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Defensive strategies of schooling prey under predatory stress Palermo, R. V. 1982

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DEFENSIVE STRATEGIES OF SCHOOLING PREY UNDER PREDATORY STRESS by R. V . PALERMO BSc ( HON ) U n i v e r s i t y Of T oronto 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept t h i s t h e s i s as conforming to th r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA September 1982 (c) R. V . ' Pa lermo, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department K The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6 (3/81) i i ABSTRACT The s t r a t e g y and t a c t i c s of a v o i d i n g a p r e d a t o r by a s c h o o l i n g prey a r e examined u s i n g the s p e c i f i c example of rainbow t r o u t ( Salmo q a i r d n e r i ) c h a s i n g s i n g l e and s c h o o l i n g sockeye salmon ( Oncorhyncus nerk a ) . Three g e n e r a l r u l e s of d e f e n s i v e s t r a t e g y a r e d e v e l o p e d from the e x a m i n a t i o n of p r e d a t i o n as a p r o c e s s and from p a r a l l e l s i n modern a e r i a l w a r f a r e . The f i r s t r u l e i s based on p r e y v i g i l a n c e . R ule 1. The b e s t s t r a t e g y from the prey p o i n t of view i s not t o be d e t e c t e d by a p r e d a t o r , and t o d e t e c t the p r e s e n c e of a p r e d a t o r as soon as p o s s i b l e , p r e f e r a b l y b e f o r e d e t e c t i o n . I t i s b e s t t o a v o i d a chase, which can be a c h i e v e d by h i d i n g , or moving away, so as t o i n c r e a s e the d i s t a n c e from the p r e d a t o r . The second r u l e i s based on group c o h e s i o n . Rule 2. I n d i v i d u a l s and s t r a y s from groups a r e more v u l n e r a b l e t o p r e d a t o r s , and s c h o o l s i z e and s t r u c t u r e i s l i m i t e d by s i g n a l l o s s between i n d i v i d u a l s , t h e r e f o r e , the group s h o u l d become more compact i n s p a c i n g when a t t a c k e d by p r e d a t o r s . T h i s w i l l a l l o w the e x e c u t i o n of group manoeuvres w i t h m i n i m a l group d i s i n t e g r a t i o n . The t h i r d rule i s based on t a c t i c a l manoeuvre considerations. Rule 3. The best manoeuvre that the group can perform, i f i t detects the predator at a distance that enables the manoeuvre to be executed, i s to turn toward the di r e c t i o n of the predator. This enables the individuals to move around the predator when i t engages the group. This results in positioning the predator behind and heading away from the group. The predator was found to use path prediction as an interception strategy and prey used rapid turning manoeuvres as a defensive strategy. The f i r s t response of schooling prey was to move away from the path di r e c t i o n of the predator while forming a more compact school. The second response of the school was to turn toward the path of the predator. The t h i r d response was rapid school disintegration as each individual turned rapidly and accelerated to a high linear v e l o c i t y and o s c i l l a t i n g angular v e l o c i t y . Schooling by prey confuses and l i m i t s the a b i l i t y of the predator to path predict. Consequently, predator capture success i s greater when chasing single prey. i v TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS x I n t r o d u c t i o n 1 A s p e c t s of p r e d a t i o n as a p r o c e s s 3 I . Components 3 I I . L e v e l s of G e n e r a l i t y 5 I I I . Components of A t t a c k and Escape Behav iour 8 1 . Search 8 2. Group Cohes ion 13 3. I n d i v i d u a l T a c t i c s 17 Methods and m a t e r i a l s - g e n e r a l 24 I THE PREY 24 II THE PREDATOR 24 I I I APPARATUS 25 1) The P r e d a t i o n Arena 25 2) F i l m i n g 28 3) A n a l y s i s Of F i l m 28 IV Measurement of V a r i a b l e s 30 1) P o s i t i o n V a r i a b l e s ) 30 2) K i n e m a t i c V a r i a b l e s 34 3) I n t e r c e p t i o n V a r i a b l e s 36 4) A n a l y s i s of Chase Sequences 42 V R e s u l t s 58 I S i n g l e P r e d a t o r - S i n g l e Prey I n t e r a c t i o n s 58 1) K i n e m a t i c A t t r i b u t e s 58 2) Example chase sequence- s i n g l e p r e d a t o r - s i n g l e prey 62 II S i n g l e P r e d a t o r - S c h o o l i n g Prey 88 1) Example Sequences 88 2) Schoo l Cohes ion 156 D i s c u s s i o n 161 L i t e r a t u r e c i t e d 174 Appendix 1 178 Appendix 2 179 v i L I S T OF TABLES T a b l e 1 : E1 where i n t e r c e p t c o e f f i c i e n t s i n d i c a t e t r a c k i n g 72 v i i LIST OF FIGURES F i g u r e 1. The P r e d a t i o n Arena 27 F i g u r e 2 P o s i t i o n v a r i a b l e s 31 F i g u r e 3 I n t e r c e p t i o n v a r i a b l e s 37 F i g u r e 4 I n t e r c e p t i o n geometry 43 F i g u r e 5 D e t e r m i n a t i o n of prey a n g u l a r v e l o c i t y 46 F i g u r e 6 T r a c k i n g s t r a t e g y I 50 F i g u r e 7 T r a c k i n g s t r a t e g y I I 52 F i g u r e 8 T r a c k i n g s t r a t e g y I I I 55 F i g u r e 9 A n g u l a r v e l o c i t y and l i n e a r v e l o c i t y of p r e d a t o r and prey 59 F i g u r e 10 Time t r a j e c t o r y chase sequence [4] 74 F i g u r e 11 L i n e a r v e l o c i t y of p r e d a t o r and p r e y over time ...76 F i g u r e 12 A n g u l a r v e l o c i t y of p r e d a t o r and prey over time ..78 F i g u r e 13 C l o s u r e d i s t a n c e and D i s t a n c e a t C l o s e s t Approach over time 80 F i g u r e 14 E r r o r t r a c k i n g a n g l e and o f f s e t a n g l e over time ..82 F i g u r e 15 I n t e r c e p t i o n c o e f f i c i e n t s over time 84 F i g u r e 16 PDDIP and PYDIP over time 86 F i g u r e 1S.1 time t r a j e c t o r y s c h o o l : sequence 1S 89 F i g u r e 1S.2 p r e d a t o r l i n e a r and a n g u l a r v e l o c i t y : sequence 1S 91 F i g u r e 1S.3 c l o s u r e d i s t a n c e over time : sequence 1S 93 F i g u r e 1S.4 D i s t a n c e a t C l o s e s t Approach over time : sequence 1S 95 v i i i F i g u r e 1S.5 PDDIP over time : sequence 1S 97 F i g u r e 1S.6 PYDIP over time : sequence 1S 99 F i g u r e 1S.7 e r r o r t r a c k i n g a n g l e over time : sequence 1S ..101 F i g u r e 1S.8 o f f s e t a n g l e over time : sequence 1S 103 F i g u r e 1S.9 prey l i n e a r v e l o c i t y over time : sequence 1S ..105 F i g u r e 1S.10 prey a n g u l a r v e l o c i t y over time : sequence 1S 107 F i g u r e s 2S.1a and 2S.1b time t r a j e c t o r y s c h o o l : sequence 2S 1 12 F i g u r e 2S.2 p r e d a t o r l i n e a r and a n g u l a r v e l o c i t y : sequence 2S 114 F i g u r e 2S.3 c l o s u r e d i s t a n c e over time : sequence 2S 116 F i g u r e 2S.4 D i s t a n c e a t C l o s e s t Approach over time : sequence 2S 118 F i g u r e 2S.5 PDDIP over time : sequence 2S 120 F i g u r e 2S.6 PYDIP over time : sequence 2S 122 F i g u r e 2S.7 e r r o r t r a c k i n g a n g l e over time : sequence 2S ..124 F i g u r e 2S.8 o f f s e t a n g l e over time : sequence 2S 126 F i g u r e 2S.9 prey l i n e a r v e l o c i t y over time : sequence 2S ..128 F i g u r e 2S.10 prey a n g u l a r v e l o c i t y over time : sequence 2S 130 F i g u r e s 3S.1a and 3S.1b time t r a j e c t o r y s c h o o l : sequence 3S 134 F i g u r e 3S.2 p r e d a t o r l i n e a r and a n g u l a r v e l o c i t y : sequence 3S 136 F i g u r e 3S.3 c l o s u r e d i s t a n c e over time : sequence 3S 138 F i g u r e 3S.4 D i s t a n c e a t C l o s e s t Approach over time : sequence 3S 140 F i g u r e 3S.5 PDDIP over time : sequence 3S 142 ix F i g u r e 3S.6 PYDIP over time : sequence 3S 144 F i g u r e 3S.7 e r r o r t r a c k i n g ang le over time : sequence 3S . .146 F i g u r e 3S.8 o f f s e t ang le over t ime : sequence 3S 148 F i g u r e 3S.9 prey l i n e a r v e l o c i t y over time : sequence 3S . . 150 F i g u r e 3S.10 prey a n g u l a r v e l o c i t y over time : sequence 3S 152 F i g u r e 17 Zm response s u r f a c e : sequence 2S, frame 1 157 F i g u r e 18 Zm over t ime : u n a t t a c k e d s c h o o l 158 F i g u r e 19 Zm over t ime : sequence 2S, frame 1 to 80 159 F i g u r e 20 p r e d a t o r success as a f u n c t i o n of s c h o o l s i z e . . . 1 6 2 X ACKNOWLEDGEMENTS I s h o u l d l i k e t o e x p r e s s my s i n c e r e g r a t i t u d e t o a number of p e o p l e whose work a l l o w e d t h i s p r o j e c t t o r e a c h c o m p l e t i o n . Mr. P a u l Lakowski p r o v i d e d much of h i s time i n the c o n s t r u c t i o n of the a p p a r a t u s . Messr. B i l l Webb and Dave Z i t t i n s u p p l i e d a d v i c e on computer programming and p r o c e d u r e s . D r s . Tony S m i t h and John P a r s l o w p r o v i d e d c r i t i c a l comments and m a t h e m a t i c a l a d v i c e throughout the p r o j e c t . D r s . R. B l a k e and D M c P h a i l p r o v i d e d u s e f u l comments and c r i t i q u e s . I would e s p e c i a l l y l i k e t o thank my s u p e r v i s o r s ; Dr. C.S. H o l l i n g , f o r h i s u n s t i n t i n g f i n a n c i a l and moral s u p p o r t , and Dr. P. A. L a r k i n , f o r h i s sup p o r t and guidance i n p r o d u c i n g t h i s t h e s i s . Without such s u p p o r t , t h i s r e s e a r c h would not have been done. My w i f e / S h e i l a , w i t h her u n f a l t e r i n g moral s u p p o r t and encouragement, d e s e r v e s the g r e a t e s t c r e d i t f o r t h i s p r o j e c t . 1 INTRODUCTION Most p r e d a t i o n s t u d i e s have c o n c e n t r a t e d on the e f f e c t s of p r e d a t i o n r a t h e r than i n v e s t i g a t i n g i t s mode. There have been few a t t e m p t s t o d e f i n e and s y n t h e s i z e the b e h a v i o u r a l components of p r e d a t o r - p r e y systems, c o n t r a s t e d t o the many t h a t have d e s c r i b e d e c o l o g i c a l e f f e c t s . C u r i o (1976) p o i n t s out t h a t e c o l o g i c a l models of p r e d a t o r - p r e y systems s u f f e r from u n r e a l i s t i c assumptions c o n c e r n i n g b e h a v i o u r a l p a r a m e t e r s , and t h a t the models c o u l d g a i n immeasurably i n r e a l i s m , p r e c i s i o n , and g e n e r a l i t y by i n t e g r a t i n g b e h a v i o u r a l f i n d i n g s w i t h e c o l o g i c a l t h e o r y . T h i s study was aimed a t examining one of the l e a s t i n v e s t i g a t e d f a c e t s of p r e d a t o r - p r e y systems; the s t r a t e g y and t a c t i c s of a v o i d i n g a p r e d a t o r . The aim was t o e v o l v e g e n e r a l r u l e s a p p l i c a b l e w i d e l y t o p r e d a t i o n systems, by examining i n d e t a i l : (1) the e v o l u t i o n and importance of f o r m a l i z e d communication b e h a v i o u r and i n f o r m a t i o n h a n d l i n g systems, (2) the components which d e f i n e the p r e d a t i o n p r o c e s s , and. (3) the e v o l u t i o n of e v a s i o n s t r a t e g y and t a c t i c s . From the s e e x a m i n a t i o n s , h y potheses g e n e r a t e d by s y n t h e s i s of the s e t h e o r e t i c a l c o n c e p t s c o u l d then be t e s t e d by e x p e r i m e n t a l a n a l y s i s of a p r e d a t i o n p r o c e s s . 2 O b s e r v a t i o n s were made of a p r e d a t o r y f i s h ( rainbow t r o u t ( Salmo q a i r d n e r i ) ) a t t a c k i n g s c h o o l i n g and s i n g l e prey ( sockeye salmon ( Oncorhyncus nerka ) ) . A l s o , a s tudy was made of computer d e s i g n e d , gaming s i m u l a t i o n s of modern a i r w a r f a r e , from which many of the hypotheses c o n c e r n i n g e v a s i o n s t r a t e g y and t a c t i c s were c o n c e p t u a l i z e d . 3 ASPECTS OF PREDATION AS A PROCESS I_. Components S p e c i f i c types of p r e d a t o r prey i n t e r a c t i o n s , or prey c a p t u r e / p r e d a t o r avo idance s t r a t e g i e s , depend upon the r e l a t i v e importance of b a s i c components of the p r o c e s s . P r e d a t i o n can be c o n s i d e r e d to be d r i v e n by a number of i n t e r n a l f a c t o r s , such as m o t i v a t i o n and p h y s i o l o g i c a l s t a t u s in r e s p e c t to energy needs (hunger ) , and has four o p e r a t i o n a l components that can be measured and e v a l u a t e d w i t h r e s p e c t to prey c a p t u r e . These four b a s i c components are (1) s earch (or p e r c e p t i o n or awareness ) , (2) s t a l k , ( 3 ) a t t a c k , and (4) subduing of p r e y . The parameters tha t d e f i n e the a c t i o n s and i n t e r a c t i o n s of these components determine the r e l a t i v e importance of each to any p r e d a t i o n s t r a t e g y . For g r e g a r i o u s prey s p e c i e s , the components that determine p r e d a t o r avo idance and escape s t r a t e g i e s a r e , ( 1 ) the p e r c e p t i o n of p r e d a t o r s ( v i g i l a n c e ) , (2) e f f e c t of group s t r u c t u r e on d e f e n s i v e manoeuvres, and (3) group r e - f o r m a t i o n . I t i s important t h a t the parameters tha t d e f i n e each component be i d e n t i f i e d , and c o n s i d e r e d in terms of t h e i r i n t e r a c t i o n s and r e l a t i v e importance to the o b j e c t of prey c a p t u r e . Parameters which are r e s p o n s i b l e for prey c a p t u r e have been d e f i n e d and examined by H o l l i n g (1965), E l l i o t ( 1 9 7 2 ) , C u r i o ( l 9 7 6 ) , and o t h e r s . Brock and R i f f e n b u r g h (1960), 4 Howland(1974) , Radakov(1973) , and P a r t r i d g e ( 1 9 8 0 , 1982 ) are the o n l y r e s e a r c h e r s ( to my knowledge) to d a t e , t h a t have begun to i d e n t i f y and measure parameters that r e l a t e to p r e d a t o r avo idance or escape s t r a t e g i e s . In order to make hypotheses r e g a r d i n g p r e d a t o r avo idance or escape s t r a t e g i e s , the i d e n t i f i c a t i o n of the parameters w i t h i n each p r e d a t i o n component, and t h e i r e f f e c t on the component i n t e r a c t i o n s , i s n e c e s s a r y . To a c c o m p l i s h t h i s end , the l e v e l of g e n e r a l i t y of the study must f i r s t be d e f i n e d . 5 I I . L e v e l s of G e n e r a l i t y The r e a c t i o n of g r e g a r i o u s prey s p e c i e s t o p r e d a t o r s t r e s s can be d i v i d e d i n t o 3 l e v e l s of g e n e r a l i t y . At the h i g h e s t l e v e l , t he group, or s c h o o l of a n i m a l s can be c o n s i d e r e d as an i n t e l l i g e n t ( c a p a b l e of d i r e c t e d movement) p a t c h of food f o r a p r e d a t o r w i t h i n some environment. The p a t c h e s can c o n t a i n d i f f e r e n t amounts of energy as f u n c t i o n s of t h e i r mass and q u a l i t y . The p r i m a r y concern of s t u d i e s a t t h i s l e v e l , r e l a t i v e t o p r e d a t i o n , r e s t s on the concept of p a t c h d e t e c t i o n by p r e d a t o r s , t h e i r e x p l o i t a t i o n , and c o n s i d e r a t i o n s of s e a r c h times between s u c c e s s f u l p a t c h d e t e c t i o n . These s t u d i e s have c o n t r i b u t e d t o o p t i m a l f o r a g i n g and o p t i m a l p a t c h use t h e o r i e s . In r e s p e c t t o the prey s p e c i e s , o p t i m a l p r e d a t o r a v o i d a n c e s t r a t e g i e s a re based on f u n c t i o n s of p r e d a t o r and prey d e n s i t i e s , and e n v i r o n m e n t a l h e t e r o g e n e i t y (Paloheimo 1971 f o r example) . A second and lower l e v e l of g e n e r a l i t y i s c h a r a c t e r i z e d by s t u d i e s t h a t f o c u s on the r e l a t i v e b e h a v i o u r of the p r e d a t o r and p r e y , once the p r e d a t o r has d e t e c t e d a p a t c h and p r e p a r e s t o u t i l i z e the p a t c h f o r food ( a t t a c k and subdue). From the p r e d a t o r ' s p o i n t of view, the i m p o r t a n t c o n s i d e r a t i o n s a r e ; (1) d i s t a n c e t o the p a t c h , (2) p r o b a b i l i t y of a p p r o a c h i n g the p a t c h u n d e t e c t e d ( s t a l k ) , ( 3 ) r e a c t i o n d i s t a n c e of the p a t c h t o the presence of the p r e d a t o r ,(4) when t o exe c u t e an a t t a c k w i t h a 6 h i g h p r o b a b i l i t y of success , ( 5 ) r e l a t i v e r i s k of f a i l u r e , and consequent energy l o s s due to c a p t u r e e f f o r t , and ( 6 ) r e l a t i v e r i s k of damage from d e f e n s i v e mechanisms of the p a t c h . An o p t i m a l a t t a c k s t r a t e g y can be expressed in terms of maximiz ing the p r o b a b i l i t y of net energy g a i n . From the p o i n t of view of the g r e g a r i o u s prey s p e c i e s , the important c o n s i d e r a t i o n s a r e ; ( l ) d i s t a n c e to the p r e d a t o r , ( 2 ) t i m i n g of d e f e n s i v e manoeuvres tha t reduce p r o b a b i l i t y of d e t e c t i o n by the p r e d a t o r , ( 3 ) t i m i n g of manoeuvres tha t e f f e c t s t r u c t u r a l c o h e s i o n of the group , ( 4 ) p a t t e r n of change wi th i n c r e a s i n g p r o x i m i t y of danger , and ( 5 ) t i m i n g of manoeuvres t h a t w i l l l e a d to minimum l o s s e s for the g r o u p . O p t i m a l e v a s i o n or escape s t r a t e g i e s can be expressed as group b e h a v i o u r s that o p t i m i z e an i n d i v i d u a l ' s escape p r o b a b i l i t y . The t h i r d l e v e l of g e n e r a l i t y , the most p a r t i c u l a r , d e a l s w i t h the s i t u a t i o n when a p r e d a t o r has d e t e c t e d a group and beg ins an a t t a c k on a s e l e c t e d i n d i v i d u a l , or a s e l e c t e d p o r t i o n of the g r o u p . At t h i s l e v e l the pr imary concerns are the t a c t i c s of e scape , or c a p t u r e . The important c o n s i d e r a t i o n s at t h i s l e v e l are : ( 1 ) group s t r u c t u r e , r e l a t i v e to the aims of the group and the p r e d a t o r , ( 2 ) r e l a t i v e o r i e n t a t i o n of the prey to the p r e d a t o r a t the time of the a t t a c k , and to the o ther members of the prey group, ( 3 ) r e l a t i v e d i s t a n c e , v e l o c i t i e s ,and a c c e l e r a t i o n c a p a b i l i t i e s of both p r e d a t o r and p r e y , ( 4 ) e f f e c t s of the f o r e g o i n g on m a n o e u v r a b i l i t y of p r e d a t o r and p r e y , ( 5 ) r e a c t i o n d i s t a n c e to the p r e d a t o r or p r e y , ( 6 ) h a n d l i n g time per 7 prey for the p r e d a t o r , and ( 7 ) , the c o n t r i b u t i o n of l e a r n e d components to the behav iour of both p r e d a t o r and p r e y . The e x p r e s s i o n of escape or c a p t u r e t a c t i c s depends on the r e l a t i v e importance of these parameters i n the contex t of maximiz ing the p r o b a b i l i t y of escape or c a p t u r e . The focus of t h i s i n v e s t i g a t i o n i s on t h i s t h i r d l e v e l of g e n e r a l i t y . 8 I I I . Components of A t t a c k and Escape Behaviour J _ . Search I t i s assumed that a l l s t r a t e g i e s and t a c t i c s of p r e d a t i o n h inge on whether a p r e d a t o r , or prey can t r a c k the o t h e r . We can h y p o t h e s i z e t h e r e f o r e t h a t s e l e c t i o n has maximized sensory p e r c e p t i o n or awareness d i s t a n c e , such t h a t the r e l a t i v e p o s i t i o n s , and d i r e c t i o n of movement of each can be t r a c k e d by the o t h e r . C o n v e r s e l y ; s e l e c t i o n has m i n i m i z e d the s i g n a l s r e l e a s e d by p r e d a t o r or prey such that i t i s more d i f f i c u l t f or the o ther to t r a c k i t . For example, the c r o u c h i n g behaviour of a l i o n s t a l k i n g i t s prey a c t s to minimize s i g n a l s t h a t the prey can p e r c e i v e . From the p o i n t of view of the p r e y , the a b i l i t y to d e t e c t and t r a c k the p r e d a t o r i s mandatory i f i t i s to implement avo idance and escape s t r a t e g i e s and t a c t i c s . F u r t h e r m o r e , the implementat ion of such s t r a t e g i e s must occur as soon as neces sary to maximize escape ( or a v o i d a n c e ) , p r o b a b i l i t i e s . From the p r e d a t o r v i e w p o i n t , i t i s neces sary to d e t e c t prey be fore be ing d e t e c t e d , e n a b l i n g s e l e c t i o n of a v i c t i m and d i r e c t i n g the focus of a t t a c k such that d e t e c t i o n and d e f e n s i v e manoeuvres by the prey are m i n i m i z e d . 9 To d e t e c t p r e y , or p r e d a t o r s , t h e r e has been a g r e a t development i n s e a r c h i n g and v i g i l a n c e b e h a v i o u r s and mechanisms. From the p r e d a t o r v i e w p o i n t , s e a r c h b e h a v i o u r can be c o n s i d e r e d a c t i v e , i n the sense t h a t motor p a t t e r n s , and s c a n n i n g of s i g n a l s a r e d e s i g n e d t o maximize d e t e c t i o n of p r e y . Prey s p e c i e s may not n e c e s s a r i l y a c t i v e l y seek out p r e d a t o r s , but they a l s o need t o d e t e c t the presence of a p o t e n t i a l p r e d a t o r as soon as p o s s i b l e . T h i s b e h a v i o u r of prey i s termed v i g i l a n c e (Brown 1975,Smith 1977). The f i r s t r u l e of d e f e n s i v e s t r a t e g y i s prey v i g i l a n c e . R ule 1. The b e s t s t r a t e g y from the prey p o i n t of view i s not t o be d e t e c t e d by a p r e d a t o r , and t o d e t e c t t h e p r e s e n c e of a p r e d a t o r as soon as p o s s i b l e , p r e f e r a b l y b e f o r e d e t e c t i o n . I t i s b e s t t o a v o i d a chase, which can be a c h i e v e d by h i d i n g , or moving away, so as to i n c r e a s e the d i s t a n c e from the p r e d a t o r . Presumably, i f prey a r e unable t o d e t e c t a p r e d a t o r , and a r e themselves d e t e c t e d , the p r o b a b i l i t y of escape i s d e c r e a s e d ( t h i s i s the b a s i c s t r a t e g y of ambush p r e d a t o r s ) . I f both p r e d a t o r and prey d e t e c t each o t h e r , then a l t e r n a t i v e s t r a t e g i e s a r e n e c e s s a r y t o ensure c a p t u r e or escape. P u r s u i t s , such as l i o n s c h a s i n g w i l d e b e a s t , or bass c h a s i n g minnows, a r i s e from mutual p r e d a t o r / p r e y d e t e c t i o n . H a b i t a t h e t e r o g e n e i t y i s an i m p o r t a n t component i n the 10 response and e v o l u t i o n of s t r a t e g i e s . In open env ironments , such as g r a s s l a n d s , open waters , and s k i e s , there i s l i t t l e i n t e r f e r e n c e to b lock p e r c e p t i o n between p r e d a t o r s and p r e y . I t would t h e r e f o r e be expected tha t prey s p e c i e s that e v o l v e d in such environments would have deve loped e x c e l l e n t mechanisms for p e r c e p t i o n of p r e d a t o r s . P u r s u i t appears to be found p r i m a r i l y i n such env ironments . In heterogenous env ironments , w i t h complex h a b i t a t s t r u c t u r e , a p r e d a t o r may l o s e t r a c k of a prey due to the convergence and o b s c u r i n g of e n v i r o n m e n t a l s i g n a l s w i t h prey s i g n a l s . Ambush p r e d a t o r s evo lve i n such env ironments , and prey s p e c i e s e v o l v e c r y p t i c t a c t i c s to a v o i d p r e d a t i o n ( Edmunds (1974), and Robinson (1969)) .* H a m i l t o n (1971) proposed t h a t g r e g a r i o u s n e s s arose as a response of an imal s i n open environments to p r e d a t i o n . H i s r a t i o n a l e i s that each an imal would seek to h i d e behind another an imal , p u t t i n g another an imal between the p r e d a t o r and i t s e l f , r e d u c i n g the p e r s o n a l r i s k of c a p t u r e . T h e o r e t i c a l work by Triesman ( 1975a,1975b ) and V i n e ( 1971, 1973 ) support and expand t h i s i d e a . The hypotheses tha t emerge from these c o n c e p t s , wi th r e s p e c t to the d e f e n s i v e s t r a t e g i e s and t a c t i c s of s c h o o l i n g prey s p e c i e s under p r e d a t o r s t r e s s are : (1) the s t r u c t u r a l c o n f i g u r a t i o n of s c h o o l s i s c o n s t r a i n e d by v i g i l a n c e b e h a v i o u r . (2) the s t r u c t u r e of s c h o o l s f u n c t i o n s to a) e l i m i n a t e b l i n d 11 spots such that the members on the p e r i p h e r y moni tor the complete area around the s c h o o l , and b) presen t the l e a s t p o s s i b l e t a r g e t to a s e a r c h i n g p r e d a t o r . Though p e r i p h e r a l members of a s c h o o l may not c o n s c i o u s l y moni tor for p r e d a t o r s , t h e i r p o s i t i o n enables them to ac t in t h i s manner. Breder ( 1976 ) , L i g h t h i l l ( 1975 ) and Weihs ( 1973 ) , p o i n t out tha t hydromechanica l c o n s i d e r a t i o n s a lone can be used to d e s c r i b e observed s t r u c t u r e of s c h o o l s , but do not e x p l a i n the observed behav iour of the groups . Breder ( 1967 ) , Brock and R i f f e n b u r g h ( 1960 ) , and van O l s t and Hunter ( 1970 ) p o i n t out that the s p h e r i c a l shape of s c h o o l s p r e s e n t s a minimum s u r f a c e area and tha t t h i s c o n f i g u r a t i o n enables comprehensive m o n i t o r i n g of the s u r r o u n d i n g env ironment . In gaming s i m u l a t i o n s of modern a i r w a r f a r e , s c e n a r i o s which beg in wi th both s i d e s out of c o n t a c t in a p a r t i c u l a r a i r s p a c e , and proceed such t h a t o n l y the a i r c r a f t of one s i d e d e t e c t s the oppos ing a i r c r a f t , always r e s u l t in l o s s to the s i d e tha t does not d e t e c t the o t h e r . H i s t o r i c a l l y , Johnson ( 1964 ) r e p o r t s that 80% of the 352 a i r c r a f t shot down by a German ace d u r i n g WW I I , never saw the enemy a i r c r a f t u n t i l i t was too l a t e . The environment of e a r l i e r a i r warfare s c e n a r i o s was r e l a t i v e l y open, which l e d to the b e l i e f tha t on ly groups of 1 2 a i r c r a f t c o u l d succeed in t h e i r m i s s i o n s by employing mutual s u p p o r t . The modern a i r warfare environment i s h i g h l y he terogeneous . Wi th the advances in t e c h n o l o g y , e l e c t r o n i c countermeasures ( ECM ) of modern a i r c r a f t f u n c t i o n to i n t r o d u c e s t r u c t u r a l h e t e r o g e n e i t y . Thus s i n g l e a i r c r a f t , or p a i r s , can per form t h e i r m i s s i o n s w i t h a minimum of mutual s u p p o r t . Animals and a i r c r a f t have analogous I n f o r m a t i o n H a n d l i n g Systems ( IHS ) . There are mechanisms that are used to d e t e c t p r e d a t o r s or prey at long ranges ( h e a r i n g , o l f a c t i o n = radar ) , and s h o r t ranges ( eyes ight= i n f r a r e d d e t e c t o r s ) , and mechanisms tha t m a i n t a i n c o n t a c t between i n d i v i d u a l s ( s p e c i f i c d i s p l a y s , p h y s i o l o g i c a l a d a p t a t i o n s = r a d i o ) . The ECM of a i r c r a f t a c t to confuse and m i s l e a d the s i g n a l s p e r c e i v e d by the enemy IHS, i n a f a s h i o n s i m i l a r to the e f f e c t of s t r u c t u r a l h e t e r o g e n e i t y of h a b i t a t , i n t e r f e r i n g wi th t r a c k i n g s i g n a l s between prey and p r e d a t o r . The g e n e r a l r u l e r e g a r d i n g s e a r c h and d e t e c t i o n aims a l s o a p p l i e s to a i r c r a f t in a i r war fare s c e n a r i o s . I t i s i n t e r e s t i n g to note tha t the s t r a t e g i e s of a i r warfare have e v o l v e d in an analogous manner to the e v o l u t i o n of g r e g a r i o u s n e s s , w i th r e s p e c t to e n v i r o n m e n t a l h e t e r o g e n e i t y . 13 2. Group Cohesion A n i m a l s t h a t t r a v e l i n o r g a n i z e d groups must t o some e x t e n t be a b l e t o communicate w i t h , or a t l e a s t t r a c k each o t h e r t o have c o h e s i v e movements. Even i n n o n - h i e r a r c h i a l systems, n e a r l y spontaneous e x e c u t i o n s of manoeuvres o c c u r , such as t u r n i n g . Assuming t h a t s i g n a l s f o r the s e responses a r e g e n e r a t e d and t r a v e l from i n d i v i d u a l t o i n d i v i d u a l , and i f the IHS model h o l d s , l a g times w i l l o c cur f o r the e v a l u a t i o n of s i g n a l s and the e x e c u t i o n of d e c i s i o n s . The s i z e of groups of a n i m a l s l i v i n g i n open environments may be a f u n c t i o n of l a g time . An a d a p t a t i o n t o overcome t h i s problem i s moving c l o s e r t o g e t h e r , d e c r e a s i n g the d i s t a n c e between i n d i v i d u a l s when im p o r t a n t manoeuvres are t o be made. F i s h s c h o o l s and b i r d f l o c k s a r e known t o respond t o p r e d a t i o n by d e c r e a s i n g the .d i s t a n c e between i n d i v i d u a l s ( Radakov 1973 ). For example, the a u t h o r has observed a f l o c k of a g g r e g a t i n g s t a r l i n g s s p l i t i n t o s m a l l e r f l o c k s when r a p i d t u r n i n g manoeuvres were i n i t i a t e d by l e a d elements of the f l o c k . Sometimes the s m a l l e r f l o c k s r e f o r m i n t o a l a r g e f l o c k ; but r a p i d manoeuvres c o n t i n u e t o s p l i t up l a r g e f l o c k s . The s p l i t t i n g i s p r o b a b l y due t o the s i g n a l l o s s phenomenon. Above a c e r t a i n group s i z e , the s i g n a l l o s s from the l e a d elements t o the f o l l o w i n g elements i s such t h a t some p a r t of the group w i l l be " out i n f r o n t " b e f o r e they r e a l i z e t h a t the l e a d i n g elements have t u r n e d . H i g h speed f i l m s of the manoeuvres of 14 l a r g e f l o c k s c o u l d be used t o measure the l a g t i m e s between s i g n a l g e n e r a t i o n t o s i g n a l l o s s by the u n r e s p o n d i n g elements. Recent o b s e r v a t i o n by the a u t h o r of f i s h s c h o o l s c o n s i s t i n g of many i n d i v i d u a l s r e v e a l s the same phenomenon. Presumably, s i m i l a r problems of s i g n a l l o s s f a c e any g r e g a r i o u s s p e c i e s whose group i s l a r g e , when i t i s s u b j e c t e d t o p r e d a t i o n . I f the s i g n a l l o s s causes p a r t i a l d i s i n t e g r a t i o n of group s t r u c t u r e such t h a t i n d i v i d u a l s , or s m a l l groups of i n d i v i d u a l s s t r a y from the main group, the p r e d a t o r would b e n e f i t , as s m a l l e r groups, or i n d i v i d u a l s have a reduced escape s u c c e s s i n open e n v i r o n m e n t s . A d a p t a t i o n s t h a t reduce s i g n a l l o s s , and f u n c t i o n t o m a i n t a i n group c o h e s i o n are t o be e x p e c t e d . S p e c i f i c i n t e r group d i s p l a y s and communication, r e d u c t i o n of i n t e r i n d i v i d u a l d i s t a n c e , and o b s e r v e d s i z e l i m i t s of g r oups, can be c o n s i d e r e d such a d a p t a t i o n s (Smith 1977 ). P r e d a t o r s t r y t o f o r c e s t r a y s when a t t a c k i n g groups, ( C u r i o 1975, E l l i o t 1972), s u g g e s t i n g t h a t s t r a y s have reduced escape p r o b a b i l i t i e s . L i o n s o f t e n t r y t o f o r c e s i c k i n d i v i d u a l s or c a l v e s away from herds of w i l d e b e a s t ( E l l i o t 1972 ). To reduce the chance of becoming a s t r a y , an a n i m a l must be a b l e t o respond q u i c k l y t o sudden manoeuvres of the group. In t h i s r e s p e c t , the s p a t i a l o r g a n i z a t i o n of the group i s of importance. For the group t o a c t c o h e s i v e l y , the organisms must be a b l e t o s i m u l t a n e o u s l y t r a c k each o t h e r w i t h i n the group , and some at l e a s t must t r a c k the p r e d a t o r . 15 The second r u l e of d e f e n s i v e s t r a t e g y i s based on. group c o h e s i o n . Rule 2. I n d i v i d u a l s and s t r a y s from groups a r e more v u l n e r a b l e t o p r e d a t o r s , and s c h o o l s i z e and s t r u c t u r e i s l i m i t e d by s i g n a l l o s s ; t h e r e f o r e , the group s h o u l d become more compact i n s p a c i n g when a t t a c k e d by p r e d a t o r s . T h i s w i l l a l l o w the e x e c u t i o n of group manoeuvres w i t h m i n i m a l group d i s i n t e g r a t i o n . The manoeuvres of s c h o o l s i n response t o p r e d a t o r s a r e a l s o a f u n c t i o n of the approach d i r e c t i o n of the p r e d a t o r . Radakov (1973) p o i n t s out t h a t i n head on s i t u a t i o n s , s c h o o l response i s t o s i m p l y a v o i d c o l l i s i o n w i t h the p r e d a t o r . I n d i v i d u a l s i n the p a t h of the p r e d a t o r d i s p l a c e t o a s p e c i e s s p e c i f i c c h a r a c t e r i s t i c a n g l e and d i s t a n c e from the p r e d a t o r as i t pa s s e s through the s c h o o l . These d i s p l a c e m e n t s a f f e c t the s c h o o l s t r u c t u r e by f o r c i n g s i m i l a r d i s p l a c e m e n t of the i n d i v i d u a l s t hroughout the remainder of the group. T h i s r e s u l t s i n the s p l i t t i n g of the s c h o o l j u s t ahead of the p r e d a t o r , and i t s r e -f o r m a t i o n b e h i n d i t . The same s t r a t e g y i s employed i n a i r w a r s i m u l a t i o n s t o a v o i d m i s s i l e s or i n t e r c e p t i n g a i r c r a f t . The d e f e n d i n g a i r c r a f t ( the " prey " ) move i n t o the path of the. m i s s i l e or i n t e r c e p t o r s ( " the p r e d a t o r " ), as the m i s s i l e or i n t e r c e p t o r 16 and the de fend ing a i r c r a f t are about to come t o g e t h e r , the defender r o l l s away from the a t t a c k e r . T h i s i s i d e n t i c a l in form to the f i s h example and presumes tha t the p r e d a t o r has been s p o t t e d . The manoeuvre f u n c t i o n s to i n c r e a s e s e p a r a t i o n d i s t a n c e between prey and p r e d a t o r . I f the p r e d a t o r a t t a c k s the s c h o o l from any p o s i t i o n r e l a t i v e to the s c h o o l , and i f the prey have d e t e c t e d the p r e d a t o r at a d i s t a n c e t h a t enables them to execute a response , the response to the t h r e a t i s to face the p r e d a t o r . Rule 3. The best manoeuvre tha t the group can perform , i f i t d e t e c t s the p r e d a t o r a t a d i s t a n c e that enables the manoeuvre to be executed , i s to t u r n toward the d i r e c t i o n of the p r e d a t o r . T h i s enab les the i n d i v i d u a l s to d i s p l a c e around the p r e d a t o r when i t engages the g r o u p . T h i s r e s u l t s i n p o s i t i o n i n g the p r e d a t o r behind and heading away from the group d i r e c t i o n . Before the p r e d a t o r can t u r n a r o u n d , the s e p a r a t i o n d i s t a n c e between prey and p r e d a t o r , and the prey awareness of the t h r e a t , can make f u r t h e r a t t a c k s by the p r e d a t o r u n l i k e l y . The hypotheses t h a t emerge from these c o n s i d e r a t i o n s are : 1) Schoo l s i z e i s l i m i t e d by the s i g n a l l o s s phenomenon. 2) The s i g n a l l o s s i s measurable , and i s important in the r e g u l a t i o n of group c o h e s i o n . 17 3) The group tends to remain t o g e t h e r , and i n t e r - i n d i v i d u a l d i s t a n c e i s decreased under p r e d a t o r s t r e s s , because lone i n d i v i d u a l s have a h i g h e r r i s k of c a p t u r e in open env ironments . 4) P r e d a t o r a t t a c k d i r e c t i o n has d i r e c t consequences on the manoeuvres and o r i e n t a t i o n of the group . 5) Rules 2 and 3 are u n i v e r s a l phenomenon a p p l i c a b l e to a l l analogous p r e d a t i o n s i t u a t i o n s . 6) P e r c e p t i o n and awareness through p h y s i c a l mechanisms i s o p t i m i z e d t o f u n c t i o n such t h a t the time between d e t e c t i o n of the p r e d a t o r , and the e x e c u t i o n of d e f e n s i v e manoeuvres i s maximized. 7) The manoeuvre of f a c i n g toward, and d i s p l a c i n g around the p r e d a t o r may ac t to confuse the p r e d a t o r by f l o o d i n g the IHS w i t h a l a r g e number of t r a c k i n g problems s i m u l t a n e o u s l y . T h i s may p a r t i a l l y e x p l a i n why lone i n d i v i d u a l s are more v u l n e r a b l e to p r e d a t i o n in open env ironments . 3_. I n d i v i d u a l Tac t i c s Group d i s i n t e g r a t i o n o c c u r s when the p r e d a t o r succeeds in g e t t i n g so c l o s e to the group tha t d e t e c t i o n was not made be fore 18 the a t t a c k commenced. In such c a s e s , the c a p t u r e success p r o b a b i l i t y of the p r e d a t o r i s very h i g h . The g r o u p ' s best response i n such a c i r c u m s t a n c e i s to d i s p e r s e away from the p r e d a t o r . The d i s p e r s a l i s u s u a l l y performed without o r d e r , and the group appears to d i s i n t e g r a t e as a c o h e s i v e s t r u c t u r e . The group can however, subsequent ly r e f o r m . I f the p r e d a t o r has not yet c a p t u r e d a prey i n d i v i d u a l when the group d i s i n t e g r a t e s , the d i s o r d e r l y movement c o u l d i n c i d e n t a l l y ac t to confuse p r e d a t o r t r a c k i n g of the s e l e c t e d t a r g e t . When t h i s c o n f u s i o n o c c u r s , the p r e d a t o r must l o c a t e and t r a c k another t a r g e t . T h i s u s u a l l y r e s u l t s i n the c l a s s i c s c e n a r i o of a p r e d a t o r c h a s i n g a d e s p e r a t e l y manoeuvring p r e y , as d e s c r i b e d by Howland ( 1974 ) f o r example. Howland ( 1974 ) p o i n t e d out that the t a c t i c s of defense in t h i s s i t u a t i o n are based on the r e l a t i v e a b i l i t y of prey and p r e d a t o r wi th r e s p e c t to speed and m a n o e u v r a b i l i t y . These are the r e s u l t of the s t r u c t u r a l components t h a t f u n c t i o n toge ther to d e s c r i b e the c h a r a c t e r i s t i c l ocomot ion p a t t e r n , or k i n e m a t i c s , of the organ i sm. I f a p r e d a t o r i s c h a s i n g a prey i n d i v i d u a l , presumably i t i s t r a c k i n g the prey p o s i t i o n r e l a t i v e to i t s e l f and f u r t h e r , the p r e d a t o r must a n t i c i p a t e the d i r e c t i o n tha t the prey w i l l 19 t a k e . To s o l v e t h i s t r a c k i n g problem the p r e d a t o r must have a c a p a c i t y t o e v a l u a t e a l e a d p u r s u i t f u n c t i o n . The l e a d p u r s u i t t a c t i c d e f i n e s a p o i n t t h a t i s ahead of the prey and the p r e d a t o r aims f o r t h i s p o i n t . As the d i s t a n c e between the p r e d a t o r and prey d e c r e a s e s , the l e a d p o i n t converges t o the p r e y . Capture i s a t the convergence of the l e a d p o i n t and the p r e y . The prey has s e v e r a l d e f e n s i v e o p t i o n s : 1 ) d e c o u p l e i t s e l f from the p r e d a t o r IHS by h i d i n g , or manoeuvre i n t o a p o s i t i o n such t h a t the p r e d a t o r cannot t r a c k i t . 2 ) o u t r u n the p r e d a t o r , or 3 ) s t o p and f i g h t the p r e d a t o r . In open environments i t i s not o f t e n p o s s i b l e t o h i d e from a c h a s i n g p r e d a t o r u n l e s s the prey s p e c i e s f i n d s some cov e r t h a t i s i m p a s s a b l e t o the p r e d a t o r . P r e d a t o r s have c o - e v o l v e d w i t h t h e i r p r e y ; speed advantages by prey a r e a c c o r d i n g l y r a r e . F u r t h e r , f o r f i s h . s p e c i e s , the prey i s u s u a l l y s m a l l e r , and f o r p h y s i c a l reasons i s sl o w e r but more manoeuvrable. Many a n i m a l s t h a t have the c a p a b i l i t y t o f i g h t t h e i r p r e d a t o r s do so o n l y as a l a s t r e s o r t , no doubt because of the h i g h r i s k of i n j u r y or d e a t h , the g r e a t e r l i k e l i h o o d of f a t i g u e , and the p o s s i b i l i t y t h a t the p r e d a t o r can c o n t i n u e t o t r a c k the p r e y . The best d e f e n s i v e t a c t i c by t h e prey i s t o outmanoeuvre the p r e d a t o r . The r e s u l t s of a s u c c e s s f u l d e f e n s i v e manoeuvre i s t h a t the prey i s i n a p o s i t i o n t h a t ( 1 ) d e c o u p l e s i t from the p r e d a t o r ' s IHS, and ( 2 ) reduces the p r o b a b i l i t y of a s u c c e s s f u l a t t a c k i f the 20 p r e d a t o r r e g a i n s i t s p e r c e p t i o n of the p r e y . I f the prey has a g r e a t e r maximum v e l o c i t y , a c c e l e r a t i o n , and endurance , the s i m p l e , and o p t i m a l manoeuvre i s movement d i r e c t l y away from the p r e d a t o r at the maximum v e l o c i t y . In such a c a s e , the p r e d a t o r w i l l never c a t c h the prey ( i f there was any d i s t a n c e t h a t i n i t i a l l y s e p a r a t e d them ) . I f the p r e d a t o r i s capab le of g r e a t e r a c c e l e r a t i o n , v e l o c i t y , or endurance , then the s t r a i g h t ahead run of the prey i s not an e f f e c t i v e a n t i -c a p t u r e t a c t i c , for the p r e d a t o r w i l l always c a t c h up w i t h the p r e y . The s t r a i g h t ahead manoeuvre i s r a r e l y seen i n n a t u r e , p r o b a b l y because p r e d a t o r s would l e a r n from e x p e r i e n c e not to chase s p e c i e s whose a b i l i t y f o r s u s t a i n e d maximum v e l o c i t y and a c c e l e r a t i o n are g r e a t e r than t h e i r s . O b s e r v a t i o n s of chase s c e n a r i o s o f t en r e v e a l d e s p e r a t e t u r n i n g manoeuvres by both prey and p r e d a t o r as they attempt to g a i n a p o s i t i o n of advantage . The p o s i t i o n of advantage for the prey i s t h a t which maximizes the escape p r o b a b i l i t y . C o n v e r s e l y , the p o s i t i o n of advantage for the p r e d a t o r i s the p o s i t i o n tha t maximizes the p r o b a b i l i t y of prey c a p t u r e . Howland ( 1974 ) s t a t e s t h a t the r e l a t i v e t u r n i n g a b i l i t y of the p r e d a t o r and prey i s the c r i t i c a l f a c t o r in d e t e r m i n i n g the outcome of an a t t a c k . I f the prey can t u r n more s h a r p l y , and i f the i n i t i a l s e p a r a t i o n i s l a r g e , the prey w i l l always escape . I f the p r e d a t o r has a b e t t e r r e l a t i v e t u r n i n g a b i l i t y , the prey 21 w i l l never e scape . These c o n c l u s i o n s are too s i m p l i s t i c and u n r e a l i s t i c . I t i s more c r i t i c a l to know when to execute a t u r n i n g manoeuvre than to have the a b i l i t y to t u r n s h a r p l y . When an an imal ( a i r c r a f t , or any o ther moving o b j e c t ) beg ins a t u r n i n g manoeuvre, the c e n t r i p e t a l f o r c e s needed to m a i n t a i n a c i r c u l a r path r e s u l t in l o s s of momentum and v e l o c i t y . T h u s , the d e c i s i o n to execute a t u r n i n g manoeuvre must be made wi th c a r e . The r e s u l t of s u s t a i n i n g a t u r n i s tha t v e l o c i t y w i l l drop to some l e v e l t h a t i s a f u n c t i o n of the f o r c e s necessary to m a i n t a i n tha t t u r n ; and i s f a r below the maximum l i n e a r v e l o c i t y . I f the t u r n i s a t tempted too soon, the decrease in prey v e l o c i t y makes the c l o s u r e r a t e of the p r e d a t o r much g r e a t e r ; or enables the p r e d a t o r to d e c e l e r a t e and match the t u r n of the p r e y . T h i s negates any d e f e n s i v e advantage and p r o b a b l y decreases the p r o b a b i l i t y of e scape . There are at l e a s t four b a s i c d e f e n s i v e t u r n i n g manoeuvres tha t were c o n c e i v e d in a i r warfare s i m u l a t i o n s , and that are a l s o observed in a n i m a l s . The f i r s t manoeuvre i s c a l l e d the maximum performance t u r n and i s executed by e n t e r i n g , and s u s t a i n i n g the minimum p o s s i b l e c i r c u l a r pa th at some c o n s t a n t v e l o c i t y . The t i m i n g of t h i s manoeuvre i s d i f f i c u l t to judge; improper t i m i n g can be d i sadvantageous ( for the reasons s t a t e d in the p r e v i o u s p a r a g r a p h ) . The second manoeuvre i s c a l l e d the d e f e n s i v e t u r n . As the 22 p r e d a t o r approaches the p r e y , the prey beg ins to t u r n s l o w l y away from the p r e d a t o r . As the p r e d a t o r a p p r o a c h e s , the prey c o n t i n u e s to t u r n at a g r e a t e r r a t e ; but s t i l l in the same d i r e c t i o n . When the p r e d a t o r i s almost i n a p o s i t i o n for c a p t u r e ; the prey t u r n s at a maximum r a t e . I f the p r e d a t o r i s t r a v e l l i n g at a g r e a t e r v e l o c i t y than the p r e y , and was m a i n t a i n i n g a l e a d p u r s u i t , t h e r e i s a h i g h p r o b a b i l i t y tha t i t w i l l "overshoot" the prey when the maximum t u r n p o r t i o n of the manoeuvre i s executed . T h i s can e f f e c t i v e l y p l a c e the prey in a p o s i t i o n of advantage . The t i m i n g for e x e c u t i n g the d i f f e r e n t phases of t h i s manoeuvre i s c r i t i c a l and depends on the r e l a t i v e k i n e m a t i c parameters of the p a r t i c u l a r p r e d a t o r and p r e y . Whi le t u r n i n g , the prey a l s o has the advantage of be ing a b l e to c o n t i n u a l l y t r a c k the p r e d a t o r . Presumably t h i s a l l o w s the prey to judge c l o s u r e r a t e s and o ther parameters r e l a t i v e to proper t i m i n g . The t h i r d manoeuvre i s c a l l e d the r e v e r s a l . I f the p r e d a t o r d e t e c t s tha t the prey has begun a d e f e n s i v e t u r n , i t may d e c e l e r a t e i n order to c o n t i n u e the l e a d p u r s u i t and match the prey t u r n i n g manoeuvre. I f the prey r e a l i z e s the p r e d a t o r counter t a c t i c , i t can wait u n t i l the p r e d a t o r has committed i t s e l f to the t u r n . Then as the p r e d a t o r c l o s e s w i t h the p r e y ; the prey can execute a t u r n 180 degrees to the p r e v i o u s d i r e c t i o n . P r o p e r l y e x e c u t e d , t h i s manoeuvre w i l l cause the p r e d a t o r to "overshoot", and face in one d i r e c t i o n whi le the prey faces a n o t h e r , and u s u a l l y o p p o s i t e d i r e c t i o n . The a b i l i t y 23 of the prey to c o n t i n u a l l y t r a c k the p r e d a t o r i s of importance to the j u d i c i o u s t i m i n g of the manoeuvre. P o o r l y t i m e d , the prey w i l l be i n the same d i f f i c u l t y as w i t h the maximum performance t u r n . The f o u r t h manoeuvre i s c a l l e d the s c i s s o r s . T h i s i s a s e r i e s of r e v e r s a l s and r e s u l t s i n a z i g - z a g c o u r s e , c h a r a c t e r i s t i c of many chase s c e n a r i o s . T h i s manoeuvre i s used to counter a p r e d a t o r that c o r r e c t l y a n t i c i p a t e s the o r i g i n a l r e v e r s a l . A g a i n , t i m i n g i s c r i t i c a l . The z i g - z a g g i n g of the prey may a l s o f u n c t i o n to confuse the p r e d a t o r . The s c i s s o r s manoeuvre q u i c k l y e s t a b l i s h e s a p a t t e r n , making a n t i c i p a t i o n e a s i e r for the p r e d a t o r . The c e s s a t i o n of the manoeuvre by the prey and the b e g i n n i n g of an u n a n t i c i p a t e d manoeuvre ( w i t h r e s p e c t to the p r e d a t o r ) , can r e s u l t in t r a c k i n g l o s s by the p r e d a t o r . The t e s t i n g of these h y p o t h e s i z e d manoeuvres r e s t s on the a n a l y s i s of v e l o c i t y and t u r n i n g performances in a chase sequence. 24 METHODS AND MATERIALS - GENERAL I THE PREY The prey used throughout were j u v e n i l e sockeye salmon ( Oncorhyncus nerka ) , l a b o r a t o r y r e a r e d at 9 C in freshwater and fed Oregon M o i s t p e l l e t s d a i l y . For e x p e r i m e n t a l p u r p o s e s , f i s h of t o t a l l e n g t h 75 to 100 mm were used . The f i r s t s e r i e s of o b s e r v a t i o n s c o n s i s t e d of t r a n s f e r r i n g a s i n g l e f i s h from the r e a r i n g c o n t a i n e r ( 45 g a l . F i b r e g l a s s tank ) , to the p r e d a t i o n a r e n a . The f i s h was l e f t for 3 days to a c c l i m a t e . For the second s e r i e s of o b s e r v a t i o n s , 6 to 12 f i s h were i n t r o d u c e d to the arena and l e f t f or 3 days to a c c l i m a t e . A f t e r f i l m i n g , the f i s h were removed to a 45 g a l . t ank . 11 THE PREDATOR The p r e d a t o r used throughout were a d u l t rainbow t r o u t ( Salmo g a i r d n e r i ) , tha t prey n a t u r a l l y on j u v e n i l e sockeye salmon. The t r o u t were taken from a l a b o r a t o r y r e a r e d p o p u l a t i o n and ranged from 300 to 350 mm i n t o t a l l e n g t h . Three p r e d a t o r s were used i n the e x p e r i m e n t s . They were h e l d s e p a r a t e l y and fed e x c l u s i v e l y on both dead and l i v e j u v e n i l e sockeye . 25 One t r o u t at a t ime was p l a c e d in the h o l d i n g p o r t i o n of the f i l m i n g tank . Over a p e r i o d of two weeks, the t r o u t were c o n d i t i o n e d to accept and chase j u v e n i l e Sockeye . Before f i l m i n g , a t r o u t was not fed for 3 d a y s . I l l APPARATUS ]_) The P r e d a t i o n Arena The p r e d a t i o n arena was a l a r g e (300 x 240 x 30 cm) f i b e r g l a s s aquarium tha t was d i v i d e d i n t o two s e c t i o n s of 225 x 240 x 30 cm and 75 x 240 x 30 cm by a white p l e x i g l a s s b a r r i e r . The p r e d a t o r - p r e y i n t e r a c t i o n s were observed and f i l m e d i n the l a r g e r s e c t i o n , whi l e the s m a l l e r s e c t i o n was the p r e d a t o r h o l d i n g a r e a . The wall's of the arena were c o n s t r u c t e d of t r a n s l u c e n t f i b e r g l a s s wh i l e the bottom was u n i f o r m l y white f i b e r g l a s s to p r o v i d e c o n t r a s t between f i s h and background. The p r e d a t o r c o u l d be r e l e a s e d i n t o the arena v i a a s l i d i n g p l e x i g l a s s door on the b a r r i e r . V i e w i n g and f i l m i n g was a c c o m p l i s h e d i n d i r e c t l y v i a a l a r g e m i r r o r mounted at 45 d e g r e e s . A wide ang le ( 10 mm) l e n s on a Bolex 16 mm Ref l ex camera was used to r e c o r d the e n t i r e 225 x 240 x 30 cm arena on one frame of 16 mm f i l m wi th minimal 26 d i s t o r t i o n ( F i g . 1 ) . F i l m i n g was run at 24 frames per s e c , at f 2.8 , u s i n g a Body Motor d r i v e mounted on the camera. T h i s was the maximum f i l m i n g speed p o s s i b l e wi th the Bolex Motor . The l e n s to water s u r f a c e d i s t a n c e was 3.2 m. PLUS - X r e v e r s a l f i l m of 400 ASA at normal p r o c e s s i n g was used to r e c o r d the i n t e r a c t i o n s . Three banks of 240 cm f l o u r e s c e n t l i g h t s i n groups of four were c o n s t r u c t e d a long the t r a n s l u c e n t s i d e s of the arena and c o v e r e d wi th l i g h t b a f f l e s to e l i m i n a t e s t r a y r e f l e c t i o n s . These l i g h t s p r o v i d e d even , d i f f u s e i l l u m i n a t i o n throughout the a r e n a . The e n t i r e arena was housed in a s t e e l frame and covered wi th b l a c k f e l t . T h i s e l i m i n a t e d s t r a y l i g h t and r e f l e c t i o n s i n t o the a r e n a , and p r o v i d e d a b a r r i e r between the f i s h and e x p e r i m e n t e r . Water l e v e l was m a i n t a i n e d at 10 cm to make the i n t e r a c t i o n s e s s e n t i a l l y two d i m e n s i o n a l , and kept at 9*C by the use of an automat ic f lowthrough system and r e c i r c u l a t i o n pump. The systems were shut o f f and the tank l e f t to s t a b i l i z e for one hour b e f o r e any f i l m i n g was done in o r d e r to e l i m i n a t e any e f f e c t s of ( water c u r r e n t s . P r e l i m i n a r y o b s e r v a t i o n s i n d i c a t e d that b o t h p r e d a t o r and prey would r e a c t to the no i se from the camera. To a l l e v i a t e t h i s prob lem, the f i s h were t r a i n e d to ignore the camera n o i s e by r u n n i n g the empty camera d u r i n g r e g u l a r f e e d i n g s c h e d u l e s . 2 7 F i g u r e 1 The A r e n a f o r o b s e r v i n g p r e d a t i o n o f sockeye salmon (Oncorhyncus nerka) by ra i n b o w t r o u t (Salmo g a i r d n e r i ) 1 foot 1 i n t e r a c t i o n a r e n a 2 P r e d a t o r h o l d i n g a r e a 3 S l i d i n g r e l e a s e d o o r 4 M i r r o r 5 one-way g l a s s V i e w i n g p o r t 6 Camera 7 L i g h t Banks 8 8 f t x 10 f t F i b r e g l a s s t a n k 9 L i g h t p r o o f f e l t c o v e r i n g e n t i r e a r e n a 28 2) F i l m i n g When i t was judged that a l l f a c t o r s were s t a b i l i z e d , the p r e d a t o r was r e l e a s e d i n t o t h e - a r e n a v i a the s l i d i n g d o o r . The camera was swi tched on when the exper imenter f e l t that a chase was imminent. From p r e v i o u s o b s e r v a t i o n s , the exper imenter was a b l e to p r e d i c t w i th a c c u r a c y when chases would o c c u r . 3) A n a l y s i s Of F i l m A l l f i l m s were examined on a PCD-16 MOTION ANALYZER wi th a Vanguard 16 mm P r o j e c t i o n Head. A PCD D i g i t i z e r and T e c h t r a n Di sk D r i v e a t t a c h e d to a H a z e l t i n e 1500 t e r m i n a l were used to r e c o r d d i r e c t l y onto d i s k the frame by frame x and y c o o r d i n a t e p o s i t i o n data for p r e d a t o r and p r e y . For each chase sequence the x and y p o s i t i o n s of the p r e d a t o r and prey from a s t a n d a r d r e f e r e n c e p o i n t were measured u s i n g the c r o s s - h a i r v i e w f i n d e r of the d i g i t i z e r . The c r o s s - h a i r was p l a c e d on the c e n t r a l a x i s of each f i s h , a p p r o x i m a t e l y 1/3 of the body l e n g t h from the snout . T h i s p o s i t i o n was chosen because i t i s c l o s e to the body cen ter of g r a v i t y , l e a s t e f f e c t from the n a t u r a l o s c i l l a t i o n s of swimming m o t i o n . Twenty chase sequences were f i l m e d f o r each o b s e r v a t i o n a l s e r i e s . The 29 sequences ranged from 75 to 150 frames in l e n g t h p r o v i d i n g 150 to 300 x-y p o s i t i o n o b s e r v a t i o n s per sequence. The t ime i n t e r v a l between each frame was 1/24 s e c . For the second s e r i e s of exper iments 6 to 12 f i s h were used , y i e l d i n g up to 2400 o b s e r v a t i o n s per sequence. To reduce edge e f f e c t s , on ly those i n t e r a c t i o n s tha t o c c u r r e d near the c e n t e r of the arena were used i n data a n a l y s i s . The x , y p o s i t i o n data were read onto tape and d i s k by a PDP-11 computer and the r e l a t i v e k inemat ic data i e . P o s i t i o n , v e l o c i t y , a c c e l e r a t i o n , o r i e n t a t i o n , and c l o s u r e d i s t a n c e were c a l c u l a t e d by computer programs w r i t t e n in F o r t r a n I V . Some data were a n a l y s e d on the APPLE II P l u s m i c r o - c o m p u t e r , programmed i n B a s i c . 30 IV Measurement of V a r i a b l e s 1 ) P o s i t i o n V a r i a b l e s At any time t , X1,Y1 r e f e r to the p r e d a t o r p o s i t i o n r e l a t i v e to a r e f e r e n c e p o i n t , d e f i n e d as Xr =0, Yr=0 , t h e bottom l e f t c o r n e r of the p r e d a t i o n a r e n a . X2, Y2 r e f e r to the prey p o s i t i o n from the same r e f e r e n c e p o i n t . C , the c l o s u r e d i s t a n c e was then c a l c u l a t e d as C - ( (X 2 - Xif + ( y 2 _ Y l f } h ( 1 ) and measures the s t r a i g h t l i n e d i s t a n c e between p r e d a t o r and prey ( F i g . 2) . The p r e d a t o r d i r e c t i o n ang le ( 61 ) , i s measured r e l a t i v e to the r e f e r e n c e p o i n t as the d i r e c t i o n a l o n g the X a x i s equa l to 0.0 d e g r e e s / r a d i a n s . At each time i n t e r v a l 61 i s c a l c u l a t e d by Q i ( t ) = tan 1 ( t ) X i ( t - 1 ) ( t ) " X l ( t - i ) Y i y J 360 ° >0i > 0° ( 2 ) The prey d i r e c t i o n ang le ( 62 ) was c a l c u l a t e d s i m i l a r l y u s i n g the prey c o - o r d i n a t e d a t a . 01 i s the prey p o s i t i o n ang le and i s the angle between the s t r a i g h t l i n e from p r e d a t o r to prey and the r e f e r e n c e d i r e c t i o n . 31 F i g u r e 2 P o s i t i o n v a r i a b l e s measured a t each time frame. X1,Y1 and X2,Y2 r e f e r to the c o o r d i n a t e s of the p r e d a t o r and prey r e s p e c t i v e l y . 0 1, © 2 are the d i r e c t i o n of t r a v e l f o r p r e d a t o r and p r e y . E1, E2 are the e r r o r t r a c k i n g a n g l e and o f f s e t a n g l e . 0 1, p2 a re the d i r e c t i o n a n g l e s f o r p r e d a t o r and p r e y . Figure 2. P o s i t i o n variables measured at each time frame. 33 T h i s i s the d i r e c t i o n the p r e d a t o r would be f a c i n g i f i t p o i n t e d d i r e c t l y a t the pre y . I t i s c a l c u l a t e d by 4>i- ( t )- tan" 1 Y 2 ( t ) / Y l ( t ) l X 2Ct) " X 2 ( t ) 360" > <h > 0° ( 3 ) <j>2t i s the p r e d a t o r p o s i t i o n a n g l e and i s the a n g l e between the s t r a i g h t l i n e from prey t o p r e d a t o r and the r e f e r e n c e d i r e c t i o n . <jft2 i s c a l c u l a t e d by * 2 ( t ) - tan" 1 Y l ( t ) - Y 2 ( t ) X l - x2 (t) " 2 ( t ) J '-t 360° > cjb'i > 0° ( 4 ) T h i s i s the d i r e c t i o n the prey would face i f i t f a c e d d i r e c t l y a t the p r e d a t o r . E1 i s the t r a c k i n g e r r o r a n g l e ( a l s o c a l l e d l e a d a n g l e ) and i s d e f i n e d as the a n g u l a r d i f f e r e n c e between the p r e d a t o r c u r r e n t heading and the prey p o s i t i o n a n g l e . T h i s i s a measure of the a n g u l a r d i f f e r e n c e between where the p r e d a t o r i s heading and where the prey i s . E1 i s c a l c u l a t e d as E i ( t ) = { 0 i ( t ) ~ ^(g)) 180° > E i > - 1 8 0 u ( 5 ) T h i s v a l u e was a d j u s t e d such t h a t i f the prey was t o the r i g h t of the p r e d a t o r , ( i e . </n(t) > ©1(t) ) then E l t was m u l t i p l i e d by minus 1. N e g a t i v e v a l u e s of E1(t) i n d i c a t e t h a t the prey was t o the r i g h t of the p r e d a t o r , p o s i t i v e v a l u e s of E1t i n d i c a t e t h a t t h e prey p o s i t i o n was t o the l e f t of the p r e d a t o r . T h i s c o n v e n t i o n was adopted t o measure changes i n the p r e d a t o r h e a d i n g i n response t o pr e y p o s i t i o n . Thus,a©i was n e g a t i v e f o r 34 r i g h t t u r n s and p o s i t i v e f o r l e f t t u r n s . E2(t) i s a measure of the t h r e a t a n g l e , or ang le o f f , and i s c a l c u l a t e d by 180° > E 2 > -180° ( 6 ) T h i s va lue measures the a n g u l a r d i f f e r e n c e between the prey heading and the p r e d a t o r p o s i t i o n a n g l e . T h i s v a l u e was a d j u s t e d such that i f the p r e d a t o r was to the r i g h t of the p r e y , E2 was n e g a t i v e . The r a t i o n a l e f o r t h i s adjustment was the same as tha t for E 1 . 2) K i n e m a t i c V a r i a b l e s For each frame at t ime t , v e l o c i t y of both p r e d a t o r and prey ( V l t and V2t) were c a l c u l a t e d by V 1 ( t ) = { ( A X X ) 2 + ( A Y j ) 2 }/ At . ( 7 ) V 2 ( t ) = { ( A X 2 ) 2 + ( A Y , ) 2 } / At " . M 8 ) where^x = - X(t} and = Y(t+1) - Y(t) and t i s the time d i f f e r e n c e between frames . For t h i s s t u d y , t= .01467 s e c . , or 1/24 s e c . , and i s the r e c i p r o c a l of f i l m i n g speed . E 2 ( t ) " { 0 2 ( t ) ^ ( t ) ] . A n g u l a r v e l o c i t i e s of p r e d a t o r and prey ( W1 and W2) were c a l c u l a t e d by w 1 ( t ) { AGi / At } = { e 1 ( t + 1 ) - e 1 ( t ) } / {(t+i) - t} ( 9 ) w 2 ( t ) = { AG2 / At } = { o 2 ( t + 1 ) - e 2 ( t ) } / {(t+l) - t} ( 10 ) where 01 and 02 are the d i r e c t i o n of t r a v e l of p r e d a t o r and p r e y . A c c e l e r a t i o n was c a l c u l a t e d by a i ( t ) = { AV!/ At } ={ V l ( t + 1 ) - V 1 ( t ) } / { (t+l) - t} ( 11 ) (t+l) ~ V 2 ( t ) and a n g u l a r a c c e l e r a t i o n by 8 2 (t) = { A V 2 / A t } ={ VHt+l) ~ V 2 ( t ) } 1 { <t+1> " t) ( 12 ) < ^ i ( t ) = ( AW:/ At } = { W1(t+1) -W 1 ( t ) } / { (t+l) - t} ( 13 ) w 2 ( t ) = ( AW,/ At } = { W , ( t + 1 ) - W2(t)} / { (t+l) - t} ^  1 4 ) The t ime to maximum v e l o c i t y K/was c a l c u l a t e d from X t = X 0 + V m t - ( V m - V 0 ) (1 - e I C t) 7 k ( 15 ) (Okubo 1980, E l l i o t et a l 1977). X ( t ) i s the d i s p l a c e m e n t in 36 time t , Vm i s the maximum v e l o c i t y , Vo i s the s t a r t i n g v e l o c i t y , a n d X i s the s t a r t i n g p o s i t i o n . 3) In t e r c e p t i o n V a r i a b l e s ( F i g . 3) At each frame , from p o s i t i o n and k i n e m a t i c v a r i a b l e s , the i n t e r c e p t c o e f f i c i e n t s A and B, the l e a d ang le BA, c r o s s t r a c k ang le AA, and o r i e n t a t i o n ang le CA were c a l c u l a t e d as f o l l o w s : At t ime t + 1 the p r e d a t o r p o s i t i o n can be d e s c r i b e d as X t+ 1 = x t + B cos 0 L T Y t+ 1 = Y t + B s i n 0 1 t ( 16 ) and the prey p o s i t i o n as [ t + i = x t + A c o s 0 2 t = +.A s i n 0 2 t Y^.i Y;  2 . ( 17 ) I f the p r e d a t o r i s to c a p t u r e the p r e y , then t h e i r paths shou ld c r o s s such tha t 37 F i g u r e 3 I n t e r c e p t i o n v a r i a b l e s c a l c u l a t e d at each t ime frame. V1,V2 are the r e s p e c t i v e l i n e a r v e l o c i t y v e c t o r s for p r e d a t o r and p r e y . C i s the c l o s u r e d i s t a n c e . P o i n t A i s the i n t e r c e p t p o i n t and PDDIP i s the p r e d a t o r d i s t a n c e to the i n t e r c e p t p o i n t , PYDIP i s the prey d i s t a n c e to the i n t e r c e p t p o i n t . 33 Figure 3. Interception Variables Calculated at each time frame. 39 Y t ( 18 ) t At t h i s p o i n t X t + B c o s 0 i t = Xj. + A c o s 0 2 ( 19 ) Y t + B s i n 0 i t = Y' + A s i n 0 2 S o l v i n g f o r B and A ( Appendix 1 ). B t = ( (X^.- X t) s i n 0 2 1 + (Y t - Y') cos 0 ^ } / { s i n ( 0 ^ - 0 , f c ) } ( 20 ) A f c = { ( X t - Xj.) s i n ' 0 i t + (Y£ - Y t ) cos 0 ^ } / { s i n ( 0 X t - 0 2 t ) } ( 21 ) The p o i n t where the p a t h s c r o s s ( i f i t e x i s t s ) i s Ax = X + B cos 0 i t t t t A y t = Y t + B t s i n 0 l t " The v a l u e s of A and B may be i n t e r p r e t e d as f o l l o w s ; both p o s i t i v e : i n t e r c e p t a t some subsequent time (aim p o i n t Ax,Ay ahead of p r e y ) A p o s i t i v e B n e g a t i v e i n t e r c e p t p o i n t b e h i n d p r e d a t o r = X^ + A t cos 0 2 = Yj. + A t s i n 0 2 t ( 2 2 ) 40 ( p r e d a t o r moving away from p r e y ) A n e g a t i v e B p o s i t i v e i n t e r c e p t p o i n t behind prey both n e g a t i v e aim p o i n t beh ind both p r e d a t o r and prey ( moving away from each o ther ) . The a n g l e s BA and CA are equa l r e s p e c t i v e l y to E1 ( t r a c k i n g ang le ) and E2 ( t h r e a t a n g l e ) . At each frame, the Time to C l o s e s t Approach and D i s t a n c e at C l o s e s t Approach were c a l c u l a t e d from the p o s i t i o n s of the p r e d a t o r and p r e y . The p r e d a t o r p o s i t i o n in each frame may be r e p r e s e n t e d as V i = xt + V V i - Yt + V ( 2 3 > where U1 i s the v e l o c i t y component i n the X d i r e c t i o n and V1, i s the v e l o c i t y component in the Y d i r e c t i o n . S i m i l a r l y , the prey p o s i t i o n in each frame may be r e p r e s e n t e d as ' • N x t + i - x; + V n + i - Y t + v , , ( 24 ) 41 where U2 and V2 are as above but r e f e r to the p r e y . At t ime t , the d i s t a n c e between p r e d a t o r and prey i s D t = { ( x t " x t ) 2 + ( Y t " Y t ) 2 } 1 ( 25 ) T a k i n g the f i r s t d e r i v a t i v e of t h i s e q u a t i o n w i t h r e s p e c t to t , we f i n d d ( D 2 ) d t { ( X t + U l t ) - ( X ' - U 2 t ) } 2 + { ( Y t - V l t ) - ( Y ' - V 2 t ) } : ( 26 ) when ddD 2 ) / ( dt ) = 0.0 the Time to C l o s e s t Approach i s t , = {-(yx;)(yu 2) - ( Y ^ H V ^ ) > { (v rv 2) 2+ (u r u 2 ) 2 } ( 27 ) By s u b s t i t u t i n g t* in e q u a t i o n 23 the p o i n t at c l o s e s t approach i s x V i = x t + u i c" Y * t + 1 = Y t + v l c* ( 28 ) S i m i l a r l y the q u a n t i t i e s X ' * and Y ' * can be c a l c u l a t e d , and the D i s t a n c e at C l o s e s t Approach i s D*fc = { ( X * t - X ' * t ) 2 + ( Y * t - Y * * t ) ^ }^ ( 29 ) 42 (appendix 2 g i v e s the d e r i v a t i o n of t* and D * ) . R e g a r d l e s s of the model used to a n a l y z e p r e d a t o r - p r e y k i n e m a t i c s , the concepts of Time to C l o s e s t Approach and D i s t a n c e at C l o s e s t Approach are the most, i m p o r t a n t . The Time to C l o s e s t Approach can be i n t e r p r e t e d as the t ime at which the d i s t a n c e between the p r e d a t o r and prey w i l l be m i n i m i z e d , g i v e n the c u r r e n t p o s i t i o n , o r i e n t a t i o n , and k i n e m a t i c s of b o t h . The D i s t a n c e at C l o s e s t Approach i s the d i s t a n c e between p r e d a t o r and prey at t h i s t i m e . I f a p r e d a t o r i s to c a p t u r e the p r e y , then at some time in the f u t u r e , the d i s t a n c e between them must be m i n i m i z e d to some prey non-escape t h r e s h o l d . R e g a r d l e s s of t* , i f D* i s at 0 or some minimum, then there i s i n d i c a t i o n that the p r e d a t o r i s t r a c k i n g the prey and i s a d j u s t i n g i t s k i n e m a t i c s a c c o r d i n g l y . T h e o r e t i c a l l y , c a p t u r e shou ld occur when both t* and D* are 0 ; p r e d a t o r and prey are a t the same p o i n t at the'same t i m e . 4^ ) A n a l y s i s of Chase Sequences There are 3 p o s s i b l e i n t e r c e p t s t r a t e g i e s tha t a p r e d a t o r may employ to converge w i t h an in tended p r e y . The f i r s t and s i m p l e s t i s for the p r e d a t o r to c a l c u l a t e the q u a r r y f l i g h t p a t h , u s i n g i n f o r m a t i o n i n t e g r a t e d upon f i r s t s i g h t i n g , and then to c a l c u l a t e an i n t e r c e p t i o n c o u r s e . The geometry and k i n e m a t i c s for t h i s s t r a t e g y are p r e s e n t e d in F i g . 4, u s i n g the 43 F i g u r e 4 I n t e r c e p t i o n geometry for s t r a t e g y I . N o t a t i o n i s as in f i g u r e s 2 and 3. See t e x t for f u l l e x p l a n a t i o n . 44 Figure 4. Interception Geometry for Strategy I. I prey C= Closure Distance At point I : (x t ,.Yt) = (X' , Y 1 ) 45 a n g u l a r c o n v e n t i o n s p r e s e n t e d e a r l i e r . To a c h i e v e an i n t e r c e p t i o n c o u r s e , the p r e d a t o r needs to know at f i r s t s i g h t i n g , in a d d i t i o n to i t s own k i n e m a t i c a b i l i t y : (1) the a n g u l a r p o s i t i o n of the prey <f)\ . (2) the a n g u l a r v e l o c i t y of the prey r e l a t i v e to the p r e d a t o r (dE2/dt). (3) the l i n e a r v e l o c i t y (V2) of the p r e y . (4) the d i s t a n c e to the p r e y , CLD. Assuming tha t the p r e d a t o r beg ins w i t h V1 = 0.0 and i s o r i e n t e d toward the prey ( ^1 = ©1 ) then the a n g u l a r v e l o c i t y of the prey r e l a t i v e to the p r e d a t o r can be measured as ( F i g 5 ) • g* = { V 2 s i n E 2 / CLD } ( 30 ) I f V2 remains c o n s t a n t the p r e d a t o r has a d i r e c t measurement of the r e l a t i v e course of the prey by E 2 = s i n " 1 { g* • CLD / V 2 } ( 31 ) I f 61 yt 01 then the p r e d a t o r can o r i e n t i t s p o s i t i o n to e q u a l i z e these q u a n t i t i e s . 46 F i g u r e 5 D e t e r m i n a t i o n of p r e y a n g u l a r v e l o c i t y . See t e x t f o r f u l l e x p l a n a t i o n . Figure 5. Determination of prey angular v e l o c i t y . 48 To s u c c e s s f u l l y i n t e r c e p t , the p r e d a t o r must t r a v e l PI in the same time as the prey t r a v e l s P ' l , a r r i v i n g at I . T o a c c o m p l i s h t h i s , i t i s neces sary for the p r e d a t o r to c a l c u l a t e E ' 2 and to c h a n g e . o r i e n t a t i o n such that © t + 1 = E ' 2 . T h i s i s done by f i r s t c a l c u l a t i n g the t ime to i n t e r c e p t i o n g i v e n E2 at f i r s t s i g h t i n g and the k i n e m a t i c p a r a m e t e r s . By a p p l y i n g the c o s i n e r u l e to t r i a n g l e PP'I ( F i g . 4 ) , the time to i n t e r c e p t i s c a l c u l a t e d as P ' I2 =(P'I2 - 2 P ' I P ' P c o s E 2 ) i 5 ( 32 ) S i n c e P ' l = V 2 t , PI= A t 2 / 2 and P'P=C, then { V 2 t 2 + (CLD) 2 - .25 a V } ( 33 ) 0.0 - cos E 2 {2V (CLD) t} There may be s e v e r a l r o o t s to t h i s e q u a t i o n ; but i t i s assumed tha t a p r e d a t o r would wish to min imize the t ime to i n t e r c e p t the prey in order to min imize the d e t e c t i o n p r o b a b i l i t y and energy c o n s u m p t i o n . For t h i s r e a s o n , the s h o r t e s t p o s s i b l e t ime for the i n t e r c e p t i s used . The n e c e s s a r y o r i e n t a t i o n change E'1 i s then c a l c u l a t e d by the a p p l i c a t i o n of the s ine r u l e to PP'I • EJ = s i n " 1 {(2V/at) s i n (E,) } ( 34 ) The course © 1 t + E ' 1 i s that which the p r e d a t o r must take to 49 i n t e r c e p t the p r e y . C o l l e t t and Land (1978) show t h a t t h i s method of i n t e r c e p t i o n i s used by h o u s e f l i e s ( E r i s t a l i s ) to c a t c h c o n s p e c i f i c mates. With t h i s s t r a t e g y there i s no t r a c k i n g i n v o l v e d and i t t h e r e f o r e can be c o n s i d e r e d a c l o s e d l o o p s o l u t i o n ( F i g . 6 ) . The p r e d a t o r uses the i n i t i a l k i n e m a t i c assessment of the p r e y to de termine an i n t e r c e p t i o n p o i n t , then makes a ' g o ' , ' no -go ' d e c i s i o n , and i f ' go ' , t u r n s away from the prey and proceeds toward tha t p o i n t wi th the p r o p e r k i n e m a t i c s for i n t e r c e p t i o n . We would expect a p r e d a t o r u s i n g t h i s s t r a t e g y to show l i t t l e d e v i a t i o n in o r i e n t a t i o n d u r i n g movement to the i n t e r c e p t i o n p o i n t , h i g h a c c e l e r a t i o n r a t e s , and h i g h v e l o c i t i e s . The i n t e r c e p t i o n p o i n t o c c u r s at some p o i n t a l o n g the p r o j e c t e d prey p a t h . The second i n t e r c e p t i o n s t r a t e g y i n v o l v e s an open l o o p system ( F i g . 7 ) . The p r e d a t o r r e c e i v e s c o n s t a n t i n f o r m a t i o n about the prey k i n e m a t i c s and r e l a t i v e p o s i t i o n and uses t h i s i n f o r m a t i o n to a l t e r i t s own p o s i t i o n and k i n e m a t i c s such t h a t i t c o n t i n u a l l y p o i n t s toward the prey throughout the c h a s e . The p r e d a t o r must a s ses s both prey o r i e n t a t i o n and k i n e m a t i c s and a c c o r d i n g l y a d j u s t i t s own o r i e n t a t i o n , i n c l u d i n g presumably , an a l l o w a n c e for i t s response t i m e . T h i s p r o c e s s may be modeled in the same manner as the f i r s t s t r a t e g y but where 0 1 ' = E ' . l i s the new p r e d a t o r course such that 50 F i g u r e 6 T r a c k i n g s t r a t e g y I . ( i ) The p r e d a t o r uses the i n i t i a l k inemat i c assessment of the prey to determine an i n t e r c e p t i o n p o i n t , and then t u r n s away from the prey and proceeds toward that p o i n t w i t h the proper k i n e m a t i c s for i n t e r c e p t i o n . ( i i ) T y p i c a l p r e d a t o r -prey t r a j e c t o r y wi th t h i s s t r a t e g y . 51 Tracking Strategy I i ) Prey I n i t i a l P o s i t i o n + Assess Prey Kinematics Calculate New Orientaion and Interception Point Motor A c t i v i t y ->- A l t e r o r i e n t a t i o n and kinematics to a r i v e at calculated i n t e r c e p t i o n point at the same time as prey. i i ) <- * o* prey 5 predator o r i e n t a t i o n at f i r s t s i g h t i n g of prey predator 52 F i g u r e 7 T r a c k i n g s t r a t e g y I I . ( i ) The p r e d a t o r r e c e i v e s c o n s t a n t i n f o r m a t i o n about the prey k i n e m a t i c s and r e l a t i v e p o s i t i o n and uses t h i s i n f o r m a t i o n t o a l t e r i t s own p o s i t i o n and k i n e m a t i c s such t h a t i t c o n t i n u a l l y p o i n t s toward the prey throughout ( i i ) T y p i c a l p r e d a t o r -prey t r a j e c t o r y w i t h t h i s s t r a t e g y . T r a c k i n g S t r a t e g y I I i ) P r e y I n i t i a l P o s i t i o n a t F i r s t S i g h t i n g A s s e s s P r e y k i n e m a t i c s , o r i e n t a t i o n and new p r o j e c t e d p r e y p o s i t i o n C a l c u l a t e new P r e d a t o r o r i e n t a t i o n t o p o i n t toward p r e y . Motor A c t i v i t y A l t e r o r i e n t a t i o n and k i n e m a t i c s t o move toward p r e y a t t h e p r o j e c t e d o r i e n t a t i o n t o t h e p r e y p o s i t i o n . Time I n t e r v a l + Time Step i i ) 1 o • — • 5 o p r p r e y \ 5 « i i p r e d a t o r 54 a t time t , 01t = ^ 1 t , and E1 i s c o n s t a n t l y e v a l u a t e d t o g i v e the c u r r e n t prey p o s i t i o n . The c a l c u l a t e d i n t e r c e p t i o n p o i n t w i l l c o i n c i d e w i t h the prey c u r r e n t p o s i t i o n a t a l l t i m e s . I f the prey has b e t t e r m a n o e u v r e b i l i t y , i t can w a i t u n t i l the p r e d a t o r i s v e r y c l o s e , then execute a h i g h d e c e l e r a t i o n and r a p i d t u r n i n g manoever t o escape . Howlands (1974 ) s i m p l e model of the t u r n i n g gambit i s an e x p l i c i t e v a l u a t i o n of t h i s s i t u a t i o n ; i f the square of the n o r m a l i z e d v e l o c i t y . ( V2/V1 ^ i s g r e a t e r than the n o r m a l i z e d t u r n r a d i u s ( R2/R1) then the pr e y w i l l escape. T h i s r e l a t i o n s h i p y i e l d s o p t i m a l n o r m a l i z e d s t a r t i n g d i s t a n c e s f o r t h e t u r n Xo. T u r n i n g a b i l i t y i s a f u n c t i o n of v e l o c i t y and the c o n t r o l s u r f a c e s needed t o a p p l y the r e q u i r e d f o r c e ; t h e r e f o r e , t h e r e s h o u l d be s i g n i f i c a n t k i n e m a t i c a d j u s t m e n t s i n a p r e d a t o r r e s p o n d i n g so as t o keep E1 a t z e r o . The t h i r d s t r a t e g y f.or i n t e r c e p t i o n can be c o n s i d e r e d a v a r i a t i o n of the second w i t h more c o m p l e x i t y . I t i s termed the l e a d p u r s u i t and was d e f i n e d e a r l i e r . I t i s an open l o o p system ( F i g 8 ) i n which the p r e d a t o r r e c e i v e s c o n s t a n t i n f o r m a t i o n about prey k i n e m a t i c s , r e l a t i v e p o s i t i o n and o r i e n t a t i o n . U s i n g t h i s i n f o r m a t i o n the p r e d a t o r a l t e r s i t ' s own k i n e m a t i c s and o r i e n t a t i o n such t h a t i t i s p o i n t i n g t o a p o i n t where the paths a r e i n t e r s e c t i n g . The p r e d a t o r i s path p r e d i c t i n g and t r a c k i n g . R e g a r d l e s s of the c u r r e n t p r e d a t o r / p r e y k i n e m a t i c s and 55 F i g u r e 8 T r a c k i n g s t r a t e g y III . ( i ) The p r e d a t o r r e c e i v e s cons tant i n f o r m a t i o n about the prey r e l a t i v e k i n e m a t i c s , r e l a t i v e p o s i t i o n , and o r i e n t a t i o n to a l t e r i t s course and k i n e m a t i c s such that i t i s p o i n t i n g to an i n t e r e c p t i o n p o i n t ahead of the p r e y . ( i i ) T y p i c a l p r e d a t o r - p r e y t r a j e c t o r y wi th t h i s s t r a t e g y . Tracking Strategy III (Path Prediction) Prey I n i t i a l P o s i t i o n at F i r s t Sighting Assess Prey kinematics and o r i e n t a t i o n and new p o s i t i o n i n future (aim point) Calculate Aim Point as a function of prey-predator o r i e n t a t i o n and kinematics Motor A c t i v i t y A l t e r o r i e n t a t i o n and kinematics to move toward Aim Point Time Interval + Time Step 5 o Prey o • t predator 57 o r i e n t a t i o n , the D i s t a n c e at C l o s e s t Approach (DCA ) w i l l t h e o r e t i c a l l y be z e r o u n t i l c a p t u r e . In p r a c t i c e the D i s t a n c e a t C l o s e s t Approach w i l l p r o b a b l y never be z e r o because of prey avo idance behav iour and l a g s i n the p r e d a t o r r e s p o n s e . T h i s proces s may be modeled i n the same manner as the f i r s t where a t t ime t , | j 6 l t - © 1 t | . = E1t and E1t i s the l e a d a n g l e p o i n t i n g to the i n t e r c e p t p o i n t c a l c u l a t e d by the p r e d a t o r g i v e n the prey k i n e m a t i c s and o r i e n t a t i o n . Not o n l y are the manoeuvre type and t i m i n g important for a prey a t t e m p t i n g to s u r v i v e a t t a c k , the p r e d a t o r i s a l s o c o n s t r a i n e d in. i t s t i m i n g of the a t t a c k . The prey must by d e f i n i t i o n be w i t h i n a t r a c k i n g range , and the p r e d a t o r s h o u l d time the a t t a c k to be e f f e c t i v e in m i n i m i z i n g energy, consumption and f a t i g u e , and s t i l l c a p t u r e the p r e y . 58 RESULTS L S i n g l e P r e d a t o r 2 S i n g l e Prey I n t e r a c t i o n s J_) K i n e m a t i c A t t r i b u t e s . The maximum r e c o r d e d l i n e a r v e l o c i t y found i n 20 chase sequences f o r the t r o u t in these exper iments was 7.3 f t / s e c , t h a t of the sockeye 5.65 f t / s e c . These r e s u l t s are not unexpected because l a r g e r f i s h shou ld be a b l e to swim f a s t e r than s m a l l e r ones ( Howland 1974, B a i n b r i d g e 1976) . The mean of the maximum l i n e a r v e l o c i t y r e c o r d e d i n each sequence was 4.98 f t / s e c f o r the t r o u t and 4.76 f t / s e c for the sockeye . Webb (1975) r e p o r t e d o v e r a l l maximum v e l o c i t i e s of 8.5 f t / s e c f o r rainbow t r o u t ( Salmo g a i r d n e r i ) wi th b u r s t v e l o c i t i e s of up to 20 f t / s e c . Mean o v e r a l l a c c e l e r a t i o n r a t e s were c a l c u l a t e d as 2.32 f t / s e c x f o r the p r e d a t o r and 1.98 f t / s e c ^ f o r the p r e y ; w i t h b u r s t a c c e l e r a t i o n s of 6.03 f t / s e c ^ a n d 4.7 f t / s ec* - f or p r e d a t o r and prey r e s p e c t i v e l y . Angular v e l o c i t y and l i n e a r v e l o c i t y are p l o t t e d in F i g 9. The data may be i n t e r p r e t e d as maximum t u r n i n g a b i l i t y in d e g r e e / s e c at the i n i t i a l l i n e a r v e l o c i t y b e f o r e e x e c u t i o n of a t u r n and show that the p r e d a t o r had a h i g h e r t u r n i n g a b i l i t y than the prey at h i g h e r v e l o c i t i e s . Up to v e l o c i t i e s of 1.75 5 9 F i g u r e 9 Angular v e l o c i t y and l i n e a r v e l o c i t y of p r e d a t o r and prey ) .The a n g u l a r v e l o c i t y i s the mean maximum angu lar v e l o c i t y r e c o r d e d at the i n d i c a t e d l i n e a r v e l o c i t y for 2 0 chase sequences . Angu lar v e l o c i t i e s for l i n e a r v e l o c i t i e s l e s s than 0 . 5 f t / s e c were not o b s e r v e d . F i g u r e ?. A n g u l a r V e l o c i t y vs L i n e a r V e l o c i t y . 61 f t / s e c , p r e d a t o r and prey t u r n e d e q u a l l y w e l l , but at h i g h e r v e l o c i t i e s , the p r e d a t o r changed d i r e c t i o n f a s t e r than the p r e y . However, the minimum t u r n i n g r a d i u s of the p r e d a t o r a t a l l v e l o c i t i e s was g r e a t e r than t h a t of the p r e y . T h i s minimum r a d i u s was found by s e t t i n g the c e n t r i f u g a l f o r c e a c t i n g on the f i s h e q u a l to the f o r c e a v a i l a b l e f o r the t u r n and s o l v i n g for the r a d i u s . Parameters to s a t i s f y e q u a t i o n 15 ( Time to Maximum V e l o c i t y ) were taken from 15 chase sequences where the p r e d a t o r and prey i n i t i a l v e l o c i t i e s were below 0.2 f t / s e c and reached t h e i r r e s p e c t i v e maximum v e l o c i t i e s for tha t c h a s e . The mean v a l u e of K was 0.566 sec +•• .12 f o r the p r e d a t o r and 0.3059 +-.08 f o r the p r e y . These v a l u e s d i f f e r s i g n i f i c a n t l y ( t - t e s t , t=6.37 ( P<.01) n= 15), i n d i c a t i n g that the prey reaches maximum v e l o c i t y f a s t e r than the p r e d a t o r . To summarize the k inemat i c a t t r i b u t e s of p r e d a t o r and p r e y : (1) The p r e d a t o r a c h i e v e s a h i g h e r l i n e a r v e l o c i t y than the p r e y . (2) The prey reaches maximum v e l o c i t y i n n e a r l y h a l f the time of the p r e d a t o r . ( 3 ) The p r e d a t o r a c h i e v e s a h i g h e r a n g u l a r v e l o c i t y at h igh l i n e a r v e l o c i t y , but at the cos t of a h i g h e r 62 t u r n i n g r a d i u s . (4) The l i n e a r a c c e l e r a t i o n of the p r e d a t o r i s h i g h e r than tha t of the p r e y . 2) Example chase sequence- s i n g l e p r e d a t o r - s i n g l e prey In many r e s p e c t s the 20 chase sequences showed c o n s i d e r a b l e s i m i l a r i t y . I t i s conven ient to beg in the p r e s e n t a t i o n of these r e s u l t s w i t h a d e t a i l e d d e s c r i p t i o n of a t y p i c a l sequence. Chase sequence [4] was chosen to i l l u s t r a t e a s i n g l e p r e d a t o r - s i n g l e prey sequence in which the p r e d a t o r s u c c e s s f u l l y c a p t u r e d the p r e y . . Time t r a j e c t o r i e s of chase sequence [4] are p r e s e n t e d in F i g . 10. K inemat i c measurements are p r e s e n t e d in F i g s . 1 1 to 16. At the b e g i n n i n g of the sequence, p r e d a t o r and prey were 3.15 f t a p a r t , t r a v e l l i n g in almost o p p o s i t e d i r e c t i o n s . From frame 1 to 13, the p r e d a t o r executed a t u r n to the l e f t . The a n g u l a r v e l o c i t y was moderate ly h i g h and ranged from +600 deg / sec to -500 d e g / s e c . The l i n e a r v e l o c i t y of the p r e d a t o r remained n e a r l y c o n s t a n t , wi th a s l i g h t l y i n c r e a s i n g t r e n d . The prey meanwhile c o n t i n u e d in an u n a l t e r e d d i r e c t i o n of t r a v e l w i th a n e a r l y cons tant l i n e a r v e l o c i t y ( F i g . 11 ) . A l t h o u g h the a n g u l a r v e l o c i t y ( F i g . 1 2 ) of the prey showed 63 some s p i k e s ( no tab le at frame 6 and 7 ) , these may have been movements u n r e l a t e d t o the p r e d a t o r . I f the p r e d a t o r was d e t e c t e d at t h i s p o i n t , a change i n the l i n e a r v e l o c i t y of the prey s h o u l d have been seen . The p r e d a t o r had d e t e c t e d the p r e y , and t h i s c o n c l u s i o n i s supported by the i n t e r c e p t c o - e f f i c i e n t s and e r r o r t r a c k i n g a n g l e ( F i g 15 , F i g 14 ) . The e r r o r ang le d e v i a t e d s l i g h t l y around the zero p o s i t i o n , and the i n t e r c e p t c o - e f f i c i e n t s i n d i c a t e that the i n t e r c e p t p o i n t was f l u c t u a t i n g from ahead to behind the p r e y . F i g . ( 16 ) i n d i c a t e s the d i s t a n c e to the i n t e r c e p t p o i n t for both p r e d a t o r and p r e y . Large s p i k e s appeared up to frame s i x , i n d i c a t i n g that the p r e d a t o r had d e t e c t e d the prey and was a l t e r i n g o r i e n t a t i o n to fo l l ow or get an a c c u r a t e " f ix" on the k inemat ic parameters of the p r e y . Between frames 6 and 12, the i n t e r c e p t parameters i n d i c a t e t h a t the p r e d a t o r p a t h was i n t e r s e c t i n g ahead of the p r e y . The e r r o r t r a c k i n g angle ( F i g . 14 ) for frames 6 to 12 showed an adjustment at frame s i x and a f l a t t e n i n g out at frame 10 to 12. The p l a t e a u c o i n c i d e d wi th an e r r o r ang le E1 of a p p r o x . -20 degrees ( the prey was 20 degrees to the r i g h t of the p r e d a t o r path ) . The o f f s e t angle E2 for frames 6 to 12 shows l i t t l e v a r i a t i o n , i n d i c a t i n g a r e l a t i v e cons tant p r e d a t o r o f f s e t ang le of a p p r o x . 50 degrees ( the p r e d a t o r was approx . 50 degrees to the l e f t of the prey path ) . T h i s i s f u r t h e r i n d i c a t i o n tha t the prey might not as yet have been aware of the p r e d a t o r ' s p r e s e n c e . 64 The c l o s u r e d i s t a n c e ( F i g . 13 ) between frames 1 and 12 s l o w l y decreases as the p r e d a t o r and prey were t r a v e l i n g toward each o t h e r . The D i s t a n c e at C l o s e s t Approach a l s o decreased i n d i c a t i n g t r a c k i n g by the p r e d a t o r . Frames 13 and 14 show a d i r e c t i o n change by the p r e y , and the response by the p r e d a t o r . F i g u r e 12 shows a l a r g e sp ike at frame 13 for the prey and the p r e d a t o r . The reason for the prey change of d i r e c t i o n in frame 13 i s u n c l e a r , b u t , the r e s u l t of the move was to momentar i ly break the t r a c k i n g by the p r e d a t o r . The i n t e r c e p t c o - e f f i c i e n t s ( F i g . 15 ) for frame 13 i n d i c a t e t h a t the i n t e r c e p t i o n p o i n t was beh ind the p r e y . A d d i t i o n a l l y , the d i s t a n c e to the i n t e r c e p t i o n p o i n t for both p r e d a t o r and prey ( F i g . 16 ) shows an i n c r e a s e , r a t h e r than the expected decrease i f t r a c k i n g was s t i l l i n p r o g r e s s . T r a c k i n g of the prey by the p r e d a t o r resumes at frame 14 and c o n t i n u e s to frame 27 ( F i g . 15 ) . The h i g h angu lar changes of the prey in frame 13 and 14 appeared to " t r i g g e r " a q u i c k response by the p r e d a t o r . The p r e d a t o r c l e a r l y was aware of the prey and responded by a c c e l e r a t i n g to a h i g h l i n e a r v e l o c i t y ( F i g 11 ) , peak ing at frame 20 and m a i n t a i n e d to frame 27. From F i g . 10 i t i s q u i t e c l e a r that the p r e d a t o r was not heading toward the p r e y , but was path p r e d i c t i n g . T h i s i s f u r t h e r i n d i c a t e d in F i g u r e 14 where for frames 14 to 26, the t r a c k i n g e r r o r i s cons tant at approx . -20 degrees , and F i g u r e 12 where 65 the a n g u l a r v e l o c i t y for the p r e d a t o r i s s m a l l . As the l i n e a r v e l o c i t y of the p r e d a t o r i n c r e a s e d , the r a t e of c l o s u r e i n c r e a s e d , and t h i s i s r e f l e c t e d in F i g u r e 13 , where the s l o p e of the c l o s u r e d i s t a n c e i n c r e a s e s s h a r p l y at frame 20. The D i s t a n c e a t C l o s e s t Approach c o n t i n u e s to decrease from frame 14 w i t h d e c r e a s e d o s c i l l a t i o n s . At frame 20, the D i s t a n c e at C l o s e s t Approach i s n e a r l y zero and i s m a i n t a i n e d at a very low v a l u e u n t i l frame 25. T h i s i n d i c a t e s tha t the p r e d a t o r was t r a c k i n g the prey by path p r e d i c t i o n . In c o n t r a s t , the prey l i n e a r v e l o c i t y decreased from frame 14 to 24 ( F i g . 11 ) , and the o f f s e t ang le E2 ( F i g . 14 ) s l i g h t l y i n c r e a s e d , i n d i c a t i n g a moving away t r e n d by the p r e y . Prey awareness of the p r e d a t o r may have o c c u r r e d in frame 14 as shown by the v e l o c i t y decrease and moving away t r e n d . The responses c l e a r l y show a change in p a t t e r n of the prey k i n e m a t i c s to the awareness of some o b j e c t . Frames 25 to 40 demonstrate the prey escape re sponse . B e g i n n i n g at frame 25, the prey a c c e l e r a t e d to maximum l i n e a r and a n g u l a r v e l o c i t y ( F i g s . 11 ,12 ) , t u r n i n g away from the p r e d a t o r . The o f f s e t ang le E2 d r a s t i c a l y changes ( F i g . 14 ) and the e r r o r t r a c k i n g angle E1 a l s o i n c r e a s e s , i n d i c a t i n g a l o s s of t r a c k i n g by the p r e d a t o r . T h i s i s f u r t h e r supported by the i n t e r c e p t c o - e f f i c i e n t s ( F i g . 15 ) f or frames 26 to 32. The l i n e a r v e l o c i t y of the p r e d a t o r decreased as the a n g u l a r 66 v e l o c i t y i n c r e a s e d ( F i g s . 11, 12 frame 27 ) as a t u r n i n g manoeuvre was at tempted to match the t u r n i n g response of the p r e y . The p r e d a t o r was p a r t i a l l y s u c c e s s f u l as i t responded to the prey i n c r e a s e s ( frame 26 to 35 ) . The p r e d a t o r appeared to r e g a i n t r a c k i n g of the prey ( frames 32 to 37 ) as i n d i c a t e d by the d e c r e a s i n g D i s t a n c e at C l o s e s t Approach , c l o s u r e d i s t a n c e , P r e d a t o r D i s t a n c e to I n t e r c e p t P o i n t ( PDDIP ) , and Prey D i s t a n c e to I n t e r c e p t P o i n t ( PYDIP ) ( F i g . 16 ) , d e s p i t e the f a c t tha t the i n t e r c e p t p o i n t i s o s c i l l a t i n g from ahead to beh ind the prey ( F i g . 15 ) . The h i g h a n g u l a r v e l o c i t y of the prey at frame 35 r e s u l t e d in the prey c r o s s i n g the path of the p r e d a t o r . At frame 36 the prey t u r n e d to the l e f t as the p r e d a t o r t u r n e d to the r i g h t in response to the h i g h a n g u l a r v e l o c i t y of the p r e y . T h i s " s c i s s o r s " manoeuvre by the prey was s u c c e s s f u l in that h i g h a n g u l a r v e l o c i t i e s i n o p p o s i t e d i r e c t i o n s can e f f e c t i v e l y break t r a c k i n g by the p r e d a t o r . In frames 40 to 43 and from F i g u r e s 15 and 10 the p r e d a t o r and prey were moving away from each o t h e r . The D i s t a n c e at C l o s e s t Approach and c l o s u r e d i s t a n c e ( F i g . 13 ) both i n c r e a s e as does the PDDIP and PYDIP ( F i g . 16 ) i n d i c a t i n g that the p r e d a t o r had " los t" the p r e y . At frame 44 the p r e d a t o r responded to the prey p o s i t i o n as t r a c k i n g was r e - e s t a b l i s h e d . The h i g h p r e d a t o r angu lar v e l o c i t y 67 toward the prey p o s i t i o n at frame 44 c l e a r l y i n d i c a t e s a r e s p o n s e . From frame 45 to 50, the i n t e r c e p t c o - e f f i c i e n t s i n d i c a t e p a t h p r e d i c t i o n and the c l o s u r e d i s t a n c e s decreased as the p r e d a t o r l i n e a r v e l o c i t y i n c r e a s e d ( F i g . 13 ) . At frame 47 the D i s t a n c e a t C l o s e s t Approach c l e a r l y d e c r e a s e d as d i d the PDDIP, i n d i c a t i n g that the p r e d a t o r was once a g a i n t r a c k i n g the p r e y . At frame 52, the prey t u r n e d away from the p r e d a t o r and a c c e l e r a t e to maximum v e l o c i t y ; momentari ly c a u s i n g d i s r u p t i o n of t r a c k i n g . The p r e d a t o r response was to d e c e l e r a t e and at frame 53, was once aga in a b l e to t r a c k the p r e y . Prey c a p t u r e o c c u r e d at frame 57 as i n d i c a t e d by the zero E1 ( e r r o r ang le ) and the -180 degree E2 ( o f f s e t a n g l e ) . In frames 58 to 60 the prey was c a r r i e d in the mouth of the p r e d a t o r . The t o t a l time e l a p s e d for t h i s e n t i r e sequence was 2.5 s e c . Chase sequence [4] was i n s t r u c t i v e in that the prey i n i t i a l l y decoup led from the p r e d a t o r t r a c k i n g w i t h a t u r n i n g manoeuvre f o l l o w e d by a s c i s s o r s ( frames 25 to 41 ) , but at frame 47, a t u r n in the " wrong " d i r e c t i o n by the prey enabled the p r e d a t o r to r e - a c q u i r e t r a c k i n g that e v e n t u a l l y l e d to prey c a p t u r e a t frame 57. T h i s sequence a l s o i l l u s t r a t e d p r e d a t o r t r a c k i n g from head on and s t e r n p o s i t i o n s . From F i g u r e s 10 and 16, i t i s q u i t e c l e a r that the p r e d a t o r d i d not d i r e c t l y head toward the p r e y , 68 but appeared to o r i e n t such t h a t the paths of p r e d a t o r and prey i n t e r s e c t e d ahead of the p r e y ; and t h i s path p r e d i c t i o n was used r e g a r d l e s s of d i r e c t i o n of a p p r o a c h . The sequence d i s c u s s e d in the f o r e g o i n g was t y p i c a l of a l l the sequences in types of behav iour e x h i b i t e d by both p r e d a t o r and p r e y . Of p a r t i c u l a r i n t e r e s t was the methodology the p r e d a t o r employed to t r a c k the p r e y . A l l s i n g l e p r e d a t o r - s i n g l e prey sequences showed remarkable s i m i l a r i t y i n the p a t t e r n of i n t e r c e p t v a r i a b l e s . The s lope , o r c l o s u r e r a t e , remained n e a r l y c o n s t a n t ( frames 1 to 16 ). There was a marked i n c r e a s e in s l o p e i n d i c a t i n g . a n i n c r e a s e d c l o s u r e r a t e , due to an i n c r e a s e i n p r e d a t o r v e l o c i t y ( frames 17 to 26 ). The c l o s u r e . r a t e remained very low or n e a r l y z e r o due to e i t h e r d e f e n s i v e manoeuvres by the p r e y , or to the p r e d a t o r l o s i n g t r a c k i n g ( frame 27 on ) . T h i s p a t t e r n was seen in a l l chase sequences . The average c l o s u r e d i s t a n c e at the p o i n t where the s lope of the c l o s u r e d i s t a n c e showed a marked i n c r e a s e ( C1 ) was 2.13 + .28 f t (SE , n=lO ) . The average c l o s u r e d i s t a n c e at the p o i n t where the D i s t a n c e at C l o s e s t Approach became l e s s than 0.1 f ee t ( C2 ) and the p r e d a t o r was m a i n t a i n i n g t r a c k i n g ( as i n d i c a t e d by the i n t e r c e p t c o e f f i c i e n t s ) was found to be 1.01 + .09 f ee t ( n = l 0 ) . The average v e l o c i t y of the p r e d a t o r at t h i s p o i n t was 4.26 + .36 f e e t / s e c ( n = l 0 ) . In a l l chase sequences the D i s t a n c e at C l o s e s t Approach up to p o i n t C1 was c h a r a c t e r i z e d by l a r g e o s c i l l a t i o n s around a 69 d e c r e a s i n g t r e n d l i n e . None of the o s c i l l a t i o n s was g r e a t e r than the c l o s u r e d i s t a n c e . Between p o i n t C 1 and C 2 , the D i s t a n c e at C l o s e s t Approach showed a marked decrease in o s c i l l a t i o n s . From C 2 , the D i s t a n c e at C l o s e s t Approach remained s m a l l r e l a t i v e to the c l o s u r e d i s t a n c e u n t i l e i t h e r the prey executed a d e f e n s i v e manoeuvre or was c a p t u r e d . I t appears tha t the p r e d a t o r undergoes t h r e e phases when t r a c k i n g . The f i r s t phase up to p o i n t C 1 i s marked by a low but s l i g h t l y i n c r e a s i n g l i n e a r v e l o c i t y and l a r g e o s c i l l a t i o n s in the D i s t a n c e at C l o s e s t Approach and a n g u l a r v e l o c i t y . D u r i n g t h i s phase , the p r e d a t o r o r i e n t a t i o n changes such tha t i t i s in the g e n e r a l d i r e c t i o n of the p r e y , and the o s c i l l a t i o n s of the D i s t a n c e at C l o s e s t Approach , E 1 and angu lar v e l o c i t y i n d i c a t e adjustment of the k i n e m a t i c parameters of the p r e d a t o r to e s t a b l i s h t r a c k i n g . T h i s procedure may be a k i n to s t a l k i n g and t a r g e t a c q u i s i t i o n . The second phase , between C 1 and C 2 , shows dampening of a n g u l a r v e l o c i t i e s , E 1 , D i s t a n c e at C l o s e s t Approach v a l u e s , and an a c c e l e r a t i o n to a h i g h l i n e a r v e l o c i t y r e s u l t i n g in an i n c r e a s e d c l o s u r e r a t e . From e a r l i e r arguments , an h y p o t h e s i s was p r e s e n t e d that once a p r e d a t o r has a c q u i r e d a t a r g e t and a l t e r s o r i e n t a t i o n and k i n e m a t i c s to i n t e r c e p t p r e y , the best s t r a t e g y i s to a c c e l e r a t e r a p i d l y so as to min imize time to i n t e r c e p t i o n . T h i s would 70 decrease the time in which the prey can r e a c t to the a p p r o a c h i n g p r e d a t o r as w e l l as p l a c i n g the p r e d a t o r n e a r e r the p r e y . The second phase f u n c t i o n s to a c c o m p l i s h these a i m s . The t h i r d phase , from p o i n t C2 to when the prey i s c a p t u r e d or escapes shows D i s t a n c e at C l o s e s t Approach v a l u e s near z e r o , i n d i c a t i n g t r a c k i n g , low v a r i a t i o n in t r a c k i n g e r r o r angle ( E 1 ) , and l i n e a r and angu lar v e l o c i t i e s of the p r e d a t o r changing in an attempt to match the prey k i n e m a t i c s . U n f o r t u n a t e l y , the f i l m i n g speed proved to be too slow to d e t e c t m e a n i n g f u l p r e d a t o r r e a c t i o n t imes to prey movement d u r i n g t r a c k i n g . The e r r o r t r a c k i n g ang le E 1 , was found to be independent of D i s t a n c e at C l o s e s t Approach or c l o s u r e d i s t a n c e d u r i n g t r a c k i n g , and as s t a t e d e a r l i e r , remained n e a r l y c o n s t a n t d u r i n g t r a c k i n g segments. From F i g u r e 4 i f E1 i s c o n s t a n t , as the c l o s u r e d i s t a n c e d e c r e a s e s , the t r i a n g l e ABC s h r i n k s r e s u l t i n g in the movement of the aim p o i n t ( the p o i n t where the p r e d a t o r and prey paths c r o s s ) toward the a c t u a l p o s i t i o n of the prey ( d e c r e a s i n g the prey d i s t a n c e to i n t e r c e p t p o i n t , PYDIP) . The p r e d a t o r d i s t a n c e to i n t e r c e p t p o i n t (PDDIP) ( F i g s . 12 ) and prey d i s t a n c e to i n t e r c e p t p o i n t (PYDIP) show s i m i l a r t rends to the c l o s u r e d i s t a n c e and D i s t a n c e a t C l o s e s t Approach ( F i g . 16) . For the segments where the i n t e r c e p t c o e f f i c i e n t s i n d i c a t e tha t the paths are c r o s s i n g in the f u t u r e , ( frames 14 to 24 in sequence [4] for example ) , there i s an a lmost p e r f e c t match between c l o s u r e d i s t a n c e and PDDIP and between DCA and PYDIP. 71 T h i s f u r t h e r suppor t s the h y p o t h e s i s of a c o n s t a n t ( p l u s e r r o r ) t r a c k i n g e r r o r by the p r e d a t o r . For a l l chase sequences , the mean e r r o r ang le E1 was c a l c u l a t e d for those segments where the i n t e r c e p t c o e f f i c i e n t s i n d i c a t e d t r a c k i n g ( Tab le 1 ) . A Watson and W i l l i a m s t e s t ( M a r d i a 1972) was used to t e s t the n u l l h y p o t h e s i s tha t there was no d i f f e r e n c e among the E1 v a l u e s . An Fs v a l u e of 1.156 ( P [Fs=1.156] > . 25 , df= 5,54 ) i n d i c a t e s the acceptance of the n u l l h y p o t h e s i s . The grand mean (E1) was found to be 13.37' degrees . A M o d i f i e d R a y l e i g h t e s t ( M a r d i a 1972 ) was used to t e s t the n u l l h y p o t h e s i s that the p r e f e r e d e r r o r t r a c k i n g ang le was equa l to z e r o ( i e . The p r e d a t o r always heads toward the prey ) . A c a l c u l a t e d V v a l u e of 57.34 ( P << .05 , df=60) i n d i c a t e s a r e j e c t i o n of the n u l l h y p o t h e s i s . However, as c l o s u r e d i s t a n c e d e c r e a s e s , the prey d i s t a n c e to i n t e r c e p t p o i n t decreases as does the p r e d a t o r d i s t a n c e to the i n t e r c e p t p o i n t . F i g s . 17 and 18 show that for p o i n t s where the i n t e r c e p t c o - e f f i c i e n t s i n d i c a t e p a t h p r e d i c t i o n , t h e r e i s a l i n e a r r e l a t i o n s h i p between the p r e d a t o r d i s t a n c e to the i n t e r c e p t p o i n t and the c l o s u r e d i s t a n c e ; and the prey d i s t a n c e to the i n t e r c e p t p o i n t and c l o s u r e d i s t a n c e . At any g iven c l o s u r e d i s t a n c e , the prey i s c l o s e r to the i n t e r c e p t p o i n t than the p r e d a t o r i s . At c l o s u r e d i s t a n c e s l e s s the 1.0 feet ( approx p o i n t C2 ) , the p o i n t of i n t e r c e p t i o n n e a r l y c o i n c i d e s w i t h the prey p o s i t i o n . T h i s 72 T a b l e 1 E r r o r a n g l e (E^) where t h e i n t e r c e p t c o e f f i c i e n t s i n d i c a t e t r a c k i n g . I ) t e s t o f H Q: No s i g n i f i c a n t d i f f e r e n c e among E r r o r a n g l e s . H,.: T h e r e e x i s t s a s i g n i f i c a n t d i f f e r e n c e among E r r o r a n g l e s . Sequence 4 5 6 7 8 9 L s i n E ^ 3.23 1.39 .701 .927 3.46 3.92 13.63 EcosE^ 10.36 8.77 4.94 5.91 12.02 15.33 57.34 n 11 9 5 6 13 16 60 r .987 .987 .997 .996 .962 , .989 . 9S2 R 10.85 8.88 4.99 5.98 , 12.51 15.83 58. 94 11 17.32 8.97 8.07 8.93 16.04 14.53" 13.37 U s i n g Watson and W i l l i a m s t e s t ( M a r d i a 1972) .-. Fc = 1. 156 ( d f = 5, 54) ••• P (Fc = 1.156)>0. 25 A c c e p t t h e N u l l Hypothesis. 2) t e s t o f H ^ : P r e f e r r e d d i r e c t i o n i s 0.0°in E r r o r a n g l e ( P r e d a t o r p o i n t s t o w a r d p r e y ) H^: P r e f e r r e d d i r e c t i o n i s not 0.0° i n E r r o r a n g l e . Ep ( p r e f e r r e d a n g l e ) = 0 . 0 d e g r e e s U s i n g t h e M o d i f i e d R a y l e i g h T e s t ( M a r d i a ]972) V = R c o s t E ^ - Ep) V = 57.338 P (V' = 57.338) « 0.05 •'• R e j e c t t h e N u l l H y p o t h e s i s 73 suggests that at s m a l l c l o s u r e d i s t a n c e s , the p r e d a t o r may sw i t c h t r a c k i n g s t r a t e g y from path p r e d i c t i o n to p o i n t i n g at the p r e y . The measurement e r r o r s i n v o l v e d i n d i g i t i z i n g the f i l m sequences may have masked t h i s s w i t c h i n g . From a t a c t i c a l p o i n t of v iew, to c a p t u r e the p r e y , the p r e d a t o r must be at the same p o i n t at the same time as the p r e y ; t h e r e f o r e , at some time the p r e d a t o r must be p o i n t i n g at the prey ( + some angular s t r i k e d i s t a n c e ) . 7 4 F i g u r e 10 Time t r a j e c t o r y chase sequence [4] . The p r e d a t o r (+) and prey (x) are p l o t t e d for each frame; r e p r e s e n t i n g 1/24 second t ime i n t e r v a l s . 0 i n d i c a t e s the r e l a t i v e s t a r t i n g p o s i t i o n for the p r e d a t o r and p r e y . . P r e d a t o r path p r e d i c t i o n i s e a s i l y seen in frames 15 to 20, where the p r e d a t o r path i s i n t e r s e c t i n g ahead of the prey p a t h . The d e f e n s i v e manoeuvre by the prey can be seen at frames 25 to 30. Prey c a p t u r e by the p r e d a t o r i s seen at frame 57. The a x i s are n o r m a l i z e d u n i t s from the r e f e r e n c e X0,Y0 p o s i t i o n and are used to s c a l e the t r a j e c t o r y p l o t s . Figure 10 Time Trajectory Chase Sequence (4) .u cu CJ - 5: END J X Prey •S : I: 1 0 k Sv'-'X ,>,-^::i >f.;-.< . --<K 5 5 5 5 0 , ; i -ft* 3 o 2 5 4— 2 0 G U predator t - r - t — r - r - r - -1—1—1—I—\~\—1 I I I -I 1 I 1 1 1 1 -i-t-D • U 3-E Feet 76 F i g u r e 11 L i n e a r v e l o c i t y of p r e d a t o r and prey over t ime . The p r e d a t o r response to the prey can be seen at frames 15 to 20 and 45 to 50 as i n c r e a s e s in l i n e a r v e l o c i t y . The prey v e l o c i t y shows an i n c r e a s i n g t r e n d from frames 25 to c a p t u r e at frame 57. F i g u r e 11 PREY VELCCITT CS-4 6. 5. U J FRRME U / 2 4 SEC) PREDRTOR VELOCITY CS-4 7. C 3 i n •— •— r s j r s j < — ' — ^- i n t / i o l / i t z j O i o t n a L n c a t n FRAME (1/24 SEC) 78 F i g u r e 12 Angular v e l o c i t y of p r e d a t o r and prey over time . The d e f e n s i v e t u r n i n g manoeuvre by the prey can be seen as the i n c r e a s e in angu lar v e l o c i t y at frame 24 to 25. The p r e d a t o r at tempts to match t h i s manoeuvre at frames 26 to 27. Nega t ive v a l u e s of the angu lar v e l o c i t y i n d i c a t e a t u r n to the r i g h t . 79 Figure 12 fSET ANGULAR VELOCITY VS TIME FRAME t j / 2 4 SEC) P A S T O R ANGULAR VELOCITY VS T I K E 2 4 0 0 T FRAME f 1/7.4 SECi ure 13 C l o s u r e d i s t a n c e and D i s t a n c e at C l o s e s t Approach over time . The form of the c l o s u r e d i s t a n c e i s c h a r a c t e r i s t i c of a l l s i n g l e p r e d a t o r - s i n g l e prey chase sequences . Path p r e d i c t i o n by the p r e d a t o r i s c l e a r l y seen in frames 20 to 25 and 49 to 52 of the d i s t a n c e at c l o s e s t approach g r a p h . 81 !3 CLOSURE DISTRNCE VS TIME 0, 82 F i g u r e 14 E r r o r t r a c k i n g angle and o f f s e t angle over time . The e r r o r t r a c k i n g ang le shows a marked i n c r e a s e at frame 26 i n d i c a t i n g t r a c k i n g l o s s caused by the d e f e n s i v e manoeuvre of the p r e y . The c o r r e s p o n d i n g o f f s e t angle shows the c h a r a c t e r i s t i c moving away t r e n d from the s t a r t of the sequence to frame 25 and the e f f e c t of the d e f e n s i v e manoeuvre at frame 26. F i g u r e 14 ERROR TRACKING ANGLE FRAME C1/24 SEC) OFFSET ANGLE ISO, 301 -901 FRAME (1/24 SEC) 84 F i g u r e 15 I n t e r c e p t i o n c o e f f i c i e n t s over time . Where the c o e f f i c i e n t s are both p o s i t i v e i n d i c a t e s p a t h p r e d i c t i o n by the p r e d a t o r . Where the c o e f f i c i e n t s are both nega t ive , p r e d a t o r and prey are moving away from each o t h e r . Where A i s p o s i t i v e and B i s n e g a t i v e , the p r e d a t o r i s moving away from the p r e y . Where A i s n e g a t i v e and B i s p o s i t i v e , the i n t e r c e p t i o n p o i n t i s beh ind the p r e y . E 3 LD CO INTERCEPT CO-EFFICIENTS !! II i B B tp O BP [cn | I I ' i 11 i - i ii a 11 a a FRAME (1/24 SEC) cn U-B o-a -> fl CO-EFFICIENT -> B CO-EFFICIENT ure 16 PDDIP and PYDIP over time . The p r e d a t o r and prey d i s t a n c e to i n t e r c e p t p o i n t graphs show s i m i l a r t r e n d s to the c l o s u r e d i s t a n c e and d i s t a n c e at c l o s e s t approach graphs r e s p e c t i v e l y . T h i s was common in a l l s i n g l e p r e d a t o r - s i n g l e prey chase sequences . 87 F i g u r e 16 PREDATOR DISTANCE TO INTERCEPT POINT FRAME t 1 / 2 4 SEC; PREY DISTANCE TO INTERCEPT P3INT FRAME ( 1 / 2 4 SEC) 88 II S i n g l e P r e d a t o r - S c h o o l i n g Prey J_) Example Sequences Three chase sequences of a s i n g l e p r e d a t o r a t t a c k i n g s c h o o l i n g prey are p r e s e n t e d to i l l u s t r a t e t y p i c a l l y observed p r e d a t o r - s c h o o l i n t e r a c t i o n s . Sequence [1S] i l l u s t r a t e s an a t t a c k by the p r e d a t o r on a c o h e s i v e s c h o o l . Sequence [2S] i l l u s t r a t e s an a t t a c k on a c o h e s i v e s c h o o l in which one i n d i v i d u a l became s e p a r a t e d from the s c h o o l . Sequence [3S] i l l u s t r a t e s a s i t u a t i o n when one member of the s c h o o l was s e p a r a t e d from the o ther s c h o o l members at the b e g i n n i n g of the chase sequence. In a l l t h r e e cases the s c h o o l was composed of s i x i n d i v i d u a l s . Time t r a j e c t o r i e s of chase sequence [IS] for the p r e d a t o r and one of the prey ( prey 5 ) ( the time t r a j e c t o r i e s for the o ther s c h o o l members were s i m i l a r ) are p r e s e n t e d in f i g u r e 1S.1 . The k inemat i c parameters for the p r e d a t o r and prey 4, 5, and 6, are p r e s e n t e d in f i g u r e s 1S.2 to 1S.10 . The data for sequence [1S] i s i n d i c a t i v e of s c h o o l i n g as a d e f e n s i v e s t r a t e g y . The l i n e a r and angu lar v e l o c i t y of the p r e d a t o r remained r e l a t i v e l y c o n s t a n t through the sequence and 89 F i g u r e 1 S . 1 t ime t r a j e c t o r y s c h o o l : sequence 1S , prey 5 . Only prey 5 i s p l o t t e d as the o t h e r s were s i m i l a r . The a x i s are n o r m a l i z e d u n i t s from the r e f e r e n c e X 0 , Y 0 p o s i t i o n and are used to s c a l e the t r a j e c t o r y p l o t s . 1 .'i -i-Figure IS.5 Time Trajectory : Sequence IS prey 5 o TJfc. . •"tfa predator + *3r. 9 0 prey 1 7 8 6 3 FEET G-C vo o 91 F i g u r e 1S.2 p r e d a t o r l i n e a r and a n g u l a r v e l o c i t y : sequence 1S See t ex t f o r i n t e r p r e t a t i o n . Figure IS.2 Predator Linear V e l o c i t y 4«b o Frame 93 F i g u r e 1S.3 c l o s u r e d i s t a n c e over time : sequence 1S for prey 4,5 and 6. Note the concave and s i m i l a r response for a l l three p r e y . See t e x t for i n t e r p r e t a t i o n . F i g u r e IS.3 O l d v s Time ( f r a m e ) 7 • D 4>::5 0 . 1-5 D«D 7-0 B-D .. 4»E5 3-0 - i -I V 3 0 - UOO-0-0 7-0 3-0 i : 0 • ICO -0 • Frame IDC' • P r e y 4 P r e y 5 P r e y 6 95 F i g u r e 1 S . 4 D i s t a n c e at C l o s e s t Approach over time : sequence 1S for prey 4 , 5 and 6 . Note t h a t there i s no i n d i c a t e d path p r e d i c t i o n by the p r e d a t o r . Figure IS.4 Distance at Closest Approach (DCA) vs Time (frame) 7-D . B»0 . 4 - 5 . 3«Q . 1 - 5 j D ' D 7-D . B'D . 5 0 - 1DC>. 3 - 0 . 1 - 5 I I—\ irvAM / i1 UOO-7-D . B-0 . i - 5 : n 0 - 0 111 If '! i I. .1 --I h — h 5 0 -Prey 4 Prey 5 Prey 6 U X i • Frame 97 F i g u r e 1S.5 PDDIP over time : sequence 1S for prey 4,5 and 6. Figure IS. 5 Predator Distance to Intercept Point (PDDIP) - T t : r .•• • -. J n. [j 100 • -I h Frame ICO • Prey 4 Prey 5 Prey 6 99 F i g u r e 1S.6 PYDIP over time : sequence 1S for prey 4,5 and 6. Figure IS•6 Prey Distance to Intercept Point (PYDIP) vs Time (frame) i n • r.i UDO <D 4 . CD ^ ^ 4-E1-1-D»'D U .UV. V, 'j 50- i—h 100--I 1 1 1 1 •ICO-Prey 4 Prey 5 Prey 6 Frame 101 F i g u r e 1S.7 e r r o r t r a c k i n g angle over time : sequence 1S for prey 4,5 and 6. 102 Figure is•7 1EO" E r r o r Tracking Angle (El) vs Time (frame) -1BD--UBD' I S O -H 1 h ED-cn oC O 100--1BO--1ED-1BD-0- H 1 1 1DO. BO--1ED--1E0- H 1 1 1 1 1 h Frame UOO-Prey 4 Prey 5 Prey 6 103 F i g u r e 1S.8 o f f s e t angle over time : sequence 1S for prey 4,5 and 6. 105 F i g u r e 1S.9 prey l i n e a r v e l o c i t y over time : sequence 1S for prey 4,5 and 6. F i g u r e IS.9 7-0 T.. P r e y L i n e a r V e l o c i t y • •0 1 4«5 3 - 0 1 o 7-0 50- ICO-o CD (fl 4'f5 3-D . 1-5 D«0 B'O 3 • L'J 100 • 1-f. 0-0 o -- i — i — h H 1 1 100-Frame P r e y 4 P r e y 5 P r e y 6 1 07 F i g u r e 1S.10 prey angu lar v e l o c i t y over time : sequence 1S for prey 4,5 and 6. Figure IS.10 Prey Angular V e l o c i t y vs Time (frame) TOOT" _ E5CQ. -ssoo-7rxo« TLXO-0 -^ — I — I iro-% 23DD-w Cl) 60 Q c 5CO--7TXO-3 3 • 100 • -1, 1 1 _ l/'i 1 =5co - : 1 '1 !/ I o--y f Frame -t 1- -I 1 100' 108 Prey 4 Prey 5 Prey 6 109 the c l o s u r e d i s t a n c e c u r v e s show a concave response i n d i c a t i n g a d e c r e a s i n g r a t e of c l o s u r e . The D i s t a n c e at C l o s e s t Approach ( DCA ) f or each prey i n d i v i d u a l e x h i b i t s l a r g e f l u c t u a t i o n through the sequence. F u r t h e r m o r e , none of the d e c r e a s i n g DCA response t r e n d s seen in the s i n g l e p r e d a t o r - s i n g l e prey sequences were e v i d e n t . The i n t e r c e p t c o e f f i c i e n t s are not p l o t t e d , but these showed no r e g u l a r p a t t e r n that would i n d i c a t e pa th p r e d i c t i o n . The l a r g e n o i s e components i n the DCA graphs would i n d i c a t e that the p r e d a t o r was unable to "lock" onto a p a r t i c u l a r t a r g e t f i s h i n the s c h o o l . T a r g e t s w i t c h i n g by the p r e d a t o r c o u l d not be d i r e c t l y a s ses sed because of these n o i s e components. In sequence [1S] the prey remained c l o s e t o g e t h e r and responded s i m i l a r i l y and almost i n s t a n t a n e o u s l y w i th r e s p e c t to each other as the p r e d a t o r approached . T h i s i s e s p e c i a l l y e v i d e n t in the angu lar and l i n e a r v e l o c i t y graphs of the prey where t r e n d s and peaks were very s i m i l a r . The sharp i n c r e a s e i n l i n e a r v e l o c i t y c o i n c i d e d wi th the c l o s e s t d i s t a n c e to the s c h o o l a c h i e v e d by the p r e d a t o r at frames 80 to 82. The o f f s e t ang le s (E2) of a l l the prey showed an i n c r e a s i n g t r e n d to frame 60 for prey 1 ,3 ,and 4, and to frames 40-45 for prey 2 and 6. Prey 5 showed a response b e g i n n i n g at frame 20 i n d i c a t i n g a moving away from the p r e d a t o r t r a j e c t o r y . For a l l p r e y , h i g h a n g u l a r v e l o c i t i e s commenced at frame 13 and c o n t i n u e d wi th i n c r e a s i n g ampl i tudes through the sequence wi th peaks c o r r e s p o n d i n g to the changes in the o f f s e t ang les ( E 2 ) . The h i g h 110 a n g u l a r v e l o c i t i e s e x h i b i t e d by the prey e a r l y in the sequence w h i l e the p r e d a t o r was r e l a t i v e l y d i s t a n t may have f u n c t i o n e d to confuse prey t r a c k i n g . Prey 5 responded in frame 20 by t u r n i n g a lmost 180 degrees from the p r e d a t o r t r a j e c t o r y . Prey 6 responded in frame 30 wi th a s i m i l a r manoeuvre. At these frames , prey 5 and 6 were not the c l o s e s t to the p r e d a t o r . D u r i n g frames 20-30 prey 1-4 showed i n c r e a s e d angu lar v e l o c i t i e s but no d r a s t i c changes in o v e r a l l h e a d i n g . However, at frames 55-62 a l l prey e x h i b i t e d a d r a s t i c change in d i r e c t i o n and a n g u l a r v e l o c i t y . At t h i s p o i n t , the mean p r e d a t o r d i s t a n c e was 2.31 f t . The DCA,PDDID , and PYDID data i n d i c a t e tha t no t r a c k i n g by the p r e d a t o r was o c c u r r i n g . From frames 65-80 the prey c o n t i n u e d moving away from the p r e d a t o r in the same g e n e r a l d i r e c t i o n as i n d i c a t e d by the o f f s e t ang le s ( E 2 ) . At frames 81-82 the p r e d a t o r a c h i e v e d minimum c l o s u r e d i s t a n c e and at tha t p o i n t , a l l prey responded by i n c r e a s i n g l i n e a r v e l o c i t y through frame 90. The p r e d a t o r then t u r n e d away from the s c h o o l . S i m i l a r p a t t e r n s were e x h i b i t e d i n k inemat i c data for both p r e d a t o r and prey in a l l sequences in which the prey remained r e l a t i v e l y c l o s e toge ther and t u r n e d in the same d i r e c t i o n , m a i n t a i n i n g c l o s e c o n t a c t and s i m i l a r a n g u l a r and l i n e a r v e l o c i t i e s . The prey began t u r n i n g away from the p r e d a t o r t r a j e c t o r y wi th i n c r e a s i n g a n g u l a r v e l o c i t y o s c i l l a t i o n s . T h i s i n c r e a s e in o s c i l l a t i n g a n g u l a r v e l o c i t y wi thout a c o r r e s p o n d i n g major d i r e c t i o n change has been termed " d i t h e r i n g " behav iour by H o l l i n g ( p c ) . At a mean c l o s u r e d i s t a n c e of 2.4 +- .3 f e e t , 111 major d i r e c t i o n a l change f o l l o w e d by i n c r e a s e d l i n e a r v e l o c i t y were seen . In these sequences , no measurable t r a c k i n g by the p r e d a t o r were seen, and c l o s u r e r a t e s showed concave re sponses . P r e d a t o r l i n e a r v e l o c i t y remained r e l a t i v e l y c o n s t a n t and low i n s t e a d of the expected i n c r e a s e i f t r a c k i n g to i n t e r c e p t o c c u r r e d . The data i n d i c a t e s tha t " d i t h e r i n g " and c l o s e p r o x i m i t y of the prey i n d i v i d u a l s serve to confuse the p r e d a t o r , d e s t r o y i n g the p r e d a t o r t r a c k i n g s o l u t i o n . Time t r a j e c t o r i e s of chase sequence [2S] f o r the p r e d a t o r and two of the prey ( prey 4 and 5 ) are p r e s e n t e d in f i g u r e s 2S.1a and 2 S . 1 b . The c o r r e s p o n d i n g k inemat ic parameters for the p r e d a t o r and prey 4 , 5 , and 6, are p r e s e n t e d i n f i g u r e s 2S.2 to 2 S . 1 0 . Sequence [2S] i s of i n t e r e s t because the p r e d a t o r a t t a c k r e s u l t s in one prey i n d i v i d u a l , d e s i g n a t e d prey 5 , becoming s e p a r a t e d from the s c h o o l . The l i n e a r v e l o c i t y of the p r e d a t o r showed an immediate i n c r e a s e to a maximum by frame 40, r e s u l t i n g i n a convex c l o s u r e d i s t a n c e p a t t e r n s i m i l a r to that observed in s i n g l e p r e d a t o r -s i n g l e prey i n t e r a c t i o n s . The c l o s u r e d i s t a n c e graphs i n d i c a t e tha t the minimum c l o s u r e d i s t a n c e o c c u r r e d at frame 48-55. Prey 5 was c l o s e s t to the p r e d a t o r at frame 48. From the prey l i n e a r a n g u l a r v e l o c i t y graphs for prey 5, a response can be seen at t h i s p o i n t . Up to frame 48, the prey e x h i b i t e d a c h a r a c t e r i s t i c 1 12 F i g u r e s 2S.1a and 2S.1b time t r a j e c t o r y s c h o o l : sequence the p r e d a t o r and prey 4 and 5. Figure 2S.la Time Trajectory Sequence 2S : prey 4 predator 70 180 •50 "%c - i i i i i i i i i m o B-C Feet to CO Figure 2S.lb Time Trajectory Sequence 2S : prey 5 1 14 Figure- 2S.2 p r e d a t o r l i n e a r and a n g u l a r v e l o c i t y : sequence Figure 2S.2 Predator Linear V e l o c i t y vs Time (frame) o CO CD <U I 1 I I I I I I I I I I 1 1 I I I I 1BC>. Predator Angular V e l o c i t y vs Time (frame) 7CC0-£ ESTJO- ± to 01 CU V J 60 CU Q -E500- t -TOCO- I I 1 I I I I I I I I I I I I I I I O- ± 9 0 -Frame 1 16 F i g u r e 2S.3 c l o s u r e d i s t a n c e over time : sequence 2S for prey 4,5 and 6. Note the convex response for prey 5, frames 90-110. . Figure 2S.3 Closure Distance (CLD) vs Time (frame) 1 - 5 1 V 0-7-0 ^ B-0 I 1 I I I I I I I I I 1 I I I I 1 I ISO-4-1 CD CD r -D«0 \ s V V ) u - U30-7-D : B'D 4 - 5 0-0 J .i \ i I I 1 I I I I I 1 1 1 I I 1 I 1 I 1 O • UEO • Frame Prey 4 Prey 5 Prey 6 118 F i g u r e 2S.4 D i s t a n c e at C l o s e s t Approach over time : sequence 2S for prey 4,5 and 6. Path p r e d i c t i o n by the p r e d a t o r can be seen for prey 5, frames 90-110. See t e x t for f u l l e x p l a n a t i o n . Figure 2S.4 Distance at Closest Approach (DCA) vs Time (frame) 7-0 6-0 1 3*0 1-5 D-D /1 -t—t i i i i i i i r i " i i i 1B0-Prey 4 7-D E»0 4-L:. 3-D . D-D \4d i r i i i i 'i i i i .rJ' ISO. Prey 5 D-D Frame IBO-Prey 6 120 F i g u r e 2S.5 PDDIP over time : sequence 2S for prey 4,5 and 6. 121 Figure"2S.5 Predator Distance to Intercept Point (PDDIP) vs Time (frame) E-5 ; E-5 5-5 4-5 3-5 3-5 , 1-5 X 0-5 D-D \ i i i i i i i-l\ 1B0-Prey 4 •^•S i E-4-5 1-5 D-5 D-D .1 i i i i I I I i i i i ' r T - h - i 1B0-Frame 1B0-Prey 5 Prey 6 122 F i g u r e 2S.6 PYDIP over time : sequence 2S for prey 4,5 and 6. Figure 2S.6 Prey Distance to Intercept Point (PYDIP) vs Time (frame) 1Q-D D-5 D-D Prey 4 ISO-1D-D ^ cu a) B- 5 —r r~ / • E-cr _ i • _ J 4- rrr _ J i " ZZl " - J ' i d " r:r ...j 1- 5 i—i cr _ J D- D i n - D 9- _ J E- t_-_ J ~7 c : _ j E- c:r ... j cr _ i • cr _. i 4- r : ... J cr —' _j •—i i*r . J 1 . - cr: ... j cr XJ • _ j D- D i i f - r - + i L J Prey 5 1BO-Prey 6 ISO-Frame 124 F i g u r e 2S.7 e r r o r t r a c k i n g ang le over time : sequence 2S for prey 4,5 and 6. D e f e n s i v e manoeuvres by the s c h o o l can be seen as the l a r g e f l u c t u a t i o n s in t r a c k i n g e r r o r . See t ext for f u l l e x p l a n a t i o n . Figure 2S.7 Er r o r tracking Angle (El) vs Time (frame) 1B0« -1EO- l -1B> fl O-II I I I I fl I1 I I I I I I I I I I uao 1B0' CO S EC', i M 60 CU Q -1EO- X -1ED« 1BD« rt i 1 /('if 1BO--:1E;U--1EO' U3D-125 Prey 4 Prey 5 Prey 6 rarae 126 F i g u r e 2S.8 o f f s e t angle over time : sequence 2S for prey 4,5 and 6. Frame 128 F i g u r e 2S.9 prey l i n e a r v e l o c i t y over t ime : sequence 2S for prey 4,5 and 6. Figure 2S.9 Prey Linear V e l o c i t y vs Time (frame) B«0 ' Prey 5 Prey 6 ISO-Frame 1 30 F i g u r e 2S.10 prey angu lar v e l o c i t y over time : sequence 2S for prey 4,5 and 6. Figure 2S..10 Prey Angular V e l o c i t y vs Time (frame) TUX'" .r cEEEO Prey 4 7LXO» ,. m ESOQ- t 60 CJ o -ESDD--7000• 3DD- | 1 I I I I H I 1 I 1 I 1 I I 1 1 I 0- 190 • Mm! •2500- : \i 1 I J T X O « 4-r--h-|-r-r-+-t-i-r-r-+~t- f - f - r - r - M O • • rame 190-Prey 5 Prey 6 1 32 moving away from the p r e d a t o r t r a j e c t o r y as i n d i c a t e d in the o f f s e t a n g l e (E2) g r a p h s . Prey 5 was the f i r s t to respond by a q u i c k t u r n ' to the l e f t . T h i s i s i n d i c a t e d in the e r r o r a n g l e ( E 1 ) , a n g u l a r v e l o c i t y , and o f f s e t ang le (E2) g r a p h s . Up to frame 48 the DCA d a t a , and the c o r r e s p o n d i n g PDDIP ,PYDIP, and e r r o r ang le (E1) data for prey 5 showed l e s s f l u c t u a t i o n than those of the other' s c h o o l members, s u g g e s t i n g that prey 5 was the t a r g e t p r e y . The DCA data showed l a r g e f l u c t u a t i o n s and were however, not as "c lean" as those for s i n g l e p r e d a t o r - s i n g l e prey i n t e r a c t i o n s . The t u r n i n g manoeuvre at frame 48 by the prey r e s u l t e d in the p r e d a t o r l o s i n g t r a c k i n g and t u r n i n g away. From the l i n e a r v e l o c i t y graphs of the p r e y , i t can be seen tha t prey 5 m a i n t a i n e d a h i g h e r l i n e a r v e l o c i t y f o r a g r e a t e r l e n g t h of t ime than the o ther s c h o o l members. As prey 1 , 2 , 3 , 4 , and 6 slowed down and t u r n e d g e n t l y to the l e f t , r e f o r m i n g the s c h o o l , prey 5 c o n t i n u e d in the o p p o s i t e d i r e c t i o n . From the c l o s u r e d i s t a n c e and DCA d a t a , i t i s q u i t e c l e a r t h a t the p r e d a t o r responded to prey 5, and i n i t i a t e d a new a t t a c k . The p r e d a t o r response appears at frame 80 and c o n t i n u e s to frame 117. At minimum c l o s u r e d i s t a n c e , prey 5 responded w i t h a q u i c k l e f t t u r n and approached the reformed s c h o o l . The k inemat ic data i n d i c a t e t r a c k i n g by the p r e d a t o r for a s h o r t t ime , but the l a r g e o s c i l l a t i o n s in DCA,PDDIP, and PYDIP i n d i c a t e e v e n t u a l t r a c k i n g l o s s . As in sequence 1S, the prey in 2S e x h i b i t e d i n c r e a s e d a n g u l a r v e l o c i t i e s ( " d i t h e r i n g " ) and moving away from the p r e d a t o r t r a j e c t o r y . At frame 160 , the p r e d a t o r moved away from the s c h o o l . 133 Time t r a j e c t o r i e s of the p r e d a t o r and prey 1 and 2 for chase sequence [3S] are p r e s e n t e d i n f i g u r e s 3S.1a and 3 S . 1 b . The c o r r e s p o n d i n g k inemat i c parameters for the p r e d a t o r and prey 1 ,2 ,and 3 are p r e s e n t e d in f i g u r e s 3S.2 to 3S.10 . The l i n e a r and a n g u l a r v e l o c i t y data of the p r e d a t o r show the c h a r a c t e r i s t i c response of a t t a c k i n d i c a t e d by the r a p i d l i n e a r a c c e l e r a t i o n . The c l o s u r e d i s t a n c e da ta a l s o show the c h a r a c t e r i s t i c a t t a c k p a t t e r n . From the DCA,PDDIP, PYDIP, and e r r o r ang le (E1) d a t a , i t i s q u i t e c l e a r tha t prey 1 was the t a r g e t ' a n d that the p r e d a t o r was t r a c k i n g t h i s i n d i v i d u a l . At a d i s t a n c e of 2.35 f ee t at frame 30, prey 1 responded w i t h an i n c r e a s e d l i n e a r v e l o c i t y ; t u r n e d away from the p r e d a t o r and headed toward the s c h o o l . Up to frame 30, the a n g u l a r and l i n e a r v e l o c i t y of the s c h o o l remained low and the o f f s e t (E2) shows an i n c r e a s i n g t r e n d i n d i c a t i n g a moving away from the p r e d a t o r t r a j e c t o r y . As prey 1 approached the s choo l in frames 30-40, the s c h o o l responded w i t h an i n c r e a s e d angu lar and l i n e a r v e l o c i t y l e a d i n g to l o s s of t r a c k i n g by the p r e d a t o r . By frame 55, the p r e d a t o r moved away from the s c h o o l . The DCA,PDDIP, PYDIP, and e r r o r ang le (E2.) data show that from frames 40-50 there may have been t r a c k i n g by the p r e d a t o r , but i t i s u n c l e a r as to which prey i s t r a c k e d . The t r a c k i n g e r r o r i n c r e a s e d for a l l i n d i v i d u a l s of the s c h o o l from frame 46 onwards. Up to frame 38 the e r r o r angle for prey 1 showed l i t t l e d e v i a t i o n and was a c o n s t a n t response , s i m i l a r to that seen in s i n g l e p r e d a t o r -134 F i g u r e s 3S.1a and 3S.1b time t r a j e c t o r y s c h o o l : sequence the p r e d a t o r and prey 1 and 2. Figure 3S.la Time Trajectory Sequence 3S: prey 1 j j j ^ u predator :ir.' 3 0 prey PfHHHH-r+H-f-r-H^f-r-f^^ l - D Feet 9 7-3 a) 1-G D»D - H -3 •  0 Figure 3S.lb Time Trajectory Sequence 3S: prey 2 , | _ h H ^ ^ ^ ^ h 1 „ h ^ | - ^ | - H H - - r - h - - 1 | | 1 | 1 | | | | 1 1 | r H - H - H - H cd Feet 136 F i g u r e 3S.2 p r e d a t o r l i n e a r and a n g u l a r v e l o c i t y : sequence Figure 3S.2 7«rj B-0 . Predator Linear V e l o c i t y 4 - 5 3 - D 1 - 5 0-0 7 0 0 0 -f o-ESOO. -3S0O-- 7 D D D - ± 1 f 1 1 5 0 - 1 0 0 -Predator Angular V e l o c i t y O- so-Frame .100" 138 F i g u r e 3S.3 c l o s u r e d i s t a n c e over time : sequence 3S for prey 1,2 and 3. 7 - 0 ^ B - 0 4 - 5 3 • O .1 1 - 5 1 n . p Figure 3S.3 Closure Distance (CLD) vs Time (frame) \ \ 0 - 5 0 --I 1 (-7 - D B - 0 4 - 5 3 - D 1 - 5 . D - D \ \ O-7 - D . B - D 3-D D-D Frame i 1 1 UX' 1 0 0 -Prey 1 Prey 2 Prey 3 140 F i g u r e 3S.4 D i s t a n c e at C l o s e s t Approach over time : sequence 3S for prey 1,2 and 3. Note the attempted path p r e d i c t i o n for prey 1 by the p r e d a t o r . ' Figure 3S. 4 Distance at Closest Approach (DCA) vs Time (frame) 7 ' D E-0 . 4-FJ 3-0 1 1-5 M D-D 0-' A . 50- ICO-Prey 1 Q) CD E-0 4..E5 3 - D 7-0 E'O 4 - 5 . 3 - 0 J.. 1 - 5 . . . F i K 1 --i — i — J V — h - H — 1 — 1 _ 1 1 , 0- so-f '4\ O • i h V so-Frame 1 D 0 -i 1 r — i ICO Prey 2 Prey 3 142 F i g u r e 3S.5 PDDIP over time : sequence 3S for prey 1,2 and 3. 143 figure 3S.5 Predator Distance to Intercept Point (PDDIP) vs Time (frame) B-5 7' 5 E-5 4-5 1-5 • 5 D-D D-5 *i i. V -v. o-— f — i — - + -130 • 50-B-5 E • 5 4-5 1-5 0-5 0»D M O- 50-Frame Prey 1 100-Prey 2 100-Prey 3 1V s i P J Vi - I — ¥ — I — I — h H \ IOC 144 F i g u r e 3S.6 PYDIP over time : sequence 3S for prey 1,2 and 3. 10'0 9-5 B-5 7-5 E-5 cr r.r — i -... J 4-5 2-5 E-5 1-5 D-5 0-0 Figure 3S.6 Prey Distance to Intercept Point (PYDIP) vs Time (frame) o-ip»p. 9-5 B-5 7-5 E-5 cr cr CJ 4 . 5 . . i E-5 1-5 D-5 D-D -H. o-"4 i r 50-JD>D Q-5 E-5 E-5 cr cr _j •... j 4-5 D-5 13 • D • iii'V'ij'^ V-- i 1 » vji, >' 50-Frame Prey 1 UOO. Prey 2 H 1 1 IOC' Prey 3 H 1 1 100-1 46 F i g u r e 3S.7 e r r o r t r a c k i n g angle over time : sequence 3S for prey 1,2 and 3. 147 Figure 3S.7 Er r o r Tracking Angle (El) vs Time (frame) U30-ED--1E0- I -1ED' O-- i 1 r 50-1E0> tn to 0) Q E0--1BD« UBO-o-H 1 1 1— 50-1D0-i 1 1 100 Prey 1 Prey 2 3> -1B"J'< Prey 3 i r O • -r r 1 h 100. Frame 1 48 F i g u r e 3S.8 o f f s e t ang le over time : sequence 3S for prey and 3. 1 50 F i g u r e 3S.9 prey l i n e a r v e l o c i t y over time : sequence 3S for prey 1,2 and 3. 151 7-0 B-0 4«f. 3 - 0 Figure 3S.9 Prey Linear V e l o c i t y vs Time (frame) o u 1 - 5 0 . 0 B-0 4 - 5 3 - 0 | 1 ' 5 1—I—h 5 0 -n M o-o '** 0-7-0 E-0 ~. 4-5 3-0 o-o V J • I A' i Prey 1 i H 1 uoo. Prey 2 100-Prey 3 O- 50- ICO Frame F i g u r e 3S.10 prey angu lar v e l o c i t y over time : sequence 3S for prey 1,2 and 3. Figure 3S.10 Prey Angular V e l o c i t y vs Time (frame) 1 54 s i n g l e prey e n c o u n t e r s . Sequences 1S,2S,3S demonstrate that g i v e n a c h o i c e , a p r e d a t o r p r e f e r s to a t t a c k s i n g l e i n d i v i d u a l s . In these a t t a c k s where i n d i v i d u a l s were s e p a r a t e d from the s c h o o l , i t was not s u r p r i s i n g that the k inemat ic v a r i a b l e s showed s i m i l a r p a t t e r n s to those of s i n g l e p r e d a t o r - s i n g l e prey sequences . When the p r e d a t o r approached a s c h o o l , the k inemat ic parameters for a l l the prey and the p r e d a t o r showed i n c r e a s e d v a r i a n c e , and t r a c k i n g was e i t h e r not a c c o m p l i s h e d or l o s t . I t appears that when c o n f r o n t e d by m u l t i p l e t a r g e t s the p r e d a t o r cannot m a i n t a i n t r a c k i n g even i f a p a r t i c u l a r f i s h i s i n i t i a l l y the t a r g e t . T h i s i s p r o b a b l y due to d i s t r a c t i n g movements of the o ther members of the s c h o o l . The on ly c a p t u r e s observed i n s i n g l e p r e d a t o r - s c h o o l i n g prey sequences o c c u r r e d when one or more i n d i v i d u a l s were s e p a r a t e d from the s c h o o l and swam a l o n e . S c h o o l i n g prey demonstrated remarkably s i m i l a r k inemat i c parameter v a l u e s and executed s i m i l a r manoeuvres almost s i m u l t a n e o u s l y . As wi th s i n g l e p r e y , the s c h o o l i n i t i a l l y responded to the p r e d a t o r by s l o w l y moving away from the d i r e c t i o n of a t t a c k . At a d i s t a n c e of 2.3 + 0.4 f e e t , i n c r e a s e d l i n e a r and a n g u l a r v e l o c i t i e s were i n i t i a t e d by the p r e y . The common escape response was the q u i c k t u r n away from the p r e d a t o r , w i th i n c r e a s e d a n g u l a r o s c i l l a t i o n s ( " d i t h e r i n g " ) . 155 T h i s response appears to be an e f f e c t i v e t r a c k i n g b r e a k i n g mechanism. F o u n t a i n and f l a s h expans ion b e h a v i o u r s , as d e s c r i b e d by P a r t r i d g e (1982) were r a r e l y o b s e r v e d . T h i s may be due to the s m a l l s i z e of the s c h o o l s used i n these experiments. . The r e l a t i o n s h i p s between k inemat i c v a r i a b l e s found for s i n g l e p r e d a t o r - s i n g l e prey encounters were the same as those found i n s i n g l e p r e d a t o r - s c h o o l i n g prey sequences . 1 56 2) S c h o o l Cohes ion In o r d e r to measure the two d i m e n s i o n a l s p a t i a l s t r u c t u r e of the s c h o o l , the f o l l o w i n g approach from s t a t i s t i c a l t h e o r y was t a k e n . At any frame ( time i n t e r v a l ) , the members of the s c h o o l can be c o n s i d e r e d as p o i n t s on a s u r f a c e . W i t h i n the minimum and maximum x , y c o o r d i n a t e s of these p o i n t s , t h e r e e x i s t s a p o i n t termed the c e n t e r of mass. At t h i s p o i n t , the mean sum of the d i s t a n c e s from the c e n t e r of mass to each of the p o i n t s ( f i s h c o o r d i n a t e s ) i s a minimum. T h i s d i s t a n c e was d e s i g n a t e d Zm. As f i s h move c l o s e r toge ther Zm d e c r e a s e s , and as f i s h move f a r t h e r a p a r t Zm i n c r e a s e s . C o m p u t a t i o n a l l y , f i n d i n g Zm i s a m i n i m i z i n g l e a s t squares prob lem. Z = min m f n i , .£{ (X. - C ) 2 + (Y. - C ) 2 } 1 = ^ 1 X 1 y 2 ( 35 ) The c o o r d i n a t e of the c e n t e r of mass CMx,CMy ( where Z i s a minimum ) was found for each frame u s i n g a r a v i n e s e a r c h method ( Bard 1974 ) over the Z response s u r f a c e . F i g u r e 17 i l l u s t r a t e s the response s u r f a c e f o r sequence 2S , frame 1. P l o t t i n g Zm vs time f o r a s c h o o l not s u b j e c t e d " t o p r e d a t o r a t t a c k i s p r e s e n t e d in f i g u r e 18, and for the f i r s t 80 frames of sequence 2S are p r e s e n t e d i n f i g u r e 19. The mean minimum d i s t a n c e from the c e n t e r of mass for n o n - a t t a c k e d s c h o o l s was 0.36 feet which i s s l i g h t l y g r e a t e r than the mean body l e n g t h of the prey s p e c i e s . . For s c h o o l s that were a t t a c k e d , the response of Zm wi th t ime was 157 F i g u r e 17 Zm response s u r f a c e : sequence 2S, frame 1. The i n v e r s e of Zm i s p l o t t e d to show i t as a maximum f o r c l a r i t y . The c e n t e r of g r a v i t y at p o i n t CMx,CMy i s where Zm i s m i n i m i z e d over the resonse s u r f a c e . CMx, CMy i 1 58 F i g u r e 18 Zm over time : u n a t t a c k e d s c h o o l . The response of Zm over time shows a r e l a t i v e l y c o n s t a n t l e v e l at 0.36 f t which i s s l i g h t l y g r e a t e r than the prey mean body l e n g t h . T h i s i n d i c a t e s a s t a b l e s c h o o l s t r u c t u r e . 01 fl) o •: 'i •rame 159 F i g u r e 19 Zm over time : sequence 2S, frame 1 to 80 . The Zm response for sequence 2S i s t y p i c a l of the response for a t t a c k e d s c h o o l s . Zm shows and i n i t i a l d e c r e a s i n g t r e n d i n d i c a t i n g t h a t the s c h o o l i n g members move c l o s e r t o g e t h e r . The d e f e n s i v e manoeuvre by the s c h o o l can be seen as the r a p i d i n c r e a s e i n Zm, i n d i c a t i n g that the s c h o o l members are moving away from each o t h e r . E n 1-1:1 I'H! O' B D -: 3 n»i.) f i - f ICO-Frame 160 remarkably s i m i l a r , showing a decrease wi th c l o s u r e d i s t a n c e of the p r e d a t o r . The minimum Zm for these s i t u a t i o n s was found to be 0.26 feet or a p p r o x i m a t e l y 3/4 of the mean prey body l e n g t h . F i g u r e 18 ( for the f i r s t 80 frames of the s c h o o l in seguencs 2S ) i s t y p i c a l of the re sponse . The minimum Zm was found to c o i n c i d e wi th the minimum c l o s u r e d i s t a n c e by the p r e d a t o r i n d i c a t i n g that the s c h o o l i n g f i s h were c l o s e s t toge ther when the p r e d a t o r was at a c l o s e d i s t a n c e , j u s t b e f o r e a c t i v e k inemat i c e v a s i v e manoeuvres were i n i t i a t e d by the s c h o o l . The data suppor t s the h y p o t h e s i s tha t s c h o o l i n g f i s h move c l o s e r toge ther when a t t a c k e d by p r e d a t o r s , or when a t h r e a t i s p e r c e i v e d . 161 DISCUSSION As noted by P a r t r i d g e (1982) n e a r l y h a l f of a l l f i s h s p e c i e s s c h o o l throughout or d u r i n g some time of t h e i r l i v e s . T h i s behav iour suggests tha t some e v o l u t i o n a r y advantage i s ga ined by s c h o o l i n g ; and i t i s thought to be p r i m a r i l y a p r o t e c t i o n from p r e d a t o r s . The r e s u l t s of t h i s a n a l y s i s c o n f i r m s t h a t at l e a s t one of the f u n c t i o n s of s c h o o l i n g as a d e f e n s i v e s t r a t e g y l e a d s to reduced p r e d a t o r s u c c e s s . F i g u r e 20 p r e s e n t s p r e d a t o r success f r e q u e n c i e s as a f u n c t i o n of s c h o o l s i z e as r e v e a l e d d u r i n g t h i s s t u d y . S i g n i f i c a n t l y , those f i s h caught by the p r e d a t o r a t t a c k i n g s c h o o l s were i n d i v i d u a l s that somehow became s e p a r a t e d from the s c h o o l and swam a l o n e . No prey were observed caught d u r i n g the i n i t i a l a t t a c k by the p r e d a t o r on a' s c h o o l . The mechanisms tha t reduce the success r a t i o of the p r e d a t o r on s c h o o l i n g prey are t w o f o l d : (1 ) , the reduced d e t e c t i o n p r o b a b i l i t y of the s c h o o l , which was not s t u d i e d d u r i n g t h i s i n v e s t i g a t i o n , but i s summarized by P a r t r i d g e (1982), and (2) sensory c o n f u s i o n of the p r e d a t o r by m u l t i p l e t a r g e t s . P r e s e n t e d e a r l i e r were three p o s s a b l e p r e d a t o r i n t e r c e p t i o n s t r a t e g i e s . The f i r s t s t r a t e g y c o n s i s t e d of the p r e d a t o r c a l c u l a t i n g the q u a r r y f l i g h t path u s i n g i n f o r m a t i o n upon f i r s t s i g h t i n g and then t u r n away from the prey and proceed to the 162 Figure 20. Predator success as a function of school s i z e . Success i s defined as prey capture. The r a t i o s are the (number of captures/total t r i a l s ) . • 25 tn A! o CO u o P <J-I tfl tn tu o tfl O T 3 P 0 ) o 0 ) ! ^ 4-1 o e p cr a) u Pn ( 5/20) (2/20) (2/20) (1/16) 12 Number of prey i n school 163 i n t e r s e c t i o n p o i n t ; a d j u s t i n g i t s k i n e m a t i c s to a r r i v e at that p o i n t at the same time as the p r e y . The second i n t e r c e p t i o n s t r a t e g y was for the p r e d a t o r to c o n t i n u a l l y p o i n t at the prey throughout the c h a s e . Howland's s imple model of p r e d a t o r - p r e y i n t e r a c t i o n i s based on the p r e d a t o r t r a c k i n g the prey by c o n s t a n t l y heading towards i t . Another name for t h i s s t r a t e g y c o u l d be c a l l e d z e r o - e r r o r p o s i t i o n i n g . The z e r o - e r r o r r e f e r s to a t r a c k i n g system that a t tempts to reduce the l e a d ang le E1 to zero at each r e a c t i o n t i m e , e f f e c t i v e l y p o s i t i o n i n g the t r a c k e r toward the t a r g e t . Sensed d e v i a t i o n s from the zero p o s i t i o n cause motor a c t i o n s to r e - e s t a b l i s h z e r o - e r r o r p o s i t i o n i n g . Heat s e e k i n g m i s s i l e s of the modern a i r combat environment work on t h i s p r i n c i p l e , homing onto the heat exhaust from j e t e n g i n e s . In the t a c t i c a l s i t u a t i o n , they are most s u c c e s s f u l when f i r e d from beh ind and the t a r g e t a i r c r a f t ( prey ) does not ' see ' the m i s s i l e coming. S t a t i s t i c s of a i r combat show t h a t i f a p i l o t sees a m i s s i l e coming he can time h i s break ( hard turn) to a v o i d the m i s s i l e because a i r c r a f t , a l t h o u g h s l o w e r , are much more manoeuvrable . L a t e s t t e c h n o l o g i c a l advances have i n t r o d u c e d improved seekers and v e c t o r e d t h r u s t i n g to improve m i s s i l e m a n o e u v r a b i l i t y ( Preyss 1978, M i l l a r and Dahlem 1978 ) . The t h i r d i n t e r c e p t i o n s t r a t e g y i s the l e a d p u r s u i t . The p r e d a t o r r e c e i v e s and e v a l u a t e s cons tant i n f o r m a t i o n about prey k i n e m a t i c s , r e l a t i v e p o s i t i o n , and o r i e n t a t i o n . U s i n g t h i s 164 i n f o r m a t i o n , the p r e d a t o r k i n e m a t i c s are a l t e r e d such t h a t i t i s p o i n t i n g to a p o i n t where the c u r r e n t paths are i n t e r s e c t i n g , ahead of the p r e y . The p r e d a t o r i s pa th p r e d i c t i n g and t r a c k i n g . In open environments t h i s s t r a t e g y appears to be the best p o s s i b l e i n t e r c e p t s t r a t e g y for the p r e d a t o r . Not o n l y does the •predator have g r e a t e r freedom of response to prey e v a s i v e b e h a v i o u r , but the problems a s s o c i a t e d wi th the second s t r a t e g y are s o l v e d . The p r e d a t o r does not n e c e s s a r i l y f o l l o w a g r e a t e r path d i s t a n c e . The p o i n t of aim i s ahead of the p r e y ; t h e r e f o r e , the p r e d a t o r i s p r e d i c t i n g where the prey w i l l be and can move toward t h a t p o i n t . The prey can not always outguess the p r e d a t o r because the p r e d a t o r path i s not p o i n t i n g toward i t , but to one of many p o s s i b l e p o i n t s in the f u t u r e . T h i s i m p l i e s t h a t a more complex d e f e n s i v e s t r a t e g y on the p a r t of the prey i s needed. Radar Homing ( RH ) m i s s i l e s of the modern a i r combat environment work on the l e a d p u r s u i t p r i n c i p l e . An enemy a i r c r a f t i s f i r s t ' l o c k e d ' by the a t t a c k e r ' s r a d a r . T h i s means that the radar computer i s c o n t i n u o u s l y e v a l u a t i n g the t a r g e t k i n e m a t i c s , p o s i t i o n and r e l a t i v e a t t a c k parameters from the radar r e t u r n s i g n a l s . The RH m i s s i l e i s then launched and guided to the t a r g e t by the r a d a r . The radar e v a l u a t e s an i n t e r c e p t i o n p o i n t ahead of the t a r g e t ( pa th p r e d i c t i n g ) and sends s i g n a l s that a l t e r the RH m i s s i l e o r i e n t a t i o n such tha t the D i s t a n c e at C l o s e s t Approach i s t h e o r e t i c a l l y zero throughout the chase . S t a t i s t i c s of modern a i r combat ( D r e n d e l 1974, M i d d l e t o n 1976) show tha t i n environments of low s t r u c t u r a l h e t e r o g e n e i t y ( low 165 ECM ) the RH m i s s i l e i s the most e f f e c t i v e a i r to a i r weapon. As d i s c u s s e d p r e v i o u s l y , the a i r c r a f t must ' see ' the incoming m i s s i l e to a v o i d i t . Modern a i r c r a f t c a r r y an a r r a y of d e v i c e s to i n t r o d u c e s t r u c t u r a l h e t e r o g e n e i t y i n the environment tha t ac t to d i s a b l e the t r a c k i n g f u n c t i o n s of the a t t a c k r a d a r . T h i s s tudy shows that at l e a s t rainbow t r o u t ( Salmo  g a i r d n e r i ) employ p a t h - p r e d i c t i o n t r a c k i n g when a t t a c k i n g p r e y . T h i s method i n v o l v e s s o p h i s t i c a t e d i n t e g r a t i o n of both p r e d a t o r and prey k i n e m a t i c s by the p r e d a t o r p e r i p h e r a l nervous system and IHS, but i s an o p t i m a l t r a c k i n g s t r a t e g y . The data show however, that when a t t a c k i n g s c h o o l i n g p r e y , the p r e d a t o r i s unable to m a i n t a i n t r a c k i n g of an i n d i v i d u a l p r e y , even i f i t was i n i t i a l l y a b l e to do so . Given a c h o i c e , the p r e d a t o r always p r e f e r s to a t t a c k i n d i v i d u a l prey tha t become s e p a r a t e d from the s c h o o l . The s t r a t e g y employed by the s c h o o l i n g prey to de fea t p r e d a t o r t r a c k i n g i n v o l v e s four t a c t i c s w i t h i n c r e a s i n g l e v e l s of k i n e m a t i c , and c o n s e q u e n t l y e n e r g e t i c , a c t i v i t y . The d e t e c t i o n and r e a c t i o n d i s t a n c e of the prey were found to be the same in i n d i v i d u a l and s c h o o l i n g s i t u a t i o n s . Once the p r e d a t o r or t h r e a t i s d e t e c t e d , the f i r s t t a c t i c of the s c h o o l i s to t u r n away from the a t t a c k t r a j e c t o r y wi th a s l owly i n c r e a s i n g t u r n r a t e . T h i s was c l e a r l y seen i n the o f f s e t ang le (E2) data p r e s e n t e d e a r l i e r . The second t a c t i c , which o c c u r s 1 66 s i m u l t a n e o u s l y w i th the f i r s t , i s the compress ion of the s c h o o l . The data suggest that the f u n c t i o n of the f i r s t t a c t i c i s t w o f o l d . F i r s t , as a mechanism of t h r e a t e v a l u a t i o n . I f the v e l o c i t y and path of the t h r e a t o b j e c t remain c o n s t a n t , then the moving away t a c t i c i s a prudent avo idance behav iour i n v o l v i n g min imal energy e x p e n d i t u r e . I f the t h r e a t o b j e c t v e l o c i t y i n c r e a s e s and the t r a j e c t o r y changes toward the s c h o o l , t h i s can then be i n t e r p r e t e d as a genuine t h r e a t . S e c o n d l y , moving away from the o b j e c t path f o r c e s the p r e d a t o r to f o l l o w an i n c r e a s i n g l y curved p a t h , c o n s e q u e n t l y i n c r e a s i n g the time to i n t e r c e p t . The s imul taneous t a c t i c of s c h o o l compress ion f u n c t i o n s to decrease the area of the s c h o o l and c o n s e q u e n t l y , the d e t e c t i o n s u r f a c e . F u r t h e r , P a r t r i d g e and P i t c h e r (1980) show that i n s c h o o l i n g f i s h , v i s u a l c l u e s are used to m a i n t a i n a n g u l a r and d i s t a n c e s e p a r a t i o n and l a t e r a l l i n e sensors re spond ing to water d i s p l a c e m e n t are used to determine v e l o c i t y and d i r e c t i o n . The e x e c u t i o n of e v a s i v e manoeuvres r e q u i r e s knowledge of the k i n e m a t i c s of other members of the s c h o o l , or at l e a s t that of the neares t n e i g h b o u r s . T h i s suggests tha t the compress ion of the s c h o o l may a l s o f u n c t i o n to min imize s i g n a l l o s s . A f u r t h e r b e n e f i t of c o m p r e s s i o n , e s p e c i a l l y i f the s c h o o l i s s m a l l , i s that i t may i n i t i a l l y presen t a s i n g l e t a r g e t to the p r e d a t o r . The DCA data for some s c h o o l s show p o s s i b l e 167 t r a c k i n g by the p r e d a t o r on the s c h o o l as a s i n g l e u n i t , a l t h o u g h l a r g e " no i se " components appear i n the g r a p h s . As the p r e d a t o r approaches the r e a c t i o n d i s t a n c e of the s c h o o l the t h i r d and f o u r t h t a c t i c s of maximum t u r n and s c i s s o r s ( " d i t h e r i n g " ) o c c u r , r e s u l t i n g in s c h o o l d i s i n t e g r a t i o n . These t a c t i c s occur when the p r e d a t o r l i n e a r v e l o c i t y and c o r r e s p o n d i n g t u r n r a d i u s are h i g h . At h i g h l i n e a r v e l o c i t i e s , the manoeuvre o p t i o n s of the p r e d a t o r are low. The data show tha t the expanding area of . the s c h o o l and the s imul taneous i n c r e a s e d a n g u l a r and l i n e a r v e l o c i t i e s of the i n d i v i d u a l prey r e s u l t i n g from these t a c t i c s de fea t p r e d a t o r t r a c k i n g . P a r t r i d g e (1982) ha.s termed t h i s l o s s of p r e d a t o r t r a c k i n g as the c o n f u s i o n e f f e c t and compares i t t o a t e n n i s p l a y e r t r y i n g to h i t s e v e r a l t e n n i s b a l l s at once . The mechanism for t h i s e f f e c t p r o b a b l y l i e s w i t h i n the p e r i p h e r a l nervous system of the p r e d a t o r and i s the sensory c o n f u s i o n caused by the presence of m u l t i p l e t a r g e t s . T h i s idea i s supported by the data i n sequence 3S. I n i t i a l l y , the p r e d a t o r c l e a r l y shows t r a c k i n g of the i n d i v i d u a l that i s away from the s c h o o l . As t h i s prey i n d i v i d u a l approached the s c h o o l , t r a c k i n g by the p r e d a t o r was l o s t and not r e - e s t a b l i s h e d . The f a i l u r e to r e - e s t a b l i s h t r a c k i n g by the p r e d a t o r of any i n d i v i d u a l suggest c o n f u s i o n r a t h e r than s imple t a r g e t l o s s . The advantage of s c h o o l i n g in r e d u c i n g the chance of be ing 168 d e t e c t e d and c o n f u s i n g a p r e d a t o r once the s c h o o l i s found i s p r i m a r i l y a f u n c t i o n of the form of the s c h o o l . The e v a s i v e t a c t i c s employed to de fea t p r e d a t o r t r a c k i n g are a f u n c t i o n of c o - o p e r a t i o n of the s c h o o l members. Radakov (1973) and P a r t r i d g e (1982) d e s c r i b e two e v a s i v e t a c t i c s termed the f o u n t a i n e f f e c t and f l a s h e x p a n s i o n . In the f o u n t a i n e f f e c t , the a t t a c k e d s c h o o l s p l i t s i n t o two groups t h a t flow behind the p r e d a t o r which i s c a r r i e d forward by i t s own momentum. The f l a s h expans ion i s c h a r a c t e r i z e d by a r a p i d expans ion i n the form of a sphere by the members of the a t t a c k e d s c h o o l away from the p r e d a t o r t r a j e c t o r y . D u r i n g these t a c t i c s , no c o l l i s i o n s between s c h o o l members were o b s e r v e d , i n d i c a t i n g that each f i s h must "know" where i t s ne ighbour i s g o i n g . A l t h o u g h these t a c t i c s are most dramat i c i n l a r g e s c h o o l s , they are a l s o seen i n s m a l l s c h o o l s , f l a s h expans ion be ing most e a s i l y r e c o g n i z e d . Sequence 3S i s an example of f l a s h e x p a n s i o n . The f o u n t a i n e f f e c t was r a r e l y seen in t h i s i n v e s t i g a t i o n , and o n l y w i t h s c h o o l s of 20 or more i n d i v i d u a l s . Moreover , t h i s t a c t i c was used o n l y in head on or t a i l on approaches by the p r e d a t o r . Exper iments w i th s c h o o l s of l a r g e s i z e were not conducted because of the l i m i t e d s i z e of the p r e d a t i o n a r e n a . Even wi th s c h o o l s of 12 f i s h , edge e f f e c t s and c o r n e r seek ing o c c u r r e d f r e q u e n t l y . In g e n e r a l however, even when schoo l s were c l o s e to edges or c o r n e r s , the escape b e h a v i o u r s and e v a s i v e t a c t i c s e x h i b i t e d f o l l o w e d the same p a t t e r n as seen in s m a l l e r s c h o o l s and s i t u a t i o n s where the exper imenter f e l t that edge 169 e f f e c t s were not a c o n t r i b u t i n g f a c t o r . A n a l y s e s of s c h o o l s t r u c t u r e summarized by P a r t r i d g e (1982) suggests t h a t s c h o o l s t r u c t u r e i s not f i x e d , i e . i n a r e g u l a r geometr ic form such as a c u b i c l a t t i c e ( Shaw 1970,1976 ) c h a r a c t e r i s t i c of some c r y s t a l s . O b s e r v a t i o n s from t h i s study i n d i c a t e that the s c h o o l s t r u c t u r e i s a l o o s e , and as P a r t r i d g e puts i t , a p r o b a b i l i s t i c s t r u c t u r e . G e n e r a l l y , the f i s h m a i n t a i n an empty space around each i n d i v i d u a l and for sockeye salmon f r y i t i s s l i g h t l y g r e a t e r than one body l e n g t h . I n d i v i d u a l s r e g u l a r l y change p o s i t i o n in the s c h o o l as a f u n c t i o n of v e l o c i t y and d i r e c t i o n change. When a t t a c k e d , the s c h o o l i n i t i a l l y e x h i b i t s a more r i g i d s t r u c t u r e w i t h r e s p e c t to v e l o c i t y and d i r e c t i o n by c o m p r e s s i o n . The p r e f e r r e d compressed i n d i v i d u a l s p a c i n g was 3/4 of a body l e n g t h . The p o s s i b l e a d a p t i v e s i g n i f i c a n c e of s c h o o l compress ion was d i s c u s s e d e a r 1 i e r . To summarize, the data support the three d e f e n s i v e s t r a t e g y r u l e s p r e s e n t e d e a r l i e r and the hypotheses that emerged from the subsequent t h e o r e t i c a l d i s c u s s i o n . Rule 1. The best s t r a t e g y from the prey p o i n t of view i s not to be d e t e c t e d by a p r e d a t o r , and to d e t e c t the presence of a p r e d a t o r as soon as p o s s i b l e , p r e f e r a b l y , be fore d e t e c t i o n by a p r e d a t o r . I t i s best to a v o i d a chase , which can be a c h i e v e d by h i d i n g , or moving away, so as to i n c r e a s e the d i s t a n c e from 1 70 the p r e d a t o r . The data show t h a t the f i r s t r e a c t i o n of the s choo l i s to s l o w l y t u r n away from the path of the a p p r o a c h i n g p r e d a t o r . As the t h r e a t a p p r o a c h e s , the t u r n r a t e and v e l o c i t y of the s c h o o l i s i n c r e a s e d . The data suppor t s the f i r s t r u l e . Rule 2. I n d i v i d u a l s and s t r a y s from groups are more v u l n e r a b l e to p r e d a t o r s , and s c h o o l s i z e and s t r u c t u r e i s l i m i t e d by the s i g n a l l o s s ; t h e r e f o r e , the group should become more compact in s p a c i n g when a t t a c k e d by p r e d a t o r s . T h i s w i l l a l l o w the e x e c u t i o n of group manoeuvres w i th minimal group d i s i n t e g r a t i o n . The Zm ( minimum mean d i s t a n c e from the c e n t e r of mass ) data for a l l s c h o o l s that were a t t a c k e d showed an i n i t i a l decrease as the p r e d a t o r approached the s c h o o l . T h i s data s u p p o r t s the h y p o t h e s i s tha t s c h o o l i n g f i s h move c l o s e r t o g e t h e r when a t h r e a t i s p e r c e i v e d . Rule 3. The best manoeuvre that the group can p e r f o r m , i f i t d e t e c t s the p r e d a t o r at a d i s t a n c e that enables the manoeuvre to be exe c ute d , i s to t u r n in the d i r e c t i o n of the p r e d a t o r . T h i s enab les the i n d i v i d u a l s to d i s p l a c e around the p r e d a t o r when i t engages the group . T h i s r e s u l t s in p o s i t i o n i n g the p r e d a t o r beh ind and heading away from the group d i r e c t i o n . Before the p r e d a t o r can t u r n a r o u n d , the s e p a r a t i o n d i s t a n c e 171 between prey and p r e d a t o r , and the prey awareness of the t h r e a t , can make f u r t h e r a t t a c k s by the p r e d a t o r u n l i k e l y . T h i s manoeuvre was r a r e l y seen in t h i s i n v e s t i g a t i o n . The p r i m a r y reason for t h i s may have been the l i m i t e d s i z e of the p r e d a t i o n a r e n a . The on ly o c c a s i o n s where the s c h o o l t u r n e d to face the p r e d a t o r were a f t e r s c h o o l r e f o r m a t i o n f o l l o w i n g an a t t a c k . Subsequent p r e d a t o r a t t a c k s were from head on, l e a d i n g the the f o u n t a i n e f f e c t manoeuvre. T h i s suggests tha t t u r n i n g to face a t h r e a t may be a secondary d e f e n s i v e s t r a t e g y a f t e r an i n i t i a l a t t a c k and the t h r e a t i d e n t i f i e d . Sources of e r r o r in t h i s a n a l y s i s stem from three pr imary s o u r c e s . F i r s t , the p r e d a t i o n arena was of l i m i t e d s i z e and d e n s i t y e f f e c t s may be s i g n i f i c a n t . A l t h o u g h on ly those i n t e r a c t i o n s that appear not to have been i n f l u e n c e d by edge e f f e c t s were used i n the d e t a i l e d a n a l y s i s , i t i s v i r t u a l l y i m p o s s i b l e to e l i m i n a t e edge e f f e c t s . The arena w a l l s were w e l l w i t h i n the v i s u a l a c u i t y range of the s p e c i e s used . With l a r g e s c h o o l s , those g r e a t e r than e i g h t i n d i v i d u a l s , the i n d i v i d u a l s would o f t e n t r a v e l next to the w a l l s a f t e r s c h o o l r e - f o r m a t i o n f o l l o w i n g a t t a c k ; or remain m o t i o n l e s s in a c o r n e r . The i n t e r a c t i o n s were c o n s t r a i n e d to two d imens ions for t e c h n i c a l r e a s o n s , and a l t h o u g h s c h o o l i n g behav iour s t u d i e d by P a r t r i d g e (1980,1982) was in three d i m e n s i o n a l s i t u a t i o n s , the f i n d i n g s concur wi th h i s work. The extent of the e f f e c t of the two d i m e n s i o n a l c o n s t r a i n t on escape behav iours i s not known. F i s h 172 however are o p t i m i z e d for r a p i d h o r i z o n t a l movement; the v e r t i c a l d imens ion t h e r e f o r e may not have as much s i g n i f i c a n c e on the d e f e n s i v e maoeuvres per se . The a t t a c k approach by a p r e d a t o r r e l a t i v e to the s c h o o l i n the v e r t i c a l d imens ion may determine the degree of d e f e n s i v e manoeuvres and schoo l s t r u c t u r e . M a t h e m a t i c a l l y , the a n a l y s i s t e c h n i q u e s p r e s e n t e d are a p p l i c a b l e to three d i m e n s i o n s , and f u r t h e r work s h ou l d be aimed at e x p e r i m e n t a l s i t u a t i o n s where t h r e e d imens ions of movement of the s c h o o l and p r e d a t o r can be p r o v i d e d . The second source of e r r o r comes from the f i l m i n g speed used i n t h i s i n v e s t i g a t i o n . For t e c h n i c a l reasons the f a s t e s t f i l m speed a v a i l a b l e was 24 f r a m e s / s e c o n d . O b s e r v a t i o n s of the chase sequences show ev idence t h a t s i g n i f i c a n t i n f o r m a t i o n l o s s may have o c c u r r e d at the f i l m i n g speed u s e d . Subsequent work shou ld be done at f i l m i n g speed of at l e a s t 120 f r a m e s / s e c o n d . The t h i r d source of e r r o r came from the f i l m d i g i t i z i n g a p p a r a t u s . Every attempt was made to d i g i t i z e the p o s i t i o n data of each p r e d a t o r and prey wi th minimum e r r o r , but the r e c o r d i n g s c a l e of the apparatus r e l a t i v e to the s i z e of the f i s h on the f i l m frame may have produced as much as a 7 % p o s i t i o n e r r o r . The l a c k of r e l i a b i l i t y of the equipment wi th r e s p e c t to r e c o r d i n g data to d i s k was a c o n s t a n t nu i sance which r e q u i r e d that each sequence be examined in d e t a i l f or w r i t i n g e r r o r s . Large e r r o r s in p o s i t i o n data were e a s i l y s p o t t e d , but smal l e r r o r s may have escaped u n d e t e c t e d , c o n t r i b u t i n g to the v a r i a n c e 1 73 in the a n a l y s i s . The t o t a l c o n t r i b u t i o n and confound ing of these e r r o r sources i s unknown but are obv ious sources of c o n c e r n . Smoothing t e c h n i q u e s ( Tukey 1979 ) were at tempted but in a l l cases i n f o r m a t i o n was l o s t , e s p e c i a l l y i n t u r n i n g and e v a s i v e s i t u a t i o n s . Prey commonly changed heading by as much as 250 degrees in 1/24 of a second, and smoothing data over such s i t u a t i o n s i s not w o r t h w h i l e . Presumably , at h i g h e r f i l m i n g speeds smoothing may be u s e f u l . 174 LITERATURE CITED A i r w a r - 8 0 : S i m u l a t i o n of modern a i r warfare 1950-1980. S t r a t e g i c S i m u l a t i o n s P u b l i c a t i o n s , NY. A o k i , I 1980. An a n a l y s i s of the s c h o o l i n g behav iour of f i s h : i n t e r n a l o r g a n i z a t i o n and communication p r o c e s s . B u l l . Ocean Res. I n s t . Tokyo no 12. B a r d , Y . 1974 N o n l i n e a r Parameter E s t i m a t i o n . Academic P r e s s , London. B r e d e r , C M . , J r . 1967. On the s u r v i v a l va lue of f i s h s c h o o l s , Z o o l o g i c a 52:25-40. 1976. F i s h s c h o o l s as o p e r a t i o n a l s t r u c t u r e s . F i s h e r y B u l l e t i n 74:471-502. B r o c k , V . E . and R . H . R i f f e n b u r g h 1960. F i s h s c h o o l i n g : a p o s s i b l e f a c t o r in r e d u c i n g p r e d a t i o n . J o u r n . du C o n s e i l 25:307-317. Brown, J . L . 1975. The e v o l u t i o n of b e h a v i o u r . W.W. Norton & Co, NY. C o l l e t , T . S . and M . F . Land 1978. How h o u s e f l i e s compute i n t e r c e p t i o n c o u r s e s . J . Comp. P h y s i o l . 125:191-204. D r e n d e l , L . 1974. M i g K i l l e r s - A irwar over V i e t n a m . S i g n a l P u b l i c a t i o n s . C u r i o , E . 1976. The e tho logy of p r e d a t i o n . S p r i n g e r - V e r l a g , NY, Edmonds, M. 1974. Defense in a n i m a l s . Har low, Essex:Longman Group L t d . E l l i o t , J . 1972. Prey c a p t u r e s t r a t e g i e s of the l a r g e r F i s s i p e d s . Ph . D. T h e s i s , U n i v e r s i t y of B r i t i s h C o l u m b i a . 175 E l l i o t , J.,McTaggart Cowan, I . , H o l l i n g , C.S. 1977. Prey Capture by the A f r i c a n L i o n . Can. J . Z o o l . 55;1811-1828. H a m i l t o n , W.D. 1971. Geometry f o r the s e l f i s h h e r d . J . T h e o r e t . B i o l . 31:295-311. H o l l i n g , C.S. 1965. The f u n c t i o n a l response of p r e d a t o r s t o prey d e n s i t y and i t s r o l e i n mimicry and p o p u l a t i o n r e g u l a t i o n . Mem. Entomol. Soc. Canada 45:1-62. Howland, H.C. 1974. O p t i m a l s t r a t e g i e s f o r p r e d a t o r a v o i d a n c e : the r e l a t i v e importance of speed and m a n o e u v r a b i l i t y . J . Theor. B i o l . 47:333-350. Jander,R. 1975. E c o l o g i c a l a s p e c t s of s p a t i a l o r i e n t a t i o n . An. Review E c o l o g y and S y s t e m a t i c s 6:171-181. Johnson, J.E. 1964. F u l l C i r c l e : T h e t a c t i c s of a i r f i g h t i n g , 1914-1964. B a l l a n t i n e , NY. L i g h t h i l l , J . 1975. M a t h e m a t i c a l b i o f l u i d d y n a m i c s . S o c i e t y f o r i n d u s t r i a l and a p p l i e d mathematics. P h i l a d e l p h i a , Penn. M a r d i a , K.V. 1972. S t a t i s t i c s of d i r e c t i o n a l d a t a . Academic P r e s s , London. M i d d l e t o n , D. 1976. A i r w a r Vietnam. Armour P r e s s , London. M i l l a r , E.A. and V. Dahlem 1978. S u p e r c r u i s e r F i g h t e r a n a l y s i s . NATO a d v i s o r y group Aerospace r e s e a r c h and development. P r o c e e d i n g no 241 ( c l a s s i f i e d ) . M o s t e l l e r , F. and J.W. Tukey 1977. Data a n a l y s i s and r e g r e s s i o n . Addison-Wesley, N.Y. Okubo, A. 1980. D i f f u s i o n and E c o l o g i c a l Problems: M a t h e m a t i c a l Models. S p r i n g e r - V e r l a g , N.Y. Paloheimo, J.E. 1971. On a t h e o r y of s e a r c h . B i o m e t r i c k a , 58:61-75. 176 Partridge, B.L. 1982. The structure and function of f i s h schools. S c i . Amer. 246:114-123. Partridge, B.L. and T.J. Pitcher 1980. The sensory basis of f i s h schools. J. of Comp. Physiol. 135:315-325. Preyss, A.E. 1978. Air Combat. NATO advisory group Aerospace research and development. Proceeding no 241 ( c l a s s i f i e d ) Radakov, D.V. 1973. Schooling in the ecology of f i s h . Wiley, N.Y. Robinson, M.H. 1969. Defenses against v i s u a l l y hunting predators. In Evolutionary Biology , 3rd edi t i o n . T. Dobzhansky, M. Hecht, W. Steere, editors. Appleton-Century-Crofts, N.Y. Shaw, E. 1970. Schooling in fishes: a c r i t i q u e and review. In development and evolution of behaviour. L.A Aronsom et a l Ed. W.H. Freeman, San francisco. Smith, W.J. 1977. The behaviour of communicating: An ethological approach. Harvard University Press Cambridge, Mass. Treisman, M 1975a. Predation and the evolution of gregariousness. I. models for concealment and evasion. Anim. Behav. 32:779-800. 1975b. Predation and the evolution of gregariousness. I I . Economic models for predator-prey interaction. Anim. Behav. 23:801-825. Vine, I. 1971. Risk of vi s u a l detection and pursuit by a predator and the selective advantage of flocking behaviour. J. Theor. B i o l . 30:405-422. 1973. Detection of prey flocks by predators. J. Theor. B i o l . 40:207-210. 1 77 Van 0 1 s t , J . C . and J . R. Hunter 1970. Some a s p e c t s of the o r g a n i z a t i o n of f i s h s c h o o l s . J . F i s h . Res . Board C a n . 27: 1225-1238. Webb, P.W. 1975. A c c e l e r a t i o n performance of rainbow t r o u t ( Salmo g a i r d n e r i ) and green s u n f i s h ( . Lepomis c y a n e l l u s ) . J . E x p . B i o l . 63:451-465. Weihs , D. 1973. Hydromechanics of f i s h s c h o o l i n g . Nature 241: 290-291. 178 APPENDIX 1 D e r i v a t i o n o f t h e I n t e r c e p t i o n C o e f f i c i e n t s . A t any t i m e t , t h e p r e d a t o r p o s i t i o n can be d e s c r i b e d as X = X + B cos 0 i . ( A M ) Yt + 1 = Y t + B s i n G i t and t h e p r e y p o s i t i o n as X! = X' + A c o s 0 2 (A1.2) Y t + 1 " Y t + A S i n 0 2 t For t h e p r e d a t o r t o c a p t u r e t h e p r e y , t h e i r p a t h s s h o u l d c r o s s s u c h t h a t x t = x ; Y = y' (A1.3) t t A t t h i s p o i n t Xfc + B cos 0 i t = X' + A c o s 0 2 (A1.4) Y t + B s i n 0 i t = V + A s i n 0 2 (A1.5) To s o l v e f o r A ; (A1.4) * s i n 0 i X s i n G , + BcosGi s i n G i = X ' s i n Q i + A c o s G 2 s i n Q i (A1.6) (A1.5) * c o s 0 i Y t c o s 0 i t + B s i n G i t c o s 0 i t = Y ' c o s 0 i t + A s i n 0 2 t c o s 0 i f c (A1.7) (A1.6) - (A1.7) X s i n 0 i - Y..COS01 = X ' s i n G i - Y ' c o s 0 i + A c o s 0 2 g i n 0 i - A c o s 0 i s i n 0 2 ^ (A1.8) t t t t t t t • t t t t t X t s i n Q i t - X ^ s i n G i t + Y|.cosQ l t - Y t c o s Q i t = s i n ( 0 i - 0 2 t ) A (A1.9) T h e r e f o r e A t = { ( X t ~ X t } S i n 0 1 t + ( Y t ~ Y t } C O S G l t } 1 { s i n ( 0 1 t ~ 0 2 t ) > ( A L I O ) B i s s i m i l a r l y s o l v e d by ( A l . 4 ) * s i n 0 2 , (A1.5) * c o s 02 find s u b t r a c t i o n . t = { ( X t ~ X t } S i n ° 2t + ( Y t " Y t } C O S ° 2 t } 1 { s i n ( 0 2 t - Q i t > > ( A l . l l ) B 179 APPENDIX 2 D e r i v a t i o n o f E q u a t i o n s f o r Time a t C l o s e s t A p p r o a c h and D i s t a n c e a t C l o s e s t Approach F o r each time i n t e r v a l t , t h e p o s i t i o n o f the p r e d a t o r can be d e s c r i b e d as Xt + i = x t + V Y t + i = Y t + V ( A 2 , 1 ) where i s t h e v e l o c i t y component i n t h e X d i r e c t i o n and i s t h e v e l o c i t y component i n t h e Y d i r e c t i o n . S i m i l a r l y , t h e p r e y p o s i t i o n may be r e p r e s e n t e d as x;+ 1 = x; + u 2t Y i + i = Y t + v 2 t A t t i m e t , the d i s t a n c e between p r e d a t o r and p r e y i s (A2.2) D t = ( ( X t " X t ) 2 + ( Y t ~ Y t ) 2 } ( A 2 ' 3 ) E x p a n d i n g e q u a t i o n (A2.3) D 2 = { ( X t - X') + ( U x - U 2 ) t } 2 + { ( Y t - Y') + ( V 1 - V 2 ) t } 2 (A2.4) Ex p a n d i n g e q u a t i o n (A2.4) D t = ( X t ~ X t ) 2 + 2 { ( X t ~ X t ) ( ( U l ~ U 2 ) t ) } + { ( U 1 " U 2 ) 2 t 2 } + ( Y t " Y t ) 2 + 2 { ( Y t Y ' ) ( ( V 1 - V 2 ) t ) } + -{(Vj - V 2 ) 2 t 2 } (A2.5) A t t h e p o i n t o f C l o s e s t A p p r o a c h , d ( D 2 ) / d t = 0.0. From e q u a t i o n (A2.5) d ^ 2 ) - ( 2 { ( X t - X p ( U 1 - U 2) + ( Y t - Y ^ ) ( V 1 - V 2 ) } t 2 t { ( U 1 - U2)2+(V^V^2} (A2.6) When d ( D 2 ) / d t = 0 . 0 the Time t o C l o s e s t Approach i s (-(X - X ' ) ( U - U ) - (Y - Y')(V - V ) } t = (A2.7) { (vx - v 2) 2 + (u1 - u 2) 2 } The D i s t a n c e a t C l o s e s t A p p r o a c h i s then c a l c u l a t e d by s u b s t i t u t i n g t i n e q u a t i o n s (A2.1) and (A2.2) and s o l v i n g f o r D . 

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