{"http:\/\/dx.doi.org\/10.14288\/1.0093111":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Science, Faculty of","type":"literal","lang":"en"},{"value":"Zoology, Department of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Gossard, Thomas W.","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2011-03-21T21:06:43Z","type":"literal","lang":"en"},{"value":"1973","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#relatedDegree":[{"value":"Master of Science - MSc","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeGrantor":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"Experimental components analysis (Holling 1966) is used to develop a computer model of the four processes of sexual reproduction: mating, egg production, egg fertilization, and oviposition site selection.\r\nA general function of interacting populations is developed, and its application to mating and oviposition site selection is discussed. Data from the literature on mating are used to estimate parameter values for this function.\r\nA model of egg production and egg fertilization is developed from an experimental study of the vg strain of Drosophila melanogaster. Egg production is a complex process consisting of four components affecting individual ovarioles: ovariole activation, ovariole production, vitellegenesis, and ovariole deactivation. Threshold effects are found to exist for all four components. Egg fertilization is a simple process involving number of sperm stored and a constant probability of successful fertilization. However, results indicate that both egg fertilization and egg production become more complex beyond the range of treatments used here.\r\nAssumptions, not supported by data, are made for the processes of oviposition site selection, aging, mortality, and development. These assumptions are combined with the models of mating, egg production, and egg fertilization\r\ninto a single tentative model for sexual reproduction. Simulations using this model suggest possible effects of ecological importance: a sigmoid relationship between reproductive rate and density; and a chance in tactics with increasing mortality due to predation.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/32676?expand=metadata","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"AN EXPERIMENTAL COMPONENT ANA L Y S I S OF SEXUAL REPRODUCTION I . The E g g P r o d u c t i o n a n d E g g F e r t i l i z a t i o n P r o c e s s e s , w i t h some C o n s i d e r a t i o n o f t h e M a t i n g P r o c e s s , f o r D r o s o p h i l a m e l a n o g a s t e r M e i g e n by Thomas W. G o s s a r d B . S c , U n i v e r s i t y o f C a l i f o r n i a a t D a v i s , 1968 A THESIS SUBMITTED I N P A R T I A L FULFILLMENT OF \"THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e D e p a r t m e n t o f Z o o l o g y ^ We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA S e p t e m b e r , 1973 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Thomas W. Gossard Department of Zoology The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date 25 September 1973 ABSTRACT E x p e r i m e n t a l c o m p o n e n t s a n a l y s i s ( H o l l i n g 1966) i s u s e d t o d e v e l o p a c o m p u t e r m o d e l o f t h e f o u r p r o c e s s e s o f s e x u a l r e p r o d u c t i o n : m a t i n g , e g g p r o d u c t i o n , e g g f e r t i l i -z a t i o n , a n d o v i p o s i t i o n s i t e s e l e c t i o n . A g e n e r a l f u n c t i o n o f i n t e r a c t i n g p o p u l a t i o n s i s d e v e l o p e d , a n d i t s a p p l i c a t i o n t o m a t i n g a n d o v i p o s i t i o n s i t e s e l e c t i o n i s d i s c u s s e d . D a t a f r o m t h e l i t e r a t u r e o n m a t i n g a r e u s e d t o e s t i m a t e p a r a m e t e r v a l u e s f o r t h i s f u n c t i o n . A m o d e l o f e g g p r o d u c t i o n a n d e g g f e r t i l i z a t i o n i s d e v e l o p e d f r o m a n e x p e r i m e n t a l s t u d y o f t h e v g s t r a i n o f D r o s o p h i l a m e l a n o g a s t e r . E g g p r o d u c t i o n i s a c o m p l e x p r o c e s s c o n s i s t i n g o f f o u r c o m p o n e n t s a f f e c t i n g i n d i v i d u a l o v a r i o l e s : o v a r i o l e a c t i v a t i o n , o v a r i o l e p r o d u c t i o n , v i t e l l e g e n e s i s , a n d o v a r i o l e d e a c t i v a t i o n . T h r e s h o l d e f f e c t s a r e f o u n d t o e x i s t f o r a l l f o u r c o m p o n e n t s . E g g f e r t i l i z a t i o n i s a s i m p l e p r o c e s s i n v o l v i n g number o f s p e r m s t o r e d a n d a c o n s t a n t p r o b a b i l i t y o f s u c c e s s f u l f e r t i l i -z a t i o n . H o w e v e r , r e s u l t s i n d i c a t e t h a t b o t h e g g f e r t i l i -z a t i o n a n d e g g p r o d u c t i o n become more c o m p l e x b e y o n d t h e r a n g e o f t r e a t m e n t s u s e d h e r e . A s s u m p t i o n s , n o t s u p p o r t e d b y d a t a , a r e made f o r t h e p r o c e s s e s o f o v i p o s i t i o n s i t e s e l e c t i o n , a g i n g , m o r t a l i t y , a n d d e v e l o p m e n t . T h e s e a s s u m p t i o n s a r e c o m b i n e d w i t h t h e m o d e l s o f m a t i n g , e g g p r o d u c t i o n , a n d e g g f e r t i l i z a t i o n i n t o a s i n g l e t e n t a t i v e m o d e l f o r s e x u a l r e p r o d u c t i o n . S i m u l a t i o n s u s i n g t h i s m o d e l s u g g e s t p o s s i b l e e f f e c t s o f e c o l o g i c a l i m p o r t a n c e : a s i g m o i d r e l a t i o n s h i p b e t w e e n r e p r o d u c t i v e r a t e a n d d e n s i t y ; a n d a c h a n c e i n t a c t i c s w i t h i n c r e a s i n g m o r t a l i t y due t o p r e d a t i o n . i i i . TABLE OF CONTENTS Page ABSTRACT i LIST OF TABLES v i i LIST OF FIGURES X LIST OF EQUATIONS x i i i ACKNOWLEDGEMENTS x v i GENERAL INTRODUCTION 1 REVIEW OF INSECT REPRODUCTION MODELS 5 SEXUAL REPRODUCTION: PROCESSES AND COMPONENTS 7 PART I MATING INTRODUCTION 12 MODEL OF INTERACTING POPULATIONS 13 Development of the Model 13 Further Development of the Model 17 Components of the Model 20 Application of the Model to Reproduction i n Drosophila me lanogas t e r 25 PARAMETER ESTIMATION FOR MATING MODEL 32 Rate of Successful Search 32 Time Exposed and Handling Time 37 Ex p l o i t a t i o n , Interference, S o c i a l F a c i l i -t a t i o n and Motivation * 37 i v . Page Motivation: Density of Receptive Females and Males 38 CONCLUSION OF PART I 43 PART II EGG PRODUCTION INTRODUCTION . 44 FIRST EGG PRODUCTION EXPERIMENT .. 47 Introduction 47 Methods 47 Results 50 MATED FEMALES 56 Model Development 56 Parameter Estimation 65 VIRGIN FEMALES 74 Model Development 74 Parameter Estimation 76 SECOND EGG PRODUCTION EXPERIMENT . 79 Introduction 79 Methods 80 Results 83 Model Development . 84 Parameter Estimation 87 CONCLUSION OF PART II 93 V. Page PART III EGG FERTILIZATION INTRODUCTION AND METHODS 95 SPERM STORAGE 98 SPERM RELEASE 102 PARAMETER ESTIMATES 105 CONCLUSION OF PART III 108 A TEST OF THE PREDICTIVE POWERS OF MODELS DEVELOPED IN PARTS II AND III 110 OTHER PROCESSES 117 Aging 117 Morta l i t y 117 PART IV THE MODEL OF SEXUAL REPRODUCTION INTRODUCTION 120 CONSTRUCTION AND PROGRAMMING. 121 SIMULATION 127 RESULTS . 130 DISCUSSION 133 GENERAL CONCLUSION 143 BIBLIOGRAPHY 144 v i . Page APPENDICES I. E s t i m a t i n g f l y v e l o c i t y knowing the number of c o n t a c t s of f l i e s w i t h a 0.018 m. diameter c o n t a c t area 150 I I . P h y s i o l o g i c a l b a s i s o f the two a l t e r -n a t i v e egg p r o d u c t i o n f u n c t i o n s : Equations 23 and 24 152 I I I . E f f e c t of food i n t a k e on parameters of the egg p r o d u c t i o n f u n c t i o n 155 I n t r o d u c t i o n 155 Data f o r Podisus m a c u l i v e n t r i s .... 156 Data f o r D r o s o p h i l a melanogaster ... 162 D i s c u s s i o n 168 IV.\u2022 Symbols f o r equations i n P a r t IV 172 v i i . LIST OF TABLES Page Table 1. A disaggregation of the sexual re-productive process 9 Table 2. A comparison of d e f i n i t i o n s of para-meters common to both Holling's predation function and the general function f o r i n t e r a c t i n g populations ... 14 Table 3. Components of the predation process .... 21 Table 4. Possible components of the processes involving i n t e r a c t i n g populations 22 Table 5. Possible components of the mating process for Drosophila melanogaster .... 26 Table 6. Possible components of the o v i p o s i t i o n s i t e s e l e c t i o n process involving female Drosophila melanogaster and ov i p o s i t i o n s i t e s . . . 29 Table 7. A comparison of parameters common to both the general function for i n t e r -acting populations and the s p e c i f i c function for mating 31 Table 8. Relationship between f l y density and f l y v e l o c i t y 34 Table 9. Analysis of variance for l i n e a r r e-gression, Equation 11, using f l y v e l o c i t y data i n Table 8 35 Table 10. Analysis of variance f o r regression, Equation 16, using female r e c e p t i v i t y data i n Figure 5 42 Table 11. Two-way non-orthogonal analysis of variance of rate of egg production on 1) age of female and 2) whether female was i s o l a t e d or paired 51 Table 12. Relationship between age at copulation and 1) age at f i r s t egg laying, 2) maxi-mum egg production rate, and 3) age at maximum egg production rate 52 v i i i . Page Table 13. Relationship among parameters of the three egg production functions showing the sameness of the three equations 66 Table 14. Analysis f o r regression, Equation 25, using part of the egg production data i n Figures 7-11: i n d i v i d u a l estimates of parameter c f o r each treatment 68 Table 15. Analysis of variance for regression, Equation 22, using egg production data i n Figures 7-10: i n d i v i d u a l estimates of a and b f o r a l l treatments 70 Table 16. Analysis of variance for regression, Equation 22, using egg production data i n Figure 10 71 Table 17. Comparison of parameter estimates and c e r t a i n independent variables for the x egg production model 73 Table 18. Analysis of variance for regression, Equation 22, using egg production data i n Figure 11 77 Table 19. Analysis of variance for regression, Equation 25, using part of the egg production data i n Figure 14: single estimate of a and c for a l l t r e a t -ments . .. . . 89 Table 20. Analysis of variance for regression, Equation 25, using part of the egg production data i n Figure 14: i n d i -v i d u a l estimates of a and c for each treatment 90 Table 21. Analysis of variance for regression, Equation 22, using egg production data i n Figure 14: sing l e estimate of a, b, and c f o r a l l treatments 91 Table 22. Analysis of variance for regression, Equation 22, using egg production data i n Figure 14: i n d i v i d u a l estimates of a and b f o r each treatment . ... 92 i x . Page Table 23. Analysis of variance f o r regression, Equation 29, using f e r t i l e egg data i n Figures 17 and 18 106 Table 24. Comparison of parameter estimates f o r the egg f e r t i l i z a t i o n model 107 Table 25. Linear regression parameters f o r com-paring experimental observation from second experiment to p r e d i c t i o n of the egg production and egg f e r t i l i z a t i o n models 114 Table 26. Linear regression parameters for com-paring experimental observation from x f i r s t experiment to pre d i c t i o n of the egg production and egg f e r t i l i z a t i o n models 116 Table 27. Comparison of parameter estimates for the mortality function 118 Table 28. C l a s s i f i c a t i o n of population types for model simulation 129 Table 29. Relationship between food a v a i l a b i l i -ty and food intake for female Podisus macu1iventr i s 158 Table 30. Relationship between food l e v e l and 1) age at f i r s t egg laying, 2) maximum egg production r a t e , and 3) age at maximum egg production rate 160 Table 31. Analysis of variance f o r regression, Equation 22, using egg production data i n Figure 27: i n d i v i d u a l estimates of b and c for each treatment 161 Table 32. Analysis of variance f o r regression, Equation 22, using egg production data i n Figure 28: i n d i v i d u a l estimates of a for each treatment 165 Table 33. Analysis of variance f o r regression, Equation 22, using egg production data i n Figure 28: i n d i v i d u a l estimates of b and c for each treatment ............. 166 Table 34. Comparison of parameter estimates and ce r t a i n independent variables for the \"new\"egg production function ... 167 X . LIST OF FIGURES Page Figure 1. Flow diagram of the re l a t i o n s h i p s among the processes of sexual repro-duction and of the r e l a t i o n s h i p of sexual reproduction to other e c o l o g i c a l processes 8 Figure 2. A p a r t i a l disaggregation of the generalized process of i n t e r a c t i o n between two populations 23 Figure 3. Flow diagram of the rela t i o n s h i p s among the components of mating 27 Figure 4. Flow diagram of the rela t i o n s h i p s among the components of o v i p o s i t i o n 30 Figure 5. E f f e c t of age of v i r g i n female Drosophila melanogaster on proportion of females accepting a courting male .... 39 Figure 6. Flow diagram of the re l a t i o n s h i p s among the components of egg production .. 45 Figure 7. E f f e c t of age o f female Drosophila melanogaster on r a t e of egg production for age at f i r s t egg laying of 5 days: f i r s t experiment 54 Figure 8. E f f e c t of age of female Drosophila me1anogaster on r a t e of egg production for age at f i r s t egg laying of 10 days: f i r s t experiment 55 Figure 9. E f f e c t of age of female Drosophila melanogaster on r a t e of egg production for age at f i r s t egg laying of 15 days: f i r s t experiment 57 Figure 10. E f f e c t of age of female Drosophila melanogaster on r a t e of egg production for age at f i r s t egg laying of 30 days: f i r s t experiment 58 x i . Page Figure 11. E f f e c t of age of v i r g i n female Drosophila melanogaster on egg pro-duction r a t e : f i r s t experiment 59 Figure 12. E f f e c t of age of female Drosophila melanogaster on rate of egg production for age at copulation of 1 to 5 days: second experiment 81 Figure 13. E f f e c t of age of female Drosophila melanogaster on rate of egg production for age at copulation of 10 days: second experiment 82 Figure 14. E f f e c t of age of female Drosophila melanogaster on egg production rate for various ages at copulation: second experiment 85 Figure 15. E f f e c t of age of v i r g i n female Drosophila melanogaster on egg produc-t i o n r a t e : second experiment 86 Figure 16. Flow diagram of the re l a t i o n s h i p s among the components of egg f e r t i l i z a -t i o n 96 Figure 17. E f f e c t of age at f i r s t egg laying on t o t a l number of f e r t i l e eggs l a i d by mated Drosophila melanogaster: f i r s t experiment . . 99 Figure 18. E f f e c t of age at copulation on t o t a l number of f e r t i l e eggs l a i d by mated female Drosophila melanogaster: second experiment 100 Figure 19. Proportion of eggs f e r t i l i z e d as a function of the percentage of the t o t a l number of f e r t i l e eggs l a i d 103 Figure 20. Plot of observed on expected f e r t i l e egg production rate f o r mated female Drosophila melanogaster: second experiment I l l Figure 21. Plot of observed on expected f e r t i l e egg production rate f o r mated female Drosophila melanogaster: f i r s t experi-ment 112 x i i . P a 9 e Figure 22. Flow diagram of the model of sexual reproduction 122 Figure 23. Flow diagram of the computer program for sexual reproduction 125 Figure 24. Simulation r e s u l t s for the sexual reproduction model 131 Figure 25. Three hypotheses for the e f f e c t of population density on the egg produc-t i o n of insects 136 Figure 26. Interaction of various fecundity and mortality curves 139 Figure 27. E f f e c t of age of female Podisus maculiventris on egg production rate for various food intake l e v e l s 159 Figure 28. E f f e c t of age of female Drosophila melanogaster on egg production rate for various food intake l e v e l s 163 Figure 29. E f f e c t of age of female Podisus maculiventris on egg production rate for various food intake l e v e l s 171 x i i i . LIST OF EQUATIONS P a ? e Equation 1. Holling's predation function '.. 15 Equation 2. Modification of Holling's predation function 15 Equation 3. Preliminary function f o r in t e r a c t i n g populations 15 Equation 4. Preliminary function for in t e r a c t i n g populations 16 Equation 5. Function for i n t e r a c t i n g populations 16 Equation 6. Function for i n t e r a c t i n g populations 16 Equation 7. Function for i n t e r a c t i n g populations: modified to include interference 19 Equation 8. Mating function 28* Equation 9. Preliminary function for rate of successful search 32 Equation 10. Function for estimating f l y v e l o c i t y 33, 151 Equation 11. Preliminary f l y v e l o c i t y function ... 33 Equation 12. F l y v e l o c i t y function 36 Equation 13. Preliminary r e l a t i v e v e l o c i t y function 36 Equation 14. Relative v e l o c i t y function 36 Equation 15. Function for rate of successful search 37* \u2022Equation included i n l i s t i n g of fragmentary equations (THE MODEL: CONSTRUCTION AND PROGRAMMING). xiv. Page Equation 16. Female r e c e p t i v i t y function 40* Equation 17. Function for density of receptive females 41* Equation 18. Function for density of receptive males 41* Equation 19. Function for age at f i r s t egg layi n g : f i r s t experiment 53,93* Equation 20. Function for age at maximum egg production rat e : f i r s t experiment .. 53,93* Equation 21. Preliminary egg production func-t i o n 61 Equation 22. Egg production function 63,93,155* Equation 23. Al t e r n a t i v e egg production function 64,152 Equation 24. Second a l t e r n a t i v e egg pro-duction function 64,153 Equation 25. Si m p l i f i e d egg production function 65 Equation 26. Log transformation of Equation 25 67 Equation 27. Function for age at f i r s t egg layi n g : second experiment 87 Equation 28. Function for age at maximum egg production rate: second experiment 87 Equation 29. Sperm storage function 98,108* Equation 30. Sperm release function 104,108* Equation 31. Function for determining propor-t i o n of females dying 119* Equation 32. Female s u r v i v a l function: aging 119* Equation 33. Male aging function 121* XV. Page E q u a t i o n 34. Female aging f u n c t i o n 121* E q u a t i o n 35. F u n c t i o n f o r t o t a l female d e n s i t y 121* E q u a t i o n 36. Female s u r v i v a l f u n c t i o n : p r e d a t i o n 123* E q u a t i o n 37. \"New\" egg p r o d u c t i o n f u n c t i o n .... 168 x v i . ACKNOWLEDGEMENTS I w o u l d l i k e t o t h a n k W i l f C u f f , N e i l G i l b e r t , M o n i c a G o s s a r d , Buzz H o l l i n g \/ P a t J e n k i n s o n , P e t e r L a r k i n , R o b i n L i l e y , a nd B i l l W e l l i n g t o n f o r t h e i r h e l p d u r i n g t h e c o u r s e o f t h i s s t u d y . GENERAL INTRODUCTION An i n d i v i d u a l organism may be v i s u a l i z e d as a system that combines a l l actions and interactions within the organism and between the organism and i t s environment. Interdependence of these actions and interactions precludes complete separation into d i s t i n c t groupings, but i t i s possible to approximate such groupings or processes. These processes can be general or s p e c i f i c . They can be broken i n t o smaller processes which themselves may be further subdivided. The desired l e v e l of understanding of the system determines the degree of t h i s disaggregation. There i s no need to d i s t i n g u i s h between a hierarchy of types of processes provided r e l a t i o n s h i p s among the actual processes are made c l e a r . Grouping actions and int e r a c t i o n s into processes i s the f i r s t step i n the modeling approach to studying complex problems. This approach has been applied to i n d i v i d u a l organisms (Holling 1966; Hubble 1971), groups of organisms (Paulik and Greenough 1966), and human s o c i a l systems (Holling and Chambers 1973) . Once i d e n t i f i e d , the action of each process can be summarized by regression equations describing observed re l a t i o n s h i p s between independent and dependent va r i a b l e s . The equations constitute a mathematical model which through simulation gives i n s i g h t i n t o the processes. During simu-l a t i o n , however, as a consequence of the regression approach, values of independent variables are li m i t e d to the range over which observations were made. Thus, these models give at best, high p r e d i c t a b i l i t y over the normal range of con-d i t i o n s but usually f a i l i n p r e d i c t i n g the outcome of any traumatic disturbance of conditions that c a r r i e s values beyond those observed. Experimental components analysis i s an a l t e r n a t i v e approach to modeling that overcomes the l i m i t a t i o n s of l i n e a r additive multiple regression equations. Experimental com-ponents analysis \" i s based on the argument that e c o l o g i c a l processes can be broken into^components that are defined as responses to variables, these responses being simple func-t i o n a l r e l a t i o n s h i p s * \" (Holling 1966). Having broken the processes into smaller processes, the components of each process are i d e n t i f i e d . Components are c l a s s i f i e d as basic i f \"shared by a l l examples of the process\" and subsidiary i f \"present i n some situ a t i o n s and not i n others\" (e.g. Table 1). Possible hypotheses with appropriate equations are constructed to explain the workings of each component. Experiments are then conducted to determine the v a l i d i t y of these hypotheses. Guidance for hypotheses comes from two sources: a p r i o r i knowledge and previous experiments. I n i t i a l l y , i n t u i t i o n and l i t e r a t u r e review suggest a l t e r n a t i v e hypo-theses with a l t e r n a t i v e equations for each component. *0r more formally, \"...these responses having mono-tonic d i f f e r e n t i a l s \" (Holling pers. comm.). 3. C a r e f u l l y d e s i g n e d e x p e r i m e n t s a r e c o n d u c t e d t o d i s t i n g u i s h among t h e s e a l t e r n a t i v e s . S e c o n d l y , e x p e r i m e n t a l r e s u l t s w i l l u s u a l l y show one h y p o t h e s i s t o be b e t t e r , p r o v i d e d i t i s m o d i f i e d . M o d i f i -c a t i o n o f t h i s h y p o t h e s i s w i l l s u g g e s t a new s e t o f h y p o t h e s e s and e q u a t i o n s . A g a i n , e x p e r i m e n t s c a n d i s t i n g u i s h among t h e s e a l t e r n a t i v e s . T h i s s e c o n d s t e p i s r e p e a t e d u n t i l t h e d e s i r e d r e s o l u t i o n o f t h e h y p o t h e s i s i s a c h i e v e d . F o r e x a m p l e , c u r s o r y k n o w l e d g e o f i n s e c t s m i g h t s u g g e s t t h e f o l l o w i n g h y p o t h e s e s a n d e q u a t i o n s . R a t e o f egg p r o d u c -t i o n (dE\/dT) as a f u n c t i o n o f age (A) i s 1) c o n s t a n t , i n d e p e n d e n t o f a g e : dE\/dT = a 2) r i s e s t o a maximum w i t h a g e : dE\/dT = a - ( l - b A ) o r 3) r i s e s t o a maximum and t h e n d e c l i n e s w i t h a g e : dE\/dT = a - ( l - b A ) - c A E x p e r i m e n t a t i o n m i g h t show t h a t t h e t h i r d h y p o t h e s i s i s m ost d e s c r i p t i v e b u t s u g g e s t s a new s e t o f h y p o t h e s e s . T T R a t e o f egg p r o d u c t i o n , a-(1-b )\u00abc , i s e i t h e r : 1) i n d e p e n d e n t p f age a t c o p u l a t i o n : T = A o r 2) d e p e n d e n t on age a t c o p u l a t i o n ( T c ) : T = A - T c E x p e r i m e n t a t i o n w o u l d a g a i n be u s e d t o s e l e c t one o f t h e two h y p o t h e s e s , and t h e r e s u l t s m i g h t s u g g e s t new h y p o t h e s e s . Once a l l components of the various processes are analysed, r e s u l t i n g functions can be linked together into a simulation model. The model w i l l give i n s i g h t into the o r i g i n a l process provided that 1) the model describes the whole system and not just some of i t s parts; 2) the des-c r i p t i o n of each process i s r e a l i s t i c ; 3) values of dependent variables generated are precise estimates of the observed values; and 4) the model has general a p p l i c a t i o n to organisms other than those a c t u a l l y studied (Holling 1966 p. 6). Ho l l i n g (1966 p. 6-7) believes that experimental components analysis \"provides at l e a s t the hope that the four q u a l i t i e s mentioned e a r l i e r w i l l be retained. Wholeness i s achieved since each step i s not considered as an end i n i t s e l f but i s combined with other steps so that progressively more and more of the process i s consi-dered. Reality i s ensured by the intimate union established between theory and experiment, with experiment d i c t a t i n g theory and theory suggesting experiments i n many small, successive steps. P r e c i s i o n i s assured because the demands of the mathematics forces us to cast the explanation i n a form precise enough to permit t e s t i n g of i t s adequacy. F i n a l l y , a degree of generality i s achieved by c l a s s i f y i n g each example by the u n i v e r s a l i t y of the components\". REVIEW OF INSECT REPRODUCTION MODELS Past attempts at constructing insect reproduction models have had shortcomings (Watt 1968 p. 295-302; Conway 1969 p. 37). The models of Lotka (1923), V o l t e r r a (1928), F u j i t a and Utida (1953), and F u j i t a (1954) attempted i n t u i t i v e b i o l o g i c a l realism without reference to data. The models of Pearl and Parker (1922), Pearl (1932), and Anderson (1957) f i t t e d equations to data, but the equation's parameters did not represent b i o l o g i c a l processes or values. Both Watt and Conway t r i e d to overcome these problems by building \"inductive-deductive\" models based on the data of others with consideration for reproductive biology. More quickly constructed that experimental components models, inductive-deductive models can be an important t o o l i n management situations such as Conways. However, inductive-deductive models are l i m i t e d by t h e i r necessary reliance on published data. Such data i s often c o l l e c t e d with l i t t l e e f f o r t to develop a synthesized understanding of the process involved. This lack of syn-thesis i s i l l u s t r a t e d by experiments purporting to show ef f e c t s of interference between parasites. These experi-ments were conducted at densities f a r greater than those found n a t u r a l l y ; there i s no interference e f f e c t at r e a l i s t i c densities ( G r i f f i t h s and Holling 1969 p. 797-799). B i o l o g i c a l i n s i g h t and data are not enough to construct r e a l i s t i c and general functions. What i s needed i s the 6 . continual feedback between i n s i g h t and data generated by the experimental components analysis approach outlined above (GENERAL INTRODUCTION). Models of Drosophila melanogaster reproduction are of i n t e r e s t because t h i s was my experimental animal. The work of Pearl and Parker (1922) and Pearl (1932) has already been mentioned. Of more i n t e r e s t i s accomparative, between s t r a i n study of d a i l y egg production as a function of age ( F i t z - E a r l e , McMillan, Butler, and Robson 1969; McMillan, F i t z - E a r l e , Butler, and Robson 1970a; McMillan, F i t z - E a r l e , and Robson 1970b). The equation they develop i s i d e n t i c a l to one of the equations t h i s author derives below from d i f f e r e n t p h y s i o l o g i c a l considerations. Their study included copulation only at or near eclosion, but the present study includes e f f e c t s of copu-l a t i o n at d i f f e r e n t ages, as well as d i f f e r e n t food l e v e l s and the dynamics of male-female population i n t e r a c t i o n . This necessitated modification of the common basic equation and the addition of a mating model. Past insect reproduction models have evolved through time i n t o models that are extremely u s e f u l : Conway (1969) at the pest managerial l e v e l ; F i t z - E a r l e e t a l . (1969), McMillan et a l . (1970a,b), and F i t z - E a r l e (1971) f o r the study of reproductive inheritance. However, there i s s t i l l need for models that give an understanding of the reproductive process i t s e l f and are not tools of the applied ecologist or g e n e t i c i s t . SEXUAL REPRODUCTION: PROCESSES AND COMPONENTS The process of sexual reproduction has been subdivided into i t s i n t e r a c t i n g processes and components. Sexual repro-duction can be considered as having four c h a r a c t e r i s t i c s (Figure 1): 1) four external inputs: male density, v i r g i n female density, energy for eggs, and o v i p o s i t i o n s i t e density; 2) f i v e external processes that generate these inputs: aging, mortality, feeding, energy p a r t i t i o n i n g , and o v i p o s i t i o n s i t e creation; 3) one output density of i n f e r t i l e and f e r t i l e eggs l a i d ; 4) four component processes that modify inputs and generate the output: mating, egg production, egg f e r t i l i z a t i o n and o v i p o s i t i o n s i t e s e l e c t i o n (Table 1).* The density by age group of males and v i r g i n females re s u l t s from t h e i r i n t e r a c t i o n with the external processes of aging and mortality (Figure 1). These two densities i n t e r -act with the component process of mating to give density of mated females by age and age at copulation. This l a t t e r density also i n t e r a c t s with the processes of aging and mor-t a l i t y i n the same way as males and v i r g i n females. Energy a v a i l a b l e for eggs i s a product of the energy p a r t i t i o n i n g process. This process allocates energy form feeding and stored energy among the various energy require-*A more d e t a i l e d consideration of the four component processes i s given i n the sections dealing with each: Mating, Figure 3: Oviposition s i t e s e l e c t i o n , Figure 4; Egg production, Figure 6; Egg f e r t i l i z a t i o n , Figure 16. c Figure 1. Flow diagram of the re l a t i o n s h i p s among the processes of sexual reproduction and of the r e l a t i o n s h i p of sexual reproduction to other ecolo-g i c a l processes. Rectangles represent variables, hexagons represent processes. 8 . ^Feeding^ Energy Intake Energy P a r t i t i o n i n g Stored Energy O v i p o s i t i o n S i t e Density O v i p o s i t i o n S i t e Creation Male Density Energy f o r Eggs Aging and Mo r t a l i t y V i r g i n Female Density Mating^ SEXUAL REPRODUCTION Mated Female Density Egg Product U n f e r t i l i z e d Eggs Egg F e r t i l i z a t i o n F e r t i l i z e d Eggs Ovip o s i t i o n S i t e Selection Density of Eggs Laid ( F e r t i l e and I n f e r t i l e ) 9. Ta b l e 1. A d i s a g g r e g a t i o n o f the s e x u a l r e p r o d u c t i v e p r o c e s s . Processes and components c l a s s i f i e d as b a s i c : process or component always p a r t o f s e x u a l r e p r o d u c t i o n , or s u b s i d i a r y ( s u b s i d . ) : process o r component o p t i o n a l t o s e x u a l r e p r o d u c t i o n ( H o l l i n g 1966). \u2022 -Processes Components Occurrence Mating B a s i c Rate of s u c c e s s f u l s e a r c h a B a s i c B a s i c B a s i c Time exposed Handling time E x p l o i t a t i o n I n t e r f e r e n c e S u b s i d . Subsid. S u b s i d . Subsid. Subsid. S o c i a l f a c i l i t a t i o n L e a r n i n g M o t i v a t i o n Egg P r o d u c t i o n B a s i c O v a r i o l e a c t i v a t i o n . O v a r i o l e p r o d u c t i o n V i t e l l o g e n e s i s 3 O v a r i o l e d e a c t i v a t i o n b B a s i c B a s i c B a s i c Subsid. Egg F e r t i l i z a t i o n B a s i c Sperm storage Sperm r e l e a s e Subsid. B a s i c 10. Table 1. (continued) Processes Components Occurrence Oviposition S i t e Selection Subsid. Rate of successful search Time exposed Handling time E x p l o i t a t i o n Interference S o c i a l f a c i l i t a t i o n Motivation Learning Components modeled with data from l i t e r a t u r e . Components modeled with experimenter's data. Basic Basic Basic Subsid. Subsid. Subsid. Subsid. Subsid. 11. ments (e.g. r e s p i r a t i o n , egg production) and energy storage. The egg production process produces u n f e r t i l i z e d eggs by combining density of mated females with energy avail a b l e for eggs, thus, decreasing the store of available energy. Egg f e r t i l i z a t i o n unites stored sperm with u n f e r t i l i -zed eggs. This increases the store of f e r t i l i z e d eggs and decreases the store of u n f e r t i l i z e d eggs. Oviposition s i t e s e l e c t i o n determines density of eggs l a i d through i n t e r a c t i o n of mated females with o v i p o s i t i o n s i t e d . This reduces the store of f e r t i l i z e d and u n f e r t i l i z e d eggs. Mating, egg production and egg f e r t i l i z a t i o n were con-sidered basic as they are common to a l l sexually reproducing animals. Oviposition s i t e s e l e c t i o n by females was considered subsidiary, as some insects i n d i s c r i m i n a t e l y deposit t h e i r eggs wherever the female happens to be (Engelmann 1970 p. 193). 12. PART I MATING INTRODUCTION Mating i s considered to include a l l time consuming a c t i v i t i e s that are exclusive to male-female i n t e r a c t i o n leading to insemination. Thus mating would include court-ship, copulation, insemination, and any post copulatory refractory period. If mating i s considered to be one of many time consuming a c t i v i t i e s engaged i n by i n d i v i d u a l s , such as eating, feeding, o v i p o s i t i o n s i t e s e l e c t i o n , and predator avoidance, then i t may be possible to develop a single equation, or set of equations, that would be applicable to a l l these population i n t e r a c t i o n s . In the development of models for the processes of sexual reproduction, t h i s model of i n t e r a c t i n g populations could be used both for mating, the i n t e r a c t i o n between males and females, and for o v i p o s i t i o n s i t e s e l e c t i o n , the in t e r a c t i o n between females and o v i p o s i t i o n s i t e s . 13. MODEL OF INTERACTING POPULATIONS D e v e l o p m e n t o f t h e M o d e l . N o t i n g t h e e x p a n s i o n o f H o l l i n g ' s (1965, 1966) p r e d a t i o n m o d e l t o i n c l u d e a c o m b i n a t i o n o f p a r a s i t e s m a n d o v i p o s i t i o n s i t e s e l e c t i o n ( G r i f f i t h s and H o l l i n g 1 9 6 9 ) , N e i s h ( p e r s . comm.) s t a t e d t h a t t h e p r e d a t i o n m o d e l c a n be v i e w e d as a g e n e r a l m o d e l f o r r e s o u r c e u s e by an o r g a n i s m . M o r e o v e r , a s m o d i f i e d b e l o w , t h e p r e d a t i o n m odel c a n f u r t h e r be v i e w e d a s a g e n e r a l m o d e l f o r any i n t e r a c t i o n b e tween two d i s c r e t e p o p u l a t i o n s ; one o r b o t h o f w h i c h i s a n i m a t e . F o r c o n t i n u i t y , H o l l i n g ' s n o t a t i o n f o r h i s p r e d a t i o n m o d e l (1966 p . 11) i s u s e d f o r t h i s g e n e r a l m o d e l o f i n t e r -a c t i n g p o p u l a t i o n s ( T a b l e 2 ) . * I n t h e m o d e l o f i n t e r a c t i n g p o p u l a t i o n s t h e r e a r e no p r e c o n c e p t i o n s a b o u t r e l a t i v e r o l e s o f t h e two p o p u l a t i o n s (No a n d P, T a b l e 2 ) ; t h e y a r e i n t e r -c h a n g e a b l e . E i t h e r c o u l d be t h e p r e e a t o r o r p r e y , o r t h e m a l e o r f e m a l e d u r i n g m a t i n g , o r t h e c l e r k o r c u s t o m e r a t a g r o c e r y s t o r e c h e c k o u t . H o l l i n g ' s p r e d a t i o n m o d e l d o e s n o t a l l o w f o r t h e i n t e r -c h a n g e a b i l i t y o f t h e two p o p u l a t i o n s . The b a s i c p r e d a t i o n f u n c t i o n ( m o d i f i e d f r o m G r i f f i t h s a n d H o l l i n g 1969 p . 789) : * I n t h i s t e x t a l l l o w e r c a s e l e t t e r s d e n o t e c o n s t a n t s ( a , c , e, g, e t c . ) . U p p e r c a s e l e t t e r s u s u a l l y d e n o t e v a r i a b l e s LA, Co, d E \/ d T , Mr, e t c . ) , a l t h o u g h t h e y o c c a s i o n a l l y d e n o t e c o n s t a n t s (D, D r , Ds, and F ) . 14. Table 2. A comparison of d e f i n i t i o n s of parameters common to both Holling's predation function (Equation 1) and the general function for i n t e r a c t i n g populations (Equation 6). Parameter Predation (Holling 1966) Interacting Populations (Present Paper) Na Density prey attacked Density of interactions No Prey density Density of f i r s t population P Predator density Density of second population Rate of successful search Rate of successful search Tt Time prey exposed to predators Time two populations together Th Time spent handling prey Time per i n t e r a c t i o n 15. Na = A-No-(Tt-P-Th'Na) (1) assumes, for a constant predator density (P), that density of attacks (Na) increases with prey density (No). This increase i s negatively accelerated r e s u l t i n g i n density of attacks (Na) approaching a plateau for high prey density (No). Interchanging the two populations gives: Na = A\u00abP\u00ab (Tt-Na-Th-Na) (2) which assumes a p o s i t i v e , l i n e a r r e l a t i o n s h i p between density of attacks (Na) and prey density (No). Holling (1966) has shown that such a r e l a t i o n s h i p does not e x i s t and that density of attacks (Na) approaches a plateau for high prey densities (No) as predicted by Equation 1. Holling's function, adequate as a model of predation, can not be used as a general function for i n t e r a c t i n g popu-la t i o n s because of these preconceptions about roles of the two populations. The simplest predation function (modified from Holling 1966 p. 9), and thus, the simplest function f o r i n t e r a c t i n g populations, assumes density of interactions i s a l i n e a r function of rate of successful search, time exposed, and density of both populations: Na = A'Tt-No-P (3) multiplying by Tt gives: 16. Na\u00abTt = A\u00ab(Tt-No)\u2022(Tt-P) (4) where (Tt \u00abNo) and (Tt\u00abP) are t o t a l time avai l a b l e to the populations for i n t e r a c t i o n . In terms of predation, (Tt\u00abNo) represents t o t a l time a v a i l a b l e for prey to be handled, and (Tt\u00abP) represents t o t a l time avai l a b l e for predators to handle prey. If (Th-Na) represents time l o s t to both popu-l a t i o n s due to i n t e r a c t i o n s , then: Na-Tt = A-(Tt-No-Th-Na)\u2022(Tt\u00abP-Th-Na) (5) transposing gives: .. .7 _, Th'.Na. Th'-Na. , -. Na = A-Tt.No-P. * ( 1 - T t T p - ) ( 6 ) which i s the basic function f o r the model of i n t e r a c t i n g populations. This equation was derived i n a manner s i m i l a r to the d e r i v a t i o n of the predation function (Equation 1 above) by H o l l i n g (1966 p. 11). I t i s interchangeable with respect to the two populations (No and P) s e t t i n g no preconditions on r e l a t i v e roles of the two populations. The general function f o r i n t e r a c t i n g population (Equation 6) i s s i m i l a r to the function from which i t was derived (Equation 3). Equation 6 i s equal to Equation 3 m u l t i p l i e d by the expressions ( l - ^ [ ^ ) and (,l-^]p a) which represent the proportion of each population not presently engaged i n i n t e r a c t i o n . Holling's predation function (Equation 1) i s a s p e c i a l case of the general function for i n t e r a c t i n g populations 17. (Equation 6). Assume for predation that prey density i s much greater than predator density (No>>P). As both populations engage i n the same density of interactions (Na) with the same handling time (Th), the proportion of prey engaged i n i n t e r -action i s much less than the proportion of predators so Th\u2022Na Th\u00abNa engaged ( j^- No\"<<:Tt P ^ \" A s t' i e P r o P o r t ; L O n \u00b0f predators engaged i s at most one (^fp\u2014\u00a3l)\u00bb the proportion of prey Th \u2022 Na engaged i s much less than one ( N - <<1). Therefore, the proportion of prey not engaged i s approximately one, i . e . , Th\u00abNa . \u201e , ... , . , ,, Th.Nav . , Tt.No Substituting one for ( l ~ T t . ^ Q ) i n t n e general function (Equation 6) gives, with transposing, the predation function (Equation 1). Thus, Holling's predation function i s a l i m i t i n g case of the general function for i n t e r a c t i n g popu-l a t i o n s where density of one population i s much greater than that of the other. The general function applies only where the populations are approximately equal i n density (No - P) or where f l u c t u a t i o n s i n population density are such that f i r s t one and then the other has the higher density: P t = l < N o t = l ; N o t = 2 < P t = 2 ' Further Development of the Model. There are three further complexities to the general function for i n t e r a c t i n g popu-l a t i o n s (Equation 6): 1) i n t e r a c t i o n a f f e c t s upon either population ( e x p l o i t a t i o n ) ; 2) other interactions which compete for the av a i l a b l e time (interference), and 3) the 18. frequency d i s t r i b u t i o n of inte r a c t i o n s among ind i v i d u a l s of the two populations. Long term e x p l o i t a t i o n i s handled by d i v i d i n g the time the two populations are together (Tt) into short i n t e r v a l s , and adjucting eit h e r one or both population densities (No and\/ or P) as i s appropriate at the end of each i n t e r v a l ( G r i f f i t h s and H o l l i n g 1969 p. 801-802). Short-term e x p l o i t a t i o n i s already included i n the general function (Equation 6); Th'Na. , ,, Th'Na, . . , . . . ^ ( l ~ T t < N o ) and ( l - _ - p \u2014 ) measure current involvement i n i n t e r -action and, thus, are indices of temporary reduction (exploitation) i n the two populations. Secondly, interference between two populations occurs when population growth or other a t t r i b u t e s of each population are d i r e c t l y i n h i b i t e d by the other (Odum 1971 p. 211). Thus, time spent by a predator attacking a prey i n t e r f e r e s with the a b i l i t y of both predator and prey to f i n d a mate. Broadly, interference, r e l a t i v e to the i n t e r a c t i o n i n question, comes about when one or both populations i s engaged i n a second i n t e r a c t i o n e i t h e r with a t h i r d population or with i t s e l f . The l a t t e r i s a second l i m i t i n g case of the general function of i n t e r a c t i n g population (Equation 6) occurring when No and P are the same population. I t describes i n t e r -ference within a population. I t i s assumed that the two inter a c t i o n s do not occur at the same time. If one population (P) engages i n a second time consuming i n t e r a c t i o n where N equals density of interactions and T equals 19. handling time, then N'T i s the time taken for the second i n t e r a c t i o n . This time (N\u00abT) represents the interference e f f e c t of the second i n t e r a c t i o n on the f i r s t i n t e r a c t i o n and reduces the proportion of the population (P) l e f t for i n t e r a c t i o n with the other population (No) to ( 1 - T n ' N ^ t + p T * N ) . Thus, the general function f o r i n t e r a c t i n g populations (Equation 6) becomes: KT , m. \u00bbir \u00ab n Th\u00abNa N ,, Th-Na + T-Nv No = A-Tt-No-P. ( l - T t . N p ) \u2022 (1- rtTP~ } ( 7 ) F i n a l l y , the frequency d i s t r i b u t i o n of interactions among members of each i n t e r a c t i n g population i s complex. In b r i e f , there are two basic s i t u a t i o n s : i n d i v i d u a l s can i n t e r -act only once, or i n d i v i d u a l s can i n t e r a c t more than once. Individuals only capable of a single i n t e r a c t i o n (e.g. a prey can only be eaten once) are handled as outlined above i n the discussion of long-term e x p l o i t a t i o n . I f , however, individ u a l s are capable of repeated i n t e r a c t i o n s , then i t may be necessary to model the frequency of occurrence of the various multiple i n t e r a c t i o n s ( i . e . how many females never copulate, copulate once, twice, three times, e t c . ) . The general function for i n t e r a c t i n g populations (Equation 6) predicts t o t a l number of i n t e r a c t i o n s , not frequency d i s t r i b u t i o n of those i n t e r -actions. At the extreme, there are two possible e f f e c t s of multiple i n t e r a c t i o n s : 1) No e f f e c t of i n t e r a c t i o n a f t e r the f i r s t ; \" or 2) e f f e c t of i n t e r a c t i o n s may be independent and a d d i t i v e . 20. I n n a t u r e , many e x a m p l e s o f m u l t i p l e i n t e r a c t i o n may be more compl e x and f a l l b e t w e e n t h e s e s i m p l e e x t r e m e s . A d d i t i o n a l i n t e r a c t i o n s w i l l h a v e some e f f e c t , b u t t h e e f f e c t m i g h t d i m i n i s h a t h i g h f r e q u e n c y w i t h s u c c e s s i v e i n t e r a c t i o n s ( G r i f f i t h s a n d H o l l i n g 1969 p . 7 9 6 ) . Components o f t h e M o d e l . H o l l i n g (1966) s e p a r a t e d t h e components o f p r e d a t i o n i n t o two t y p e s : 1) t h o s e d e a l i n g w i t h t h e f u n c t i o n a l r e s p o n s e t o p r e y d e n s i t y ; and 2) t h o s e d e a l i n g w i t h t h e f u n c t i o n a l r e s p o n s e t o p r e d a t o r d e n s i t y , ( T a b l e 3 ) . A more g e n e r a l a p p r o a c h i s t o c l a s s i f y components i n t o t h r e e t y p e s : 1) t h o s e i n v o l v i n g r e s p o n s e s t o i n t e r -a c t i o n b e t w e e n two p o p u l a t i o n s ; 2) t h o s e i n v o l v i n g r e s p o n s e s t o a c t i o n w i t h i n one p o p u l a t i o n ; and 3) t h o s e i n v o l v i n g r e s p o n s e s t o i n d i v i d u a l e x p e r i e n c e f r o m p a s t i n t e r a c t i o n s and a c t i o n s ( T a b l e 4, F i g u r e 2 ) . T h e r e i s no r e l a t i o n s h i p b e t w e e n H o l l i n g ' s component t y p e and i t s o c c u r r e n c e ( T a b l e 3 ) ; components c l a s s i f i e d as a r e s p o n s e t o p r e d a t o r d e n s i t y , o r t o p r e y d e n s i t y , c a n be e i t h e r b a s i c o r s u b s i d i a r y . A r e l a t i o n s h i p d o e s e x i s t f o r t h e new s y s t e m o f c l a s s i f i c a t i o n ( T a b l e 4 ) ; components c l a s s i f i e d a s a r e s p o n s e t o i n t e r a c t i o n b e t w e e n two p r i m a r y p o p u l a t i o n s , b u t n o t w i t h some t h i r d p o p u l a t i o n , a r e a l w a y s b a s i c w h i l e components c l a s s i f i e d a s r e s p o n s e s e i t h e r t o a c t i o n w i t h i n a p o p u l a t i o n o r t o i n d i v i d u a l e x p e r i e n c e f r o m p a s t a c t i o n s and i n t e r a c t i o n s a r e a l w a y s s u b s i d i a r y . 21. Table 3. Components of the predation process. Components c l a s s i f i e d as the functional response to eith e r prey or predator (pred.) density (Holling 1966). Component Type Occurrence Rate of successful search prey basic Time exposed prey basic Handling time prey basic E x p l o i t a t i o n pred. basic Interference between predators pred. subsid. S o c i a l f a c i l i t a t i o n pred. subsid. Hunger (motivation) prey subsid. Learning by predator prey subsid. I n h i b i t i o n by prey prey subsid. Avoidance learning by prey pred. subsid. T a b l e 4. P o s s i b l e components o f t h e p r o c e s s e s i n v o l v i n g i n t e r a c t i n g p o p u l a t i o n s . Components c l a s s i f i e d as b e i n g b e t w e e n : component i n v o l v e s i n t e r a c t i o n b e t w e e n p o p u l a t i o n s ; w i t h i n : component i n v o l v e s a c t i o n w i t h i n a p o p u l a t i o n ; o r e x p e r i e n c e : component i n v o l v e s i n d i v i d u a l e x p e r i e n c e f r o m p a s t i n t e r a c t i o n s and a c t i o n s . Component T y p e O c c u r r e n c e R a t e o f s u c c e s s f u l s e a r c h b e t w e e n b a s i c Time e x p o s e d b e t w e e n b a s i c H a n d l i n g t i m e b e t w e e n b a s i c E x p l o i t a t i o n : s h o r t - t e r m l o n g - t e r m b etween e x p e r i e n c e b a s i c s u b s i d . I n t e r f e r e n c e b e t w e e n a s u b s i d . S o c i a l f a c i l i t a t i o n w i t h i n s u b s i d . M o t i v a t i o n e x p e r i e n c e s u b s i d . L e a r n i n g : t h r e s h o l d e f f e c t s t e c h n i q u e e f f e c t s e x p e r i e n c e e x p e r i e n c e s u b s i d . s u b s i d . Si Component i n v o l v e s a s e c o n d i n t e r a c t i o n b e t w e e n one o f t h e two p o p u l a t i o n s i n v o l v e d i n t h e f i r s t i n t e r a c t i o n and some t h i r d p o p u l a t i o n . F i g u r e 2. A p a r t i a l d i s a g g r e g a t i o n o f t h e g e n e r a l i z e d p r o c e s s o f i n t e r a c t i o n b e t w e e n two p o p u l a t i o n s . R e s p o n s e t o i n t e r a c t i o n b e t w e e n two p o p u l a t i o n s G e n e r a l i z e d p r o c e s s -R e s p o n s e t o a c t i o n w i t h i n one p o p u l a t i o n -R e s p o n s e t o i n d i v i d u a l e x p e r i e n c e f r o m p a s t i n t e r a c t i o n s and a c t i o n s R a t e o f s u c c e s s f u l s e a r c h -P r o b a b i l i t y o f s u c c e s s R e a c t i v e d i s t a n c e ^ R e l a t i v e v e l o c i t y - T i m e e x p o s e d \u2014 - H a n d l i n g t i m e S h o r t t e r m ^_ e x p l o i t a t i o n - I n t e r f e r e n c e -_ S o c i a l f a c i l i t a t i o n \u2022 L o n g t e r m e x p l o i t a t i o n - M o t i v a t i o n \u2014 T h r e s h o l d e f f e c t \u2022 - L e a r n i n g T e c h n i q u e e f f e c t Certain of Holling's components (Table 3) have been combined i n l i g h t of the new c l a s s i f i c a t i o n of components (Table 4 ) . Learning by predators, i n h i b i t i o n by prey, and avoidance learning by prey have been lumped under the term \"learning\", which can have p o s i t i v e or negative reinforcement. Learning i s s p l i t into threshold and technique e f f e c t s : the former i n t e r a c t i n g with motivation, and the l a t t e r changing handling time. E x p l o i t a t i o n has been s p l i t into short-term e x p l o i t a -t i o n (the loss of i n t e r a c t i n g i n d i v i d u a l s from both populations due to handling time) and into long-term e x p l o i t a t i o n (temporary or permanent removal of individuals from either population due to e f f e c t s of the i n t e r a c t i o n ) . E x p l o i t a t i o n , interference, s o c i a l f a c i l i t a t i o n , and moti-vation (Holling's hunger) have been expanded to include both populations. A l l these changes are designed to make the components general by applying them equally to both popu-l a t i o n s . The eight components generally do not change i n terms of being basic or subsidiary i n the change from predation to general i n t e r a c t i o n of populations. Rate of successful search, time exposed, and handling time remain basic while interference, s o c i a l f a c i l i t a t i o n , motivation and learning are s t i l l subsidiary (Tables 3 and 4 ) . However, while short-term e x p l o i t a t i o n remains basic, long-term e x p l o i t a t i o n becomes subsidiary. Presence of long-t e r m e x p l o i t a t i o n w i l l d e p e n d on t y p e o f p o p u l a t i o n i n t e r -a c t i o n . I t o c c u r s i n a l l f o r m s o f p r e d a t i o n b u t n o t i n a l l c a s e s o f o v i p o s i t i o n s i t e s e l e c t i o n , p a r a s i t i s m , a n d m a t i n g . T h u s , i t i s c l a s s i f i e d a s s u b s i d i a r y . ( F o r e x a m p l e , a f e m a l e may o r may n o t m a t e more t h a n o n c e ) . A p p l i c a t i o n o f t h e M o d e l t o R e p r o d u c t i o n i n D r o s o p h i l a m e l a n o - g a s t e r . The two p o p u l a t i o n s i n t e r a c t i o n s a p p l i c a b l e t o s e x u a l r e p r o d u c t i o n , m a t i n g a n d o v i p o s i t i o n s i t e l o c a t i o n , u s e t h e t h r e e b a s i c c o m p o n e n t s p l u s a s u b s e t o f t h e f i v e s u b s i d i a r y c o m p o n e n t s w h i c h d e p e n d on t h e n a t u r e o f t h e two i n t e r a c t i n g p o p u l a t i o n s . W h i l e l o n g - t e r m e x p l o i t a t i o n a n d i n t e r f e r e n c e n e e d n o t be c o m p o n e n t s o f m a t i n g , t h e f o r m e r o c c u r s f o r f e m a l e D. m e l a n o g a s t e r , a n d t h e l a t t e r o c c u r s f o r m a l e s ( T a b l e 5 ) . S i m i l a r l y , s o c i a l f a c i l i t a t i o n n e e d n o t o c c u r i n a l l c a s e s o f m a t i n g , b u t i t d o e s o c c u r f o r b o t h f e m a l e a n d m a l e D. m e l a n o g a s t e r . M o t i v a t i o n i s i m p o r t a n t f o r f e m a l e s b u t , f o r t h e p r e s e n t , i t i s a s s u m e d n o t t o be f o r m a l e s . L e a r n i n g i s n o t e x h i b i t e d b y e i t h e r s e x . A t e n t a t i v e r e l a t i o n s h i p among t h e s e c o m p o n e n t s ( F i g u r e 3) shows t h e r e a r e t w o i n p u t s , v i r g i n f e m a l e d e n s i t y a n d m a l e d e n s i t y , a n d one o u t p u t , m a t e d f e m a l e d e n s i t y . G i v e n v i r g i n f e m a l e d e n s i t y , m o t i v a t i o n d e t e r m i n e s r e c e p t i v e f e m a l e d e n s i t y . T h r o u g h r a t e o f s u c c e s s f u l s e a r c h , m a l e d e n s i t y a n d r e c e p t i v e f e m a l e d e n s i t y g i v e d e n s i t y o f m a l e -26. T a b l e 5. P o s s i b l e components of the mating process f o r D r o s o p h i l a melanogaster. Components c l a s s i f i e d as b e i n g 6*,$>: component i n v o l v e s i n t e r a c t i o n between male and r e c e p t i v e female p o p u l a t i o n s ; 6*,6* and o,c^: component i n v o l v e s a c t i o n w i t h i n the male or r e c e p t i v e female p o p u l a t i o n ; or (j>: component i n v o l v e s i n d i v i d u a l e x p e r i e n c e by r e c e p t i v e females from p a s t i n t e r a c t i o n s and a c t i o n s . Component Type Rate o f s u c c e s s f u l s e a r c h Time exposed 6*,o. Ha n d l i n g time 6 E x p l o i t a t i o n : s h o r t - t e r m 6*,cj> long-term
m i . TT \/ i \" T r a'\u00abCo, Tnt ' C O x \/ o x Co-Ac.Tt-Mr-W. ( 1 \u2014 _ ) . (!-___) (8) 29. Table 6 . Possible components of the o v i p o s i t i o n s i t e s e l e c t i o n process inv o l v i n g female Drosophila melanogaster and o v i p o s i t i o n s i t e s . Components c l a s s i f i e d as being o , s i t e and 0 , 6 * : component involves i n t e r a c t i o n , r e s p e c t i v e l y , between mated females and ov i p o s i t i o n s i t e s , and between mated females and males; 0*9: component involves i n t e r a c t i o n within the mated female population; or