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
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Predator-prey functional responses and predation by staghorn sculpins (Leptocottus armatus) on chum salmon… Mace, Pamela M. 1983
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Title | Predator-prey functional responses and predation by staghorn sculpins (Leptocottus armatus) on chum salmon fry (Oncorhynchus keta) |
Creator |
Mace, Pamela M. |
Publisher | University of British Columbia |
Date Issued | 1983 |
Description | Mathematical models describing the components of predator-prey interactions are reviewed and evaluated, and new equations representing selected aspects of the relationship are proposed. A model of prey selection that distinguishes between predator performance and prey vulnerability is devised and shown to lead to conclusions that may be qualitatively different from those produced using previous methods. The feeding habits of staghorn sculpins (Leptocottus armatus), the extent to which they utilize estuarine habitats and their predatory response to chum salmon fry (Oncorhynchus keta) are examined for the purposes of (i) ascertaining the factors shaping sculpin foraging behaviour and (ii) assessing their potential for limiting survival of juvenile salmon. During periods of fry migration, sculpin populations in the estuaries of Big Qualicum River, Salmon Creek and Rosewall Creek (on Vancouver Island, B. C.) were composed predominantly of small juveniles less than 80 mm in length. Tolerance to waters of low salinity, which decreased with sculpin size, was found to be the major variable governing residence in these areas. There was little evidence that the migration of fry was important in attracting sculpins to estuaries. Sculpins preyed on a wide diversity of fauna concentrating on benthic crustaceans, particularly the amphipod Eogammarus confervicolus. Juveniles were active throughout the day, but feeding became progressively more restricted to periods of low light intensity as they grew. The smallest that captured fry were 40-45 mm in length. When chum fry were offered to starved sculpins in field enclosures, the response of those less than 80 mm in length was type 2 (Holling 1965) whereas that of 80-99 mm sculpins was type 3 (sigmoid). Predation on fry was inversely related to light intensity from dawn to dusk, and positively correlated with' light levels during the night. When benthic invertebrates were added, sculpins exhibited an overall preference for fry, which were 4-5 times more profitable in terms of net energy intake. However, preference for fry declined markedly as their abundance relative to other prey increased, indicating a divergence from the usual predictions of optimal foraging theory. Capture rates by sculpins initially naive to salmon fry increased up to three-fold over 3-5 two hour trials. It is suggested that the foraging strategy of sculpins given a choice between salmonid fry and benthic invertebrates represents a balance between the requirement of minimizing risk of starvation and the need to evade their own predators (particularly birds). The schooling behaviour of fry requires that sculpins, even when experienced, must devote considerable attention to the attack process and in so doing, run the risk of being eaten themselves. The combined effects of the schooling response, which reduces the incentive to attack fry, and a profusion of alternative prey, which decreases average hunger levels, were thought to be responsible for low fry consumption in natural situations. In Big Qualicum River, an estimated 240,000 and 40,500 chum were captured by sculpins in 1979 and 1980, respectively. This represents corresponding percentages of only 0.51% and 0.06% of the fry populations, and was calculated to be less than one-tenth of the potential that could have been realized. Predation rates on coho fry (0. kisutch) were considerably greater, despite a smaller population size. Estimated consumption was 817,700 (42.97%) and 144,000 (9.09%) in 1979 and 1980. Systems where sculpins could consume higher proportions of chum fry populations were identified as small, shallow, warm estuaries of intermediate to high salinity with relatively few suitable benthic invertebrates and small numbers of fry. Recommendations for reducing sculpin predation in such cases are proposed. Birds, particularly Bonaparte's gulls (Larus Philadelphia), were found to be even more avid predators than sculpins on juvenile salmon in Big Qualicum River. In contrast to sculpins, they exhibited pronounced numerical responses to the appearance of fry in the estuary. An estimated 10-25% of the hatchery-reared chinook salmon (O. tshawytscha) and 2-4% of the coho were removed by birds in the years 1979-81. |
Subject |
Sculpins Predation (Biology) |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2010-05-02 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0095873 |
URI | http://hdl.handle.net/2429/24317 |
Degree |
Doctor of Philosophy - PhD |
Program |
Zoology |
Affiliation |
Science, Faculty of Zoology, Department of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
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