UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Prey avoidance learning and the functional response of predators Dill, Lawrence Michael 1972

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1972_A1 D54.pdf [ 5.5MB ]
Metadata
JSON: 831-1.0093102.json
JSON-LD: 831-1.0093102-ld.json
RDF/XML (Pretty): 831-1.0093102-rdf.xml
RDF/JSON: 831-1.0093102-rdf.json
Turtle: 831-1.0093102-turtle.txt
N-Triples: 831-1.0093102-rdf-ntriples.txt
Original Record: 831-1.0093102-source.json
Full Text
831-1.0093102-fulltext.txt
Citation
831-1.0093102.ris

Full Text

PREY AVOIDANCE LEARNING AND THE FUNCTIONAL RESPONSE OF PREDATORS by LAWRENCE M. DILL BSc , U n i v e r s i t y o f B r i t i s h Columbia , 1966 MSc, U n i v e r s i t y o f B r i t i s h Columbia , 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department o f Zoology We accept t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA JULY 1972 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . LAWRENCE M. DILL D e p a r t m e n t o f ZOOLOGY The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8 , Canada i i ABSTRACT The research attempts to determine the e f f e c t on the number o f prey eaten by predators o f the a d d i t i o n o f the component "avoidance l e a r n i n g by prey" to a computer model o f the p r e d a t i o n process developed by H o l l i n g (1966). G e n e r a l i t y was r e t a i n e d by c o n c e n t r a t i n g upon o n l y a few aspects o f the p r e y ' s b e h a v i o u r , p a r t i c u l a r l y i t s d i s t a n c e o f r e a c t i o n to an approaching p r e d a t o r . The zebra danio (Brachydanio r e r i o ) , a smal l f r e s h w a t e r f i s h , was used as an analogue o f a general v e r t e b r a t e p r e y . P r e d a t o r s used were p l e x i g l a s s models , f i l m s o f approaching o b j e c t s , and largemouth bass ( M i c r o p t e r u s s a l m o i d e s ) . I t was shown t h a t the r e a c t i v e d i s t a n c e o f zebra danios c o u l d be p r e d i c t e d from the e q u a t i o n : where V = p r e d a t o r approach v e l o c i t y S = p r e d a t o r diameter k = t h r e s h o l d r a t e o f change o f angle subtended at the eye o f the prey by the p r e d a t o r (= .43 r a d / s e c ) . Thus , r e a c t i v e d i s t a n c e i n c r e a s e d w i t h both p r e d a t o r s i z e and v e l o c i t y . Escape v e l o c i t y was independent o f these same parameters . The t h r e s h o l d r a t e o f change o f v i s u a l a n g l e , and hence the r e a c t i v e d i s t a n c e , was not a f f e c t e d by prey hunger. However, r e a c t i v e d i s t a n c e i n c r e a s e d w i t h num-ber o f p r e v i o u s e x p e r i e n c e s , a p p a r e n t l y because o f secondary c o n d i t i o n i n g to o t h e r f e a t u r e s o f the p r e d a t o r , such as shape and c o l o r . The i n c r e a s e d prey r e a c t i v e d i s t a n c e d'je to exper ience was shown to i n c r e a s e p r e d a t o r p u r s u i t time and h y p o t h e s i z e d to decrease p r e d a t o r p u r s u i t tu s u c c e s s . These r e l a t i o n s h i p s were expressed m a t h e m a t i c a l l y and b u i l t i n t o H o l l i n g ' s model o f the p r e d a t i o n p r o c e s s , a long w i t h an e q u a t i o n c a u s i n g r e a c t i v e d i s t a n c e to i n c r e a s e f o l l o w i n g an u n s u c c e s s f u l a t t a c k . S i m u l a t i o n was used to e x p l o r e the consequences o f these a d d i t i o n s . The c a p a b i l i t y o f l e a r n i n g s u b s t a n t i a l l y i n c r e a s e d the p r e y ' s p r o b a b i l i t y o f s u r v i v i n g subsequent a t t a c k . A d d i t i o n o f the avoidance l e a r n i n g com-ponent caused d e c l i n e s i n the p r e d a t o r ' s f u n c t i o n a l responses to both prey and p r e d a t o r d e n s i t y . The new component was a l s o suggested to dec-rease the p r e d a t o r ' s numerical response to prey d e n s i t y and to i n c r e a s e the p r o b a b i l i t y o f s t a b i l i t y i n a p r e d a t o r - p r e y i n t e r a c t i o n . iv TABLE OF CONTENTS TITLE PAGE ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS I GENERAL INTRODUCTION II GENERAL METHODS AND MATERIALS 1 The Prey 2 The P r e d a t o r 3 The T e s t i n g Apparatus a The p r e d a t i o n arena b The model p r e d a t o r c The c inematographic p r e d a t o r 4 A n a l y s i s o f F i lms I I I THE AVOIDANCE STIMULUS AND RESPONSE 1 I n t r o d u c t i o n 2 Theory and Mathematical Model • 3 Methods and R e s u l t s a S t u d i e s w i t h model p r e d a t o r s ( i ) t e s t o f the hypothes is o f a t h r e s h o l d doc/dt ( i i ) e f f e c t o f model shape ( i i i ) e f f e c t o f prey s i z e on t h r e s h o l d d<x/dt ( i v ) e f f e c t o f o r i e n t a t i o n angle on t h r e s h o l d dot/dt (v) escape v e l o c i t y as a f u n c t i o n o f r e a c t i v e d i s t a n c e , b S t u d i e s w i t h the c inematographic p r e d a t o r c P r e d a t o r - p r e y i n t e r a c t i o n s i n the p r e d a t i o n arena ( i ) agreement w i t h model p r e d a t o r r e s u l t s ( i i ) t h r e s h o l d dot/dt o f schooled prey 4 D i s c u s s i o n 5 C o n c l u s i o n s IV CHANGE OF dtt/dt THRESHOLD WITH EXPERIENCE 1 I n t r o d u c t i o n 2 Methods a Model p r e d a t o r b Cinematographic p r e d a t o r V Page 3 R e s u l t s 47 a Model p r e d a t o r 47 ( i ) change i n response w i t h exper ience 47 ( i i ) g e n e r a l i z a t i o n over model s i z e 50 b Cinematographic p r e d a t o r 51 ( i ) l e a r n i n g 51 ( i i ) c o n t r o l 53 4 D i s c u s s i o n 54 5 C o n c l u s i o n s 64 V THE EFFECT OF HUNGER ON THE THRESHOLD RATE OF CHANGE OF VISUAL ANGLE 6 5 1 I n t r o d u c t i o n 65 2 Methods * 66 3 R e s u l t s 69 a Hunger as a f u n c t i o n o f d e p r i v a t i o n time 69 b T h r e s h o l d dN/dt as a f u n c t i o n o f hunger 73 4 D i s c u s s i o n 7 5 5 C o n c l u s i o n s 80 VI ADDITION OF THE AVOIDANCE LEARNING COMPONENT TO A GENERALIZED . • MODEL OF THE PREDATION PROCESS 81 1 I n t r o d u c t i o n 81 2 Fi lmed I n t e r a c t i o n s Between P r e d a t o r s and Prey 85 a Methods 85 b R e s u l t s and d i s c u s s i o n 86 3 The S i m u l a t i o n Model 96 4 R e s u l t s and D i s c u s s i o n 105 5 C o n c l u s i o n s 116 LITERATURE CITED 119 vi LIST OF TABLES I P h y s i c a l dimensions (cm) o f the largemouth bass used i n the experiments I I Mean r e a c t i v e d i s t a n c e (cm) o f n a i v e danios o f d i f f e r e n t s i z e s and v e l o c i t i e s I I I E f f e c t o f model shape on r e a c t i v e d i s t a n c e o f naive zebra danios IV T h r e s h o l d dw/dt (k) a n d/3 - . O / k ) f o r two s i z e c l a s s e s o f na ive danios V Rates o f change o f v i s u a l angle (dc(/dt f i ^ ) at the t imes o f response o f danios to the c inematographic p r e d a t o r . VI Rates o f change o f v i s u a l angle ( d < * / d t t o t a l ) a t the times o f response o f danios to the c inematographic p r e d a t o r . VII Data from f i l m e d o b s e r v a t i o n s o f largemouth bass - na ive zebra danio i n t e r a c t i o n s V I I I Summary o f data on t h r e s h o l d do(/dt o f zebra danios to v a r i o u s p r e d a t o r s IX Mean observed and p r e d i c t e d r e a c t i v e d i s t a n c e s o f zebra danios to largemouth bass o f two s i z e s X Comparison o f responses o f t r a i n e d danios to model p r e d a t o r s o f two s i z e s XI Comparison o f the f r i g h t responses o f the c o n t r o l danios to the c inematographic p r e d a t o r before and a f t e r 10 days i n the exper imenta l aquarium X I I Mean and s t a n d a r d e r r o r o f the weight (grams) o f food eaten by zebra danios a f t e r d i f f e r e n t p e r i o d s o f d e p r i v a t i o n X I I I Hunger and t h r e s h o l d r a t e o f change o f v i s u a l angle a f t e r v a r i o u s t imes o f food d e p r i v a t i o n XIV The components o f p r e d a t i o n and t h e i r subcomponents as concep-t u a l i z e d by H o l l i n g (1963, 1965, 1966). XV C a l c u l a t e d c o r r e l a t i o n c o e f f i c i e n t s f o r the b e h a v i o u r a l p a r a -meters o f the b a s s - d a n i o i n t e r a c t i o n s v i i Page XVI S t r i k e success (SS) f o r bass s t r i k i n g a t danios from d i s -tances l e s s than o r g r e a t e r than 6.4 cm (mean DS observed) 93 XVII The meanings and values o f a l l parameters i n the s i m u l a t i o n model 104 v i i i LIST OF FIGURES Page 1 Diagrammatic r e p r e s e n t a t i o n o f the p r e d a t i o n arena 6 2 The model p r e d a t o r suspended from a p l e x i g l a s s c a r r i a g e 8 3 Apparatus used f o r p r e s e n t a t i o n o f the model p r e d a t o r , i n c l u d -i n g a p l a n view o f the prey h o l d i n g chamber 8 4 A . Apparatus used f o r p r e s e n t a t i o n o f the c inematographic p r e d a t o r 11 B. T e s t i n g chambers 5 Schematic r e p r e s e n t a t i o n o f the eye o f an observer and the v i s u a l angles (cx^CX-j) subtended by an o b j e c t o f s i z e S a t d i s t a n c e s D Q and D-j. 16 6 E f f e c t o f d i s t a n c e between o b j e c t and o b s e r v e r on the angle subtended by the o b j e c t a t the o b s e r v e r ' s eye (<*). 16 7 E f f e c t o f model s i z e and v e l o c i t y on the r e a c t i v e d i s t a n c e o f naive zebra danios 19 2 2 8 R e g r e s s i o n o f (4D + S )/4S on model v e l o c i t y 19 9 Method o f b l o c k i n g the data by angle o f o r i e n t a t i o n r e l a t i v e to the d i r e c t i o n o f the approaching model . 24 10 . Values o f dw/dt w i t h time f o r f o u r danios responding more than once to the c inematographic p r e d a t o r . The values are c a l c u l a t e d both w i t h o u t r e f e r e n c e to the f i s h ' s v e l o c i t y , and i n c l u d i n g the f i s h ' s v e l o c i t y as a component 28 11 E f f e c t o f e x p e r i e n c e o f the model p r e d a t o r on t h r e s h o l d dw/dt o f zebra danios 49 12 E f f e c t o f e x p e r i e n c e on mean t o t a l escape v e l o c i t y , and escape v e l o c i t y d i r e c t e d 180 away, o f danios responding t o the model p r e d a t o r 49 13 E f f e c t o f e x p e r i e n c e o f the c inematographic p r e d a t o r on t h r e s h -o l d dc*/dt o f zebra danios 52 14 E f f e c t o f exper ience on mean t o t a l escape v e l o c i t y 5 and escape v e l o c i t y d i r e c t e d 180 away, o f danios responding to the c inematographic p r e d a t o r 52 15 E f f e c t o f d e p r i v a t i o n time on hunger (mg o f food accepted) i n the zebra danio 70 i x Page 16 Hunger data transformed to t e s t e q u a t i o n (25) i n the t e a t 72 17 E f f e c t o f hunger on t h r e s h o l d do/dt o f danios responding to the c inematographic p r e d a t o r 74 18 Diagrammatic r e p r e s e n t a t i o n o f the p u r s u i t o f a prey by a p r e d a t o r 84 19 R e l a t i o n s h i p between observed approach t ime and p r e d i c t e d approach time f o r the b a s s - d a n i o i n t e r a c t i o n s 87 20 Regress ion o f observed c l o s u r e time on p r e d i c t e d c l o s u r e t ime f o r the b a s s - d a n i o i n t e r a c t i o n s 89 21 Observed r e l a t i o n s h i p between danio r e a c t i v e d i s t a n c e and bass c l o s u r e t i m e , and the p r e d i c t e d r e l a t i o n s h i p assuming constant escape v e l o c i t y , p u r s u i t v e l o c i t y , and s t r i k e d i s t a n c e 91 22 C o r r e l a t i o n between danio r e a c t i v e d i s t a n c e and bass s t r i k e d i s t a n c e 94 23 Flow diagram o f s u b r o u t i n e CHASE 98 24 Flow diagram o f s u b r o u t i n e SUMRY 101 25 Flow diagram o f s u b r o u t i n e ADCOM 102 26 S i m u l a t i o n o f the f u n c t i o n a l response o f p r e d a t o r s to prey w i t h and w i t h o u t the a b i l i t y to l e a r n 106 27 E f f e c t o f v a r i o u s b e h a v i o u r a l and environmental parameters on the p r o b a b i l i t y o f capture o f prey w i t h d i f f e r e n t amounts o f p r e v i o u s e x p e r i e n c e , as s i m u l a t e d by the model 110 28 S i m u l a t i o n o f the d e n s i t y o f prey a t t a c k e d as a f u n c t i o n o f prey d e n s i t y , f o r cases w i t h and w i t h o u t prey l e a r n i n g 111 29 S i m u l a t i o n o f the number o f prey a t t a c k e d per p r e d a t o r per day as a f u n c t i o n o f p r e d a t o r d e n s i t y , f o r cases w i t h o u t prey l e a r n i n g and w i t h l e a r n i n g r a t e s o f . 5 0 and .75 112 30 E q u i l i b r i u m e f f e c t s o f the f u n c t i o n a l response to prey d e n s i t y w i t h and w i t h o u t the prey l e a r n i n g component 114 X ACKNOWLEDGEMENTS I s h o u l d l i k e to express my s i n c e r e g r a t i t u d e to a number o f people whose hard work a l l o w e d t h i s p r o j e c t to reach c o m p l e t i o n . M e s s r s . Frank Maurer and J i m Duncan p r o v i d e d much needed t e c h n i c a l a s s i s t a n c e , p a r t i c u l a r l y i n the area o f apparatus c o n s t r u c t i o n . E x p e r t i s e i n com-p u t e r programming was p r o v i d e d by Miss Sandra Buckingham and M e s s r s . Ian Banks and Hok Woo. Mr. N e i l G i l b e r t and D r s . C a r l W a l t e r s , Tom N o r t h c o t e , Robin L i l e y and John Krebs c r i t i c a l l y commented upon the r e s e a r c h a t i t s v a r i o u s s t a g e s . The bass were o b t a i n e d from the C a l i f -o r n i a Department o f F i s h and Game through the c o u r t e s y o f M r . Leonard F i s k . M r s . L . F i l t e a u typed the t h e s i s . Above a l l , however, I s h o u l d l i k e t o thank my s u p e r v i s o r , 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 support d u r i n g the past three y e a r 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 p o s s i b l e . I GENERAL INTRODUCTION An e f f e c t i v e t h e o r e t i c a l framework f o r t i le management o f animal popu-l a t i o n s can o n l y be based upon a thorough understanding o f the e c o l o g i c a l processes by which the p o p u l a t i o n s i n t e r a c t w i t h the o t h e r components o f t h e i r ecosystems. S i n c e p r e d a t i o n i s an almost u n i v e r s a l e c o l o g i c a l p r o -c e s s , an unders tanding o f i t s mechanisms w i l l have c o n s i d e r a b l e p r a c t i c a l v a l u e . H o l l i n g (1965, 1966) made a s i g n i f i c a n t conceptual advance i n the study o f e c o l o g i c a l processes w i t h the i n t r o d u c t i o n o f " e x p e r i m e n t a l com-ponents a n a l y s i s . " The process o f p r e d a t i o n , f o r example, was conceived as being s t r u c t u r e d from a number o f d i s c r e t e components.- Some o f these ( e . g . t ime a v a i l a b l e f o r s e a r c h i n g ) are c h a r a c t e r i s t i c o f a l l examples o f p r e d a t i o n and are termed " b a s i c " ; o thers [e.g. l e a r n i n g by the p r e d a t o r ) are c h a r a c t e r i s t i c o f o n l y some examples o f the process and are termed " s u b s i d i a r y " . These components and t h e i r i n t e r a c t i o n s may be s t u d i e d e x p e r i m e n t a l l y , one a t a t i m e , and then recombtned m a t h e m a t i c a l l y to p r o -duce a s i m u l a t i o n model whose p r e d i c t i o n s may be t e s t e d a g a i n s t the behav-i o u r o f r e a l p r e d a t o r - p r e y i n t e r a c t i o n s . Such " i n t i m a t e 1 wedding" o f e x p e r i m e n t a t i o n and computer s i m u l a t i o n produces.models w h i c h , i n theory a t l e a s t , are r e a l i s t i c , h o l i s t i c , general and p r e c i s e , and whose p r e -d i c t i v e u t i l i t y has a l r e a d y been demonstrated ( H o l l i n g , 1966). One s u b s i d i a r y component o f the p r e d a t i o n process w h i c h has not y e t been e x p e r i m e n t a l l y examined and added to the model i s t h a t o f "avoidance l e a r n i n g by p r e y . " P r e v i o u s s t u d i e s o f p r e d a t o r avoidance have been l a r g e l y 2 anecdota l and those few e x p e r i m e n t a l s t u d i e s which have been conducted do not f i t i n t o any cohes ive t h e o r e t i c a l framework. I t i s the aim o f t h i s s tudy to examine avoidance l e a r n i n g i n the context o f a p a r t i c u l a r t h e o r e t i c a l framework, to examine the i n t e r a c t i o n s between t h i s component and others a l r e a d y examined, to add the new component to the s i m u l a t i o n model , and to examine the consequences o f i t s a d d i t i o n . The b a s i c p h i l o s o p h y u n d e r l y i n g the r e s e a r c h i s t h a t "however i n t r i g u i n g and nec-essary the a n a l y s i s o f an i n d i v i d u a l fragment i t s va lue i s d r a s t i c a l l y l i m i t e d i f there i s no u n i f y i n g framework to p r o v i d e i n s i g h t i n t o the a c t i o n and i n t e r a c t i o n o f a l l the fragments" ( H o l l i n g , 1964). 3 II GENERAL METHODS ,AND MATERIALS 1 The Prey The prey used throughout were a d u l t zebra d a n i o s , Brachydanio  r e r i o , a s m a l l f r e s h w a t e r c y p r i n i d n a t i v e to I n d i a . They are s c h o o l -i n g f i s h e s w h i c h , a c c o r d i n g to S t e r b a CT962) i n h a b i t both s t a n d i n g and f l o w i n g w a t e r s . S i n c e i t was des i rab le f o r some o f the experiments t h a t the prey had no p r i o r e x p e r i e n c e w i t h p r e d a t o r s , o r even wtt f i l a r g e moving o b j e c t s , a l l o f the danios used i n these experiments were l a b o r a t o r y r e a r e d . A d u l t danios were a l lowed to spawn i n 10 g a l . a q u a r i a over a bottom o f a r t i f i c i a l v e g e t a t i o n . The spawners were removed p r i o r to the h a t c h i n g o f the f r y , and the v e g e t a t i o n s h o r t l y a f t e r . The f i s h were grown to a l e n g t h o f about 20 mm. before being t r a n s f e r r e d to o t h e r h o l d i n g f a c i l i t i e s , a p p r o x i m a t e l y t h r e e months a f t e r h a t c h i n g . For the purposes o f t h i s s t u d y , these danios were c o n s i d e r e d to be n a i v e . For o t h e r e x p e r i m e n t s , the requirement o f n a i v e t y c o u l d be r e -l a x e d . The danios used i n these experiments were o b t a i n e d from t r o p i -c a l f i s h h a t c h e r i e s o r l o c a l aquarium shops. These f i s h had a l s o been reared i n the absence o f a d u l t s , but i n l a r g e outdoor ponds. The p o s s i b i l i t y t h a t they had e x p e r i e n c e d p r e d a t i o n , t h e r e f o r e , c o u l d not be e n t i r e l y r u l e d o u t . These danios were c o n s i d e r e d to be " n o n - n a i v e " . 4 2 The P r e d a t o r When r e a l p r e d a t o r s were u s e d , these were largejnouth black, b a s s , M i c r o p t e r u s salmotdes (Lacepe.de) o b t a i n e d from a C a l i f o r n i a h a t c h e r y . The s i z e s o f the two bass used are shown i n Table I . Table I P h y s i c a l dimensions (cm) o f the largemouth bass used i n the e x p e r i m e n t s . A l l measurements o b t a i n e d from f i l m s . Height and w i d t h as seen i n f r o n t v iew. R A C C * OVERALL u r T r u T i IT n-pij HEIGHT/ HEIGHT/ WIDTH/ BAbb# LENGTH H h l b H 1 W i U I H WIDTH LENGTH LENGTH 1 14.3 3.24 1.87 1.7 0 .23 .13 2 20.1 4.50 2.65 1.7 0.22 .13 The bass were h e l d s e p a r a t e l y between experiments and were fed a d i e t c o n s i s t i n g almost e x c l u s i v e l y o f zebra d a n i o s . Occas-i o n a l l y , meals c o n s i s t e d o f o t h e r smal l f i s h (gupptes , m o l l i e s , c o n v i c t c i c h l i d s , pumpkinseed s u n f i s h , y e l l o w perch^chopped e a r t h -worms, meal worms, and commercial f i s h food moistened and r o l l e d i n t o smal l p e l l e t s . 5 3 The Apparatus Three s p e c i a l i z e d p ieces o f apparatus were used i n the e x p e r i -ments. To a v o i d r e p e t i t i o n , g e n e r a l i z e d d e s c r i p t i o n s are g iven h e r e . Methodology s p e c i f i c to a p a r t i c u l a r experiment i s d e t a i l e d i n the a p p r o p r i a t e s e c t i o n . a) 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 Q . 8 3 x 2.44m) aquarium tn which b a s s - d a n i o i n t e r a t i o n s were observed and photographed. The w a l l s and bottom o f the arena were u n i f o r m l y w h i t e to p r o v i d e maximum c o n t r a s t between f i s h and background f o r f i l m i n g purposes . The p r e d a t o r and prey c o u l d be i n t r o d u c e d to the tank d i r e c t l y or through s l i d i n g doors from h o l d i n g a q u a r i a a t one end. Viewing and f i l m i n g were done from the s i d e through a l a r g e m i r r o r mounted at a 45° ang le . Us ing a w i d e - a n g l e (10mm) lens on a Bolex camera, i t was p o s s i b l e to r e c o r d the e n t i r e tank area on one frame o f 16 mm f i l m . F i l m i n g was conducted a t 16 f r . / s e c - w i t h a l e n s - t o - w a t e r s u r f a c e d i s t a n c e o f 4.5m a t f 2 . 8 , w i t h P l u s - X r e v e r s a l f i l m pushed one s top i n p r o c e s s i n g . Q u a r t e r - r o u n d panels o f w h i t e p l e x i g l a s s were p l a c e d i n each corner o f the tank so t h a t the prey 'would not become trapped by the bass i n the 90° c o r n e r s , as had o c c u r r e d i n p r e l i m -i n a r y e x p e r i m e n t s . Water l e v e l was m a i n t a i n e d a t 10cm F i g u r e 1 Diagrammatic r e p r e s e n t a t i o n o f the p r e d a t i o n a r e n a . A l l dimensions expressed as m. 6 7 to keep the i n t e r a c t i o n e s s e n t i a l l y t w o - d i m e n s i o n a l , and to make f i l m i n g e a s i e r . The water was m a i n t a i n e d at 23C by means o f c i r c u l a t i n g heated a i r (25c) i n the l a b o r a t o r y . S i d e -l i g h t i n g was p r o v i d e d by banks o f f l u o r e s c e n t l i g h t s l o c a t e d behind each o f the 2.44m opaque p l e x i g l a s s s i d e s , thus e l i m -i n a t i n g the problem o f s u r f a c e r e f l e c t i o n . b) The model p r e d a t o r For some e x p e r i m e n t s , i t was r e q u i r e d t h a t a s t i m u l u s o f c o n t r o l l e d s i z e and v e l o c i t y be presented to the d a n i o s . A r t i f i c i a l " p r e d a t o r s " o f two t y p e s , model and cinemato-g r a p h i c , were designed f o r t h i s purpose. The model p r e d a t o r apparatus i s shown d i a g r a m m a t i c a l l y i n F i g s . 2 & 3. Model v e l o c i t y was c o n t r o l l e d by an e l e c t r i c motor and a v a r i a b l e speed t r a n s f o r m e r , and had a range o f 11.6 to 108.5 cm/sec. Models o f d i f f e r e n t s i z e and shape c o u l d be a t tached to the overhead c a r r i a g e ( c o n s t r u c t e d o f c l e a r p l e x i g l a s s ) w i t h o u t s i g n i f i c a n t l y a f f e c t i n g the v e l o -c i t y . The danio to be t e s t e d was p l a c e d i n the c i r c u l a r chamber 15 m i n . p r i o r to the experiment and a c c l i m a t e d to the n o i s e o f the motor running a t top speed. The chamber s e r v e d to c o n f i n e the f i s h and to keep v i b r a t o r y s t i m u l i to a minimum. F i g u r e 2 The model p r e d a t o r suspended from a p l e x i g l a s s c a r r i a g e . A l l d i s t a n c e s i n cm. F i g u r e 3 Apparatus used f o r p r e s e n t a t i o n o f the model p r e d a t o r , i n c l u d i n g a p l a n view o f the prey h o l d i n g chamber. A l l d i s t a n c e s i n cm. Legend: 1 C a r r i a g e c o n s t r u c t e d o f .64 cm p l e x i g l a s s 2 Screws f o r attachment o f rope 3 White n y l o n rope 4 C u r t a i n t r a c k r a i l on dexion support 5 B a l l race wheels covered w i t h foam rubber 6 M o d e l , c o n s t r u c t e d o f p l e x i g l a s s and p a i n t e d b l a c k 7 P u l l e y s 8 P l e x i g l a s s model s u p p o r t ( .64 cm p l e x i g l a s s ) 9 M i r r o r s 10 Prey h o l d i n g chamber 11 A x l e o f e l e c t r i c motor 8 9 P r e l i m i n a r y experiments i n d i c a t e d t h a t f i s h a c c l i m a t e d f o r 15 m i n . behaved the same as those a c c l i m a t e d f o r 23 h r s . During t h i s a c c l i m a t i o n p e r i o d , the model was s i t u a t e d a t the o p p o s i t e end o f the p r e d a t i o n a r e n a , a p p r o x i m a t e l y 2.1 m away. A f t e r the 15 m i n . p e r i o d , the a x l e was reconnected to the e l e c t r i c motor and the model moved down the l e n g t h o f the tank toward the p r e y . The prey was always s t a t i o n a r y when the p r e d a t o r began moving and t h e r e was no evidence o f r e a c t i o n to the motor noise at the i n i t i a t i o n o f the t e s t . Some f i s h would n o t , f o r one reason o r a n o t h e r , m a i n t a i n a s t a t i o n a r y p o s i t i o n between the m i r r o r s p r i o r to the t e s t . These were d i s c a r d e d and r e p l a c e d . The r e a c t i o n s o f the prey were recorded from 0.84m above t h e ' water s u r f a c e w i t h a m o t o r i z e d Bolex 16 mm camera a t 16 frames/ sec and f l . 6 . P l u s - X r e v e r s a l f i l m was used. c) The c inematographic p r e d a t o r A s h o r t motion p i c t u r e o f an approaching o b j e c t was produced i n o r d e r t h a t a s o l e l y o p t i c a l s t i m u l u s c o u l d be presented to the d a n i o s . I t was made by t a k i n g 120 s i n g l e frame photo-graphs o f an 8mm diameter dot on a w h i t e background from . v a r y i n g d i s t a n c e s on an o p t i c a l bench CBolex T i t l e r ) . The f i r s t frame was exposed a t a d i s t a n c e o f 681 mm and the l a s t at 205mm, w i t h exposures every 4mm between these extremes. 1 0 The s h u t t e r a p e r t u r e and d i s t a n c e s e t t i n g s on the Bolex 16 mm camera were adjusted a t i n t e r v a l s a long the bench to p r o -v i d e c o n s t a n t image i l l u m i n a t i o n and f o c u s . The frame num-ber was w r i t t e n above the o b j e c t and photographed a long w i t h i t . I t appeared i n the upper p o r t i o n o f each frame o f the f i l m . When the sequence was presented to human observers a t a speed o f 24 f rames/sec , they p e r c e i v e d i t as an o b j e c t app-r o a c h i n g them a t a c o n s t a n t v e l o c i t y . A l though no data are a v a i l a b l e on the f l i c k e r f u s i o n frequency o r moment span o f the danio v i s u a l system, i t i s assumed t h a t they a l s o p e r c e i v e d a smooth approach. The p e r s i s t e n c e t ime o f the r e t i n a o f the c y p r i n i d Phoxinus l a e v i s (von S c h i l l e r , 1934) and the c r i t i c a l f l i c k e r frequency o f the s u n f i s h Lepomis (Wolf and Z e r r a h n - W o l f , 1936) are both very s i m i l a r to those o f man. T h i s " c i n e m a t o g r a p h i c p r e d a t o r " was presented to i n d i v i d u a l prey i n one o f s i x s m a l l chambers c o m p r i s i n g the e x p e r i m e n t a l aquarium ( F i g 4 ) . The water system was common to the s i x , but each was i n d i v i d u a l l y f i l t e r e d by a s u b - g r a v e l f i l t e r . Opaque p l e x i g l a s s p a r t i t i o n s separated the compartments and e l i m i n a t e d v i s u a l c o n t a c t between f i s h . Each chamber was 15 cm long by 10cm wide and was f i l l e d to a depth o f 7.5 cm F i g u r e 4 A . Apparatus used f o r p r e s e n t a t i o n o f the c inematographic p r e d a t o r B t e s t i n g chambers. A l l d i s t a n c e s expressed i n cm. 11 projector (24 fr/sec) 1 -75-lamp 30 lamp ^ 16 mm Bolex j camera 7 port lamp 50 b o a r d , tracing ^ paper ^ - 1 5 -21 one-way mirror 7.5 B 10-opa que parti ions •filter 12 over a bottom o f coarse y e l l o w g r a v e l . F i s h above t h i s s u b -s t r a t e p r o v i d e d maximum c o n t r a s t when f i l m e d from above. The water was m a i n t a i n e d a t 23C by h e a t i n g the a i r tn the plywood box e n c l o s i n g the chambers. L i g h t i n g was p r o v i d e d from above and from the s i d e by t h r e e f l u o r e s c e n t lamps. The f i l m s t r i p presented to the danios c o n s i s t e d o f 25 sec o f c l e a r l e a d e r to accustom them to p r o j e c t i o n n o i s e , 2 sec (48 frames) o f the o b j e c t f i l m e d a t 681 mm, and 5 sec (120 frames) o f the approaching o b j e c t . This was p r o j e c t e d from a d i s t a n c e o f 75 cm onto a p i e c e o f t r a c i n g paper t i g h t l y taped to the w a l l o f the chamber. The frame numbers were p r o j e c t e d on the t i l t e d board i n f r o n t o f the aquarium, A Bolex 16 mm camera w i t h a 10 mm lens mounted 50 cm above the water s u r f a c e recorded the behaviour o f the f i s h and the frame number s i m u l t a n e o u s l y . F i l m i n g was conducted at 32 f r / s e c at f 4 . 0 . 4 A n a l y s i s o f the Fi lms A l l f i l m s were examined on a Vanguard Motion A n a l y z e r (Model M-16 CW). P o s i t i o n s , v e l o c i t i e s , and angles o f o r i e n t a t i o n o f the p r e y , and i n some cases the p r e d a t o r , were o b t a i n e d by measuring d i r e c t l y on the p r o j e c t i o n screen o r by punching the x , y c o o r d i n a t e s o f p o s i t i o n s and angles o f o r i e n t a t i o n frame-by-frame on to paper t a p e . The tape was read by an IBM 1130 computer and the r e l e v a n t data ( i n c l u d i n g c a l c u l a t e d v e l o c i t i e s ) t a b u l a t e d and graphed. 13 I I I THE AVOIDANCE STIMULUS AND RESPONSE 1 I n t r o d u c t i o n The zebra d a n i o , i n these e x p e r i m e n t s , i s e s s e n t i a l l y being c o n s i d e r e d an analogue o f a genera l prey a n i m a l . S ince any p r e y , r e g a r d l e s s o f i t s p r e c i s e b e h a v i o u r a l t a c t i c , must make a d e c i s i o n w i t h r e s p e c t to when to i n i t i a t e i t s escape, a t t e n t i o n w i l l be focused on one aspect o f the response: the r e a c t i o n d i s t a n c e o r f l i g h t d i s t a n c e ( H e d i g e r , 1934). I t i s the purpose o f t h i s s e c t i o n to determine the nature o f the s t i m u l u s f o r avoidance o f p r e d a t o r s by zebra d a n i o s . S i n c e a model o f avoidance l e a r n i n g by prey i s the u l t i m a t e goal o f t h i s s tudy and s i n c e , i n g e n e r a l , complex l e a r n i n g processes are the p e r o g a t i v e s o f v e r t e b r a t e s , o n l y a v e r t e b r a t e prey was used. S ince a h i g h l y developed v i s u a l sense c h a r a c t e r i z e s most v e r t e b r a t e s , • i t i s assumed to be the dominant m o d a l i t y p r o v i d i n g i n f o r m a t i o n to the p r e y . T h i s i s not to suggest t h a t o t h e r sensory m o d a l i t i e s have no i m p o r t a n c e , but o n l y t h a t they have l e s s importance except i n s p e c i a l cases . A prey o r g a n i s m , having become aware o f an o b j e c t i n i t s v i s u a l f i e l d , must dec ide whether to c o n t i n u e about i t s bus iness o r to take a p p r o p r i a t e d e f e n s i v e a c t i o n . I t must t h e r e f o r e assess the degree o f p o t e n t i a l danger p r e s e n t e d . Three cues which may be used i n t h i s assessment are s i z e , d i s t a n c e and r e l a t i v e v e l o c i t y o f the s i g h t e d o b j e c t . S i z e and v e l o c i t y are i m p o r t a n t s i n c e , i n g e n e r a l , the l a r -ger and f a s t e r an o r g a n i s m , the more l i k e l y i t i s to have predacious i n t e n t . D i s t a n c e i s i m p o r t a n t s i n c e , i f the p r e d a t o r i s a l l o w e d to 14 J get too c l o s e , the prey may not have time to reach s a f e t y . A l t e r -n a t i v e l y , i f the prey r e a c t s too soon, i t may waste t ime and energy a v o i d i n g non-hungry o r o t h e r w i s e innocuous p r e d a t o r s . The p r e y , t h e r e f o r e , must have some way o f a s c e r t a i n i n g these t h r e e c h a r a c t e r i s e D i s t a n c e and s i z e may be u n e q u i v o c a l l y determined by means o f b i n o c u l a r v i s i o n , but i n most c a s e s , the b i n o c u l a r f i e l d o f prey s p e c i e s o f f i s h i s r e l a t i v e l y s m a l l , c o v e r i n g o n l y a smal l area d i r e c t l y i n f r o n t . S i n c e a t t a c k s can o r i g i n a t e from the s i d e o r r e a r , the prey must e i t h e r be able to determine s i z e and d i s t a n c e monocular ly o r waste v a l u a b l e time t u r n i n g to f i x a t e the p r e d a t o r . Monocular cues f o r d i s t a n c e e s t i m a t i o n e x i s t ( G i b s o n , 1950) but such es t imates may be i m p r e c i s e , o r even u n a v a i l a b l e i n a f e a t u r e l e s s environment ( e . g . i n the case o f p e l a g i c f i s h e s ) . In the case o f e i t h e r b i n o c u l a r o r monocular v i s i o n , v e l o c i t y may be determined i f s i z e i s known and i f two s u c c e s s i v e d i s t a n c e e s t i m a t i o n s can be o b t a i n e d . However, t a k i n g two v i s u a l f i x e s may be non-adapt ive i n many s i t u a t i o n s , s i n c e the d i f f e r e n c e between the " q u i c k and the dead" may be o n l y a m a t t e r o f a few m i l l i s e c o n d s i n r e a c t i o n time (Roeder, 1959). Some a l t e r n a t e s t i m u l u s f o r avoidance i s t h e r e f o r e r e q u i r e d . T h i s s t i m u l u s should i d e a l l y be q u i c k l y o b t a i n e d and r e s u l t i n the prey r e a c t i n g to l a r g e r and/or more r a p i d l y approaching predators from g r e a t e r d i s t a n c e s than to s m a l l e r o r s lower ones. The s t i m u l u s s h o u l d a l s o be so general t h a t i t i s a s s o c i a t e d w i t h every type o f p r e d a t o r w i t h which the prey i s l i k e l y to i n t e r a c t . One s t i m u l u s which possesses a l l o f these p r o p e r t i e s i s " r a t e o f change o f v i s u a l a n g l e . " The hypothes is w i l l be t e s t e d t h a t once t h i s r a t e exceeds a t h r e s h o l d v a l u e , zebra danios show avoidance b e h a v i o u r . 15 2 Theory and Mathematical Model C o n s i d e r an o b j e c t moving towards the eye o f an o b s e r v e r as i n F i g . 5. As the o b j e c t moves towards the e y e , the v i s u a l angle sub-tended (oc) i n c r e a s e s as shown i n F i g . 6. The r a t e o f change o f the v i s u a l a n g l e , dcx/dt, t h e r e f o r e i n c r e a s e s as d i s t a n c e and time to c o l l i s i o n decrease . This r a t e i s determined by the s i z e and v e l o -c i t y o f the o b j e c t and by i t s d i s t a n c e from the o b s e r v e r . I f D i s d i s t a n c e , S o b j e c t s i z e , and -V o b j e c t v e l o c i t y towards the o b s e r v e r , then.: tanoc/2 = S/2D and oc ( r a d i a n s ) = 2 arctan[S/2D) S u b s t i t u t i n g - V t f o r D g i v e s : = 2 a r c t a n ( S / - 2 V t ) . . . ( 1 ) T h e r e f o r e do/dt ( r a d i a n s / s e c ) 4VS = 4VS . . . ( 2 ) 4 V 2 t 2 + S 2 4D 2 + S 2 I f prey r e a c t when da/dt exceeds a c o n s t a n t ( k ) , then t h e i r r e a c t i v e d i s t a n c e (RD) s h o u l d be d e s c r i b e d by the e q u a t i o n (sub-s t i t u t i n g k=doc/dt i n t o (2) and r e a r r a n g i n g ) : F i g u r e 5 Schematic r e p r e s e n t a t i o n o f the eye o f an o b s e r v e r and the v i s u a l angles (o^oC-)) subtended by an o b j e c t o f s i z e S at d i s t a n c e s D Q and . F i g u r e 6 E f f e c t o f d i s t a n c e between o b j e c t and o b s e r v e r on the angle subtended by the o b j e c t at the o b s e r v e r ' s eye (<x). S = o b j e c t d i a m e t e r . 16 DISTANCE ( c m ) 17 3 Methods and R e s u l t s a) S t u d i e s w i t h model predators The model p r e d a t o r apparatus was used to t e s t the h y p o t h e s i s t h a t dcx/dt a t the time o f r e a c t i o n ( f l i g h t ) i s c o n s t a n t , i r r e s p e c t i v e o f p r e d a t o r s i z e o r v e l o c i t y . Four v e l o c i t i e s were chosen : 11 .6 , 4 3 . 6 , 6 2 . 8 , and 108.5 cm/sec. Three o b j e c t diameters ("S" i n F i g . 5) were used: 2 . 5 4 , 3.81 and 5 .08 cm. The s i z e s and v e l o c i t i e s were presented i n a 3 x 4 f a c t o r i a l d e s i g n w i t h s i x r e p l i c a t e s ( i . e . n = 7 2 ) . A con-t r o l experiment was conducted by r u n n i n g the c a r r i a g e and a p l e x i g l a s s s t r i p w i t h o u t a model a t tached towards s i x i n d i v i d u a l n a i v e danios a t 108.5 cm/sec. Four naive prey were t e s t e d on each t e s t i n g day.On a g i v e n day model s i z e was h e l d c o n s t a n t and the f o u r v e l o c i t i e s presented - i n random o r d e r . The o r d e r o f p r e s e n t a t i o n o f d i f f e r e n t s i z e d models was randomly s e l e c t e d between days . The prey were fed to s a t i a t i o n 24 hours before t e s t i n g i n o r d e r t h a t t h e i r hunger l e v e l would be c o n s t a n t . S i n c e not a l l prey would m a i n t a i n a s t a t i o n a r y p o s i t i o n between the m i r r o r s i n the t e s t chamber, 104 prey were used to o b t a i n 72 p ieces o f d a t a . A f t e r p r e -s e n t a t i o n o f the model , the prey were measured to the n e a r e s t 0 . 5 mm and d i s c a r d e d , i . e . no f i s h was t e s t e d more than once. R e a c t i v e d i s t a n c e , i n i t i a l angle o f o r i e n t a t i o n r e l a t i v e to the approach o f the model , and v e l o c i t y o f escape were recorded from the f i l m s . R e a c t i v e d i s t a n c e was measured at the t ime the 18 danio showed a sudden i n c r e a s e i n v e l o c i t y d i r e c t e d away from the model. In one e x p e r i m e n t , two types o f models were presented f o r purposes o f comparison: f u s i f o r m p l e x i g l a s s models and round b a l l b e a r i n g s . Both types were coated with, black, epoxy p a i n t . Al though both appeared round i n f r o n t v i e w , the apparent shape o f the f u s i f o r m model v a r i e d w i t h viewer aspect . Model s i z e and v e l o c i t y were 3.81 cm and 6 2 . 8 cm/sec r e s p e c t i v e l y . ( i ) t e s t o f the hypothes is o f a t h r e s h o l d dfl/dt A c c o r d i n g to e q u a t i o n ( 3 ) , both model s i z e and v e l o c i t y should have s i g n i f i c a n t e f f e c t s on r e a c t i v e d i s t a n c e o f the p r e y . A f a c t o r i a l a n a l y s i s o f v a r i a n c e conducted on the r e a c t i v e d i s t a n c e data (Table n and F i g . 7} r e v e a l e d s i g -n i f i c a n t e f f e c t s o f both v a r i a b l e s . Table II Mean r e a c t i v e d i s t a n c e (cm) o f naive danios to model p r e d a t o r s o f d i f f e r e n t s i z e s and v e l o c i t i e s VELOCITY S I Z E < c m ) (an/sec) 2.54 3.81 5 .08 11.58 11.46 18.21 9 .90 43.59 13.80 22.41 24.81 62.79 20.40 24.96 26.49 108.51 25.20 33.00 31.35 S i z e F ( 2 , 6 0 ) = 3 - 7 8 8 9 5 s i g n i f . at .05 V e l o c i t y F ^ 6 f ^ = l 0 . 4 0 6 7 7 s i g n i f . a t .005 S i z e X V e l o c i t y and W i t h i n R e p l i c a t e s components not s i g n i f i c a n t . F i g u r e 7 E f f e c t o f model s i z e and v e l o c i t y on the r e a c t i v e d i s t a n c e o f na ive zebra d a n i o s . Each p o i n t i s the mean o f s i x o b s e r v a t i o n s . F igure 8' R e g r e s s i o n o f (4D + S )/4S on model v e l o c i t y . The r e -g r e s s i o n was : c o n d i t i o n e d to go through the o r i g i n and the r e c i p r o c a l o f the s l o p e (k) taken as the best e s t i m a t e o f the t h r e s h o l d do/dt . The upper l i n e (k = .36) was d e r i v e d from the raw d a t a ; the lower one (k = .43) was d e r i v e d from the n o r m a l i z e d d a t a . Each p o i n t and bar demonstrate the mean o f 18 r e p l i c a t e s ± one s t a n d a r d e r r o r . VELOCITY (cm/sec) 20 E q u a t i o n (2) may a l s o be rearranged to the form: 4 D 2 + S 2 = 1 . V . . . ( 4 ) 4S k I f the h y p o t h e s i s has any b i o l o g i c a l r e a l i t y , then a r e g r e s -2 2 s i o n o f C4D + S )/4S on V s h o u l d produce a s t r a i g h t l i n e w i t h s l o p e 1/k and a y - i n t e r c e p t equal to z e r o . An i n i t i a l r e g -r e s s i o n d i d not produce a y - i n t e r c e p t s i g n i f i c a n t l y d i f f e r e n t from zero ( $ Q = 40.7198 ± 2 5 . 9 0 8 3 ) . A second r e g r e s s i o n [ F i g . 8 ) , c o n d i t i o n e d to pass through the o r i g i n , was conducted to o b t a i n ' an e s t i m a t e o f k. This e s t i m a t e was .38 rad/sec (/S^  = 1/k - 2 . 5 9 9 4 ± 0 . 1 9 8 5 ) . The r e g r e s s i o n was h i g h l y s i g n i f i c a n t CF = 161.92 w i t h 1,70 d f ) but the ( r e g r e s s i o n X b l o c k s ) and c u r v a t u r e components were n o n - s i g n i f i c a n t . 2 2 The dependent v a r i a b l e i n the r e g r e s s i o n ( (4D + S )/4S) was examined f o r each v e l o c i t y and found to be skewed i n the d i r e c t i o n o f smal l v a l u e s . Consequent ly , the e s t i m a t e o f k i s not the best p o s s i b l e one, a l though the s i g n i f i c a n c e o f the r e g r e s s i o n i s not i n v a l i d a t e d by t h i s p a r t i c u l a r v i o l a t i o n o f the assumptions u n d e r l y i n g i t ( N . G i l b e r t , pers comm.). A b e t t e r e s t i m a t e o f k may be o b t a i n e d by examining the o r i g i -nal d a t a and c a l c u l a t i n g the mean dot/dt. However, s i n c e the d i s t r i b u t i o n o f da/dt was i t s e l f skewed, i t was f i r s t n o r m a l i z e d by a l o g a r i t h m i c t r a n s f o r m a t i o n . The a n t i l o g o f the mean l n dtf/dt i s the bes t e s t i m a t e o f k. T h i s va lue (0 .43 rad/sec) i s a l s o shown on F i g . 8. As an a d d i t i o n a l t e s t o f the h y p o t h e s i s o f constant 21 t h r e s h o l d doc/dt, a f a c t o r i a l a n a l y s i s o f v a r i a n c e was con-ducted on In dw/dt (the n o r m a l i z e d d a t a ) . N e i t h e r s i z e nor v e l o c i t y had a s i g n i f i c a n t , e f f e c t a t p = 0 . 0 5 , as r e q u i r e d by the h y p o t h e s i s . None o f the danios presented w i t h o n l y the c a r r i a g e and the p l e x i g l a s s s t r i p showed a f r i g h t r e a c t i o n . In f a c t , they appeared to be t o t a l l y o b l i v i o u s to i t s approach. I t i s t h e r e f o r e concluded t h a t the r e a c t i o n s to the model were s o l e l y i n response to i t s v i s u a l q u a l i t i e s , and not to some o t h e r c h a r a c t e r i s t i c o f the t e s t i n g s i t u a t i o n , such as motor noise o r v i b r a t i o n . C i i ) e f f e c t o f model shape The round and f u s i f o r m models were each presented to s i x randomly s e l e c t e d naive d a n i o s . There was no e f f e c t o f model shape on r e a c t i v e d i s t a n c e (Table I I I ) . Presumably the f i s h were r e s t r i c t e d to a smal l enough area t h a t the e f f e c t o f v iewer aspect was i n s i g n i f i c a n t . Table I I I E f f e c t o f model shape on r e a c t i v e d i s t a n c e o f n a i v e zebra danios SHAPE X FISH SIZE (mm) REACTIVE DISTANCE (cm) X ± Sy t F u s i f o r m 27.3 28.5 ± 3.58 0.5147 NS B a l l 26.9 35.2 + 4.61 22 ( i i i ) e f f e c t o f prey s i z e on t h r e s h o l d doc/dt In o r d e r to examine the e f f e c t o f prey s t z e on t h r e s h o l d doc/dt, the data were s p l i t i n t o two groups a c c o r d i n g . t o danio l e n g t h . These were entered i n t o the r e g r e s s i o n as two b l o c k s and t h e ( r e g r e s s i o n * b l o c k s ) s o u r c e o f v a r i a n c e examined. T h i s prove'd to be a s i g n i f i c a n t component ( F ^ 6 g ^= 10.352 p<.005) . C o n s e q u e n t l y , a r e g r e s s i o n c o n d i t i o n e d to go through the o r i g i n was conducted f o r each b l o c k . The t h r e s h o l d da/dt was g r e a t e r f o r the s m a l l f i s h (Table I V ) . In o t h e r words , l a r g e f i s h r e a c t a t a g r e a t e r d i s t a n c e than do smal l f i s h presented the same s t i m u l u s . Table IV T h r e s h o l d da/dt (k) and / 9 , ( l / k ) f o r two s t z e c l a s s e s o f n a i v e d a n i o s . PREY SIZE /O a. T C LT A .IA4. ft ± 1 S . E . doydt MIN MEAN MAX THRESHOLD 26.0 28.74 30.0 2.1992 ± 0.2302 .4547 30.5 31.21 33.0 3.5699 ± 0.3585 .2801 D e s p i t e t h i s s i g n i f i c a n t d i f f e r e n c e between l a r g e and smal l p r e y , a r e g r e s s i o n o f da/dt on prey s i z e d i d not prove s i g n i f i c a n t ( FQ 1.116). There was an i n d i c a t i o n o f a maximum dd/dt t h r e s h o l d at an i n t e r m e d i a t e prey s i z e (around 28 mm). T h i s problem, w h i l e i n t e r e s t i n g , was beyond the scope o f t h i s study and was not pursued f u r t h e r . 23 Civ) e f f e c t o f o r i e n t a t i o n angle on t h r e s h o l d dot/dt The e f f e c t o f o r i e n t a t i o n angle was s t u d i e d i n an analogous manner to t h a t o f s i z e . O r i e n t a t i o n angles were d i v i d e d i n t o the t h r e e b l o c k s shown i n F i g . 9 and the r e g r e s -s i o n r e p e a t e d . S i n c e t h e ( r e g r e s s i o n * blocks)component was n o n - s i g n i f i c a n t , the r e a c t i v e f i e l d may be c o n s i d e r e d c i r c u l a r . (v) escape v e l o c i t y as a f u n c t i o n o f r e a c t i v e d i s t a n c e A r e g r e s s i o n o f prey escape v e l o c i t y on prey r e a c t i o n d i s -tance was conducted but was not s i g n i f i c a n t . The prey tended to escape a t a c o n s t a n t v e l o c i t y o f 18.2 cm/sec. S t u d i e s w i t h the c inematographic p r e d a t o r Al though the c inematographic p r e d a t o r was used p r i m a r i l y to o b t a i n data on the e f f e c t o f exper ience on t h r e s h o l d do(/dt, i t a l s o p r o v i d e d some s u p p o r t i n g evidence f o r the concept o f a con-s t a n t t h r e s h o l d . Some o f the danios (non-naive) i n the e x p e r i -mental aquarium responded to each sequence more than once. That i s , they f l e d from the " p r e d a t o r " , turned to face i t when t h e i r f l i g h t was stopped by a w a l l o f the t a n k , and then f l e d a g a i n . The c inematographic p r e d a t o r has the a d d i t i o n a l advantage o f b e i n g an e x c l u s i v e l y v i s u a l s t i m u l u s . S i n c e the frame number o f the c inematographic p r e d a t o r appeared on each frame of the data f i l m , i t was p o s s i b l e to c o r r e l a t e the p r e y ' s p o s i t i o n and v e l o c i t y w i t h the s i z e and r a t e c f change o f the image on the w a l l of the chamber and t o p l o t d«/dt F i g u r e 9 Method o f b l o c k i n g the data by angle o f o r i e n t a t i o n r e -l a t i v e to the d i r e c t i o n o f the approaching model ( 0 ° ) . CM 25 a g a i n s t t i m e . This was done f o r f o u r sequences i n which m u l t i p l e responses o c c u r r e d . The image s i z e ( W ) i s the diameter o f the image on the f i l m (W) m u l t i p l i e d by the enlargement f a c t o r o f the p r o j e c t o r a t . 75 cm, e m p i r i c a l l y determined to be 2 7 . 4 . The diameter o f the image on the f i l m i s d e f i n e d as ...(5) where S = o b j e c t diameter = 8 mm f = lens f o c a l l e n g t h = 55 mm D = f i l m i n g d i s t a n c e (681 to 205 mm) The s i z e o f the image on the screen i s t h e r e f o r e : W = S f (27.4) D = 12,056/D . . . ( 6 ) and dW' = 12,056 . . . ( 7 ) dD D 2 The r a t e o f change o f d iameter o f the c inematographic p r e d a t o r w i t h t ime i s : dW = 12056 . dD . . . (8) dt Q 2 d t where dD = 4mm . 24 frame = 96 mm/sec d t frame sec . 26 I f the danio i s o b s e r v i n g the image o f s i z e W from a d i s -tance D' from the s c r e e n , then tanO(/2 = W / 2 D ' . . . ( 9 ) where & = the v i s u a l angle subtended a t the eye. There fore l_sec 2(ot/2)da = 1 dW 2 d t 2D' d t 1 + t a n 2 * d * = 1_ dWJ_ . . . ( 1 0 ) dt D' dt S u b s t i t u t i n g (9) i n t o (10) and r e a r r a n g i n g , g ives doL = ( d W ' / d t ) ( 4 D ' ) . . . ( 1 1 ) d t f i l m C 4 D ' 2 + W ' 2 ) T h i s f o r m u l a t i o n assumes t h a t the p r e y ' s own v e l o c i t y r e l a t i v e to the screen i s not a f a c t o r i n d e t e r m i n i n g i t s measurement o f da/dt . The r a t e o f change o f s i z e o f a s t a t i o n a r y image due to the f i s h ' s own v e l o c i t y (V) i s g iven by e q u a t i o n ( 2 ) , a f t e r s u b s t i t u t i n g W f o r S and D' f o r D. i . e . d a ' = 4 V W ' / ( 4 D ' 2 + W ' 2 ) . . . ( 1 2 ) d t f i s h S i n c e these two r a t e components are a d d i t i v e , the t o t a l r a t e o f change o f v i s u a l angle a t any i n s t a n t o f time i s d a = ( d W 7 d t ) ( 4 D ' ) + 4VW d t t o t a l ( 4 D ' 2 + W ' 2 ^ ( 4 D ' 2 + W ' 2 ^ 27 = ( d W 7 d t ) ( 4 D > ) + 4VW . . . ( 1 3 ) C 4 D ' 2 + W ' 2 ) For each frame o f the data f i l m D 1 was measured and W and dW'/dt c a l c u l a t e d . V e l o c i t y (V) was computed as A D ' ( 3 2 ) ( s i n c e f i l m i n g speed was 32 frames/sec). A D 1 was p o s i t i v e i f toward the s c r e e n , and negat ive i f away. These data a l l o w e d the c a l c u l a t i o n o f dw/dtf-j-| m and dcv/dt^otal a n d p l o t t i n g o f both a g a i n s t t i m e . Two p l o t s were t h e r e f o r e o b t a i n e d from each o f f o u r sequences ( F i g . 1 0 ) . The f o u r graphs on the l e f t show dot/dtf.,--|m. On each graph the f i r s t r e d u c t i o n o f dcx/dt corresponded to the observed p o i n t o f r e a c t i o n o f the f i s h . A t each o f these p o i n t s , da/dt was a t a maximum, i . e . i t had not p r e v i o u s l y exceeded t h i s v a l u e . ' In a l l but one c a s e , the subsequent r e a c t i o n s o f the danios o c c u r r e d a t s i m i l a r l e v e l s o f dct/dt (Table V ) . Table V Rates o f change o f v i s u a l angle ( d « / d t ) ^ - j m a t the times o f response o f danios to the c inematographic p r e d a t o r SEQUENCE d o t / d t , . , AT TIME OF REACTION \ 0 m f i l m 1st REACTION 2nd REACTION 3rd REACTION 1 .134 .144 2 .139 .131 3 .034 .085 4 .042 .049 .081 F i g u r e 10 Values of dcv/dt with time for four danios responding more than once to the cinematographic predator. The values are calculated both without reference to the f i s h ' s ve loc i ty Cleft -hand graphs, " F i l m O n l y " ) , and inc luding the f i s h ' s ve loc i ty as a component Cright hand graphs, " T o t a l " ) . The arrows indicate the times at which the danios were seen to respond on the data f i l m . 28 TIME (sec) 29. In c o n t r a s t d o t / d t t o t a i > ( r i g h t hand graphs) was never maximal at the observed p o i n t o f r e a c t i o n but had exceeded t h i s va lue p r e v i o u s l y . In a d d i t i o n the subsequent r e a c t i o n s o f the danios i n a l l cases o c c u r r e d at q u i t e d i f f e r e n t dcx/dt l e v e l s (Table V I ) . T a b l e VI Rates o f change o f v i s u a l angle ( d c * / c l t ) t o t a l at the t imes o f response o f danios to the c inematographic p r e d a t o r d<x/dt. n. , AT TIME OF REACTION SEQUENCE NO. 1st REACTION 2nd REACTION 3rd REACTION 1 1.106 0.126 2 1.245 0.175 3 0.084 - 0 . 0 5 0 4 - 0 . 0 2 6 0.085 0.044 The evidence supports the hypothes is o f a t h r e s h o l d r a t e o f change o f v i s u a l angle (dot/dt), but o n l y when t h i s i s measured w i t h o u t r e f e r e n c e to the v e l o c i t y o f the p r e y . I f t h i s i s t r u e , then the prey must have some means o f s e p a r a t i n g the component o f dtx/dt caused, by the motion o f the p r e d a t o r towards i t , from the component o f da/dt caused by i t s own motion toward (or away from) the p r e d a t o r . The danio can o b t a i n an independent e s t i m a t e o f i t s own v e l o c i t y by means o f i t s l a t e r a l l i n e o r g a n s , but how the danio c o r r e c t s i t s measure o f da/dt by t h i s amount i s not known. 30 P r e d a t o r - p r e y i n t e r a c t i o n s fn the p r e d a t i o n arena ( i ) agreement w i t h model p r e d a t o r r e s u l t s In o r d e r to check the r e s u l t s o f the experiments w i t h model p r e d a t o r s , a number o f danios were a l l o w e d to i n t e r a c t w i t h bass o f two s i z e s i n the p r e d a t i o n arena. Naive danios were p r e s e n t -ed one at a time to a bass which was a c c l i m a t e d to the tank. The danios were t r a n s f e r r e d from t h e i r h o l d i n g a q u a r i a to an opague p l a s t i c c o n t a i n e r and f l o a t e d i n the arena f o r 15 minutes before r e l e a s e . The danios presented to each bass were from a s i n g l e spawning, but d i f f e r e n t s tocks were presented to the two d i f f e r e n t bass . A l l f i s h were about the same s i z e and were l a s t fed 24 hours before the exper iment . The smal l bass was fed a maximum o f f o u r prey per day; the l a r g e one, s i x . The v a r i a b l e s recorded from the data f i l m were: r e a c t i v e d i s t a n c e o f p r e y , v e l o c i t y o f p r e d a t o r a t time o f r e a c t i o n , and escape v e l o c i t y o f p r e y . A f t e r the complet ion o f the experiments the bass were t r a n s f e r r e d to 10 g a l . g l a s s a q u a r i a and photo-graphed head-on to e s t i m a t e t h e i r s i z e as seen by an a t t a c k e d prey (Table I ) . These data a l l o w e d the c a l c u l a t i o n o f da/dt from e q u a t i o n ( 2 ) . The w i d t h measurement was used as the e s t i m -ate o f S , s i n c e f i s h are r e p o r t e d to be more s e n s i t i v e to h o r i -z o n t a l than to v e r t i c a l movement on the r e t i n a (Jacobson & Gaze, 1964; C r o n l y - D i l l o n , 1964).. The data are shown i n Table VII and summarized i n Table V I I I . S ince the v a r i a n c e s and sample s i z e s were d i f f e r e n t , t ' f 31 CSteel and Tor r te , 1960) were used to compare the. sets of data to those obtained tn response to the model predators. Since the calculated t ' s were in both cases less than the calculated t 1 both samples of ln dcrf/dt, and hence dcH/dt. Table VII Data from fi lmed observations of largemouth bass - naive zebra danio in te rac t ions . REACTIVE ESCAPE BASS BASS WIDTH DANIO DISTANCE VELOCITY VELOCITY k Ink SIZE (cm) NUMBER (cm) (cm/sec) (cm/sec) SMALL 1.87 1 21.04 31.21 11.69 0.049 -3.016 2 9.35 46.76 14.02 0.297 -1.214 3 10.52 -56.11 79.49 1.333 0.287 4 5.85 74.82 46.76 2.491 0.913 5 26.30 42.08 19.87 0.054 -2 .925 6 2.92 28.06 37.41 7.440 2.007 X 12.66 46.51 34.87 1.944 -0 .658 LARGE 2.65 1 9.35 74.82 65.46 1.945 0.665 2 27.47 53.77 42.08 0.147 -1 .914 3 10.52 74.82 45.59 1.076 0.072 4 15.20 46.76 30.39 0.346 -1.062 5 20.46 51.44 22.21 0.140 -1.966 6 6.43 65.46 56.11 3.450 1.238 7 24.55 65.46 37.41 0.164 -1 .808 8 9.35 25.72 32.73 0.973 -0 .028 9 18.70 35.07 40.92 0.309 -1.176 X 15.78 54.81 41.43 0.950 -0.664 REACTING TO Table VIII Summary of data on threshold dw/dt of zebra danios to various predators LN d<x/dt COMPARED WITH MODEL t ' 05 BEST k ESTIMATE anti log (X LN doy'dt) MODEL SMALL BASS LARGE BASS - . 8 3 0 - . 6 5 8 - .664 .8464 4.2944 1.3587 .202 .411 2.502 2.284 .43 .52 ,51 32 may be considered to have been drawn from the same popul a t i o n as those sampled i n the experiments with the model predator. Equation (3) may be used to p r e d i c t a mean r e a c t i v e d i s -tance f o r the danios by using the mean bass v e l o c i t y as an estimate o f V, the da/dt t h r e s h o l d determined i n the model predator experiments (.43) as an estimate o f k, and bass width as an estimate of S. The p r e d i c t e d and observed r e a c t i v e d i s -tances are shown i n Table IX. Although the mean observed value i s i n both cases q u i t e s i m i l a r to the p r e d i c t e d one, i t was not p o s s i b l e to a c c u r a t e l y p r e d i c t the r e a c t i v e d i s t a n c e f o r i n d i v i d u a l danios because of the l a r g e variance of k. Only p r e d i c t i o n s at the p o p u l a t i o n l e v e l are p o s s i b l e at t h i s time. Table IX Mean observed and p r e d i c t e d r e a c t i v e d i s t a n c e s o f zebra danios to largemouth bass of two s t z e s . BASS PREDICTED REACTION OBSERVED REACTION SIZE DISTANCE (cm) . DISTANCE(cm) ± 1 S.E. SMALL 12.28 12.66 ± 3.71 MEDIUM 15.92 . 15.78 ± 2.48 The mean v e l o c i t i e s o f escape from both s i z e s o f bass were s i g n i f i c a n t l y g r e a t e r than that.from the model predators. However, the v e l o c i t i e s of escape from the two bass were not s i g n i f i c a n t l y d i f f e r e n t from one another ( t ^ ^ y 1.658). 33 ( i i ) t h r e s h o l d da/dt o f schooled prey The zebra danio might be c a l l e d an " o b l i g a t o r y " s c h o o l i n g f i s h , s i n c e i t apparently never e x i s t s s o l i t a r i l y i n nature. For a v a r i e t y of p r a c t i c a l reasons, however, the danios used i n t h i s study were t e s t e d as i n d i v i d u a l s . I t was t h e r e f o r e d e s i r a b l e to determine whether t h i s procedure i n v a l i d a t e s the a p p l i c a t i o n of these r e s u l t s to schooled prey. The responses o f i n d i v i d u a l and schooled zebra danios to largemouth bass were examined and the mean dd/dt thresholds and t h e i r variances compared. The prey (35-40 mm long) were placed i n the predation arena, e i t h e r i n d i v i d u a l l y o r f i v e at a time, f i v e minutes before the t e s t . A medium s i z e d bass was then r e l e a s e d from one of the ho l d i n g tanks and the response of the danios to i t s attack f i l m e d . When f i v e danios were t e s t e d together, the bass was not r e l e a s e d u n t i l they had formed up i n t o a s c h o o l . In one case, only four o f the f i v e prey d i d so. Seventeen prey were t e s t e d i n d i v i d u a l l y , and 20 (19) i n s c h o o l s . The danios were fed four hours before the t e s t and the bass 24 h r s . p r e v i o u s l y . A l l of the schooled prey showed f l i g h t responses to the bass, while only 11 o f the prey t e s t e d i n d i v i d u a l l y d i d so. The mean l n k f o r the i n d i v i d u a l danios (-.652, k = .52) was compared to the mean of group mean In k's (0.416; k = 1.52) by means of a t - t e s t . The d i f f e r e n c e was not s i g n i f i c a n t a t p = .05. 2 To compare the estimates of o" of the two groups, i t was f i r s t necessary to conduct a one-way a n a l y s i s of variance on 34 the grouped f t s h data. The withtn-groups mean square (.78279, 15 df) was taken as the best estimate o f cJ . This was compared with the variance of i n d i v i d u a l f i s h 0-62472, 10 df) with an F t e s t . Again, the d i f f e r e n c e was not s i g n i f i -cant at p = .05, although i t was s i g n i f i c a n t at p = .10. I d e n t i c a l r e s u l t s were obtained when k, i n s t e a d of In k, was used as the v a r i a b l e i n the a n a l y s i s . In c o n c l u s i o n , t h e r e were no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s between the means or variances of f i s h t e s t e d i n d i v i d u a l l y or i n groups. However, there were strong sugges-t i o n s t hat d i f f e r e n c e s d i d indeed e x i s t . T h is was supported by the 100% response rate o f schooled f i s h compared to the 65% r a t e from i n d i v i d u a l s , and by the observation that schools of danios seemed to r e a c t a t almost the same time. Since the f i s h were at d i f f e r e n t d i s t a n c e s from the bass a t the times o f response, however, t h i s r e s u l t e d i n d i f f e r e n t estimates o f k. Further experiments might reveal that only one f i s h i n the school responds to the predator, and the others f o l l o w s u i t , responding to the f l i g h t o f the schoolmate r a t h e r than to the predator per se. 4 Di s c u s s i o n When an animal becomes aware o f a p o t e n t i a l predator, i t may demonstrate one o f a number of types of behaviour. T h i s may take the form of f l i g h t (avoidance), f r e e z i n g i n place o r even a t t a c k i n g the 35 predator (mobbing). The f l t g h t or avoidance response may or may not be d i r e c t e d towards cover, and i n the former case the cover may be environmental s h e l t e r or an aggregation o f c o n s p e c i f i c s . Regardless o f the escape t a c t i c used, the prey must allow t t s e l f enough time to execute i t s u c c e s s f u l l y . The prey must t h e r e f o r e recognize the predator and r e a c t to i t while i t i s s t i l l some d i s t a n c e away. Hediger (1934) coined the term " f l i g h t d i s t a n c e " to d e s c r i b e the d i s t a n c e to which a predator can approach a prey without causing f l i g h t . F l i g h t distances have been recorded i n a number o f types of animals (Crane, 1941; Hediger, 1964; Benzie, 1965; Walther, 1969) and are considered to be a general a t t r i b u t e of a prey's response to predators. Exceptions occur i n some gastropod molluscs (e.g. B u l l o c k , 1963) which apparently do not respond u n t i l touched by the predator ( s t a r f i s h , other m o l l u s c s ) . In these cases, however, con t a c t i t s e l f . i s not f a t a l ; i t i s prolonged contact which must be avoided. Even some gastropods respond to the predator from a d i s t a n c e by means of chemoreception (Kohn and Waters, 1966) and perhaps v i s i o n (unpublished observations on response o f Strombus luhuanus to Conus pennaceous i n Hawaii by the author). In order to respond to an approaching predator, the prey must use sense organs capable of d i s t a n t r e c e p t i o n . These i n c l u d e the organs of s i g h t , chemoreception and hearing, and i n the lower v e r t e -brates the l a t e r a l l i n e organs. While examples o f predator r e c o g n i -t i o n through a l l o f these sensory m o d a l i t i e s have been recorded, the s i n g l e most important modality, at l e a s t i n v e r t e b r a t e s , appears to be the v i s u a l one. For t h i s reason, the theory of predator r e c o g n i t i o n 36 d e s c r i b e d above was developed f o r the v i s u a l sense. It i s b e l i e v e d that s i m i l a r l i n e s of argument could be used to cover cases- where other senses are used. D i j k g r a a f 0 9 6 3 ) , f o r example, reported t h a t the r e a c t i v e d i s t a n c e of b l i n d e d f i s h to approaching p l a t e s of g l a s s depen-ded on the s i z e and v e l o c i t y of the p l a t e s , being g r e a t e r i n response to l a r g e r and more r a p i d l y approaching ones. The f i s h i n t h i s instance were apparently responding to water damming phenomena with t h e i r l a t -e r a l l i n e organs. There has been co n s i d e r a b l e c o n f l i c t of o p i n i o n regarding the type o f warning s t i m u l i to which prey respond. Some authors [e.g. Nice and ter Pelkwyk,l941; Barraud, 1961) have suggested t h a t animals respond i n s t i n c t i v e l y to a p a r t i c u l a r species or type of predator. Thorpe (1963), however, considered t h i s type of response to be r a t h e r rare and suggested t h a t prey tend to avoid danger s i g n a l s , .novel s t i m u l i , high i n t e n s i t y s t i m u l i , or sudden s t i m u l i . T h i s hypothesis o f a g e n e r a l i z e d warning stimulus agrees w i t h Hebb's (1946) conception of f e a r as being "due to the d i s r u p t i o n of temporally or s p a t i a l l y organized c e r e b r a l a c t i v i t i e s " . Chance and R u s s e l l (1959) hypothesized that a g e n e r a l i z e d s t i m u l u s , or key s t i m u l u s , would be used "when i t i s e s p e c i a l l y important not to l o s e a chance of r e a c t i n g to the r i g h t o b j e c t , while r e a c t i o n s to the wrong o b j e c t are o f minor disadvantage". This would presumably be the case i n most predator-prey s i t u a t i o n s . Furthermore, a l a r g e number of s t u d i e s on a wide v a r i e t y o f species have shown that f r i g h t responses may be e l i c i t e d by s t i m u l i which only very a b s t r a c t l y , i f at a l l , resemble 37 an a c t u a l predator (examples, tn fish., are reported by Garrey, 1905; Goethe, 1939; Noble & C u r t i s , 1939; Baerends & Baerends van Roon, 1950; Welker & Welker, 1958; Kuenzer & Kuenzer, 1962; O t i s & C e r f , 1963; Rodgers e t al_, 1963; and R u s s e l l , 1967). Galapagos f i n c h e s (Geospiza s p ) , who have no natural p r e d a t o r s , show f e a r responses to hawks, v u l t u r e s , and ravens when kept i n c a p t i v i t y (Orr, 1945). The hypothesis o f a th r e s h o l d l e v e l o f a s t i m u l u s , i . e . a l e v e l which i f exceeded causes avoidance, i s another way of saying t h a t "high i n t e n s i t y " s t i m u l i cause f l i g h t , a view s t r o n g l y advocated by S c h n e i r l a (1965). T h e problem of determining a t h r e s h o l d i s one of d e f i n i n g "high". The concept o f a t h r e s h o l d , combined with t h a t o f f l i g h t d i s t a n c e ( r e a c t i v e d i s t a n c e f o r f l i g h t ) , suggests t h a t the stimulus monitored by the prey changes as a f u n c t i o n of the d i s t a n c e between the prey and the predator. In a d d i t i o n , as described i n the i n t r o d u c t i o n , the stimulus should: (a) be q u i c k l y obtained; (b) cause the r e a c t i v e d i s t a n c e to be s e n s i t i v e to predator s i z e and approach v e l o c i t y ; (c) be genera] enough to be a s s o c i a t e d with a l l predators l i k e l y to be encountered ( i . e . be a key s t i m u l u s ) . One stimulus which meets a l l o f these c r i t e r i a i s the ra t e o f change of the angle subtended by the predator at the eye of the prey. The hypothesis that prey take f l i g h t when doi/dt reaches a c r i t i c a l l e v e l (threshold) could not be disproved experimentally f o r zebra danios. I t was demonstrated t h a t the mechanism produces a r e a c t i v e 38 d i s t a n c e f o r f l i g h t which depends on both the s i z e and v e l o c i t y of the predator. The response was a l s o shown to be general, i n t h a t responses to two types of models and to r e a l predators were not s i g n i f i c a n t l y d i f f e r e n t . The model assumes t h a t the prey has some method o f monitoring da/dt. In f a c t , the prey may a c t u a l l y monitor the c l o s e l y r e l a t e d stimulus r a t e of change of image s i z e on the r e t i n a . P h y s i o l o g i c a l s t u d i e s have demonstrated the e x i s t e n c e of neuronal elements s e n s i t i v e to d i r e c t i o n o f movement of an image i n the r e t i n a o f the r a b b i t (Barlow and H i l l , 1963}, g o l d f i s h ( C r o n l y - D i l l o n , 1964; Jacobson & Gaze, 1964) and f r o g (Maturana e_t al_, 1960; Grusser and Grusser-Cornehls, 1968). The last-named authors have even recorded r e t i n a l neurons s e n s i t i v e to the angular v e l o c i t y of a moving o b j e c t . One r e s p e c t i n which the model may f a l l somewhat s h o r t of r e a l i t y i s t h a t there i s assumed to be no l a g between perception o f t h r e s h o l d d«/dt and r e a c t i o n to i t . Since the o b j e c t moves toward the prey during t h i s l a g time the r a t e of change of a at the time of r e a c t i o n (the measured value) w i l l be somewhat greater than the true t h r e s h o l d . Further, the e r r o r w i l l i n c r e a s e with the v e l o c i t y o f the predator. Because o f the good f i t obtained to the model, the l a g i s presumably small enough to be considered i n s i g n i f i c a n t . As a consequence o f the v i s u a l mechanism d e s c r i b e d , a prey's r e a c t i v e d i s t a n c e w i l l be s m a l l e r , the lower the s i z e and/or v e l o c i t y o f the predator. This may help to e x p l a i n why many t e r r e s t r i a l preda-tors crouch when approaching prey, thus e f f e c t i v e l y reducing t h e i r angular s i z e . In a d d i t i o n , wolves approaching moose (Mech, 1970) and 39 A f r i c a n hunting dogs s t a l k i n g zebra and wildebeests (van Lawick-Goodall & van Lawick-Goodall, 1970) have been reported to reduce t h e i r v e l o c i t y the c l o s e r they get to the prey, thus reducing the rate of i n c r e a s e o f dot/dt. The predators may have e i t h e r learned or evolved such t a c t i c s to counteract those o f the prey. The model al s o p r e d i c t s t h a t to very slow predators (those with V <Sk/4) prey w i l l have no r e a c t i v e d i s t a n c e . Another r e a c t i o n mech-anism may come i n t o play at very low v e l o c i t i e s , or these may simply not occur i n nature. For example, a one inch diameter bass would have to approach at 0.27 cm/sec (1/l50th of i t s true approach v e l o c i t y ) i n order not to cause a danio to f l e e . At a l l v e l o c i t i e s g r e a t e r than Sk/4 r e a c t i v e d i s t a n c e increases with s i z e up to S=2V/k and then f a l l s o f f to zero at 4V/k. For a bass approaching at 100 cm/sec, r e a c t i v e d i s t a n c e would increase with S up to 465 cm diameter i n f r o n t view; i . e . f o r a l l p r a c t i c a l purposes, the greater the predator's s i z e , the g r e a t e r the prey's r e a c t i v e d i s t a n c e . Two r e l a t e d v i s u a l s t i m u l i which have been considered as p o s s i b l e avoidance s t i m u l i are angular s i z e (<*) and time to c o l l i s i o n . Wein-berger (1971) has shown that time to c o l l i s i o n may be obtained from a knowledge o f image s i z e on the r e t i n a (A) and rate of change o f image s i z e (d«/dt). I f time to c o l l i s i o n were the important s t i m u l u s , then r e a c t i v e d i s t a n c e would be independent of predator s i z e . S c h i f f (1965) reported that f i d d l e r crabs and chicks showed avoid-ant behaviour to an o p t i c a l r e p r e s e n t a t i o n of an approaching o b j e c t (an e n l a r g i n g shadow) when i t was magnified beyond approximately 30° 40 of v i s u a l angle. I f the hypothesis o f a t h r e s h o l d cx were c o r r e c t then r e a c t i v e d i s t a n c e would be independent o f predator v e l o c i t y . Both of these hypotheses may t h e r e f o r e be r e j e c t e d f o r the r e a c t i o n o f zebra danios to predators. Walther (1969) found that the f l i g h t d i s t a n c e of Thompson's g a z e l l e was a l s o dependent upon both the s i z e and v e l o c i t y o f the predator. Estes & Goddard (1967) reported t h a t the f l i g h t d i s t a n c e of g a z e l l e s to packs of A f r i c a n dogs in c r e a s e d with the dogs' v e l o c i t y and E i b l - E i b e s f e l d t (1965) found that the f l i g h t d i s t a n c e of r e e f f i s h to sharks was dependent upon the shark's v e l o c i t y i n the same manner. Besides crabs and c h i c k s , a number of other species show avoidance behaviour when presented with an e n l a r g i n g shadow. These i n c l u d e rhesus monkeys ( S c h i f f et al_, 1962), frogs ( S c h i f f , 1965), t u r t l e s (Hayes & S a i f f , 1967; I r e l a n d e t al_, 1962), and human i n f a n t s ( B a l l & T r o n i c k , 1971). In none of these cases, however, has any attempt been made to q u a n t i f y the stimulus f o r the behaviour, or to record r e a c t i v e d i s t a n c e s . Re-examination o f the raw data may or may not provide evidence to support the g e n e r a l i t y o f the avoidance mechanism used by zebra danios. Although r e a c t i v e distances have seldom been repo r t e d , a number of s t u d i e s on the i n t e n s i t y o r frequency of f l i g h t responses have suggested the importance of both o b j e c t s i z e and v e l o c i t y . These i n c l u d e s t u d i e s on g y r i n i d b eetles (Brown and Hatch, 1929), perch (Boulet, 1960),frogs (Griisser and Grusser-Cornehls, 1968; Ewert, 1970) 41 and g a l l i n a c e o u s b i r d s ( S c h l e i d t , 1961). S c h n e i r l a (1965) l i s t s l a r g e s i z e and high v e l o c i t y as s t i m u l i causing withdrawal i n animals i n general. The apparent c i r c u l a r i t y o f the r e a c t i v e f i e l d (the two-dimensional r e p r e s e n t a t i o n o f r e a c t i v e d i s t a n c e ) i s of c o n s i d e r a b l e i n t e r e s t . Since a predatory attack may o r i g i n a t e from the s i d e or the r e a r , t h i s c i r c u l a r i t y i s c l e a r l y o f advantage to the prey. In a d d i t i o n , the c i r c u l a r i t y demonstrates that the v i s u a l mechanism i s , at l e a s t , i n p a r t , a monocular one, s i n c e i n most f i s h the b i n o c u l a r f i e l d ranges from 10° to 80° (Brawn, 1964; Duke-Elder, 1958; Polyak, 1957). In c o n t r a s t , the monocular f i e l d of f i s h i s l a r g e , ranging from 110-— 170° (Duke-Elder, i b i d ) . Prey i n general tend to have a l a r g e r v i s u a l f i e l d and a s m a l l e r b i n o c u l a r f i e l d than do predators (Duke-E l d e r , i b i d ) . Most f i s h e s have v i s u a l f i e l d s above and below the plane o f the body, t h e i r extent determined by the s p e c i e s ' morphology. I t may t h e r e f o r e be assumed t h a t the r e a c t i v e f i e l d of the zebra danio i s three dimensional. C a n e l l a (1936) demonstrated that monocular f i s h ( b l i n d e d i n one eye) were able to s u c c e s s f u l l y avoid o b j e c t s . Some evidence was presented that the r e a c t i o n t h r e s h o l d was g r e a t e r and hence the r e a c t i v e distance to a given predator lower f o r small danios than f o r l a r g e ones. This may be due to the f a c t that v i s u a l performance i n f i s h i n creases with body s i z e , as Baerends e t a l (1961) demonstrated f o r a c u i t y i n Aequidens p o r t a l e g r e n s i s , and 42 Hester (T968) f o r c o n t r a s t p e r c e p t i o n tn goldfish.. The g e n e r a l i t y o f t h i s r e l a t i o n s h i p i s u n c e r t a i n , however. Benzie Cl965) found that 8 week o l d three-spine s t i c k l e b a c k s (Gasterosteus) reacted to pike from greater distances than d i d 13 week o l d i n d i v i d u a l s . The s i t u a t i o n was reversed i n P u n g i t i u s , the nine-spine s t i c k l e b a c k . Sub-adult Thompson's g a z e l l e s have longer f l i g h t d i s t ances than do a d u l t s , a t l e a s t to cars [Walther, 1969). Since the danios were shown to be r e a c t i n g to da/dt and not to d i s t a n c e from the predator, the l a c k of a r e l a t i o n s h i p between escape v e l o c i t y and r e a c t i v e d i s t a n c e i s not s u r p r i s i n g . Benzie [1965), however, suggested t h a t the escape v e l o c i t y of s t i c k l e b a c k s increased as the d i s t a n c e to the predator decreased. No data were given to support t h i s statement. S t r a n g e l y , the v e l o c i t y of escape by a danio from a r e a l predator was three times that from an a r t i f i c i a l one. In l i g h t of the f a c t t h at the comparable dcx/dt thresholds were not d i f f e r e n t , t h i s t h ree-f o l d change i n escape v e l o c i t y i s d i f f i c u l t to e x p l a i n . I t suggests t h a t the prey can t e l l the d i f f e r e n c e between the two types o f predator but do not use the i n f o r m a t i o n to s e t t h e i r r e a c t i v e d i s t a n c e . Real predators, o f course, pursue t h e i r prey and i t may be that the danios do not a c c e l e r a t e g r e a t l y unless the predator continues to f o l l o w them a f t e r they have moved from i t s d i r e c t path. 43 5 Conclusions Ci) Zebra danios use a v i s u a l mechanism to avoid approaching predators. ( i i ) T h e i r r e a c t i v e d i s t a n c e f o r f l i g h t CD) may be p r e d i c t e d from the r e l a t i o n s h i p : \J k 4 where V = predator approach ve loc i t y (on/sec) S = predator f ront diameter Ccm) k = threshold rate of change of Y i s u a l angle Cradians/sec) C i i i ) The best o v e r a l l estimate of k i s .43 r a d i a n s / s e c , but i s lower i n l a r g e r danios than i n smaller ones. Civ) The r e a c t i v e f i e l d i s c i r c u l a r , demonstrating that the mechanism i s not a s o l e l y b i n o c u l a r one. (v) The escape v e l o c i t y i s not a f u n c t i o n o f r e a c t i v e d i s -tance but i s higher i n response to real predators than to a r t i c i f i c a l ones. ( v i ) The response of schooled danios i s not s i g n i f i c a n t l y d i f f e r e n t from that, of danios tested i n d i v i d u a l l y . 44 IV CHANGE OF dQ/dt THRESHOLD WITH EXPERIENCE 1 I n t r o d u c t i o n To t h i s p o i n t i t has been demonstrated t h a t the naive danio has a t h r e s h o l d rate o f change o f v i s u a l angle which, i f exceeded by an approaching o b j e c t , r e s u l t s i n avoidance. Consequently, f o r an o b j e c t o f a given s i z e and v e l o c i t y , there e x i s t s a s p e c i f i c r e a c t i v e d i s t a n c e . This r e a c t i v e d i s t a n c e f o r escape by prey i s e x a c t l y analogous to the r e a c t i v e d i s t a n c e f o r p u r s u i t by predators. H o l l i n g [1965) has t h e o r i z e d that the p u r s u i t d i s t a n c e , a b a s i c sub-component o f the predation process, may be modified through experience, becoming l a r g e r f o r p a l a t a b l e and s m a l l e r f o r unpalatable prey. Beukema (1968)and Ware (1971) have demonstrated increases i n r e a c t i v e d i s t a n c e with experience i n s t i c k l e b a c k s ( G a s t e r o s t e u s aculeatus) and rainbow t r o u t (Salmo g a i r d n e r i ) r e s p e c t i v e l y . Both H o l l i n g (1965) and Croze (1970) have considered t h i s learned change i n behaviour to be a p a r t i a l e x p l a n a t i o n f o r the phenomenon of "search image formation" (Tinbergen, 1960). I f the approach o f an o b j e c t , c h a r a c t e r i z e d by a c e r t a i n s e t o f v i s u a l or other s t i m u l i , c o n s i s t e n t l y leads to a " f r i g h t e n i n g " ( i . e . g r e a t e r than threshold) rate o f change of v i s u a l angle, i t i s p o s s i b l e t h a t i n time the prey may a s s o c i a t e the two. Consequently, the prey could r e a c t to the stimulus s e t p r i o r to the " f r i g h t e n i n g " da/dt. This would r e s u l t i n the prey responding at increased distances to an 45 approaching predator and could be conceptualized as a d e c l i n e i n the da/dt t h r e s h o l d . Such a process could be the basis f o r "avoidance l e a r n i n g " or"avoidance c o n d i t i o n i n g " . The purpose o f t h i s s e c t i o n o f the research i s to determine i f the f l i g h t t h r e s h o l d i n zebra danios i s a f u n c t i o n o f the number of previous experiences. 2 Methods Both the model and cinematographic predators were used to examine the e f f e c t o f experience on the t h r e s h o l d rate o f change of v i s u a l angle. a) Model predator Six naive danios which reacted to the stimulus on f i r s t pre-s e n t a t i o n (day 1) were s e l e c t e d f o r t h i s p o r t i o n of the study. T h e i r lengths, determined at the end o f the experiment, ranged from 29.0 to 32.0 mm and averaged 30.9 mm. During the e x p e r i -ment the prey were kept i n d i v i d u a l l y i n 16 oz. wide mouth j a r s i n t o which they were placed two days before the f i r s t t e s t . These j a r s were f l o a t e d i n separate aquaria so that the f i s h had no contact with c o n s p e c i f i c s during the experiment. The prey were t r a n s f e r r e d i n t o the t e s t chamber by gently pouring them from the j a r , and v i c e versa a f t e r each t e s t . T h i s obviated n e t t i n g o f the prey. Immediately a f t e r each t e s t , the prey were fed i n the j a r s , which were cleaned d a i l y . T e s t i n g and f i l m i n g procedures were i d e n t i c a l to those described i n S e c t i o n I I , except that the model was not run back to i t s 46 s t a r t i n g p o s i t i o n , i . e . away from the prey, u n t i l the l a t t e r was removed from the t e s t chamber. The t e s t s were not syn-chronized s i n c e not a l l the danios responded on t r i a l 1, and these had to be r e p l a c e d . On each of days 1 through 14, the danios were presented with a 2.54 cm black f u s i f o r m stimulus approaching at approximately 90 cm/sec. On t e s t day 15 the stimulus was switched to a 5.08 cm o b j e c t with otherwise i d e n t i c a l c h a r a c t e r i s t i c s . A l l 90 i n t e r a c t i o n s were f i l m e d and the r e a c t i v e d i s t a n c e o f the danio, v e l o c i t y of the model at the time of r e a c t i o n , t o t a l prey escape v e l o c i t y and escape v e l o c i t y d i r e c t e d 180° from the approaching model subsequently recorded from each f i l m . Cinematographic predator The s i x non-naive danios used i n t h i s experiment ranged from 31.5 to 35.0 mm and averaged 32.8 mm. They were placed i n the experimental aquarium 2 days p r i o r to the s t a r t o f the e x p e r i -ment and fed there each day. On each of the f o l l o w i n g 10 days the prey were presented with the standard cinematographic preda-t o r and t h e i r response f i l m e d . They were fed a f t e r t e s t i n g . The f i s h were f e d , but not exposed to the s t i m u l u s , on each o f days 11-19. They were subsequently t e s t e d on day 20 to examine the e f f e c t o f t h i s 10-day p e r i o d without s t i m u l a t i o n on e x t i n c t i o n of any learned response. A c o n t r o l experiment was conducted to determine whether the 47 response o f the danios was to the cinematographic predator or to some other aspect o f the stimulus s i t u a t i o n , such as p r o j e c t o r n o i s e , and to determine whether any change i n response over the 10 day p e r i o d was due to repeated p r e s e n t a t i o n o f the predator or to increased f a m i l i a r i t y with the t e s t i n g s i t u a t i o n . Six prey (mean length 31.3 mm, range 30-33.5 mm) were t r e a t e d as before except t h a t only c l e a r f i l m l e a d e r was presented on days 2 through 9. The responses o f the danios were f i l m e d on days 1, 5 and 10. For each f i l m e d response, da/dt at the time of r e a c t i o n was c a l c u l a t e d . In the case o f the experimental treatment, t o t a l escape v e l o c i t y and escape v e l o c i t y d i r e c t e d 180° from the screen were a l s o recorded. 3 Results a) Model predator Ci) change i n response with experience The data suggest a d e c l i n e of do/dt a s y m p t o t i c a l l y to a t h r e s h o l d with i n c r e a s i n g experience CFig. 11). The f i r s t few experiences appear to have more e f f e c t on the response than l a t e r ones. This hypothesis may be expressed as: dE m" n 48 where k = dw/dt t h r e s h o l d a t a given l e v e l o f experience E (E = 1 at f i r s t exposure) a = a rate constant ^min = rnl"n1'mum p o s s i b l e value of da/dt This i n t e g r a t e s to: k - e " a E + C * kmn - ( « ) = k m i n + E ° ^ -..(16) A value o f "a" was chosen which minimized the r e s i d u a l mean square and a r e g r e s s i o n a n a l y s i s conducted on the data f o r days 1 through 14, excepting day 9 when only two o f the s i x danios responded. The p r e d i c t i v e equation, dotted l i n e i n F i g . 11, was: k = .3034 + 2.161le " - 6 2 ( E ) The r e l a t i o n s h i p does not s a t i s f a c t o r i l y d e s c r i b e the data during the l a s t h a l f o f the p e r i o d , apparently because o f the unusually l a r g e variance (cause unknown) on day 10. An i d e n t v cal a n a l y s i s o f the data, excluding the day 10 f i g u r e s , gave the equation: , k = .2349 + 1.9845e ~ , 5 ° ( E ) ...(17) This equation, s i g n i f i c a n t at p = .001 ( F Q 5 Q J = 38.42) i s taken to be the best d e s c r i p t i o n o f the data and i s shown as a s o l i d l i n e i n F i g . 11. Figure 11 E f f e c t o f experience of the model predator on t h r e s h o l d dft/dt (k) of zebra danios (mean ± standard e r r o r ) . Lines f i t t e d by r e g r e s s i o n on data transformed i n accord-ance with equation (16). The broken l i n e i s f i t t e d to a l l data; the s o l i d l i n e i s f i t t e d to a l l data exclud-ing day 10. Figure 12 E f f e c t of experience on mean t o t a l escape v e l o c i t y (T; s o l i d c i r c l e s and l i n e ) and escape v e l o c i t y d i r e c t e d 180 away (A; open c i r c l e s and broken l i n e ) of danios responding to the model predator. Lines f i t t e d by r e g r e s s i o n . 49 1.5 E X P E R I E N C E N U M B E R 50 In a d d i t i o n , a t ' - t e s t was conducted to compare the mean values o f l n dot/dt (assuming a skewed d i s t r i b u t i o n as i n the Section III data) on days 1 and 14. The d i f f e r e n c e was s i g n i f i -cant at p =.05. There was no evidence that the t o t a l escape v e l o c i t y or the escape v e l o c i t y d i r e c t e d 180° from the approaching predator, both measured i n the f i r s t .125 to .25 seconds a f t e r r e a c t i o n , were a f f e c t e d by experience ( F i g . 12). The danios tended to f l e e the model at a t o t a l v e l o c i t y o f 17.1 cm/sec, with a v e l o c i t y d i r e c t e d 180° from the model o f 10.2 cm/sec. They t h e r e f o r e tended to begin t h e i r f l i g h t a t an angle o f 90° + s i n " 1 (10.2/17.1) =127°. ( i i ) g e n e r a l i z a t i o n over model s i z e The responses of the danios to the small and l a r g e models on days 14 and 15 r e s p e c t i v e l y provide f u r t h e r evidence that the change i n response r e s u l t e d from a change i n t h r e s h o l d da/dt. I t was shown i n Sec III that t h i s t h r e s h o l d was indepen-dent o f model s i z e i n naive danios. Comparison o f the responses a f t e r 14 days experience with the small model leads to the same con c l u s i o n (Table X). Thus, g e n e r a l i z a t i o n over o b j e c t s i z e may be considered to be complete. 51 Table X Comparison of responses o f t r a i n e d danios to model predators o f two s i z e s MODEL DIAMETER PRESENTATION MEAN SIGNIFICANT (cm) DAY LN .(da/dt) AT 2.54 14 -1.649 > 0.05 5.08 15 -0.963 Cinematographic predator ( i ) l e a r n i n g As was the case when the model predator was the s t i m u l u s , dd/dt a t the time o f r e a c t i o n decreased s i g n i f i c a n t l y as a r e s u l t o f experience ( F i g . 13). In t h i s s i t u a t i o n , however, the data were best d e s c r i b e d by the l i n e a r model: k = 0.1871 - 0.0113 (Experience number) This r e l a t i o n s h i p was s i g n i f i c a n t at p = .025 ( F ^ ^  = 6.845). Blocking the data by i n d i v i d u a l f i s h i n c r e a s e d the l e v e l o f s i g n i f i c a n c e to p = .005 ( F ^ ^ Q) = 10.654) and demonstrated that the r e g r e s s i o n was homogeneous i n d i f f e r e n t b l o c k s , i . e . t h e ( r e g r e s s i o n * blocks)component of the variance was n o n - s i g n i f i c a n t . Each o f the s i x regressions (one per f i s h ) had a negative s l o p e . Both t o t a l escape v e l o c i t y and escape v e l o c i t y d i r e c t e d 180° from the screen decreased with experience i n t h i s s i t u a -t i o n ( F i g . 14). The two regressions were: Figure 13 E f f e c t o f experience o f the cinematographic predator on th r e s h o l d dw/dt (JO o f zebra danios (mean ± one standard e r r o r ) . Line f i t t e d by r e g r e s s i o n . Figure 14 E f f e c t of experience on mean t o t a l escape v e l o c i t y ( s o l i d c i r c l e s and l i n e ) and escape v e l o c i t y d i r e c t e d 180 away (open c i r c l e s and broken l i n e ) o f danios responding to the cinematographic predator. Lines f i t t e d by r e g r e s s i o n . 53 TOTAL EV = 15.35 - .85 (EXPER N O ) ; F ^ 4 Q ) = 10.871 p<.005 180°AWAY EV = 12.50 - .89 (EXPER NO) ; F Q 4 Q ) = 9.491 p<.005 Since the slopes o f the two regressions are not s i g n i f i c a n t l y d i f f e r e n t , i t may be concluded t h a t the danios tended to begin t h e i r f l i g h t at a constant angle of 90° + s i n - 1 ( 1 2 . 5 0 / 15.35) = 145°. There was no s i g n i f i c a n t e f f e c t o f the 10 day per i o d with-out experience on da/dt at the time o f r e a c t i o n C t ^ ^ j = .959), although the mean value of doc/dt increased from .062 to .126 rad/sec. Nevertheless, i t must be concluded that no s i g n i f i c a n t degree o f e x t i n c t i o n occurred during t h i s p e r i o d . ( i i ) c o n t r o l None of the s i x f i s h t e s t e d on day 5 showed any f r i g h t response to the l a s t f i v e seconds of c l e a r leader (correspond-ing to the f i v e second approach sequence o f a normal presenta-t i o n ) . I t i s t h e r e f o r e concluded t h a t the experimental danios were responding to the o p t i c a l p r o p e r t i e s o f the standard s t i m u l u s . Table XI compares da/dt at the time o f response, and the measures of escape v e l o c i t y d escribed above, f o r the c o n t r o l group o f danios presented with the standard stimulus on days 1 and 10, but c l e a r leader on i n t e r v e n i n g days. 54 Table XI Comparison o f the f r i g h t responses of the c o n t r o l danios to the cinematographic predator before and a f t e r 10 days i n the experimental aquarium. BEHAVIOURAL DAY 1 DAY 10 MEASURE n j s 2 n X S 2 ]- t a i l dot/dt 4 .099 .00143 5 .175 .00167 2.862 < .05 To t a l escape V e l o c i t y (cm/sec) 4 14.01 22.6341 5 14.98 11.4743 0.359 >.25 180°-away escape V e l o c i t y (cm/sec) 4 8.54 55.8079 5 8.15 28.9499 0.091 >.25 None o f the parameters decreased as a r e s u l t o f f a m i l i a r i t y with the t e s t i n g s i t u a t i o n . In f a c t , da/dt at the time o f r e a c t i o n increased s i g n i f i c a n t l y . I t i s t h e r e f o r e concluded t h a t the changes i n response c h a r a c t e r i s t i c s o f the experimental danios were due to experience with the cinematographic predator. 4 D i s c u s s i o n P r i o r to a d i s c u s s i o n o f the s i g n i f i c a n c e o f t h i s p o r t i o n o f the resea r c h , a few words o f ex p l a n a t i o n w i l l be given f o r using two types o f experimental apparatus. Some of the l i m i t a t i o n s o f the apparatus, i n l i g h t o f which the r e s u l t s should be considered, w i l l a l s o be men-ti o n e d . Two t e c h n i c a l problems were a s s o c i a t e d with the use o f the model 55 predator. In the f i r s t p l a c e , the danios had to be t r a n s f e r r e d to the t e s t i n g chamber before each t e s t and returned to t h e i r h o l d i n g b o t t l e s immediately afterward. Although t r a n s f e r was done by pouring r a t h e r than n e t t i n g , the e f f e c t of the disturbance on the rate o f l e a r n i n g i s unknown. Secondly, unless the danio's r e a c t i v e d i s t a n c e was q u i t e l a r g e , i t was impossible to stop the model's approach before i t c o l l i d e d with the p l e x i g l a s s p l a t e i n f r o n t of the f i s h . This c o l l i s i o n no doubt produced a shock wave i n the t e s t compartment which may have served to r e i n f o r c e the learned response to the v i s u a l q u a l i t i e s o f the model. The cinematographic predator was designed to e l i m i n a t e these problems. The danios remained i n the t e s t i n g chamber between presentations o f an e x c l u s i v e l y v i s u a l stimulus. In both types o f apparatus, however, i t was necessary to confine the f i s h to a small area i n order that they would be d i r e c t l y i n l i n e with the approaching s t i m u l u s . As a r e s u l t , they were never r e a l l y able to "escape", s i n c e t h e i r path was r e s t r i c t e d by the walls of the chamber. I f complete escape i s necessary to s u s t a i n the learned response, i t i s not e v i d e n t from the data, s i n c e r e a c t i v e d i s t a n c e showed no tendency to d e c l i n e through h a b i t u a t i o n , even though Breder and Halpern (1946) found t h a t B. r e r i o q u i c k l y become habituated to i n i t i a l l y f r i g h t e n i n g s t i m u l i . Other authors have a l s o reported h a b i t u a t i o n to f r i g h t s t i m u l i . Hinde (1954) found that c h a f f i n c h e s cease to mob owls a f t e r repeated p r e s e n t a t i o n ; Hayes and S a i f f (1967) and I r e l a n d e_t al_ (1969) found t h a t t u r t l e s q u i c k l y become habituated to an e n l a r g i n g shadow, which i n i t i a l l y produced head withdrawal; and 56 H i r s c h e t al (1955) found that f e a r responses of chickens to predator models can be extinguished with repeated s t i m u l a t i o n . In a l l cases where rates of p r e s e n t a t i o n have been reported, however, these were g r e a t l y i n excess o f the rates a t which prey might reasonably be expected to encounter predators i n nature. In a d d i t i o n , some workers have observed that during h a b i t u a t i o n o f ov e r t f l i g h t responses, o r i e n t i n g responses to the stimulus do not d e c l i n e (Melzack, 1961 f o r m a l l a r d ducks; Rodgers e t al_, 1963, f o r g o l d f i s h ; Hinde, 1966, f o r c h a f f i n c h e s ; and Russel1 , 1967, f o r guppies) and may a c t u a l l y i n c r e a s e (Martin & Melvin, 1964, f o r bobwhite q u a i l ) . Thus, the q u a l i t y o f the response may change as a r e s u l t o f repeated presenta-t i o n . A change i n response q u a l i t y (measured as escape v e l o c i t y ) was noted i n the present study when the stimulus was a cinematographic p r e d a t o r , but not when i t was a model. This d i f f e r e n c e may be r e l a t e d to the p o s s i b i l i t i e s of a d d i t i o n a l reinforcement d e s c r i b e d above f o r the model predator. Despite the d i f f e r e n c e s i n methodology, however, the t h r e s h o l d r a t e o f change o f v i s u a l angle decreased, and r e a c t i v e d i s t a n c e increased,as a r e s u l t o f experience i n both t e s t i n g s i t u a t i o n s . This may be considered to be a learned change i n the behaviour o f the danios, according to Thorpe's (1963) d e f i n i t i o n o f l e a r n i n g as a "process which manifests i t s e l f by adaptive changes i n i n d i v i d u a l behaviour as a r e s u l t o f experience". An inc r e a s e d d i s t a n c e o f reac-t i o n to an approaching predator i s assumed to be adaptive, an assump-57 t i o n which i s supported by the data of Benzie (1965) f o r s t i c k l e b a c k s , and which w i l l be examined i n gr e a t e r d e t a i l i n Sec. VI Three p o s s i b l e mechanisms might be invoked to e x p l a i n the i n c r e a s e i n r e a c t i v e d i s t a n c e with experience. The f i r s t p o s s i b i l i t y i s t h a t the l a g between pe r c e p t i o n of the stimulus (doi/dt) and the response to i t d e c l i n e s with experience. A decrease i n l a g time of .21 seconds would be r e q u i r e d to account f o r the observed change of dot/dt at the time of r e a c t i o n to the model predator. Thus, the i n i t i a l l a g between perc e p t i o n and response would have to exceed t h i s amount. Although lags o f even g r e a t e r magnitude have been reported f o r s i m i l a r types of v i s u a l s t i m u l i (e.g. Hunter, 1969, found that jack mackerel r e s -pond to v e l o c i t y changes o f schoolmates with l a t e n c i e s varying from 1 to 2.5 sec) i t i s u n l i k e l y that such a l a r g e l a g operated i n the 2 2 present system. I f i t d i d , the p l o t o f (4D + s )/4S a g a i n s t V (Se c t i o n I I I ) would have a pronounced p o s i t i v e curvature which i s not evi d e n t from the data. The second p o s s i b i l i t y i s that k ( t h r e s h o l d da/dt) a c t u a l l y dec-l i n e s with experience. A s i m i l a r mechanism was proposed by Harlow (1939) who found t h a t a f t e r g o l d f i s h were given a strong shock, "the limen to shock was g r e a t l y reduced and weak shocks, p r e v i o u s l y i n e f f e c t i v e , i n v a r i a b l y e l i c i t e d a response". The data i n d i c a t i n g g e n e r a l i z a t i o n over model s i z e provide some evidence f o r t h i s mechanism, although they can als o be explained by the f o l l o w i n g one. This t h i r d p o s s i b i l i t y , d e s c r i b e d i n the i n t r o d u c t i o n to t h i s s e c t i o n and considered to be the most l i k e l y one, i s that the danios 58 a s s o c i a t e the v i s u a l c h a r a c t e r i s t i c s of the approaching predator with the f a c t o f i t s subsequent looming and begin to respond to t h e s e , p r i o r to dct/dt reaching the t h r e s h o l d l e v e l . Since the two s i z e s o f model were both black and round i n f r o n t view, i t i s not p o s s i b l e to separate t h i s p o s s i b i l i t y from the previous one using the data on g e n e r a l i z a t i o n over model s i z e . The present mechanism i s well known i n psychology, however, and i s termed "secondary reinforcement". Deese (1958) defined i t as "any stimulus t h a t acquires r e i n f o r c i n g power because i t i s p a i r e d with a primary or unlearned reinforcement" and b e l i e v e d the concept to be important s i n c e i t "accounts f o r l e a r n i n g i n which there seems to be no reinforcement based upon a known b i o l o g i c a l d r i v e " . S i m i l a r l y , S c h n e i r l a (1965) s t a t e d ; "a c o n s i s t e n t arousal o f [withdrawal-processes] may s e t up a c o n t i g u i t y c o n d i t i o n i n g to the o b j e c t ' s general p r o p e r t i e s " . Regardless o f the mechanism, however, the r e s u l t i s c l e a r : the d i s t a n c e from which the prey respond to an approaching predator increases with experience. Such an i n c r e a s e i n r e a c t i v e d i s t a n c e f o r f l i g h t with i n c r e a s i n g experience has a l s o been noted f o r the response o f s t i c k l e b a c k s (Gasterosteus) to pike (Benzie, 1965), sparrows to men with guns (Greppin, 1911) and Thompson's g a z e l l e s to men i n areas where they have been hunted (Walther, 1969). As noted i n the i n t r o d u c t i o n , the r e a c t i v e d i s t a n c e f o r p u r s u i t of prey by predators has a l s o been observed to i n c r e a s e with experience. Rate of change o f v i s u a l angle at the time o f response to the model predator d i d not d e c l i n e i n f i n i t e l y but became asymptotic to 59 a low l e v e l . Thus r e a c t i v e d i s t a n c e became asymptotic to a high l e v e l . In c o n t r a s t , dot/dt at the time o f response to the cinematographic predator appeared to decrease l i n e a r l y . The most l i k e l y e x p l a n a t i o n f o r t h i s d i f f e r e n c e l i e s i n the f a c t t h a t the f i s h used i n the l a t t e r case were not t o t a l l y naive, and the l e a r n i n g evidenced by them a c t u a l l y represented only the l a t t e r p a r t o f a f u l l l e a r n i n g curve, and there-f o r e approximated a l i n e a r r e l a t i o n s h i p . The f a c t o r which operates to s e t an upper l i m i t to r e a c t i v e d i s -tance i s not known. I t i s p o s s i b l e that objects a t gre a t e r distances were not perceived owing to the f a c t that the c o n t r a s t between the o b j e c t and i t s background, which decreases with d i s t a n c e i n water (Duntley, 1963), was below the c o n t r a s t t h r e s h o l d o f the danio's v i s -ual system. I t i s not p o s s i b l e , u n f o r t u n a t e l y , to c a l c u l a t e the maximum s i g h t i n g range without some info r m a t i o n about the f i s h ' s c o n t r a s t s e n s i t i v i t y , the radiances o f the o b j e c t and the background and the s p e c t r a l volume att e n u a t i o n c o e f f i c i e n t of the water. [ I t should be noted that c o n t r a s t s were e s s e n t i a l l y unchanged with f i l m -i n g d i s t a n c e i n the case o f the cinematographic predator. This may provide a f u r t h e r e x p l a n a t i o n f o r the d i f f e r e n c e i n shape o f the two le a r n i n g c u r v e s ) . A second p o s s i b i l i t y i s that the maximum di s t a n c e was s e t by the v i s u a l a c u i t y o f the eye. V i s u a l a c u i t y i s defined as the r e c i p r o c a l o f the minimum r e s o l v a b l e v i s u a l angle [Senders, 1948). In other words, oc at the maximum di s t a n c e o f r e a c t i o n may have been t h i s minimum r e s o l v a b l e angle. This was i n the neighbourhood o f 3°30' f o r danios responding to the 2.54 cm diameter model, and g r e a t l y exceeds minimum r e s o l v a b l e v i s u a l angles o f those few f i s h 60 s t u d i e d to date (Tamura, 1957; Hester, 1968). These two explanations are not independent, however, s i n c e the c o n t r a s t t h r e s h o l d o f the eye increases as v i s u a l angle subtended decreases (Hester, 1968). I t i s , o f course, p o s s i b l e t h a t objects a t greater d i s t a n c e s , and hence lower rates o f incre a s e o f da/dt, were perceived but not reacted t o . S t i m u l i with da/dt below some other t h r e s h o l d l e v e l may not be f r i g h t e n i n g to the danios and may even cause approach behaviour, a p o s s i b i l i t y which w i l l be considered i n more d e t a i l i n S e c t i o n V. No e x t i n c t i o n o f the learned change i n response could be demon-s t r a t e d a f t e r 10 days without experience o f the cinematographic predator. This experiment was not continued longer f o r p r a c t i c a l reasons. However, i t would be u n l i k e l y i f prey d i d not experience predators at l e a s t t h i s f r e q u e n t l y i n nature. Retention times i n f i s h g e n e r a l l y appear q u i t e long. Manteifel e_t al_ Cl969) concluded t h a t c o n d i t i o n e d r e f l e x e s i n f i s h , once acquired, do not disappear even a f t e r a month's i n t e r r u p t i o n o f t e s t s . E x t i n c t i o n o f a learned response o f rainbow t r o u t CSalmo g a i r d n e r i ) , to d i s c o v e r prey from g r e a t e r d i s t a n c e s , took between 14 and 90 days (Ware, 1971) and T a r r a n t Cl964) found that a co n d i t i o n e d response o f sockeye salmon, to seek food when a l i g h t was turned on, remained s t a b l e up to 280 days without reinforcement. G e n e r a l i z a t i o n o f the learned response over model shape, c o l o r , e t c . was not examined. An e v o l u t i o n a r y l i n e o f argument, however, leads to the c o n c l u s i o n t h a t g e n e r a l i z a t i o n should not be complete. I f i t were, then experience with any o b j e c t v/ould cause r e a c t i v e d t s -61 tances to a l l other objects (whether predators or not) to i n c r e a s e . I f t h i s were the case then those prey with high da/dt thresholds (low r e a c t i v e d i s t a n c e s ) would be at a s e l e c t i v e disadvantage u n t i l they had learned to r e a c t to lower da/dt l e v e l s . Natural s e l e c t i o n pre-sumably would have operated to produce prey with the lowest thresholds p o s s i b l e , which has p a t e n t l y not been the case, at l e a s t f o r zebra danios. In a d d i t i o n , Hediger (1964) has shown that i t i s p o s s i b l e to reduce an animal's f l i g h t d istance to some s t i m u l i through t r a i n i n g . Ware (1971), however, showed that rainbow t r o u t g e n e r a l i z e learned changes i n r e a c t i v e d i s t a n c e over at l e a s t some prey c o l o r s . In c o n t r a s t , Beukema (1968) found t h a t s t i c k l e b a c k s do not do so. Hinde (1966) reported that "exposure to a f r i g h t e n i n g stimulus o f t e n r e s u l t s i n an increased responsiveness to a wide v a r i e t y o f s t i m u l i e l i c i t i n g s i m i l a r types o f behaviour". This t r a n s f e r i s c a l l e d "pseudo-conditioning". On the other hand, Kramer and von St. Paul (1951) found that the f r i g h t e n i n g e f f e c t produced by chasing a b u l l -f i n c h with a mounted k i n g f i s h e r was t r a n s f e r r e d only to other members of the k i n g f i s h e r f a m i l y . Thus the problem o f the extent o f genera-l i z a t i o n i s a complex one which w i l l r e q u i r e a major study to e l u c i d a t e . Examples o f avoidance l e a r n i n g by f i s h to model or r e a l predators have been reported i n the l i t e r a t u r e , but not i n the context o f changes i n r e a c t i v e d i s t a n c e . Goz (1941) found t h a t minnows learned to avoid pike by a s s o c i a t i n g the odor of the pike with f r i g h t substance r e l e a s e d from the s k i n of a schoolmate t h a t had been attacked. Thompson (1966), Kanayama e_t al_ (1964), Kanayama & Tuge (1968), and Popov (1953) r e p o r t -ed t h a t f r y o f chinook salmon, rainbow t r o u t , chum salmon, and roach, 62 r e s p e c t i v e l y , l e a r n to avoid model predators p a i r e d with e l e c t r i c 1 shock. Rasbora l e a r n to a s s o c i a t e the occurrence o f a f l a s h l i g h t with the presence o f f r i g h t substance obtained from the s k i n of con-s p e c i f i c s (Thines and Vandenbussche, 1966). Lescheva (1968) has even reported that roach allowed to watch through a glass p a r t i t i o n while c o n s p e c i f i c s were eaten by pike l a t e r prove l e s s s u s c e p t i b l e to predation than the o r i g i n a l performers. The p o s s i b i l i t y t hat the actual a s s o c i a t i o n was made between roach f r i g h t substance and the s i g h t or odor of the pike was not r u l e d out, however. S i m i l a r l y , G i r s a ( i 9 6 2 ) and Veselov (1962), found that i n verkhovka (Leucaspius d e l i n e a t u s ) and Vimba vimba r e s p e c t i v e l y , the s u r v i v o r s o f one bout o f predation were subsequently l e s s s u s c e p t i b l e . However, i n n e i t h e r case was there any c o n s i d e r a t i o n of the a l t e r n a t e e x p l a n a t i o n of s e l e c t i o n of the most s u s c e p t i b l e prey during the i n i t i a l bout. Studies on animals other than f i s h are r a t h e r more r a r e but Nice and t e r Pelkwyk (1941) f e l t t h at young song sparrows recognize cats and cowbirds as enemies by a s s o c i a t i n g t h e i r appearance with the alarm c a l l of the a d u l t sparrow. Although the danios were t r a i n e d and t e s t e d o n l y as i n d i v i d u a l s , i t i s o f i n t e r e s t to speculate upon the f u n c t i o n of the school i n avoidance l e a r n i n g . I t i s p o s s i b l e , as suggested by Lescheva 0 9 6 8 ) , th a t prey observing schoolmates e i t h e r being s u c c e s s f u l l y attacked or being able to s u c c e s s f u l l y escape, may l e a r n the appropriate f r i g h t response. Such "empathic l e a r n i n g " has a l s o been reported f o r ducks ( K l o p f e r , 1957). Secondly, as discussed i n S e c t i o n I I I , f i s h may 63 respond to t h e i r schoolmates and not d i r e c t l y to the approaching predator. Thus a number o f experienced f i s h tn the school could cause the e n t i r e school to behave as i f a l l i t s members were experienced. For example, Verheijen (1956) found t h a t a f r i g h t response to alarm substance by Rasbora heteromorpha could be v i s u a l l y t r a n s f e r r e d to c o n s p e c i f i c s which had not been exposed to the substance. O'Connell (1960) reported t h a t naive sardines (Sardinops caerula) added to a school which had been t r a i n e d to come to a feeding area whenever a l i g h t was switched on, acted e n t i r e l y i n unison with the school from the f i r s t t r i a l . Perhaps f o r these reasons Hunter & Wisby (1964) found t h a t carp t r a i n e d to avoid a moving net learned f a s t e r , under some conditions,when t r a i n e d tn groups than as i n d i v i d u a l s . A s c h o o l , t h e r e f o r e , may serve p r e c i s e l y t h a t f u n c t i o n . S i m i l a r advantages may accrue to f l o c k i n g b i r d s & herding mammals. The l e a r n i n g process has been discussed i n r e l a t i o n to a c t i v e search and p u r s u i t predators, but i t may be p o s s i b l e f o r animals preyed upon by ambush predators to use a v a r i a n t of the mechanism. In t h i s s i t u a t i o n the prey would not see the predator coming from a d i s t a n c e but would s t i l l experience a s h o r t p e r i o d o f looming. Such prey may be able to a s s o c i a t e the f e a t u r e s o f the l o c a l e where attack occurred with the f a c t of looming and t h e r e f o r e avoid such areas i n the f u t u r e . The e f f e c t , maintenance of a g r e a t e r d i s t a n c e from the predator, would be i d e n t i c a l . 64 5 Conclusions ( i ) The r a t e of change o f v i s u a l angle at the time o f response to an a r t i f i c i a l predator d e c l i n e s as a f u n c t i o n o f the number of previous experiences of that predator, ( i i ) The prey apparently a s s o c i a t e the v i s u a l c h a r a c t e r i s t i c s of the predator with the f a c t o f i t s subsequent s u p r a - t h r e s h o l d r a t e o f looming, and begin to respond to the v i s u a l charac-t e r i s t i c s p r i o r to da/dt exceeding k ( i i i ) The da/dt t h r e s h o l d (k) d e c l i n e s r a p i d l y a t f i r s t and then more s l o w l y , becoming asymptotic to some low l e v e l . Reactive d i s t a n c e shows a n e g a t i v e l y a c c e l e r a t e d r i s e to an asymptote, ( i v ) The change of da/dt a t the time of response i s not due to growth, maturation, or i n c r e a s i n g f a m i l i a r i t y with the t e s t i n g s i t u a t i o n during the l e a r n i n g p e r i o d , (v) No e x t i n c t i o n of the learned response i s evident a f t e r 10 days without experience o f the predator, ( v i ) The angle of escape i s not a f f e c t e d by experience, ( v i i ) Escape v e l o c i t y d e c l i n e s with experience o f the cinematographic predator, but not with experience o f the model predator. 65 V THE EFFECT OF HUNGER ON THE THRESHOLD RATE OF CHANGE OF VISUAL ANGLE 1 I n t r o d u c t i o n H o l l i n g ( i n prep) has shown that the di s t a n c e from which the mantid (Hierodula crassa) w i l l begin to s t a l k prey i s dependent upon the accuracy o f the mantid's estimate of d i s t a n c e (<$)• The process o f d i s t a n c e estimation i n the mantid i s a b i n o c u l a r one, and the rate o f change o f the angle o f b i n o c u l a r v i s i o n (/3) with rate o f change o f di s t a n c e from the eye o f the mantid to the prey (RP) determines the accuracy o f the process. H o l l i n g showed that d/3 = 2 (ES + L) ...(18) dRP 4 R p 2 + + L ) 2 where ES = i n t e r o c u l a r d i s t a n c e o f mantid L = length o f prey d/3/dRP was constant at the time o f i n i t i a t i o n o f the s t a l k and equal to the th r e s h o l d £ . . ^mi n This equation,conceptualized i n a t o t a l l y d i f f e r e n t f a s h i o n , i s analogous to equation (2) derived i n Sect i o n III above. Since dRP = -V ...(19) dt t h e r e f o r e d/3 = -2V(ES + L) ...(20) d t 4RP 2+(ES+L) 2 When D and S are s u b s t i t u t e d f o r RP a n d ! r e s p e c t i v e l y , to keep n o t a t i o n constant, then d ^ = -2V(ES + S) ... (21) d t 4D 2+(ES+S) 2 6 6 I f ES i s ignored as being small r e l a t i v e to S (as would be the case when the prey i s s m a l l e r than the predator approaching i t ) then d/3 = -2VS ...(22) d t 4 D 2 + S 2 Equation (22) i s nearly i d e n t i c a l to equation ( 2 ) . I t t h e r e f o r e appears that mantids s t a l k i n g prey and danios f l e e i n g predators use e s s e n t i a l l y s i m i l a r mechanisms bf d e c i s i o n making. The mantids begin to s t a l k when d/3/dRP exceeds £, and the danios f l e e approaching objects when the c l o s e l y r e l a t e d measure do/dt exceeds k. H o l l i n g a l s o demonstrated that § was a f f e c t e d by hunger i n such a way that the hungrier the mantid, the l e s s demanding i t s requirement f o r accurate d i s t a n c e e s t i m a t i o n . He f e l t t h a t a hungry predator would be "more w i l l i n g " to accept the r i s k that an o b j e c t was a l a r g e enemy r a t h e r than a small prey." Since the f l i g h t mechanism of the danios i s so s i m i l a r , i t seemed l o g i c a l to ask whether the f l i g h t t h r e s h o l d i s a f f e c t e d by hunger i n a s i m i l a r f a s h i o n . The hypothesis t e s t e d i n t h i s s e c t i o n i s that the hungrier the danio, the higher i t s da/dt t h r e s h o l d and, hence, the lower i t s r e a c t i v e d i s t a n c e to a predator o f constant s i z e and approach v e l o c i t y . This i s based upon the reasoning that a hungry prey would be more " w i l l i n g " to accept the p o s s i b i l i t y t h at the approaching o b j e c t was a food item r a t h e r than a p o t e n t i a l predator. 2 Methods In order to assess the e f f e c t o f hunger on the t h r e s h o l d r a t e of change o f v i s u a l angle, i t was f i r s t necessary to de f i n e hunger 67 i n terms o f a v a r i a b l e which could be e a s i l y c o n t r o l l e d experimentally Time o f food d e p r i v a t i o n was chosen f o r t h i s purpose. Twenty-four danios were placed i n t o i n d i v i d u a l 16 oz. wide-mouth j a r s and allowed to become acclimated to the j a r s f o r a p e r i o d o f three days, during which time they were fed twice. On the f o u r t h day the f i s h were allowed to feed to s a t i a t i o n during a 25 minute p e r i o d . Excess food was then siphoned from the j a r s . Three danios each were then refed at 1, 2, 4, 8, 12, 24, 36 and 48 hours a f t e r t h i s i n i t i a l f e e d i n g . The weight of food (Tetramtn f l a k e s ) accepted by each danio was recorded. This procedure was repeated with a new group of 24 danios, to give a t o t a l of 6 r e p l i c a t e s at each of the 8 de-p r i v a t i o n times. The danios averaged 29.6 mm fork length (range 27.0-32.0). The water temperature throughout the experiment was 23-24°C. The f l a k e s o f food were presented one at a time from a p l a s t i c p e t r i d i s h u n t i l the danio would accept no more. The d i f f e r e n c e between the pre- and p o s t - f e e d i n g weights of the d i s h , was c o r r e c t e d as follows to give the actual weight of food eaten. A c o n t r o l p e t r i d i s h c o n t a i n i n g a s i m i l a r amount o f food was c a r r i e d about with the ones from which the feedings were made. The pre- and po s t - f e e d i n g weights o f t h i s d i s h were never the same, apparently because o f d i f -ferences i n humidity between the rooms used f o r weighing and fe e d i n g . A c o r r e c t i o n f a c t o r (post weight o f food/pre-weight o f food) was t h e r e f o r e computed f o r each feeding and a p p l i e d to the pre-weights of the food i n the experimental d i s h e s . The weight of food eaten by the danio could then be a c c u r a t e l y determined. 68 Two other procedural points should be mentioned. F i r s t , the s a t i a t i o n feedings were conducted from 0800 to 0855 hours and the experimental feedings a t 0925, 1030, 1235, 1640, 2040, 0845, 2050, and 0900 hours. That i s , the experimental feedings were c a r r i e d out at d i f f e r e n t times o f day. A p r e l i m i n a r y experiment, however, i n d i c a t e d no d i u r n a l p e r i o d i c i t y i n w i l l i n g n e s s to feed i n t h i s stock of f i s h ( hatchery-reared). Secondly, the danios were not i n v i s u a l contact with each other during the feedings. Thus the amount of food was a measure of hunger, and was not confounded with any s o c i a l f a c i l i t a t i o n e f f e c t . Having defined hunger as a f u n c t i o n of time of food d e p r i v a t i o n , the next step was to determine the r e l a t i o n s h i p o f the l a t t e r to the ra t e o f change o f v i s u a l angle at the time o f response to the c i n e -matographic predator. A number o f danios i n a l a r g e holding aquarium were fed to s a t i a t i o n and the excess food removed. Six danios each were removed from the tank at 1, 3, 5, 8 and 11 hours a f t e r feeding and t r a n s f e r r e d to the six-chambered experimental tank where they were allowed one hour o f a c c l i m a t i o n before being presented with the standard s t i m u l u s . D e p r i v a t i o n times, t h e r e f o r e , were 2, 4, 6, 9 and 12 hours. This procedure was repeated to provide a t o t a l o f 12 r e p l i c a t e s a t each of the f i v e d e p r i v a t i o n times. These danios averaged 29.4 mm i n length (range 26.0 - 34.0 mm). The water tem-peratures were the same as those i n the hunger experiments. The da/dt a t the time of response was recorded f o r each f i s h t h a t responded to the cinematographic predator. In a d d i t i o n , the 69 t o t a l escape v e l o c i t y and the component of t h i s d i r e c t e d 180 from the screen were recorded to determine whether response q u a l i t y changed with hunger. 3 Results a) Hunger as a f u n c t i o n o f d e p r i v a t i o n time The weight o f food eaten by the danios at each of the e i g h t d e p r i v a t i o n times i s shown i n Table XII and F i g . 15. Table XII Mean and standard e r r o r o f the weight (grams)of food eaten by zebra danios a f t e r d i f f e r e n t periods of d e p r i v a t i o n DEPRIVATION WEIGHT EATEN (grams) TIME n X S£ 1 4 .0031 .0010 2 . 6 .0049 .0008 4 4 .0062 .0009 8 5 .0077 .0014 12 5 .0086 .0012 24 5 .0065 .0012 36 5 .0061 .0015 48 , 5 .0081 .0012 During the f i r s t 12 hours the hunger rose smoothly towards an apparent asymptote. A f t e r t h i s time, however, hunger appear-ed to d e c l i n e and then i n c r e a s e again,suggesting a d i f f e r e n t stage i n the hunger process. In the subsequent a n a l y s i s , there-f o r e , only the data from the f i r s t 12 hours o f d e p r i v a t i o n were Figure 15 E f f e c t of d e p r i v a t i o n time on hunger (mg of food accepted) i n the zebra danio (mean ± one standard e r r o r ) . 70 DEPRIVATION T IME (hrs) 71 considered. The r e s u l t s should not be e x t r a p o l a t e d beyond t h i s range. The form o f the r e l a t i o n s h i p shown i n F i g . 15 i s very s i m i l a r to t h a t of a number of hunger curves d e s c r i b e d by H o l l i n g (1966). An i d e n t i c a l model was t h e r e f o r e assumed. According to t h i s model: dH dTF = AD (HK - H) (23) Where H = hunger (weight o f food eaten) TF = d e p r i v a t i o n time AD = constant, instantaneous rate of d i g e s t i o n HK = maximum gut c a p a c i t y (maximum weight of food intake p o s s i b l e ) Thus: and, transforming, In HK H = HK (1 e-ADCTF), AD(TF) H K - H .(24) ..(25) The data were t h e r e f o r e transformed to t h i s l i n e a r form and a value o f HK determined which minimized the r e s i d u a l sum o f squares i n the r e g r e s s i o n a n a l y s i s . The r e g r e s s i o n was f o r c e d through the o r i g i n to s a t i s f y the requirement o f no i n t e r c e p t and the value of the slope o f the r e g r e s s i o n taken as the estimate o f AD. The transformed data are shown i n F i g . 16 and the r e g r e s s i o n was s i g n i f i c a n t at p<.005. The best estim-ates o f HKand AD were .0089 grams and .2773 h r - i r e s p e c t i v e l y . Figure 16 Hunger data transformed to t e s t equation C25) i n the t e x t . 72 DEPRIVATION T IME (hrs) 73 S u b s t i t u t i n g these i n t o equation (24) leads to the f o l l o w i n g p r e d i c t i v e equation: H = .0089 (1 - e - - 2 7 7 3 ( T F ) } b) Threshold dfl/dt as a f u n c t i o n o f hunger The t h r e s h o l d da/dt measures of those f i s h which responded to the cinematographic predator are shown i n Table XIII along with the hunger l e v e l s corresponding to each d e p r i v a t i o n time. The da/dt measures are p l o t t e d a g a i n s t hunger l e v e l s i n F i g . 17. Table XIII Hunger and t h r e s h o l d rate o f change of v i s u a l angle a f t e r various times o f food d e p r i v a t i o n . Hunger l e v e l s were c a l c u l a t e d from the equation H = .0089(1 - e"' 2 7 7 3 T F ) TF (hrs) n HUNGER (gms) THRESHOLD da/dt (rad/sec) X Sj 2 4 .0038 .129 .030 4 8 .0060 .181 .022 6 6 .0072 .146 .015 9 7 .0082 .193 .035 12 7 .0086 .172 .025 A r e g r e s s i o n analysts of t h r e s h o l d d a/dt (k) ag a i n s t hunger d i d not i n d i c a t e the ex i s t e n c e o f a slope s i g n i f i c a n t l y d i f -f e r e n t from zero at p = .05. Further, i n d i v i d u a l t - t e s t s between the mean k at TF = 2 hours and each o f the other mean k's demonstrated t h a t none o f these d i f f e r e n c e s were s i g n i f i c a n t . Figure 17 E f f e c t of hunger on t h r e s h o l d da/dt (k) o f danios r e s -ponding to the cinematographic predator. The bars represent the means ± one standard e r r o r . 74 1 1 I I I L 4 6 8 H U N G E R (mg) 75 I t must t h e r e f o r e be concluded that hunger had no e f f e c t on the r e a c t i v e d i s t a n c e of these danios to p o t e n t i a l p r e d a t o r s , at l e a s t w i t h i n the range of hungers used. In a d d i t i o n , there was no e f f e c t o f hunger on the t o t a l escape v e l o c i t y of the danios or the component o f t h i s v e l o c i t y d i r e c t e d 180° from the screen. The danios tended to escape at a v e l o c i t y of 19.1 cm/sec with an escape v e l o c i t y d i r e c t e d away from the screen o f 10.8 cm/sec. In other words, t h e i r i n i t i a l angle o f f l i g h t averaged 90° + s i n " 1 (10.8/19.1) = 124°. Thus, the q u a l i t y o f t h e f l i g h t response was a l s o unaffected by hunger. 4 D i s c u s s i o n For the purposes of t h i s experiment, hunger was c o n c e p t u a l i z e d as the unused c a p a c i t y o f the stomach and was o p e r a t i o n a l l y defined as the amount o f food accepted by the f i s h during an ad libidum feeding s e s s i o n . The amount of food consumed by the danios a f t e r various d e p r i v a t i o n times was described very well by a model which assumes that the maximum amount eaten represents the maximum stomach c a p a c i t y (HK) and t h a t the instantaneous rate at which food consump-t i o n increases with d e p r i v a t i o n time i s the same rate at which food i s passed through the stomach (AD). An i d e n t i c a l model has been used to d e s c r i b e hunger i n the mantids Hierodula crassa and Mantis  r e l i g i o s a , and the blowfly Phormia regina ( H o l l i n g , 1966). However, i n none of these cases were AD and HK determined independently; they were estimated by l e a s t squares curve f i t t i n g techniques. To determine whether the model i s explanatory, r a t h e r than simply d e s c r i p t i v e , would r e q u i r e independent estimates of parameter values. 76 There i s some evidence that the amount of food accepted by animals, a t l e a s t by v e r t e b r a t e s , i s not a p e r f e c t e s t i m a t o r o f the amount of unused space i n the d i g e s t i v e t r a c t . I t may be e i t h e r an over- or underestimate. Overesttmation may be the r e s u l t o f long term hunger mechanisms independent o f the f u l l n e s s o f the gut. De R u i t e r (.1963), f o r example, presented evidence that hunger i s a f f e c t e d by the l e v e l s o f glucose, and perhaps other n u t r i e n t s , i n the blood. T h i s slow-acting mechanism could cause overeating a f t e r prolonged d e p r i v a t i o n , a phenomenon reported f o r f i s h by Brown (1957). Under-e s t i m a t i o n has been a l l u d e d to by Kariya e t aJL(1968) and documented by B r e t t (1971) who found t h a t the rate at which a p p e t i t e i n sockeye salmon increases with time of food d e p r i v a t i o n i s l e s s than the rate at which the stomach empties. The reasons f o r the discrepancy are u n c l e a r but p a r t o f the e x p l a n a t i o n may l i e i n the p a r t i c l e s i z e o f the food. I f the s i z e o f the p a r t i c l e exceeds the unused stomach volume, i t w i l l not be accepted. In a d d i t i o n , i n the case o f both the danios and the salmon, the f i s h had to recognize, s t r i k e at and eat the food. The hunger thresholds f o r these a c t i v i t i e s may be higher than t h a t which had to be exceeded by the mantids, whose mouthparts were a c t u a l l y touched by the food ( H o l l i n g , 1966). Despite the discrepancy, however, B r e t t ( i b i d ) concluded t h a t the major f a c -t o r c o n t r o l l i n g a p p e t i t e was the emptying o f the stomach. S i m i l a r l y , Beukema (1968) concluded t h a t the amount o f space a v a i l a b l e tn the gut o f the s t i c k l e b a c k was o f d e c i s i v e i n f l u e n c e on the amount eaten. 77 The amount eaten by the danios tn the present study w t l l t h e r e f o r e be considered a reasonable f i r s t approximation o f the f u n c t i o n a l s t a t e o f the i n t e r n a l hunger mechanism, i . e . o f hunger m o t i v a t i o n . H o l l i n g [1966) presented evidence t h a t r e a c t i v e distances f o r awareness and p u r s u i t i n the mantid CH. crassa) i n c r e a s e d as a l i n e a r f u n c t i o n o f hunger. The mantid was aware of prey at a l l hunger l e v e l s , but pursued them only i f i t s hunger exceeded a t h r e s h o l d l e v e l (HTP). L a t e r work ( H o l l i n g , i n prep) i n d i c a t e d t h a t p u r s u i t d i s t a n c e d i d not i n c r e a s e l i n e a r l y with hunger but was c h a r a c t e r i z e d by a n e g a t i v e l y a c c e l e r a t e d r i s e to a plateau. Beukema (1968) reported that d i s t a n c e o f perception i n the s t i c k l e b a c k was not a f f e c t e d by hunger and concluded t h a t t h i s would r e q u i r e a change i n H o l l i n g ' s g e n e r a l i z e d model o f the predation process. However, the d e p r i v a t i o n times used by Beukema a l l exceeded 24 hours. The stomachs of the s t i c k l e b a c k s were t h e r e f o r e probably e q u a l l y empty at a l l d e p r i v a t i o n times. Hence, hunger, as defined by H o l l i n g Ci bid) and used i n the present study, would have been constant. In f a c t , Beukema d i d f i n d t h a t the chance of a prey being discovered by a s t i c k l e b a c k a t a given d i s t a n c e increased with hunger at low hunger l e v e l s . Even here, t h e r e f o r e , d i s t a n c e o f r e a c t i o n was a f f e c t e d by hunger." Some p r e l i m i n a r y data by Ware (1971) i n d i c a t e d t h a t the s h o r t term changes i n the amount o f food ingested by t r o u t CSalmo g a i r d n e r j ) d i d not a f f e c t t h e i r responsiveness to prey. However, the data i s not extensive enough to allow r e j e c t i o n o f the hypothesis. In the absence of such data, i t w i l l be assumed that the r e a c t i v e d i s t a n c e 78 of predators to prey increases w i t h Increasing hunger up to some maximum l e v e l . The s i m i l a r i t y between the mechanisms used by v i s u a l predators and by v i s u a l prey to s e t t h e i r r e a c t i v e distances to prey and predators r e s p e c t i v e l y , has been commented upon i n the i n t r o d u c t i o n to t h i s s e c t i o n . In both cases the animals respond to rates o f change o f v i s u a l angles. Few animals, other than herbivores or top c a r n i v o r e s , can be d e s c r i b e d only as predators or prey. Most animals are both simultaneously: feeding on some organisms and being fed upon by o t h e r s . These animals presumably have tv/o t h r e s h o l d s , s e t t i n g two r e a c t i v e d i s t a n c e s : one f o r p u r s u i t and one f o r escape. The f a c t t h at two animals as d i s p a r a t e as mantids and danios use s i m i l a r mechanisms f o r these two behaviours i s s t r o n g l y suggestive of the .existence of two f u n c t i o n a l l y s i m i l a r d e c i s i o n making mechanisms i n any one animal. Thus, an o b j e c t exceeding one t h r e s h o l d may be pur-sued, but i f the same o b j e c t exceeds a second t h r e s h o l d i t may cause f l i g h t . In a somewhat more f o r m a l i z e d f a s h i o n t h i s p r e c i s e l y expresses the notion of S c h n e i r l a (1965) t h a t , i n a l l animals, low s t i m u l a t i v e i n t e n s i t i e s tend to e l i c i t approach while high i n t e n s i t i e s tend to e l i c i t withdrawal. Evidence f o r t h i s approach/withdrawal d u a l i t y i s widespread and convincing. A few references are p e r t i n e n t i n the context o f predator-prey i n t e r a c t i o n s (see S c h n e i r l a , 1965, f o r a thorough review o f the evidence i n other c o n t e x t s ) . Breder and Halpern (1946) found that an a r t i f i c i a l f i s h (painted cardboard drawn past an aquarium) presented to zebra danios caused f l i g h t i f g r e a t e r than 32 79 sq. tn, tn area, but caused i n c r e a s i n g frequencies o f advance with decreasing s t z e down to 4 sq. tn. This s i z e d " f i s h " c o n s i s t e n t l y e l i c i t e d approach. Boulet Cl960) found t h a t objects 4-7 mm. long provoked p u r s u i t tn perch, while longer objects provoked f l i g h t . S i m i l a r l y , the optimum angular v e l o c i t i e s o f the o b j e c t were 26 and 65°/sec to provoke p o s i t i v e and negative r e a c t i o n s , r e s p e c t i v e l y . Both Ewert (1970) and Gr'usser and Grusser-Cornehls (1968) reported that both prey capture and escape behaviour were dependent upon s i z e , angular v e l o c i t y and c o n t r a s t o f the o b j e c t presented to anurans. The p r o b a b i l i t y o f e l i c i t i n g e i t h e r response was dependent on angular s i z e and v e l o c i t y (Ewert, i b i d ) with higher s i z e s and v e l o c i t i e s e l i c i t i n g avoidance, lower ones o r i e n t i n g a c t i v i t y . Owing to t h i s apparent s i m i l a r i t y o f the two mechanisms, the e f f e c t o f hunger on-the t h r e s h o l d rate o f change of v i s u a l angle f o r escape was i n v e s t i g a t e d . Within the range o f hungers examined, no e f f e c t could be detected. There was some suggestion o f an i n c r e a s -ing doc/dt t h r e s h o l d (and hence a decreasing r e a c t i v e d i s t a n c e ) but t h i s was not s t a t i s t i c a l l y s i g n i f i c a n t . Extension o f the range o f hungers may i n d i c a t e e f f e c t s on f l i g h t d i s t a n c e , but at the present time i t must be concluded t h a t a hungry danio i s not w i l l i n g to accept higher r i s k s o f predation i n the hope that the approaching o b j e c t may a c t u a l l y be a food p a r t i c l e . Avoidance o f predators appears to be o f o v e r i d i n g importance i n determining the response o f the danio to objects tn i t s v i s u a l f i e l d . 8 0 5 Conclusions (t) Hunger, o p e r a t i o n a l l y d e f ined as the amount o f food eaten by an i n d i v i d u a l i n an ad libidum feeding s e s s i o n , has no e f f e c t on the t h r e s h o l d doc/dt f o r f l i g h t i n zebra danios. ( i i ) S i m i l a r l y , hunger has no e f f e c t on the danios escape v e l o c i t y or i t s angle o f escape r e l a t i v e to the approaching predator. 81 VI ADDITION OF THE AVOIDANCE LEARNING COMPONENT TO A GENERALIZED MODEL OF THE PREDATION PROCESS 1 I n t r o d u c t i o n The experiments d e s c r i b e d above have shown that the r e a c t i v e d i s t a n c e of zebra danios to an approaching predator may be p r e d i c t e d from the equation RD = / VS - S^ ....(3) J k 4 Where V = approach v e l o c i t y of predator (cm/sec); $ = maximum width o f predator (cm); and k = t h r e s h o l d r a t e o f change o f v i s u a l angle ( r a d / s e c ) . I t has a l s o been shown that k decreases as a f u n c t i o n o f experience, according to an equation o f the form ^ n ...07) Where E = number o f past experiences with the predator; and k ^ , EC and EONK are p o s i t i v e constants. As a consequence o f these two r e l a t i o n s h i p s , r e a c t i v e d i s t a n c e f o r f l i g h t e x h i b i t s a n e g a t i v e l y a c c e l e r a t e d r i s e to a plateau with i n c r e a s i n g experience. There were i n s u f f i c i e n t data i n the l i t e r a t u r e to t e s t the g e n e r a l i t y o f e i t h e r o f these r e l a t i o n s h i p s i n a q u a n t i t a t i v e manner, but several l i n e s o f argument support the contention that they have g e n e r a l i t y , at l e a s t i n a broad, q u a l i t a t i v e sense. I t w i l l be assumed that the r e a c t i v e d i s t a n c e o f any prey to an a c t i v e l y searching predator can be p r e d i c t e d from equation ( 3 ) , and t h a t equation (17) describes the way i n which t h r e s h o l d do(/dt changes with experience i n a l l prey capable o f a s s o c i a t i v e l e a r n i n g . 82 The above equations provide a q u a n t i t a t i v e expression o f the avoidance component of the predation process and make p o s s i b l e i t s a d d i t i o n to H o l l i n g ' s (1965, 1966) g e n e r a l i z e d predation model. This w i l l be done by experimentally determining the i n t e r a c t i o n s between the new component and e x i s t i n g components and subcomponents of the model (Table XIV). Table XIV The components o f predation and t h e i r subcomponents as conceptualized by H o l l i n g 0 9 6 3 , 1965, 1966). 1 Rate o f s u c c e s s f u l search (a) Predator's r e a c t i v e d i s t a n c e f o r prey (b) Predator's v e l o c i t y (c) Prey's v e l o c i t y (d) Capture success 2 Time prey are exposed to (a) Time spent i n non-attack predators a c t i v i t i e s (b) Time a v a i l a b l e f o r attack 3 Handling time per prey (a) Time spent pursuing and subduing (b) Time spent e a t i n g (c) Time spent i n d i g e s t i v e pause 4 Hunger Ca) D i g e s t i v e rate (b) Maximum stomach c a p a c i t y 5 E x p l o i t a t i o n 6 Int e r f e r e n c e between predators 7 Learning by predator 8 I n h i b i t i o n by prey 9 S o c i a l f a c i l i t a t i o n Components one through s i x are present, i n the most advanced ve r s i o n of the model published to date ( G r i f f i t h s and H o l l i n g , 1959); components 83 seven and e i g h t have been conceptualized mathematically and added to a model c o n t a i n i n g the f i r s t f o u r components ( H o l l i n g , 1965); component number nine has not been examined. The way i n which the new component of avoidance l e a r n i n g has been conceptualized suggests that i t s e f f e c t s w i l l be manifested through i n t e r a c t i o n s with capture success (which may be f u r t h e r sub-d i v i d e d i n t o successes o f r e c o g n i t i o n , p u r s u i t , s t r i k i n g , subduing, and e a t i n g ) and time spent pursuing. Time spent pursuing w i l l be a fu n c t i o n o f the r e a c t i v e d i s t a n c e o f the prey, and p u r s u i t success w i l l be a f u n c t i o n o f the r e l a t i o n s h i p between p u r s u i t time and the time which the prey needs to reach e f f e c t i v e cover. The way i n which prey r e a c t i v e d i s t a n c e i s hypothesized to a f f e c t p u r s u i t time i s shown diagrammatically i n F i g . 18. The predator s i g h t s the prey at a dis t a n c e ROp^ and begins to approach i t at a given v e l o c i t y (AV). Once the predator has approached to RPp^rryj the prey begins to f l e e . The time taken to cl o s e the dist a n c e R Dp R fr D - R D P R E Y ^ S T H E A P P R O A C N T I M E ( T A ) A N D i s expressed as: TA = R DPRED " R DPREY. ,,c* '. .' AV ...Uo; Once the prey has begun to f l e e (with escape v e l o c i t y EV), the predator pursues i t with v e l o c i t y PV u n t i l i t i s w i t h i n the s t r i k e d i s t a n c e (DS). In order to s t r i k e at the prey the predator must c l o s e the d i s t a n c e RDppjry - DS. I t does so at a r e l a t i v e v e l o c i t y , which equals PV-EV i f the prey moves d i r e c t l y away, but which i s some func-t i o n o f the r e l a t i v e v e l o c i t y i n the case o f any other escape t r a -j e c t o r y . For s i m p l i c i t y , the r a t e o f c l o s u r e i s assumed to be Figure 18 Diagrammatic r e p r e s e n t a t i o n of the p u r s u i t o f a prey by a predator. RD = r e a c t i v e d i s t a n c e ; DS = predator s t r i k e d i s t a n c e . See t e x t f o r complete ex p l a n a t i o n . 84 wt titflnm, t i i — • I1% *-RDPREY« wDS^.>capture ? RD, PRED 85 REL = a (PV-EV) ...(27) Time taken to c l o s e the d i s t a n c e i s t h e r e f o r e TC = RD, PREY - DS ...(28) The time taken to c l o s e the d i s t a n c e DS i s assumed to be i n s t a n -taneous and constant. T o t a l p u r s u i t time (TP) can t h e r e f o r e be expressed as The hypotheses expressed q u a n t i t a t i v e l y above were t e s t e d with data c o l l e c t e d by f i l m i n g i n t e r a c t i o n s between predators and prey. R e l a t i o n s h i p s v e r i f i e d e xperimentally were added to the model o f the predation process and t h e i r e f f e c t s examined by means o f computer s i m u l a t i o n experiments. ' 2 Filmed i n t e r a c t i o n s between predators and prey (a) Methods A t o t a l o f 78 i n t e r a c t i o n s between non-naive zebra danios and the l a r g e r bass were f i l m e d i n the predation arena. The bass was allowed to consume a maximum of f i v e prey per day and the experiment was run over a p e r i o d of three months ( A p r i l 15 to J u l y 10, 1971). The bass, however, d i d not grow during t h i s p e r i o d . The danios were not measured p r i o r to the experiments but were a l l judged to be 27-33 mm long. At the s t a r t of a t r i a l , the bass was already i n the arena. When i t was i n a p o s i t i o n on the opposite s i d e o f the arena TP = TA + TC ...(29) 86 from the s l i d i n g doors, a s t n g l e prey was introduced. The prey was contained i n a styrofoam cup h a l f - f i l l e d with water which f l o a t e d on the surface o f the tank. A s t r i n g connected to the bottom o f the cup was p u l l e d to t i p the cup and i n t r o -duce the danio i n t o the arena. Filming began with the i n t r o -d u c t i o n o f the danio and ended with i t s capture. F i f t e e n minutes separated consecutive t r i a l s . A n a l y s i s o f f i l m s c o n s i s t e d o f recording the f o l l o w i n g para-meters o f the i n t e r a c t i o n : predator r e a c t i v e d i s t a n c e , preda-t o r approach v e l o c i t y , prey r e a c t i v e d i s t a n c e , time taken to approach (TA), prey escape v e l o c i t y , predator p u r s u i t v e l o c i t y , s t r i k e d i s t a n c e , time taken to c l o s u r e (TC), and whether or not the s t r i k e was s u c c e s s f u l . The prey were not always v i s i b l e and, i n f a c t , only 33 sequences gave useful data. Cb) Results and d i s c u s s i o n The observed predator and prey r e a c t i v e distances and the approach v e l o c i t y o f the predator were used to p r e d i c t an approach time f o r each encounter according to equation (26). These were compared with the observed approach times f o r the same encounters by means o f a r e g r e s s i o n ( F i g . 19). The regres-s i o n was h i g h l y s i g n i f i c a n t ( F ^ ^  ~ 1074.13) and the i n t e r -cept and the slope d i d not d i f f e r s i g n i f i c a n t l y from zero and one r e s p e c t i v e l y . Approach time (TA) may t h e r e f o r e be ac c u r a t e l y p r e d i c t e d from RD p R f £ D > R D p R E Y , and A v according to equation (26). Figure 19 R e l a t i o n s h i p between observed approach time (TA) and pre d i c t e d approach t i m e ( ( R D p R E D - RDpRr£Y)/VRr£L) ^ o r the bass-danio i n t e r a c t i o n s . The s o l i d l i n e i s the p r e d i c t e d (1:1) r e l a t i o n s h i p . 87 •5 1.0 1.5 2.0 2.5 PREDICTED TA (sec) 88 S i m i l a r l y , the observed prey r e a c t i v e distances and escape v e l o c i t i e s , and the predator s t r i k e d i s t ances and p u r s u i t v e l o c i t i e s , were used to c a l c u l a t e a p r e d i c t e d c l o s u r e time f o r each encounter according to equations (27) and (28). These were then compared with the observed c l o s u r e times by means of a r e g r e s s i o n . The r e l a t i o n s h i p i s shown i n F i g . 20 f o r values of V ^ L between 20 and 90 cm/sec. The r e g r e s s i o n was conditioned to have a zero i n t e r c e p t and was h i g h l y s i g -n i f i c a n t (F^ -jy 910.89). The best estimate of the slope was .79 which was not q u i t e s i g n i f i c a n t l y d i f f e r e n t from 1.0 at p = .05. However, F i g . 20 s t r o n g l y suggests that the value o f "a" i n equation (27) i s g r e a t e r than 1.0. The best estimate i s 1.0/.79 or about 1.27. Thus observed c l o s u r e times were l e s s than p r e d i c t e d , presumably because the angle o f f l i g h t o f the prey to the approach path o f the predator was l e s s than 180° Gas observed i n Sec. IV f o r r e a c t i o n s to a r t i f i c i a l predators) and because the predator d i d not track the prey's f l i g h t from p o i n t to p o i n t but tended to "head o f f " the prey. When the r e l a t i v e v e l o c i t y (PV - EV) exceeded 90 cm/sec, observed c l o s u r e times were always .0625 or 1/16 sec. Lower c l o s u r e times, however, would be recorded as 1/16 sec s i n c e the f i l m i n g speed was 16 frames/sec. I t i s assumed that f i l m i n g at a higher speed (impossible i n t h i s experiment f o r Figure 20 Regression o f observed c l o s u r e time (TC) on p r e d i c t e d c l o s u r e time ( (RDp^y - D S ) / V ^ ) ^ o r ^ e ^ a s s d a n i ' ° i n t e r a c t i o n s . The dotted l i n e i s the 1:1 l i n e ; the s o l i d l i n e t h a t o f best f i t . 89 PREDICTED TC (sec) 90 p r a c t i c a l reasons) would show that c l o s u r e times a t high r e l a t i v e v e l o c i t i e s can a l s o be p r e d i c t e d from equations (27 & 28) with a = 1.27. The r e l a t i o n s h i p could not be used to p r e d i c t c l o s u r e times i n the three cases i n which V R E L was l e s s than 20 cm/sec. The reasons f o r t h i s f a i l u r e are not known. I t i s probable that the c l o s u r e time equations are not explanatory but only d e s c r i p t i v e o f most cases. How-ever, t h i s w i l l be s u f f i c i e n t f o r the present purposes. Thus, time to c l o s u r e may be p r e d i c t e d from the equation. TC = R DPREY " D S ...(30) 1.27 (PV - EV) Schoener (1969) used a s i m i l a r equation to represent t o t a l p u r s u i t time i n a t h e o r e t i c a l model used to p r e d i c t optimal s i z e s f o r predators. The explanation f o r t h i s conceptual discrepancy l i e s i n Schoener 1s t a c i t assumption that the predator and prey begin to respond to"each other at the same i n s t a n t . Thus, TA would be zero i n the expression TP = TA + TC. I f DS, PV and EV were constants, then the r e l a t i o n s h i p between TC and RDp^y would be a l i n e a r one with an i n t e r c e p t o f -.79 DS/(PV - EV) and a slope o f .79/(PV - EV). A p l o t o f the observed TC and RDp R£y values ( F i g . 21) f i t s such a r e l a t i o n -s h i p very p o o r l y . Apparently, one or more o f the parameters assumed to be constants were not. The data were t h e r e f o r e examined i n two ways. F i r s t , c o r r e l a t i o n c o - e f f i c i e n t s were c a l c u l a t e d f o r each p a i r o f behavioural parameters. These Figure 21 Observed r e l a t i o n s h i p (data p o i n t s ) between danio r e a c t i v e d i s t a n c e (RD) and bass c l o s u r e time (TC), and the p r e d i c t e d r e l a t i o n s h i p ( s o l i d l i n e ) assuming constant escape v e l o c i t y , p u r s u i t v e l o c i t y , and s t r i k e d i s t a n c e . 91 P R E Y RD (cm) 92 are shown tn Table XV. Secondly, the e f f e c t s o f hunger and experience on the parameters o f the behaviour o f the bass were examined by means o f a m u l t i p l e r e g r e s s i o n a n a l y s i s . TABLE XV C a l c u l a t e d c o r r e l a t i o n c o e f f i c i e n t s f o r the behavioural parameters of the bass-danio i n t e r a c t i o n s (n = 24). PARAMETER PARAMETER AV R DPREY EV PV DS AV 1.000 0.441* 0.164 0.749** 0.042 R DPREY 1.000 -0.198 0.566** 0.513* EV 1.000 0.096 0.037 PV 1.000 -0.112 DS 1.000 Table XV shows that both DS and PV were s i g n i f i c a n t l y cor-r e l a t e d w i t h R D p R £ Y ' P r e y i " e a c t i v e distances tended to be a s s o c i a t e d with high p u r s u i t v e l o c i t i e s and s t r i k e d i s -tances. The c o r r e l a t i o n between p u r s u i t v e l o c i t y and prey r e a c t i v e d i s t a n c e may have r e s u l t e d from the f a c t that both are c o r r e l a t e d with approach v e l o c i t y (AV). The c o r r e l a t i o n between AV and RDppjry i s a r e s u l t o f t h e i r f u n c t i o n a l r e l a t i o n -s h i p v e r i f i e d i n Sec I I I . The c o r r e l a t i o n between AV and PV may r e s u l t from both being under the c o n t r o l o f the same i n -t e r n a l m o t i v a t i o n a l system. This i s evidenced by the f a c t t h a t both increase s i g n i f i c a n t l y with i n c r e a s i n g experience [measured as the number o f previous eats i n the t e s t s e r i e s ) , ' but that n e i t h e r i s i n f l u e n c e d by hunger over the range o f 0 93 to 4 previous eats on the same t e s t day. In both cases, the l e v e l s of s i g n i f i c a n c e o f the regressions on experience (E) or on E were about the same. Maldonado (1963) has reported that the approach phase of the attack c y c l e o f Octopus v u l g a r i s becomes p r o g r e s s i v e l y more r a p i d with i n c r e a s i n g experience. The b i o l o g i c a l s i g n i f i c a n c e of the c o r r e l a t i o n between predator s t r i k e d i s t a n c e and r e a c t i v e d i s t a n c e o f the prey ( F i g . 22) i s unknown. S t r i k e d i s t a n c e was not a f f e c t e d by e i t h e r hunger or experience l e v e l . Yet i t was c o r r e l a t e d with a v a r i a b l e which was, i n d i r e c t l y , a f f e c t e d by the number o f previous experiences o f the bass. The r e l a t i o n s h i p between them t h e r e f o r e appears to be a d i r e c t one, the bass e l e c t i n g to s t r i k e from a greater d i s t a n c e at a prey with a greater "head s t a r t " . The data i n Table XVI, though not q u i t e s i g n i f i c a n t , suggest that long s t r i k e s were l e s s s u c c e s s f u l than s h o r t e r ones. Thus prey r e a c t i v e d i s t a n c e may have an i n d i r e c t e f f e c t on s t r i k e suc-cess (SS). Table XVI S t r i k e success (SS) o f bass s t r i k i n g at danios from distances l e s s than or greater than 6.4 cm (mean DS observed). N DS ~ S S 15 < X .80 10 > X .50 F i s h e r exact p r o b a b i l i t y = .106 The true r e l a t i o n s h i p between s t r i k e d i s t a n c e and s t r i k e suc-cess may be c o n s i d e r a b l y more complicated than t h i s , however. / Figure 22 C o r r e l a t i o n between danio r e a c t i v e d i s t a n c e CRD) and bass s t r i k e d i s t a n c e CDS). The l i n e i s f i t t e d by eye. 95 Nyberg (1971) s t u d i e d the largemouth bass and showed that the s t r i k e distances which were s u c c e s s f u l depended upon the bass v e l o c i t y during the l a s t .02 sec before the jaws began to open. At any v e l o c i t y there was an optimum range o f s t r i k e d i s t a n c e s , with s t r i k e s i n i t i a t e d at greater or l e s s e r d i s -tances tending to be u n s u c c e s s f u l . Both the upper and lower bounds on the optimum range increased with v e l o c i t y . The r e l a t i o n s h i p was due to the f a c t t h a t s t r i k e s were most l i k e l y to be s u c c e s s f u l i f the mouth was f u l l y open when i t reached the prey, and to the f a c t t h at the rate at which the mouth opened was constant and independent o f the bass v e l o c i t y . I f the v e l o c i t y i n the l a s t .02 sec before jaw opening increases with experience i n the same manner as the p u r s u i t v e l o c i t y , then s t r i k e d i s t a n c e should a l s o i n c r e a s e with experience i f s t r i k e success i s to remain constant. However, s t r i k e d i s -tance d i d not i n c r e a s e s i g n i f i c a n t l y with experience i n the present study. There was a l s o no apparent e f f e c t o f hunger on DS. In c o n t r a s t , Maldonado (1964) found that both experience and hunger caused an increase i n the s t r i k e d i s t a n c e (termed "length o f the f i n a l p a t t e r n of a c c e l e r a t i o n " ) i n the octopus. S t r i k e success decreased as s t r i k e d i s t a n c e increased i n inexperienced octopuses, but not i n experienced ones. More experimental s t u d i e s w i l l be required to work out the i n t r i c a t e i n t e r - r e l a t i o n s h i p s between predator and prey behaviour and the m o t i v a t i o n a l s t a t e s o f both. In the s i m u l a t i o n model to 96 be developed tn Sec VI.3, DS w t l l be assumed to be constant. 3 The Simulation Model The basis f o r the present model i s the one de s c r i b e d i n some d e t a i l by G r i f f i t h s and H o l l i n g (1969). T h e r e f o r e , only those changes i n the b a s i c model n e c e s s i t a t e d by the a d d i t i o n o f the new component of avoidance l e a r n i n g w i l l be discussed i n t h i s account. The model begins by a s s i g n i n g a unique r e a c t i v e d i s t a n c e to each o f ten c l a s s e s o f prey, each c l a s s corresponding to a d i f f e r e n t number o f previous experiences with the predator, according to the f o l l o w i n g FORTRAN program: LOOMT = LPAR DO 220 I = 1,10 RD(I) = SQRT(VP*SIZE/(L00MT*3600)-.25 * SIZE*SIZE) E = I + 1 220 LOOMT = KMIN + EC * EXP (-E0NK*E) CALL ADCOM The program d e f i n i t i o n s o f RD (I) and LOOMT correspond with t e x t equations (3) and (17) r e s p e c t i v e l y . When the model enters subroutine ADCOM the d e n s i t y o f prey i n the f i r s t c l a s s , AN0(1), i s s e t equal to the t o t a l prey d e n s i t y , TANO. The d e n s i t i e s o f a l l other c l a s s e s are s e t to zero. ADCOM then c a l l s subroutine FR to c a l c u l a t e a s t a b l e attack r a t e , A, instantaneous with respect to predator d e n s i t y P. Subroutine FR i s i d e n t i c a l to Hoi l i n g ' s (1966) model o f the e f f e c t o f prey d e n s i t y on att a c k , with the exception o f the m o d i f i c a t i o n s described below. 97 Search time (TS) was defined by H o l l i n g (1965) as the time taken f o r the area swept by the searching predator to equal the average area c o n t a i n i n g one catchable prey (G = 1/(TAN0*SR*SP*SS)). Thus, time spent u n s u c c e s s f u l l y pursuing prey was i m p l i c i t l y con-t a i n e d i n TS. Since t h i s time component (TUP) i s made e x p l i c i t i n the present model, G has been r e d e f i n e d as: G = 1.0/(TANO*SR*PVULN) where PVULN i s the percentage of prey with r e a c t i v e distances l e s s than t h a t of the predator. Prey with higher r e a c t i v e distances are assumed to take evasive a c t i o n before they have been s i g h t e d by the predator. Since the predator's r e a c t i v e d i s t a n c e i s assumed to i n c r e a s e with hunger, the proportions o f vulnerable prey before and a f t e r TS may be d i f f e r e n t . I f t h i s occurs, then an average PVULN i s c a l c u l a t e d and a new TS c a l c u l a t e d using t h i s average value. A f t e r TS has been determined, subroutine FR c a l l s a new subroutine CHASE, shown as a flow diagram i n Figure 23. This subroutine uses a random number to determine the c l a s s to which the s i g h t e d prey belongs and thus i t s r e a c t i v e d i s t a n c e . TA and TC are c a l c u l a t e d according to t e x t equations (26) and (30) above. The prey may escape e i t h e r by having a TP which exceeds the maximum amount o f time which the predator i s w i l l i n g to expend on p u r s u i t (TPMAX) or by reaching cover. The prey may only reach cover i f TC exceeds TR, the time to refuge. TR i s determined by s e l e c t i n g a random number between 0 and 1, and mul-t i p l y i n g t h i s by twice the mean TR (an input parameter). Thus, TR i s assumed to have a uniform d i s t r i b u t i o n with a range from 0 to 2X". Figure 23 Flow-diagram o f subroutine CHASE XTP = XTP + TP1 + TGAIN XTR = XTR - TC - TGAIN TC = MAN*(GAIN-DS)/VR TP1 = TC HI = HK + (H1-HK)*EXP(-AD+TP1) P.N = FRAND(O) i r - ^ ^ NO H> HTC YES TUP = TA + TC TUP = 0 Wl = W EATEN( I I ) = 1+EATEN(II) TP1 •= TP1 + XTP . JJ = 2 R E T U R N ^ ^ -RN1 = TANO * FRAND(O) 1= 1.NMAX YES RN1 = RNl-ANO(I). 11 = I TA = (REACT-RD(II))/VP YES JJ = 1 » ^ RETURN ^ TGAIN=GAIN/(VP-VR) TC=MAN*(RD ( I I ) - D S ) / V R TP1= TA + TC XTP = 0 H l l = HI VO 00 TPMAX = PAR1*(H1 - HTP) (1+PAR2(H1-HTP)J STUP = STUP + TUP + XTP HI = HK+(H11-HK*EXP(-AD*STUP)) ESCAP(II) = ESCAP(II) + 1 99 The maximum p u r s u i t time f u n c t i o n i s b u i l t i n t o the model to provide f o r a number.of observations reported i n the l i t e r a t u r e . Estes and Goddard (1967), f o r example, found that A f r i c a n hunting dogs w i l l not attempt to pursue g a z e l l e s which r e a c t from d i s t a n c e s g r e a t e r than 300 yards. I t i s not known however whether t h i s i s based on past experience that a g a z e l l e with such a long head s t a r t w i l l always escape or whether the dogs are unable to c l o s e such a gap without t i r i n g . S i m i l a r y , Mech (1970) s t a t e d that i f a moose stayed more than 100 yards ahead o f pursuing wolves f o r 10 or 15 sec, the wolves u s u a l l y gave up the chase. The maximum p u r s u i t time b u i l t i n t o the model i s conceived as i n c r e a s i n g with i n c r e a s i n g hunger. I f the predator gets c l o s e enough to the prey to s t r i k e but i s unsuccessful (occurs when a random number exceeds s t r i k e s u c c e s s ) , then TC and TR are r e c a l c u l a t e d . Subroutine CHASE returns to FR under one o f two c o n d i t i o n s : (1) J J = 1, STUP has a value, TP = 0, and the number o f escapes from the cl a s s o f prey c o n t a i n i n g the u n s u c c e s s f u l l y pursued one, ESCAP ( I I ) , i s incremented by one. The predator then searches f o r another prey and pursues i t . This process continues u n t i l a prey has been captured (JJ = 2 ) , the STUP's and TS's being accumulated. (2) J J = 2, STUP = 0, TP has a value, and the number of captures from the c l a s s o f prey c o n t a i n i n g the s u c c e s s f u l l y pursued one, EATEN ( I I ) , i s incremented by one. Once the r e t u r n to FR i s made with J J = 2, FR c a l l s another subroutine, SUMRY. 100 SUMRY, shown as a flow diagram tn Figure 24, c a l c u l a t e s the attack r a t e , A, as meals per u n i t time, where: MEAL = XEATEN (I) TIME = 2TI = £ ( T D + TS + STUP + TP + TE). The subroutine returns to FR with e i t h e r a s t a b l e attack r a t e (JJ=2) or an unstable one (JJ = 1). In the l a t t e r case the predator must continue c a p t u r i n g prey u n t i l A becomes s t a b l e . The program i s designed so t h a t a minimum number of f i v e captures must occur before FR w i l l accept a value o f J J = 2. SUMRY a l s o keeps t r a c k o f the number o f captures and escapes from each c l a s s o f prey during t h i s process o f s t a b i l i z a t i o n , and c a l c u l a t e s f o r each c l a s s the pro p o r t i o n o f s u c c e s s f u l ( S P ( I ) ) , and unsuccessful (FP(I)) attacks by the predator and the rates o f attack (AA(I)) and escape (AESC(I)). Subroutine FR then c a l c u l a t e s A from the average of the l a s t two values given by SUMRY and returns to ADCOM ( F i g . 25). This subroutine c a l c u l a t e s the time p e r i o d (T) during which no more than 2 percent of the prey w i l l be eaten and determines the d e n s i t i e s o f prey i n each o f the 10 c l a s s e s a f t e r time T has elapsed. To do so i t uses the estimates o f attack and escape rates generated by SUMRY. Note t h a t prey are not only removed from a c l a s s by being eaten, but a l s o by being u n s u c c e s s f u l l y attacked. In the l a t t e r case, they are s h i f t e d i n t o the next h i g h e s t c l a s s . Under c e r t a i n c o n d i t i o n s the c a l c u l a t e d number to be removed from a c l a s s may exceed the number present. When t h i s occurs, T i s adjusted downward so that no c l a s s o f prey becomes negative. Once the c l a s s d e n s i t i e s have been adjusted, the t o t a l d e n s i t y o f prey remaining, TANO, i s determined and another Figure 24 Flow diagram of subroutine SUMRY. 101 F R E E = 0. M E A L = 0. T I M E = T I M E + T1 M E A L = ^ E A T E N (I) www F R E E = ^> E S C A P (I) A = M E A L / T I M E A D I F F = |A-XA|/A X A = A Y E S T S P = M E A L / ( M E A L + F R E E ) J J = 2 1= 1 , N M A X 1 X1 = E A T E N ( I ) X2 = E S C A P ( I ) A T T A C K = X1 +X2 A A ( I ) ^ X1/TIME A E S C ( I ) = X2/TIME S P ( I ) = 0. F P ( I ) = 0. SP(1) =X1/ A T T A C K F P ( I ) = X2/ A T T A C K Y E S A A ( I ) = 0. S P ( I ) = 0. > I=NMAX+1,10 F P ( I ) = 0. J <3-Figure 25 Flow diagram o f subroutine ADCOM. SUMT = 0 T = 0 TANOX =TANO AHA = 0 • a t — — <I>— Z=TAN0/(TAN0-.02TAN0X) Z-Z**(1.0/AK) T=TAN0*AK*(Z-1)/(A*P) INDEX = 1 SUMTR = SUMT T=ANO(I)/DEN0M ANO(I) * 0 TNA (I) = 0 ESC(l) ' 0 INOEX =1+1 DENOM = P*(AA(I)+AESC(I)) SUMT = SUMTR + T YES T = TAG - SUMTR SUMT = TAG TOTNA = A*T*P YES TNA(I) = AA(I)*T*P ESC(l) = AESC(I)*T*P REMOVE=TNA(I)+ESC(I) 1 = 1.NMAX YES I = K.10 YES I = INOEX.NMAX 1.NMAX TANO = 0 IN = 0 ATT= TNA(I) OUT= ESC(I) AND(I)=ANO(I)-ATT-OUT+IN ANO(I) = 0 ANHA(I)=ANHA(I)+ATT TANO = TANO + ANO(I) IN = OUT YES 1= 1,10 EATEN(I) = 0 ESCAP(I) - 0 CALL FR O r o NMAX TANHA = TANHA + ANHA(I) 103 c a l l made to subroutine FR. This continues u n t i l a l l of the time a v a i l a b l e f o r attacks (TAG) i s used up, or u n t i l no prey are l e f t to a t t a c k . The t o t a l d e n s i t y o f prey eaten, TANHA, i s the sum of the d e n s i t i e s of prey eaten from each c l a s s , ANHA(I), during the e n t i r e p e r i o d o f a t t a c k , SUMT. I t i s w i t h i n subroutine ADCOM, t h e r e f o r e , that changes i n the frequency d i s t r i b u t i o n of prey with d i f f e r e n t r e a c t i v e distances are c a r r i e d out. Any prey which s u c c e s s f u l l y avoids capture during one round of attack has a higher r e a c t i v e d i s t a n c e during the next one. No f o r g e t t i n g process i s incorporated i n the model s i n c e the bookkeeping procedure r e q u i r e d to e f f e c t t h i s would be immense. However, the experimental data presented i n Sec IV suggests t h a t t h i s i s not a s e r i o u s omission p r o v i d i n g TAG i s s h o r t e r than 10 days. TAG was s e t equal to 24 hours i n a l l of the s i m u l a t i o n s . The meanings and values of a l l parameters used i n these simulations are given i n Table XVII. A second model was w r i t t e n i n which no prey l e a r n i n g occurred, thus producing a " c o n t r o l " f o r the s i m u l a t i o n s t u d i e s . In t h i s v e r s i o n , a l l prey s t a r t and end with the same r e a c t i v e d i s t a n c e , r e g a r d l e s s o f the number o f times they have been u n s u c c e s s f u l l y attacked. In a l l other r e s p e c t s , i n c l u d i n g the a d d i t i o n o f subroutines CHASE and SUMRY, the i n c l u s i o n o f prey r e a c t i v e d i s t a n c e , and the modified v e r s i o n of G, the two models are i d e n t i c a l . Nevertheless the no-p r e y - l e a r n i n g model gave i d e n t i c a l r e s u l t s to that o f G r i f f i t h s and H o l l i n g (1969) when the same parameter values were used (those o f Table XVII). A l l s i m u l a t i o n s were run on an IBM 360/67. 104 Table XVIT The meanings and values o f a l l parameters i n the si m u l a t i o n model. PARAMETER VALUE . UNITS MEANING SOURCE AD AK AKE CAPT DS EC EONK EYE GAIN HK HONP HOPT KA KMIN LOPT LPAR 0.2 hr" Instantaneous rate o f d i g -e s t i o n . 3.0 - Di s p e r s i o n c o - e f f i c i e n t of negative binomial .00001 hr Time to eat one gram o f prey 1.0 - Ratio between t h r e s h o l d hungers f o r ' c a p t u r e and f o r p u r s u i t 5.8 cm S t r i k e d i s t a n c e 1.9845 rad/sec Constant i n prey l e a r n i n g equation exper- _, Rate o f prey l e a r n i n g iences cm Distance between predator's eyes cm Distance gained by prey r e s u l t i n g from unsuccess-f u l s t r i k e gm Maximum gut ca p a c i t y cm/gm Constant r e l a t i n g pur-s u i t d i s t a n c e to hunger gm Hunger t h r e s h o l d f o r p u r s u i t (HTP) when L = LOPT Areal constant r e l a t i n g predator's f i e l d o f r e a c t i o n to di s t a n c e o f r e a c t i o n s t r a i g h t ahead Minimum p o s s i b l e da/dt t h r e s h o l d 3.0 cm Prey length 4.0 cm Optimum prey length 1.5 rad/sec Naive dw/dt thr e s h o l d 0.5 2.0 16.0 1.8 1.0 0.3 3.1416 ,2349 rad/sec Glass (1971) G r i f f i t h s & H o l l i n g (196$) Measured Hypothetical Measured Sec IV.3 Sec IV.3 Measured Measured Measured Hypothetical Hypothetical Hypothetical Sec IV.3 Measured Hypothetical Measured 105 PARAMETER VALUE UNITS .. . MEANING SOURCE MAN 0.8 R e l a t i v e manoeuverability o f prey Sec VI.2 MYOP 16.56 gm/cm -1 sq. m Constant r e l a t i n g dHTP/dL to (LOPT-L) Mantid ( H o l l -i n g , i n prep) P 0.2 Predator d e n s i t y Hypothetical PARI 0.222 hrs/gm gm"1 Parameter i n TPMAX c a l c u -l a t i o n Hypothetical PAR2 0.02 Parameter i n TPMAX c a l c u -l a t i o n H ypothetical SIZE 2.65 cm Predator diameter Measured SR 0.8 - Recognition success Hypothetical SS 0.8 - S t r i k e success Table XIII TAG 24 hrs Time a v a i l a b l e f o r generating attacks Hypotheti cal TR .00007 hrs Mean time f o r prey to reach cover Hypothetical VP 5600 m/hr Predator's v e l o c i t y Measured VR 3600 m/hr Predator's r e l a t i v e v e l o c i t y Measured W 0.27 gm Weight o f one prey Measured 4 Results and D i s c u s s i o n The r e s u l t s o f simulations of predator-prey i n t e r a c t i o n s with and without prey l e a r n i n g are shown i n F i g . 26 where d e n s i t y o f attacks Cprey/sq. m) i s p l o t t e d a g a i n s t i n i t i a l prey d e n s i t y . Without prey l e a r n i n g , the d e n s i t y o f attacks rose s t e e p l y with prey d e n s i t y to s i x sq.m and remained approximately constant t h e r e a f t e r . The explana-t i o n f o r t h i s shape ( H o l l i n g type I f u n c t i o n a l response) i s as f o l l o w s . At prey d e n s i t i e s l e s s than s i x , the predator was able to eat nearly a l l o f the prey i n le s s than 24 hours; a t d e n s i t i e s greater than s i x the predator's consumption was l i m i t e d by the amount o f time r e q u i r e d Figure-26 Simulation o f the f u n c t i o n a l response o f predators to prey with, and without the a b i l i t y to l e a r n . Predator d e n s i t y CP) = .2/sq. m; TANO = d e n s i t y o f prey a v a i l a b l e ; TANHA = d e n s i t y o f prey attacked. 106 5 10 TANO 107 to f i n d , capture and d i g e s t one prey ( T I ) . Since TI changed very l i t t l e from s i x onward, the d e n s i t y o f attacks remained nearly con-s t a n t . Thus a type I response can occur when predator r e a c t i v e d i s -tance increases with hunger, p r o v i d i n g TI i s a h i g h l y i n s e n s i t i v e to r e a c t i v e d i s t a n c e ( c f . H o l l i n g , 1965). When prey l e a r n i n g was added to the model the r e s u l t was not markedly changed. At low d e n s i t i e s , the predator required somewhat longer to consume a l l of the prey, but s t i l l was able to do so. At very high d e n s i t i e s , the p r o b a b i l i t y of encountering an experienced prey was low, s i n c e there were such a large number of naive prey s t i l l present. Only at intermediate d e n s i t i e s d i d prey l e a r n i n g have any s o r t of e f f e c t , and even here i t was s m a l l . The maximum advantage to the prey population occurred at a d e n s i t y o f f i v e prey/sq. m., where about .085 prey/sq. m. s u r v i v e d which otherwise would not have done so. Although t h i s e f f e c t i s small on a per square meter b a s i s , i t may r e s u l t i n the s u r v i v a l o f a l a r g e number o f prey i n any reasonably s i z e d h a b i t a t . Furthermore, i t has the e f f e c t of t r e b l i n g the s u r v i v a l rate (from .85 to 2.52%) at that d e n s i t y . I t i s a l s o o f i n t e r e s t to note t h a t although TI was not g r e a t l y d i f f e r e n t i n the two s i t u a t i o n , the predator d i s t r i b u t e d i t s time budget r a t h e r d i f f e r e n t l y . At the d e n s i t y o f f i v e / s q . m. f o r example the predator feeding on non-learning prey spent 19.8 hours d i g e s t i n g prey and 4.2 hours searching f o r and c a p t u r i n g them. The predator feeding on prey capable o f l e a r n i n g spent 18.9 and 5.1 hours r e s p e c t i v e l y on these same a c t i v i t i e s . Using the equations of Glass (1971) f o r 108 the r o u t i n e and a c t i v e metabolic rates of a 454 gm bass, and assuming the r o u t i n e r a t e during d i g e s t i o n and the a c t i v e one during search and p u r s u i t (at 150 cm/sec) i t was p o s s i b l e to c a l c u l a t e the oxygen requirements (mg) o f each predator. These were converted to c a l o r i e s according to the r e l a t i o n s h i p ca l = mg0 ? x 1 ml x 4.85 c a l 1.428 mg m!02 The c a l o r i c expenditure o f the predator feeding on non-learning prey was 7105 c a l , while that f o r the predator feeding on prey capable o f l e a r n i n g was 7548, an increase o f 6.2%. Since the number o f prey captured per predator (TANHA/P) decreased from 24.79 to 24.37 with the a d d i t i o n o f l e a r n i n g the c a l o r i c expenditure per prey captured a c t u a l l y rose from 287 to 310, an increase o f 8%. Consequently, a predator feeding on prey capable o f l e a r n i n g would have a lower net energy gain than one feeding on non-educable prey. As a r e s u l t , the r e p r o d u c t i v e r a t e o f the predator might be l e s s i n the l a t t e r s i t u a t i o n , r e s u l t i n g i n a s m a l l e r numerical response to prey d e n s i t y (Solomon, 1949). Prey l e a r n i n g may t h e r e f o r e have e f f e c t s on both the f u n c t i o n a l and numerical responses o f predators to prey d e n s i t y . The advantage conferred upon an i n d i v i d u a l prey by i t s a b i l i t y to i n c r e a s e i t s r e a c t i v e d i s t a n c e through experience was a l s o explored using the model. Three hundred prey of each o f the 10 c l a s s e s were run. through subroutine CHASE and the number of s u c c e s s f u l captures recorded. A number of parameters o f the i n t e r a c t i o n were then v a r i e d , one at a time, to determine t h e i r e f f e c t on capture p r o b a b i l i t i e s . 109 The r e s u l t s o f these s i m u l a t i o n s are shown i n F i g . 27. Some v a r i a b l e s (EC, DS, GAIN] had l i t t l e e f f e c t ; others (SIZE, MAN, SS) a f f e c t e d a l l c l a s s e s of prey about e q u a l l y . Only changes i n predator v e l o c i t y (VP), mean time to refuge (TR), minimum dtv/dt t h r e s h o l d (KMIN), and prey l e a r n i n g r a t e (EONK), conferred d i f f e r e n t advantages to each prey c l a s s . Changing the d i s t r i b u t i o n o f time to refuge from uniform to gamma decreased the p r o b a b i l i t i e s o f capture f o r each group about e q u a l l y . Since predator v e l o c i t y had the g r e a t e s t e f f e c t on p r o b a b i l i t y o f capture, the s i m u l a t i o n o f the f u n c t i o n a l response was re-run with VP and VR s e t to 4000 and 2000 r e s p e c t i v e l y ( i . e . prey v e l o c i t y was l e f t unchanged). The r e s u l t s ( F i g . 28) show' an increased advantage to the prey p o p u l a t i o n o f avoidance l e a r n i n g when compared with those o f the previous s i m u l a t i o n ( F i g . 26). The maximum advantage conferred was .116 prey/sq. m. (cf.085/sq. :m) and occurred at a d e n s i t y of 6 prey/sq. m. The model was a l s o used to examine the e f f e c t o f avoidance l e a r n i n g by prey on the f u n c t i o n a l response o f predators to t h e i r own d e n s i t y , s i n c e avoidance l e a r n i n g i s a c t u a l l y a form o f p a r t i a l e x p l o i t a t i o n o f the prey p o p u l a t i o n by the predator. In c o n t r a s t to c l a s s i c a l e x p l o i t a t i o n the prey do not become completely u n a v a i l a b l e to the predators by reason o f being eaten, but become l e s s a v a i l a b l e as a r e s u l t o f being u n s u c c e s s f u l l y attacked. The r e s u l t s ( F i g . 29) show t h a t the e f f e c t on the f u n c t i o n a l response to predator d e n s i t y was maximal a t intermediate predator d e n s i t i e s . At low predator d e n s i t i e s , there was a surplus o f prey a v a i l a b l e and e x p l o i t a t i o n Ftgure 27 E f f e c t of various behavioural and environmental para-meters on the p r o b a b i l i t y o f capture o f prey with d i f f e r e n t amounts of previous experience, as simulated by the model. Refer to Table XVII f o r an explanation o f the meaning and u n i t s of the various parameters. no PREY CLAS  Figure 28 Simulation of the d e n s i t y of prey attacked (TANHA) as a f u n c t i o n o f prey d e n s i t y , f o r cases with and without prey l e a r n i n g . VP = 4000; VR = 2000. I l l 6 r 1 2 3 4 5 6 7 8 P R E Y / S Q . M. Figure 29 Simulation o f the number o f prey attacked per predator per day (FRNHA) as a f u n c t i o n of predator d e n s i t y , f o r cases without prey l e a r n i n g and with l e a r n i n g rates of .50 and .75. VP = 4000, VR = 2000. 112 • 1 1 I L. .1 .15 .2 .25 .3 PREDATORS/SQ.M. 113 had l i t t l e e f f e c t ; at high predator d e n s i t i e s nearly a l l the prey were eaten, regardless o f whether or not they were capable o f l e a r n i n g , and e x p l o i t a t i o n due to avoidance l e a r n i n g again was of l i t t l e conse-quence. The maximum e f f e c t of avoidance l e a r n i n g was to reduce each predator's consumption by about .57 prey/day. At l e a s t over a c e r t a i n range, t h e r e f o r e , the expectation of G r i f f i t h s and H o l l i n g (1969) th a t "the g r e a t e r the predator d e n s i t y , the g r e a t e r the chance that each prey w i l l have acquired an e f f e c t i v e way o f a v o i d i n g a t t a c k . . . and the lower the attack r a t e " was v e r i f i e d . Increasing the l e a r n i n g rate (EONK) from 0.50 to 0.75 accentuated the e f f e c t o f prey l e a r n i n g at intermediate predator d e n s i t i e s but had no e f f e c t a t very high or very low predator d e n s i t i e s . The e f f e c t o f the a d d i t i o n o f prey avoidance l e a r n i n g to a predator prey i n t e r a c t i o n on the predator's a b i l i t y to regulate the prey population was a l s o explored using the model. The curves of actual m o r t a l i t y shown i n F i g . 30 are those generated by the model i n s i t u a t i o n s where the prey are incapable (ACT) and capable (ACT 1) o f a s s o c i a t i v e l e a r n i n g . The p r o p o r t i o n of prey destroyed i s i n i t i a l l y constant (ACT), or nearly so (ACT'), and then becomes i n v e r s e l y pro-p o r t i o n a l to prey d e n s i t y once the number o f prey destroyed becomes nearly constant, i e . at the i n f l e c t i o n .point o f the f u n c t i o n a l response curve. The curve l a b e l l e d NEC i n F i g . 30 represents t h a t m o r t a l i t y necessary to produce a s t a b l e population from generation to generation. The domed form o f the curve r e s u l t s from the f o l l o w i n g assumptions ( H o l l i n g , 1965): Figure 30 E q u i l i b r i u m e f f e c t s o f the f u n c t i o n a l response to prey d e n s i t y with and without the prey l e a r n i n g component. NEC = percent m o r t a l i t y necessary to s t a b i l i z e the popu-l a t i o n ; ACT and ACT' = actual percent predation when prey are incapable and capable of l e a r n i n g , r e s p e c t i v e l y ; EX = t h r e s h o l d d e n s i t y f o r population e x t i n c t i o n , EQ = s t a b l e e q u i l i b r i u m d e n s i t y ; ES = t h r e s h o l d d e n s i t y f o r population escape. A and B d i f f e r only i n the charac-t e r i s t i c s o f the curve o f necessary m o r t a l i t y . PREY DENSITY 115 ( i ) a t low d e n s i t i e s chances f o r contact between i n d i v i d u a l s becomes so s l i g h t t h a t reproductive rate w i l l drop and the amount o f predation m o r t a l i t y r e q u i r e d to s t a b i l i z e the prey p o p u l a t i o n w i l l be low; ( i i ) as de n s i t y i n c r e a s e s , reproductive success i n c r e a s e s , and t h i s must be matched by a pro p o r t i o n a t e i n c r e a s e i n pre-dation m o r t a l i t y i f the prey population i s to remain s t a b l e ; ( i i i ) a t high prey d e n s i t i e s s u r v i v a l and reproduction w i l l be decreased as a r e s u l t o f resource l i m i t a t i o n and i n t r a s p e c i f i c s t r e s s , and the a d d i t i o n a l m o r t a l i t y necessary to s t a b i l i z e the prey p o p u l a t i o n w i l l again d e c l i n e . Population e q u i l i b r i a occur at a l l points where ACT = NEC. These may be o f three kinds: a s t a b l e e q u i l i b r i u m (EQ) and t r a n s i e n t e q u i l i b r i a f o r e x t i n c t i o n (EX) or escape (ES). A s t a b l e e q u i l i b r i u m can occur only when the prey p o p u l a t i o n increases below the i n t e r s e c t i o n o f the two curves and decreases above i t . T r a n s i e n t e q u i l i b r i a occur i f the pop u l a t i o n decreases below the i n t e r s e c t i o n p o i n t and increases above i t . The q u a n t i t a t i v e and q u a l i t a t i v e c h a r a c t e r i s t i c s o f the NEC curve determine which kinds o f e q u i l i b r i a w i l l occur ( c f F i g s . 30A and 30B), but given a p a r t i c u l a r curve, the p r o b a b i l i t i e s o f occurrence o f these e q u i l i b r i a are i n f l u e n c e d by the a d d i t i o n o f the avoidance l e a r n i n g component. Depending upon the p o s i t i o n o f the maximum p o i n t o f the NEC curve r e l a t i v e to that o f the i n f l e c t i o n o f the ACT curve, the a d d i t i o n o f prey l e a r n i n g may s h i f t the t r a n s i e n t e q u i l i b r i u m (EX:ES) downward ( F i g 30A), or may r e s u l t i n the i n t r o d u c t i o n o f a s t a b l e 116 e q u i l i b r i u m and d i s t i n c t thresholds f o r e x t i n c t i o n (EX) and escape (ES) ( F i g . 30B). Since the actual m o r t a l i t y without prey l e a r n i n g i s 100% over such a l a r g e range o f prey d e n s i t i e s , the p r o b a b i l i t y o f a s t a b l e e q u i l i b r i u m i s l e s s than i n an i n t e r a c t i o n which inc l u d e s t h i s component. Further d i s c u s s i o n o f the i m p l i c a t i o n s f o r popul a t i o n r e g u l a t i o n are considered unwarranted.for se v e r a l reasons. In the f i r s t p l a c e , no data e x i s t on the c h a r a c t e r i s t i c s of the NEC curve f o r zebra danios. Secondly, the a d d i t i o n o f predator l e a r n i n g to the model w i l l l i k e l y r e s u l t i n q u i t e a d i f f e r e n t curve of actual m o r t a l i t y . Since only a few s i t u a t i o n s can be envisioned i n which only the prey are capable o f l e a r n i n g (although a q u a t i c i n s e c t s preying upon f i s h may be such a c a s e ) , the usefulness of the model i s s e r i o u s l y l i m i t e d u n t i l t h i s a d d i t i o n i s made. T h i r d l y , the g r a p h i c a l method used to explore s t a b i l i t y i s concerned only with the f u n c t i o n a l response to prey d e n s i t y and prevents d i s c u s s i o n o f the i m p l i c a t i o n s to popul a t i o n r e g u l a t i o n o f the f u n c t i o n a l response to predator d e n s i t y and the numerical response. Since the a d d i t i o n of prey avoidance l e a r n i n g d e f i n i t e l y i n f l u e n c e s the former, and l i k e l y has e f f e c t s on the l a t t e r as w e l l , both should be includ e d i n the model before any d e t a i l e d i n v e s t i g a t i o n of popul a t i o n r e g u l a t i o n i s conducted. 5 Conclusions ( i ) An increase i n r e a c t i v e d i s t a n c e o f the prey through avoidance l e a r n i n g a f f e c t s predator p u r s u i t time according to the r e l a t i o n s h i p s : 117 TP = TA + TC TA = ( R D p R E D - r d p r e y ) / V P R E D TC = ( R D p R E Y - DS)/1.27 V R E L These r e l a t i o n s h i p s were b u i l t i n t o H o l l i n g ' s g e n e r a l i z e d model o f the predation process. ( i i ) The opportunity f o r avoidance l e a r n i n g to occur was provided by making escape i n e v i t a b l e whenever time to c l o s u r e (TC) exceeded time to refuge (TR). ( i i i ) Data c o l l e c t e d from fil m e d i n t e r a t i o n s between largemouth bass and zebra danios a l s o suggest that an increased prey r e a c t i v e d i s t a n c e might decrease predator s t r i k e success, by i n c r e a s i n g s t r i k e d i s t a n c e . The r e l a t i o n s h i p , however, was not b u i l t i n t o the model. ( i v ) Other changes n e c e s s i t a t e d i n the model by the a d d i t i o n o f the avoidance l e a r n i n g component i n c l u d e d : a) M o d i f i c a t i o n s of the c a l c u l a t i o n o f search time to remove a p r e v i o u s l y i m p l i c i t time spent u n s u c c e s s f u l l y pursuing prey, and to c o r r e c t the d e n s i t y of prey to account f o r those whose r e a c t i v e distances exceed that of the predator and are t h e r e f o r e not s u s c e p t i b l e to d i s c o v e r y ; b) I n c l u s i o n of a new subroutine (CHASE) to c a l c u l a t e p u r s u i t time, unsuccessful p u r s u i t time, p u r s u i t success, and s t r i k e success; c) Changes i n subroutine ADCOM to assign prey to d i f f e r e n t 118 c l a s s e s [with d i f f e r e n t r e a c t i v e d i s t a n c e s ) according to the number o f times they have been u n s u c c e s s f u l l y attacked; d) A d d i t i o n o f a s t o c h a s t i c element v i a random numbers to determine the c l a s s to which an attacked prey belongs, the time to refuge, and the predator's s t r i k e success. (v) Simulation s t u d i e s using subroutine CHASE show that the c a p a b i l i t y to l e a r n to avoid predators s u b s t a n t i a l l y increases the prey's chance o f s u r v i v i n g subsequent encounters with a predator. The degree o f advantage conferred depends upon the values o f parameters o f refuge d i s t r i b u t i o n , and prey and predator behaviour. ( v i ) A t the l e v e l of the p o p u l a t i o n , the a d d i t i o n of avoidance l e a r n -ing by prey decreases s l i g h t l y the f u n c t i o n a l response of predators to both prey and predator d e n s i t y . The p o s s i b i l i t y o f e f f e c t s on the numerical response of predators to prey d e n s i t y i s a l s o suggested. ( v i i ) When a predator-prey i n t e r a c t i o n contains the s u b s i d i a r y com-ponent "avoidance l e a r n i n g by prey" there i s a higher pro-b a b i l i t y that the prey p o p u l a t i o n may be regulated by p r e d a t i o n . The consequences f o r s t a b i l i t y are unknown, however, f o r cases i n which the predator i s a l s o capable o f l e a r n i n g . 119 LITERATURE CITED Baerends,CP. and J.M. Baerends van Roon. 1950. An introduction to the study of the ethology of ci c h l i d fishes. Behaviour, Suppl. 1_: 1-242. Baerends,G.P., Bennema,B.A. and A.A. Vogelzang. 1960. Uber die Anderung der Sehscharfe mit dem Wachstum bei Aequidens portalegrensis (Hensel) (Pisces,Cichlidae). Zool. Jb., Abst. Syst., Okol. Geogr. Tiere, 88: 67-78. Ball,W. and E. Tronick. 1971. Infant responses to impending c o l l i s i o n : optical and real. Science, 171: 818-820. Barlow,H.P. and R.M. H i l l . 1963. Selective sensitivity to direction of movement in ganglion cells of the rabbit retina. Science, 139: 412-414. Barraud, E.M. 1961. The development of behaviour in some young passerines. Bird Study, _8: 111-118. Benzie, V.L. 1965. Some aspects of the anti-predator responses of two species of stickleback. DPhil. Thesis, Univ. of Oxford. 149 pp. Beukema, J.J. 1968. Predation by the three-spined stickleback (Gaster- osteus aculeatus L.): The influence of hunger and experience. Behaviour, _3_1: 1-126. Boulet, P.C. 1960. Experiences sur l a perception visuelle du mouvement chez l a perche. Bull, franc. P i s e , ^32(196): 81-95. Braum, E. 1964. Experimentelle Untersuchungen zur ersten Nahrungs-aufnahme und Biologie an Jungfischen von Blaufelchen (Coregonus  wartmanni Bloch), Weiszfelchen (Coregonus fera Jurine) und Hechten (Esox lucius L.). Arch. Hydrobiol., Suppl. 28; 183-244. Breder, CM., Jr. and F. Halpern. 1946. Innate and acquired behaviour affecting the aggregation of fishes. Physiol. Zool., 19_: 154-190. Brett, J.R. 1971. Satiation time, appetite and maximum food intake of sockeye salmon (Oncorhynchus nerka). J. Fish. Res. Bd. Canada, 28: 409-415. Brown, CR. and M.H. Hatch. 1929. Orientation and "fright" reactions of whirligig beetles (Gyrinidae). J. Comp. Psychol., _9: 159-189. Brown, M.E. 1957. Experimental studies on growth. Pp. 361-400 in : Brown, M.E. (ed). Physiology of Fishes Vol. I. Academic Press, N.Y. Bullock, T.H. 1953. Predator recognition and escape responses in some intertidal gastropods in the presence of starfish. Behaviour, 5_: 130-140. 120 Canella, F. 1936. Quelques recherches sur l a vision monoculaire. CR. Soc. Biol. Paris, 122: 1221-1224. (Cited in Walk.R.D. 1965. The study of depth and distance perception in animals. Pp. 99-154 in : Lehman, D.S., Hinde, R.A. and E. Shaw (eds). Advances in the Study of  Behavior. Vol. I. Academic Press, N.Y.) Chance, M.R.A. and W.M.S. Russell. 1959. Protean displays: a form of allaesthetic behaviour. Proc. Zool. Soc. London, 132: 65-70. Crane, J. 1941. Crabs of the genus Uca from the west coast of central America. Zoologica, N.Y., 26: 145-208. Cronly-Dillon, J.R. 1964. Units sensitive to direction of movement i n goldfish optic tectum. Nature (Lond.) >:203: 214-215. Croze, H. 1 9 7 0 . Searching image in carrion crows. Z. Tierpsychol., Suppl. 5} 1 - 8 6 . Deese, J. 1 9 5 8 . The Psychology of Learning. Second edition.McGraw-Hill, Toronto. 367 pp. Dijkgraaf,S. 1 9 6 3 . The functioning and significance of the lateral-line organs. Biol. Rev., _38: 5 1 - 1 0 5 . Duke-Elder, S. 1 9 5 8 . System of Opthalmology. Vol. I The Eye in Evolution. Henry Kimpton, London. 843 pp. Duntley, S.Q. 1 9 6 3 . Light in the sea. J. opt. Soc. Am., _53: 2 1 4 - 2 3 3 . Eibl-Eibesfeldt, I. 1 9 6 5 . Land of a Thousand Atolls: A Study of Marine  Life in the Maldive and Nicobar Islands. MacGibbon and Kee, London. 195 pp. Estes, R.D. and J. Goddard. 1 9 6 7 . Prey selection and hunting behaviour of the African wild dog. J. Wildl. Mgmt., _3JL: 5 2 - 7 0 . Ewert, J.-P. 1 9 7 0 . Neural mechanisms of prey-catching and avoidance behaviour in the toad (Bufo bufo L.). Brain Behav. Evol., _3: 3 6 - 5 6 . Garrey, W.E. 1 9 0 5 . A sight reflex shown by sticklebacks. Biol. Bull., 8 : 7 9 - 8 4 . Gibson, J.J. 1 9 5 0 . The Perception of the Visual World. Houghton M i f f l i n , Boston. 235 pp. Girsa, I.I. 1 9 6 2 . The effect of the formation of defensive conditioned reflexes by young fish on their reduced accessibility to predators. Vop. Ikhtiol., 2: 7 4 7 - 7 4 9 . (Translation available from U.S. Bur. Comm. Fish., Washington, D.C). Glass, N.R. 1 9 7 1 . Computer analysis of predation energetics i n the largemouth bass. Pp. 3 2 5 - 3 6 3 in: B.C. Patten (ed.) Systems Analysis  and Simulation in Ecology. Vol. I. Academic Press, N.Y. 121 Goethe, F. 1 9 3 9 . Eine Flucht-bzw Schreckreaktion b e i jungen Hechten (Esox  l u c i u s L.) wahrend der e r s t e n Lebenstage. Z. T i e r p s y c h o l . , 2\ 3 1 4 . Goz, H. 1 9 4 1 . Uber den A r t - und I n d i v i d u a l g e r u c h b e i Fischen. Z. v e r g l . P h y s i o l . , 2 9 : 1 - 4 5 . Greppin, L. 1 9 1 1 . N a t u r w i s s e n s c h a f t l i c h e Betrachtungen 'uber d i e g e i s t i g e n F a h i g k e i t e n des Menschen und der T i e r e . B i o l . Z e n t r a l b l . , _31. ( C i t e d i n Hediger, H. 1 9 6 8 . The Psychology and Behaviour of Animals i n Zoos  and C i r c u s e s . Dover, N.Y. 166 pp. G r i f f i t h s , K.J. and C.S. H o l l i n g . 1 9 6 9 . A competition submodel f o r para-s i t e s and predators. Can Ent., 1 0 1 : 7 8 5 - 8 1 8 . G r i i s s e r , O.-J. and U. Grusser-Cornehls. 1 9 6 8 . Neurophysiologische Grund-lagen v i s u e l l e r angeborener Auslosmechanismen beim Frosch. Z. v e r g l . P h y s i o l . , 59.: 1 - 2 4 . Harlow, H.F. 1 9 3 9 . Forward c o n d i t i o n i n g , backward c o n d i t i o n i n g and pseudo c o n d i t i o n i n g i n the g o l d f i s h . J . Genetic P s y c h o l . , 5 5 : 4 9 - 5 8 . Hayes, W.N. and E.I. S a i f f . 1 9 6 7 . V i s u a l alarm r e a c t i o n s i n t u r t l e s . Anim. Behav., JL5: 1 0 2 - 1 0 6 . Hebb, D.O. 1 9 4 6 . On the nature of f e a r . P s y c h o l . Rev., 5 3 : 2 5 9 - 2 7 6 . Hediger, H. 1 9 3 4 . Zur B i o l o g i e und Psychologie der F l u c h t b e i T i e r e n . B i o l . Z e n t r a l b l . , _54: 2 1 - 4 0 . Hediger, H, 1 9 6 4 . Wild Animals i n C a p t i v i t y . Dover, N.Y. 207 pp. Hester, F.J. 1 9 6 8 . V i s u a l c o n t r a s t thresholds of the g o l d f i s h (Carassius  a'uratus). V i s i o n Res., j$: 1 3 1 5 - 1 3 3 6 . Hinde, R.A. 1 9 5 4 . Factors governing the changes i n s t r e n g t h of a p a r t i a l l y i nborn response, as shown by the mobbing behaviour of the c h a f f i n c h ( F r i n g i l l a c o e l e b s ) : I . The nature of the response, and an examination of i t s course. Proc. Roy. Soc. B, 1 4 2 : 3 0 6 - 3 3 1 . Hinde, R.A. 1 9 6 6 . Animal Behaviour: A Synthesis of Ethology and Compar- a t i v e Psychology. McGraw-Hill, Toronto. 534 pp. H i r s c h , J . , L i n d l e y , R.H. and E.C. Tolman. 1 9 5 5 . An experimental t e s t of an a l l e g e d i n n a t e s i g n s t i m u l u s . J . Comp. P h y s i o l . P s y c h o l . , 4 8 : 2 7 8 - 2 8 0 . H o l l i n g , C.S. 1 9 6 4 . The a n a l y s i s of complex p o p u l a t i o n processes. Can.' Ent., 9 6 : 3 3 5 - 3 4 7 . H o l l i n g , C.S. 1 9 6 5 . The f u n c t i o n a l response of predators to 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. Ent. Soc. Canada, 4 5 : 1 - 6 0 . 122 Holling, CS. 1966. The functional response of invertebrate predators to prey density. Mem. Ent. Soc. Canada, 4j5: 1-86. Holling, CS. (in preparation). Predation and prey size. Hunter, J.R. 1969. Communication of velocity changes in jack mackerel (Trachurus symmetricus) schools. Anim. Behav., _17: 507-514. Hunter, J.R. and W.J. Wisby. 1964. Net avoidance behavior of carp and other species of fis h . J. Fish. Res. Bd. Canada, 21^ 613-633. Ireland, L.C, Hayes, W.N. and L.H. Laddin. 1969. Relation between frequency and amplitude of visual alarm reactions in Pseudemys scripta. Anim. Behav., 386-388. Jacobson, M. and R.M. Gaze. 1964. Types of visual response from single units in the optic tectum and optic nerve of the goldfish. Quart. J. Exp. Physiol., 49:199-209. Kanayama, Y., Kodama, Y. and H. Tuge. 1964. Studies of the conditioned reflex in the lower vertebrates. IX. Defensive conditioned reflex of the fish larvae in group. Noto Marine Lab., Ann. Rept., j i : 3-8. Kanayama, Y. and H. Tuge. 1968. The use in fisheries of (elaborated) defensive conditioned reflexes in young chum salmon. Prob. Ichthyol., 8: 834-837. Kariya, T., Shirahata, S. and Y. Nakamura. 1968. An experiment to estimate the satiation rate of feeding fi s h . Bull. Jap. Soc. Sci. Fish., 34: 29-35. Klopfer, P.H. 1957. Empathic learning i n ducks. Amer. Nat., 9_1: 61-63. Kohn, A.J. and V. Waters. 1966. Escape responses of three herbivorous gastropods to .the predatory gastropod Conus textile. Anim. Behav., * 24: 340-345. Kramer, G. and U. von St. Paul. 1951. Uber Angeborenes und Erworbenes Feinderkennen beim Gimpel (Pyrrhula pyrrhula L.). Behaviour, _3: 243-255. Kuenzer, E. and P. Kuenzer. 1962. Untersuchungen zur Brutplege der Zwerg-cichliden Apistogramma r e i t z i g i und A. b o r e l l i . Z. Tierpsychol., 19: 56-83. Lawick-Goodall, H. van and J. van Lawick-Goodall. 1970. Innocent K i l l e r s . Collins, London. 222 pp. Leshcheva, T.S. 1968. Formation of defensive reflexes in roach (Rutilus  rutilus L.) larvae through imitation. Probl. Ichthyol., J3: 838-841. Maldonado, H. 1963. The positive learning process in Octopus vulgaris. Z. vergl. Physiol., 47: 191-214. 123 Maldonado, H. 1 9 6 4 . The c o n t r o l of a t t a c k by Octopus. Z. v e r g l . P h y s i o l . , 4 7 : 6 5 6 - 6 7 4 . M a n t e i f e l , B.P., Radakov, D.V., Nikonorov, I.V. and A.I. Treschev. 1 9 6 9 . Main ternds and some r e s u l t s of f i s h behaviour s t u d i e s i n the U.S.S.R. Pp. 8 0 9 - 8 1 5 i n : Ben-Tuvia, A. and W. Dickson (eds.). Proceedings of the FAQ Conference on F i s h Behaviour i n R e l a t i o n to F i s h i n g Techniques and  T a c t i c s . V o l . 3 . FAO F i s h . Rept., 6 2 . M a r t i n , R.C. and K.B. M e l v i n . 1 9 6 4 . Fear responses of bobwhite q u a i l (Colinus v i r g i n i a n u s ) to a model and a l i v e r e d - t a i l e d hawk (Buteo  j a m a i c e n s i s ) . P s y c h ol. Forschung., 2 7 : 3 2 3 - 3 3 6 . Maturana, H.R., L e t t v i n , J.Y., McCulloch, W.S. and W.H. P i t t s . 1 9 6 0 . Anat-omy and physiology of v i s i o n i n the f r o g (Rana p i p i e n s ) . J . Gen. P h y s i o l . , 4 3 : 1 2 9 - 1 7 5 . Mech, D.L. 1 9 7 0 . The Wolf: The Ecology and Behavior of an Endangered  Species. N a t u r a l H i s t o r y P r e s s , Garden C i t y , N.Y. 384 pp. Melzack, R. 1 9 6 1 . On the s u r v i v a l of ma l l a r d ducks a f t e r " h a b i t u a t i o n " to the hawk-shaped f i g u r e . Behaviour, J 7 : 9 - 1 6 . N i c e , M.M. and J . J . t e r Pelkwyk. 1 9 4 1 . Enemy r e c o g n i t i o n by the song sparrow. Auk, 5 8 : 1 9 5 - 2 1 4 . Noble, G.K. and B. C u r t i s . 1 9 3 9 . The s o c i a l behavour of the j e w e l f i s h , Hemichromis bimaculatus G i l l . B u l l . Amer. Mus. Nat. H i s t . , 7_6_: 1 - 4 6 . Nyberg, D.W. 1 9 7 1 . Prey capture i n the largemouth bass. Amer M i d i . Nat., 8 6 : 1 2 8 - 1 4 4 . O'Connell, C P . 1 9 6 0 . Use of f i s h s chool f o r con d i t i o n e d response exper-iments . .Anim. Behav., jS: 2 2 5 - 2 2 7 . Orr, R.T. 1 9 4 5 . A study of c a p t i v e Galapagos f i n c h e s of the genus Geospiza. Condor, 47_: 1 7 7 - 2 0 1 . O t i s , L.S. and J.A. Cerf. 1 9 6 3 . Conditioned avoidance l e a r n i n g i n two f i s h s p e c i e s . P s y c h ol. Repts., J^2: 6 7 9 - 6 8 2 . Polyak, S. 1 9 5 7 . The Vertebrate V i s u a l System. Univ. Chicago P r e s s , 1390 pp. Popov, T.B. 1 9 5 3 . Data on the study of conditioned defensive r e f l e x e s i n f i s h f r y . Zh. Vysshei Nervnoi D e y a t e l ' n o s t i , _ 3 ( 5 ) : 7 7 4 - 7 8 8 . ( C i t e d i n Thompson, R.B. 1 9 6 6 ) . Rodgers, W.L., Melzack, R. and J.R. Segal. 1 9 6 3 . T a i l - f l i p response i n the g o l d f i s h . J . Comp. P h y s i o l . P s y c h o l . , 56_: 9 1 7 - 9 2 3 . Roeder, K.D. 1 9 5 9 . A p h y s i o l o g i c a l approach to the r e l a t i o n between predator and prey. Smithson. Misc. C o l l . , 1 3 7 : 2 8 7 - 3 0 6 . 124 R u i t e r , L . de. 1963. The physiology of ver tebrate feeding behaviour : towards a synthes is of the e t h o l o g i c a l and p h y s i o l o g i c a l approaches to behaviour . Z . T i e r p s y c h o l . , ^ 0 : 498-516. R u s s e l l , E . M . 1967. Changes i n the behaviour of L e b i s t e s r e t i c u l a t u s upon a repeated shadow s t i m u l u s . Anim. Behav. , _15_: 574-585. S c h i f f , W . 1965. Percept ion of impending c o l l i s i o n : A study of v i s u a l l y d i r e c t e d avoidant b e h a v i o r . P s y c h o l . Monogr. , _79_(H): 1-26. S c h i f f , W. , Caviness , J . A . and J . J . Gibson. 1962. P e r s i s t e n t fear responses i n rhesus monkeys to the o p t i c a l s t imulus of looming. S c i e n c e , 136: 982-983. S c h i l l e r , P. von. 1934. Kinematopisches Sehen der F i s c h e . Z . v e r g l . P h y s i o l . , 20: 454-462. S c h l e i d t , W.M. 1961. Reaktion von Truth'uhnern auf f l i e g e n d e Raubvogel und versuche zur Analyse i h r e r A A M ' s . Z . T i e r p s y c h o l . , 18^: 534-560. S c h n e i r l a , T . C . 1965. Aspects of s t i m u l a t i o n and o r g a n i z a t i o n i n approach/ withdrawal processes u n d e r l y i n g ver tebrate b e h a v i o r a l development. Pp. 1-74 i n : Lehrman, D . S . , Hinde, R . A . and E . Shaw ( e d s . ) . Advances i n  the Study of Behavior . V o l . I . Academic P r e s s , N . Y . Schoener, T.W. 1969. Models of opt imal s i z e f o r s o l i t a r y p r e d a t o r s . Amer. N a t . , 103: 277-313. Senders, V . L . 1948. The p h y s i o l o g i c a l b a s i s of v i s u a l a c u i t y . P s y c h o l . B u l l . , 45: 465-490. Solomon, M . E . 1949. The n a t u r a l c o n t r o l of animal p o p u l a t i o n s . J . Anim. E c o l . , 28 : 1-35. S t e e l , R . G . D . and J . H . T o r r i e . 1960. P r i n c i p l e s and Procedures of  S t a t i s t i c s . M c G r a w - H i l l , Toronto . 481 pp. Sterba , G. 1962. Freshwater Fishes of the World. V i s t a Books, London. 868 pp. Tamura, T . 1957. A study of v i s u a l p e r c e p t i o n i n f i s h , e s p e c i a l l y on r e s o l v i n g power and accomodation. B u l l . Jap. Soc. S c i . F i s h . , 22: 536-557. T a r r a n t , R . M . , J r . 1964. Rate of e x t i n c t i o n of a condi t ioned response i n j u v e n i l e sockeye salmon. T r a n s . Amer. F i s h . S o c , 93 :^ 399-401. T h i n e s , G. and E . Vandexibussche. 1966. The e f f e c t s of alarm substance on the s c h o o l i n g behaviour of Rasbora heteromorpha i n day and night c o n d i t i o n s . Anim. Behav. , _14: 296-302. Thompson, R . B , 1966. E f f e c t s of predator avoidance c o n d i t i o n i n g on the 125 p o s t - r e l e a s e s u r v i v a l r a t e of a r t i f i c i a l l y propagated salmon. PhD. t h e s i s , Univ. of Wasington, S e a t t l e . 155 pp. Thorpe, W.H. 1 9 6 3 . Learning and I n s t i n c t i n Animals Second e d i t i o n . Methuen, London. 558 pp. Tinbergen,L. 1 9 6 0 . The n a t u r a l c o n t r o l of i n s e c t s i n pinewoods. I . Factors i n f l u e n c i n g the i n t e n s i t y of p r e d a t i o n by songbirds. Arch, n e e r l . Zool. , JL3: 2 6 5 - 3 4 3 . V e r h e i j e n , F.J. 1 9 5 6 . Transmission of a f l i g h t r e a c t i o n amongst a s c h o o l of f i s h and the u n d e r l y i n g sensory mechanisms. E x p e r i e n t i a , _12: 2 0 2 -2 0 4 . Veselov, E.A. 1 9 6 4 . Simplest methods f o r s t u d i e s on some r e f l e x e s of f i s h l a r v a e and f r y . Pp. 2 9 7 - 3 1 1 i n : P a v l o v s k i i , E.N. (ed.). Techniques  f o r the I n v e s t i g a t i o n of F i s h Physiology. I s r a e l Program f o r S c i e n t i f i c T r a n s l a t i o n s , Jerusalem. Walther, F.R. 1 9 6 9 . F l i g h t behaviour and avoidance of predators i n Thomson's g a z e l l e ( G a z e l l a thomsoni Guenther 1 8 8 4 ) . Behaviour 3 4 : 1 8 4 - 2 2 1 . Ware, D.M. 1 9 7 1 . The predatory behaviour of rainbow t r o u t (Salmo g a i r d n e r i ) . PhD t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver. 158 pp. Weinberger, H. 1 9 7 1 . Conjecture on the v i s u a l e s t i m a t i o n of r e l a t i v e r a d i a l motion. Nature (Lond.), 2 2 9 : 5 6 2 . Welker, W.I. and J . Welker. 1 9 5 8 . Reaction of f i s h (Eucinostomus gula) to environmental changes. Ecology, _3_9: 2 8 3 - 2 8 8 . Wolf, E. and G. Zerrahn-Wolf. 1 9 3 6 . Threshold i n t e n s i t y of i l l u m i n a t i o n and f l i c k e r frequency f o r the eye of the s u n f i s h . J . Gen. P h y s i o l . , 1 9 : 4 9 5 - 5 0 2 . 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0093102/manifest

Comment

Related Items