Open Collections

PREDATOR-PREY FUNCTIONAL RESPONSES AND PREDATION BY STAGHORN SCULPINS (LEPTOCOTTUS ARMATUS) ON CHUM SALMON FRY (ONCORHYNCHUS KETA) by PAMELA MARGARET MACE B.Sc. Hons., U n i v e r s i t y Of Canterbury, C h r i s t c h u r c h , New Zealand, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March 1983 (c) Pamela Margaret Mace, 1983 In p r e s e n t i n g 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 a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t 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 r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e 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 or her r e p r e s e n t a t i v e s . I t i s understood t h a t 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 g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of ^ C n Q 1 0 The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date K (\f*W 1 ^ 9 3 DE-6 (3/81) i DEDICATION To my p a r e n t s , Jim and Margaret Mace, f o r t h e i r support, encouragement and p a t i e n c e throughout t h i s endeavour. i i ABSTRACT Mathematical models d e s c r i b i n g the components of p r e d a t o r -prey i n t e r a c t i o n s are reviewed and evaluated, and new equations r e p r e s e n t i n g s e l e c t e d aspects of the r e l a t i o n s h i p are proposed. A model of prey s e l e c t i o n t h a t d i s t i n g u i s h e s between predator performance and prey v u l n e r a b i l i t y i s d e v i s e d and shown to l e a d to c o n c l u s i o n s that may be q u a l i t a t i v e l y d i f f e r e n t from those produced using p r e v i o u s methods. The f e e d i n g h a b i t s of staghorn s c u l p i n s (Leptocottus  armatus), the extent to which they u t i l i z e e s t u a r i n e h a b i t a t s and t h e i r predatory response to chum salmon f r y (Oncorhynchus  keta) are examined f o r the purposes of ( i ) a s c e r t a i n i n g the f a c t o r s shaping s c u l p i n f o r a g i n g behaviour and ( i i ) a s s e s s i n g t h e i r p o t e n t i a l f o r l i m i t i n g s u r v i v a l of j u v e n i l e salmon. During p e r i o d s of f r y m i g r a t i o n , s c u l p i n p o p u l a t i o n s i n the e s t u a r i e s of Big Qualicum R i v e r , Salmon Creek and Rosewall Creek (on Vancouver I s l a n d , B. C.) were composed predominantly of small j u v e n i l e s l e s s than 80 mm i n l e n g t h . Tolerance to waters of low s a l i n i t y , which decreased with s c u l p i n s i z e , was found to be the major v a r i a b l e governing r e s i d e n c e i n these a r e a s . There was l i t t l e evidence that the m i g r a t i o n of f r y was important i n a t t r a c t i n g s c u l p i n s to e s t u a r i e s . S c u l p i n s preyed on a wide d i v e r s i t y of fauna c o n c e n t r a t i n g on benthic c r u s t a c e a n s , p a r t i c u l a r l y the amphipod Eogammarus c o n f e r v i c o l u s . J u v e n i l e s were a c t i v e throughout the day, but feeding became p r o g r e s s i v e l y more r e s t r i c t e d to p e r i o d s of low l i g h t i n t e n s i t y as they grew. The s m a l l e s t that captured f r y were 40-45 mm i n l e n g t h . When chum f r y were o f f e r e d to st a r v e d s c u l p i n s i n f i e l d e n c l o s u r e s , the response of those l e s s than 80 mm i n l e n g t h was type 2 ( H o l l i n g 1965) whereas that of 80-99 mm s c u l p i n s was type 3 ( s i g m o i d ) . P r e d a t i o n on f r y was i n v e r s e l y r e l a t e d to l i g h t i n t e n s i t y from dawn to dusk, and p o s i t i v e l y c o r r e l a t e d with' l i g h t l e v e l s d u r i n g the n i g h t . When benthic i n v e r t e b r a t e s were added, s c u l p i n s e x h i b i t e d an o v e r a l l p r e f e r e n c e f o r f r y , which were 4-5 times more p r o f i t a b l e i n terms of net energy i n t a k e . However, pre f e r e n c e f o r f r y d e c l i n e d markedly as t h e i r abundance r e l a t i v e to other prey i n c r e a s e d , i n d i c a t i n g a divergence from the usual p r e d i c t i o n s of optimal f o r a g i n g theory. Capture r a t e s by s c u l p i n s i n i t i a l l y naive to salmon f r y i n c r e a s e d up to t h r e e - f o l d over 3-5 two hour t r i a l s . I t i s suggested that the f o r a g i n g s t r a t e g y of s c u l p i n s given a c h o i c e between salmonid f r y and bent h i c i n v e r t e b r a t e s r e p r e s e n t s a balance between the requirement of minimizing r i s k of s t a r v a t i o n and the need to evade t h e i r own predators ( p a r t i c u l a r l y b i r d s ) . The s c h o o l i n g behaviour of f r y r e q u i r e s that s c u l p i n s , even when experienced, must devote c o n s i d e r a b l e a t t e n t i o n to the a t t a c k process and i n so doing, run the r i s k of being eaten themselves. The combined e f f e c t s of the s c h o o l i n g response, which reduces the i n c e n t i v e to a t t a c k f r y , and a p r o f u s i o n of a l t e r n a t i v e prey, which decreases average hunger l e v e l s , were thought to be r e s p o n s i b l e f o r low f r y consumption i n n a t u r a l s i t u a t i o n s . In B i g Qualicum R i v e r , an estimated 240,000 and 40,500 chum were captured by s c u l p i n s i n 1979 and 1980, i v r e s p e c t i v e l y . T h i s r e p r e s e n t s corresponding percentages of only 0.51% and 0.06% of the f r y p o p u l a t i o n s , and was c a l c u l a t e d to be l e s s than one-tenth of the p o t e n t i a l t h at c o u l d have been r e a l i z e d . P r e d a t i o n r a t e s on coho f r y (0. k i s u t c h ) were c o n s i d e r a b l y g r e a t e r , d e s p i t e a s m a l l e r p o p u l a t i o n s i z e . Estimated consumption was 817,700 (42.97%) and 144,000 (9.09%) i n 1979 and 1980. Systems where s c u l p i n s c o u l d consume higher p r o p o r t i o n s of chum f r y p o p u l a t i o n s were i d e n t i f i e d as s m a l l , shallow, warm e s t u a r i e s of intermediate to h i g h s a l i n i t y with r e l a t i v e l y few s u i t a b l e benthic i n v e r t e b r a t e s and small numbers of f r y . Recommendations f o r reducing s c u l p i n p r e d a t i o n i n such cases are proposed. B i r d s , p a r t i c u l a r l y Bonaparte's g u l l s (Larus P h i l a d e l p h i a ) , were found to be even more a v i d p r e d a t o r s than s c u l p i n s on j u v e n i l e salmon i n Big Qualicum R i v e r . In c o n t r a s t to s c u l p i n s , they e x h i b i t e d pronounced numerical responses to the appearance of f r y i n the e s t u a r y . An estimated 10-25% of the h a t c h e r y - r e a r e d chinook salmon (O. tshawytscha) and 2-4% of the coho were removed by b i r d s i n the years 1979-81. V TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES x i i LIST OF FIGURES xv ACKNOWLEDGEMENTS x x i i PREFACE xx i v PART I: THEORETICAL CONCERNS 1 Chapter 1: GENERAL INTRODUCTION TO PREDATOR-PREY AND PARASITOID-HOST RESPONSES 2 1.1 I n t r o d u c t i o n 2 1.2 The Components of P r e d a t i o n 3 1.3 F u n c t i o n a l Response to Prey Dens i t y 9 1.4 F u n c t i o n a l Response to Predator D e n s i t y 13 1.5 S y n t h e s i s of Responses to Prey and Predator D e n s i t y 16 1.6 Extension to M u l t i s p e c i e s Models 24 Chapter 2: EVALUATION AND DEVELOPMENT OF MODELS INCORPORATING VARIABLE RATES OF EFFECTIVE SEARCH 28 2.1 I n t r o d u c t i o n 28 2.2 Comparison of Models D e s c r i b i n g Type 3 Responses ... 34 2.3 Simple Formulations f o r Non-Random Search i n Predator-Prey and P a r a s i t o i d - H o s t Systems 49 v i B asic method of model d e r i v a t i o n 50 P a r a s i t o i d models 54 Predator models 60 Behaviour and e v a l u a t i o n of the models 65 2.4 Suggestions f o r More General Models 79 2.5 D i s t i n g u i s h i n g Response Types i n Two-prey Systems .. 84 Chapter 3: PREFERENCE, SWITCHING AND TYPE 3 RESPONSES 91 3.1 I n t r o d u c t i o n 91 Common symbols used 94 3.2 Murdoch's Model of Predator Switching 94 3.3 New Preference and Switching Hypotheses 104 3.4 Cases I n v o l v i n g E x p l o i t a t i o n 112 3.5 Design of Switching Experiments 113 3.6 Switching and Type 3 Responses: An Example 117 Switching 118 E f f e c t s of hunger 127 Type 3 responses 131 3 .7 D i s c u s s i o n 137 PART I I : FIELD AND EXPERIMENTAL RESULTS 141 Chapter 4: GENERAL INTRODUCTION: FISH PREDATION STUDIES ...142 4.1 A Short Review of F i s h Feeding Stu d i e s 142 4.2 P r e d a t i o n as an Agent of M o r t a l i t y i n Salmonids ....149 4.3 I n t e r a c t i o n s Between C o t t i d s and J u v e n i l e Salmonids 151 v i i 4.4 The Present Study . 155 SECTION A: EXPERIMENTAL RESULTS 1 58 Chapter 5: IDENTIFICATION OF FACTORS AFFECTING FORAGING BEHAVIOUR AND PRELIMINARY EXPERIMENTS 159 5.1 I n t r o d u c t i o n 159 5.2 D e s c r i p t i o n of System 161 5.3 Experimental E n c l o s u r e s and Experimental Animals ...162 5.4 Behaviour of Fry and S c u l p i n s i n E n c l o s u r e s 164 5.5 D i e l P a t t e r n of Feeding 169 ( i ) F i e l d samples 169 ( i i ) L a boratory experiments 170 5.6 Reduction of F a c t o r s to Consider E x p l i c i t l y 178 5.7 P r e l i m i n a r y Experiments 179 ( i ) E n c l o s u r e c h a r a c t e r i s t i c s 179 ( i i ) Time of day 180 ( i i i ) Water depth 182 ( i v ) D i g e s t i o n r a t e s 182 (v) I n t e r f e r e n c e and e x p l o i t a t i o n 186 ( v i ) Maximum f r y d e n s i t i e s 189 5.8 Summary 191 Chapter 6: EXPERIMENTAL ANALYSIS OF FACTORS AFFECTING PREDATION 193 6.1 I n t r o d u c t i o n 193 v i i i 6.2 General Methods 197 C o l l e c t i o n and storage procedures. 197 Experimental procedure 198 A n a l y s i s of data 201 ( i ) S i n g l e - p r e y experiments 201 ( i i ) Two-prey experiments 204 6.3 The.Baseline F u n c t i o n a l Response: E f f e c t s of Fry De n s i t y 209 Methods and r e s u l t s 210 D i s c u s s i o n 218 6.4 E f f e c t s of S c u l p i n S i z e l. ....220 Methods and r e s u l t s 220 D i s c u s s i o n 227 6.5 D i s a g g r e g a t i o n of Fry Densi t y and S c u l p i n S i z e E f f e c t s ..233 Methods and r e s u l t s 233 D i s c u s s i o n 240 6.6 E f f e c t s of A l t e r n a t i v e Prey 242 Methods and r e s u l t s 242 D i s c u s s i o n 255 6.7 E f f e c t s of S c u l p i n S i z e on S e l e c t i v i t y 261 Methods and r e s u l t s 261 D i s c u s s i o n 271 6.8 E f f e c t s of Predator Experience on Prey S e l e c t i v i t y .275 Methods and r e s u l t s 275 D i s c u s s i o n 288 6.9 E f f e c t s of L i g h t I n t e n s i t y 293 ix Methods and r e s u l t s 294 D i s c u s s i o n 297 6.10 S y n t h e s i s and General D i s c u s s i o n 300 The predator s a t i a t i o n h y p othesis 301 The f r y s c h o o l i n g hypothesis 307 The f o r a g i n g s t r a t e g y of s c u l p i n s 314 SECTION B: FIELD SAMPLING RESULTS 323 Chapter 7: DESCRIPTION OF SAMPLING AREAS 324 7.1 I n t r o d u c t i o n ' 324 7.2 B i g Qualicum R i v e r 327 ("i ) General d e s c r i p t i o n 327 ( i i ) Hatchery data 328 ( i i i ) D e s c r i p t i o n of estuary 336 ( i v ) Sampling s t a t i o n s 339 (v) S a l i n i t y p r o f i l e s 339 ( v i ) Fry movements through estuary 342 ( v i i ) I n v e r t e b r a t e fauna 345 ( v i i i ) I n c i d e n t a l catches i n t r a p s 349 7.3 Salmon Creek ...352 7.4 Rosewall Creek 356 7.5 Comparison of Areas 358 Chapter 8: UTILIZATION OF ESTUARIES BY STAGHORN SCULPINS ..359 8.1 I n t r o d u c t i o n , 359 X 8.2 Methods 360 ( i ) Sampling methods and areas sampled 360 ( i i ) Determination of seasonal occurrence and s p a t i a l d i s t r i b u t i o n 363 ( i i i ) Marking procedures 365 ( i v ) Determination of extent of movement 366 (v) D e n s i t y c a l c u l a t i o n s 368 8.3 R e s u l t s 369 ( i ) Seasonal occurrence 369 ( i i ) S p a t i a l d i s t r i b u t i o n s 377 ( i i i ) Movement w i t h i n the e s t u a r y 388 ( i v ) S c u l p i n abundances 391 8.4 D i s c u s s i o n 405 Chapter 9: FEEDING HABITS OF STAGHORN SCULPINS 412 9.1 I n t r o d u c t i o n 412 9.2 Methods 415 ( i ) Sampling methods and areas sampled 415 ( i i ) P r o c e s s i n g of gut contents 416 ( i i i ) Data a n a l y s i s 422 9.3 R e s u l t s 425 ( i ) Feeding h a b i t s i n Big Qualicum River 425 ( i i ) Consumption of benthic i n v e r t e b r a t e s 433 ( i i i ) Consumption of salmon f r y 436 ( i v ) Feeding h a b i t s i n other areas 449 9.4 D i s c u s s i o n 456 x i SECTION C: SYNTHESIS 466 Chapter 10: IMPACT OF STAGHORN SCULPINS ON SALMON FRY 467 10.1 I n t r o d u c t i o n 467 10.2 Rate of G a s t r i c Evacuation 468 10.3 Average D a i l y Consumption 472 10.4 Estimated Impact 475 10.5 P o t e n t i a l Impact 480 10.6 D i s c u s s i o n 481 Chapter 11: SYNTHESIS AND CONCLUDING REMARKS 487 Scope of the sculpin-salmon f r y i n t e r a c t i o n 488 Systems s u s c e p t i b l e to s c u l p i n p r e d a t i o n 492 Methods of reducing s c u l p i n p r e d a t i o n 495 Current and f u t u r e r e s e a r c h on predator-prey i n t e r a c t i o n s : 497 LITERATURE CITED 504 APPENDIX: BIRD PREDATION ON JUVENILE SALMONIDS IN THE BIG QUALICUM ESTUARY, VANCOUVER ISLAND 527 x i i LIST OF TABLES Table 1.1 Comparison of parameter val u e s estimated from d i s c and random predator equations 21 Table 2.1 R e l a t i v e f l e x i b i l i t y of s e v e r a l equations d e s c r i b i n g type 3 curves 36 Table 2.2 Parameter val u e s estimated from s e v e r a l equations f i t t e d to type 3 curves of d i f f e r e n t shapes 42 Table 3.1 H y p o t h e t i c a l example showing how predator s w i t c h i n g can be i n f e r r e d e r r o n e o u s l y 103 Table 3.2 C a l c u l a t i o n s of pre f e r e n c e f o r data from Akre and Johnson (1979) f o r s t a r v e d p r e d a t o r s 122 Table 3.3 C a l c u l a t i o n s of pre f e r e n c e f o r data from Akre and Johnson (1979) f o r s a t i a t e d p r e d a t o r s 123 Table 3.4 H y p o t h e t i c a l example showing how a hunger-motivated s h i f t i n search mode can le a d to apparent c o u n t e r - s w i t c h i n g .....129 Table 3.5 H y p o t h e t i c a l example showing how a hunger-motivated s h i f t i n search mode can l e a d to apparent predator s w i t c h i n g 130 Table 5.1 E f f e c t of time of day on consumption of chum f r y and amphipods by s c u l p i n s 181 Table 5.2 E f f e c t of water depth on consumption of chum f r y by s c u l p i n s 183 Table 5.3 E f f e c t of s c u l p i n d e n s i t y on average chum f r y consumption with 10 f r y a v a i l a b l e 187 x i i i Table 5.4 E f f e c t of s c u l p i n d e n s i t y on average chum f r y consumption with 20 f r y a v a i l a b l e 188 Table 5.5 Numbers of chum f r y consumed by s c u l p i n s at high f r y d e n s i t i e s 190 Table 6.1 Parameter values estimated from s e v e r a l equations f o r the b a s e l i n e f u n c t i o n a l response of 61-75 mm s c u l p i n s f e e d i n g on chum f r y 213 Table 6.2 Parameter val u e s estimated from the Real equation f o r subsets of the b a s e l i n e f u n c t i o n a l response 217 Table 6.3 Parameter val u e s estimated from s e v e r a l equations f o r 47-60 mm and 80-99 mm s c u l p i n s f e e d i n g on chum f r y .226 Table 6.4 Summary of ANOVA r e s u l t s f o r s i x v a r i a b l e s r e l a t e d to the behaviour of s c u l p i n s i n the presence of f r y 238 Table 6.5 E f f e c t of s c u l p i n s i z e on h a n d l i n g time per f r y .239 Table 6.6 Parameter values estimated from two equations f o r the response of naive 61-75 mm s c u l p i n s f e e d i n g on chum f r y and amphipods 249 Table 6.7 Test of the hy p o t h e s i s that r a t e of e f f e c t i v e search f o r amphipods was independent of amphipod d e n s i t y 250 Table 6.8 ANOVA comparing the f i t of two equations to data from a l t e r n a t i v e prey experiments .....251 Table 6.9 L i k e l i h o o d r a t i o t e s t s comparing p r e d i c t e d and observed p r o p o r t i o n s of f r y i n the d i e t i n a l t e r n a t i v e prey experiments 258 Table 6.10 Parameter val u e s estimated from the m u l t i s p e c i e s x i v d i s c equation f o r 61-75 mm and 85-99 mm s c u l p i n s f e e d i n g on coho f r y and amphipods 268 Table 6.11 Parameter values estimated from the m u l t i s p e c i e s d i s c equation f o r s c u l p i n s of d i f f e r i n g l e v e l s of experience f e e d i n g on chum f r y and amphipods 287 Table 8.1 E f f e c t s of b a i t on capture r a t e s of s c u l p i n s by minnow t r a p s 362 Table 8.2 Sampling p e r i o d s and sample s i z e s f o r mark-recapture experiments i n Salmon Creek and B i g Qualicum R i v e r . 367 Table 8.3 S e b e r - J o l l y estimates of p o p u l a t i o n s i z e , °-s u r v i v a l and recruitment of s c u l p i n s i n the B i g Qualicum es t u a r y i n 1980 397 Table 9.1 Food organisms found i n stomachs of staghorn s c u l p i n s 417 Table 9.2 Estimates of p r e f e r e n c e by s c u l p i n s f o r v a r i o u s benthic i n v e r t e b r a t e s 437 Table 10.1 Estimated and p o t e n t i a l consumption of chum f r y by s c u l p i n s i n Big Qualicum R i v e r , 1979 and 1980 478 Table 10.2 Estimated consumption of coho f r y by s c u l p i n s i n Big Qualicum R i v e r , 1979 and 1980 479 XV LIST OF FIGURES F i g u r e 1.1 The four types of f u n c t i o n a l response to prey d e n s i t y 5 F i g u r e 1.2 F u n c t i o n a l responses generated from the d i s c equation and random predator equation 22 F i g u r e 2.1 E i g h t pathways l e a d i n g to v a r i a b l e r a t e s of e f f e c t i v e search by predators 31 F i g u r e 2.2 Type 3 curves generated from s e v e r a l equations when i n f l e c t i o n p o i n t s are f i x e d 38 F i g u r e 2.3 Type 3 curves generated from s e v e r a l equations when the r a t e of approach to the asymptote i s f i x e d .... 40 F i g u r e 2.4 Best f i t s by s e v e r a l equations to type 3 curves of d i f f e r e n t shapes 44 F i g u r e 2.5 R e l a t i o n s h i p between r a t e of e f f e c t i v e search and prey d e n s i t y i n Eq. 2.25a 62 F i g u r e 2.6 R e l a t i o n s h i p between number of hosts a t t a c k e d and the parameter k f o r n o n - d i s c r i m i n a t i n g p a r a s i t o i d s i n Eq. 2.22 66 F i g u r e 2.7 R e l a t i o n s h i p between number of hosts a t t a c k e d and the parameter k f o r d i s c r i m i n a t i n g p a r a s i t o i d s i n Eq. 2.23 68 F i g u r e 2.8 R e l a t i o n s h i p between number of prey eaten and the parameter k f o r p r e d a t o r s i n Eq. 2.28 70 F i g u r e 2.9 F u n c t i o n a l response curves from Eq. 2.22 f o r p a r a s i t o i d s 73 x v i F i g u r e 2.10 F u n c t i o n a l response curves from Eq. 2.28 f o r preda t o r s 75 F i g u r e 2.11 F u n c t i o n a l response curves generated from Eq. 2.35 82 Fi g u r e 2.12 Type 3 responses that can look l i k e type 2 i n the presence of an a l t e r n a t i v e prey 87 F i g u r e 2.13 Type 3 responses that can look l i k e type 4 i n the presence of an a l t e r n a t i v e prey 89 F i g u r e 3.1 Demonstration of s w i t c h i n g from Eq. 3.1 96 F i g u r e 3.2 L i n e s of constant p r e f e r e n c e from Eq. 3.2 98 Fi g u r e 3.3 E v a l u a t i o n of s w i t c h i n g i n data from Akre and Johnson (1979) f o r s t a r v e d p r e d a t o r s 119 F i g u r e 3.4 E v a l u a t i o n of s w i t c h i n g i n data from Akre and Johnson ( 1979) f o r s a t i a t e d p r e d a t o r s 124 F i g u r e 3.5 F u n c t i o n a l response curves generated when a predator e x h i b i t s constant p r e f e r e n c e f o r one prey over another 134 F i g u r e 5.1 Numbers of chum f r y captured by smal l s c u l p i n s .167 F i g u r e 5.2 D i u r n a l v a r i a t i o n i n volume of stomach contents of s c u l p i n s from B i g Qualicum R i v e r .171 F i g u r e 5.3 D i u r n a l v a r i a t i o n i n number of mysids eaten by s c u l p i n s i n l a b o r a t o r y experiments 174 F i g u r e 5.4 D i u r n a l v a r i a t i o n i n number of mysids eaten by most v o r a c i o u s s c u l p i n 176 F i g u r e 6.1 B a s e l i n e f u n c t i o n a l response of naive 61-75 mm s c u l p i n s to chum f r y 211 F i g u r e 6.2 Comparison of d i s t r i b u t i o n of chum f r y captures x v i i in b a s e l i n e response with Poisson model 214 F i g u r e 6.3 E f f e c t s of s c u l p i n s i z e on b a s e l i n e f u n c t i o n a l response 222 F i g u r e 6.4 Percent chum f r y p r e d a t i o n by s c u l p i n s of d i f f e r e n t s i z e s 224 Fi g u r e 6.5 Comparison of d i s t r i b u t i o n of chum f r y captures by 47-60 mm s c u l p i n s with Poisson model 228 Fi g u r e 6.6 Comparison of d i s t r i b u t i o n of chum f r y captures by 80-99 mm s c u l p i n s with Poisson model 230 F i g u r e 6.7 Movements, p u r s u i t s and s t r i k e s by three s i z e s of s c u l p i n s at three d e n s i t i e s of chum f r y 235 Fi g u r e 6.8 E f f e c t s of a l t e r n a t i v e prey (amphipods) on b a s e l i n e f u n c t i o n a l response 244 F i g u r e 6.9 R e l a t i o n s h i p between r e l a t i v e numbers of chum f r y and amphipods a v a i l a b l e and numbers captured by 61-75 mm s c u l p i n s 246 Fi g u r e 6.10 Preference by naive 61-75 mm s c u l p i n s f o r chum f r y over amphipods 253 F i g u r e 6.11 Test f o r s w i t c h i n g by naive 61-75 mm s c u l p i n s f e e d i n g on chum f r y and amphipods 256 Fi g u r e 6.12 Number of coho f r y captured by s c u l p i n s of two s i z e s , with and without a l t e r n a t i v e prey (amphipods) ...263 F i g u r e 6.13 R e l a t i o n s h i p between r e l a t i v e numbers of coho f r y and amphipods a v a i l a b l e and numbers captured by s c u l p i n s of two s i z e s 266 F i g u r e 6.14 Pre f e r e n c e by two s i z e s of s c u l p i n s f o r coho f r y over amphipods 269 x v i i i F i g u r e 6.15 Test f o r s w i t c h i n g by s c u l p i n s of two s i z e s f e e d i n g on coho f r y and amphipods 272 Fi g u r e 6.16 Number of chum f r y eaten by i n i t i a l l y - n a i v e 61-75 mm s c u l p i n s over s u c c e s s i v e t r i a l s i n e n c l o s u r e s ....278 Fi g u r e 6.17 E f f e c t s of predator experience on chum f r y consumption i n the presence of few amphipods 280 Fi g u r e 6.18 E f f e c t s of predator experience on chum f r y consumption i n the presence of many amphipods 282 F i g u r e 6.19 Number of amphipods eaten by 61-75 mm s c u l p i n s with v a r i o u s l e v e l s of experience 285 Fi g u r e 6.20 Pref e r e n c e by 61-75 mm s c u l p i n s with v a r i o u s l e v e l s of experience f o r chum f r y over amphipods 289 F i g u r e 6.21 Tes t s f o r s w i t c h i n g by 61-75 mm s c u l p i n s of v a r i o u s l e v e l s of experience f e e d i n g on chum f r y and amphipods 291 Fi g u r e 6.22 E f f e c t s of l i g h t i n t e n s i t y on consumption of coho f r y by 60-75 mm s c u l p i n s 295 Fi g u r e 6.23 E f f e c t s of l i g h t i n t e n s i t y on consumption of chum f r y by 60-75 mm s c u l p i n s 298 Fi g u r e 6.24 Hypothesized e f f e c t s of hunger on pre f e r e n c e by s c u l p i n s f o r f r y and amphipods 304 Fi g u r e 6.25 E f f e c t s of d e n s i t y on the p r o b a b i l i t y of f r y being w i t h i n v a r i o u s d i s t a n c e s of each other 310 Fi g u r e 6.26 Hypothesized r e l a t i o n s h i p between c l o s e n e s s of f r y and success r a t e s of s c u l p i n s 312 Fi g u r e 6.27 T o t a l energy consumption by s c u l p i n s of v a r i o u s l e v e l s of experience f e e d i n g on chum f r y , with and x i x without amphipods present 316 F i g u r e 7.1 L o c a t i o n map showing study areas 325 F i g u r e 7.2 Discharge r a t e s i n Big Qualicum R i v e r i n 1979 and 1980 329 F i g u r e 7.3 Numbers of chum f r y descending B i g Qualicum R i v e r i n 1979 and 1980 332 F i g u r e 7.4 Numbers of coho f r y descending B i g Qualicum R i v e r i n 1979 and 1980 334 F i g u r e 7.5 L o c a t i o n of sampling s t a t i o n s i n the Big Qualicum estuary 337 F i g u r e 7.6 T i d a l v a r i a t i o n i n s a l i n i t i e s at sampling s t a t i o n s i n the Big Qualicum es t u a r y 340 F i g u r e 7.7 Numbers of benthic i n v e r t e b r a t e s at sampling s t a t i o n s i n the Big Qualicum estuary 347 F i g u r e 7.8 S i z e d i s t r i b u t i o n s of Eogammarus c o n f e r v i c o l u s at sampling s t a t i o n s i n the B i g Qualicum es t u a r y 350 F i g u r e 7.9 I n c i d e n t a l catches i n minnow t r a p s set at sampling s t a t i o n s i n the Big Qualicum estuary 353 F i g u r e 8.1 Length-frequency d i s t r i b u t i o n s of s c u l p i n s i n the B i g Qualicum es t u a r y 1979, 1980, 1981 370 F i g u r e 8.1a S c u l p i n s l e s s than 120 mm i n l e n g t h 371 Fi g u r e 8.1b S c u l p i n s g r e a t e r than 90 mm i n l e n g t h 372 F i g u r e 8.2 Length-frequency d i s t r i b u t i o n s of s c u l p i n s i n the Salmon Creek sampling area, 1978-79 374 F i g u r e 8.2a -Sculpins l e s s than 120 mm i n l e n g t h 375 Fi g u r e 8.2b S c u l p i n s g r e a t e r than 90 mm i n l e n g t h 376 F i g u r e 8.3 Length-frequency d i s t r i b u t i o n s of s c u l p i n s at XX Big Qualicum sampling s t a t i o n s UR and MR 378 F i g u r e 8.4 Length-frequency d i s t r i b u t i o n s of s c u l p i n s at Big Qualicum sampling s t a t i o n FP 380 F i g u r e 8.5 Length-frequency d i s t r i b u t i o n s of s c u l p i n s at Big Qualicum sampling s t a t i o n SP 382 F i g u r e 8.6 Length-frequency d i s t r i b u t i o n s of s c u l p i n s at Big Qualicum sampling s t a t i o n LR 384 F i g u r e 8.7 Length-frequency d i s t r i b u t i o n s of s c u l p i n s at Big Qualicum sampling s t a t i o n TP 386 F i g u r e 8.8 P r o p o r t i o n of recaptured s c u l p i n s that moved between sampling s t a t i o n s i n the Big Qualicum e s t u a r y ..389 F i g u r e 8.9 Length-frequency d i s t r i b u t i o n s of s c u l p i n s captured i n the upper reaches of the Big Qualicum estuary at d i f f e r e n t t i d a l h e i g h t s 392 F i g u r e 8.10 Abundance estimates f o r s c u l p i n s exceeding 45 mm i n l e n g t h i n the B i g Qualicum estuary i n 1980 ....395 F i g u r e 8.11 Abundance estimates f o r s c u l p i n s exceeding 45 mm i n l e n g t h i n the B i g Qualicum estuary i n 1979 ....399 F i g u r e 8.12 Abundance estimates by s i z e - c l a s s f o r s c u l p i n s i n the Big Qualicum estuary i n 1979 and 1980 401 F i g u r e 8.13 Abundance estimates f o r s c u l p i n s exceeding 60 mm i n l e n g t h i n the Salmon Creek estuary i n 1978 ....403 F i g u r e 9.1 Percent frequency and volume of v a r i o u s prey types found i n the stomachs of Big Qualicum s c u l p i n s ...426 F i g u r e 9.2 Percent frequency and volume of v a r i o u s c a t e g o r i e s of f i s h remains found i n the stomachs of Big Qualicum s c u l p i n s 431 xxi F i g u r e 9.3 Numbers of v a r i o u s benthic i n v e r t e b r a t e s found i n the stomachs of Big Qualicum s c u l p i n s , compared to estimated i n v e r t e b r a t e abundances 434 F i g u r e 9.4 Numbers of chum f r y found i n the stomachs of B i g Qualicum s c u l p i n s compared to estimated numbers descending the r i v e r 438 F i g u r e 9.5 Numbers of coho f r y found i n the stomachs of B i g Qualicum s c u l p i n s 442 F i g u r e 9.6 Comparison of numbers of chum f r y consumed by s c u l p i n s from two d i f f e r e n t h a b i t a t s i n the Big Qualicum est u a r y 444 F i g u r e 9.7 Comparison of numbers of coho f r y consumed by s c u l p i n s from two d i f f e r e n t h a b i t a t s i n the Big Qualicum est u a r y 447 F i g u r e 9.8 Percent frequency and volume of v a r i o u s prey types found i n the stomachs of Salmon Creek s c u l p i n s ...450 Fi g u r e 9.9 Percent frequency and volume of v a r i o u s prey types found i n the stomachs of Rosewall Creeek s c u l p i n s 454 F i g u r e 10.1 Rates of g a s t r i c evacuation by s c u l p i n s e i t h e r s t a r v e d a f t e r an i n i t i a l meal or e l s e given continuous access to a d d i t i o n a l food 470 F i g u r e 10.2 Average d a i l y f r y consumption by s c u l p i n s feeding i n cages 473 x x i i ACKNOWLEDGEMENTS Many people have c o n t r i b u t e d to the development of t h i s study. I thank my o r i g i n a l s u p e r v i s o r , Dr. C. S. H o l l i n g , who g r e a t l y i n f l u e n c e d many of my i n i t i a l ideas and ensured that I had exposure to a broad range of other academic p u r s u i t s . Dr. C. J . Walters p r o v i d e d v a l u a b l e c r i t i s m of the t h e o r e t i c a l s e c t i o n s i n the t h e s i s and h e l p f u l suggestions on i n t e r p r e t a t i o n of experimental r e s u l t s , as w e l l as g e n e r a l guidance and encouragement throughout. He began s u p e r v i s i n g t h i s p r o j e c t i n 1981 when Dr. H o l l i n g went on leave of absence. I a l s o b e n e f i t t e d from the advice of the other members of my s u p e r v i s o r y committee, Drs. T. R. Parsons, T. G. Northcote and P. A. L a r k i n . Dr. Parsons c r i t i c a l l y reviewed the t h e s i s t e x t . I am g r a t e f u l f o r the e x p e r t i s e of Dick Harvey, Grant Ladouceur and other personnel at the Big Qualicum hatchery who taught me much about salmon b i o l o g y and s u p p l i e d f r y and other m a t e r i a l s ° f o r experiments; Grant Johnson and Bob Humphries who informed me about the Rosewall Creek study a r e a ; Fergus O'Hara of the Zoology workshop who designed and b u i l t s e v e r a l p i e c e s of f i e l d equipment; Dave Z i t t e n and B i l l Webb of the B i o l o g y Data Center who gave h e l p f u l advice on computer programming; Bing Sanson who typed a l a r g e p o r t i o n of the o r i g i n a l manuscript; and It s u o Yesaki who drew a number of the f i g u r e s . My a p p r e c i a t i o n i s a l s o due to Ted Perry f o r o v e r s e e i n g the work i n the B i g Qualicum estuary, and to the B i g Qualicum Indian Band f o r being s u p p o r t i v e of t h i s p r o j e c t and g i v i n g p e r m i s s i o n to work on t h e i r l a n d . X X I 1 1 I thank Jeneen Weekes f o r i d e n t i f y i n g marine a l g a e , a s s i s t i n g with fieldwork i n 1979 and h e l p i n g to analyse f i s h stomach co n t e n t s ; Debbie M i l l e r f o r p r o c e s s i n g f i e l d samples in the l a b o r a t o r y , i d e n t i f y i n g f i s h remains and coding data; and Granger Jung f o r a l s o counting samples and coding d a t a . Ron G r i f f i t h s keyed out the a q u a t i c i n s e c t s . Bob Carveth i d e n t i f i e d some of the f i s h samples. Steve Campana demonstrated the o t o l i t h burn technique. Tim Webb s u p p l i e d a computer program to analyse nearest-neighbour d i s t a n c e s . Laura Richards and Peter Morrison c o n s t r u c t i v e l y c r i t i c i s e d some s e c t i o n s of the t h e s i s . I am indebted to a number of other f r i e n d s and f e l l o w graduate students f o r t h e i r moral support and p r a c t i c a l h e l p i n times of need. They i n c l u d e R a c h e l l e B o u f f a r d , Bruce Crawford, T e r r y Crawford, Roberta O l e n i c k , Adrienne Peacock, Dave Reader, Joan Sharp, Mike S t a l e y , Mary T a i t t , C h r i s Wood and E r i c Woodsworth. Two people, above a l l , deserve s p e c i a l mention. The f i r s t i s Dr. P. A. L a r k i n who became my s u p e r v i s o r when Dr. Walters l e f t f o r s a b b a t i c a l i n 1982. He somehow found time from h i s busy schedule to read the e n t i r e t h e s i s thoroughly, and to make numerous h e l f u l suggestions and e d i t o r i a l comments. He a l s o o f f e r e d encouragement at times when completion of t h i s p r o j e c t seemed an u n a t t a i n a b l e g o a l . The second person i s Maria Hamilton, who a s s i s t e d me i n the f i e l d d u r i n g the s p r i n g and summer of 1980. Without her d e d i c a t i o n , good humour and a b i l i t y f o r continuous work, those f i e l d experiments and sampling programs forming the c e n t r a l focus of t h i s t h e s i s would never have been performed. xxiv PREFACE . T h i s t h e s i s p r e s e n t s i n f o r m a t i o n on a number of d i f f e r e n t aspects of predator-prey r e l a t i o n s h i p s , i n c l u d i n g t h e o r e t i c a l concerns, experimental a n a l y s i s of the nature of the i n t e r a c t i o n , d e t e r m i n a t i o n of predator numbers, a n a l y s i s of predator stomach c o n t e n t s , computations of the p r o p o r t i o n of prey removed by p r e d a t o r s , and i d e n t i f i c a t i o n of systems where p r e d a t i o n c o u l d be i n t e n s e . Here, I summarize the t o p i c s covered i n each chapter and d e s c r i b e the degree of l i n k a g e between s e c t i o n s , so that the reader i n t e r e s t e d only i n s p e c i f i c areas can decide which p a r t s to t a c k l e . Part I, T h e o r e t i c a l Concerns (chapters 1-3), i n v e s t i g a t e s the p r o p e r t i e s of predator-prey systems, e v a l u a t e s mathematical models used to d e s c r i b e the i n t e r a c t i o n s , and develops new models of some components of the predator response. I t covers a wide range of the p o s s i b l e i n t e r a c t i o n s r a t h e r than being r e s t r i c t e d to the s p e c i f i c s i t u a t i o n s examined i n subsequent s e c t i o n s . The f i r s t two c h a p t e r s c o n s i d e r r e l a t i o n s h i p s between i n s e c t p a r a s i t o i d s and t h e i r h osts as w e l l as those between pr e d a t o r s and prey. In chapter 1, the components of p r e d a t i o n ( p a r a s i t i s m ) are i d e n t i f i e d and the e x i s t i n g mathematical models d e s c r i b i n g each component are presented and compared to one another i n terms of t h e i r u t i l i t y , s i m p l i c i t y and g e n e r a l i t y . The review covers the f u n c t i o n a l response to prey (host) d e n s i t y , the f u n c t i o n a l response to predator ( p a r a s i t o i d ) d e n s i t y , and the e f f e c t s of prey d e p l e t i o n on the o v e r a l l a t t a c k r a t e , and g e n e r a l i z e s r e s u l t s to systems i n v o l v i n g more than one XXV prey type. The f u n c t i o n a l response to predator d e n s i t y ( s e c t i o n 1.4) i s not d i s c u s s e d f u r t h e r . Chapter 2 i s concerned with suggestions f o r new types of predator-prey and p a r a s i t o i d - h o s t models and most of i t i s beyond the scope of the r e s t of the t h e s i s , although i n d i c a t i v e of the r e l a t i v e importance given to p a r t i c u l a r components of p r e d a t i o n i n other s e c t i o n s . In s e c t i o n 2.2, three models o r i g i n a l l y presented i n chapter 1 and used l a t e r are compared fo r t h e i r a b i l i t y to d e s c r i b e type 3 (sigmoid) responses. P a r a s i t o i d - h o s t i n t e r a c t i o n s are omitted from c o n s i d e r a t i o n a f t e r chapter 2. In chapter 3, models of prey s e l e c t i o n t h a t d i s t i n g u i s h between predator performance and prey v u l n e r a b i l i t y are d e v i s e d . S e v e r a l of these are used to t e s t f o r predator s w i t c h i n g i n experiments r e p o r t e d i n Part I I . An example from the l i t e r a t u r e which c l a i m s to demonstrate predator s w i t c h i n g u s i n g a p r e v i o u s , commonly-used model i s r e - a n a l y z e d by the new method. T h i s example i s a l s o used to demonstrate how hunger can a f f e c t e v a l u a t i o n of p r e f e r e n c e , and to examine the d i f f i c u l t i e s i n v o l v e d i n d i s t i n g u i s h i n g between types of f u n c t i o n a l responses i n c e r t a i n c ircumstances. Part I I , F i e l d and Experimental R e s u l t s (chapters 4-11), i s concerned with the i n v e s t i g a t i o n of a s p e c i f i c p r edator-prey system: that of staghorn s c u l p i n s (Leptocottus armatus) fee d i n g on chum salmon f r y (Oncorhynchus k e t a ) . The major o b j e c t i v e was to examine the f e e d i n g h a b i t s and f o r a g i n g behaviour of L. armatus to determine the most important components a f f e c t i n g xxvi t h e i r i n t e r a c t i o n with j u v e n i l e chum, the p r o p o r t i o n s of chum f r y p o p u l a t i o n s l o s t to s c u l p i n p r e d a t i o n i n p a r t i c u l a r l o c a t i o n s , and the c h a r a c t e r i s t i c s of systems where s c u l p i n s c o u l d p o t e n t i a l l y l i m i t the s i z e of chum p o p u l a t i o n s . Chapter 4 pr o v i d e s a b r i e f review of the f i s h f eeding s t u d i e s that form a background f o r the present r e s e a r c h , and o u t l i n e s the areas covered i n chapters 5-11. Chapters 5 and 6 (S e c t i o n A of Part II) c o n t a i n the r e s u l t s of experiments performed to a s c e r t a i n which f a c t o r s are the most important to the s c u l p i n - f r y i n t e r a c t i o n , and t h e i r mode of o p e r a t i o n . In chapter 5, components of the i n t e r a c t i o n are i d e n t i f i e d on the b a s i s of p r e v i o u s l i t e r a t u r e (chapter 4), o b s e r v a t i o n s of behaviour i n f i e l d e n c l o s u r e s , and f i e l d sampling programs and l a b o r a t o r y experiments conducted to determine d i e l f eeding p a t t e r n s . P r e l i m i n a r y experiments r e l e v a n t to the design of the keystone experiments r e p o r t e d i n chapter 6 are a l s o d e t a i l e d . Chapter 6 forms the nucleus of the t h e s i s . E f f e c t s of the components of s c u l p i n p r e d a t i o n s e l e c t e d f o r study i n chapter 5 are examined i n d i v i d u a l l y i n f i e l d e n c l o s u r e s , and r e s u l t s are sy n t h e s i z e d i n t o an e v a l u a t i o n of the c a u s a l i t y of f o r a g i n g behaviour i n s c u l p i n s . F a c t o r s e x p l i c i t l y i n v e s t i g a t e d are f r y d e n s i t y , s c u l p i n s i z e , f r y s o c i a l i n h i b i t i o n and f a c i l i t a t i o n , presence of a l t e r n a t i v e prey, predator experience and l i g h t i n t e n s i t y . Some experiments on s c u l p i n p r e d a t i o n on coho salmon f r y (0. k i s u t c h ) are a l s o i n c l u d e d . Models t h a t a i d i n i n t e r p r e t i n g the r e s u l t s are brought foward from cha p t e r s 1-3. F i e l d sampling r e s u l t s ( S e c t i o n B) are presented i n xxvi i chapters 7-9. Chapter 7 i s mostly d e s c r i p t i v e , d e t a i l i n g the important c h a r a c t e r i s t i c s of the three e s t u a r i n e systems sampled on Vancouver I s l a n d , B. C. (Big Qualicum R i v e r , Salmon Creek and Rosewall C r e e k ) . I t i n c l u d e s data on water s a l i n i t i e s , f a u n a l composition and s i z e s of f r y m i g r a t i o n s . T h i s i n f o r m a t i o n i s accessed by a l l remaining chapters w i t h i n Part I I . Chapter 8 i s concerned with the seasonal occurrence and abundance of s c u l p i n s of d i f f e r e n t s i z e s , t h e i r s p a t i a l d i s t r i b u t i o n s and movements w i t h i n the Big Qualicum and Salmon Creek e s t u a r i e s . I t i n v o l v e s mark-recapture experiments and d e t e r m i n a t i o n of length-frequency d i s t r i b u t i o n s , and u t i l i z e s data from chapter 7 o n l y . Chapter 9 i s devoted to a n a l y s i s of the stomach co n t e n t s of s c u l p i n s from the three study a r e a s . The o b j e c t i v e s were to determine g e n e r a l c h a r a c t e r i s t i c s of s c u l p i n f e e d i n g h a b i t s and to t e s t experimental r e s u l t s generated from chapters 5 and 6. Data from chapters 5-8 f a c i l i t a t e i n t e r p r e t a t i o n of the r e s u l t s . Chapters 10 and 11 ( S e c t i o n C) represent a s y n t h e s i s of the important r e s u l t s from c h a p t e r s 5-9. Information from chapters 7-9 forms the b a s i s f o r e s t i m a t i o n of the a c t u a l and p o t e n t i a l (maximal) impact of Big Qualicum s c u l p i n s on salmon f r y (both chum and coho), and that from chapters 5-6 suggests why s c u l p i n s do not r e a l i z e t h e i r p o t e n t i a l under n a t u r a l c o n d i t i o n s (chapter 10). Major elements of the s c u l p i n - f r y i n t e r a c t i o n are drawn from p r e v i o u s s e c t i o n s and summarized i n chapter 11, and the p h y s i c a l and b i o l o g i c a l a t t r i b u t e s of systems i n which s c u l p i n s c o u l d l i m i t salmon p r o d u c t i o n are i d e n t i f i e d . P o s s i b l e remedies x x v i i i f o r s i t u a t i o n s where s c u l p i n p r e d a t i o n i s inte n s e are a l s o proposed. The Appendix, B i r d P r e d a t i o n on J u v e n i l e Salmonids i n the Bi g Qualicum Estuary, Vancouver I s l a n d , i s an adjunct to the s c u l p i n study and can be read s e p a r a t e l y , although i t addresses s i m i l a r q u e s t i o n s and uses some of the same techniques f o r e s t i m a t i n g impacts on salmon p o p u l a t i o n s . I t c o n t a i n s i t s own t a b l e of co n t e n t s , summary and r e f e r e n c e s . 1 PART I: THEORETICAL CONCERNS 2 CHAPTER 1: GENERAL INTRODUCTION TO PREDATOR-PREY AND PARASITOID-HOST RESPONSES J_.J_ I n t r o d u c t i o n A comprehensive e v a l u a t i o n of the i n t e r a c t i o n between pr e d a t o r s and t h e i r prey i n v o l v e s d e t e r m i n a t i o n of f u n c t i o n a l , numerical and developmental responses. The f u n c t i o n a l response d e s c r i b e s how the d e n s i t y of p r e d a t o r s and prey a f f e c t s consumption by i n d i v i d u a l p r e d a t o r s , the numerical response how the d e n s i t y of predators responds to the d e n s i t y of prey, and the developmental response how prey consumption i s t r a n s l a t e d i n t o predator r e p r o d u c t i o n . T h i s t h e s i s i s concerned with the f i r s t of these, the f u n c t i o n a l response, which has three d i s t i n c t elements: the f u n c t i o n a l response to prey d e n s i t y , the f u n c t i o n a l response to predator d e n s i t y ( H o l l i n g 1961) and the e f f e c t s of prey d e p l e t i o n on the o v e r a l l a t t a c k r a t e . In t h i s chapter, I review the components of the f u n c t i o n a l response and the types of p o s s i b l e responses i n systems c o n t a i n i n g only one s p e c i e s of prey and predator ( s e c t i o n 1.2), as w e l l as the models that have been used to d e s c r i b e each element of the process ( s e c t i o n s 1.3-1.5). Only models that are simple and t r a c t a b l e , with parameters having a b i o l o g i c a l i n t e r p r e t a t i o n are presented. Methods of g e n e r a l i z i n g to s i t u a t i o n s i n v o l v i n g more than one s p e c i e s of prey are o u t l i n e d b r i e f l y ( s e c t i o n 1.6). The review i n c l u d e s ( i n s e c t ) p a r a s i t o i d -host i n t e r a c t i o n s i n a d d i t i o n to pre d a t o r - p r e y i n t e r a c t i o n s , as many of the u n d e r l y i n g mechanisms are common to both cases. 3 j_.2 The Components of P r e d a t i o n Much of the i n i t i a l development of b i o l o g i c a l l y r e a l i s t i c models of the f u n c t i o n a l response of p r e d a t o r s to t h e i r prey was c a r r i e d out by H o l l i n g (1959a, b, 1961, 1963, 1965, 1966 and 1968). H o l l i n g emphasized the need f o r an experimental components approach to the a n a l y s i s and understanding of complex e c o l o g i c a l p r o c e s s e s . T h i s c o n s i s t s of f i r s t d i s a g g r e g a t i n g a process i n t o i t s c o n s t i t u e n t components, determining the e f f e c t s of each component e x p e r i m e n t a l l y and o r g a n i z i n g the components by the u n i v e r s a l i t y of t h e i r occurrence; and then i d e n t i f y i n g each q u a l i t a t i v e l y d i s t i n c t r e p r e s e n t a t i o n of the p r o c e s s . H o l l i n g began h i s a n a l y s i s of the p r e d a t i o n process by c o n s i d e r i n g the two most fundamental v a r i a b l e s t h at a f f e c t p r e d a t i o n : the d e n s i t y of the prey and the d e n s i t y of the p r e d a t o r s ( H o l l i n g 1959a, 1961). He d e f i n e d e i g h t components a s s o c i a t e d with the e f f e c t s of prey d e n s i t y : ( i ) time predator and prey are exposed ( i i ) r a t e of e f f e c t i v e search (product of area covered per time and the l i k e l i h o o d that a prey w i l l be captured once encountered) ( i i i ) h a n d l i n g time (time taken to pursue, subdue, eat and d i g e s t each prey) ( i v ) l e v e l of predator hunger (v) f a c i l i t a t i o n by prey c o n t a c t s (e.g. predator experience l e a d i n g to improved capture success) ( v i ) i n h i b i t i o n by prey c o n t a c t s (e.g. predator experience i n r e c o g n i z i n g d i s t a s t e f u l prey) 4 ( v i i ) prey s o c i a l f a c i l i t a t i o n ( i n d i v i d u a l prey become e a s i e r to capture as prey d e n s i t y i n c r e a s e s ) ( v i i i ) prey s o c i a l i n h i b i t i o n ( i n d i v i d u a l prey become more d i f f i c u l t to capture as prey d e n s i t y i n c r e a s e s ) , and f i v e components a s s o c i a t e d with the e f f e c t s of predator d e n s i t y : ( i x ) e x p l o i t a t i o n ( d e p l e t i o n of prey through p r e d a t i o n ) (x) i n t e r f e r e n c e between p r e d a t o r s ( x i ) s o c i a l f a c i l i t a t i o n between pre d a t o r s ( x i i ) d i s t u r b a n c e of prey by p r e d a t o r s ( x i i i ) avoidance l e a r n i n g by prey. Components ( i ) — ( i i i ) and ( i x ) - ( x ) were c o n s i d e r e d to be b a s i c e f f e c t s , as every predator must search f o r i t s prey, be exposed to i t s prey and spend time h a n d l i n g i t s prey ( H o l l i n g 1959b), and every predator must e x p l o i t ( deplete) i t s prey and, i n so doing, must i n t e r f e r e with other p r e d a t o r s . The remaining e i g h t components are s u b s i d i a r y and may or may not be present i n a given predator-prey system. T h e r e f o r e , there are p o t e n t i a l l y 2 8 d i f f e r e n t forms of p r e d a t i o n ; however, these can be reduced to four q u a l i t a t i v e l y d i s t i n c t responses to prey d e n s i t y (types 1,2, 3 and 4, F i g . 1.1) and two q u a l i t a t i v e l y d i s t i n c t responses to predator d e n s i t y ( F u j i i e_t al_. 1978). When the b a s i c components of the response to prey d e n s i t y are the only components o p e r a t i n g , a type 2 response ( H o l l i n g 1959b) i s generated. The f i v e s u b s i d i a r y components modify the b a s e l i n e response i n d i f f e r e n t ways. As prey d e n s i t y i n c r e a s e s , average hunger l e v e l of the p r e d a t o r s w i l l decrease and r e s u l t cr o I-< Q LU cr cr LU Q_ CO < r-h-< L L , O cr LU m CO o LU < f* CO Type Type 2 Type 3 Type 4 PREY DENSITY 7 i n a corresponding decrease i n the rate of a t t a c k ( H o l l i n g 1966). I f pre d a t o r s feed at a constant r a t e and spend a n e g l i g i b l e amount of time h a n d l i n g prey u n t i l a hunger (or, more a c c u r a t e l y , " s a t i a t i o n " ) t h r e s h o l d i s reached, a type 1 response ( F i g . 1.1) r e s u l t s . T h i s t h r e s h o l d e f f e c t has been shown to e x i s t f o r some f i l t e r - f e e d i n g c rustaceans (see, f o r example, Richman 1958 and Burns and R i g l e r 1967). I f the e f f e c t of d e c r e a s i n g hunger i s p r o g r e s s i v e , a somewhat depressed type 2 response, which i s q u a l i t a t i v e l y s i m i l a r to the b a s e l i n e response r e s u l t s . I f g r a z i n g ceases at some low prey d e n s i t y , a m o d i f i e d type 2 response c r o s s i n g the a b s c i s s a to the r i g h t of the o r i g i n i s ob t a i n e d . T h i s v a r i a n t was f i r s t d e s c r i b e d by Parsons e_t a_l. (1967) f o r s e v e r a l s p e c i e s of zooplankton. Type 3 responses are generated i f reward r a t e s at low prey d e n s i t i e s are i n s u f f i c i e n t to maintain constant s e a r c h i n g a c t i v i t y ( H a s s e l l 1978), or i f p r e d a t o r s become p r o g r e s s i v e l y more e f f i c i e n t at c a p t u r i n g prey as the r a t e of encounter i n c r e a s e s . I t may happen that at low prey d e n s i t i e s few prey are co n t a c t e d and p r e d a t o r s take a long time to r e a l i z e that they are prey, whereas at hi g h d e n s i t i e s the p r e d a t o r s l e a r n q u i c k l y and a t t a c k at a c o r r e s p o n d i n g l y h i g h e r r a t e (Murdoch 1973). Type 3 responses can a l s o be produced by some kinds of prey s o c i a l f a c i l i t a t i o n . In some s i t u a t i o n s , prey v e l o c i t y i n c r e a s e s as t h e i r d e n s i t y i n c r e a s e s (Haynes and S i s o j e v i c 1966). Prey may produce a s t i m u l u s , such as a chemical, whose c o n c e n t r a t i o n i n c r e a s e s with d e n s i t y and causes the predator to hunt f a s t e r (Murdoch and Oaten 1975). 8 If pronounced i n h i b i t o r y e f f e c t s are o p e r a t i n g , type 4 responses can r e s u l t . H o l l i n g (1965) produced type 4 responses from a s i m u l a t i o n model of p r e d a t i o n on a m i l d l y d i s t a s t e f u l prey. As the r a t e of c o n t a c t s i n c r e a s e d , the l e a r n e d a s s o c i a t i o n between the stimulus from the prey and i t s d i s t a s t e f u l n e s s became e s t a b l i s h e d and the number of a t t a c k s d e c l i n e d . Some kinds of prey behaviour may a l s o i n h i b i t p r e d a t i o n . The prey may possess a group defense r e a c t i o n which becomes p r o g r e s s i v e l y b e t t e r developed as t h e i r d e n s i t y i n c r e a s e s (Tostowaryk 1972). A l t e r n a t i v e l y , they may d i s t u r b a predator d u r i n g an a t t a c k by bumping i n t o i t (Mori -and Chant 1966). The two b a s i c components of the response to predator d e n s i t y ( ( i x ) and (x)) would both tend to make the number of prey a t t a c k e d d e c l i n e as predator d e n s i t y i n c r e a s e s . T h i s b a s i c response can be m o d i f i e d by the s u b s i d i a r y components, ( x i ) -( x i i i ) , t o produce two q u a l i t a t i v e l y d i s t i n c t types: one that d e c l i n e s r e g u l a r l y with i n c r e a s i n g predator d e n s i t y and one that i n i t i a l l y r i s e s and then d e c l i n e s ( F u j i i et §_1. 1978). Most experimental and a n a l y t i c a l work on p r e d a t o r - p r e y and p a r a s i t o i d - h o s t f u n c t i o n a l responses has c o n c e n t r a t e d on determining e f f e c t s of the b a s i c components of the response to prey d e n s i t y only. Models that have been used e x t e n s i v e l y to d e s c r i b e these responses, and models that are p o t e n t i a l l y u s e f u l f o r d e s c r i b i n g the e f f e c t s of the other components are presented below. D e t a i l e d accounts of the behaviour of some of the models are p r o v i d e d i n reviews by Royama (1971), H a s s e l l et a l . (1976) and H a s s e l l (1978). 9 I ' l Funct i o n a l Response to Prey D e n s i t y The t h r e e e q u a t i o n s most commonly used to d e s c r i b e type 2 p r e d a t o r - p r e y responses a r e : A(N 0) = W l " e-aN0) (1.1) AnaxNo A(N 0) = C1.2) Km + N 0 aTN0 and A(N 0) = (1.3) 1 + ahN 0 where N 0 = i n i t i a l prey d e n s i t y T = t o t a l time predator and prey are exposed a = r a t e of e f f e c t i v e s e arch h = time spent h a n d l i n g each prey A(N 0) = e f f e c t o f . prey d e n s i t y on the instantaneous number of a t t a c k s per predator d u r i n g time T Amax = maximum number of a t t a c k s d u r i n g time T Km = the prey d e n s i t y at which A(N 0) = 0.5Amax. The f i r s t e q u ation was d e r i v e d independently by Gause (1934) and I v l e v (1961), the second i s the Michaelis-Menten equation of enzyme k i n e t i c s , and the t h i r d i s the d i s c e q uation developed by H o l l i n g (1959b). Equations 1.2 and 1.3 are s t r u c t u r a l l y e q u i v a l e n t and d i f f e r only i n t h e i r d e r i v a t i o n s and the s i t u a t i o n s to which they have been a p p l i e d . 10 A number of d i f f e r e n t authors have compared the a b i l i t i e s of the Gause and d i s c equations to d e s c r i b e type 2 responses. F u j i i et_ a_l. (1978) f i t t e d the two equations to 21 s e t s of data o b t a i n e d from the l i t e r a t u r e . S m a l l e s t r e s i d u a l sums of squared d e v i a t i o n s were obtained f o r the Gause equation in nine of the 21 cases and f o r the d i s c e quation i n 12 c a s e s . Glass (1970) i n h i s r e - a n a l y s i s of G r i f f i t h ' s (1969) data found that the d i s c e q u a t i o n was the b e t t e r d e s c r i p t o r i n most of the cases s t u d i e d . H o l l i n g (1959b) obtained s i m i l a r r e s u l t s . However, i t does not seem p o s s i b l e to conclude that e i t h e r equation i s c o n s i s t e n t l y b e t t e r than the other f o r f i t t i n g type 2 responses. Although Eqs. 1.1-1.3 cannot d e s c r i b e types 1, 3 or 4 responses, they are a c l e a r improvement over the L o t k a - V o l t e r r a (Lotka 1925, V o l t e r r a 1928) and N i c h o l s o n - B a i l e y (1935) models which assume a l i n e a r r e l a t i o n s h i p between the instantaneous r a t e of a t t a c k and prey d e n s i t y . To generate type 3 responses, the r a t e of e f f e c t i v e s e a rch, a, must be an i n c r e a s i n g f u n c t i o n of the prey d e n s i t y , N 0. The f u n c t i o n AmaxN0n A(N0) = (1.4) B + N 0 n where B and n are p o s i t i v e c o n s t a n t s with n > 1 (Murdoch and Oaten 1975) has f r e q u e n t l y been used to d e s c r i b e the sigmoid response. In t h i s e x p r e s s i o n , the time necessary to l o c a t e each prey item i s a d e c r e a s i n g f u n c t i o n of the number of prey encounters, r a t h e r than a l i n e a r f u n c t i o n of prey d e n s i t y . An e q u i v a l e n t e x p r e s s i o n i s that proposed by Real (1977) through an 11 analogy between f e e d i n g and the k i n e t i c s of a l l o s t e r i c enzyme r e a c t i o n s : bTN n A(N 0) = - (1.5) 1 + bhN 0 n where b i s a c o n s t a n t . In t h i s e q u a t i o n , the r a t e of e f f e c t i v e s e a r c h i s expressed by a(N Q) = bNo""1 ( 1 > 6 ) Real c a l l e d t h i s term the r a t e of p o t e n t i a l d e t e c t i o n and i n t e r p r e t e d n as the number of encounters a p r e d a t o r must have with i t s prey before i t i s maximally e f f e c t i v e on t h a t prey item. He c o n s i d e r e d the type 3 response to r e s u l t from a s s o c i a t i v e l e a r n i n g by the p r e d a t o r . H a s s e l l et a_l. (1977) a n a l y z e d s e v e r a l s e t s of data from s p e c i e s t h a t e x h i b i t sigmoid f u n c t i o n a l responses and found that o f t e n the r a t e of e f f e c t i v e s e a r c h c o u l d be expressed as a f u n c t i o n of prey d e n s i t y by a r e l a t i o n s h i p of the form bN 0 a(N Q) = (.1.7) g + N 0 where b and g are c o n s t a n t s . S u b s t i t u t i n g t h i s e x p r e s s i o n f o r a i n t o the d i s c e quation (1.3) y i e l d s bTN 0 2 A(N Q) = (1.8) g + N 0 + bhNQ2 F u j i i et a_l. (1978) used a s i m i l a r method to develop another 12 model d e s c r i b i n g type 3 responses. They assumed t h a t a(N 0) = be^O (1.9) where b and d are c o n s t a n t s , and s u b s t i t u t e d Eq. 1.9 i n t o Eq. 1.3 to g i v e be d N°TNo A(N0) = (1.10) 1 + be^OhNg Here, the parameter d can be thought of as a f a c i l i t a t i o n c o n s t a n t , with d < 0 i n d i c a t i n g an i n h i b i t o r y e f f e c t of prey d e n s i t y (components ( v i ) or ( v i i i ) ) , d > 0 a f a c i l i t a t i v e e f f e c t (components (v) or ( v i i ) ) and d = 0 no e f f e c t . The r e l a t i v e a b i l i t i e s of each of Eqs. 1.4, 1.5, 1.8 and 1.10 to d e s c r i b e p r e d a t o r - p r e y f u n c t i o n a l responses that appear to be sigmoid i n shape has not been i n v e s t i g a t e d . (For t h i s reason, an e v a l u a t i o n of t h e i r comparative f l e x i b i l i t i e s i s d e t a i l e d i n s e c t i o n 2.2). A l l are capable of d e s c r i b i n g type 2 as w e l l as type 3 responses. The d i s c equation i s regained i f n = 1 i n Eqs. 1.4 and 1.5 or i f g = 0 and d = 0 i n Eqs. 1.8 and 1.10, r e s p e c t i v e l y . Equation 1.10 i s the only e x p r e s s i o n s p e c i f i c a l l y developed to d e s c r i b e a l l four types of responses. Although the equation cannot generate a true type 1 response with a l i n e a r r i s e to a p l a t e a u , i t can produce a response that i s l i n e a r a t low prey d e n s i t i e s . T h i s c o n d i t i o n occurs when d = bh. Type 2 responses are generated i f 0 < d < bh, type 3 responses i f d > bh and type 4 responses i f d < 0. In the l a t t e r case, the maximum a t t a c k 1 3 r a t e occurs when N 0 = - 1/d and A = T/(h - de/b). In a l l other cases, and f o r b i o l o g i c a l l y f e a s i b l e ranges of the parameter estimates i n Eqs. 1.5 and 1.8, an asymptote given by A = T/h i s approached as N 0 tends to i n f i n i t y . Equation 1.8 w i l l , however, produce "type 4" (dome-shaped) responses i f the parameters are allowed t o assume ( b i o l o g i c a l l y u n r e a l i s t i c ) negative v a l u e s . The maximum number of a t t a c k s , A = 4bgT/(4bgh - 1) i s generated when N 0 = - 2g. j_.4 F u n c t i o n a l Response to Predator D e n s i t y Equations d e s c r i b i n g instantaneous a t t a c k responses to predator d e n s i t y have not been n e a r l y so w e l l developed as those f o r responses to prey d e n s i t y , although there has been c o n s i d e r a b l e work i n t h i s area i n recent years (see, f o r example, H a s s e l l and V a r l e y 1969, H a s s e l l 1971, Royama 1971, H a s s e l l and May 1973, Rogers and H a s s e l l 1974, Beddington 1975, Lawton et a l . 1975, H a s s e l l et a l . 1976 and Free et a l . 1977). The response to predator d e n s i t y i n v o l v e s the e f f e c t s of d i r e c t i n t e r f e r e n c e and s o c i a l f a c i l i t a t i o n between p r e d a t o r s , as w e l l as the e f f e c t s of i n d i r e c t i n t e r f e r e n c e caused by pr e d a t o r s d i s t u r b i n g t h e i r prey or by prey l e a r n i n g to a v o i d t h e i r p r e d a t o r s . D i r e c t i n t e r f e r e n c e between p r e d a t o r s i s the only component that has been c o n s i d e r e d i n d e t a i l . Even though the other components may o f t e n be more important, they have not been w e l l - q u a n t i f i e d i n simple models. I n t e r f e r e n c e has been modelled i n two ways: e m p i r i c a l l y as e x e m p l i f i e d by the models of Watt (1959) and H a s s e l l and V a r l e y (1969), and b e h a v i o u r a l l y , as 1 4 e x e m p l i f i e d i n the works of Rogers and H a s s e l l (1974) and Beddington (1975). O b s e r v a t i o n s on p a r a s i t o i d - h o s t systems where the a t t a c k r a t e per p a r a s i t o i d d e c l i n e d r e g u l a r l y with i n c r e a s i n g p a r a s i t o i d d e n s i t y l e d both Watt (1959) and H a s s e l l and V a r l e y (1969) to propose an equation i n which the a t t a c k r a t e was expressed by A(P) = qP-m ( 1 . 1 1 ) where P = p a r a s i t o i d ( p r e d a t o r ) d e n s i t y A(P) = e f f e c t of p a r a s i t o i d d e n s i t y on the instantaneous number of a t t a c k s per p a r a s i t o i d q = constant a t t a c k r a t e i n the absence of i n t e r f e r e n c e m = mutual i n t e r f e r e n c e constant ^ 0. In l o g a r i t h m form the model g i v e s a l i n e a r r e l a t i o n s h i p between a p a r a s i t o i d ' s s e a r c h i n g e f f i c i e n c y and i t s p o p u l a t i o n d e n s i t y : log(A(P)) = log(q) - mlog(P) ( 1 . 1 2 ) T h i s e q u a t i o n p r o v i d e s a reasonable d e s c r i p t i o n of much of the a v a i l a b l e data although i n many cases (e.g. H a s s e l l 1971, H a s s e l l and Rogers 1972) i t does not. T h i s i s not s u r p r i s i n g as there are s e v e r a l t h e o r e t i c a l problems a s s o c i a t e d with i t s f o r m u l a t i o n (Royama 1971, H a s s e l l and May 1973, Cheke 1974, Free et a l . 1977). H a s s e l l and V a r l e y (1969) themselves mentioned that much of t h e i r data would have been b e t t e r f i t t e d by a non-l i n e a r model. On t h e o r e t i c a l grounds the r e l a t i o n s h i p should be c u r v i l i n e a r with an i n c r e a s i n g l y negative slope as p a r a s i t o i d 15 d e n s i t y r i s e s . These problems, along with the p u r e l y e m p i r i c a l nature of the H a s s e l l - V a r l e y equation, have l e d s e v e r a l authors to propose more complex b e h a v i o u r a l models. Rogers and H a s s e l l (1974) developed two b e h a v i o u r a l models f o r i n t e r f e r e n c e , one (A) f o r i n t e r f e r e n c e between s e a r c h i n g a d u l t p a r a s i t o i d s and another (B) f o r i n t e r f e r e n c e between a p a r a s i t o i d and a p a r a s i t i z e d host. Both assumed that a c e r t a i n amount of time (tw) i s wasted each time a p a r a s i t o i d makes an u n p r o f i t a b l e encounter ( i n terms of being a b l e to d e p o s i t an egg). In Model A, p a r a s i t o i d s which encounter each other then abandon the search f o r hosts f o r a f i x e d p e r i o d of time. For a given number of p a r a s i t o i d s t h i s e v e n t u a l l y r e s u l t s i n an e q u i l i b r i u m between the number of p a r a s i t o i d s c e a s i n g and resuming s e a r c h . In Model B, p a r a s i t o i d s encountering a host t h a t has a l r e a d y been p a r a s i t i z e d then abandon the search f o r a f i x e d p e r i o d of time. U n l i k e Model A, i n t e r f e r e n c e i n Model B depends on both p a r a s i t o i d d e n s i t y and host d e n s i t y . By v a r y i n g the parameters of both models, Rogers and H a s s e l l were a b l e to show that the r e l a t i o n s h i p between the l o g a r i t h m of s e a r c h i n g e f f i c i e n c y and the l o g a r i t h m of the number of p a r a s i t o i d s would tend to become l i n e a r only at very high l e v e l s of mutual i n t e r f e r e n c e . The assumptions of Beddington's (1975) model of i n t e r f e r e n c e : 16 aT A(P) = (1.13) 1 + rt^CP " 1) where r i s the r a t e of encounter between p a r a s i t o i d s , are s i m i l a r t o those i n Rogers and H a s s e l l ' s Model A. The r e l a t i o n s h i p between l o g A(P) and l o g (P - 1) was shown to be l i n e a r o n l y f o r very l a r g e v a l u e s of rtw and c u r v i l i n e a r f o r s m a l l e r v a l u e s . T h i s model i s more b i o l o g i c a l l y r e a l i s t i c than Eq. 1.11, but i s a l s o more r e s t r i c t e d i n i t s a p p l i c a t i o n . I t cannot be used to d e s c r i b e responses to p r e d a t o r d e n s i t y other than t h a t of d i r e c t i n t e r f e r e n c e . The H a s s e l l - V a r l e y model (Eq. 1.11) may be more u s e f u l i n p r o v i d i n g a f i r s t approximation to d e s c r i b i n g responses where other f a c t o r s (components ( x i ) -( x i i i ) ) are thought to be o p e r a t i n g . Here, a p o s i t i v e v alue of m es t i m a t e d from the data q u a l i t a t i v e l y suggests an e f f e c t of d i r e c t or i n d i r e c t i n t e r f e r e n c e , and a negative value q u a l i t a t i v e l y suggests that some form of s o c i a l f a c i l i t a t i o n between p a r a s i t o i d s i s o p e r a t i n g . j_.5 S y n t h e s i s of Responses to Prey and Predator D e n s i t y Of the 13 components l i s t e d i n s e c t i o n 1.2, the onl y one th a t cannot be d e s c r i b e d r e a l i s t i c a l l y or e m p i r i c a l l y by any of the above models i s that of e x p l o i t a t i o n , i . e . , d e p l e t i o n of prey by t h e i r p r e d a t o r s . E x p r e s s i o n s f o r the instantaneous response to prey d e n s i t y (A(N 0)) and to pr e d a t o r d e n s i t y (A(P)) should not be used i n the forms presented to determine prey 17 consumption (host a t t a c k ) u n l e s s the amount of e x p l o i t a t i o n i s very s m a l l ( l e s s than about 10% of the i n i t i a l p o p u l a t i o n ) or prey are r e p l e n i s h e d c o n t i n o u s l y as they are eaten. The r a t e of prey d e p l e t i o n depends on the response of the pre d a t o r to the d i s t r i b u t i o n of i t s prey. Most e x p l o i t a t i o n models assume random encounters between p r e d a t o r s ( p a r a s i t o i d s ) and t h e i r prey ( h o s t s ) . For p a r a s i t o i d s , the p r o p o r t i o n of hosts k i l l e d i s expressed as one minus the p r o b a b i l i t y of occurrence i n the zero category of a Poisson d i s t r i b u t i o n with mean A(N 0,P)P/N 0, where A(N 0,P) i s the combined e f f e c t of the instantaneous responses to host and p a r a s i t o i d d e n s i t y on the t o t a l number of a t t a c k s . Hence the number of hosts a t t a c k e d , NA i s c a l c u l a t e d from N A = N 0 ( l - e-A(N 0,P)P/No) (1.14) If t here i s no i n t e r f e r e n c e between p a r a s i t o i d s A(N 0,P) = A(N 0) (1.15) and i f A(N 0) i s given by the d i s c equation (Eq. 1.3) N A = N Q(1 - e-aPT/d+ahNo)) ( 1 . 1 6 ) The most widely used model f o r r e p r e s e n t i n g non-random search by p a r a s i t o i d s i s the negative b i n o m i a l d i s t r i b u t i o n ( G r i f f i t h s and H o l l i n g 1969, May 1978). The mean of the d i s t r i b u t i o n i s assumed to be i d e n t i c a l to that of the Poisson d i s t r i b u t i o n so that the number of hosts a t t a c k e d i s expressed 18 by A(N 0,P)P N A = N 0{1 - (1 + (1.17) where k i s the d i s p e r s i o n c o e f f i c i e n t of the neg a t i v e b i n o m i a l . T h i s equation has o f t e n been found to p r o v i d e a good d e s c r i p t i o n of the d i s t r i b u t i o n of p a r a s i t o i d a t t a c k s per h o s t . Anderson and May (1978) t a b u l a t e d 15 e m p i r i c a l p a r a s i t o i d - h o s t s t u d i e s f o r which good f i t s to the negative b i n o m i a l were o b t a i n e d . G r i f f i t h s and H o l l i n g (1969) found that the d i s t r i b u t i o n of a t t a c k s by the ichneumonid p a r a s i t o i d , P l e o l o p h u s b a s i z o n u s , on the sawfly, N e o d i p r i o n s e r t i f e r was d e s c r i b e d w e l l by Eq. 1.17. They a l s o surveyed 14 other p a r a s i t o i d - h o s t f u n c t i o n a l response experiments, of which 11 conformed to Eq. 1.17 with k > 0 and three e x h i b i t e d r e g u l a r d i s t r i b u t i o n s (k < 0). In other cases, use of the n e g a t i v e b i n o m i a l d i s t r i b u t i o n has been c r i t i c i z e d on the grounds that k i s an i n c o n s i s t e n t measure of a g g r e g a t i o n i n p r a c t i c e ( T a y l o r et a l . 1978, 1979). Equ a t i o n s 1.14, 1.16 and 1.17 are i n a p p r o p r i a t e f o r pr e d a t o r s because, u n l i k e p a r a s i t o i d s , p r e d a t o r s remove t h e i r prey as they a t t a c k them. For randomly s e a r c h i n g p r e d a t o r s , the mean of the Poisson d i s t r i b u t i o n must be a f u n c t i o n of the number of prey removed from the system. I f A(N 0) i s given by the d i s c equation (Eq. 1.3) and there i s no e f f e c t of predator d e n s i t y , the a p p r o p r i a t e mean i s 19 u = a(PT - hNA) (1.18) (Rogers 1972). The same r e s u l t can be o b t a i n e d by Royama's (1971) method of e x p r e s s i n g the instantaneous number of a t t a c k s as a d i f f e r e n t i a l equation i n Nt, the number of prey remaining at time t , and i n t e g r a t i n g over time. For example, f o r the d i s c e q u a t i o n , prey consumption would be c a l c u l a t e d by s o l v i n g the e q u a t i o n dNt - aPNt (1.19) dt 1 + ahNt between the l i m i t s t = 0, T and Nt = N 0, N 0 - NA. Both methods y i e l d the s o - c a l l e d "random predator e q u a t i o n " (Rogers 1972): N A = N 0 ( l - e-a( p T" h NA)) (1.20) which i s analogous to the "random p a r a s i t e e q u a t i o n " (Eq. 1.16). An e x p r e s s i o n f o r p r e d a t o r s that search non-randomly, c o r r e s p o n d i n g to Eq. 1.17 f o r p a r a s i t o i d s , has not yet been d e r i v e d . (The a p p r o p r i a t e model i s d e r i v e d i n s e c t i o n 2.3). I n c o r p o r a t i n g e x p l o i t a t i o n i n t o p r e d a t o r - p r e y models does not a l t e r the type of response produced, but i t does a f f e c t the v a l u e s of the parameters (a and h) i f these are e s t i m a t e d from data on the i n i t i a l and f i n a l numbers of prey i n an experiment, or p r e d i c t i o n s of numbers of prey eaten i f these are based on known parameter v a l u e s . When the d i s c equation (Eq. 1.3) and the 20 random pr e d a t o r e q u a t i o n (Eq. 1.20) are f i t t e d to the same set of d a t a , the value of a e s t i m a t e d i n the l a t t e r case i s s l i g h t l y l a r g e r (Table 1.1). T h i s d i f f e r e n c e i s g r e a t e s t when t h e r e i s s u b s t a n t i a l e x p l o i t a t i o n (through, f o r example, a h i g h r a t e of e f f e c t i v e s e a r c h ) . If data are generated from the d i s c e q u a t i o n , the a b i l i t y of the random pr e d a t o r equation to d e s c r i b e them decreases with i n c r e a s i n g e x p l o i t a t i o n (Table 1.1). The i n i t i a l s l o p e of the d i s c e q u a t i o n (aT) i s always l a r g e r than the i n i t i a l s l o pe of the random pr e d a t o r equation (1 - e x p ( - a T ) ) , so t h a t when prey consumption i s c a l c u l a t e d from the same set of parameter v a l u e s i n each e q u a t i o n , the response produced from the d i s c equation i s g r e a t e r ( F i g . 1.2). The d i s c e quation reaches h a l f - s a t u r a t i o n (0.5Amax) at a lower prey d e n s i t y than the random predator e q u a t i o n , but the two curves converge at h i g h prey d e n s i t i e s . When i n t e r f e r e n c e between p r e d a t o r s or some other response to p r e d a t o r d e n s i t y i s o p e r a t i n g , i t i s necessary to combine these e f f e c t s with the response to prey d e n s i t y p r i o r to i n c o r p o r a t i n g the t o t a l response i n t o an e x p l o i t a t i o n model, i . e . to c a l c u l a t e A ( N 0 , P ) . The H a s s e l l - V a r l e y (Eq. 1.11) and d i s c e quations (Eq. 1.3) are r e a d i l y combined by assuming that the d i s c equation can be s u b s t i t u t e d f o r q i n Eq. 1.11. Hence, A(N 0,P)P = — (1 -21) 1 + ahN0 A l t e r n a t i v e l y , the t o t a l number of a t t a c k s can be d e r i v e d by combining the d i s c e quation with Beddington's e q u a t i o n (Eq. 21 Table 1.1. Parameter estimates and sums of squared d e v i a t i o n s from p r e d i c t e d v a l u e s (sse) obtained by f i t t i n g the random predator equation, R.P.E. (Eq. 1.20) to three s e t s of data generated from the d i s c equation (Eq. 1.3) with T = 1 and N = 5, 10, 15, ... 320. Parameters used i n d i s c equation Parameters estimated from R.P.E. a h sse 0.1000 0.0500 approx. 0 0.1043 0.0508 0.0024 h a sse 0.5000 0.0500 approx. 0 0.581 5 0.0510 0.4394 h a sse 0.9000 0.0500 approx. 0 1.1504 0.0511 1.6992 22 F i g u r e 1.2. F u n c t i o n a l responses generated from the d i s c equation (Eq. 1.3) and random predator equation (Eq. 1.20) with T = 1, a = 0.90 and h = 0.05. Dotted l i n e s i n d i c a t e prey d e n s i t y at which number of prey eaten i s 0.5 Amax. N U M B E R O F P R E Y P R E S E N T 24 1.13) g i v i n g aN0PT { 1 2 2 ) A(N0,P)P 1 + ahN0 + rt^P-1) (Beddington 1975). E x p r e s s i o n s based on other models of the response to prey d e n s i t y (Eqs. 1.5, 1.8 and 1.10) are o b t a i n e d by making the a p p r o p r i a t e s u b s t i t u t i o n for a i n Eq. 1.21 or 1.22. New models u s i n g a m o d i f i e d approach to d e s c r i b i n g the response t o prey d e n s i t y , and i n c o r p o r a t i n g the e x p l o i t a t i o n component, but o m i t t i n g the response to predator d e n s i t y , are pr e s e n t e d i n chapter 2. j_.6 E x t e n s i o n to M u l t i s p e c i e s Models The d i s c e quation (Eq. 1.3) has been g e n e r a l i z e d to the so-c a l l e d " m u l t i s p e c i e s d i s c e q u a t i o n " independently by s e v e r a l authors i n c l u d i n g Charnov (1973) and Murdoch (1973). They assumed t h a t , as i n the d i s c equation, the instantaneous number of a t t a c k s on a given s p e c i e s , A i , i s d i r e c t l y r e l a t e d to the d e n s i t y of t h a t s p e c i e s , N i , by the r e l a t i o n s h i p Ai = aiT sNi (1.23) where Ts = time predator spends s e a r c h i n g and a i = r a t e of e f f e c t i v e s e arch f o r prey s p e c i e s i . The time spent s e a r c h i n g i s the d i f f e r e n c e between the t o t a l time spent i n f e e d i n g a c t i v i t i e s (T) and the t o t a l time spent h a n d l i n g prey, i . e . 25 T„ = T - .Z-hjAj (1.24) or T = T + f h,a.T_N. s j = 1 3 3 s j where s i s the number of s p e c i e s p r e s e n t . I f Eq. 1.24 i s rearranged and the r e s u l t f o r Ts i s s u b s t i t u t e d i n t o Eq. 1.23, the s o l u t i o n f o r Ai i s given by A . (1.25) 1+1 a ^ N i 3=1 3 3 3 In Eq. 1.25, the response to each s p e c i e s i s type 2. To r e p r e s e n t type 3 and type 4 responses, a s i m i l a r approach can be used to g e n e r a l i z e Eqs. 1.5, 1.8 and 1.10. For example, the m u l t i s p e c i e s v e r s i o n of Eq. 1.5 i s a.TN,ni A i = i - J : CI-26) 1 + Z a,h,N,nJ 3=1 3 3 3 and produces both type 2 and type 3 responses. One problem with these kinds of f o r m u l a t i o n s i s that i n p r a c t i c e , i t may be d i f f i c u l t to determine which types of responses o p e r a t e . (The d i f f i c u l t i e s i n v o l v e d i n d i s t i n g u i s h i n g between response types i n m u l t i - p r e y systems are i n v e s t i g a t e d i n s e c t i o n 2.5). The a c t u a l numbers of prey eaten ( r a t h e r than the instantaneous number of a t t a c k s ) can be determined i n an 26 analogous manner to s i n g l e s p e c i e s cases by e x p r e s s i n g the equations as a set of d i f f e r e n t i a l equations and i n t e g r a t i n g over time u s i n g methods s i m i l a r to those employed by Lawton e_t a l . ( 1 9 7 4 ) . For Eqs. 1 . 2 5 , the d i f f e r e n t i a l e q uations _ ' a i N i (1.27) dt 1 + f a^h-iNi 0=1 J 3 J are s o l v e d to g i v e s N A i = N ± ( l - e - ^ - ^ / J ^ j ) ) (1.28) G e n e r a l i z a t i o n s i n c o r p o r a t i n g the response to p r e d a t o r d e n s i t y a l s o f o l l o w d i r e c t l y . I f Beddington's model for A(P) i s used, NAi i s found by s o l v i n g s - a .(PT- Z h-NA.) N A i = N ± ( l - e 1 + ^w^-D ) (1.29) Equations 1 . 2 9 i n c o r p o r a t e a l l of the b a s i c components of p r e d a t i o n i n a m u l t i s p e c i e s c o n t e x t . T h e i r a p p l i c a b i l i t y to n a t u r a l systems i s , however, l i m i t e d . Equations 1 . 2 5 , 1 . 2 8 and 1 . 2 9 a l l assume that a predator faced with a c h o i c e between a number of d i f f e r e n t p o t e n t i a l prey s p e c i e s w i l l simply capture each s p e c i e s i n d i r e c t p r o p o r t i o n to i t s r e l a t i v e abundance in the environment. Equation 1 . 2 6 assumes that the r e l a t i o n s h i p between the p r o p o r t i o n of each s p e c i e s i n the d i e t and i t s 27 p r o p o r t i o n i n the environment i s a simple f u n c t i o n of r e l a t i v e abundance. None of the models allow f o r the p o s s i b i l i t y of a c t i v e s e l e c t i o n by the p r e d a t o r . Probably t h e i r most u s e f u l f u n c t i o n i s one of p r o v i d i n g a mathematical statement of the n u l l h y p o t h e s i s that no p r e f e r e n c e or other complex behaviours are being expressed. (They' w i l l be used f o r t h i s purpose in subsequent s e c t i o n s of t h i s t h e s i s ) . More complex models, that i n c o r p o r a t e prey s e l e c t i o n , are c o n s i d e r e d i n chapter 3. 28 CHAPTER 2: EVALUATION AND DEVELOPMENT OF MODELS INCORPORATING VARIABLE RATES OF EFFECTIVE SEARCH 2.1_ I n t r o d u c t i o n Although most of the c l a s s i c p r e d a t i o n (and p a r a s i t i s m ) models have been based on the assumption of random search (Lotka 1925, V o l t e r r a 1928, Ni c h o l s o n and B a i l e y 1935, H o l l i n g 1959b, 1965), many recent experiments have shown that p r e d a t o r s o f t e n adopt s p e c i f i c (non-random) search s t r a t e g i e s , and that these s t r a t e g i e s may be enhanced or i n h i b i t e d by the behaviour of the prey themselves ( I v l e v 1961, Werner and H a l l 1974, Murdoch and Oaten 1975, Eggers 1977, 1978, 1982, H a s s e l l et a l . 1977, Pyke et a l . 1977, H a s s e l l 1978, Akre and Johnson 1979, H e l l e r and M i l i n s k i 1979). The important consequence of some forms of non-random search (e.g. the a b i l i t y to l o c a t e areas of hig h prey d e n s i t y ) i s that they are p o t e n t i a l l y major f a c t o r s promoting s t a b i l i t y i n predator-prey i n t e r a c t i o n s . T h i s has been demonstrated both e x p e r i m e n t a l l y and by t h e o r e t i c a l arguments (e.g. Huffaker 1958, Smith 1972, May 1973, 1978, Murdoch 1977). For t h i s reason, i t i s e s s e n t i a l to i n c o r p o r a t e mechanisms d e s c r i b i n g or e x p l a i n i n g non-random search i n t o p r e d a t o r - p r e y models. In terms of the instantaneous response to the d e n s i t y of a s i n g l e prey, random search i s represented by models i n which no s u b s i d i a r y components ( s e c t i o n 1.2) are o p e r a t i n g and the parameters r e p r e s e n t i n g the b a s i c components are con s t a n t ; namely, the d i s c equation (Eq. 1.3) or the random p a r a s i t e and 29 random predator equations (Eqs. 1.16 and 1.20). A l l other f u n c t i o n a l response models can be c o n s i d e r e d to represent some form of non-random search. The s u b s i d i a r y components (predator hunger, f a c i l i t a t i o n or i n h i b i t i o n by prey c o n t a c t s and prey s o c i a l f a c i l i t a t i o n and i n h i b i t i o n ) exert t h e i r i n f l u e n c e by ca u s i n g the b a s i c components to vary. As most of the h a n d l i n g time w i l l u s u a l l y c o n s i s t of a d i g e s t i v e pause, s u b s i d i a r y components are l i k e l y to have the g r e a t e s t e f f e c t on the r a t e of e f f e c t i v e search, a. T h i s v a r i a b l e can be expressed i n terms of i t s subcomponents as f o l l o w s : a = (area covered per t i m e ) . Pr ( r e c o g n i t i o n ! encounter). Pr ( p u r s u i t | r e c o g n i t i o n ) . Pr (attack attempt| p u r s u i t ) . Pr (success| a t t a c k attempt). The f i r s t subcomponent i s the encounter r a t e , ER, that would have r e s u l t e d i f a l l the pr e d a t o r ' s time was spent i n s e a r c h i n g f o r prey and not i n a t t a c k i n g and consuming them. For s i m p l i c i t y , the product of c o n d i t i o n a l p r o b a b i l i t i e s i s amalgamated i n t o one parameter, Pr ( s u c c e s s ) . When only one s p e c i e s of prey i s pre s e n t , the v a r i a b l e s most l i k e l y to a f f e c t the two subcomponents of a, v i a the s u b s i d i a r y components, are the d e n s i t y (and d i s t r i b u t i o n ) of prey present at a given time (Nt) and the number of prey p r e v i o u s l y a t t a c k e d s u c c e s s f u l l y ( A t ) . Dependence of a on Nt suggests that s e a r c h i n g p a t t e r n s a l t e r with the d e n s i t y of prey; dependence of a on At suggests that both the hunting s t r a t e g y and i t s success may depend on the amount of pr e v i o u s c o n t a c t the predator has a l r e a d y had with i t s prey. Although the hunger l e v e l of the predator can a l t e r the 30 search s t r a t e g y , i t can o f t e n be thought of as simply i n c r e a s i n g the h a n d l i n g time per prey (by i n c r e a s i n g the d i g e s t i v e pause) and i s not c o n s i d e r e d f u r t h e r . The remaining subcomponents a c t through e i t h e r Nt or At, but not both, to give e i g h t d i f f e r e n t pathways l e a d i n g to v a r i a b l e s r a t e s of e f f e c t i v e search ( F i g . 2.1). The r e s u l t of each of these i n t e r a c t i o n s i s that the b a s e l i n e random (type 2) response i s transformed i n t o a m o d i f i e d type 2, a type 3 or a type 4 response. P r o v i d e d that the f a c i l i t a t i v e e f f e c t i s s u f f i c i e n t l y strong, a l l pathways i n v o l v i n g f a c i l i t a t i o n w i l l probably produce type 3 responses. Pathways i n v o l v i n g i n h i b i t i o n w i l l l e a d to type 2 responses that are depressed r e l a t i v e to the b a s e l i n e response t h a t would have been obtained i f the components were not o p e r a t i n g , or type 4 responses i f the i n h i b i t o r y e f f e c t i s pronounced. Pathways 2 and 4 are u n l i k e l y to r e s u l t i n type 4 responses as t h i s would r e q u i r e s u b s t a n t i a l r e d u c t i o n s i n encounter r a t e s as prey d e n s i t y i n c r e a s e d . Type 4 responses are the most l i k e l y to be produced v i a pathway 8, p a r t i c u l a r l y i f the prey are d i s t a s t e f u l or capable of causing t h e i r p r e d a t o r s i n j u r y d u r i n g an a t t a c k attempt. Models d e r i v e d to d e s c r i b e d i f f e r e n t types of f u n c t i o n a l responses (chapter 1) have not u s u a l l y c o n s i d e r e d the d i s t i n c t i o n between mechanisms producing the response. The dilemma i s whether to develop models that are b i o l o g i c a l l y r e a l i s t i c , o f t e n i n c o r p o r a t i n g l a r g e numbers of parameters, or models that are . capable of d e t e c t i n g the shape of a response, but are p u r e l y d e s c r i p t i v e . B i o l o g i c a l l y r e a l i s t i c models, which 31 F i g u r e 2.1. E i g h t pathways l e a d i n g to v a r i a b l e r a t e s of e f f e c t i v e search v i a the subcomponents ER (encounter r a t e ) and P r ( s u c c e s s ) . Each i s a f f e c t e d by e i t h e r the prey d e n s i t y at time t (Nt) or the number of s u c c e s s f u l a t t a c k s to time t ( A t ) . V e r t i c a l arrows i n d i c a t e whether the pathway w i l l r e s u l t i n an i n c r e a s e or decrease in prey consumption over the b a s e l i n e response ( i n which no s u b s i d i a r y components o p e r a t e ) . <"SS ^ ° 1 N. A t N ST t A t 2 3 5 6 7 8 PREY SOCIAL FACILITATION PREY SOCIAL INHIBITION FACILITATION BY PREY CONTACTS INHIBITION BY PREY CONTACTS PREY SOCIAL FACILITATION E R PREY SOCIAL INHIBITION Direction of influence Pr (success) FACILITATION BY PREY CONTACTS INHIBITION BY PREY CONTACTS 1 EXAMPLES Prey v e l o c i t y i n c r e a s e s w i t h i n c r e a s i n g N 2 Prey v e l o c i t y decreases w i t h i n c r e a s i n g N Increased a b i l i t y t o l o c a t e 3 p a r t i c u l a r prey types w i t h i n c r e a s i n g experience . Learn t o avoi d areas con-" t a i n i n g p a r t i c u l a r prey types r I n c r e a s i n g numbers of weak ^ prey w i t h i n c r e a s i n g N Group defense r e a c t i o n be-5 comes p r o g r e s s i v e l y b e t t e r developed w i t h i n c r e a s i n g N t 7 Experience leads t o improved ' capture success Experience leads t o a de-g crease i n the p r o b a b i l i t y of attempting an at t a c k 33 c o n s i d e r the u n d e r l y i n g mechanisms l e a d i n g to the end r e s u l t , are d e s i r a b l e because they u s u a l l y have g r e a t e r p r e d i c t i v e power. However, an equation that i s b i o l o g i c a l l y r e a l i s t i c f o r one mechanism may be b i o l o g i c a l l y unreasonable as a r e p r e s e n t a t i o n of another mechanism. For example, a l l models developed to date to d e s c r i b e type 3 responses have assumed that the rate of e f f e c t i v e sea