n had lower av er a ge n e t revenu es b u t were r i s k e f f i c i e n t f o r some i n d i v i d u a l s . This i m p l i e s t h a t some growers w it h c h o i c e s e t s i d e n t i c a l t o t h e one in t h e model would be h u r t by t h e banning o f ca p t a n . The v a r i a n c e in t h e r e s u l t s between t h e t h r e e p e s t s and t h e d i f f e r e n t p r o d u c t i o n s c e n a r i o s a n a l y z e d , s t r e s s e s t h e p o i n t t h a t in p e s t management 251 where b i o l o g i c a l c o n d i t i o n s can vary from one subsystem t o a n o t h e r , i t i s i m p e r a t i v e t h a t t h e d e c i s i o n s e t t i n g be c o n s i d e r e d and g e n e r a l i z a ­ t i o n s av oi d ed . 8.3 F u r t h e r Research and Extensions Thi s r e s e a r c h has uncovered a number o f a r e a s which j u s t i f y fu rth er investigation. F i r s t , t h e system d e f i n e d by th e model should be expanded t o i n c l u d e a d d i t i o n a l p e s t s and t h e problem o f d e f i n i n g m u l t i - p e s t economic t h r e s h o l d s t o gu ide t h e use o f " c o c k t a i l s p r ay s " sh ou ld be examined. The m u l t i - s e a s o n a l problems o f r e s i s t a n c e and i n c r e a s e d o v e r w i n t e r i n g should be a d d r e s s e d as v/ell as s e v e r a l s p e c i f i ­ c a t i o n problems were uncovered by comparing model p r e d i c t i o n s w ith t h e s t a t e m e n t s on a n t i c i p a t e d system b e h a v i o r . The e n t i r e b a s i s o f t h e p r e s c r i p t i v e , d e s c r i p t i v e , and p r e d i c t i v e work on d e c i s i o n making l a c k s c r e d i b i l i t y due t o t h e f a c t t h a t t h e EuH model has n o t been f u l l y j u s t i f i e d . A d d it i o n a l e v a l u a t i o n s us ing th e two c o n d i t i o n s o f t h e G ie r e t e s t sh ould be p ur su ed. F u r t h e r work a l s o needs t o be c o n ti nu ed on e s t a b l i s h i n g p r o b a b i l i t y f u n c t i o n s t o t r e a t t h e s t o c h a s t i c v a r i a b l e s d e a l i n g with market p r i c e s , packout r a t e s and yields. A y i e l d s i m u l a t o r which coul d c o r r e l a t e p e s t damage t o th e h e a l t h o f t h e t r e e would be a major c o n t r i b u t i o n . P robability functions i d e n t i f i e d by t h e model co ul d be improved by r e f i n e d damage e s t i m a t e s and e r r o r terms on t h e i n t r o d u c t i o n o f th e growth f u n c t i o n s which s i m u l a t e t h e p e s t p o p u l a t i o n development. F i n a l l y , th e a r e a which a p p e a r s t o have t h e g r e a t e s t p o t e n t i a l f o r f u t u r e r e s e a r c h in t h i s t o p i c i s t h e s u b j e c t i v e as s es sm en t o f p r o b a b i l i t i e s . L i t t l e work has been done i n t h i s a r e a even though i t may p la y a c r u c i a l r o l e in t h e s e l e c t i o n o f p e s t management s t r a t e g i e s . 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Risk Management in A g r i c u l t u r e : B e h a v i o r a l, M a n a g e r ia lf and P o lic y I s s u e s . AE-4478^ Department o f A g r i c u l t u r a l Economics, U n i v e r s i t y o f I l l i n o i s . 151) Z e n t e r , R.P. e t a l . 1981. O rd in ary and G e n e ra liz e d S t o c h a s t i c Dominance: A P r im e r. S t a f f Paper P81-27. Department o f A g r i c u l t u r a l and A p plied Economics, U n i v e r s i t y o f M innesota. "T h ird-D egree S t o c h a s t i c Dominance." Vol. 60. pp. 457-459. American APPENDICES APPENDIX I CUMULATIVE PROBABILITY DISTRIBUTIONS Net Income Per Ten Acre B lock P r o b a b ility o f R eceiving Income Level o r Less -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 .295 .658 .817 .857 .891 .968 1 .0 0 1 .0 0 1 .0 0 1 .0 0 T able 1. Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Scab Control S t r a t e g y 1: Medium Y ie ld . Net Income Level Per Ten Acre Block -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 Table 2. P r o b a b i l i t y o f R eceiving Income Level o r Less .030 .080 .247 .538 .662 .788 .858 .912 .960 1.000 Cum ulative P r o b a b ilit y D is t r ib u t io n f o r Scab C o n tro l S tra te g y 2: Medium Y ie ld . Net Income Level Per Ten Acre B lock -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 T ab le 3. P r o b a b ilit y o f R eceiving Income Level o r Less .032 .087 .270 .543 .662 .797 .863 .919 .974 1.000 C um ulative P r o b a b i l i t y D i s t r i b u t i o n f o r Scab C ontrol S t r a t e g y 3: Medium Y ie ld . Net Income Level P r o b a b i l i t y o f R eceiv in g Per Ten Acre Block____________________________ Income Level o r Less -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 T able 4 . .034 .119 .259 .571 .698 .823 .873 .911 .965 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Scab C ontrol S t r a t e g y 4: Medium Y ie ld . 266 Net Income Per Ten Acre B lock -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 Table 5. P r o b a b ilit y o f R eceiving Income Level o r Less .030 .075 .224 .507 .643 .762 .851 .902 .962 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Scab C ontrol S t r a t e g y 5: Medium Y ie ld . Net Income P r o b a b i l i t y o f R eceiving Per Ten Acre Block_____________________________ Income Level o r Less -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 Table 6. .033 .089 .274 .545 .664 .799 .864 .920 .975 1.000 C um ulative P r o b a b ilit y D is t r ib u t io n f o r Scab C o n tro l S tra te g y 6: Medium Y ie ld . 267 Net Income P r o b a b ilit y o f R e ceiving Per Ten Acre B lock___________________________ Income Level o r Less -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 .030 .076 .250 .525 .652 .786 .857 .911 .969 1.000 T able 7. Net Income P er Ten Acre Block -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 Table 8. Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Scab C ontrol S t r a t e g y 7: Medium Y ield . P r o b a b i l i t y o f R eceivin g Income Level o r Less .029 .074 .238 .533 .658 .782 .855 .917 .968 1.000 C um ulative P r o b a b ilit y D is t r ib u t io n f o r Scab C o n tro l S tra te g y 8: Medium Y ie ld . Net Income Per Ten Acre Block -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 T ab le 9. P r o b a b ility o f R eceiving Income Level o r Less .029 .074 .294 .583 .656 .782 .856 .910 .955 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Scab Control S t r a t e g y 9: Medium Y ie ld . Net Income P r o b a b i l i t y o f R eceiv ing Per Ten Acre Block_____________________________Income Level o r Less -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 T able 10. .032 .081 .232 .522 .647 .772 .849 .911 .966 1.000 Cum ulative P r o b a b ility D is t r ib u t io n f o r Scab C o n tro l S tra te g y 10: Medium Y ie ld . 269 Net Income P r o b a b ilit y o f R eceiving Per Ten Acre B l o c k _________________________ Income Level o r Less____ -7858 -4699 -1541 1617 4775 7934 11092 14250 17408 20567 T able 11. Net Income Per Ten Acre Block -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 12. ,025 .050 .228 .488 .616 .759 .830 .921 .974 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Scab Control S t r a t e g y 11: Medium Y ie ld . P r o b a b i l i t y o f R eceiving Income Level o r Less .508 .767 .952 .976 1.000 1.000 1.000 1.000 1.000 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 1; Medium Y ield and High I n i t i a l P o p u la tio n D en sity . 270 Net Income P er Ten Acre Block -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 13. Net Income P er Ten Acre Block -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 14. P r o b a b i l i t y o f Earning Income Level o r Less .064 .195 .397 .596 .681 .805 .860 .908 .946 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 2: Medium Y ield and High I n i t i a l P o p u la tio n D en sity . P r o b a b i l i t y o f Earning Income Level o r Less .081 .234 .510 .625 .695 .820 .873 .918 .957 1.000 C um ulative P r o b a b ilit y D is t r ib u t io n f o r C o dling Moth S tra te g y 3: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . 270 Net Income P r o b a b ilit y o f Earning Per Ten Acre Block___________________________ Income Level o r Less -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 13. Net Income Per Ten Acre Block -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 14. .064 .195 .397 .596 .681 .805 .860 .908 .946 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 2: Medium Y ield and High I n i t i a l P o p u la tio n D en sity . P r o b a b i l i t y o f Earning Income Level o r Less .081 .234 .510 .625 .695 .820 .873 .918 .957 1.000 C um ulative P r o b a b ilit y D is t r ib u t io n f o r C odling Moth S tra te g y 3: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . 271 Net Income Level P r o b a b ility o f Earning Per Ten Acre Block_________________________Income Level o r Less -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 T able 15. Net Income Level Per Ten Acre Block -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 16. .053 .150 .392 .607 .682 .807 .861 .911 .956 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r C odling Moth S t r a t e g y 4: Medium Y ield and High I n i t i a l P o p u la tio n D e n s ity . P r o b a b i l i t y o f E arning Income Level o r Less .060 .188 .462 .620 .687 .813 .866 .916 .963 1.000 C um ulative P r o b a b ilit y D is t r ib u t io n f o r C o d lin g Moth S tra te g y 5: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level Per Ten Acre Block P r o b a b ilit y o f Earning Income Level o r Less -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 T able 17. Net Income Level P e r Ten Acre Block .053 .150 .392 .607 .682 .807 .861 .911 .956 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 6: Medium Y ield and High I n i t i a l P o p u la tio n D e n s ity . _____ P r o b a b i l i t y o f Earning Income Level o r Less .060 .188 .462 .620 .687 .813 .866 .916 .962 1.000 -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 18. C um ulative P r o b a b ilit y D is t r ib u t io n f o r C odling Moth S tra te g y 7: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . 273 Net Income Level P r o b a b ilit y o f Earning Per Ten Acre Block__________________________ Income Level o r Less -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 T able 19. .053 .150 .391 .607 .682 .807 .861 .909 .947 1.000 Cumulative P r o b a b i l i t y D i s t r i u t i o n f o r Codling Moth S t r a t e g y 8: Medium Y ield and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level P r o b a b i l i t y o f Earning P er Ten Acre B l o c k __________________________ Income Level o r Less -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 Table 20. .060 .188 .462 .620 .687 .813 .866 .914 .952 1.000 C um ulative P r o b a b ility D is t r ib u t io n f o r C odling Moth S tra te g y 9: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level Per Ten Acre Block -5845 -3099 -352 2394 5141 7887 10634 13381 16127 18874 T able 21. Net Income Level P er Ten Acre Block -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 Table 22: P r o b a b ilit y o f Earning Income Level o r Less__ .053 .150 .392 .607 .682 .807 .861 .911 .956 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 10: Medium Y ield and High I n i t i a l P o p u la tio n D e n sity . P r o b a b i l i t y o f Earning __________ Income Level o r Less .138 .365 .548 .659 .758 .825 .872 .916 .957 1.000 C um ulative P r o b a b ilit y D is tr ib u tio n f o r C o d lin g Moth S tra te g y 11: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level Per Ten Acre Block -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 T able 23. Net Income Level Per Ten Acre Block -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 Table 24. P r o b a b ilit y o f Earning Income Level o r Less .124 .350 .539 .653 .699 .820 .868 .911 .951 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 12: Medium Y ield and High I n i t i a l P o p u la tio n D e p s ity . P r o b a b i l i t y o f Earning Income Level o r Less .124 .350 .539 .653 .699 .820 .868 .911 .951 1.000 C um ulative P r o b a b ilit y D is t r ib u t io n f o r C odling Moth S tra te g y 13: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . 276 Net Income Level Per Ten Acre Block -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 Table 25. Net Income Level Per Ten Acre Block -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 Table 26. P r o b a b i l i t y o f Earning Income Level o r Less .138 .365 .549 .659 .758 .825 .872 .916 .957 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 14 : Medium Y ield and High I n i t i a l P o p u la tio n D e n s ity . P r o b a b i l i t y o f Earning Income Level o r Less .122 .350 .535 .653 .699 .820 .868 .910 .943 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r C odling Moth S t r a t e g y 15: Medium Y ield and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level Per Ten Acre Block P r o b a b ilit y o f Earning Income Level o r Less -3711 -1276 1179 3624 6070 8515 10960 13405 15850 18295 .136 .365 .548 .659 .758 .825 .872 .914 .947 1.000 Table 27. Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Codling Moth S t r a t e g y 16: Medium Y ield and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level Per Ten Acre B l o -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 Table 28. c k P r o b a b i l i t y o f Earning __________________ Income Level o r Less .124 .350 .535 .653 .699 .820 .868 .910 .943 1.000 C um ulative P r o b a b ilit y D is t r ib u t io n f o r C o dling Moth S tra te g y 17: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level Per Ten Acre Block -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 T able 29. P r o b a b ilit y o f Earning Income Level o r Less .138 .365 .548 .659 .758 .825 .872 .914 .947 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r C odling Moth S t r a t e g y 18: Medium Y ield and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level P r o b a b i l i t y o f Earning P er Ten Acre Block____________________________ Income Level o r Less -3711 -1266 1179 3624 6070 8515 10960 13405 15850 18295 Table 30. .138 .365 .548 .659 .758 .825 .872 .914 .947 1.000 Cum ulative P r o b a b ilit y D is t r ib u t io n f o r C o dling Moth S tra te g y 19: Medium Y ie ld and High I n i t i a l P o p u la tio n D e n s ity . Net Income Level Per Ten Acre Block -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 P r o b a b ility o f R eceiving Income Level o r Less .128 .347 .556 .649 .750 .827 .910 .930 .953 1.000 Table 31. Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Mite S t r a t e g y 1: Medium Y ield and Weekly S co u tin g . Net Income Level P r o b a b i l i t y o f R eceiving P er Ten Acre Block_____________________________ Income Level o r Less .127 .327 .553 .636 .696 .829 .885 .925 .961 1.000 -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 Table 32. C um ulative P r o b a b ilit y D is tr ib u tio n f o r Revised M ite S tra te g y 4: Medium Y ie ld and Weekly S co u tin g . 280 Income Level P r o b a b ility o f R eceiving Per Ten Acre Block___________________________ Income Level o r Less -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 Table 33. Income Level P er Ten Acre Block -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 Table 34. .127 .321 .553 .633 .725 .830 .885 .922 .951 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Revised Mite S t r a t e g y 5: Medium Y ield and Weekly S c o u tin g . P r o b a b i l i t y o f R eceiving __________________________ Income Level o r Less .127 .322 .546 .631 .711 .830 .893 .924 .951 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Revised Mite S t r a t e g y 7: Medium Y ield and Weekly S c o u tin g . Income Level Per Ten Acre Block -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 Table 35. P r o b a b i l i t y o f R eceiving Income Level o r Less .127 .327 .564 .636 .697 .829 .885 .925 .961 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Revised Mite S tr a t e g y 11: Medium Y ield and Weekly S c o u tin g . ^• Income Level P r o b a b i l i t y o f R eceiving P er Ten Acre Block______________________________ Income Level o r Less -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 Table 36. .127 .321 .554 .633 .697 .829 .885 .922 .951 1.000 C um ulative P r o b a b ilit y D is tr ib u tio n f o r Revised M ite S tra te g y 12: Medium Y ie ld and Weekly S co u tin g . Income Level Per Ten Acre B lock -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 Table 37. P r o b a b ility o f R eceiving Income Level o r Less .127 .324 .541 .633 .699 .827 .883 .920 .949 1.000 Cumulative P r o b a b i l i t y D i s t r i b u t i o n f o r Revised Mite S t r a t e g y 13: Medium Y ield and Weekly S co u tin g Income Level P r o b a b i l i t y o f R eceiving Per Ten Acre Block_____________________________ Income Level o r Less -3559 -1004 1549 4103 6658 9212 11766 14320 16874 19428 Table 38. .127 .321 .528 .633 .699 .826 .890 .923 .951 1.000 Cum ulative P r o b a b ility D is t r ib u t io n f o r Revised M ite S tra te g y 14: Medium Y ie ld and Weekly S co u tin g . APPENDIX I I STATISTICAL TESTS ON SCAB DAMAGE ESTIMATES 283 A s ta n d a r d t - t e s t was conducted t o t e s t i f t h e av era g e damage p r e ­ d i c t e d by th e s im u l a ti o n model s t a t i s t i c a l l y d i f f e r e d from t h e avera g e damage observed in e x p erim en tal o r c h a r d s . f o r two s t r a t e g i e s : IPM ( 5 ) . The h y p o th e s is was t e s t e d t h e c o n v e n tio n a l c a l e n d a r (7) and t h e p o s t - i n f e c t i o n In bo th c a s e s , t h e r e i s no s i g n i f i c a n t d i f f e r e n c e between t h e two damage e s t i m a t e s a t .975 s i g n i f i c a n c e l e v e l . These r e s u l t s i n d i c a t e t h a t t h e model i s j u s t i f i e d f o r damage p r e d i c t i o n s f o r t h e s e two s t r a t e g i e s . E xperim ental d a t a were n o t a v a i l ­ a b l e f o r th e n e c e s s a r y t e s t s o f th e rem aining s t r a t e g i e s . I t s h o u ld be no ted t h a t th e e x p e rim e n ta l o b s e r v a ti o n s were o b ta in e d from s t r a t e g i e s which used s l i g h t l y d i f f e r e n t ch em ica ls th a n t h e model. 284 C onventional Program* 1) H„: M, = U2 The mean damage e s t i m a t e f o r t h e model i s equal t o t h e o b serv ed damage in e x p e rim e n ta l o r c h a rd . 2) U2 H,: The mean damage e s t i m a t e f o r th e model i s n o t equal t o t h e observ ed damage in e x p e rim e n ta l o r c h a r d . 3) Under H„ | T „ | - 4) R e je c t HQi f |Ti g | r\ 0) t 19 _ 2 .6 - 5.02 80 / /"nr " 0975 ± 2.093 -2 .4 2 0 7 4 .3 6 -2 .4 2 1.83 = 1.32 Hq i s n o t r e j e c t e d * Compares S t r a t e g y 7 w ith 7 day p r o t e c t i v e tr e a tm e n t o f b i t e r t a n o l . ** B ushels damaged p e r a c r e w ith y i e l d o f 500 b u s h e ls p e r a c r e . 285 P o s t - I n f e c t i o n IPM Program* 1) H0 : M, ■= M2 The mean damage e s t i m a t e f o r th e model i s equal t o t h e observ ed damage in e x p erim en tal o r c h a r d . 2) H] : M-j f Ug The mean damage e s t i m a t e f o r th e model i s n o t equal t o th e observed damage in ex p e rim e n ta l o rc h a r d . 3) Under H„ | T „ | » 4) R e je c t HQ i f !T] g |og75 > 2.093 c, |X 16.1 - 25.1 M '1 i d9 ' “ 97 A / /4 A .3 I K6 2 7 .4 1 -9 K 6 .2 8 = 1.43 Hq i s n o t r e j e c t e d . * Compares S t r a t e g y 11 w ith p o s t - i n f e c t i o n t r e a tm e n t o f b i t e r t a n o l . ** Bushel damaged p e r a c r e w ith y i e l d o f 500 b u s h e ls p e r a c r e . APPENDIX I I I FRUIT GROWER SURVEY 206 A small survey was conducted w ith a group o f f r u i t growers from Western Michigan a t th e beginnin g o f th e s tu d y f o r two r e a s o n s . F irst, i t was n e c e s s a r y t o v a l i d a t e f o r f r u i t growers th e r e s u l t s o f l a r g e r su rv e y s which measured th e r i s k p r e f e r e n c e s o f fa rm e rs d e a l i n g w ith o t h e r com m odities. Second, a more com plete u n d e rs ta n d in g o f th e p e r s p e c t i v e s o f th e d e c i s i o n makers who a c t u a l l y make p e s t management d e c i s i o n s was d e sire d . The f o llo w in g q u e s t i o n n a i r e was used as a g u i d e l i n e in an inform al d i s c u s s i o n w ith e i g h t g ro w ers. The q u e s t i o n n a i r e i s fo llo w ed by a summary o f t h e m ajor p o i n t s o f th e d i s c u s s i o n . 287 PEST MANAGEMENT QUESTIONNAIRE 1. How much does p e s t management i n f l u e n c e t h e v a r i e t y you s e l e c t t o grow: ___________ None ___________ L i t t l e A lo t 2. Do you use th e same c o n t r o l f o r a p p le s c a b , m ite s and c o d lin g moth y e a r in and y e a r o u t? No Yes I f no, what d e te rm in e s changes in c o n t r o l s you employ from one y e a r to th e n e x t? Weather Expected ap p le p r i ces Expected i n f e s t a t i o n s Last y e a r 's e x p e r ie n c e w ith p est{ s) Chemical p r i c e s O thers 3- Do you a p p le th e same c o n t r o l o v e r th e e n t i r e o r c h a r d o r a r e some blo c k s t r e a t e d d i f f e r e n t l y than o t h e r s ? Why? ___________ Age ___________ S iz e o f Orchard ___________ V a r ie ty O ther 288 4. How would you o r d i n a l l y rank t h e s e f a c t o r s as t o th e im portan ce t h a t th e y u s u a l l y p la y in y o u r d e c i s i o n t o s e l e c t a c o n t r o l s t r a t e g y f o r m ite s ? (Use 1 th ro u g h 13 w ith a “1" i n d i c a t i n g g r e a t e s t im portance and "13" th e lo w e s t. Use each number o n ly o n c e .) ___________ Expected a p p le p r i c e s ___________ D ecisio n t o s e l l f r u i t in f r e s h o r p ro c e s s e d m arket Exp ected w e a th e r p a t t e r n s ___________ Weather e x p e r ie n c e t o d a te in th e seaso n ___________ L a s t y e a r ' s e x p e r ie n c e w ith m ite s in own o rc h a rd ___________ C ontrol s e l e c t e d f o r ap p le scab ___________ Apple v a r i e t y ___________ Type o r c a p a c i t y o f s p r a y e r equipment C osts o f a l t e r n a t i v e chem icals _Amount o f l a b o r r e q u i r e d to a p p ly a l t e r n a t i v e c o n t r o l s R e te n tio n ( w e a th e rin g ) " c a p a c ity o f c o n t r o l The r e l a t i v e p r o b a b i l i t y t h a t co n tro l w ill prev en t s u b s ta n tia l damage R e te n tio n o f t o x i c r e s i d u e O ther 289 5. How would you o r d i n a l l y rank t h e s e f a c t o r s as t o th e im portance t h a t th e y u s u a l l y p la y in y o u r d e c i s i o n s t o s e l e c t a c o n t r o l s t r a t e g y f o r c o d lin g moths? (Use 1 through 14 w ith a "1" i n d i c a t i n g g r e a t e s t im p ortance and a "14" th e lo w e s t. Use each number o n ly o n c e .) ___________ Expected a p p le p r i c e s ___________ D ecision to s e l l f r u i t in f r e s h o r p ro c e s s e d m arkets ___________ Weather e x p e rie n c e d t o d a te in th e season ___________ Expected w e a th e r p a t t e r n ___________ L ast y e a r ' s e x p e r ie n c e w ith c o d lin g moth in y o u r own o rc h a rd ___________ E x perience w ith c o d lin g moth in n e ig h b o rin g o rc h a r d s ___________ C ontrol s e l e c t e d f o r a n o t h e r p e s t ( Name:_____________________ ) ___________ C ap ac ity o r ty p e o f s p ra y equipment C osts o f a l t e r n a t i v e chem icals Amount o f l a b o r r e q u i r e d t o ap p ly a lte rn a tiv e co n tro ls R e te n tio n ( w e a th e rin g ) c a p a c i t y o f c o n tro l R e l a ti v e p r o b a b i l i t y t h a t c o n tr o l "will p r e v e n t s u b s t a n t i a l damage R e te n tio n o f t o x i c r e s i d u e s O ther 290 6. How would you o r d i n a l l y rank t h e s e f a c t o r s as t o t h e im p ortance t h a t th e y u s u a l l y p la y in y o u r d e c i s i o n s t o s e l e c t a c o n t r o l s t r a t e g y f o r ap p le s cab ? (Use 1 thro u g h 15 w ith a "1" i n d i c a t i n g g r e a t e s t im portance and a "15" th e lo w e s t. Use each number o n ly o n c e .) ___________ Expected a p p le p r i c e s ___________ D ecision t o s e l l f r u i t in f r e s h o r p ro c e s s e d m arkets ___________ Expected w e a th e r p a t t e r n ___________ Weather e x p e rie n c e d t o d a te in th e season ___________ L a s t y e a r ' s e x p e r ie n c e w ith ap p le scab in own o rc h a rd ___________ Experience w ith a p p le scab in n e ig h b o rin g o r c h a r d s ___________ Apple v a r i e t y ___________ C a p a c ity o r ty p e o f s p ra y equipment C osts o f a l t e r n a t i v e ch em ica ls Amount o f tim e needed to app ly a lte rn a tiv e co n tro ls Amount o f l a b o r needed t o app ly a lte rn a tiv e co n tro ls _Retention ( w e a th e rin g ) c a p a c i t y o f c o n tro l R elativ e p r o b a b ility t h a t co n tro l w ill p r e v e n t s u b s t a n t i a l damage R e te n tio n o f t o x i c r e s i d u e s O ther 291 7' on ^ a S a T t ^ S f P“ t P° P U lat1 ° " S (aC tual .R o u tin e ly ..O c c a s io n a lly Never 8. Do you use in fo rm al m o n ito rin g o f p e s t p o p u la tio n s ? (a) in s p e c t i o n done a lo n e w ith o u t o u t s i d e " e x p e r t" .R o u tin e ly Oc c a s i o n a l l y _ _ _________Never _ _______ i (b ) i n s p e c t i o n done w ith e x te n s ion p erso n n el R o u tin e ly O c c a s io n a lly Never (c) i n s p e c t i o n done w ith chem ical c o m p a n y /d is t r i b u to r r e p r e s e n t a t i v e — ._______ R o u tin e ly -----------------O c c a s io n a lly --------------- -N ever ( d) i n s p e c t i o n done w ith c o o p e r a tiv e r e p r e s e n t a t i v e . R o u tin e l y .O c c a s io n a lly Ne v e r (e ) i n s p e c t io n done w ith p r i v a t e c o n s u l t a n t .R o u tin e ly O c c a s io n a lly Never 292 9. To what d eg ree do E xtensio n recommendations in f l u e n c e y o u r d e c i s i o n s in (a ) s e l e c t i n g one c o n t r o l method o v er a n o t h e r ? __________v e ry i n f l u e n t i a l ; __________m o d e ra tely i n f l u e n t i a l ; o r (b) tim in g o f s p r a y s ? o f l i t t l e in flu e n c e . v ery i n f l u e n t i a l ; m o d e ra tely i n f l u e n t i a l ; o r __________o f l i t t l e in f l u e n c e . (c ) d e te rm in in g c o n c e n t r a t i o n s o r dosages o f s p r a y s ? __________very i n f l u e n t i a l ; __________m o d e ra te ly i n f l u e n t i a l ; o r ____________ o f l i t t l e in flu en ce. 10. Have you e v e r n o ti c e d a problem w ith r e s i s t a n c e o f p e s t p o p u la tio n t o a chemical you f r e q u e n t l y u s e ( d ) ? ___________ Yes No Have you e v e r a l t e r e d y o u r p e s t management due t o a r e s i s t a n c e problem? ___________ No Yes I f y e s , how? D is c o n tin u e use o f chemical Use chemical in com bination w ith a n o th e r chemical which c o n t r o l s r e s i s t a n t s t r a i n s , i . e . , (Benomyl and Captan) R o ta te use o f ch em icals in a l t e r n a t e y e a r s _Reduce dosages o r number o f s p ra y s "to av o id problems JDther ( p l e a s e e x p l a in ) 293 11. Are t h e r e any a r e a s o f p e s t management were you would l i k e t o s ee a d d i t i o n a l in f o r m a tio n p ro v id ed f o r y o u r use? Conments: 294 RISK ATTITUDE QUESTIONNAIRE Your a t t i t u d e s a b o u t r i s k i n f l u e n c e t h e d e c i s i o n s t h a t you make in th e p e s t management o f y o u r o r c h a r d . The a t t a c h e d q u e s t i o n n a i r e i s desig n ed t o h elp you t h i n k ab ou t t h e s e a t t i t u d e s . I t w i l l a l s o h e lp us t o d e te rm in e how a c c u r a t e l y y o u r r i s k p r e f e r e n c e can be measured and i n c o r p o r a t e d i n t o th e way t h a t e x t e n s i o n s p e c i a l i s t s may a s s i s t you in making p e s t management d ecisio n s. In f i l l i n g o u t th e q u e s t i o n n a i r e you w i l l be ask ed t o compare d i s ­ t r i b u t i o n s o f numbers and i n d i c a t e which you p r e f e r . The numbers r e p r e s e n t l e v e l s o f annual n e t income from one 1 0 - a c r e b lo c k . T his income i s o v er and above th e c o s t s o f p r o d u c tio n and i s a v a i l a b l e f o r f a m ily l i v i n g e x p e n s e s , ex p an sio n o f y o u r farm o p e r a t i o n and a c c e l e r a t e d d e b t repaym ent. Each d i s t r i b u t i o n s h o u ld be th o u g h t o f as a range o f p o s s i b l e outcomes t h a t can o c c u r u nder a p a r t i c u l a r management s t r a t e g y . S ix income l e v e l s a r e l i s t e d un der each c h o i c e , and each income i s c o n s id e r e d t o have one chance in s i x o f a c t u a l l y o c c u rin g n e x t y e a r . The s i x l e v e l s o f each d i s t r i b u t i o n can be viewed as t h e s i x f a c e s o f a d i e and when th e d ie i s r o l l e d each s i d e has an equal p r o b a b i l i t y o f coming fa c e up. There a r e t h r e e s e c t i o n s o f th e q u e s t i o n n a i r e w ith each s e c t i o n f o c u s in g on a d i f f e r e n t income ra n g e . Your answ ers s h o u ld r e f l e c t y o u r own a t t i t u d e s and y o u r own s i t u a t i o n . There a r e no r i g h t o r wrong an sw ers. 295 SECTION I 1. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e fe r . A B -450 -500 -50 -450 400 -350 450 500 550 1200 950 1600 I f you p r e f e r A, go t o q u e s ti o n 2. 2. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . C D -100 -150 350 50 400 150 400 450 550 1050 650 1100 I f you p r e f e r C, go t o q u e s ti o n 4. 3. I f you p r e f e r B, go t o q u e s ti o n 3. I f you p r e f e r D, go t o q u e s tio n 5. Compare th e fo llo w in g two d i s t r i b u t i o n s E and c i r c l e th e one you p r e f e r . F -500 50 50 100 350 650 900 800 950 850 1600 950 296 I f you p r e fe r E, go to q u e s tio n 6. 4. I f you p r e f e r F, go t o q u e s ti o n 7. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . G H -50 50 500 250 500 350 900 750 1050 800 1600 1400 Go t o S e c t io n I I . 5. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e t h e one you p r e f e r . I J 50 -150 200 50 300 150 550 450 600 1050 700 1100 Go t o S e c tio n I I . 6. Compare t h e f o llo w in g two d i s t r i b u t i o n s and c i r c l e t h e one you p r e f e r . K L -150 -500 50 -450 150 -350 450 500 1050 1200 1100 1600 297 Go t o S e c tio n I I . 7. Compare th e f o llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . Go to S e c tio n I I . M N 50 -250 200 -200 300 100 550 800 600 900 700 1100 298 SECTION I I 1. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . A 3400 3250 3850 3300 3900 3600 3900 4300 4050 4400 4150 4600 I f you p r e f e r A, go to q u e s tio n 2. 2. I f you p r e f e r B, go t o q u e s ti o n 3. Compare t h e fo llo w in g two d i s t r i b u t i o n s C and c i r c l e th e one you p r e f e r . D 3550 3000 3700 3550 3800 3850 4050 4400 4100 4450 4200 5100 I f you p r e f e r C, go t o q u e s ti o n 4. 3. B Compare th e f o llo w in g d i s t r i b u t i o n s E I f you p r e f e r D, go t o q u e s tio n 5. and c i r c l e th e one you p r e f e r . F 3550 3050 3700 3950 3800 4000 4050 4050 4100 4150 4200 4200 299 I f you p r e fe r E, go to q u e s tio n 6. 4. I f you p r e f e r F, go t o q u e s ti o n 7. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . G H 3700 3450 3750 4000 3900 4000 4450 4400 4450 4650 4600 5100 Go t o S e c tio n I I I . 5. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . I J 3350 3000 3450 3050 3550 3150 3700 4000 4150 4700 4300 5100 Go t o S e c tio n I I I . 6. Compare th e f o llo w in g two d i s t r i b u t i o n s and c i r c l e t h e one you p r e f e r . K Go t o S e c tio n I I I . L 3550 3250 3700 3300 3800 3600 4050 4300 4100 4400 4200 4600 300 7. Compare the fo llo w in g two d is t r ib u t io n s and c ir c le th e one you p r e fe r . Go t o S e c tio n I I I . M N 3700 3250 3750 3900 3900 4100 4450 4150 4450 4250 4600 5050 301 SECTION I I I 1. Compare th e f o llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e fe r . A B 14000 14650 14550 14850 14850 14850 15400 15100 15450 15250 16100 15500 I f you p r e f e r A, go t o q u e s ti o n 2. 2. Compare th e f o llo w in g two d i s t r i b u t i o n s and c i r c l e t h e one you p r e f e r . C D 14550 14050 14700 14950 14800 15000 15050 15050 15100 15150 15200 15200 I f you p r e f e r C, go t o q u e s ti o n 4. 3. I f you p r e f e r B, go t o q u e s t i o n 3. I f you p r e f e r D, go t o q u e s t i o n 5. Compare t h e f o ll o w i n g two d i s t r i b u t i o n s and c i r c l e t h e one you p r e f e r . E F 14400 14250 14550 14600 14650 14650 14950 15050 15550 15150 15600 16000 302 I f you p r e f e r , E, go t o q u e s t i o n 6. 4. Compare th e fo llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . G H 14550 14250 14700 14300 14800 14600 15050 15300 15100 15400 15200 15600 You have com pleted t h e q u e s t i o n n a i r e . 5. Thank you. Compare th e f o llo w in g two d i s t r i b u t i o n s and c i r c l e th e one you p r e f e r . I J 14350 14000 14550 14050 14250 14150 14950 15000 15550 15700 15600 16100 You have com pleted t h e q u e s t i o n n a i r e . 6. I f you p r e f e r F, go t o q u e s t i o n 7. Thank you. Compare t h e f o llo w in g two d i s t r i b u t i o n s and c i r c l e t h e one you p r e f e r . K L 14340 14000 14450 14550 14550 14850 14700 15400 15150 15450 15300 16100 You have com pleted th e q u e s t i o n n a i r e . Thank you. 303 7. Compare the fo llo w in g two d is t r ib u t io n s and c ir c le th e one you p r e fe r . M N 14000 14050 14050 14400 14150 14750 15000 15000 15700 15100 16100 15150 You have f i n i s h e d th e q u e s t i o n n a i r e . Thank you. 304 MAJOR POINTS OF GROWERS 1) U nlike p e s t management d e c i s i o n s d e a l in g w ith o t h e r com m odities, i t a p p e a rs t h a t e x p e c t a t i o n s on a p p le p r i c e s and th e y i e l d t o n o t in f l u e n c e th e s e l e c t i o n o f pestmangement t a c t i c s becau se o f two im p o r ta n t f a c t o r s : 1) m a rk e tin g i n s t i t u t i o n s and 2) th e long term consequences o f c o n t r o l s in any one g iv en y e a r . The g e n e ra l s t r a t e g y employed by t h e Bel din g growers i s t o produce a high q u a l i t y o f f r u i t ( a t w h atev e r c o s t ) r e g a r d l e s s o f w h eth er o r n o t i t i s in te n d e d f o r th e f r e s h o r p ro c e s s e d m a rk e ts , w h eth er o r n o t t h e r e has been f r o s t damage o r w h eth er o r n o t th e p r i c e / y i e l d o u tlo o k i s f a v o r a b l e . The r a t i o n a l e f o r t h i s s t r a t e g y i s c e n t e r e d on m a rk e tin g and long term c o n t r o l c o n c e rn s. In a good y i e l d / p o o r p r i c e y e a r i t i s n e c e s s a r y t o h a r v e s t high q u a l i t y f r u i t t o in s u r e t h a t i t w i l l be m arketed . In a poor y i e ld /g o o d p r i c e y e a r i t i s b e n e f i c i a l t o produce high q u a l i t y f r u i t h ig h e r and t o p a c k -o u t t o r e c e i v e th e h ig h e r premiums t h a t a r e p aid f o r to p g r a d e s . The consensus among th e grow ers was t h a t th e y a tte m p t t o produce high q u a l i t y f o r bo th th e f r e s h and p ro c e s s e d m a rk e ts . a (G erbers e s p e c i a l l y was noted as p r o c e s s in g f ir m demanding high q u a l i t y a p p l e s . ) Only j u i c e a p p le s were in d i c a t e d as b e in g a p o s s i b l e c a s e where q u a l i t y was l e s s im p o r ta n t in th e m a rk e tin g o f f r u i t . The c o n t r o l n e c e s s a r y to produce a high q u a l i t y f r u i t i s p ursued th r o u g h o u t th e seaso n r e g a r d l e s s o f any p o s s i b l e s h o r t term g a in s from re d u c in g c o n t r o l c o s t s when r e d u c t io n s in t h e v a lu e o f th e h a r v e s t i s l i k e l y t o w a r r a n t such cu tb a c k s (p erh ap s due t o f r o s t damage, poor p r i c e s , e t c . ) . T h is i s th e c a s e b ecause o f th e long term consequences o f p e s t c o n t r o l s . By c u t t i n g back on th e c o n t r o l s (and s a v in g some c o n t r o l c o s t s ) in one 305 y e a r , i t i s f e l t by th e grow ers t h a t th e in c re a s e d p e s t problems in f u t u r e y e a r s s t i m u l a t e d by t h e c u tb a c k s w i l l produce much h ig h e r c o n t r o l c o s t s in t h e f u t u r e and o f f s e t any g a in s by a d j u s t i n g t o th e c o n d i t i o n s o f each p a rtic u la r year. 2) I t i s u n r e a l i s t i c to i s o l a t e o u t a s i n g l e p e s t and d i s c u s s i t s management s i n c e t h e e n t i r e o rc h a rd i s o p e r a te d as a system and i t i s n e c e s s a r y t o d i s c u s s i n t e r r e l a t i o n s h i p s between p e s t s , p r e d a t o r s and c o n t r o l s . 3) P e s t management does n o t i n f l u e n c e th e v a r i e t i e s grown b u t v a r i e t y can i n f l u e n c e th e p e s t management. Market c o n d i t i o n s d i c t a t e v a r i e t y . V a r i e t a l d i f f e r e n c e s between s u s c e p t i b i l i t i e s t o p e s t s can be an im p o rta n t d e te r m in a n t in i d e n t i f y i n g c o n t r o l need s. 4) C o n tr o ls a re a d j u s t e d from one y e a r t o th e n e x t by in f o r m a tio n on th e p r e v io u s y e a r ' s e x p e rie n c e w ith th e p e s t ( s ) , chemical p r i c e s and th e ex p ec ted le v e l o f i n f e s t a t i o n . The w e a th e r p a t t e r n and th e developm ent o f new c h em ica ls a r e a l s o im p o rta n t f a c t o r s which may change th e c o n t r o l s a p p l i e d . 5) D i f f e r e n t b lo c k s a r e o f t e n t r e a t e d d i f f e r e n t l y . Two common f a c t o r s f o r d i f f e r e n t i a l tr e a t m e n t s a r e th e o v e r a l l s i z e o f t h e o rc h a r d and th e v a r i e t a l mix o f each b lo c k . I f blo c k s a r e in d i f f e r e n t l o c a t i o n s , th e d i s t a n c e between b lo c k s could r e s u l t in a d i f f e r e n t t r e a t m e n t . P ro x im ity t o n e i g h b o r 's o r c h a r d which always has problems would i n f l u e n c e t r e a t m e n t as w e l l . O c c a s io n a lly , some growers may a p p ly an e r a d i c a n t program t o some b lo c k s w h ile p u rs u in g a p r o t e c t i v e program t o o t h e r b lo c k s t o in s u r e t h a t th e y w i l l be a b l e to s p ra y a l l th e b lo c k s in t h e e r a d i c a n t program w ith i n t h e n e c e s s a r y tim e l i m i t . By f o llo w in g a p r o t e c t i v e program in some b lo c k s , 306 th e t o t a l number o f a c r e s t h a t need t o be sp ray ed in a tim e ly f a s h io n i s re d u c e d . T his p r a c t i c e can circum vent r e s t r i c t i o n s imposed by th e a v a i l a b l e sp ray er cap a city . However, most o f t h e growers do n o t use t h i s t a c t i c s in c e th e y have s u f f i c i e n t equipm ent f o r t h e i r o r c h a r d s i z e . They have matched t h e needed m achinery t o th e d e s i r e d c o n t r o l s a n d / o r have needed t o match a c o n t r o l t o th e e x i s t i n g m ach inery. I t was n o te d t h a t a t l e a s t one o f th e grow ers used a d u s t e r in some c a s e s when he was in a h u r r y s i n c e he co u ld c o v er th e o rc h a rd f a s t e r , s p ra y in th e wind and t h e d i e s e l f u e l c o s t s were s u b s t a n t i a l l y l e s s . Each block w i l l have " h o t s p o ts " which u s u a l l y r e q u i r e e x t r a a t t e n t i o n . The s i z e and freq u en cy o f t h e h o t s p o ts in each b lo c k may r e s u l t in d i f f ­ e r e n t i a l t r e a t m e n t o f th e v a r io u s b lo c k s . Hot s p o ts c o u ld be caused by t h e d i f f e r e n c e s w ith i n th e o rc h a r d as t o s i t e , m i c r o - c l i m a t e , wind p a t t e r n , age and v a r i e t y o f t r e e s , w a te r t a b l e , e t c . 6) F a c to r s t h a t were s e l e c t e d by th e grow ers as b e in g t h e most im p o r ta n t f o r t h e c o n t r o l o f m ite s were l a s t y e a r ' s e x p e r ie n c e w ith m ite s in t h e i r own o r c h a r d , th e r e l a t i v e p r o b a b i l i t y t h a t new c o n t r o l s w i l l p r e v e n t s u b s t a n t i a l damage and t h e c o s t s o f a l t e r n a t i v e c h e m ic a ls . t h e a p p le v a r i e t y . Of s eco n d ary im portance was Apple p r i c e s and th e d e c i s i o n t o s e l l th e h a r v e s te d f r u i t in th e f r e s h as opposed t o th e p r o c e s s e d m arket were deemed as bein g r e l a t i v e l y u n im p o rta n t. I t was m entioned by one o f th e grow ers t h a t p o s s i b l e d is ru p tio n s o f m ite /p re d a to r r e la tio n s h ip s in flu en ced h is co n tro l s e le c tio n . He used o i l w ith o c c a s io n a l s p r a y s o f P l i c t r a n b ecause o f a) problem s w ith r e s i s t a n c e ; b) o i l h elp ed c o n tr o l San J o s e S c a le as w e l l ; and c) i t avoided problems w ith th e p r e d a t o r / p r e y r e l a t i o n s h i p s . 7) Codling moth was n o t p e r c e iv e d by th e grow ers as b e in g much o f a problem in t h e i r a r e a . 307 8) The f a c t o r s s e l e c t e d by th e grow ers as b ein g th e most im p o r ta n t in a p p le scab c o n t r o l w ere: a) e x p e c te d w e a th e r p a t t e r n b) r e l a t i v e p r o b a b ility t h a t co n tro l w ill p re ­ v e n t s u b s t a n t i a l damage c) w e a th e r e x p e r ie n c e d t o d a t e in t h e season d) e x p e r ie n c e in n e ig h b o rin g o r c h a rd s e) a p p le v a r i e t y f) c o sts o f a lte r n a tiv e c o n tro ls g) th e amount o f tim e needed t o c o v e r o rc h a rd w ith s p r a y . P r i c e s , y i e l d s and t o x i c r e s i d u e s w i l l n o t be re g a rd e d as being v ery in flu e n tia l. One grower s t a t e d t h a t r e g a r d l e s s o f t h e p r i c e o r e f f e c t i v e ­ n ess o f d i f o l a t a n he r e f u s e d t o use i t s i n c e i t cau sed d is c o m f o rt f o r h is w orkers and i t was n o t w o rth t h e r i s k o f l a b o r p roblem s. Most o f th e growers commonly use a mix o f p r o t e c t a n t and e r a d i c a n t program s. They may a p p le a p r o t e c t a n t s p ra y on one s i d e , e v e ry o t h e r row and th e n e r a d i c a t e as problem s a r i s e . F r e q u e n tly m entioned ch em icals used were polyram , c y p re x , c a p ta n and b e n l a t e . 9) All th e grow ers i n d i c a t e d t h a t th e y r o u t i n e l y used t r a p s b u t t h a t t h i s y e a r t h e r e was a problem in t h e a v a i l a b i l i t y pheromone. 10) These grow ers had h i r e d a c o n s u l t a n t to h e lp w ith th e p e s t management so th e y i n d i c a t e d t h a t th e y o c c a s i o n a l l y i n s p e c t e d t h e i r o r c h a r d s w ith an " o u t s i d e e x p e r t " as w ell as w ith e x t e n s i o n p e r s o n n e l. I n s p e c t i o n s were n e v e r done w ith chemical c o m p a n y / d i s t r i b u t o r r e p r e s e n t a t i v e s . 11) R e s is ta n c e has been a problem e x p e rie n c e d by a l l o f t h e g ro w ers. One grower p o in te d o u t t h a t when he had poor s u c c e s s w ith c o n t r o l l i n g a p e s t 308 w ith w h atev er he had used in t h e p a s t o r knew o f someone who had b e t t e r s u c c e s s w ith a new c o n t r o l , he sw itch ed w ith o u t n e c e s s a r i l y d ia g n o s in g a r e s i s t a n c e problem. Mite r e s i s t a n c e was c i t e d as a problem which has been a d d re s s e d by r o t a t i n g ch e m ic a ls and by s h i f t i n g t o an o i l / v y d a t e ( a f t e r bloom) s c h e d u le . O c c a s i o n a l l y , ch em icals may be combined t o c o n t r o l r e s i s t a n t scab s t r a i n s . F re q u e n tly t h i s i s accom plished i n d i r e c t l y by a p p ly in g d i f f e r e n t c h em ica ls in d i f f e r e n t s t a g e s o f t h e s easo n o r as t h e w e a th e r p a t t e r n changes ( i . e . , pre-bloom use o f cyprex o r polyram and p o st-b lo o m use o f c a p ta n and b e n l a t e - in f l u e n c e d by th e w e a th e r ) . 309 RISK PREFERENCE RESULTS Grower No. Income Level $0 $4000 1 ( .0 0 0 0 , -.0 0 0 5 2 ( .001) 3 ( » , .001) 4 ( . 0 0 1 , .0003) 5 ( .0 0 0 3 , .0000) 6 ( « , . 001) ( - .0 0 0 1 , - .0 0 1 ) ( » , .001) ( - .0 0 0 1 , - .0 0 1 ) ( .0 0 0 6 , .0001) $14,000 (.0 0 0 6 , .0001) ( .0 0 0 6 , .0001) ( - .0 0 0 1 , - .0 0 1 ) ( .0 0 0 0 , - .0 0 0 5 ) ( ~ , .001) ( .0 0 0 6 , .0001) ( » , . 001) ( » , . 001) In comparing t h e r e s u l t s o f t h i s small group o f a p p le grow ers t o s t u d i e s on fa rm e rs o f v a r io u s e n t e r p r i s e s th e o n ly r e a l c o n c lu s io n i s t h a t th e p r e ­ f e r e n c e s o f both groups a r e h e te rg e n o u s b u t t h e i r p r e f e r e n c e m easures f a l l in about th e same ra n g e . The f r u i t grow ers may a p p e a r s l i g h t l y more c o n s e r v a t i v e s i n c e th e y e x h i b i t a s m a l l e r p r o p o r ti o n o f n e g a tiv e c o e f f i c i e n t s and a l a r g e r p r o p o r ti o n o f h ig h l y p o s i t i v e c o e f f i c i e n t s . I t should be noted t h a t th e l a r g e r s u rv ey asked th e re s p o n d e n ts to make f o u r p a i r w is e com parisons w h ile th e f r u i t grower s u rv e y in v o lv ed o n ly t h r e e com parisons. This r e s u l t e d in w id er i n t e r v a l s f o r t h e s h o r t e r su rv ey and e x p l a i n s why c o e f f i c i e n t s o f +«> a p p e a r f o r th e f r u i t grow ers b u t n o t in t h e Carman o r Love s u r v e y s . APPENDIX IV LISTING OF PROGRAM 1 5 10 15 20 25 30 35 40 45 50 55 60 1 5 10 15 S U B R O U T IN E S E L E C T ( I G O . I ) L O G I C A L D E B U G , M O T H , M I T £ . S C A B , IW S C O U T . HSPRAY COMMON / O B / D E B U G . MOTH.MITE.SCAB.IWSCOUr.H S P R A Y . INTSCT COMMON / I N T / G P P , SCMPOP COMMON / D A T E / I D A y . J D A Y . I Y R , I S T R A T . J S T R A T , K S T R A T , I P A R T I F ( I . E 0 . 2 ) GO TO lO O S E L E C T W H IC H MODELS ARE TO BE OP E RA TED S C A B = .F A L S E . M lT E = . TRUE. M O T H = .FA L S E . S E L E C T WHETHER R E V I S E D M I T E D E C I S I O N W I L L BE USED HSPRAY=. TRUE. S E L E C T WHETHER WEEKLY S C O U T IN G W I L L BE USED IWSCO UT = . T R U E . S E L E C T THE S C O U T IN G I N T E R V A L IN T S C T = 7 S E L E C T I N I T I A L MOTH POP L E V E L ( L O W - O . 1 , M E D - 1 . 0 . H I - 1 0 . 0 ) SCMPOP=1 . 0 S E L E C T THE GROWER PROBLEM P E R C E P T I O N FOR M I T E S GPP=9.0 C C S E L E C T S TR A TE G Y C O M B I N A T I O N S C O N T IN U E 100 IG O = O I F I S T R A T . E O - 5 . A N D - K S T R A T . E Q . 2 . A N D . J S T R A T . E Q . 2 ) IG O = 1 C IF IS T R A T . EO. 5 . A N D -KS T R A T. EQ. 2 . AND. J S T R A T . E O . 1 IIG O = 1 C IF IS T R A T . EO. 5 . A N D .KS TR A T. EO. 3 . AND. JS T R A T . E Q .2 ) IG O = 1 C IF IS T R A T .E O .5 . A N D .K S T R A T .E O .1 2 . A N D .J S T R A T .E O .1 )IG O = 1 C C I F IS T R A T . E O . 5 . A N D .K S T R A T .E O .1 2 . AN D . J S T R A T . E O . 1 3 ) IG 0 =1 IF K S T R A T. G T . 0 ) IG 0 = 1 CC IF JS T R A T . G T . 3 . AND. JS T R A T . L T . 8 ) IG O = 1 CC I F J S T R A T . G T . 1 0 . A N D . J S T R A T . L T . 1 5 ) IG 0 = 1 CC I F I S T R A T . E O . 5 . A N D . K S T R A T . E O . 1 3 . A N D . J S T R A T . E O . 1 ) IG O C IF IS T R A T .E O .5 . A N D .K S T R A T .E Q .1 3 . AND. JS T R A T . E O .1 3 ) IG 0 = C I F I S T R A T . E O . 7 . A N D . K S T R A T . E O . 2 . A N D . J S T R A T . E O . 1 j 1 GO =1 C I F I S T R A T . E O . 7 . A N D . K S T R A T . E Q . 2 . A N D . J S T R A T . E O - 2 ) IG O = 1 C IF IS T R A T . EO. 7 . AND. KSTR AT. EO. 3 . AND. JS T R A T . EO. 2 ) I G 0 = 1 C IF IS T R A T .E O .7 . A N D .K S T R A T .E O .1 2 . A N D .J S T R A T .E O .1 )IG O = 1 C I F IS T R A T .E O -7 . A N D .K S T R A T .E Q .1 2 . AND. J S T R A T . E O . 1 3 ) IG 0 =1 C I F I S T R A T . E O . 7 . A N D . K S T R A T . E O . 1 3 . A N D . J S T R A T . E O . 1 ) IGO = C IF IS T R A T .E O .7 . A N D .K S T R A T .E O .1 3 . AND. JS T R A T . E O .1 3 ) IG 0 = c I F I S T R A T . E O . 8 . A N D . K S T R A T . E O .2 . A N D . J S T R A T . E O . 2 } IG O = 1 C IF IS T R A T .E O -8 . A N D .K S T R A T .E O .3 . A N D .J S T R A T .E 0 .2 J IG 0 = 1 C I F IS T R A T . E O .8 . AND. K S T R A T . EO. 2 . ANO. J S T R A T . EQ. 1 ) I G 0 = 1 c IF IS T R A T .E O .8 . A N D .K S T R A T .E Q .1 2 . A N D .J S T R A T .E O .1 )IG 0 = 1 c IF IS T R A T .E O .8 . A N D .K S T R A T .E O .4 . A N D .J S T R A T .E O .1 3 ) IG 0 =1 c I F I S T R A T . E O . 8 . A N D . K S T R A T . E O . 1 3 . A N D . J S T R A T . E O . 1 ) IG O = c IF IS T R A T .E O .8 . A N D .K S T R A T .E O .1 3 . A N D .JS T R A T . E O .1 3 1 IG 0 = c IF I S T R A T . E O . 5 . A N D . J S T R A T .E O .1 3 ) IG 0 = 1 c I F IS T R A T . E O . 7 . A N D . J S T R A T .E O .1 3 ) IG 0 = 1 c IF IS T R A T .E Q .8 . A N D .J S T R A T .E O .1 3 ) IG 0 =1 c I F IS T R A T . E O . 5 . A N D .J S T R A T .E O .2 ) IG 0 = 1 c IF IS T R A T .E 0 .7 .A N D .J S T R A T .E O .2 ) IG 0 = 1 c IF I S T R A T . E O . 8 . A N D .J S T R A T .E O .2 ) IG 0 = 1 c IF ? J S T R A T . E O - 2 ) IGO= 1 I F I J S T R A T . G T . 3 . A N D . J S T R A T . L T . 1 5 ) IG O = 1 IF (J S T R A T .E O .6 ) IG 0 = 0 I F ( JS T R A T .G T . 7 . AND. JS T R A T . L T . 1 1 ) IG 0 = 0 RETURN END PROGRAM A P P E S T (T APE 1 .O U T P U T . T A P E 4 ) A P P L E P E S T MODEL S I M U L A T E S A C T I O N OF S C A B . M I T E AND C O D D L IN G MOTH OVER 2 0 - Y E A R P E R I O D FOR V A R I O U S CONTROL S T R A T E G I E S S U B R O U T IN E S : IN IT IA L IZ A T IO N S GETWET - GETS NA TURE DA TA IN IT - I N I T I A L I Z E S V A R I A B L E S A N N U A LL Y TR E E S STAGE - D E T E R M IN E S STAGE OF GROWTH FROST - C A L C U L A T E S FROST DAMAGE FOR DAY SCAB to O 20 25 30 35 40 45 50 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C S C A B IN F APPLY SCABDAM RESULTS ECON STATS - D E T E R M IN E S L E V E L OF SCAB I N F E C T I O N FOR DAY I M P L E M E N T S S P R A Y I N G S TR ATE GY C A L C U L A T E S Y I E L D LOS S E S AND A P P L I E S S P E C I A L CALCULATES CALCULATES A NNU AL L O S S . C O S T , AND REVENUE MEANS AND SOS ( C A L L S C A L C ) ARRAY ( 1} (2 ) (3 ) (4) - C I P R O I N D I C A T E S D AYS OF P R O T E C T IO N F O R : - FULL O IF O L - REDUCED D I F O L H A LF CAPTAN F U L L CA PT AN (5) - B E N L A T E ( 6 ) - 1 / 3 S TR E N G TH P L I C T R A N (7 ) 1 / 2 STR ENGT H P L IC TR A N ( 8 ) - F U L L STR ENGT H P L I C T R A N ( 9 ) - F U L L STRENGGTH C A RZ OL ( 1 0 ) - P Y R E T H R O ID TR E A TM E N T FOR C O D L I N G MOTH ( it ) - B E N L A T E IM P A C T S ON M I T E S ( 1 2 ) - G U T H IO N A R RAYS I N F L E V AND I N F P E R I N D I C A T E I N F E C T I O N L E V E L ( O = N 0 N E . 1 “ L I G H T , 2 = M 0 D E R A T E . 3 = H E A V Y ) AND I N F E C T I O N ( 0 = N 0 . 1 = Y E S ) R E S P E C T IV E L Y FOR: (1 ) - TODAY (2 ) - Y E S T ER D A Y (3 ) - DA Y BEFORE Y E S T ER D A Y 60 65 70 75 10 C 85 oo noi 20 95 P E R IO D LO G IC A L D E B U G .M O T H ,M IT E .S C A B .IW S C O U T .H S P R A Y COMMON / N A T U R E / Y I E L D ! 2 0 ) . F P R I C E ( 2 0 ) , P P R I C E I 2 0 ) , P R E C < 1 6 8 . 2 0 ) . A T E M P ( 1 6 8 . 2 0 ) , O D A Y S ,T O D D A Y S , S D D A Y S I2 0 ) . N E T R E V !2 0 ) COMMON / A C C U M / S T R A T S ( 2 0 ) . S T R A T S S ( 2 0 ) . G R A N D S ( 2 0 ) , G R A N D S S ( 2 0 ) . + N S T R A T . N G R A N D , NACCUM COMMON / T R E E / I S T A G E . F O F R U I T . S D F R U I T . C D F R U I T . D M F R U I T . T Y I E L D C OM M ON /C M S CO UT / T H E A T , M O T H K I L , M S P R A Y , E C M 1 . E C M 2 . E C M 3 . + C M L E V E L . L U C K , C M L O S S , I T E R A T . O L O . WORMAPL COMMON / S C A B 6 A T / I N F L E V ( 3 ) , I N F P E R ( 3 ) . N I N F COMMON / C H E M S / B E N L A T E .C A P T A N .D IF O L + . P L I C T R N , C A R Z O L . G U T H I O N . P Y R T H R D , I P R O ( 1 2 ) . NSPRA Y . M I S S S P . N E X T S P COMMON / D A T E / I D A Y . d D A Y . i Y R . I S T R A T . J S T R A T . K S T R A T . I P A R T COMMON / D B / D E B U G . M O T H . M I T E . S C A B . I W S C O U T . H S P R A Y . I N T S C T D A T A N S T R A T . NGRAND / 2 * 0 / DATA NEXTSP / 9 9 9 / DATA N S C A B .N M IT E .N M O T H / 1 1 . 1 7 . 1 9 / NACCUM = 2 6 DO 1 0 I - 1 . NACCUM STRATSU j= 0 .0 S T R A T S S !I ) * 0 . 0 G R A N D S ?I) = 0 . O G R A N O S S ? I) = 0 . O C O N T IN U E D E BU G ". F A LS E . + 90 (C A LLS V A R I A B L E I S T A G E I N D I C A T E S GROWTH STAGE OF T R E E : 1 = THROUGH GREEN T I P 2 = GREEN T I P TO 1 / 2 " GREEN 3 = 1 / 2 " GREEN TO T I G H T C L U S T E R 4 = T I G H T C L U S T E R TO P I N K 5 = P I N K TO BLOOM 6 = BLOOM TO P E T A L F A L L 7 = A FT E R P E T A L F A L L 55 80 SPRAY NYEAR=20 M IS S S P = 0 I F CD E B U G ) N Y E A R - 1 0 C A L L SELECT I I G 0 . 1 ) I F ( . N O T . M OTH)NMOTH = 1 I F ( . NOT.SCABJNSCAB = 1 I F I . N O T . M IT E )N M IT E = 1 I F ( S C A B . O R - M I T E . O R . MOTH)GO TO 2 0 P R IN T 9 0 0 STOP C O N T IN U E GET NATU RE DA TA C A L L GETWET B E G I N S TR A TE G Y LOOP 1 0 0 DO 5 0 0 I S T R A T = 1 . N S C A B DO 5 0 0 J S T R A T 1 .N M IT E 0 0 5 0 0 KSTRAT = 1.N M 0TH C A LL SELECT ( I G O . 2 ) I F ( I G O . E Q . O ) G O TO 5 0 0 10O I F ( I S T R A T . N E . 3 . 0 R . J S T R A T . N E . 71 GO TO 5 0 0 C A L L RANDOM I F ( M I T E ) C A L L MSTR AT I F ( M O T H ) C A L L CMSTRAT P R IN T 1 0 0 0 . IS T R A T .J S T R A T .K S T R A T P R IN T 12 0 0 D E B U G = .F A L S E . C 105 C B E G I N A N N U A L LOOP DO 4 0 0 1 Y R * 1 . N Y E A R CALL I N I T T Y IE L O = Y IE L O ( IY R ) CALL C M IN IT D D A Y S = S D D A Y S (IY R ) C B E G I N D A I L Y LOOP DO 3 0 0 J D A Y = 9 0 . 2 4 5 ID A V = JDAY - 8 9 110 115 120 C C C C I F ( I Y R ; E o V l EA N D . I S T R A T . E O . 1 ) D E B U G = . T R U E . DEBUG=. TRUE. _ . „ I F ( J D A Y . G T . 2 1 3 ) DEBUG=. F A L S E . I F I J D A Y . G T . 2 0 5 ) DEBUG=. F A L S E . C A L L DDAY C A L L STAGE 125 C + 130 I F ( IS TA G E 1 E O .B .A N D .M O T H ) T Y IE L D ) I F ( S C A B (C A L L S C AB IN F I f i f 135 140 145 : 133: SSS:SStf IS S tt 85? & n ! M I T E : A N D ^ i S s c 6 u T A 0 R GM 0 T H V c A V s C 0 U T ( I D A Y . J S T R A T ) CALL S T A T S (1 ) ° W R IT E ( 4 , 5 0 0 0 ) K S T R AT ,N E TR E V 5000 F 0 R M A t(2 X .1 2 .2 0 1 6 ) 500 C O N TIN UE C END S T R A T E G Y LOOP C P R IN T 1 1 0 0 C C F IN A L STATS P R IN T 1 2 0 0 % CALL S T A T S (2 ) 160 C C C I F { .N O T .S C A B ) S C A B = .F A L S E . NSCAB=3 900 1000 + 1100 200 170 W ° C A L L ECON 400 C O N TIN U E C END A N NU A L LOOP 155 165 C O D M O T H (A T E M P (ID A Y . I Y R ) . ^ i ^ i g G V p R l I ^ - g O w ’ lS T R A T ^ IY R T jD A Y .A T E M P lID A Y .IY R )^ + P R E C (lo iv Y . IY R ).D O A Y S .IS T A G E , IN F L E V ,IN F P E R ,IP R O .N E X tS P .N S P R A Y , + S D F R U IT .F D F R U lt.B E N L A T E ,C A P T A N .D IF O L 9000 FORMAT( “ D A I L Y : " . 1 1 . 1 2 . 1 4 , F 4 . 1 . F 4 . 2 . F 4 . 0 , 2 1 1 3 . 5 F 8 . 2 ) 300 C O N T IN U E C END D A I L Y LOOP C 150 CALL STOP "E N D OF D E B U G ” F 0 R M A T ( 1 H 1 . ” A L L MODELS D I S A B L E D . F O R M A T } 1 5 H 1 S C A B S TR A TE G Y . 1 2 / 15 H M I T E S T R A T E G Y . 1 2 / . . . CHECK V A L U E S OF M I T E . M O T H . S C A B ” ) + F 0 R M A T ( 1 H 1 ? ” RS T A T I S T I C S FOR A L L S T R A T E G I E S C O M B I N E D ” / / ) F0RMATJ53H PR ED IC T ED FROST SCAB MOTH . NET fM S H + 54H M IT E T O T A L NUMBER B E N - C A P P L IC C A R - GUTH t t + 53H P Y R Y I E L D N T DAMAGERDAMAGEED A ^A G E Y IE L D P R IC E P R IC E 5 4 H DAMAGE REVENUE OF LATE TAN D IF O L TRAN ZO L IO N 29 H ETH R O ID COSTS COSTS REVENUE / PROC ~ + 5H Y E A R , 5 ( 7 H ( B U ) ).3 (7 H (*) ).6 H + 6H ( L B ) . 6H ( G L ) , 4 ( 6 H ( L B ) > , 1 X . 3 ( 7 H + 1H . 6 H -------------, 1 3 ( 1 O H ..................... ) ) END 175 CARD N R . S E V E R IT Y D E T A IL S D IA G N O S IS C ONTRO L CONTROL CONTROL CON TRO L CON TRO L 94 95 96 109 116 S U B R O U T IN E (f) , 6 H S P R A Y S ,5H ($ ) ) / (O Z ) OF PROBL EM V A R IA B LE V A R IA B L E V A R IA B L E V A R IA B L E V AR IA B LE IN IN IN IN IN COMMON COMMON COMMON COMMON COMMON OR OR OR OR OR EQ U IV AL EN C E D , EQ U IV AL EN C E D . E Q U IV ALEN C E D , E Q U IV A L EN C E D . E Q U IV A LE N C E D , O P T IM IZ A T IO N O P T IM IZ A T IO N O P T IM IZ A T IO N O P T IM IZ A T IO N O P T IM IZ A T IO N MAY MAY MAY MAY MAY BE BE BE BE BE IN H IB IT E D . IN H IB IT E D . IN H IB IT E D . IN H IB IT E D . IN H IB IT E D . GETWET R EADS I N W E A T H E R . Y I E L D . AND P R I C E DA TA CARD TY P E ( I T ) 1 = T E M P , 2 = P R E C I P I T A T I N , 3 = Y I E L D . 4 = FR E S H P R I C E . 5 = PROCES SED P R I C E . 10 15 20 25 30 35 40 45 50 55 60 L O G I C A L D E B U G . M O T H . M I T E , S C A B . IW S C O U T . HSPRAY COMMON / D B / D E B U G . M O T H . M I T E . S C A B , I W S C O U T . H S P R A Y . I N T S C T COMMON / N A T U R E / Y ? E L D ( 2 0 ) , F P R I C E ! 2 0 ) , P P R 1 C E ( 2 0 ) . P R E C ( 1 6 8 . 2 0 ) . + A T E M P (1 6 8 . 2 0 ) .D O A Y S .T O D D A Y S . SDDAYSt 2 0 ) , N E TR E V?2 0 ) D IM E N S IO N D A T I 2 1 ) D A T A A T E M P .P R E C / 6 7 2 0 * - 9 9 . / DATA Y I E L D . F P R I C E , P P R IC E / 6 < ? « - 9 9 . / C d = Y E A R , K ■ F I R S T DAY ( d U L I A N ) R E A D ? 1 , 1 0 0 0 j l T , d , K . DAT 1 1000 F O R M A T ! 1 1 , 2 1 3 , 2 1 F 5 . 0 ) I F ( EOF( 1 ) ) 5 0 0 , 3 3 I F ? I T . G E . 1 . A N D . I T . L E . 5 ) G 0 TO 5 '.IT P R I N T * , ■ CARD T Y P E OUT OF R ANG E: STOP 5 GO TO ( 1 0 . 2 0 , 3 0 . 4 0 . 5 0 ) . I T C TEMP D A T A C N O T E : ATEMP AND PREC ARE IN D E X E D SUCH T H A T A T E M P ( 1 . Y R ) I S 9 0 T H DAY OF 10 C O N T IN U E DO 1 5 1 = 1 . 2 1 L = I+ K - 90 15 A T E M P (L.d)= D A T ( I ) GO TO C PREC D A TA 20 C O N T IN U E DO 2 5 1 * 1 . 2 1 L = I+ K - 9 0 25 P R E C (L ,d )= D A T (I) GO TO 1 C Y I E L D DA TA 30 C O N T IN U E DO 3 5 1 = 1 , 2 0 35 Y 1 E L D (I)= D A T (I) + 0 .0 GO TO 1 C FR E S H P R I C E 40 C O N T IN U E DO 4 5 1 = 1 . 2 0 , , 45 F P R IC E (I)= D A T (I) GO TO 1 C PROCESSED P R I C E 50 C O N T IN U E DO 5 5 1 = 1 . 2 0 55 P P R IC E ? I)= D A T ( I ) GO TO 1 C C C A L C U L A T E S T A R T I N G DDAYS ( S D D A Y S ) FOR EACH YEAR 500 DO 7 5 1 = 1 . 2 0 R 1= R A N F (-1) R2=RANF( - 1 ) Z = ( ( - 2 . *A L 0 G (R 1 ) ) * * ,5 )*C 0 S (6 .2 8 3 2 » R 2 ) S D D A Y S (I> = 580 . + 8 0 . *Z 75 C O N T IN U E C C CHECK NATURE DO l O O 1 = 1 , 1 6 8 DO 1 0 0 d = 1 . 2 0 I F ( A T E M P ( I . d ) . E Q . - 9 9 . ) G 0 TO 9 1 0 I F l P R E C t I . d ) . E Q . - 9 9 . ) G 0 TO 9 2 0 C O N T IN U E 1 00 GO CO 65 70 75 80 85 90 1 r; 10 15 1 5 1 C CH EC K OTHERS DO 2 0 0 1 = 1 , 2 0 I F ( Y I E L D ( I 5 . E Q . - 9 9 . ) G 0 TO 9 3 0 C S E T THE Y I E L D EQ UAL TO 5 0 0 S I N C E FROST C FOR V A R I A N C E I N Y I E L D . C Y IE L D !I ) = 500. I F ( F P R I C E ( I ) . E Q . - 9 9 . ) G 0 TO 9 4 0 I F ( P P R I C E ( I ) . E Q . - 9 9 . ) G 0 TO 9 5 0 200 C O N T IN U E C C CALL M IT E I N I T I F I M I T E ) C A L L IN T M IT E RETU RN C C ERROR MESSAGES 910 P R IN T IN C O M P L E T E STOP 920 P R IN T INCOMPLETE STOP 930 P R IN T * , * INCOMPLETE STOP 940 P R IN T IN C O M P L E T E STOP 950 P R IN T IN C O M P L E T E STOP END AND P E S T DAMAGE ACCOUNT TEMP D A T A : YEAR DAY " . I PREC D A T A : YEAR DAY " . I Y IE L D DATA" F P R IC E DATA” P PR IC E DATA" S U B R O U T IN E RANDOM COMMON / R A N S E E D / I R A N ( 5 ) C C S E T S SEE D S FOR 4 RANDOM S E R I E S : C (1 ) = SCAB IN F E C T IO N C (2 ) = SCAB DAMAGE C (3 ) = M IT E P E R C E P T I O N ERROR C (4 ) = M IT E M O N I T O R I N G ERROR I R A N I 1 ) = lO H A BC D E F G H Id I R A N I 2 ) = 10HY ZXWVUTSRQ I R A N I 3 ) = 10HA ZBY CXDW EV I R A N I 4 1 = 10 HZAYBXCWDVE I R A N I 5 ) = 10HMNOPORSTUV RETU RN END FUNCTION S R A N F ( I ) COMMON / R A N S E E D / I R A N ( 5 ) C S ET S S EE D TO RANDOM S E R I E S I , C AND S A V E S NEW SEED C A L L R A NS E T ( I R A N I I ) ) SRAN F = R A N F t - 1 ) C A L L RANGET ( I R A N ( I ) ) RETURN END S U B R O U T IN E C C C 5 10 15 ANNUAL 20 20 IS R A N F ) , IN IT IN IT IA L IZ A T IO N S COMMON / N A T U R E / Y I E L D I 2 0 ) , F P R I C E ! 2 0 ) . P P R I C E ! 2 0 ) , P R E C | 1 6 8 . 2 0 ) , + A T E M P I1 6 8 . 2 0 ) .D D A Y S . TODDAYS. S D D A Y S l2 0 ) , N E T R E V I2 0 ) COMMON / T R E E / I S T A G E . F D F R U I T . S D F R U I T . C D F R U I T . D M F R U I T . T Y I E L D COMMON / S C A B O A T / I N F L E V ( 3 ) , I N F P E R I 3 ) , N I N F COMMON / C H E M S / B E N L A T E .C A P T A N ,D IF O L + .P L IC T R N .C A R Z O L ,G U T H IO N .P Y R T H R D ,IP R O I1 2 ) .N S P R A Y .M IS S S P .N E X T S P C O MM ON /M I T E D A T / S A E R ( 2 0 ) , S A A F ( 2 0 ) . I A F D 1 2 0 ) . I E R D I 2 0 ) . + A E R , A A F . E P Y , A F F F R , Y Y , A F F C O N .E R lN d l3 ) , CON. + E M X ,E L P D P O (1 0 ),E R I(1 0 ).A F I|10) C O M M O N /M IT E D A 2 / I E C T H 1 . 1 E C T H 2 . X . N S C O U T . N X . K O N N . + IP C .IE R R O R .K E M X .S C C O S T C C C GETS RANDOM NUMBER **> IS T A G E = 1 N IN F = O DO 2 0 1 = 1 . 3 I N F L E V I I j =0 IN F P E R II)= 0 25 DO 3 0 1 = 1 . 12 IP R O (I) = O NEXTSP = 9 9 9 N S PR AY = O S C C 0 S T = 0 .0 30 30 C P LIC T R N = 0 . 0 CARZOL = 0 . 0 G U T H IO N = 0 . 0 PYR THRD = 0 . 0 BENLATE = 0 . 0 D IF O L = 0 .0 CAPTAN = 0 .0 S D F R U IT = 0 . 0 FD F R U IT = 0 . 0 C D F R U IT = 0 . 0 D M F R U IT = 0 . 0 35 40 C C C M IT E 45 50 55 60 65 IN IT IA L IZ A T IO N S DO 1 0 3 0 MY = 1 , 3 E R IN J (M Y )= 0 . 1030 C O N T IN U E YY=0. E M X = - 1. A F F C 0 N = 0 .0 DO 1 7 0 0 1 = 1 . l O E R I(I)= 0 .0 1 7 0 0 C O N T IN U E AER=0. AAF=0. C0N=0. K0NN=0 NX=8 E P Y = 0 .0 AFFFR=0. NSCOUT= 0 EPY=AER* 1. 107 KEMX=0 R E TU R N END 1 S U B R O U T IN E C C C 5 10 15 1 5 10 15 1 «*» 01 ATTEN REDUCE S D A YS OF P R O T E C T I O N (IP R O ) FOR A L L C H EM IC ALS D A IL Y COMMON / T R E E / I S T A G E , F D F R U I T . S D F R U I T . C D F R U I T . D M F R U I T . T Y I E L D COMMON / C H E M S / BEN LATE.C A P TAn .D IF O L + . P L I C T R N . C A R Z O L . G U T H IO N .P Y R T H R D . I P R O ( 1 2 ) . N S P R A Y . M I S S S P . NEXTSP DO 1 0 1 = 3 . 1 2 IP R O (I) - IP R O (I) - 1 , „ IF (IP R O ( I) .L T . O) IP R O (I) = O C O N T IN U E 10 C C FOR D I F O L . SPRAY I S A C T I V E U N T I L IF (IS T A G E . GE. 5 ) IP R O (2 )= 0 IF (IS T A G E .G E .7 )IP R O (1 )= 0 R ETURN END P IN K FOR H A L F AND P E T A L FALL FOR F U L L S U B R O U T IN E DDAY C C ACCU M U LA TE DEGREE DAYS ( B A S E 4 3 ) U S I N G AVG TEMP C COMMON / N A T U R E / Y I E L D ! 2 0 ) , F P R I C E ( 2 0 ) , P P R I C E ( 2 0 ) . P R E C ( 1 6 8 . 2 0 ) . + A T E M P ( 1 6 8 , 2 0 1 . D D A Y S . TODDA y S , S D D A Y S l 2 0 ) . N E T R E V ( 2 0 ) COMMON / D A T E / 1 D A Y , J D A Y , I Y R , I S T R A T . J S T R A T . K S T R A T . I P A R T TODD AYS = A T E M P { I D A Y . I Y R ) - 4 3 . I F ( TODDAYS) 1 0 , 1 0 , 2 0 10 RETURN 20 C O N T IN U E I F ( T O D D A Y S . G T . 4 3 . )T O D D A Y S = 4 3 DDAY S = DDAYS + TODDAYS R ETU RN END S U B R O U T IN E STAGE C 5 10 15 20 25 30 C F I N O S STA GE OF GROWTH OF TREE ( I S T A G E ) AS F U N C T I O N OF C DEGREE DAYS ( D D A Y S ) COMMON / T R E E / I S T A G E , F D F R U I T , S D F R U I T . C D F R U I T . D M F R U I T . T Y I E L D COMMON / D A T E / I D A Y . J D A Y , I Y R , I S T R A T , J S T R A T , K S T R A T . I PART COMMON / N A T U R E / Y I E L D ( 2 0 ) . F P R I C E ( 2 0 ) , P P R I C E ( 2 0 ) , P R E C ( 1 6 8 . 2 0 ) . + A T E M P (1 6 8 . 2 0 ) .D D A Y S .T O D D A Y S .S D D A Y S (2 0 ).N E T R E V (2 0 ) 1 F ( 1 S T A G E . G E . 8 ) RETURN GO TO ( 1 0 . 2 0 . 3 0 , 4 0 . 5 0 . 6 0 . 7 0 ) , I S T A G E C I S T A G E = 1 : THROUGH GR EEN T I P 10 I F ( D D A Y S . L T . 7 0 0 . JRETU RN C IS T A G E = 2 : GREEN T I P THROUGH 1 / 2 “ GREEN IS TA G E = 2 20 I F ( D D A Y S . L T . 7 5 0 . IR E T U R N C IS T A G E = 3 : 1 / 2 " GREEN THROUGH T I G H T C LU S T E R IS T A G E = 3 30 I F ( D D A Y S . L T . 8 0 0 . )R E T U R N C IS T A G E = 4 : T I G H T C LU S T E R THROUGH P I N K IS T A G E = 4 40 I F ( D D A Y S . L T . 9 0 0 ) RETURN C ISTAG E = 5 : P I N K THROUGH BLOOM IS T A G E = 5 50 I F ( D D A Y S . L T . 1 0 0 0 ) RETURN C IS T A G E = 6 : BLOOM THROUGH P E T A L F A L L IS T A G E - 6 60 I F ( D D AY S . L T . 1 100)R E TU R N C IS T A G E = 7 : AFTER PETAL F A LL IS T A G E = 7 IP F = JD A Y RETU RN 70 C O N T IN U E I F ( ( J D A Y - I P F ) . G T . 7 ) IS TA G E =8 END 1 S U B R O U T IN E FROST C C C A L C U L A T E S FROS T DAMAGE D A I L Y AS F U N C T I O N OF TEMP AND STAGE C ASSUMES M I N I M U M TEMP 1 0 DEGREES BELOW AVERAGE W 5 COMMON / N A T U R E / Y I E L D ( 2 0 ) , F P R I C E ( 2 0 ) . P P R I C E ( 2 0 ) , P R E C ( 1 6 8 . 2 0 ) , + A T E M P (1 6 8 . 2 0 ) . D D A Y S .T O D D A Y S .S D D A Y S (2 0 ). N E T R E V (2 0 ) COMMON / T R t E / f S T A G E . F D F R U I T . S D F R U I T , C D F R U I T , O M F R U I T , T Y I E L D COMMON / D A T E / I D A Y . J D A Y . I Y R , I S T R A T . J S T R A T . K S T R A T , I P A R T D IM E N S IO N A 1 ( 6 ) , B 1 1 6 ) DATA A T / 1 2 . 7 5 . 3 0 9 0 7 . . 1 . 1 2 5 E 8 . 1 . 5 1 2 E 9 , 9 . 3 1 3 E 1 3 . 1 . 7 7 7 E 1 6 / D ATA - B I / . 3 0 6 , . 5 7 4 4 , 1 . 2 5 . 1 . 1 4 8 7 5 , 1 . 1 4 8 7 5 , 1 . 3 1 2 8 6 / 10 C 15 20 25 1 5 10 15 DA TA TLOW / 7 . 0 / C NO DAMAGE A F T E R P E T A L F A L L IF (IS T A G E .G E .7 J R E T U R N DAMPER = 1 . 7 ( 1 . + A I ( I S T A G E ) * E X P ( - B I ( I S T A G E ) + ♦ (A T E M P (ID A Y .IY R )-T L O W ))) I F 1 0 A M P E R . G T . . 9 9 JRETU RN I F t O A M P E R . L T . . 2 5 ) D A M P E R =.2 5 FD = ( 1 . - DAMPER) * T Y IE L D T Y I E L D = T Y I E L D - FD F D F R U I T * F D F R U I T + FD I F ( T Y IE L D . L T . 0 . )T Y IE L D = 0 . R ETURN END S U B R O U T IN E S C A B I N F C C F I N D S SCAB I N F E C T I O N L E V E L ( I N F L E V ) AS F U N C T I O N OF PREC AND ATEMP C S C A B I N F = Q - N O N E . 1 - L I G H T , 2 - M O D E R A TE . 3 - HE AV Y C A LS O U P D A T E S I N F P E R ( I N F E C T I O N P E R I O D F L A G ) C COMMON / N A T U R E / Y I E L D ( 2 0 ) , F P R I C E ( 2 0 ) . P P R I C E ( 2 0 ) . P R E C ( 1G 3 . 2 0 ) . + ATEMP( 1 6 8 . 2 0 ) .D D A Y S .T O D D A Y S .S D D A Y S (2 0 ).N E T R E V M 2 0 ) COMMON / C H E M S / B EN LAT E . CAPTAN. D IF O L + . P L I C T R N . C A R Z O L . G U T H I O N . P Y R T H R D . I P R O ( 1 2 ) . N S P R A Y . M I S S S P . N E XT SP COMMON / S C A B D A T 7 I N F L E V ( 3 ) , I N F P E R I 3 ) , N I N F COMMON / D A T E / I D A Y . J D A Y . I Y R . I S T R A T . J S T R A T . K S T R A T . I P A R T D IM E N S IO N T L E V 1 3 ) . P L E V ( S ) . P R O B (3 . 2 5 . 3 ) D A TA T L E V / 4 5 . , 5 5 . , 6 5 . / DATA PLE V / . 0 1 . . 1 . . 3 . . 5 . 1 . 0 / DATA ( ( P R 0 B ( I . J . 1 ) . I = 1 . 3 ) . J = 1 . 2 5 > / + 1 .0 .1 .0 .1 .0 . 1 .0 .1 .0 .1 .0 . 1 .0 .1 .0 ,1 .0 , 1 .0 ,1 .0 ,1 .0 . + .938.1.0.1.00. .91 1 . .9 7 3 .1 .0 0 , .927,.958..979. .9 4 1 ..9 7 1 . 1.00. O'. 20 25 30 35 40 45 50 55 60 65 70 75 + + + + + .8 2 1 ..9 2 9 ..9 6 4 ..8 6 1 ..9 4 5 ..9 4 5 . .8 4 5 ..9 2 1 ..9 7 9 . . B75..9 5 8 ..9 5 8 . .7 5 0 ..8 3 3 ..8 3 3 ..7 9 1 ..8 3 3 ..8 7 5 . .7 5 0 ..8 7 5 ..9 7 9 . . 8 3 3 . . 9 5 8 . 1 . OO. .7 5 0 .1 .0 0 .1 .0 0 ..7 7 8 ..9 1 7 ..9 7 2 . .7 5 0 ..7 7 8 ..9 4 5 . .8 7 5 .1 .0 0 .1 .0 0 . .7 6 9 ,.8 4 6 ..8 8 5 ..8 7 5 ,.8 7 5 ..8 7 5 . .7 5 0 ,.8 4 4 ..9 0 6 . .7 5 0 ..8 3 3 ..8 3 3 . 1 .0 0 .1 .0 0 .1 .0 0 / DATA ( (P R O B ( I , J , 2 ) . I = 1 , 3 ) . J = 1 , 2 5 ) / + .8 0 6 ..9 4 5 ..9 7 3 . .7 7 8 ..8 4 1 ..9 3 6 . .8 1 0 ..9 5 3 .1 .0 . + .8 3 3 ,.9 5 8 ..9 5 8 , .7 5 0 .1 .0 0 .1 .0 0 . .6 4 3 ..6 6 8 ..7 7 5 ..7 0 8 ..8 3 3 ..9 1 6 + ,.7 6 5 ..8 8 3 ,1 .0 0 . .2 8 6 ..7 1 5 ,.8 5 8 . .4 4 4 ,.7 7 7 ,.7 7 7 ..3 8 5 ..6 9 3 ..9 2 4 + ..5 0 0 ,.8 3 3 ,.8 3 3 , 0 . O O ,. 3 3 3 . . 3 3 3 , . 1 6 7 , . 3 3 3 . . 5 0 0 . O .O O . . 5 0 0 , . 9 1 7 + . . 3 3 3 . . 8 3 3 , 1 .O O . 0 . 0 0 . 1 . 0 0 , 1 . 0 0 , . 1 11, . 6 6 6 . . 8 8 8 . O . O O ..1 1 1 ..7 7 8 + ..5 0 0 ,1 .0 0 .1 .0 0 , .0 7 6 ,.3 8 4 ..5 3 8 , .5 0 0 ..5 0 0 ..5 0 0 .O.0 0 ..3 7 5 ..6 2 5 + .0 .0 0 ,.3 3 3 ,.3 3 3 . .8 7 5 ..8 7 5 ..8 7 5 / DATA I ( P R O B ( I , J . 3 ) . 1 = 1 , 3 ) . 0 = 1 . 2 5 ) / + 1 .0 .1 .0 .1 .0 . 1 .0 .1 .0 ,1 .0 , 1 .0 ,1 .0 .1 .0 . 1 .0 ,1 .0 .1 .0 . + .8 7 5 .1 .0 0 .1 .0 0 ..8 2 0 ..9 4 5 .1 .0 0 . .8 5 5 ..9 1 7 ..9 5 9 . .8 8 2 ..9 4 1 .1 .0 0 . + .6 4 3 ..8 5 7 ,.9 2 9 ..7 2 3 ..8 8 9 ..8 8 9 . .6 8 9 ..8 4 3 ..9 5 9 . .7 5 0 ..9 1 7 ..9 1 7 . + .5 0 0 ..6 6 7 ,.6 6 7 ..5 8 3 ..6 6 7 ..7 5 0 . .5 0 0 ..7 5 0 ..9 5 9 . .6 6 7 ..9 1 7 .1 .0 0 . + .5 0 0 .1 .0 0 ,1 .0 0 ..5 5 6 ..8 3 3 ,.9 4 5 . .5 0 0 ..5 5 5 ..8 8 9 , .7 5 0 .1 .0 0 .1 .0 0 . + .5 3 8 ..6 9 2 ..7 6 9 ..5 0 0 ,.5 0 0 ..5 0 0 . .5 0 0 ..6 8 7 ..8 1 3 , .5 0 0 ..6 6 7 ..6 6 7 . + 1 .0 0 .1 .0 0 .1 .0 0 / C THE V A R I A B L E PROB I S THE P R O B A B I L I T Y OF AN I N F E C T I O N - I T I S A THREE C D I M E N S I O N A L ARRAY W I T H THE F I R S T D I M E N S I O N THE I N F E C T I O N L E V E L . THE SE C D I M E N S I O N B E I N G THE WEATHER CATEGORY AND THE L A S T D I M E N S I O N I S THE PAR C PAR T OF THE S E A S O N . I F ( J D A Y . G T . 9 6 ) GOTO 5 LEVEL=0 I C A T =1 GO TO 3 0 0 5 IC A T = 2 5 R= S R A N F ( 1 ) LEVEL=0 C F I N D P AR T OF SEASON JD A Y = I D A Y + 8 9 IP A R T = 1 I F ( J D A Y . L T . 1 2 1 ) G 0 TO 1 IP A R T = 2 I F I J D A Y . L T . 1 6 7 ) G 0 TO 1 IP A R T = 3 I F ( J D A Y . L T . 2 1 3 ) G 0 TO 1 IP A R T = 4 1 C O N T IN U E I F ( A T E M P ( I D A Y . I Y R ) . L E . 3 5 . ) GO TO 1 0 0 C F I N D TEMP CATEGORY DO 1 0 I T = 1 , 3 I F ( A T E M P ( I D A Y , I Y R ) . L T . T L E V ( I T ) ) GO TO 2 0 10 C O N T IN U E IT = 4 C F I N D PR EC CATEGORY 20 DO 3 0 I P * 1 , 5 I F ( P R E C ( I D A Y , I Y R ) . L T . P L E V ( I P ) ) GO TO 5 0 30 C O N T IN U E IP = 6 C F IN D IC A T 50 IC A T = ( I P - 1 ) • 4 + I T I F ( I C A T . G E . 1 . A N D . I C A T . L E . 2 5 ) G 0 TO 1 0 0 P R I N T * " I C A T OUT OF R A N G E : ".IC A T ,". TEMP = ", + A T E M P (ID A Y , IY R ) . " . R A IN = " . P R E C (ID A Y . IY R ) STOP C 80 CHECK SPRAY E F F E C T S ON I N F E C T I O N 1 0 0 I F ( I P A R T . E O . 4 . A N D . N I N F . L E . 2 )G 0 DO 1 0 1 1 = 1 . 5 I F ( I P R 0 1 I ) . G T . 0 ) G 0 TO 3 0 0 10 1 C O N T IN U E 85 C USE 103 90 110 95 120 C C B R IN G IN F L E V 300 IN F L E V ? 3 } IN F L E V 1 2 ) LEVEL TO 3 0 0 I C A T AND PROB TO F I N D I N F E C T I O N B AS E D ON RANDOM NU MB ER , C O N T IN U E K = IP A R T I F ( K . E O -4 )K =2 DO 1 1 0 1 = 1 , 3 I F ( R . L T . P R O B ( I , I C A T , K ) ) GO TO 1 2 0 C O N T IN U E LEVEL = 3 GO TO 3 0 0 LEVEL = 1 - 1 UP TO DA TE = IN F L E V ( 2 ) = I N F L E V ( 1) R «*> “ 1 ^ C 100 C C 1 S U B R O U T IN E C C C C 25 30 35 40 45 50 55 60 (= 1 IF TEMP GT 3 6 IM PLEMENTS AND PREC GT .0 1 . I.E .. IC A T GT 4 ) . A N D .IC A T .N E . 2 5 ) IN F = 1 IN F P E R I2 j IN F P E R I1) IN F EOUAL TO O IF BENLATE A C T IV E APPLY S P R A Y I N G S TR A TE G Y A C C O R D IN G TO IS T R A T COMMON / N A T U R E / Y I E L D I 2 0 ) . F P R I C E I 2 0 ) . P P R I C E 1 2 0 ) , P R E C I 1 6 8 . 2 0 ) . + A T E M P !1 6 8 . 2 0 ) .D D A Y S . TO DD A YS,SD D A YS t 2 0 ) . N E T R E V I2 0 ) COMMON / T R E E / I S T A G E , F D F R U I T , S D F R U I T . C D F R U I T . D M F R U I T . T Y I E L D COMMON / S C A B D A T / I N F L E V I 3 ) . I N F P E R I 3 ) . N I N F COMMON / C H E M S / B E N L A T E .C A P T A N ,D IF O L + . P L IC T R N ,C A R Z O L ,G U T H IO N .P Y R T H R D ,IP R O I1 2 ) .N S P R A Y .M IS S S P .N E X T S P COMMON / D A T E / I D A Y , J D A Y . I Y R . I S T R A T . J S T R A T . K S T R A T . I P A R T DATA M ID D L E / 1 6 6 / 10 20 = LEVEL C C S E T TH E I N F E C T I O N P E R I O D P R E D I C T O R DO 3 5 0 1 = 1 . 3 35 0 IF IIP R O 1 5 ) .G T .2 ) IN F P E R (I)= 0 RETURN END 5 15 IN FPER C O N T IN U E IN F = 0 IF (IC A T .G T . 4 IN F P E R I3 ) = IN F P E R I2 ) = IN F P E R I1) = 105 1 10 IN F L E V (I) UPDATE W H IC H S T R A T E G Y ? ID A Y = JDAY - 8 9 GO TO 1 1 0 0 , 2 0 0 , 3 0 0 , 3 0 0 . 5 0 0 , 3 0 0 , 7 0 0 . 2 0 0 , 9 0 0 , C S TR A TE G Y 1 100 C O N T IN U E R ETURN 9 0 0 .1 0 0 0 ) IS T R A T DO N O T H IN G C S TR A TE G Y 2 - D I F O L A T GREEN T I P . T H E N C A P T A N EVERY C S TR A TE G Y 8 - S A M E . B U T LOWER O l f O L DOSE 200 C O N T IN U E I F ( J D A Y . G T . 9 0 ) GO TO 2 0 1 ID T F O L * 1 N E X T = 9 -3 9 9 I F ! I S T A G E . G E . 2 ) G 0 TO 2 2 5 201 C O N T IN U E C CHEC K S P E C I A L SPRAY F L AG S I F I N E X T S P . E O . 9 9 9 . A N D . M I S S S P . E O . O ) G O TO 2 1 0 NEXT = JDAY + 7 R E TU R N 210 C O N T IN U E C CHECK I N F E C T I O N L E V E L I F ( I N F L E V ( 3 ) . L E . O > G O TO 2 1 5 NEXT * 9 9 9 R E TU R N 215 C O N T IN U E I F l I S T A G E . L T . 2 . A N D . J D A Y . G E . 9 9 ) GO TO 2 2 0 IF !IS T A G E - 2 ) 2 9 0 . 2 2 0 . 2 2 0 C C P A S T GREEN T I P 220 C O N T IN U E I F I I D I F O L . E O . O ) GO TO 2 3 0 C SPR A Y D I F O L I F N E CE SSAR Y I F I P R E C I I D A Y . I Y R ) . G E . . 0 2 )R E T U R N 225 ID IF O L = 0 I F ( I S T R A T . E Q . 2 ) D I F 0 L = D IF O L ♦ 5 I F I I S T R A T . E Q . 8 D IF O L = D IF O L + 3 I F I I S T R A T . E Q . 2 IP R O I 1 )= 1 I F I I S T R A T . E O . 8 ) IP R O I 2 )= 1 N S PR A Y = NSPRAY + 1 R ETURN 230 C O N T IN U E I F ( I S T R A T . E O - 8 ) GO TO 2 3 3 IF IIS T A G E - 7 ) 2 9 0 , 2 5 0 ,2 5 0 233 IF IIS T A G E - 5 ) 2 9 0 , 2 5 0 .2 5 0 C C PAST P E T A L F A L L 250 C O N T IN U E I F ( N E X T . E O . 9 9 9 9 )N E X T = JD A Y I F I P R E C ( I D A Y . I Y R ) . G E . . 0 2 )R E T U R N 14 D AYS AFTER PF , , *2 Oo w 65 70 75 265 80 275 290 85 90 95 10O 105 110 IF (J D A Y .G T .2 1 9 .A N D .N IN F .L T .2 )R E T U R N I F ( J D A Y . L T . N E XT)R E TU R N IC 0 V E R = 3 I F ( IS T R A T . E O .8 ) 1C0VER=5 NEXT=JDAY + 7 I F I I P A R T . G T . 2 ) N E X T * J D A Y + 14 I F ( N S P R A Y . G T . I C O V E R ) GO TO 2 6 5 I P R O ( 4 ) = 14 I F ( IP A R T . L T . 3 ) IP R 0 (4 )= 7 I F ( I P A R T . L T . 3 ) I P R O ( 4 ) =7 CAPTAN*CAPTAN + 8 . 0 IN F L E V (2 )= 0 GO TO 2 7 5 IP R O (3 )= 1 4 I F ( I P A R T . L T . 3 ) I P R O !3 ) = 5 CAPTAN = CAPTAN + 4 NSPR AY = NSPRAY + 1 IN F L E V (I) = O RETU RN C S TR A TE G Y 3 - C A P EVERY 7 D AYS T I L M I D S E A S O N : THEN EVERY C S TR A TE G Y 4 I S S A M E . B U T H A L F DOSE C S TR A TE G Y 6 I S B E N L A T E AND C A P T A N I N COMBO SAME T I M E 300 C O N T IN U E I F ( J D A Y . G T . 9 0 ) G 0 TO 3 0 1 NEXT = 1 0 0 301 C O N T IN U E C CHECK S P E C I A L SPRAY F L AG S I F ( N E X T S P . E Q . 9 9 9 . A N D . M I S S S P . E O . O ) G O TO 3 1 0 NEXT = JDAY + 7 R ETURN 310 C O N T IN U E C CH EC K I N F E C T I O N L E V E L I F ( I N F L E V ( 3 ) . L E . O ) G O TO 3 1 5 NEXT = 9 9 9 R ETU RN 315 C O N T IN U E I F J D A Y , L T . N E XT)R E TU R N I F P R E C ( I D A Y . I Y R ) . G T . . 0 2 )R ET U R N I F J D A Y . G T . 2 1 9 . A N D . N I N F . L T . 2 IR E T U R N I F I P A R T . L T . 3 ) N E X T * JDAY + 7 I F I P A R T . G E . 3 I N E X T = J D A Y + 14 IF IS T R A T -4 > 3 6 0 .3 5 0 .3 7 0 3 5 0 IP R 0 ( 3 )= 1 4 IF C IP A R T .L T .3 ) IP R 0 < 3 )= 5 CAPTAN=CAPTAN + 4 GO TO 3 8 0 3 6 0 I P R 0 ( 4 )= 14 I F ( IP A R T .L T . 3 ) IP R 0 (4 )= 7 CAPTAN=CAPTAN + IN F L E V (2 )» 0 GO TO 3 8 0 370 IP R 0 (5 )*1 4 IF fIP A R T . L T .3 ) IP R 0 ( 5 )= 7 I P R O ( 1 1 ) = 14 B E N L A T E “ B E N L A T E + 12 CAPTAN = CAPTAN + 4 IN F L E V (2 )= 0 IN F L E V (3 )= 0 3 8 0 N S P R A Y “ N SPR AY + IN F L E V (1 )= 0 RETURN 14 DAYS 8 115 120 125 130 135 140 C S TR A TE G Y 5 - A P P L Y B E N L A T E WHEN I N F P E R . U N L E S S SPR A Y ED YES TER D A Y 500 C O N T IN U E I F ( J D A Y . G T . 2 1 9 . A N D . N I N F . L T . 2 ) RETURN I F ( J D A Y . G T . 9 O ) G 0 TO 5 1 0 N E XT = 9 9 9 IY E S T = O 510 C O N T IN U E I F ( N E X T S P . N E . 9 9 9 . O R . M I S S S P . E O . 1 )R E T U R N I F I N E X T . L T . J D A Y ) G 0 TO 5 2 4 I F ( I Y E S T . N E . 1 ) G 0 TO 5 2 0 IY E S T = O RETU RN 520 I F ( I N F P E R I 2 ) . N E . 1 . A N D . I N F P E R I 3 ) . N E . 1 JRETURN I F i l P R O T s i . G E . 1 jR E T U R N 5 2 4 I F i I P R O I 5 ) . G E . 1 ) RETURN I F ( P R E C ( I D A Y . I Y R ) . L E . . 0 2 ) G 0 TO 5 2 5 U> U3 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 NEXT = JDAY RE TURN 525 C O N T IN U E C IN F P E R ( IN F E C T IO N P E R IO D ) NEXT = 9 9 9 IY E S T * 1 I P R O ( 5 ) = 14 IF (IP A R T . L T .3 ) IP R 0 (5 )= I P R O ( 11 ) = 14 B E N L A T E = B E N L A T E + 16 DO 5 3 0 1 = 1 , 3 530 IN F L E V (I) = O N SPR AY RE TURN = NSPRAY + - SPRAY 7 1 C S TR A TE G Y 7 - C A P T A N EVERY 7 D A Y S : H A L F DOSE A F T E R M ID S E A S O N 700 C O N T IN U E I F ( J D A Y . G T . 9 0 ) GO TO 7 0 1 N E XT = 1 0 0 701 C O N T IN U E C CH EC K S P E C I A L SPR AY F L AG S I F ( N E X T S P . E Q . 9 9 9 . A N D . M I S S S P . E O . O ) G O TO 7 1 0 NEXT = JDAY + 7 RETU RN 710 C O N T IN U E C CHECK I N F E C T I O N L E V E L I F ( I N F L E V ( 3 ) . L E . O ) G 0 TO 7 1 5 NEXT = 9 9 9 R ETURN 715 C O N T IN U E I F ( d D A Y . L T . N E X T JRETURN I F I P R E C (ID A Y . I Y R ) . G T . ,0 2 )R E T U R N I F ( J D A Y . G T . 2 1 9 . A N D - N I N F . L T . 2 JRETURN N E X T = dD A Y + 7 I F ( I S T A G E . G E . 7 ) N E X T = J D A Y + 14 I F ( I P A R T . L T . 3 . A N D - I S T A G E . G E . 7 ) NEXT = JDAY + 1 0 N SPR AY = NSPR AY + 1 I F ( I S T A G E . G E . 7 ) GO TO 7 2 5 IP R 0 ( 4 )= 1 4 IF (IP A R T . L T .3 ) IP R 0 (4 )= 7 CAPTAN=CAPTAN + 8 IN F L E V (2 )= 0 GO TO 7 5 0 725 IP R 0 (3 )= 1 4 I F ( I P A R T . L T . 3 ) IP R O ( 3 ) = 5 CAPTAN=CAPTAN + 4 I F ( I P A R T . L T . 3 . A N D . I S T A G E . G E . 7 ) CAPTAN=CAPTAN + 2 I F U P A R T . L T . 3 . AND. IS T A G E .G E .7 ) I P R 0 ( 3 ) = 7 C THE ABOVE S TA T E M E N T CORRECTS THE A P P L I C A T I O N A T 1ST COVER TO BE 6 L B S / A C R E 7 5 0 IN F L E V j1 )= 0 RETURN C * * S T R A T E G Y * 9 * -* D IF 0 L * A T * G R E E N * T Ip ! BENLATE*AT C S TR A TE G Y 1 0 - S A M E . B U T B E N L A T E A F T E R P I N K . 900 C O N T IN U E I F f d D A Y . G T . 2 1 9 . A N D . N I N F . L T . 2 JRETURN I F C d D A Y . G T . 9 0 ) GO TO 9 0 1 ID IF O L = 1 C I Y E S T = 1 I N D I C A T E S SPRAYED YES TER D A Y NEXT = 9 9 9 IY E S T = O I F ( I S T A G E . G E . 2 ) GO TO 9 2 5 901 C O N T IN U E . , I F ( N E X T S P - N E . 9 9 9 . O R . M I S S S P . E O . 1 JRETURN I F U S T A G E . L T . 2 . A N D . J D A Y . G E . 9 9 ) GO TO 9 2 0 IF IIS T A G E - 2 ) 9 9 0 . 9 2 0 .9 2 0 C C P A S T GREEN T I P 920 C O N T IN U E I F ( I D I F O L . E O . O ) GO TO 9 3 0 ‘ C SPRAY D I F O L I F ( P R E C ( I D A Y . I Y R ) . G T . . 0 2 JRETURN 925 ID IF O L = O IF C IS T R A T .E Q .9 ) D IF O L « D IF O L + 5 I F ( IS T R A T .E O . 10JD IFO L = D IF O L + 3 I F I I S T R A T . E Q - 9 ) IP R O ( 1) = 1 IF U S T R A T .E Q . 1 0 )IP R 0 (2 ) = 1 N S PR AY = NSPR AY + 1 RETURN IN F P E R AFTER PETA L LOW D I F O L DOSE FALL £ P? ° 930 C O N T IN U E I F C I S T R A T . E O . 1 0 ) G 0 TO 9 3 5 S TR A TE G Y 9 IF (IS T A G E - 7 ) 9 9 0 . 9 5 0 .9 5 0 C S TR A TE G Y 1 0 935 IF C IS T A G E - 5 ) 9 9 0 . 9 5 0 . 9 5 0 C C P A S T P E T A L F A L L (O R P I N K . I F 950 C O N T IN U E I F ( I Y E S T . E O . O ) GO TO 9 6 0 C 225 230 235 960 C 964 240 965 245 250 970 990 255 260 265 270 275 280 285 1 5 10) IY E S T = O RETURN C O N T IN U E IN FP E R ? I F ( N E X T . L T . U D A Y ) G 0 TO 9 6 4 I F ( I N F P E R ( 2 ) . N E . 1 . A N D . IN F P E R C 3 ) . N E . 1 )R E T U R N I F f I P R 0 I 5 ) . G E . 1 JR ETU RN I F ( P R E C ( I D A Y , I Y R ) . L E . . 0 2 ) G 0 TO 9 6 5 N E X T * dDAY RETURN C O N T IN U E I F ( I P R O ( 5 ) . G E . 1 JRETU RN N E XT = 9 9 9 IY E S T = 1 N SPR AY = NSPR AY + 1 1 P R 0 ( 5 ) = 14 IF ( IP A R T .L T . 3 ) IP R 0 ( 5 ) = 7 I P R O ( 11 > = 14 B E N L A T E * B E N L A T E + 16 DO 9 7 0 1 = 1 . 3 IN F L E V (I)= 6 RETURN C S TR A TE G Y 11 - - E R A D I C A T E W I T H B E N L A T E ( 1 6 O Z / A C ) WHEN THER E C I S AN I N F E C T I O N NOT WHEN C O N D I T I O N S HAVE B E E N R I G H T FOR AN C I N F E C T I O N TO O CCUR. ASSUMES P E R F E C T KNOWL EDGE. 1000 C O N T IN U E IF (d D A Y .G T .2 1 9 .A N D .N IN F .L T .2 ) R ETU RN I F C d D A Y . G T . 9 0 JGO TO 1 0 1 0 N E XT = 9 9 9 IY E S T = O 1010 C O N T IN U E I F ( N E X T S P . N E . 9 9 9 . O R . M I S S S P . E O . 1 JRETURN I F ( N E X T . L T . d D A Y ) G 0 TO 1 0 2 4 I F U Y E S T . N E . 1 j G 0 TO 1 0 2 0 IY E S T = O RETU RN 1020 I F ( I N F L E V ( 2 ) . E O . O . A N D . I N F L E V ( 3 ) . E O .O J R E T U R N IF (IP R 0 (5 ).G E .1 )R E T U R N 1024 I F ( I P R 0 T 5 ) . G E . 1 ) RETURN I F i P R E C ( I D A Y , I Y R ) . L E . . 0 2 ) G 0 TO 1 0 2 5 N E X T = dD AY RETU RN 1025 C O N T IN U E C IN FPER ( I N F E C T I O N P E R I O D ) - SPRAY N E X T >= 9 9 9 IY E S T = 1 I P R 0 ( 5 ) * 14 I F ( I P A R T . L T . 3 ) IP R 0 < 5 )= 7 IP R O (1 1 )» 14 B E N L A T E = B E N L A T E + 16 DO 1 0 3 0 1 = 1 . 3 1030 IN F L E V (I) = 0 NSPRAY = NSPR AY + 1 RETU RN END S U B R O U T IN E C C C C ^ l\j —* SCABDAM CALCULATES Y IE L D AS R E Q U I R E D . LO S S E S DUE TO SCAB DA MA GE. IF ANY. CALLS SPS PRAY COMMON / N A T U R E / Y I E L D ( 2 0 ) , F P R I C E ( 2 0 ) . P P R I C E ( 2 0 ) . P R E C < 1 6 8 . 2 0 ) . A T E M P (1 6 8 , 2 0 ) .D D A Y S .T O D D A Y S .S D D A Y S t2 0 ) .N E T R E V 12 0 ) COMMON / T R E E / I S T A G E . F D F R U I T . S D F R U I T . C D F R U I T . D M F R U I T , T Y I E L D COMMON / S C A B D A T / I N F L E V ( 3 ) . I N F P E R ( 3 ) . N I N F COMMON / C H E M S / E E N L A T E . C APTAN . D IF O L + . P L I C T R N , C A R Z O L . G U T H I O N . P Y R T H R D . I P R O ( 1 2 ) , N S P R A Y . M I S S S P . NEXTSP + lO STR A TE GY COMMON / D A T E / I D A Y . J D A Y . I Y R . I S T R A T , J S T R A T . K S T R A T . I P A R T R=SRANF( 2 ) I F I N F L E V ( 3 ) . GE . 2 ) N I N F = N I N F + 1 I F J D A Y . G E . N E X T S P . O R . M I S S S P . E O . 1 ) GO TO 1 0 0 I F I N F L E V ( 3 ) . E O ■ 0 ) RETURN I F I S T R A T . N E . 1 ) C A L L SPSPRAY I F I N F L E V ( 3 ) . E Q . O ) RETURN I F I N F L E V C 3 ) . E O . 1 JFACT = . 0 5 I F INFLEVC 3 I . E O . 2 jF A C T = . 1 0 - R * . 0 5 IF IN F L E V (3 ).E Q .3 )F A C T = .7 5 - R * .7 0 I F I N F L E V I 3 ) . EO . 3 . A N D . IS T A G E . L T . 2 )F A C T = . 2 0 - R * . 1 5 I F S D F R U I T . G T . O ) GO TO 5 0 IF IS T A G E .L T .3 GO TO 5 0 I F I S T A G E . E O . 8 FACT = FA C T + 0 . 3 5 I F IS TA G E . EO. 7 F A C T = FA C T * 0 . 4 5 I F IS T A G E . EO. 6 F A C T = F A C T *0 .5 8 I F IS TA G E . EO. 5 FACT = F A C T * 0 . 7 IF IIS T A G E . E O .4 FA C T = FA C T * 0_____ .7 8 _____ ____ IF F A C T . L T . . 0 5 . A N D .F A C T .G T .O .0 ) F A C T = .0 5 5 0 S D F R U I T = S D F R U I T + FACT IF (S D F R U IT .G T .1 ,0 )S D F R U IT = 1 .O I F ( I S T R A T . E O - 1 ) RETURN NEXTSP = 9 9 9 RETU RN l O O C A L L SPS PRAY IF IN FLEV R ETURN • E O .O IF IN FLEV FA C T = . 0 5 IF IN FLEV FA C T = . 1 0 - R * . 0 5 IF IN FLEV . E O . 3 FA C T = . 7 5 - R * . 7 0 I F IN FLE V . E O . 3 . A N D . 1 S T A GE. L T . 2 J F A C T = . 2 0 - R * . 15 I F S D F R U I T . G T . O ) GO TO 2 0 0 IF IS T A G E .L T .3 GO TO 2 0 0 I F 1S TA G E .E O .8 FACT=FACT * 0 . 3 5 IF 1STA G E .E Q .7 FACT = FA C T * 0 . 4 5 IF IS T A G E .E Q .6 FA C T = FA C T * 0 . 5 8 IF IS T A G E .E Q .5 F A C T = FA C T * 0 . 7 IF IS T A G E .E O .4 F A C T = FA C T * 0 . 7 8 IF F A C T . L T .. 0 5 . A N D .F A C T .G T .O .O ) F A C T = .0 5 2 0 0 S D F R U I T = S D F R U I T + FACT I F ( S D F R U I T . G T . 1 . O ) S D FR U IT = 1 . 0 RETU RN END 15 20 25 30 35 40 45 50 1 S U B R O U T IN E C C C 5 10 15 C 20 10 25 20 30 30 1 A PP LIE S SPRAY WHEN SCAB DAMAGE OCCURS COMMON / N A T U R E / Y I E L D ( 2 0 ) . F P R I C E C 2 0 ) , P P R I C E { 2 0 ) . P R E C ( 1 6 8 . 2 0 ) . A T E M P (1 6 8 . 2 0 ) . D D A Y S .T O D D A Y S .S D D A Y S 12 0),N E T R E V (2 0 ) COMMON / T R E E / i S T A G E . F D F R U I T . S D F R U I T . C D F R U I T . D M F R U I T , T Y I E L D COMMON / D A T E / I D A Y . J D A Y , I Y R . I S T R A T . J S T R A T . K S T R A T . I P A R T COMMON / S C A B D A T / I N F L E V ! 3 ) , I N F P E R ( 3 ) . N I N F COMMON / C H E M S / B E N L A T E .C A P T A N ,D IF O L + , P L IC T R N .C A R Z O L .G U T H IO N .P Y R T H R D .IP R O (1 2 ) , N S PR A Y .M IS S S P .N E X T S P ID A Y = JDAY - 6 9 I F ( P R E C ( I D A Y , I Y R ) . G T . . 0 2 ) G 0 TO 3 0 M IS S S P = O B E N L A T E * B E N L A T E + 16 I P R 0 ( 5 ) = 14 IF (IP A R T .L T .3 ) IP R 0 (5 )= 7 I P R O ( 1 1 ) * 14 N SPR AY * NSPRAY + 1 DO I O I > 1 . 3 IN F L E V ? I) = O I F ( N E X T S P . E O . 9 9 9 ) GO TO 2 0 NEXTSP = 9 9 9 R ETURN NEXTSP = JDAY T 7 RETURN M IS S S P = 1 R ETU RN END S U B R O U T IN E CALCULATES 5 SPS PRAY S P E C IA L ECOM COSTS. COMMON / D A T E / M A T E R IA L U S E .N E T REVENUE ON Y EA R LY B A S IS I D A Y , J D A Y . I Y R . I S T R A T , J S T R A T , K S T R A T . I PART Co ro ro COMMON / N A T U R E / Y I E L D ( 2 0 ) , F P R I C E 1 2 0 ) . P P R I C E 1 2 0 ) . P R E C l 1 6 8 . 2 0 ) . A TE MP I 1 6 8 , 2 0 ) . D D A Y S . T O D D A Y S . S D D A Y S I 2 0 ) . N E T R E V ! 2 0 ) COMMON / A C C U M / S T R A T S I 2 0 ) . S T R A T S S I 2 0 ) . G R A N D S ! 2 0 ) . GRA NDS SC2 0 ) . * N S T R A T .N G R A N D . N A C C U M COMMON / T R E E / I S T A G E . F D F R U I T , S D F R U I T . C O F R U I T . D M F R U I T . T Y I ELD COMMON / S C A B D A T / I N F L E V ( 3 ) . I N F P E R I 3 ) . N I N F C O M M O N /M IT E D A 2 /IE C T H 1 . IE C T H 2 . X . N S C O U t.N X , KONN. + IP C .IE R R O R .K E M X .S C C O S T C O M M O N /C M S CO UT / T H E A T , M O T H K I L , M S P R A Y . EC M1 . E C M 2 , E C M 3 . + C M L E V E L . L U C K . C M L O S S . I T E R A T . O L D . WORMA^L COMMON / C H E M S / B E N L A T E .C A P T A N .D IF O L + .P L IC T R N ,C A R Z O L ,G U T H IO N .P Y R T H R D .IP R O I1 2 ) .N S P R A Y .M IS S S P ,N E X T S P LO G IC AL M O T H .S C A B ,M IT E .IW S C O U T COMMON / D B / D E B U G . M O T H , M I T E . S C A B . I W S C O U T , H S P R A Y , I N T S C T + IO 15 20 25 30 35 40 45 50 55 60 65 70 75 80 C DAMAGE C M I T E S - M I T E D A Y S TO 0 I F ( M I T E ) C A L L E SM ITE S C SCAB - PER C E N T TO O C S D F R U IT = 0 .0 F S C A = 0 .0 P S C A = 0 .0 FSC A=SD FR UIT I F I S D F R U I T . L T . . 4 ) GOTO 6 0 FSCA=.4 P S C A = S D F R U IT -.4 6 0 C O N T IN U E S D F R U IT = T Y IE L D * S D F R U IT C MOTH C D F R U IT = C M L O S S *T Y IE L D C F Y IE L D = T Y IE L D - C D F R U IT C Y I E L D AND REVENUE T Y IE L D = T Y IE L D - S D F R U IT - C D FR U IT AP R IC E « . 4 * F P R IC E ( I Y R ) + . 6 * P P R I C E I I Y R ) T O T R E V = (F Y IE L D *!.4 -F S C A )*F P R IC E (IY R ) ) + ( F Y IE L D * I.6 -P S C A ) + *P P R IC F IIY R )) + I S D F R U rT *p P R IC c IIY R )*.7 2 5 ) CMDAM * T O T R E V * D M F R U I T T O T R E V * T O TR E V - CMDAM C C V A L U E OF DAMAGE C SCAB CSDAM= ( F Y I E L D * A P R I C E ) - TO TR E V C MOTH CCDAM * C D F R U I T * A P R I C E C M I T E ( D M F R U I T I S F R A C T I O N OF V A L U E ) C C A L C U L A T E D ABOVE (C M D A M ) C C SPRAY COSTS C SCAB S PC O S T S = B E N L A T E * . 6 5 9 + D I F O L * 2 4 . 0 + C A P T A N * 1 . B 5 I F I . N O T . SCAB)SPCO STS = 1 7 5 . 0 0 C THE D E F A U L T C O S TS FOR S CAB CONTROL ARE EQ UAL TO COSTS OF C SCAB S TR ATE GY OF 14 C A P T A N SPR AYS ( 7 F U L L DOSE AND 7 H A L F ) C T H I S I S THE C O N V E N T IO N A L SPRAY PROGRAM C MOTH SPC OS TC = M SPRAY*1 .4 1 + G U T H IO N « 1 0 .5 0 +P Y R T H RD *21 . 0 0 + 5 7 .4 1 C THE P R I C E OF THE P Y R T H R O I D I S ASSUMED TO BE 3 / 4 OF P R I C E OF I F < .N O T .M O TH )S P C O S TC = 7 1 . 7 6 C M IT E SPCOSTM = P L I C T R N * 2 7 . 7 5 + C A RZ OL « 3 3 . + NSCOUT * . 5 I F ( . N O T .M IT E )S P C O S T M = 2 0 . 0 3 C G E N ER A L - . 7 0 2 / S P R A Y L A B O R , . 6 9 8 / S P R A Y M A C H IN E N S PR AY = NSPR AY + MSPRAY I F ( IW S C O U T ) S C CO ST= 1 2 . 0 SPC OS T = NSPR AY * 1 . 4 + SPCOSTS + SPC OS TC + SPCOSTM + SCCOST C C CONTRO L COST CC ON TR L = SPCOST + CSDAM + CMDAM + CCDAM C P R O D U C T IO N COST C 3 6 3 . 5 7 = OVERHEAD C 1 . 0 1 = . 8 0 V A R I A B L E P R O D U C T I O N , . 2 1 M A R K E T IN G C 3 4 0 . 2 9 = OTHER M A T E R I A L COSTS PROCOST = 3 6 3 . 5 7 + 1 . 0 1 * F Y I E L D + SPCOST + 3 4 0 . 2 9 R E VN E T = TO TR E V - PROCOST N E T R E V II Y R )= R E V N E T * 10 P R IN T 1 C O O ,IY R , Y I E L D ! I Y R ) , F D F R U IT , S D F R U IT , C D F R U IT , T Y I E L D , + F P R I C E ! I Y R ) . P P R I C E ! I Y R ) , C M D A M .T O T R E V . N S P R A Y . B E N L A T E . C A P T A N . OJ ro Co 85 90 95 100 105 110 1 5 10 1 5 + D I F O L . P L I C T R N . C A R Z O L . G U T H I O N . P Y R T H R D . C C O N T R L . P R O C O S T , REVNET 1000 FO R M A T !1 3 . 5 F 7 . 1 . 3 F 7 . 2 . F 8 . 2 . 1 4 . 7 F 6 . 1 . I X . F 7 . 2 . 2 F 8 . 2 ) C ACCUMULA TE Y IE L D (IY R C A LL TOTAL F D F R U IT .2 C A LL TOTAL S D F R U IT ,3 C A LL TOTAL C D F R U IT ,4 C ALL TOTAL C ALL TOTAL T Y IE L D , 5 ) C ALL TOTAL F P R IC E fIY R ),6 ) P P R IC E ( I Y R ) . 7 ) C ALL TOTAL C M D A M .8 ) C ALL TOTAL TO T R E V .9 ) C ALL TOTAL F L O A T ( N S P R A Y ) lO) C ALL TOTAL B E N L A T E .11) C A L L TOTAL C A P T A N .1 2 ) C A LL TOTAL D IF O L .13) C A LL TOTAL P L IC T R N .14) C A LL TOTAL C A L L TOTAL C A R Z O L .1 5 ) G U T H I O N . 16 CA LL TOTAL C ALL TOTAL P Y R T H R D . 17 C A LL TOTAL C C O N T R L . 18 P R O C O S T . 19 C A L L TOTAL REVNET, 2 0 ) C A LL TOTAL NSTRAT = NSTRAT R ETURN END 1) + 1 S U B R O U T IN E T O T A L ( O . N ) C AC CU M U LA TE S SUM AND SUM OF SOUARES OF 0 I N N T H E LE M E N TS OF C S T R A T S AND S T R A T S S COMMON / A C C U M / S T R A T S ( 2 0 ) . S T R A T S S ( 2 0 ) . G R A N D S ! 2 0 ) . G R A N D S S ! 2 0 ) , + N S T R A T .N G R A N D . N A C C U M I F ( N . L T . 1 . O R . N . G T . N A C C U M ) G 0 TO 9 0 0 S T R A T S ( N ) = S T R A T S ( N, )j N)+ + O q * g -------------------S TR A TS S (N ) = STRATSS! RE TURN C P R IN T IM P R OP E R C A L L OF S U B R O U T IN E T O T A L . N = ".N 900 STOP END S U B R O U T IN E C C C C STATS (IT ) COMPUTES MEANS AND SDS E I T H E R OR A L L S T R A T E G I E S ( I T = 2 ) + FOR END OF S TR ATE GY (IT 15 20 25 30 35 1) COMMON / A C C U M / S T R A T S ( 2 0 ) . S T R A T S S ( 2 0 ) . G R A N D S ! 2 0 ) . G R A N D S S ( 2 0 ) . N S T R A T ,N G R A N D , N A C C U M D IM E N S IO N A V G (2 0 ) . S D ( 2 0 ) . V A R ( 2 0 ) C 10 = I F ( I T . E O . 2 ) GO TO 1 0 0 C A L L C A LC ( S T R A T S . S T R A T S S . N S T R A T . A V G . V A R . S D . N A C C U M ) P R IN T 1 1 0 0 1100 F O R M A T ! " O S T A T I S T I C S FOR A L L Y E A R S : " ) C A CCU M ULA TE GRAND T O T A L S NGRAND = NGRAND + N S T R A T DO 1 0 1 - 1 .NACCUM G R A N D S !I) = G R A N D S !I) + S T R A T S (I) G R A N D S S ? I ) = G R A N DS S ( I ) + S T R A T S S ( I ) 10 C O N T IN U E GO TO 2 0 0 C GRAND A V G . ETC C IT * 2 : C A L L CALC ( G R A N D S .G R A N D S S ,N G R A N D .A V G .V A R .S D ,N A C C U M ) 100 C C P R IN T RESULTS P R IN T 2 0 0 0 . A V G .V A R ,S D 200 C F O R M A T !3H A V . 8 F 7 . 1 , F 8 . 1 . F 4 . 0 . 7 F 6 . 1 , I X . 2 F 7 . 1 . F 8 . 1 / 2000 + 3H V R . 8 E 7 . 1 . E 8 . 1 . F 4 . 1 . 7 F 6 . 0 . 2 E 7 . 1 . E 8 . 1. / + 3H S D . 8 F 7 . 1 , F 8 . 1 . F 4 . 1 . 7 F 6 . 1 . 1 X . 2 F 7 . I . f S . 1) C I F STRAT C A L L . ZERO OUT S TR A T ACCUMS C I F ( I T . E Q . 2 ) RETURN DO 5 0 0 1 = 1 . NACCUM S T R A T S (I ) = 0 . 0 S T R A T S S II) = 0 . 0 500 C O N T IN U E W ro NSTRAT RETURN END 40 1 10 oooo S U B R O U T IN E CALC ( S . S S , N , A . V , S D . L ) D IM E N S IO N S ( L ) . S S ( L ) . A ( L ) . V ( L ) . S D ( L ) m 5 = 0 C A L C U L A T E S AVERAGE ( A ) . V A R I A N C E ( V ) , STA NDARD D E V I A T I O N ( S D ) OF L T O T A L S ( S ) . SUMS OF SQUARES ( S S ) . U S I N G N FOR EACH FOR EACH I F ( N . G E . 2 IGO TO 5 P R I N T ♦ , * N L T 2 FOR SD C A L C U L A T I O N " RETURN C O N T IN U E =N F: N = N DO 1 0 1 = 1 . S C lJ /F N vMl lI )) = ( S §S ' ( I ) - FN * A ( I ) * * 2 : ) / (F N - 1 . ) .......... O R T................ ( V ( I )) SI D D Il fI ) = S C O N T IN U E RETURN END )0 10 1=1.1, 15 0 1 5 o 10 25 oooo 20 nnoo 15 JSTRAT = 1 - B I 0 ; 2 - C A L 4 6 / 1 5 & 8 / 1 5 ; 3 - C A L 5 6 / 1 5 & 8 / 1 5 ; 4 - I P M 5 -IP M 2 8 /2 2 4 ; 6 -IP M 2 8 /7 4 ;7 -IP M 3 5 /2 5 4 ;8 -IP M 28 5 ;9 -IP M 1 0 -IP M 35 5 1 1 - 1 7 SAME AS 4 - 1 0 BU T W I T H ERROR IE C T H 1 = I C O D E H , J S T R A T ) IE C T H 2 = IC O D E ( 2 , J S T R A T ) IP C = IC O D E ( 3 . J S T R A T ) IE R R O R = I C 0 D E ( 4 . J S T R A T ) 1 5 /1 5 15 5 ; £ 5? 4; oo 30 S U B R O U T IN E MSTR AT COMMON / D A T E / I D A Y . J D A Y . I Y R , I S T R A T . J S T R A T . K S T R A T . I P A R T C O M M O N /T R E E /IS T A G E ,F D F R U IT .S D F R U IT .C D F R U IT .D M F R U lT .T Y IE L D C O M M O N /M IT E 0 A 2 /IE C T H 1 , IE C T H 2 . X . NSCOUT. N X . KONN. + IP C .IE R R O R .K E M X ,S C C O S T C O M M O N /M IT E D A T /S A E R (2 0 ) . S A A F (2 0 ) . I A F D ( 2 0 ) . IE R D < 2 0 ) . +• A E R . A A F . E P Y . A F F F R . Y Y . A F F C O N . E R I N J ( 3 ) . C O N , + E M X , ELPDPOC 1 0 ) , E R i ( 1 0 ) , A F I ( 1 0 ) C 0 M M 0 N /N A T U R E /Y IE L D (2 O ).F P R IC E (2 O ),P P R IC E (2 O ),P R E C (1 6 8 .2 0 ) , + A T E M P ( 1 6 8 , 2 0 ) .D D A Y S . TODDAYS. SDDAYS12 0 ) . N E T R E V I2 0 ) D IM E N S IO N IC O bE ( 4 . 1 7 ) 4 NUMBERS I N EACH S ET ARE I E C T H 1 . I E C T H 2 . I P C . AND IE R R O R DA TA IC O D E / O . 0 . 0 . 0 . 0 . 0 . 4 , 0 , 0 . 0 . 5 . 0 . 1 5 ,1 5 .4 ,0 . + 2 8 .2 2 .4 ,0 . 2 8 ,7 .4 ,0 , 3 5 ,2 5 ,4 .0 . 2 8 .0 ,5 ,0 . + 1 5 .0 .5 .0 . 3 5 .0 ,5 .0 . 1 5 .1 5 .4 .1 , 2 8 .2 2 .4 .1 . + 2 B .7 .4 .1 . 3 5 .2 5 .4 .1 . 2 8 .0 .5 ,1 . 1 5 .0 .5 .1 , + 3 5 .0 .5 .1 / IE R R 0R = 0 ZERO S A M P L I N G ERROR I ERROR*1 5 0 I N GROWER P E R C E P T I O N ; 5 0 I N M O N I T O R I N G RETURN END 5 lO 15 20 onnnoo 1 S U B R O U T IN E M IT E C O N *COMMON V A R I A B L E S : E L P D P O ( 1 0 ) . I P R O ( 1 2 ) , J D A Y . I E R D ( 2 0 ) . I Y R . I A F D ( 2 T H I S S U B R O U T IN E S E C T I O N C A L C U L A T E S AND A D J U S T S P O P U L A T I O N S FOR THEM B IR T H RATES AND P R E D A T I O N RATE LO G IC AL D E B U G .M O T H .M IT E .S C A B .IW S C O U T ,H S P R A Y COMMON / D A T E / I D A Y , J D A Y . I Y R . I S T R A T , J S T R A T , K S T R A T , I PAR T C O M M O N /D B /D E B U G , M O T H . M I T E . S C A B . IW S C O U T . H S P R A Y . I N T S C T C O M M O N /T R E E / 1 S T A G E , F D F R U I T . S D F R U I T . C D F R U I T . D M F R U I T . T V I E LD COM M O N/CHE M S /B E N LA TE . C A P T A N .D IF O L . + P L IC T R N ,C A R Z O L .G U T H IO N ,P Y R T H R D , I P R O ( 1 2 ) .N S P R A Y .M IS S S P .N E X T S P C 0 M M 0 N /M IT E D A 2 /IE C T H 1 , IE C T H 2 . X . NSCOUT. N X . KONN. + IP C .IE R R O R ,K E M X .S C C O S T C O M M O N /M IT E D A T /S A E R (2 0 ) , S A A F ( 2 0 ) . I A F 0 ( 2 0 ) , I E R D ( 2 0 ) , + A E R . A A F . E P Y . A F F F R . Y Y . A F F C O N . E R I N J ( 3 ) .C O N , + E M X .E L P O P O ( 1 0 ) .E R I( 1 0 ) .A F I( 10) DA TA E L P D P 0 / . 6 . . 1 4 , . 0 8 . . 0 8 , . 0 2 , . 0 1 6 , . 0 1 6 . . 0 1 6 . . 0 1 6 , . 0 1 6 / c DO 1 6 0 0 1 = 1 . 7 IF (D E B U G )P R IN T 1 6 5 0 .E L P D P 0 C I) . I , I P R 0 ( I ) 1 6 5 0 FO R M AT( * M I T E : E L P D P 0 ( I ) , I . I P R 0 ( I ) * . F 1 0 . 3 . 2 X . 2 13 ) 1 6 0 0 C O N T IN U E C 25 C I F ( J S T R A T . L T . 4 ) G 0 TO 1 9 0 I F ( I A F D ( I Y R ) . G T . J D A V . A N D . I E R D ( I Y R ) . G T . J D A Y ) RETURN 1 9 0 C O N T IN U E IF (IA F D (IY R I.E Q .J D A Y )A A F = S A A F < IY R ) I F l I E R D I I Y R J . E Q . J D A Y j A E R = S A E R ( I YR ) IF lIE R D lIY R l.E Q .J D A Y )E P Y = A E R * 1 .1 0 7 I F ( I A F D f I Y R ) . E O .JD A Y )A F F F R = A A F » .3 4 7 7 C A L L PRED I F ? J D A Y . G E . I E R D ( I Y R ) ) C A L L ERPOP I F ( J D A Y . G E . I A F D ( I Y R j ) C A L L AFPOP 30 35 45 n noono I F ( D E B U G ) P R I N T 1 0 0 0 . A A F . A E R . AAF I F ( I E R D ( I Y R ) . G T . J D A Y ) G 0 TO 3 5 0 4 40 T H I S S E C T I O N OF M I T E C A L C U L A T E S THE NUMBER OF D AYS ABOVE TH E I N J U R Y T H R E S HO LD ( 1 5 M I T E S PER L E A F ) . THE NEED FOR SPRAYS AND M I T E M O R T A L I T Y DUE TO SPR AYS CALL M IT E IN J ( J Y ) 5000 55 THE GROWER P E R C E P T I O N T H I S S E C T I O N I D E N T I F I E S FOR I P M S T R A T E G I E S WHEN A GROWER P E R C E I V E S A M I T E PROB LEM AND REQUESTS A P R O F E S S I O N A L S C O U T . THE RE I S A THREE DAY D E L A Y BET WEE N THE RE QU ES T AND THE A R R I V A L OF THE S C O U T . THE SCOUT V I S I T S TH E ORCHARD T W IC E - - THR EE D A YS A P A R T . I F ( J S T R A T . E Q . 1 ) GO TO 7 0 0 I F ( J S T R A T . G E . 4 ) GO TO 3 0 5 8 I F i J S T R A T . G T . 1 . A N D . J S T R A T . L T . 4 ) C A L L MSCOUT I F ( I E R D ( I Y R i . G T . J D A Y ) GO TO 7 0 0 I F ( J S T R A T . G T . 1 . A N D . J S T R A T . L T . 4 ) GO TO 2 3 5 4 C A L L MSCOUT GO TO 2 3 5 4 3 0 5 8 C O N T IN U E I F ( K O N N . E Q . I ) GO TO 2 1 7 5 I F l I E R R O R . E O . 1 ) G 0 TO 2 1 8 5 I F ( A E R . G T . X ) G 0 TO 2 0 5 7 GO TO 2 1 7 5 185 CALL R A N (A E R . . 2 5 . C , RANAER) I F ( R A N A E R . G T . X ) G 0 TO 2 0 5 7 GO TO 2 1 7 5 2 0 5 7 NX=7 KONN I S US ED TO I N D I C A T E T H A T M I T E PROBLEM H A S B EE N P E R C E I V E D KONN=1 NX I S USED TO P E R M I T 3 DAY D E L A Y BETWEEN M I T E PROBL EM P E R C E P T I O N ' 75 80 o o 70 oon 65 i o o 60 I F WEEKLY S C O U T IN G PROGRAM I S FO LL OW E D . AND M M O R T A L IT Y S E C T I O N S ARE S K I P P E D 3 5 0 4 I F I I W S C O U T ) G 0 TO 6 0 0 ooooo 50 I F ( D E B U G ) P R I N T 5 0 0 0 . A E R , E R I N J ( J Y ) . JD A Y F O R M A T (* M IT E IN J : A ER +*. F 7 . 2 . * E R IN J = *. F 7 .2 . * JD A Y=*.1 5 ) ooo & AND S C O U T IN G 2175 85 90 95 ( A N D BET WEEN SPR AY AND SECOND S C O U T ) I F ( N X . E O . 8 ) G 0 TO 2 3 5 4 NX=NX - 1 C I F ( D E B U G ) P R I N T 2 4 5 0 , N X . X . A E R .K O N N 2 4 5 0 FO R M AT( * M IT E : N X .X .A E R .K O N N *. lO X . 1 3 . 1 0 X . F 1 0 . 2 . lO X , F I O . 2 , 1 5 ) I F ( N X . E O . 3 ) GO TO 2 3 5 6 I F ( N X . E Q . 0 ) GO TO 2 3 5 2 GO TO 2 3 5 4 2 3 5 6 C A L L MSCOUT NS CO UT =N 5C Q U T + 1 GO TO 2 3 5 4 2 3 5 2 C A L L MSCOUT NX=8 K0NN=0 2 3 5 4 C O N T IN U E C T H I S I S THE END OF THE GROWER P E R C E P T I O N S E C T I O N C C T H I S S E C T I O N C A L C U L A T E S THE M O R T A L I T Y OF THE P O P U L A T IO N S C DUE TO THE SPRAYS I F ( DEBUG 1 P R I N T 6 0 0 1 . I P C . C A R Z O L . P L I C T R N . N S P R A Y . NSCOUT ,, g? ^ too CALL C C 600 C C O N T IN U E 105 1000 8* 110 C 700 C 6000 6001 6002 115 5 10 15 20 25 30 35 40 45 50 55 IF (D E B U G ) P R IN T 6 0 0 2 FO R M AT !‘ M I T E . A A F = * , F 8 . 3 , ‘ A A F =*, F 1 0 .3 ) A E R = *,F 8 .3 . RETURN + 1 MMORT F O R M A T ( 1 X . ‘ DEBUG 2 : I P R O ( I S T R ) ‘ 1 3 ) F O R M A T ( 1 X , ‘ DEBUG 1 ‘ , 1 0 X , ‘ C H E C K , I , C . P , N S . N S C O U T * . 5 X , 1 5 , 2 F 6 . 3 . 1 0 X . 2 F 1 0 .3 .I5 ) F O R M A T ( 1 X . ‘ DEBUG 3 ‘ ) END C C S U B R O U T IN E I N T M I T E C » * “ * “ “ “ “ COMMON V A R I A B L E : I A F D ( 2 0 ) . I E R D ( 2 0 ) . SAA F f 2 0 ) . I Y R . S A E R ( 2 0 ) C T H I S S U B R O U T IN E I N T I A L I Z E S V A R I A B L E S P R IO R T O M I T E S U B R O U T IN E C V A L U E S CHOSEN F R O M IE R FOR RED M I T E A N D I A F FOR A M B L Y S E I U S F A L L A C I S C L O G IC A L D E B U G .M O T H .M IT E .S C A B ,IW S C O U T .H S P R A Y C O M M O N /D B /D E B U G .M O T H ,M IT E . S C A B . IW S C O U T .H S P R A Y . IN T S C T COMMON / I N T / GP P .S C M P O P C O M M O N /M IT E D A 2 /IE C T H 1 . IE C T H 2 . X , NSCOUT, N X , KONN. + I P C . I E R R O R . K E M X . SCCOST C O M M O N /M IT ED A T/S A ER ( 2 0 ) , S A A F ( 2 0 ) , I A F D ( 2 0 ) , I E R D ( 2 0 ) . + A E R , A A F , E P Y , A F F F R , Y Y , A F F C O N , E R I N d ( 3 ) .C ON , + E M X .E L P D P 0 ( 1 0 ) ,E R I( 1 0 ) .A F I(10) C D IM E N S IO N I A F ( 1 0 ) , I E R ( 2 0 ) , P O P (2 0 ) DATA I E R / 2 8 , 5 7 , 6 9 , 7 6 . 8 2 . 8 7 , 9 1 , 9 5 . 9 9 . 1 0 3 , 1 0 7 . 1 1 2 . 8 1 1 7 .1 2 2 .1 2 7 .1 3 3 .1 4 0 .1 4 7 .1 5 7 ,1 6 9 / C DATA I A F / 7 9 . 9 1 . 1 0 1 . 1 1 1 . 1 2 1 . 1 3 1 . 1 4 1 . 1 5 1 . 1 6 1 . 1 7 2 / C DATA P O P / . 0 2 4 . . 3 6 5 . . 5 0 2 . . 5 9 0 , . 6 6 4 . . 7 3 8 , . 8 1 0 . . 8 8 2 . . 9 5 6 , 8 1 .0 3 1 .1 .1 1 0 .1 .1 9 2 .1 .2 8 2 .1 .3 7 6 .1 .4 8 3 .1 .6 0 9 .1 .7 5 6 ,1 .9 4 5 . 8 2 .2 0 7 .2 .6 3 6 / DO 5 0 0 I Y R = 1 , 2 0 DO 3 0 0 1 = 1 . 4 R R = 0 .0 R 1= R A N F ( 0 ) DO 1 0 0 d = 1 , 2 0 R R ‘ RR + . 0 5 I F ( R I . L T . R R ) GO TO 1 5 0 100 C O N T IN U E 150 GO TO ( 1 . 2 . 3 . 4 ) 1 1 d = (d + 1 )/2 I A F D ( I Y R ) = I A F ( d ) + 74 C D A TE OF PREDATOR EMERGENCE C GO TO 2 0 0 C DA TE OF P E S T EMERGENCE 2 IE R D (IY R )= IE R (d ) +74 C C GO TO 2 0 0 C S T A R T I N G PREDATOR P O P U L A T I O N 3 S A A F C IY R )= P O P (d ) *.1 C GO TO 2 0 0 C S T A R T IN G PEST PO P ULATIO N 4 C C 200 300 60 500 C C SET S A E R (IY R )= P O P (d ) IF (D E B U G )P R IN T lO O O .I. d .R R C O N T IM U E P R IN T 2 0 0 0 . I Y R . I A F D ( I Y R ) . I E R D ( I Y R ) . SAAF( I Y R ) . SAER( I Y R ) C O N T IN U E THRESHO LD FOR M I T E PROBLEM P E R C E P T IO N W ro ^ X * 65 C 1000 2000 1 5 10 15 20 25 30 35 C C C /iff # # # # # # # # # * # # # # # # # # * # # # # * # # # ! » * # # # # # # * * # a * # * * * # # * # # * * # * # # # * # # # / / # S U B R O U T IN E PRED C * * * * * * * * * C O M M O N V A R IA B L E S : A T E M P (1 6 8 . 2 0 ) . I Y R . J D A Y , ID A Y C C T H I S S U B R O U T IN E C A L C U L A T E S THE C O N S U M P T IO N OF THE C ER P O P U L A T I O N BY THE AF P O P U L A T I O N I N TE T RA N Y C HU S C U T R I C A E EGG E Q U I V A L E N T S ( C O N ) C LO G IC A L D E B U G ,M O T H .M IT E .S C A B ,IW S C O U T ,H S P R A Y C O M M O N /D B /D E B U G .M O T H .M ITE .S C A B ,IW S C O U T.H S P R A Y .IN TS C T COMMON / D A T E / I D A Y . J D A Y . I Y R . I S T R A T . J S T R A T . K S T R A T , I P A R T C 0 M M 0 N /N A T U R E /Y 1 E L D (2 0 ). F P R IC E ( 2 0 ) , P P R IC E ( 2 0 ) ,P R E C { 1 6 8 . 2 0 ) . + A T E M P (1 6 8 , 2 0 ) .D D A Y S .T O D D A Y S , S D D A Y S {2 0 ) , N E T R E V ( 2 0 ) C O M M O N /M IT E D A 2 /IE C T H 1 , I E C T H i . X . NSCOUT. N X . KONN. + IP C .IE R R O R .K E M X ,S C C O S T C 0 M M 0 N /M IT E D A T /s A E R (2 0 ),S A A F (2 0 ). IA F O (2 0 ) , IE R D (2 0 ) . + A E R . A A F . E P Y , A F F F R , Y Y . A F F C O N , E R I N J ( 3 ) , CON , + E M X ,E LP D P O (1 0 ) , E R I ( 1 0 ) , A F I ( I O ) C C C YY=.0 0 2 7 1 3 1 6 *A T E M P (ID A Y ,IY R )**3 - .5 3 8 5 2 * A T E M P (ID A Y ,IY R )**2 + $ 3 5 .6 8 6 8 • A T E M P (ID A Y .IY R ) - 7 8 2 .6 3 5 B = .0 0 0 2 2 7 9 * A T E M P (ID A Y . I Y R ) * * 2 - . 0 3 4 4 3 * A T E M P (IO A Y . I Y R ) + 1 .4 7 2 8 8 C IF (D E B U G )P R IN T 1 2 0 0 . A F F F R .Y Y ,B 1 2 0 0 FO R M AT( * PREO: A F F f R . Y Y . B * . 3 F 1 0 . 3 ) I F ( A A F . G T . O . O ) GO TO 1 0 0 C O N = 0 .0 IF ( D E B U G ) P R IN T 1 3 0 0 . A E R , A A F . C O N .E PY 1 3 0 0 FO R M AT( * PRED: A E R .A A F .c 6 n .E P Y * , 4 F I O . 3 ) R E TU R N lOO C O N = - A L O G ( E X P ( - Y Y * B * A A F ) - E X P ( - B * E P Y - B * V Y * A A F ) + E X P ( - B * E P Y ) ) / B C O N = ( A F F F R / A A F ) *CO N c 40 GPP FORMAT( * I N T M I T E ; I , J . R R * . 2 X , 2 1 3 , F 6 . 2 ) FORMAT ( * Y E A R , I A F D , I E R D , S A A F . S A E R * . 1 3 . 2 1 6 . 2 F 1 0 . 2 ) RETURN END lOOO C I F ( D E B U G ) P R I N T l O O O , A T E M P ( I D A Y . I Y R ) . C O N . A A F . AER FO RM AT( * P R E D : A T . C O N . A A F . A E R * . 4 F 6 . 2 ) R ETU RN END 1 C C Ceaapappppaappppapapeppaaaoeapaappaaaaaaapaaaaaaapaaaaaeaaaaaaaao 5 10 15 20 S U B R O U T IN E ERPOP _ „ C * * * .* C 0 M M 0 N V A R IA B L E S : E M X ,ID A Y , E LP D P O (1 0 ) , A T E M P (1 6 8 . 2 0 ) . I Y R . J D A Y . E R I ( 1 0 C C S U B R O U T IN E C A L C U L A T E S THE RED M I T E ( E R ) P O P U L A T I O N LO S S DUE TO C P R E D A T I O N AND S U B T R A C T S I T FROM THE P R ES EN T P O P U L A T I O N . TH E N THE C P O P U L A T I O N IN C R E A S E DUE TO R E P R O D U C T IO N I S C A L C U L A T E D AND ADDED TO C THE P O P U L A T I O N C L O G I C A L D E B U G . M O T H . M I T E . S C A B . IW S C O U T , HSPR AY COMMON / D A T E / I D A Y . J D A Y . I Y R . I S T R A T , J S T R A T . K S T R A T . I P A R T C O M M O N /D B /D E B U G . M O T H . M I T E . S C A B . I W S C O U T . H S P R A Y . I N T S C T C O M M O N /N A T U R E /Y IE L D (2 0 ) . F P R IC E ( 2 0 ) .P P R I C E ( 2 0 ) ,P R E C ( 1 6 8 , 2 0 ) . +A TE M P ( 1 6 8 . 2 0 ) . D D AY S , TODDAYS. S D D A Y S l2 0 ) . N E T R E V (2 0 ) C O M M O N /M IT E D A T /S A E R (2 0 ) .S A A F ( 2 0 ) . I A F D ( 2 0 ) . IE R D ( 2 0 ) . + A E R . A A F . E P Y . A F F F R , Y Y , A F F C O N . E R I N J ( 3 ) . CON . + E M X ,E L P D P O (1 0 ) . E R K 1 0 ) , A F I ( 1 0 ) C O M M O N /M IT E D A 2 / I E C T H 1 , 1 E C T H 2 . X . N S C O U T . N X , K O N N , + IP C .IE R R O R ,K E M X .S C C O S T D IM E N S IO N D R I 1 0 ) IF (K E M X . GT. 0 . ) GO TO 150 25 0 0 100 1 = 1 .1 0 E R I(I)= A E R *E L P D P 0 (I) * 2 .5 * .7 5 to 03 1 0 0 C O N T IN U E C 30 150 E M X = .1 4 8 *A T E M P (ID A Y ,IY R ) - 7 .5 7 C & 35 KEM X=K EMX + 1 O V IP = E M X *( E R I ( 6 ) * . 7 9 + E R I( 7 ) * . 9 6 + E R I( 8 ) * . 6 7 + E R I(9 ) * . 5 2 + E R I( 1 0 ) * . 0 5 ) IF 1 0 V IP .L T .0 .0 ) 0 V IP = 0 .0 C IF (A E R . 6 T . 7 0 )0 V IP = 0 .0 FCON=1. I F ( E P Y . G T . 0 . )F C O N = (E P V -C O N )/E P Y 40 45 50 55 C c IF (D E B U G ) P R IN T lO O O . F C O N . 4 E R . 0 V I P . C 0 N , E R I ( 1 0 ) lO O O FO R M AT( * E R P O P : F C O N , A E R , O V I P , C O N , E R I ( 1 0 ) * , 5 F 1 0 . 3 ) C T H I S SEOUENCE H A N D L E S A N A BS O L U T E R E D U C T IO N ( 3 ) I N POP DUE TO S T A R V A T I C C I F ( A E R . L T . l O O ) GO TO 4 2 5 C AER=AER * . 9 7 C 0 0 4 5 0 1 = 2 . IO C E R I( I ) = .9 7 * E R I( I ) C 4 5 0 C O N T IN U E C GO TO 4 0 0 C 4 2 5 C O N T IN U E C DR 1 ) = 1 . / ( 7 4 9 . 9 * E X P ( - . 0 6 5 * A T E M P ( I D A Y , I Y R ) ) ) DR 2 { = ( 2 . 9 1 9 5 - . 3 9 8 3 * . 7 S ) * . 0 0 1 * E X P ( . 0 7 4 5 - A T E M P ( I D A Y . I Y R ) ) DR 3 { = ( 2 . 7 8 8 3 - . 2 1 1 3 * . 7 5 ) * . 0 0 1 * E X P ( . 0 7 4 5 * A T E M P ( I D A Y . I Y R ) ) DR 4 ){ = ( 2 . 4 0 4 7 - . 1 4 8 9 * . 7 5 J * . 0 0 1 * E X P ( . 0 7 4 5 * A T E M P ( I D A Y , I Y R ) ) DR l= ( 2 . 9 7 * . 0 0 0 1 ) * E X P ( . 1 0 3 5 *A T E M P (ID A Y .IY R ) ) DR 3)= D R (8 J= D R (7 ) = D R (6 ) = 5 . / ( - . 5 3 3 * A T E M P (ID A Y , I Y R ) + 5 3 . 4 2 ) 60 ER F=AER *0DO 2 0 0 1=11-J J= 1 ,9 I F ( D R ( I ) . G T . 1 .O ) D R ( I ) = 1 . 0 IF (D R (I).L T .0 .0 )D R (I)= 0 .0 , , , . . . I F ( D E B U G ) P R I N T * . " E R PO P :D R ( I ) . E R I ( I ) . I " . D R ( I ) . E R I ( I ) , I 0 = E R I(I)« (1 .-D R (l|) B = E R I(I-1 )*D R T i -1 ) E l RR I (( Il )) = ( E R R I I( (I I )l ** (( 11 .. --CD R ( I ) ) + E “R■I ( "I - 1 ) * D R ( I - 1 ") } *F C O N 1 F (D E B U G {P R IN T *, " E R P O P ;D R (I) , E R I ( I ) , I " , D R ( I ) . E R I( I ) . I IF iD E B U G J P R IN T * ." E R l( " ,I,) = " .0 .* + " .B 65 70 A E R = A E R + E R I( I ) * 1 . 3 3 I F ( I . L E . 4 ) GOTO 2 0 0 E R F = E R F + E R I( I ) C O N T IN U E 75 200 C I F ( A E R . L T . 3 5 . ) GO TO 6 0 0 DO 5 0 0 1 = 2 , 1 0 E R I(I)= E R l(l)* .9 7 5 0 0 C O N T IN U E 6 0 0 C O N T IN U E 80 C E R I( 1 ) = E R I( 1 ) * f 1 . - D R ( 1 ))+ O V IP ---------------IF ( A E R .— G T. . . 2 ) GO GOTO 4 0 0 P 0 P IN C R = 0 . I F ( A E R . G T , 0 . 0 ) P O P I N C R = . 2 /A E R ERF=0. I F ( A E R . E O . O . 0 ) G 0 TO 1 2 0 0 AER=.2 1 2 0 0 C O N T IN U E DO 3 0 0 1 = 2 . 10 E R 1 ( 1 ) = E R I ( I ) » P O P IN C R I F 1 I . L E . 4 ) GOTO 3 0 0 E R F = E R 1 ( 1 )+ER F 3 0 0 C O N T IN U E 4 0 0 C O N T IN U E 85 90 95 100 C S C 1400 105 C EPY=1 . 3 3 *E R I( 2 ) * . 6 3 9 7 + 1 . 3 3 *E R I( 3 ) * .5 8 7 8 + (E R I(4 )+ .3 3 *E R F )*1 .3 8 3 + E R F *1 .959 IF (D E B U G ) P R IN T 1 4 0 0 . A E R , P O P IN C R . E P Y , FCON. E R I ( I O ) F O R M A T !* ERPOP: A E R . P O P IN C R , E P Y , F C O N , E R I ( 1 0 ) ♦ . 5 F 1 0 . 3 ) IF ID E B U G J P R IN T * . ” E R P O P . E R I ( 1 ) , ERF " , E R I I 1 ) . ERF U> PJ U3 R ETURN END 1 5 10 15 20 25 30 C S U B R O U T IN E AFPOP C * * * * * * * * * * ‘ COMMON V A R I A B L E S : A F F C O N , A F I ( 1 0 ) , I D A Y , E L P D P O ( 1 0 ) . A T E M P 1 1 6 8 , 2 J D A Y , EMX C L O G I C A L D E B U G . M O T H , M I T E . S C A B . IW S C O U T . HSPRAY C O M M O N / D B / D E B U G . M O T H . M I T E . S C A B . IW S C O U T , H S P R A Y . I N T S C T COMMON / D A T E / I D A Y . J D A Y . I Y R , I S T R A T . J S T R A T . K S T R A T . I P A R T C O M M O N /N A T U R E /Y IE LD ( 2 0 ) . F P R iC E ( 2 0 ) , P P R IC E I 2 0 ) , P R E C ( 1 6 8 , 2 0 ) . + A T E M P ( 1 6 8 , 2 0 ) ,D D A Y S ,T O D D A Y S , SODAYSt 2 0 ) , N E T R E V (2 0 ) C O MM ON /M I i - E D A t / S A E R ( 2 0 ) , S A A F ( 2 0 ) . I A F D 1 2 0 ) . I E R D ( 2 0 ) . + A E R . A A F . E P Y . A F F F R . Y Y . A F F C O N . E R I N J < 3 ) . C ON , + E M X .E L P D P O (IO ), E R I( 1 0 l , A F I ( 10 ) C O M M O N /M IT E D A 2/IE C T H 1 , IE C T H 2 ,X .N S C O U T .N X .K O N N . + I P C . I E R R O R . K E M X .S C C O S T D IM E N S IO N D R ( I O ) C I F ( A F F C O N . G T . O . ) GO TO 1 5 0 DO l O O 1 = 1 . 1 0 A F I( IJ = A A F *E L P D P O (I)*2 .5 = .8 lO O C O N T IN U E C 150 A = - . 0 0 0 0 5 9 8 *A T E M P (ID A Y ,IY R )**2 + .0 0 8 5 5 5 ‘ A T E M P (ID A Y ,IY R )- .3 1 1 4 B = . 0 0 0 1 1 7 6 8 *A T E M P (ID A Y IY R ) “ 3 - . 0 2 3 8 1 4 1 7 * A T E M P ( I D A Y . I Y R ) - * 2 & + 1 . 5 9 8 6 9 *A T E M P (ID A Y , iY R ) - 3 5 .3 5 6 C = - . 0 0 0 1 0 8 8 2 * A T E M P (ID A Y .IY R )** 3 + . 0 2 16 1 8 *A T E M P (ID A Y , IY R ) * * 2 & - 1 .4 2 3 5 *A T E M P (ID A Y .IY R ) + 3 0 .9 2 A F F C 0 N = O .O IF (A F F F R .G T .O .0 )A F F C O M = C O N /A F F F R EMX=A‘ A F F C O N ** 2 + B*AFFC O N + C 0 V IP = E M X * (A F I(6 )* 1 .7 4 + A F I( 7 )* 1 . 5 7 + A F I( 8 ) * . 9 + A F I(9 ) & * .5 4 + A F I( 1 0 ) * .4 ) IF (O V IP .L T .O .O ) 0 V IP = 0 .0 35 IF IF DR DR DR DR DR DR 40 D E B U G ) P R I N T * . » A F P O P ,A F F C O N ,E M X .O V IP " .A F F C O N ,E M X ,O V IP D E B U G J P R I N T * , * A F P O P ; YY ".Y Y 1)= .0 2 *A T E M P (ID A Y ,IY R ) - 1 . 1 1 2 ) = -0 4 6 *A T E M P (ID A Y , IY R ) - 2 . 6 0 3 ) = .0 4 6 *A T E M P (ID A Y , IY R ) - 2 . 5 5 4 )= .0 2 4 *A T E M P IID A Y .IY R )-1 .2 2 5 )= .0 3 5 7 *A T E M P < ID A Y ,IY R )-1 .9 0 1 O )= D R (9 )= 0 R (8 )= D R (^)= D R (6 )= (-0 0 1 8 *A T E M P (ID A Y . IY R ) - . 0 9 1 ) * 5 IF (A F F C O N .G T .Y Y *. 7 5 ) DO 1 6 0 1 = 5 . 1 0 A F I(I)= A F H i ) * 9 5 1 6 0 C O N T IN U E IF (A F F C O N .G T .Y Y *.2 5 ) 00 170 1 = 2 ,1 0 A F l(l)= A F I(I)* .8 1 7 0 C O N T IN U E 1 8 0 C O N T IN U E 45 50 GOTO 180 GOTO 180 C 55 AAF=AFF=0. DO 2 0 0 d = 1 . 9 I=11-J I F ((DDRR( (1I _______ ) . G T . 1 . 0 ) D R ( I ) = 1. . 0. I F ( DEBUG) P R IN T * , “ A FPO P; D R ( I ) , A F I ( 0= A F 1 (I ) * ( 1 -D R (i) ) B = A F I I I - 1 ) *D R (I - 1) A F I( I ) =( A F I( I ) *( 1 .-0 R (I ) ) + A F I(I IF (D E B U G )P R IN T * . " AFPOP; D R ( I ) , A F I ( IF iD E B U G J P R IN T * . " A F I ( " . I . “ ) = " . 0 . " + 60 65 70 75 C AAF=AAF + A F I ( I ) ♦ 1 . 2 5 I F ( I . L E . 4 ) GO TO 2 0 0 AFF=AFF + A F I ( I ) 2 0 0 C O N T IN U E A F I ( 1 ) = A F I ( 1 ) * ( 1 - D R ( 1 ) ) + O V IP I F ( A A F . G T . . O 2 J G 0 TO 4 0 0 PO P IN C R ’ O .O I F ( A A F . G T . 0 . 0 ) POP I N C R = . 0 2 / A A F AFF=0. A A F =.0 2 DO 3 0 0 1 = 2 . 1 0 I ) , I " . D R (I ) . A F I ( I ) . I 1 )*D R (I- 1 )) I ) . I " . D R (I) . A F I( I ) . I ".B t*> W CD A F I ( I ) = A F I( I)*P O P IN C R I F ( I . L E . 4 j GOTO 3 0 0 A F F ' A F 1 ( 1 ) + AFF C O N T IN U E C O N T IN U E 80 300 400 85 90 1 c c c A F F F R = (.1 5 6 2 * ( A F I ( 2 ) * 1 . 2 5 ) + . 1 9 9 9 * ( ( A F I ( 3 ) * 1 .2 5 ) + & A—F I ( 44 1i »* .. 2r 5- )' + . 2 4 3 6 * A F I ( 4 ) + . 1 7 4 9 « A■F"F * . 2" 5 + A FF) -------I F ( DEBUG ) P R I N T . " A F P O P . A F I ( 1 ) . A F F " . AF I ( 1 ) . A F F RETURN END C C C S U B R O U T IN E M I T E I N d ( J Y ) COMMON V A R I A B L E S : J D A Y 5 C 10 15 20 25 30 COMMON / D A T E / I D A Y , J D A Y . I Y R , I S T R A T . J S T R A T . K S T R A T . I P A R T C 0 M M 0 N /M IT E D A 2 / IE C T H 1 . I E C T H 2 . X . NSCOUT. N X , KONN. IP C ,IE R R O R .K E M X .S C C O S T C O M M O N /M IT E D A T /S A E R (2 0 ) , S A A F ( 2 0 ) . I A F D ( 2 0 ) . I E R D ( 2 0 ) . + A E R . A A F . E P Y . A F F F R , Y Y . A F F C O N . E R I N d ( 3 ) . CO N. + E M X ,E L P D P O ( 1 0 ).E R i(1 0 ),A F I(10) T H I S S U B R O U T IN E D I V I D E S THE GROWING SEASON I N T O THREE P A R T S : UP TO JU N E 1 5 ; JU N E 16 THROUGH AUGUST 1 5 ; AND FROM AUGUST L 6 O N . THE NUMBER OF M I T E S ABOVE THE TH R E S HO LD ON T H I S DA Y ARE ADDED TO THE R U N N IN G SUM K E P T FOR EACH P AR T OF THE SEASON + C C C C C C I F ( J D A Y . G T . 1 6 6 ) GO TO 1 0 0 JY = 1 GO TO 3 0 0 100 I F ( J D A Y . GT . 2 2 7 ) GO TO 2 0 0 JY=2 GO TO 3 0 0 200 JY=3 3 0 0 D A M =A ER -15. IF (D A M .L T .O .)D A M = 0 . E R I N J ( J Y ) = E R I N J ( J Y ) + DAM RETURN END W —* 1 C C 5 IO 20 C C C C C C 25 C C 15 S U B R O U T IN E MSCOUT C * * * * * * K D A Y , - J X , IN T L O G IC A L D E B U G .M O T H .M IT E .S C A B .IW S C O U T ,H S P R A Y COMMON / D A T E / I D A Y . J D A Y . I Y R . I S T R A T . J S T R A T . K S T R A T . I P A R T C O M M O N /C H E M S /B E N L A T E , C A P T A N . D I F O L , + P L IC T R N .C A R Z O L , G U T H IO N .P Y R T H R D ,IP R O (1 2 ) .N S P R A Y .M IS S S P .N E X T S P C O M M O N /M IT E D A 2 /IE C T H 1 , IE C T H 2 . X . NSCOUT. N X , KONN. + IP C ,IE R R O R ,K E M X ,S C C O S T C O M M O N /M IT E D A T /S A E R (2 0 ) .S A A F ( 2 0 ) , I A F D ( 2 C ' . I E R D ( 2 0 ) . + A E R .A A F .E P Y ,A F F F R ,Y Y . A F F C O N .E R IN J (3 ).C O N . + E M X .E L P O P O i1 0 ).E R I(1 0 ),A F I(10) C O M M O N /D B /D E B U G ,M O T H ,M ItE . S C A B . IW S C O U T .H S P R A Y . IN T S C T T H I S S U B R O U T IN E CHEC KS THE A C T I V E A M B L Y S I E U S F A L L A C I S ( A A F ) AND THE A C T I V E EUROPEAN RED M I T E ( A E R ) P O P U L A T I O N S AND MAKES A R E C O M M E N D A T IO N : I P R O ( I ) FOR NO S P R A Y . M C S ( 2 ) FOR 1 / 3 STR ENGT H P L I C T R A I P R 0 ( 7 ) FOR 1 / 2 S TR E N G TH P L I C T R A N I P R 0 ( 8 ) FOR F U L L STR ENGT H P L I C T R A N AND M C S ( 5 ) FOR F U L L S TR E N G TH CARZO DATA I S D A T E 1 / 1 8 0 / DATA I S D A T E 2 / 2 1 0 / R A N A E R 'O . DEBUG=. TRUE. IF (J S T R A T .G T .1 .A N D .J S T R A T .L T .4 ) GO TO 5 0 0 C 30 I F ( I P C . E O - 5 ) G 0 TO 5 7 0 C C THER E I S AN ERROR I N THE M O N I T O R I N G BUT 95 OF TIM E IT IS W IT H IN C C 10 35 40 810 45 50 OF A C T U A L LEVEL I F ( I E R R O R . E Q . 1 ) G 0 TO 8 1 0 I F t A E R . L T . I E C T H 2 ) G 0 TO 4 0 0 . I F 1 P L I C T R N . E Q . 0 . 0 . A N D . H S P R A Y ) GOTO 1 0 0 I F t A A F . L T . . 0 8 ) GO TO 2 0 0 I F ( A E R . G T . I E C T H 1 ) G 0 TO 2 0 0 T R P 1 = .0 9 9 *A E R - . 3 T R P 2 = . 0 8 2 6 7 * AER - . 3 4 I F ( A A F . G T . T R P 1 ) G 0 TO 4 0 0 I F ( A A F . L T . T R P 2 ) G 0 TO 1 0 0 GO TO 1 1 0 C A L L R A N I A E R . . 2 5 . 4 , RANAER) I F I R A N A E R . L T . I E C T H 2 ) GO TO 4 0 0 I F 1 P L I C T R N . E O , O . O . A N O . H S P R A Y ) GO TO 1 0 0 I F ( A A F . L T . . 0 8 ) GO TO 2 0 0 I F ( R A N A E R . G T . I E C T H 1 ) G 0 TO 2 0 0 T R P 1 = -0 9 9 *A E R - .3 T R P 2 = . 0 8 2 6 7 »AE R - . 3 4 I F ( A A F . G T . T R P 1 ) G 0 TO 4 0 0 I F ( A A F . L T . T R P 2 ) G 0 TO 1 0 0 C 110 55 C 100 60 C 200 65 C 300 70 400 6009 75 500 560 80 85 570 90 574 95 100 105 C 580 6666 C 600 600 IS P R A Y =6 P LIC T R N = P LIC T R N NSPRAY=NSPRAY + GO TO 3 0 0 + .3 3 3 1. IS P R A Y = 7 P L IC T R N = P L IC T R N N SPR AY =N S PR A Y + GO TO 3 0 0 + .5 1. IS P R A Y = IP C + 4 IF (IP C .E Q .4 }P L IC T R N = P L IC T R N I F ( I P C . E O . 5 )CARZOL=CARZOL + NSPRAY=NSPRAY * 1. + 1. 1 C O N T IN U E IP R O (IS P R A Y )= 1 4 GO TO 6 0 0 C O N T IN U E I F ( D E B U G ) P R I N T 6 0 0 9 . N SPR AY „ FO RM AT (* M S C O U T : NSPR AY * . 5 X , 1 3 ) GO TO 5 8 0 C O N T IN U E I F t J D A Y . E O . I S D A T E 1 ) G 0 TO 5 6 0 I F ( J D A Y . E O . I S D A T E 2 ) G 0 TO 5 6 0 GO TO 5 8 0 IS P R A Y = IP C + 4 NSPRAY=NSPRAY ♦ 1 IP R 0 1 IS P R A Y )= 1 4 I F I d S T R A T . E O . 3 )CARZOL=CARZOL + 1 I F t J S T R A T . E O .2 )P LIC T R N = P LIC T R N + GO TO 6 0 0 I F ( I E R R O R . E O . 1 )GOTO 5 7 4 I F ( A E R . L T . I E C T H 1 ) G 0 TO 6 0 0 I SPR AY = I P C + 4 N S PR AY = NSPR AY + 1 CARZOL =CARZOL + 1 IP R O (IS P R A Y )= 1 4 GO TO 6 0 0 C A L L R A N f A E R . . 2 5 . 4 . RANAER) I F ( R A N A E R . L T . I E C t H 1 ) GO TO 6 0 0 IS P RA Y = IP C + 4 N SPR AY = NSPR AY + 1 CARZOL*CARZOL + 1 IP R O C IS P R A Y )= 1 4 GO TO 6 0 0 .. r\3 1 IF ( D E B U G ) P R IN T 6 6 6 6 . JD A Y .N S P R AY FO R M A T ( * NO SPR AY ON J D A Y * . 1 3 , * NSPR AY = * , 1 3 ) DEBUG*. TRUE. C O N T IN U E I F ( D E B U G ) P R I N T 1 0 0 0 , A E R , A A F . I E C T H 1 . I E C T H 2 . R A N A E R . JD A Y 1 0 0 0 FO R M AT( * M S C O U T ;A E R .A A F ,1 E C T H 1 2 .R A N A E R .J M » .2 F 1 0 . 2 . 2 1 5 . + F 1 0 -2 .I5 ) C DEBUG*. F A LS E . RETURN END j ( 1 1 5 10 15 20 25 S U B R O U T IN E MMORT C * * * * * *COMMON V A R I A B L E S : I P R O ! 1 2 ) . E R I { 1 0 ) . A F I ( 1 0 > , E L P D P O t 1 0 ) C C T H I S S U B R O U T IN E C A L C U L A T E S THE M I T E M O R T A L I T Y DUE TO TH E P E S T I C I D E S C R E S I D U A L . I V A L U E S D E T E R M IN E TH E THE P E S T I C I D E : 1 FOR NO S P R A Y . 2 + 1 C I P R 0 ( 6 ) = 1 / 3 P L IC T R A N : I P R 0 ( 7 ) = 1 / 2 P L IC T R A N ; IP R O ( 8 ) -P L IC T R A N ; IP R 0 < 9 ) C C A R Z O L; I P R 0 ( 1 0 ) = P Y R E TH R O ID ; C I P R O ( 11 ) = B E N A L A T E C L O G I C A L D E B U G . M O T H . M I T E . S C A B . IW S C O U T , HSPR AY C O M M O N /D B /D E B U G . M O T H . M I T E . S C A B . IW S C O U T . H S P R A Y . I N T S C T C O M M O N /C H E M 3 /B E N L A T E , C A P T A N . D I F O L , + P L I C T R N . C A R Z O L . G U T H IO N . PYR T H RD , I P R O ( 1 2 ) , N S P R A Y , M I S S S P . NEXTSP C O M M O N /M IT E D A T/S A ER( 2 0 ) , S A A F ( 2 0 ) . I A F D ( 2 0 ) . IE R D ( 2 0 ) . + A E R .A A F .E P Y .A F F F R .Y Y .A F F C O N .E R IN J I3 ).C O N . + E M X .E L P D P O (lO j.E R f( I O ) , A F I ( I O ) D IM E N S IO N B E N M (1 5 ) . S M A F I 5 ) . SM ER(5 ) C DATA B E N M / . 0 2 . . 0 5 . . 1 4 . . 2 4 . . 3 5 , . 4 4 . . 4 8 . . 5 , . 5 . . 5 . . 4 8 . . 4 5 . . 3 8 . ft.2 2 ..0 5 / DATA S M A F / O . , . 1 0 . . 7 0 . . 9 9 . . 9 9 / DATA S M E R / . 7 0 . . 8 5 . . 9 9 . . 9 9 . . 1 0 / C c c D E BU G1 . T R U E . DO 6 0 0 I S T R = 6 , 1 1 K IS T R = IS T R - 5 I F ( I P R O ! I S T R ) . E Q . O ) GO TO 2 0 0 I F ( I S T R . E O . 1 1 ) GO TO 1 0 0 30 C IF ( D E B U G ) P R I N T * . " I S T R " . IS T R IF ID E B U G J P R IN T * , "M M O R T ,S M E R (IS ), " , S M E R (K IS T R ) . S M A F (K IS T R ) 35 AER=AER - A E R * S M E R ( K I S T R ) * E X P ( - . 2 3 * ( 1 4 - I P R O ( I S T R ) ) ) A A F = A A F -A A F *S M A F (K IS T R )*E X P (- . 2 3 * ( 1 4 - I P R 0 ( I S T R ) ) ) C I F ( D E B U G ) P R I N T * . "M M O R T. A E R . A A F " . A E R . A A F IF (D E B U G J P R IN T * , " E X P " , E X P ( - . 2 3 * ( 1 4 - IP R O ( I S T R ) ) ) 40 GO TO 1 5 0 lO O A E R = A E R - A E R * B E N M ( I P R O ( I S T R ) ) A A F = A A F -A A F *B E N M (IP R O (IS T R )) 45 1 5 0 DO 1 7 5 1 = 2 . I O E R I(I )= A E R *E L P D P 0 (I)*2 .5 *.7 5 A F I ( I ) = A A F * E L P D P O I( I) )**22 . 5- * . 8‘ IF (D E B U G ) P R IN T 2 0 0 0 . E R I ( I ) . A F I ( I ) . I 2 0 0 0 F O R M A T !* MMORT: E R I. A F I . I * . 10X. 2 F 1 0 .3 .1 3 ) 1 7 5 C O N T IN U E 50 C 200 55 60 1 C O N T IN U E IF (D E B U G )P R IN T 4 0 0 0 , A A F .A E R ,IS T R ,IP R O ( IS T R ) 4 0 0 0 FO R M A T !* MORT: . A A F . A E R . I S T R . I P R 0 ( I S T R ) * . 2 F 7 . 3 . 2 1 4 ) 600 C O N T IN U E C D E B U G *.F A L S E . R E TU R N END C C 5 10 15 S U B R O U T IN E E S M I T E S C * * * * "COMMON V A R I A B L E S : O M FR UIT C C T H I S S U B R O U T IN E C A L C U L A T E S THE MONETARY LOSS I N D O L L A R S PER ACRE DUE C TO M I T E I N J U R Y . FOR THE E A R L Y . M I D D L E AND L A T E P A R T S OF THE S EA S O N . C THE M A X IM U M L O S S / A C R E ARE 2 0 0 . 0 0 . 1 3 3 . 3 3 . AND 5 7 . 2 0 D O LL A R S C R E S P E C T I V E L Y . THE MAXIM U M I S REACHE D A T 2 0 0 0 M I T E D A Y S / L E A F . FOR C EACH OF THE THREE P A R T S BETWEEN O AND 2 0 0 0 THE F U N C T I O N IN C R E A S E S I N C A L O G I S T I C L I K E F A I S H I O N AND I S CONSTANT ABOVE 2000. C LO G IC A L D E B U G .M O TH .M ITE .S C A B .IW S C O U T .H S P R A Y C O M M O N / D B / D E B U G . M O T H . M I T E . S C A B . IW S C O U T . H S P R A Y . I N T S C T C O M M O N / T R E E / 1S T A G E . F D F R U I T . S D F R U I T , C D F R U I T . D M F R U I T . T Y I E L D C O M M O N /M IT E D A T /S A E R (2 0 ) . S A A F( 2 0 ) . I A F D ( 2 0 ) . I E R D ( 2 0 ) . bJ bo <*» + + 20 A E R . A A F . E P Y . A F F F R , Y Y . A F F C O N , E R I N J O ) , CON. EMX, E L P D P O ( 1 0 ) . E R I ( 1 0 ) . A F I ( 10) D IM E N S IO N A E R I N J ( 3 ) D M F R U IT = 0. DATA A E R I N J / . 1 2 . . 0 8 . . 0 3 4 3 2 / 25 DO 1 0 0 1 = 1 . 3 I F ( E R I N J ( I 1 . G T . 2 0 0 0 ) GO TO 5 0 X = A E R IN J (IJ » (E R IN J (I)/2 0 0 0 )**2 , , „ . , v D M F R U IT =D M F R U IT + X +X« ( ( A E R I N J ( I ) - X ) / A E R I N J ( I ) ) IF ( D E B U G ) P R IN T lO O O .D M F R U IT GO TO 1 0 0 30 50 35 1 5 10 15 20 25 30 1 0 0 C O N T IN U E 1 0 0 0 FO R M A T !» RETURN END IO 15 20 25 D M F R U IT = *, F 6 . 2 ) S U B R O U T IN E S C O U T ( I D A Y . J S T R A T ) L O G I C A L D E B U G . M O T H , M I T E . S C A B , IW S C O U T . HSPR AY C O M M O N /D B /D E B U G .M O T H ,M IT E .S C A B ,IW S C O U T .H S P R A Y . IN T S C T COMMON / C M S C O U T / T H E A T , M O T H K I L . M S P R A Y . E C M 1 . E C M 2 . E C M 3 , + C M L E V E L , L U C K . C M L O S S . H E R A T . O L D . WORMAPL C I S D A T E N = S C O U T IN G DA TE (N U M B E R ED FROM DAY 9 0 ) DATA I S D A T E 1 / 9 1 / DATA I S D A T E 2 / 1 2 1 / I F ( D E B U G ) P R IN T 2 0 0 . ID A Y 200 F O R M A T (*S C O U T *.1 5 ) I F ( . N O T . I W S C O U t ) RETURN I F ( I D A Y / I N T S C T * I N T S C T . E O . I D A Y ) G O TO 1 0 0 I F C J S T R A T . E O . 1 ) RETURN I F ( J S T R A T . L T . 4 . A N D . M I T E ) GO TO 4 0 R ETU RN 1 0 0 C O N T IN U E I F ( M O T H K I L . N E . O ) GOTO 5 0 I F ( M O T H ) C A L L CMSCOUT D E B U G = .F A L S E . 5 0 I F ( . N O T . M I T E ) RETURN I F ( J S T R A T . E O . 1 ) RETURN I F ( J S T R A T . L T . 4 ) G 0 TO 4 0 C A L L MSCOUT RETURN 4 0 C O N T IN U E I F ( I D A Y . E O . I S D A T E 1 ) C A L L MSCOUT I F ( I D A Y . E O . I S 0 A T E 2 ) C A L L MSCOUT RE TU R N END 1 S U B R O U T IN E n c iO C iC ia a 5 D M F R U IT =D M FR U IT + A E R I N J ( I ) I F ( D E B U G ) P R I N T lO O O .D M F R U IT C O D M O T H (A V T E M P . A P P L E S ) T H I S S U B R O U T IN E MODELS C O D L I N G MOTH P O P U L A T I O N D Y N A M I C S . OTHER S U B R O U T IN E S C A L L E D E X C L U S I V E L Y FROM T H I S S U B R O U T IN E ARE CMMORT, 0 G R E D A 2 . AND D E L A Y . COMMON / C M S C O U T / T H E A T . M O T H K I L . M S P R A Y . E C M 1 . E C M 2 . E C M 3 . + C M L E V E L . L U C K . C M L O S S . I T E R A T , O L D . WORMAPL COMMON / M O T H / D E L ( 5 J . D E L P ( S ) . I K ( 5 ) . X ( 6 ) . X I N ( 6 ) . + R ( 2 5 , 5 ) , S T R G (5 ) . P L R ( 5 ) COMMON / D A T E / I D A Y . J D A Y , I Y R . I S T R A T . J S T R A T . K S T R A T . I P A R T INTEGER O E L .D E L P D IM E N S IO N 0 M ( 2 5 ) DATA D D D / 2 . / 1 1 .2 5 ,7 .5 .3 .7 5 ,1 8 *0 ./ D A TA O M / O . . 1 5 . . 2 2 . 5 . 1 5 . C* C* C ***********« ***B E G IN P L R (1 )= .0 0 1 0 3 P L R (2 )= .00140 P L R (3 l= .00023 P L R 1 4 )= 0 . P L R (5 )= 0 . M O D E L. U (*> C* 30 35 40 45 50 55 60 65 I F ( M O T H K I L . E Q . O ) GOTO 1 0 0 C A L L CMMORT( R . XCMMORT. M O T H K I L ) 100 C O N T IN U E C C* C A L C U L A T E T O D A Y ' S O E G R E E - D A Y S ( D H E A T ) AND ADD TO C* A CCU MULA TE D H E AT ( T H E A T ) . C* 110 D H E A T = A V TE M P -50. 120 THEAT=THEAT+DHEAT C* C* C A L C U L A T E N I T (NU MBER OF I T E R A T I O N S ) FOR T O D A Y . C* 129 N I T = ( CHE A T + O L D ) / D D D + . 0 0 0 0 1 O LD =D H E A T +O LD -N IT *D D D I F ( N I T . L E . O ) GOTO 1 7 0 C= C« IN N E R LOOP ( 1 4 0 ) CONTROLS I T E R A T I O N S FOR T O D A Y . C* DO 1 4 0 I T = 1 , N I T C* C* LOOP 1 3 0 U P D A T E S MODEL BY ONE D D D . C* DO 1 3 0 I B = 1 , 5 IS T G = 6 -IB 130 CALL D E L A Y (X (IS T G ), X (IS T G + 1) , R( 1 , IS T G ) . P L R ( IS T G ) . + D E L (IS T G ),D E L P (IS T G ).D D D .IK (IS T G )) C* C* LOOP 1 3 3 ADOS L A R V A E TO THE C O O L I N G MOTH P O P U L A T I O N C* I N T O THE ORCHARD FROM TH E SU R O U N D IN G AREA IT E R A T = IT E R A T + 1 I F ( I T E R A T * D D D . L T . 9 0 0 ) GOTO 1 3 4 I F ( I T E R A T * D O D . G T . l O O O ) GOTO 1 3 4 I T E R A T = lO O O DO 1 3 3 0 = 6 . 1 5 C P R I N T * . " L IN E 2 2 2 3 . 5 “ 133 R ( U . 2 ) = R ( J . 2 ) + . 0 0 2 5 5 5 * A P P LE S *.0 0 2 2 C* c* C= c* 134 70 135 CALCULATE O V IP O S IT IO N T H IS DDD W H IC H BECOMES X ( 1 ) . O V IP 'O . IB = IK (5 ) DO 1 3 5 0 = 1 , I B 0 V IP = 0 V IP + 0 M (U )*R (0 ,5 )= .5 3 7 X ( 1 )= O V IP C* 75 C* I F ( M O T H K I L . E Q . O ) GOTO 1 3 9 SPR A Y M O R T A L I T Y TO NEWLY H A TC H ED L A R V A I F ( M O T H K I L . N E . O ) R ( 1 , 2 ) = R ( 1 , 2 ) * ( 1 -X C M M O R T ) C* C* 139 80 85 90 95 100 105 C A L C U L A T E NUMBER OF A P P L E S W I T H C O D L I N G MOTH LA R V A E W O R M A P L =W O R M A P L+ R (1 . 2 ) * ( A P P L E S - W O R M A P L ) / A P P L E S I F ( W O R M A P L . G T . A P P L E S ) W OR MAPL =AP PLE S C *2365C * 140 C O N T IN U E C* C* LOOP 1 6 0 C A L C U L A T E S STORAGE I N EACH S T A G E . T H I S R E PR E S EN T S C* THE NUMBER OF I N D I V I D U A L S I N EACH STA GE A T THE END OF THE D A Y . C* C» DO 1 6 0 1 = 1 . 5 SUM=0. IB = IK (I) DO 1 5 0 0 = 1 . I B 150 SU M=SUM +R ( 0 . 1 ) -----------160 S T R G ( I ) = S U M «- D-£'-.(I] l ( I ) / I K ( I ) C M LE V E L=S TR G (1 )/A P P L E S S T R G (5 ) = S TR G (5 l+ S T R G (4 ) C C THE MODEL ASSUMES T H A T THERE ARE 1 0 0 T R E E S / A C R E : 1 0 0 A P P L E S / B U C A P P L E S I S TERMS OF A P P L E S / T R E E W H I L E T Y I E L D I S I N TERMS OF C B U / A C R E SO TO CONVERT A P P L E S TO A P P L E S PER ACRE - C A P P L E S = 1 0 0 A P P L E S * B U / 1 0 0 *T R E E S » ACRE: CMLOSS I S P R O P O R T IO N C OF T O T A L A P P L E S I N F E C T E D . C M L O S S = W O R M A P L /A P P L E S C* C* OU TP U T MODEL S T A T E AT END OF THE D A Y . C* }*> in w C C* 170 2000 P R IN T 2 0 0 0 . J D A Y . D H EA T, T H E A T . S T R G (1 ) . S T R G (2 ) . S T R G O ) . S T R G (5 ) . O V IP RETURN FO R M AT( 1 X , 1 7 . 6 X . F 5 . 2 . 4 X , F 6 . 1 . 5 ( 3 X . F 7 . 2 ) ) END C ***************E N D M O D E L. S U B R O U T IN E C M I N I T C* C* 74 75 10 20 IN IT IA L IZ A T IO N S U B R O U T IN E COMMON / I N T / G P P , SCMPOP COMMON / C M S C O U T / T H E A T . M O T H K I L . M S P R A Y . E C M 1 . E C M 2 . E C M 3. + C M L E V E L . L U C K . C M L O S S , I T E R A T , O L D . WORMAPL COMMON / M O T H / D E L I 5 ) , D E L P ( 5 ) . I K < 5 ) , X < 6 ) . X I N ( 6 ) . + R ( 2 5 . 5 ) , S T R G (5 ) , P L R ( £ ) IN T E G E R D E L . D E L P D IM E N S IO N I R ( 2 5 , 5 ) DATA D E L / 1 4 5 , 5 8 7 , 2 6 5 , 5 0 . 1 7 5 / DATA I K / 5 * 15/ DATA I R / 3 0 * O t 4 , 1 2 , 1 6 . 8 , 2 , 6 , 1 0 , 1 6 , 1 8 , 8 , 8 5 * 0 / IT E R A T = 0 0LD=200. C M L E V E L = 0 .0 CMLOSS=THEAT=W0RMAPL=O. MSPRAY = L U C K = M O T H K I L = 0 DO 7 5 1 = 1 . 5 D E L P (IJ = D E L (I) S T R G lI)= X IN (I)= 0 . IB = IK (I) F IK = F L O A T (IK (I)) F D E L = F L O A T (D E L (I) ) DO 7 4 d - I . I B R J I “ FLOAT( IR ( J , I ) ) R ( J . I ) = B J I * ( f IK /F D E L )*(S C M P O P /1 0 0 .) S T R G (I)= S T R G (I) + I R ( d , I ) * (S C M P O P /1 0 O .) X (1+1)= R (IB .I) X IN 1 6 )= 0 . X ( 1) = R ( I K ( 5 ) ,5 ) RETU RN END S U B R O U T IN E D E L A Y ( V I N . V O U T . R . P L R , D E L . D E L P . D T . K ) D IM E N S IO N R ( 1) IN TE G E R D E L .D E L P F K = F L O A T (K ) B = 1 ,+ (D E L -O E L P )/(F K *D T )F P L R *D E L P /F K I D T * 1 . + 2 . * O T * F K /D E L P * A M A X 1( B , 0 . ) A = F K *D T 7 (D E L P *F L 0 A T (ID T ) ) DELP=DEL K M 1*K -f DO 2 0 d * 1 , I D T DO 1 0 I C ' I . K M I I= K -IC + 1 R (I)= R (I)+ A » (R (I-1 )-B *R (I)) R (1)= R (1)+ A *(V IN -B *R (1 )) V O U T= R (K ) RETU RN END C****************«**^***************************** C* S U B R O U T IN E CMSCOUT C* c * * ♦ „ * .* ,* * * * * * * * * * * * * * ♦ * * * * * * * * * * * ,♦ * * * * * * * ****** c* C* C* C* C* C* T H I S S U B R O U T IN E D E T E R M IN E S TH E SPRAY SCHEDULE U S IN G E ITH E R A C H AL EN DAR B A S E D SYSTEM S T A R T I N G A T F R U I T SET OR THE I P M A L G O R IT H M W H IC H C A L L S FOR SPR A Y S WHEN C O D L I N G MOTH POPS ARE OVER THE SET THR ESHO LD L O G IC A L D E B U G .M O T H .M IT E ,S C A B ,IW S C O U T .H S P R A Y C O M M O N / D B / D E B U G , M O T H . M I T E . S C A B . IW S C O U T , H S P R A Y , I N T S C T COMMON / D A T E / 1 D A Y . U D A Y . I Y R . I S T R A T . U S T R A T . K S T R A T . I PART COMMON / C M S C O U T / T H E A T , M O T H K I L . M S P R A Y . E C M 1 . E C M 2 . E C M 3 . 20 25 30 35 40 ♦ C M L E V E L . L U C K . C M L O S S . I T E R A T . O L D . WORMAPL C O M M O N /C HE M S /B E N LA TE . C A P T A N . D I F O L . + P L IC T R N , C A R Z O L. G U T H IO N ,P Y R T H D ,IP R O (1 2 ) .N S P R A Y . M IS S S P .N E X T S P COMMON / T R E E / I S T A G E . F D F R U I T . S D F R U I T . C O F R U I T . D M F R U I T , T Y I ELD c* c MO TH S T R A T E G I E S c 1 DO N O T H IN G c 2 C A LE N D A R - G U T H IO N c 3,1 C A LE N D A R - P Y R E T H R O ID c 4 , 1 I P M , NO ERROR - G U T H IO N . 0 0 1 . . 0 0 5 . . 0 0 3 c 5 , I P M , NO ERROR - P Y R E T H R O ID . 0 0 1 . . 0 0 5 . . 0 0 3 C 6 c 7 ,i C 8,' c 9 .' c 10 c 11 c 12 c 13 c 14 c 15 c 16 c 17 c 18 c 19 c c c I P M , NO ERROR - G U T H IO N . 0 0 1 . . 0 0 1 . . 0 0 1 I P M , NO ERROR - P Y R E T H R O ID . 0 0 1 . . 0 0 1 , . 0 0 1 IP M , NO ERROR - G U T H IO N . 0 0 2 . . 0 1 . .OOfe I P M , NOERROR - P Y R E T H R O I D . 0 0 2 . . 0 1 . . 0 0 6 I P M . NO ERROR - G U T H IO N . 0 0 1 5 . . 0 0 7 5 , . 0 0 4 5 I P M , NO ERROR - P Y R E T H R O ID . 0 0 1 5 . . 0 0 7 5 . . 0 0 4 5 I P M , RANDOM ERROR - G U T H IO N . 0 0 1 . . 0 0 5 . . 0 0 3 I PM. RANDOM ERROR - P Y R E T H R O ID . 0 0 1 . . 0 0 5 . . 0 0 3 I P M . R A N D O M ERROR - G U T H IO N . 0 0 1 . . 0 0 1 . . 0 0 1 I P M . RANDOM ERROR - P Y R E T H R O ID . 0 0 1 . . 0 0 1 . . 0 0 1 I P M . RANDOM ERROR - G U T H IO N . 0 0 2 , . 0 1 . . 0 0 $ I P M . RANDOMERROR - P Y R E T H R O ID . 0 0 2 . . 0 1 . . 0 0 6 I P M . RANDOM ERROR - G U T H IO N . 0 0 1 5 , . 0 0 7 $ , . 0 0 4 5 I P M . RANDOM ERROR - P Y R E T H R O ID . 0 0 1 5 , . 0 0 7 5 , . 0 0 4 5 P R I N T * , " I N C MSCOUT’ , " C M L E V E L * " . CMLEVEL D E B U G *.F A L S E . I F ( K S T R A T . E O . 1 ) RETURN I F ( K S T R A T . G T . 3 ) GOTO 1 0 0 45 C* C* C* 50 55 60 65 70 75 T H IS SPRAYS + T H E A T . I S T A G E . M S P R A Y , L U C K . M O T H K I L . JD A Y I F ( C M L E V . G T . E C M 2 ) GOTO 9 0 0 RETURN 80 C* 400 + 85 90 S E C T I O N C ONTR OL S C A LE N D A R IF ( D E B U G ) P R IN T 1 1 0 0 . K S T R A T . ECM1. ECM2. E C M 3.C M L E V E L.C M L E V , + T H E A T . I S T A G E , MSPRAY . L U C K , M O T H K I L . JD A Y 1100 FO R M A T (» K S ,E C M 1 2 3 .C M 5 .T H E A t . I S . M S . L U , M K , J D * . 4 I 3 . 2 F 5 . 3 , F 6 . 1, ^ 514) I F ( I S T A G E . L T . 8 ) RETURN I F ( T H E A T . L T . 1 7 1 0 . ) GOTO 9 0 0 RETURN C* C* C* T H I S S E C T I O N C ONTR OL S I P M SPR AYS C* 100 C O N T IN U E CM LE V = C M L E V E L IF (D E B U G ) P R IN T 1 lO O .K S T R A T . ECM 1. ECM 2. E C M 3.C M L E V E L.C M L E V . + T H E A T , I S T A G E . M S P R A Y . L U C K . M O T H K I L . JD A Y IF ( K S T R A T .L T . 12 )G 0 T 6 150 C S E T C M LE V = TO P E R C E I V E D L E V E L ( W I T H E R RO R) C A LL R A N (C M L E V E L .. 2 5 . 5 . CMLEV) 150 C O N T IN U E IF (D E B U G ) P R IN T 1 1 0 0 . K S T R A T .E C M 1 . ECM2. E C M 3.C M L E V E L.C M L E V . + T H E A T . I S T A G E , M S P R A Y , L U C K . M O T H K I L . JD A Y G O T O (2 0 0 . 3 0 0 . 4 0 0 . 1000)M SPR AY+1 C* 200 I F ( C M L E V . G T . E C M 1 ) GOTO 9 0 0 RETURN C* 300 I F ( T H E A T . G T . 8 0 0 . ) GOTO 4 0 0 IF (D E B U G ) P R IN T 1 1 0 0 . K S T R A T . ECM1, ECM2. E C M 3,C M L E V E L.C M L E V . C* C* 900 I F C T H E A T . L T . 1 2 0 0 . ) RETURN IF ( D E B U G ) P R IN T 1 1 0 0 .K S T R A T , ECM 1. ECM2. ECM3. CM LE V E L. CM LE V. T H E A T ,IS T A G E .M S P R A Y .L U C K .M O T H K IL .J D A Y I F C L U C K . E Q - 1 l RETURN I F ( C M L E V . G T . E C M 3 ) GOTO 9 0 0 RETU RN M O T H K I L * 14 I F ( DEBUG) P R IN T 1 1 0 0 . K S T R A T . ECM1. ECM2. ECM3, C M LE V E L, CMLEV, + T H E A T .IS T A G E .M S P R A Y .L U C K .M O T H K IL .J D A Y I F ( K S T R A T . E O . 2 . O R . K S T R A T . E Q . 4 . O R . K S T R A T . E Q . 6 ) G 0 TO 9 1 0 I F ( K S T R A T . E O . 8 - O R . K S T R A T . E Q . 1 0 . O R . K S T R A T . E O . 1 2 ) GO TO 9 1 0 £*» *■'* 95 910 100 920 105 1 C C* 1000 IF ( K S T R A T .E Q .1 4 . O R .K S T R A T .E O .1 6 . O R .K S T R A T .E Q .18 ) IP R O (1 2 )= 1 4 PYRTHD = PYR THD + 1 . GO TO 9 2 0 C O N T IN U E IP R 0 (1 0 )= 1 4 G U T H IO N * G U T H IO N + 1. C O N T IN U E M S P R AY =M S P R AY + 1 IF (T H E A T .G T .1 0 0 0 .) LUCK=1 P R I N T * . " S T A R T OF S P R A Y " RETURN END C*» C* S U B R O U T IN E 5 GO TO 9 1 0 CMMORT( R . XCMMORT. M O T H K I L ) C* C ** c* c* D IM E N S IO N R ( 2 5 , 5 ) C* CMMRT=. 9 * . 6 7 * * ( f 1 4 - M O T H K I L ) / 2 ) XCMMORT = . 9 * . 5 * * ( ( 1 4 . 0 0 0 0 0 1 - M O T H K I L ) / 1 4 ) P R IN T *," C M M R T = ".C M M R T ,"X C M M O R T *".X C M M O R T 10 C C* DO 15 20 100 C* lO O U * 1 . 1 5 „ , R (d .1 )= 6 (J .1 > *(1 .-C M M R T ) R ( d . 5 ) = R ( J . 5 ) * ( 1 - -C M M R T ) I F ( J . G T . 1 2 ) GO TO 10O R (d ,4 )= R (d .4 )*(1 .-C M M R T ) C O N T IN U E M 0 T H K IL = M 0 T H K IL -1 C* RETU RN END LJ m 1 5 IO cpppppppppppppppppppppppppppppppppppppppppppp C C C C C C C C S U B R O U T IN E R A N ( A M E A N . R A N G E . N S E R I E S . R A N V A R ) L O G I C A L D E B U G . M O T H . M I T E . S C A B . IW S C O U T , HSPR AY T H I S S U B R O U T IN E C A L C U L A T E S A NOR MA LL Y RANDOM V A R I A B L E W I T H A MEAN OF " M E A N " AND A STA NDARD D E V I A T I O N OF " S D E V " . TH E S DEV I S C A L C U L A T E D FROM IN F O R M A T I O N ON THE D E S I R E D RANGE W H IC H TH E RANVAR SHOULD I N T O 9 5 OF THE T I M E . (A S S U M E S T H A T C l OF 9 5 - MEAN + AND - 1 . 9 6 * S D E V SO RANGE SHOU LD B E 1 / 4 THE W I D T H OF D E S I R E D C O N F ID E N C E I N T E R V A L . 15 C C100 20 1 5 10 15 R 1 * S R A N F (N S E R IE S ) R 2 *S R A N F (N S E R IE S I Z = ((-2 .*A L 0 G (R 1 ))**.5 )*C 0 S (6 .2 8 3 2 *R 2 ) SD EV = A M E AN *R AN G E RAER=SDEV*Z R A N V A R * RAER + AMEAN IF ( D E B U G ) P R IN T 1 0 0 . A M E A N .R A N G E .Z ,R A E R .R AN V A R FO R M A T !* R A N :AM EA N .R A N G E . Z . RAER. R A N V A R * .5 F 1 1 . 2 ) RETU RN END S U B R O U T IN E CMS TR AT COMMON / D A T E / I D A Y , J D A Y , I Y R , I S T R A Y . J S T R A T , K S T R A T I P A R T COMMON / C M S C O U T / T H E A T . M O T H K I L . M S P R A Y . E C M 1 . E C M 2 . E C M 3 . + C M L E V E L , L U C K , C M L O S S . I T E R A T . O L D . WORMAPL D IM E N S IO N C O C E (3 . B ) DATA C O D E / . 0 0 1 , . 0 0 5 . . 0 0 3 . . 0 0 1 . . 0 0 5 , . 0 0 3 , + .0 0 1 ..0 0 1 ..0 0 1 . .0 0 1 ..0 0 1 ,-0 0 1 , + .0 0 2 ..0 1 ..0 0 6 . .0 0 2 .-0 1 ..0 0 6 . + .0 0 1 5 ,.0 0 7 5 ,.0 0 4 5 ..0 0 1 5 ..0 0 7 5 ..0 0 4 5 / DATA E C M 1 / . 0 0 1 / DATA E C M 2 / . 0 0 5 / DATA E C M 3 / . 0 0 3 / I F ( K S T R A T . L T . 4 ) RETURN KKSTRAT = K S T P A T -3 I F ( K S T R A T . G T . 1 1) K K S T R A T = K S T R A T - 1 1 ECM1=C0DE( 1 . KKSTRAT) E C M 3=C 0D E(2 , K KS T R A T ) EC M 2-C 0D E ( 3 . K KS T R A T ) R ETURN END