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UBC Theses and Dissertations

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

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PREY AVOIDANCE LEARNING AND THE FUNCTIONAL RESPONSE OF PREDATORS  by LAWRENCE M. DILL  BSc, U n i v e r s i t y MSc, U n i v e r s i t y  of B r i t i s h Columbia, of B r i t i s h Columbia,  1966 1968  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the  Department of Zoology  We a c c e p t t h i s t h e s i s as conforming to required standard  THE UNIVERSITY OF BRITISH COLUMBIA JULY 1972  the  In  presenting  this  thesis  an a d v a n c e d  degree  the L i b r a r y  s h a l l make i t  I  further  for  scholarly  by h i s of  agree  this  written  at  the U n i v e r s i t y freely  that permission  for  It  financial  fulfilment  of  of  Columbia,  British  available for  by  shall  the  requirements  reference copying  of  I agree and this  that  not  copying  or  be a l l o w e d w i t h o u t  LAWRENCE M. DILL  of  ZOOLOGY  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8 , Canada  Columbia  that  thesis or  publication  permission.  Department  for  study.  t h e Head o f my D e p a r t m e n t  is understood gain  for  extensive  p u r p o s e s may be g r a n t e d  representatives. thesis  in p a r t i a l  my  ii  ABSTRACT  The r e s e a r c h attempts t o d e t e r m i n e the e f f e c t on the number o f prey e a t e n by p r e d a t o r s o f the a d d i t i o n o f the component " a v o i d a n c e l e a r n i n g by p r e y " t o a computer model o f the p r e d a t i o n p r o c e s s Holling  (1966).  developed by  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  a s p e c t s o f the p r e y ' s  behaviour, 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 a p p r o a c h i n g p r e d a t o r .  The z e b r a d a n i o ( B r a c h y d a n i o r e r i o ) , a s m a l l  f r e s h w a t e r f i s h , was used as an analogue o f a general  vertebrate  prey.  P r e d a t o r s used were p l e x i g l a s s m o d e l s , f i l m s o f a p p r o a c h i n g 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 z e b r a 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 = predator diameter k = t h r e s h o l d r a t e o f change o f angle subtended a t the eye o f the prey by the p r e d a t o r (= .43 r a d / s e c ) .  T h u s , 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 p a r a m e t e r s .  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 affected  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 of previous 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  t o o t h e r f e a t u r e s o f t h e 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 t o e x p e r i e n c e was shown t o 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 t o decrease p r e d a t o r p u r s u i t  tu success.  These r e l a t i o n s h i p s were e x p r e s s e d 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 , causing reactive distance  a l o n g w i t h an e q u a t i o n  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  S i m u l a t i o n was used t o e x p l o r e t h e 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 o f s u r v i v i n g subsequent a t t a c k . ponent caused d e c l i n e s  rease the p r e d a t o r ' s  probability  A d d i t i o n o f the avoidance l e a r n i n g com-  i n the p r e d a t o r ' s  prey and p r e d a t o r d e n s i t y .  attack.  f u n c t i o n a l responses  t o both  The new component was a l s o suggested  to  dec-  n u m e r i c a l response t o prey d e n s i t y and t o i n c r e a s e  p r o b a b i l i t y of s t a b i l i t y i n a predator-prey  interaction.  the  iv  TABLE OF CONTENTS  TITLE PAGE ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS I II  GENERAL INTRODUCTION GENERAL METHODS AND MATERIALS 1 2 3  The Prey The P r e d a t o r The T e s t i n g Apparatus a b c  4 III  The p r e d a t i o n arena The model p r e d a t o r The c i n e m a t o g r a p h i c p r e d a t o r  A n a l y s i s of Films  THE AVOIDANCE STIMULUS AND RESPONSE  1 2 • 3  Introduction Theory and M a t h e m a t i c a l Model 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 h y p o t h e s i s o f a t h r e s h o l d doc/dt (ii) e f f e c t o f model shape (iii) 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 (iv) 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 i n e m a t o g r a p h i c 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 (ii) t h r e s h o l d dot/dt o f s c h o o l e d prey 4 Discussion 5 Conclusions IV  CHANGE OF dtt/dt THRESHOLD WITH EXPERIENCE 1 2  Introduction Methods a b  Model p r e d a t o r Cinematographic  predator  V  Page 3  4 5  V  Results  47  a  Model p r e d a t o r (i) change i n response w i t h e x p e r i e n c e (ii) g e n e r a l i z a t i o n o v e r model s i z e b Cinematographic predator (i) learning (ii) control  47 47 50 51 51 53  Discussion Conclusions  54 64  THE EFFECT OF HUNGER ON THE THRESHOLD RATE OF CHANGE OF VISUAL ANGLE 1 2 3  Introduction Methods Results a b  4 5  VI  *  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 T h r e s h o l d d N / d t as a f u n c t i o n o f hunger  Discussion Conclusions  Introduction Filmed I n t e r a c t i o n s a b  3 4 5  65 66 69 69 73 7  Between P r e d a t o r s and Prey  Methods R e s u l t s and d i s c u s s i o n  The S i m u l a t i o n Model R e s u l t s and D i s c u s s i o n Conclusions  LITERATURE CITED  5  5  80  ADDITION OF THE AVOIDANCE LEARNING COMPONENT TO A GENERALIZED . • MODEL OF THE PREDATION PROCESS 1 2  6  81 81 85 85 86 96 105 116 119  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  II  Mean r e a c t i v e d i s t a n c e s i z e s and v e l o c i t i e s  III  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 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 naive danios  V  Rates o f change o f v i s u a l a n g l e  VI  (cm) o f n a i v e d a n i o s o f  (dc(/dt ^ fi  different  classes  predator.  Rates o f change o f v i s u a l a n g l e  )  t o t a l  response o f d a n i o s t o the c i n e m a t o g r a p h i c  of  ) a t the times  response o f d a n i o s t o the c i n e m a t o g r a p h i c (d<*/dt  zebra  of  a t the times  of  predator.  VII  Data from f i l m e d o b s e r v a t i o n s zebra danio i n t e r a c t i o n s  o f largemouth bass -  naive  VIII  Summary o f d a t a on t h r e s h o l d do(/dt o f z e b r a danios t o predators  IX  Mean o b s e r v e d 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 t o largemouth bass o f two s i z e s  X  Comparison o f responses 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 d a n i o s t o the c i n e m a t o g r a p h i c p r e d a t o r b e f o r e and a f t e r 10 days i n t h e e x p e r i m e n t a l aquarium  XII  Mean and s t a n d a r d e r r o r o f t h e w e i g h t (grams) o f f o o d e a t e n by z e b r a d a n i o s 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  XIII  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 v a r i o u s times 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 t u a l i z e d by H o l l i n g ( 1 9 6 3 , 1965, 1966).  concep-  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 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  para-  various  of zebra  o f t r a i n e d d a n i o s t o model  danios  predators  after  vii Page XVI  XVII  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 t a n c e s l e s s than o r g r e a t e r than 6 . 4 cm (mean DS observed) The meanings and v a l u e s o f a l l parameters i n the s i m u l a t i o n model  93 104  viii  Page  LIST OF FIGURES  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  8  3  A p p a r a t u s 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 g a p l a n view o f the prey h o l d i n g chamber  4  A. B.  5  Apparatus used f o r p r e s e n t a t i o n o f the predator T e s t i n g chambers  7  11  D  Q  and D-j.  16  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 subtended by the o b j e c t a t the o b s e r v e r ' s eye (<*). 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 o f n a i v e z e b r a danios 2  (4D  angle 16  distance 19  2  Regression of  9  Method o f b l o c k i n g the d a t a by angle o f o r i e n t a t i o n t o the d i r e c t i o n o f the a p p r o a c h i n g m o d e l .  11  8  cinematographic  8  10 .  includ-  S c h e m a t i c 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 (cx^CX-j) subtended by an o b j e c t o f s i z e S a t distances  6  carriage  + S )/4S on model v e l o c i t y  19 relative 24  Values o f dw/dt w i t h time f o r f o u r danios r e s p o n d i n g more than once t o the c i n e m a t o g r a p h i c p r e d a t o r . The v a l u e s a r e 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 t o 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  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 d a n i o s r e s p o n d i n g t o the model predator 49  13  E f f e c t o f e x p e r i e n c e o f the c i n e m a t o g r a p h i c p r e d a t o r on t h r e s h o l d dc*/dt o f z e b r a d a n i o s 52  14  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 d a n i o s r e s p o n d i n g t o the cinematographic predator 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 a c c e p t e d ) i n the z e b r a d a n i o  5  70  ix  Page  16  Hunger d a t a t r a n s f o r m e d t o 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 d o / d t o f d a n i o s t o the c i n e m a t o g r a p h i c p r e d a t o r  74  18  19  20  responding  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 predator  84  R e l a t i o n s h i p between observed approach t i m e 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  R e g r e s s i o n 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 f o r the bass-danio i n t e r a c t i o n s  time 89  21  Observed r e l a t i o n s h i p between d a n i o 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 c o n s t a n t 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 d a n i o r e a c t i v e d i s t a n c e and bass s t r i k e distance  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 t o p r e y w i t h and w i t h o u t the a b i l i t y t o l e a r n  106  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 e n v i r o n m e n t a l parameters on the p r o b a b i l i t y o f c a p t u r e 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  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  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 p e r p r e d a t o r p e r 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  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 t o 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  27  28 29  30  X  ACKNOWLEDGEMENTS  I s h o u l d l i k e t o e x p r e s s my s i n c e r e  gratitude  people whose h a r d work a l l o w e d t h i s p r o j e c t  to a number o f  to reach c o m p l e t i o n .  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 p a r t i c u l a r l y i n the area o f apparatus  construction.  Messrs.  assistance,  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 M i s s 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 research  at i t s various stages.  The bass were o b t a i n e d from the  o r n i a Department o f F i s h and Game through the c o u r t e s y Fisk.  M r s . L . F i l t e a u typed the t h e s i s .  l i k e to financial support,  thank my s u p e r v i s o r ,  o f M r . Leonard  Above a l l , however,  Dr. C.S. H o l l i n g , f o r his  and moral s u p p o r t d u r i n g the p a s t t h r e e y e a r s . t h i s r e s e a r c h would not have been  possible.  Calif-  I should  unstinting W i t h o u t such  I  GENERAL INTRODUCTION  An e f f e c t i v e  theoretical  framework f o r t i l e management o f animal popu-  l a t i o n s can o n l y be based upon a thorough u n d e r s t a n d i n g o f the  ecological  p r o c e s s e s by w h i c h 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 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  c e s s , an u n d e r s t a n d i n g o f i t s mechanisms w i l l  have c o n s i d e r a b l e  of pro-  practical  value. H o l l i n g (1965, 1966) made a s i g n i f i c a n t c o n c e p t u a l  advance i n the  study o f e c o l o g i c a l  p r o c e s s e s 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 p r o c e s s  o f p r e d a t i o n , f o r example, was  as b e i n g s t r u c t u r e d from a number o f d i s c r e t e components.(e.g.  time a v a i l a b l e f o r s e a r c h i n g )  [e.g.  l e a r n i n g by the  a r e c h a r a c t e r i s t i c o f o n l y some examples o f t h e process These components  Some o f t h e s e  are c h a r a c t e r i s t i c o f a l l examples  p r e d a t i o n and are termed " b a s i c " ; o t h e r s  "subsidiary".  conceived  of  predator)  and are termed  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 t o 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 iour of real predator-prey i n t e r a c t i o n s .  Such " i n t i m a t e  1  behav-  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 t h e o r y at l e a s t ,  are r e a l i s t i c , h o l i s t i c , g e n e r a l  and p r e c i s 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  (Holling,  and whose  pre-  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 p r o c e s s 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 l e a r n i n g by p r e y . "  "avoidance  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  largely  2  a n e c d o t a 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 c o h e s i v e 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 t u d y to examine avoidance l e a r n i n g i n the c o n t e x t o f a p a r t i c u l a r theoretical  framework, t o examine the i n t e r a c t i o n s between t h i s component  and o t h e r s a l r e a d y examined, t o add the new component t o the s i m u l a t i o n m o d e l , and t o 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 necessary  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 v a l u e i s d r a s t i c a l l y  l i m i t e d i f t h e r e i s no u n i f y i n g framework t o 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"  (Holling,  1964).  3  II  GENERAL METHODS ,AND MATERIALS 1  The Prey  The prey used t h r o u g h o u t were a d u l t z e b r a d a n i o s , B r a c h y d a n i o rerio,  a small freshwater  c y p r i n i d n a t i v e to I n d i a .  They a r e 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 flowing  waters.  S i n c e i t was d e s i r a b l e 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 w t t f i l a r g e moving  objects,  a l l o f the d a n i o s used i n these experiments were  laboratory  r e a r e d . A d u l t d a n i o s were a l l o w e d to spawn i n 10 g a l . a q u a r i a o v e r a bottom o f a r t i f i c i a l  vegetation.  The spawners were removed p r i o r  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. b e f o r e b e i n g t r a n s f e r r e d 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  to  to  hatching.  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 naive. For o t h e r e x p e r i m e n t s , the r e q u i r e m e n t o f n a i v e t y c o u l d be r e laxed.  The d a n i o s used i n these experiments were o b t a i n e d from t r o p i -  cal f i s h hatcheries  o r l o c a l aquarium s h o p s .  r e a r e d i n the absence  These f i s h had a l s o  o f a d u l t s , but i n l a r g e o u t d o o r ponds.  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 , be e n t i r e l y r u l e d o u t .  been  The c o u l d not  These d a n i o s were c o n s i d e r e d t o 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 , t h e s e were largejnouth black, b a s s , M i c r o p t e r u s salmotdes hatchery.  The s i z e s  Table I  (Lacepe.de)  o b t a i n e d from a C a l i f o r n i a  o f the two bass used are shown i n T a b l e  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 . H e i g h t and w i d t h as seen i n f r o n t v i e w .  BAbb#  OVERALL 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  RACC*  u  r  T  r  u  T  H h l b H 1  i  IT  W  i  n-pij U  I  H  The bass were h e l d s e p a r a t e l y  HEIGHT/ WIDTH  HEIGHT/ LENGTH  WIDTH/ LENGTH  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 . i o n a l l y , meals c o n s i s t e d o f o t h e r s m a l l f i s h ( g u p p t e s ,  Occas-  mollies,  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  earth-  worms, meal worms, and commercial f i s h food moistened and r o l l e d i n t o small  pellets.  5  3  The Apparatus  Three s p e c i a l i z e d p i e c e s o f apparatus were used i n the e x p e r i ments. here.  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 Methodology s p e c i f i c t o a p a r t i c u l a r experiment i s  i n the a p p r o p r i a t e  a)  given detailed  section.  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 t n  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 t h e arena were u n i f o r m l y w h i t e p r o v i d e maximum c o n t r a s t between f i s h and background f i l m i n g purposes.  to  for  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  t o the tank d i r e c t l y o r 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 e n d .  V i e w i n g 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° a n g l e . a wide-angle  (10mm) l e n s on a B o l e x camera, i t was  Using possible  t o r e c o r d the e n t i r e tank a r e a 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 surface  lens-to-water  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  film  pushed one s t o p i n p r o c e s s i n g .  Q u a r t e r - r o u n d p a n e l s 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 c o r n e r o f the tank so t h a t the prey 'would not become t r a p p e d 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 inary experiments.  Water l e v e l was m a i n t a i n e d a t 10cm  Figure 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 l l dimensions e x p r e s s e d as m.  arena.  6  7  t o 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 t o make f i l m i n g e a s i e r .  The w a t e r was m a i n t a i n e d a t 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 .  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 b e h i n d each o f the 2.44m opaque p l e x i g l a s s i n a t i n g the problem o f s u r f a c e  b) The model  Side-  lights  sides,  located  thus  elim-  reflection.  predator  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 p r e s e n t e d t o the d a n i o s . Artificial  " p r e d a t o r s " o f two t y p e s , model and c i n e m a t o -  g r a p h i c , were d e s i g n e d f o r t h i s  The model p r e d a t o r apparatus F i g s . 2 & 3.  purpose.  i s shown d i a g r a m m a t i c a l l y i n  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 11.6  t o 108.5  cm/sec.  of  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 t a c h e d t o the overhead c a r r i a g e  (constructed  clear plexiglass) without s i g n i f i c a n t l y affecting  the  of  velo-  city.  The d a n i o t o 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 t o the e x p e r i m e n t and a c c l i m a t e d t o the o f the motor r u n n i n g a t top s p e e d . c o n f i n e the f i s h  The chamber s e r v e d  and t o keep v i b r a t o r y s t i m u l i  noise to  t o a minimum.  Figure 2  The model p r e d a t o r suspended from a p l e x i g l a s s A l l d i s t a n c e s i n cm.  Figure 3  A p p a r a t u s 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 2 3 4 5 6 7 8 9 10 11  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 Screws f o r attachment o f rope White n y l o n rope C u r t a i n t r a c k r a i l on d e x i o n s u p p o r t B a l l race wheels covered w i t h foam r u b b e r 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 painted black Pulleys P l e x i g l a s s model s u p p o r t ( . 6 4 cm p l e x i g l a s s ) Mirrors Prey h o l d i n g chamber A x l e o f e l e c t r i c motor  carriage.  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  for  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 . D u r i n g 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  at  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  t o the e l e c t r i c motor and the model moved down the o f the tank toward the p r e y .  The prey was always  length stationary  when the p r e d a t o r began moving and t h e r e was no e v i d e n c e r e a c t i o n t o the motor n o i s e a t the i n i t i a t i o n o f the  of  test.  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 t o the  test.  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 r e c o r d e d from 0.84m above t h e ' w a t e r s u r f a c e w i t h a m o t o r i z e d B o l e x 16 mm camera a t 16 sec and f l . 6 .  c)  Plus-X reversal  The c i n e m a t o g r a p h i c  frames/  f i l m was u s e d .  predator  A s h o r t motion p i c t u r e o f an a p p r o a c h i n g 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 t o the d a n i o s .  presented  I t was made by t a k i n g 120 s i n g l e frame p h o t o -  graphs o f an 8mm d i a m e t e r dot on a w h i t e background from . varying distances  on an o p t i c a l bench CBolex T i t l e r ) .  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 a t 205mm, w i t h exposures  e v e r y 4mm between these  The last  extremes.  10  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 B o l e x 16 mm camera were a d j u s t e d a t i n t e r v a l s a l o n g the bench t o 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-  b e r was w r i t t e n above the o b j e c t and photographed a l o n g w i t h it.  I t appeared i n the upper p o r t i o n o f each frame o f the  film.  When the sequence was p r e s e n t e d t o human o b s e r v e r s speed o f 24 f r a m e s / s e c ,  at a  they p e r c e i v e d i t as an o b j e c t  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 .  app-  A l t h o u g h no d a t a  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 d a n i o v i s u a l s y s t e m , i t i s assumed t h a t they a l s o a smooth a p p r o a c h .  The p e r s i s t e n c e  the c y p r i n i d Phoxinus l a e v i s critical  perceived  time o f the r e t i n a o f  (von S c h i l l e r , 1934) and the  f l i c k e r f r e q u e n c y 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) a r e b o t h v e r y s i m i l a r t o t h o s e 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 p r e s e n t e d to  individual  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 w a t e r system was common t o the s i x ,  b u t 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  filter.  Opaque p l e x i g l a s s p a r t i t i o n s s e p a r a t e d 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 l o n g by 10cm wide and was f i l l e d  t o a depth o f 7.5 cm  Figure 4  A . Apparatus used f o r p r e s e n t a t i o n o f the c i n e m a t o g r a p h i c p r e d a t o r B t e s t i n g chambers. A l l distances expressed i n cm.  11  ^  16 mm Bolex  camera port  j  7  lamp  lamp  50  projector (24 fr/sec)  board, tracing ^ paper ^ 7.5  -75-  1  B  21  30 lamp  -15-  10opa que parti ions •filter  one-way mirror  12  o v e r a bottom o f coarse y e l l o w g r a v e l . strate  F i s h above t h i s  sub-  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  w a t e r was m a i n t a i n e d a t 23C by h e a t i n g t h e a i r t n t h e 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 p r e s e n t e d t o the d a n i o s 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 t o accustom them t o 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  frames) o f the a p p r o a c h i n g o b j e c t .  T h i s was p r o j e c t e d  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 taped to the w a l l o f the chamber.  (120 from  tightly  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 a q u a r i u m , A B o l e x 16 mm camera w i t h a 10 mm l e n s mounted 50 cm above t h e water surface  r e c o r d e d the b e h a v i o u r o f the f i s h and t h e 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 a t 32  fr/sec  at f 4 . 0 .  4  A n a l y s i s o f the F i l m s  All M-16 CW).  f i l m s were examined on a Vanguard Motion A n a l y z e r (Model Positions, velocities,  and a n g l e s 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 s c r e e n o r by punching the x , y o f p o s i t i o n s and a n g l e s o f o r i e n t a t i o n frame-by-frame tape.  The tape was read by an IBM 1130  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 )  coordinates  on t o paper  computer and the  relevant  t a b u l a t e d and graphed.  13  III  THE AVOIDANCE STIMULUS AND RESPONSE  1  Introduction The z e b r a d a n i o , i n t h e s e e x p e r i m e n t s , i s e s s e n t i a l l y  c o n s i d e r e d an analogue o f a g e n e r a l regardless  prey a n i m a l .  being  S i n c e any  prey,  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  with respect  t o when t o i n i t i a t e i t s e s c a p e , a t t e n t i o n w i l l  f o c u s e d on one a s p e c t o f the r e s p o n s e : f l i g h t distance  (Hediger, 1934).  be  the r e a c t i o n d i s t a n c e  I t i s the purpose o f t h i s  t o determine t h e n a t u r e o f the s t i m u l u s f o r avoidance o f  or  section  predators  by z e b r a d a n i o s . S i n c e a model o f a v o i d a n c e goal o f t h i s s t u d y and s i n c e , a r e the p e r o g a t i v e s  l e a r n i n g by prey i s the u l t i m a t e  i n g e n e r a l , complex l e a r n i n g  of vertebrates,  only a vertebrate  S i n c e 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  processes  prey was  most  used.  vertebrates,  • i t i s assumed t o 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 t o the p r e y .  T h i s i s not t o s u g g e s t t h a t o t h e r s e n s o r y m o d a l i t i e s  no i m p o r t a n c e , b u t o n l y t h a t they have l e s s special  importance e x c e p t  in  cases.  A prey o r g a n i s m , h a v i n g become aware o f an o b j e c t  in its  visual  f i e l d , must d e c i d e whether t o c o n t i n u e about i t s b u s i n e s s o r t o appropriate defensive  action.  o f p o t e n t i a l danger p r e s e n t e d . assessment object.  I t must t h e r e f o r e  take  assess the degree  Three cues which may be used i n t h i s  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  sighted  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 ,  g e r 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 t o have intent.  have  the  lar-  predacious  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 t o  14 get too c l o s e ,  J  the prey may not have time t o reach s a f e t y .  n a t i v e l y , i f the prey r e a c t s  too s o o n , i t may waste time 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 . therefore,  Alter-  The p r e y ,  must have some way o f a s c e r t a i n i n g t h e s e t h r e e  characterise  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  species  of fish  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 s m a l l area d i r e c t l y i n  front.  Since attacks  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 a b l e t o determine s i z e and d i s t a n c e m o n o c u l a r l y o r waste v a l u a b l e time t u r n i n g t o f i x a t e for distance estimation e x i s t  the p r e d a t o r .  Monocular cues  ( G i b s o n , 1950) but such e s t i m a t e s  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 i n t h e case o f p e l a g i c f i s h e s ) .  environment  may (e.g.  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  if  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 .  two s u c c e s s i v e  However,  t a k i n g two v i s u a l f i x e s may be n o n - a d a p t i v e 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 ( R o e d e r , Some a l t e r n a t e s t i m u l u s f o r a v o i d a n c e  is therefore  1959). required.  T h i s s t i m u l u s s h o u l d 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 a p p r o a c h i n g  predators  from g r e a t e r d i s t a n c e s  The s t i m u l u s  than to s m a l l e r o r s l o w e r o n e s .  s h o u l d a l s o be so g e n e r a l  t h a t i t i s a s s o c i a t e d w i t h every type  p r e d a t o r w i t h which the prey i s l i k e l y t o i n t e r a c t .  of  One s t i m u l u s  which p o s s e s s e s a l l o f t h e s e 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 angle."  The h y p o t h e s i s 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 , z e b r a danios show avoidance  behaviour.  15  2  Theory and M a t h e m a t i c a l 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 Fig.  5.  As the o b j e c t moves towards the e y e ,  tended (oc) i n c r e a s e s visual  as shown i n F i g . 6.  a n g l e , dcx/dt, t h e r e f o r e  c o l l i s i o n decrease.  the v i s u a l a n g l e s u b -  The r a t e o f change o f the  increases  as d i s t a n c e and time t o  T h i s r a t e i s d e t e r m i n e d 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 I f D is distance, S object s i z e ,  observer.  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.: t a n o c / 2 = S/2D and oc ( r a d i a n s ) = 2 a r c t a n [ S / 2 D ) Substituting -Vt for D gives: =2 T h e r e f o r e do/dt  arctan(S/-2Vt)  ...(1)  (radians/sec)  4VS 4V t 2  2  + S  = 2  4VS 4D + S 2  ...(2) 2  I f p r e y 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 reactive distance  (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  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 ) :  (sub-  Figure 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 a n g l e s (o^oC-)) subtended by an o b j e c t o f s i z e S at distances D  Figure 6  Q  and  .  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 a n g l e 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  (cm)  17  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 The model p r e d a t o r apparatus was used to t e s t the that  dcx/dt  a t the time o f r e a c t i o n ( f l i g h t )  i r r e s p e c t i v e of predator s i z e o r v e l o c i t y . were chosen : 1 1 . 6 , object diameters  constant,  Four v e l o c i t i e s  4 3 . 6 , 6 2 . 8 , and 108.5 cm/sec.  ("S"  i n F i g . 5) were u s e d :  5 . 0 8 cm.  The s i z e s  factorial  design with s i x r e p l i c a t e s  trol  is  hypothesis  Three  2 . 5 4 , 3.81  and  and v e l o c i t i e s were p r e s e n t e d i n a 3 x 4 (i.e.  n = 72).  A con-  e x p e r i m e n t 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 t a c h e d towards individual  n a i v e d a n i o s a t 108.5  six  cm/sec.  Four n a i v e 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 -  i n random o r d e r .  presented  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  models was randomly s e l e c t e d between d a y s .  sized  The prey were f e d  t o s a t i a t i o n 24 hours b e f o r e 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 i e c e s o f d a t a .  After pre-  s e n t a t i o n o f the m o d e l , the prey were measured t o the  nearest  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 t h a n once.  Reactive 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 m o d e l , and v e l o c i t y o f escape were r e c o r d e d 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 time the  18 d a n i o 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 p r e s e n t e d purposes o f c o m p a r i s o n : ball  bearings.  for  f u s i f o r m p l e x i g l a s s models and round  Both types were coated with, black, epoxy p a i n t .  A l t h o u g h both appeared round i n f r o n t v i e w , the a p p a r e n t shape o f the f u s i f o r m model v a r i e d w i t h v i e w e r a s p e c t . and v e l o c i t y were 3.81  (i)  cm and 6 2 . 8 cm/sec  Model  size  respectively.  t e s t o f the h y p o t h e s i s o f a t h r e s h o l d dfl/dt A c c o r d i n g t o e q u a t i o n ( 3 ) , both model s i z e and v e l o c i t y  s h o u l d 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 prey.  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 d a t a (Table n  and F i g . 7} r e v e a l e d  n i f i c a n t e f f e c t s of both v a r i a b l e s .  Table II  the  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 d a n i o s t o 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 (an/sec)  S  I  Z  < )  E  cm  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  (2,60)  Velocity F ^  6 f  =  3  -  7  8  8  9  5  signif.  at  .05  ^ = 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 not s i g n i f i c a n t .  components  sig-  Figure 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 of naive zebra danios. Each p o i n t i s the mean o f observations.  F i g u r e 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 t o 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) t a k e n as the b e s t e s t i m a t e o f the t h r e s h o l d d o / d t . The upper l i n e (k = .36) was d e r i v e d from the raw d a t a ; the l o w e r 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 b a r 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 error. :  distance six  VELOCITY  (cm/sec)  20  E q u a t i o n (2) may a l s o be r e a r r a n g e d t o the f o r m : 4D  2  + S 4S  2  =  1 k  . V  ...(4)  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 t o z e r o .  An i n i t i a l  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 from z e r o  ($  Q  = 40.7198 ± 2 5 . 9 0 8 3 ) .  reg-  different  A second r e g r e s s i o n  [Fig.  8 ) , c o n d i t i o n e d t o pass through the o r i g i n , was conducted o b t a i n ' an e s t i m a t e o f k. 1/k - 2 . 5 9 9 4 ± 0 . 1 9 8 5 ) . CF = 161.92 w i t h 1,70  T h i s e s t i m a t e was  .38 rad/sec  to  (/S^ =  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  d f ) b u t 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 The dependent v a r i a b l e i n the r e g r e s s i o n  (  (4D  2 + S )/4S)  was examined f o r each v e l o c i t y and found t o be skewed i n the d i r e c t i o n of small values.  Consequently,  the e s t i m a t e o f k  i s not the b e s t p o s s i b l e o n e , a l t h o u g h the s i g n i f i c a n c e  of  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 e x a m i n i n g the 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  origithe  d i s t r i b u t i o n o f d a / d t 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  mean l n dtf/dt i s the b e s t e s t i m a t e o f k.  the  This value  r a d / s e c ) 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  (0.43  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 c o n d u c t e d on I n 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  hypothesis.  None o f the d a n i o s p r e s e n t e d w i t h o n l y the  carriage  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  fact,  they appeared t o be t o t a l l y o b l i v i o u s t o i t s a p p r o a c h . is therefore  It  c o n c l u d e d t h a t the r e a c t i o n s t o the model were  s o l e l y i n response t o 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 or v i b r a t i o n .  Cii)  e f f e c t o f model shape The round and f u s i f o r m models were each p r e s e n t e d t o s i x  randomly s e l e c t e d n a i v e 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 ( T a b l e I I I ) .  Presumably the  were r e s t r i c t e d t o a s m a l l enough a r e a t h a t the e f f e c t  fish of  v i e w e r a s p e c t 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 o f n a i v e z e b r a danios  SHAPE  X FISH SIZE (mm)  distance  REACTIVE DISTANCE (cm) X  ±  Sy  Fusiform  27.3  28.5  ±  3.58  Ball  26.9  35.2  +  4.61  t  0.5147 NS  22  (iii)  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 d a n i o length.  These were e n t e r e d 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. prove'd to be a s i g n i f i c a n t component ( F ^  6g  ^=  This  10.352 p < . 0 0 5 ) .  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 . f o r the s m a l l f i s h ( T a b l e I V ) .  The t h r e s h o l d da/dt was In o t h e r w o r d s , l a r g e  greater fish  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 s m a l l f i s h p r e s e n t e d  the  same s t i m u l u s .  T a b l e IV  T h r e s h o l d d a / d t (k) and / 9 , ( l / k ) f o r two s t z e classes of naive danios.  PREY SIZE  /O  a. T C LT  A .IA4.  ft ± 1 S . E .  doydt THRESHOLD .4547  MIN 26.0  MEAN 28.74  MAX 30.0  2.1992 ± 0.2302  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 s m a l 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 n o t prove significant  (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 a t an i n t e r m e d i a t e prey s i z e 28 mm).  (around  T h i s p r o b l e m , 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 s t u d y 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 t o 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 sion repeated. non-significant,  (v)  Since the(regression  regres-  * blocks)component was  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 .  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  distance  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 . t o escape a t a c o n s t a n t v e l o c i t y o f 1 8 . 2  S t u d i e s w i t h the c i n e m a t o g r a p h i c  The prey tended  cm/sec.  predator  A l t h o u g h the c i n e m a t o g r a p h i c p r e d a t o r was used p r i m a r i l y o b t a i n d a t a on the e f f e c t o f e x p e r i e n c e a l s o p r o v i d e d some s u p p o r t i n g e v i d e n c e stant threshold.  Some o f t h e d a n i o s  to  on t h r e s h o l d do(/dt,  f o r the concept o f a c o n -  ( n o n - n a i v e ) i n the e x p e r i -  mental aquarium responded t o each sequence more than once. is,  it  That  they f l e d from the " p r e d a t o r " , t u r n e d t o f a c e 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  again.  The c i n e m a t o g r a p h i c 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 i n e m a t o g r a p h i c p r e d a t o r appeared on each frame of the d a t a f i l m , the p r e y ' s  i t was p o s s i b l e t o  correlate  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  cf  change o f the image on the w a l l of the chamber and t o p l o t d«/dt  Figure 9  Method o f b l o c k i n g the d a t a by angle o f o r i e n t a t i o n r e l a t i v e t o the d i r e c t i o n o f the a p p r o a c h i n g model ( 0 ° ) .  CM  25  against time. responses  T h i s was done f o r f o u r sequences i n which m u l t i p l e  occurred.  The image s i z e  ( W ) i s the d i a m e t e r o f the image on the  film  (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 d e t e r m i n e d t o be 2 7 . 4 .  The d i a m e t e r 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 d i a m e t e r = 8 mm f = lens focal  l e n g t h = 55 mm  D = filming distance  (681 to 205 mm)  The s i z e o f the image on the s c r e e n i s W = S f  and  dW' dD  therefore:  (27.4) D  = 12,056/D  ...(6)  = 12,056 2  ...(7)  D  The r a t e o f change o f d i a m e t e r o f the c i n e m a t o g r a p h i c p r e d a t o r w i t h time i s : dW = 12056 . dD dt 2 dt  . . . (8)  Q  where dD dt  = 4mm . 24 frame = 96 mm/sec frame sec .  26  I f the d a n i o 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 , tanO(/2  then  = W/2D'  where  &  ...(9)  = the v i s u a l a n g l e subtended a t the  eye.  Therefore l_sec (ot/2)da 2 dt 2  1 + tan *  d* dt  2  = 1 dW 2D' d t  = 1_ D'  dWJ_ dt  S u b s t i t u t i n g (9) i n t o (10)  doL d t  ...(10)  and r e a r r a n g i n g ,  = (dW'/dt)(4D')  film  C  4D'  + W'  2  gives  ...(11)  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 t o the s c r e e n 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 o f da/dt.  measurement  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  due t o the f i s h ' s own v e l o c i t y  relative  image  (V) i s g i v e n 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.  da d t  '  = 4VW'/(4D' + W' ) 2  ...(12)  2  fish  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 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  da d t  total  = (dW7dt)(4D') + (  4D'  2  + W' ^ 2  4VW (  4D'  2  + W' ^ 2  rate  27  = ( d W 7 d t ) ( 4 D ) + 4VW  ...(13)  >  C4D'  2  + W' ) 2  For each frame o f the d a t a f i l m D was measured and W and 1  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 was p o s i t i v e 1  toward the s c r e e n , and n e g a t i v e the c a l c u l a t i o n o f dw/dtf-j-| both a g a i n s t t i m e . of  m  i f away.  These d a t a a l l o w e d  and dcv/dt^otal  a n d  p l o t t i n g of  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  f o u r sequences ( F i g .  10).  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 c o r r e s p o n d e d to the observed o f r e a c t i o n o f the f i s h . 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 . '  occurred at s i m i l a r l e v e l s  r e a c t i o n s o f the danios  o f dct/dt (Table V ) .  Rates o f change o f v i s u a l a n g l e  (d«/dt)^-j  the times o f response o f danios to the predator SEQUENCE \ 0  m  point  A t each o f these p o i n t s , da/dt was  In a l l but one c a s e , the subsequent  Table V  if  m  at  cinematographic  dot/dt,., AT TIME OF REACTION film 1 s t 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 f o r four danios responding more than once to the cinematographic predator. The values are c a l c u l a t e d both without reference to the f i s h ' s v e l o c i t y Cleft-hand graphs, " F i l m O n l 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 Cright hand graphs, " T o t a l " ) . The arrows i n d i c a t e the times at which the danios were seen to respond on the data film.  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 value p r e v i o u s l y .  In a d d i t i o n the subsequent  reactions  o f t h e d a n i o s i n a l l cases o c c u r r e d a t q u i t e d i f f e r e n t levels  dcx/dt  (Table V I ) .  T a b l e VI  Rates o f change o f v i s u a l a n g l e  (  d c  */ t)  a t the times o f response o f d a n i o s t o cinematographic predator  d<x/dt. . n  SEQUENCE NO.  1st  REACTION  c l  t o t a l  the  , AT TIME OF REACTION 2nd REACTION  1  1.106  0.126  2  1.245  0.175  3  0.084  -0.050  4  -0.026  0.085  3 r d REACTION  0.044  The e v i d e n c e s u p p o r t s the h y p o t h e s i s o f a t h r e s h o l d r a t e change o f v i s u a l angle without reference  of  (dot/dt), but o n l y when t h i s i s measured  t o the v e l o c i t y o f the p r e y .  If this is  then the prey must have some means o f s e p a r a t i n g t h e  true,  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 m o t i o n toward away from) the p r e d a t o r .  (or  The d a n i o 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 but how the d a n i o c o r r e c t s i s not known.  organs,  i t s measure o f d a / d t by t h i s amount  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  results  In o r d e r t o check the r e s u l t s o f the e x p e r i m e n t s w i t h model p r e d a t o r s , a number o f d a n i o s were a l l o w e d t o 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 a r e n a .  N a i v e danios were  ed one at a time t o a bass which was a c c l i m a t e d t o the  presenttank.  The d a n i o s 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 t o 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  release.  The d a n i o s p r e s e n t e d t o each bass were from a  s i n g l e s p a w n i n g , but d i f f e r e n t s t o c k s were p r e s e n t e d t o 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  f e d 24 hours b e f o r e the e x p e r i m e n t .  The s m a l l bass was f e d a  maximum o f f o u r prey per day; t h e l a r g e o n e , The v a r i a b l e s  last  six.  r e c o r d e d from the d a t a f i l m w e r e :  reactive  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 c o m p l e t i o n o f the  experiments  the bass were t r a n s f e r r e d t o 10 g a l . g l a s s a q u a r i a and p h o t o graphed head-on t o 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 d a t a 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 t h e 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 t o be more s e n s i t i v e to  hori-  z o n t a l than t o 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 d a t a are shown i n T a b l e VII VIII.  S i n c e the v a r i a n c e s  and summarized i n T a b l e  and sample s i z e s were d i f f e r e n t ,  t'  f  31  CSteel and T o r r t e , 1960) were used to compare the. s e t s of data to those obtained tn response to the model predators. Since the c a l c u l a t e d t ' s were i n both cases less than the calculated t  both samples of ln dcrf/dt, and hence dcH/dt.  1  Table VII  BASS SIZE  WIDTH (cm)  DANIO NUMBER  SMALL  1.87  1 2 3 4 5 6 X  LARGE  2.65  1 2 3 4 5 6 7 8 9 X  Data from filmed observations of largemouth bass - naive zebra danio i n t e r a c t i o n s .  REACTIVE DISTANCE (cm)  Table VIII  REACTING TO  ESCAPE VELOCITY (cm/sec)  BASS VELOCITY (cm/sec)  k  Ink  21.04 9.35 10.52 5.85 26.30 2.92 12.66  31.21 46.76 -56.11 74.82 42.08 28.06 46.51  11.69 14.02 79.49 46.76 19.87 37.41 34.87  0.049 0.297 1.333 2.491 0.054 7.440 1.944  -3.016 -1.214 0.287 0.913 -2.925 2.007 -0.658  9.35 27.47 10.52 15.20 20.46 6.43 24.55 9.35 18.70 15.78  74.82 53.77 74.82 46.76 51.44 65.46 65.46 25.72 35.07 54.81  65.46 42.08 45.59 30.39 22.21 56.11 37.41 32.73 40.92 41.43  1.945 0.147 1.076 0.346 0.140 3.450 0.164 0.973 0.309 0.950  0.665 -1.914 0.072 -1.062 -1.966 1.238 -1.808 -0.028 -1.176 -0.664  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  -.830  .8464  SMALL BASS  -.658  4.2944  .202  2.502  .52  LARGE BASS  -.664  1.3587  .411  2.284  ,51  .43  32  may be c o n s i d e r e d t o have been drawn from the same p o p u l a t i o n as those sampled i n the experiments with the model p r e d a t o r . 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 p r e d a t o r experiments (.43) as an estimate o f k, and bass width as an estimate o f 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 T a b l e 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 o f the l a r g e v a r i a n c e o f k.  Only  p r e d i c t i o n s a t 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 a t t h i s time.  Table IX  BASS SIZE SMALL MEDIUM  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 t z e s .  PREDICTED REACTION DISTANCE (cm) 12.28 15.92  .  OBSERVED REACTION . DISTANCE(cm) ± 1 S.E. 12.66 15.78  The mean v e l o c i t i e s o f escape from both  ± 3.71 ± 2.48 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 p r e d a t o r s . However, the v e l o c i t i e s o f 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  (ii)  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 a p p a r e n t l y 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 o f 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 t h r e s h o l d s and t h e i r v a r i a n c e s compared. The prey (35-40 mm long) were placed i n the p r e d a t i o n 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 test.  A medium s i z e d bass was then r e l e a s e d from one o f the  h o l d i n g tanks and the response of the danios to i t s a t t a c k f i l m e d . When f i v e danios were t e s t e d t o g e t h e r , 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 . o f the f i v e prey d i d so.  In one case, o n l y f o u r  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 f o u r 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, w h i l e o n l y 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 by means o f a t - t e s t .  In k's (0.416; k =  1.52)  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 o f v a r i a n c e on  34  the grouped f t s h data.  The withtn-groups mean square  (.78279, 15 d f ) was taken as the best estimate o f cJ . T h i s was compared with the v a r i a n c e o f i n d i v i d u a l f i s h 0-62472, 10 d f ) 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 a t p = .05, although i t was s i g n i f i c a n t a t 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 o f 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 o r variances o f f i s h t e s t e d i n d i v i d u a l l y o r i n groups.  However, there were s t r o n g sugges-  t i o n s t h a t d i f f e r e n c e s d i d indeed e x i s t .  T h i s was supported  by the 100% response r a t e 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 o b s e r v a t i o n t h a t schools of danios seemed to r e a c t a t almost the same time.  Since the  f i s h were a t 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 of 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 t h a t only one f i s h i n  the school responds to the p r e d a t o r , and the others f o l l o w s u i t , responding t o the f l i g h t o f the schoolmate r a t h e r than to the p r e d a t o r per se.  4  Discussion When an animal becomes aware o f a p o t e n t i a l p r e d a t o r , i t may  demonstrate one o f a number o f types o f behaviour.  T h i s may take the  form o f f l i g h t (avoidance), f r e e z i n g i n p l a c e o r even a t t a c k i n g the  35  p r e d a t o r (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 p r e d a t o r can approach a prey without causing flight.  F l i g h t d i s t a n c e s have been recorded i n a number o f types o f  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 o f a prey's response to predators.  Exceptions occur i n some gastropod molluscs (e.g. B u l l o c k ,  1963) which a p p a r e n t l y do not respond u n t i l touched by the p r e d a t o r ( s t a r f i s h , other m o l l u s c s ) . In these cases, however, c o n t a c t i t s e l f . i s not f a t a l ; i t i s prolonged c o n t a c t which must be avoided.  Even  some gastropods respond to the p r e d a t o r from a d i s t a n c e by means o f chemoreception (Kohn and Waters, 1966) and perhaps v i s i o n (unpublished o b s e r v a t i o n s on response o f Strombus luhuanus to Conus pennaceous i n Hawaii by the a u t h o r ) . In o r d e r to respond to an approaching p r e d a t o r , the prey must use sense organs capable o f 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 o f s i g h t , chemoreception and h e a r i n g , 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 p r e d a t o r 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 r e c o r d e d , the s i n g l e most important m o d a l i t y , 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 o f p r e d a t o r 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  t h a t s i m i l a r l i n e s o f 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 o f 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 depended on the s i z e and v e l o c i t y o f 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 i n s t a n c e  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 c o n s i d e r a b l e c o n f l i c t o f 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 o f predator. Thorpe (1963), however, considered t h i s type o f response to be r a t h e r r a r e 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 o f f e a r as being "due to the d i s r u p t i o n o f 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 t h a t 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 o f 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 o f s t u d i e s  on a wide v a r i e t y o f species have shown t h a t 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 a t a l l , resemble  37  an a c t u a l predator (examples, t n fish., a r e 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 n a t u r a l 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 ( O r r , 1945). The hypothesis o f a t h 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 o f 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). d e f i n i n g "high".  T h e problem o f determining a t h r e s h o l d i s one o f 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 o f 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 d e s c r i b e d 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 t o 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 t o 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 r a t e o f change o f the angle subtended by the predator a t the eye o f the prey. The hypothesis t h a t 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 ( t h r e s h o l d ) could not be disproved danios.  e x p e r i m e n t a l l y f o r zebra  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 g e n e r a l , i n t h a t  responses to two types o f models and to real predators were not significantly different. 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 o f change o f 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 o f neuronal elements s e n s i t i v e to d i r e c t i o n o f movement o f 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 GrusserCornehls, 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 o f 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 o f r e a l i t y i s t h a t there i s assumed to be no l a g between p e r c e p t i o n 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 o f change o f a at the time o f r e a c t i o n (the measured value) w i l l be somewhat g r e a t e r 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 p r e d a t o r . 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 p r e d a t o r . This may help to e x p l a i n why many t e r r e s t r i a l predators 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 w i l d e b e e s t s (van LawickGoodall & 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 r a t e o f i n c r e a s e o f dot/dt. The predators may have e i t h e r l e a r n e d or evolved such t a c t i c s to c o u n t e r a c t those o f the prey. The model a l s o p r e d i c t s t h a t to very slow predators (those w i t h 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 mechanism 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 a t 0.27 cm/sec ( 1 / l 5 0 t h of i t s t r u e 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 i n c r e a s e s 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 i n c r e a s e 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 g r e a t e r 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 c o n s i d e r e d 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 t h a t 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) s i z e (d«/dt).  and r a t e o f change o f image  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 o f predator s i z e . S c h i f f (1965) reported t h a t f i d d l e r crabs and c h i c k s showed avoidant behaviour to an o p t i c a l r e p r e s e n t a t i o n o f 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 o f 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 p r e d a t o r s . Walther (1969)  found t h a t the  f l i g h t d i s t a n c e o f 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 o f A f r i c a n dogs i n 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 t h a t 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 o f other s p e c i e s 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 o f 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 r e c o r d 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  p r o v i d e 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 d i s t a n c e s have seldom been r e p o 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 e e t l e s (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 t h a t 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 Elder, ibid).  (Duke-  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 t h a t 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  t h a t 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. T h i s may be due to the f a c t t h a t v i s u a l performance i n f i s h i n c r e a s e s with body s i z e , as Baerends e t al (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 t h r e e - s p i n e s t i c k l e b a c k s (Gasterosteus) r e a c t e d to pike from g r e a t e r d i s t a n c e s 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 n i n e - s p i n e s t i c k l e b a c k . Sub-adult Thompson's g a z e l l e s have l o n g e r f l i g h t d i s t a n c e s 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 p r e d a t o r , the l a c k o f 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 i n c r e a s e d as the d i s t a n c e to the p r e d a t o r 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 p r e d a t o r was three times t h a t from an a r t i f i c i a l one.  In l i g h t o f the f a c t  t h a t the comparable dcx/dt t h r e s h o l d s were not d i f f e r e n t , t h i s t h r e e 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 p r e d a t o r 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 p r e d a t o r s , o f course, pursue t h e i r prey and i t may be t h a t 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.  (ii)  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  where  k  4  V = predator approach v e l o c i t y (on/sec) S = predator f r o n t 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 o f 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 s m a l l e r 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 t h a t 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. (vi)  The response o f 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,  o f danios t e s t e d i n d i v i d u a l l y .  44 IV  CHANGE OF dQ/dt THRESHOLD WITH EXPERIENCE 1  Introduction 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 r a t e 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 distance. 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 p r e d a t i o n 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 o f "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) r a t e o f change o f 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 i n c r e a s e d d i s t a n c e s to an  45 approaching p r e d a t o r and c o u l d be c o n c e p t u a l i z e d 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 c o u l d be the b a s i s 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 r e s e a r c h 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 o f previous e x p e r i e n c e s .  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 r a t e o f change o f v i s u a l angle. a)  Model predator Six naive danios which r e a c t e d to the stimulus on f i r s t pres 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 o f the study. T h e i r l e n g t h s , determined a t 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 p l a c e d 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 a q u a r i a so t h a t the f i s h had no c o n t a c t with c o n s p e c i f i c s d u r i n g 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 g e n t l y pouring them from the j a r , and v i c e versa a f t e r each t e s t . n e t t i n g o f the prey.  This obviated  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 d e s c r i b e d i n S e c t i o n I I , except t h a t 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-  c h r o n i z e d 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 o f days 1 through 14, the  danios were presented with  a 2.54 cm b l a c k 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 d a n i o , v e l o c i t y o f the model at the time o f 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 p r e d a t o r 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 p l a c e d 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 o f the f o l l o w i n g 10 days  the prey were presented with the standard cinematographic predat o r and t h e i r response f i l m e d . They were f e d 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 o f any l e a r n e d 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 p r e d a t o r 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 p r e d a t o r or to i n c r e a s e d 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 a t the time o f r e a c t i o n was calculated.  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 p r e d a t o r Ci)  change i n response with experience The data suggest a d e c l i n e o f 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.  dE  This hypothesis may be expressed as:  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 a t f i r s t  exposure)  a = a r a t e constant ^min  =  rnl  " ' n1  p o s s i b l e value o f da/dt  mum  This i n t e g r a t e s t o : k  -  =  e  "  k m  a E  in  +  +  C  E  *  mn  - ( « )  k  ° ^  -..(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, e x c e p t i n g day 9 when only two o f the s i x danios responded.  The p r e d i c t i v e e q u a t i o n , d o t t e d 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 u n u s u a l l y l a r g e v a r i a n c e (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, e x c l u d i n g the day 10 f i g u r e s , gave the equation: , k  = .2349 + 1.9845e ~ ° ( ) , 5  ...(17)  E  This e q u a t i o n , s i g n i f i c a n t a t p = .001 ( F Q  5 Q  J = 38.42) i s  taken t o 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 o f the model predator on t h r e s h o l d dft/dt (k) o f 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 accordance 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 excluding day 10.  Figure 12  E f f e c t o f 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 ) o f danios responding to the model predator. Lines f i t t e d by regression.  49 1.5  EXPERIENCE  NUMBER  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 S e c t i o n 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 a t p =.05. There was no evidence t h a t 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 p r e d a t o r , 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 a t 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 " (10.2/17.1) =127°. 1  (ii)  g e n e r a l i z a t i o n over model s i z e The responses o f 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 t h a t 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 t h a t 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 d a n i o s . Comparison o f the responses a f t e r 14 days experience with the small model leads to the same c o n 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 c o n s i d e r e d to be complete.  51  Table X Comparison o f responses o f t r a i n e d danios t o model predators o f two s i z e s MODEL DIAMETER  PRESENTATION DAY  LN .(da/dt)  2.54  14  -1.649  5.08  15  -0.963  (cm)  Cinematographic (i)  MEAN  SIGNIFICANT AT  >  0.05  predator  learning 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 a t p = .025 ( F ^ ^ 6.845).  =  B l o c k i n g 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 t o p = .005 ( F ^ ^Q)  =  10.654)  and  demonstrated t h a t 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 o f t h e v a r i a n c e was n o n - s i g n i f i c a n t . Each o f the s i x r e g r e s s i o n s (one p e r 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 r e g r e s s i o n s were:  Figure 13  E f f e c t o f experience o f the cinematographic p r e d a t o r on t h r e s h o l d dw/dt (JO o f zebra danios (mean ± one standard e r r o r ) . L i n e 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  180°AWAY EV  = 12.50 - .89 (EXPER NO) ; F Q  NO);F^  4 Q )  = 10.871 p<.005  4 Q )  = 9.491  p<.005  Since the slopes o f the two r e g r e s s i o n s 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 a t a constant angle o f 90° + s i n ( 1 2 . 5 0 / -1  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 p e r i o d w i t h out experience on da/dt a t the time o f r e a c t i o n C t ^ ^ j = .959), although the mean value o f doc/dt i n c r e a s e d from .062 to .126 rad/sec.  N e v e r t h e l e s s , i t must be concluded t h a t 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 o c c u r r e d during t h i s p e r i o d . (ii)  control None o f 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 o f c l e a r l e a d e r (corresponding to the f i v e second approach sequence o f a normal presentation).  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 stimulus. Table XI compares da/dt a t the time o f response, and the measures o f escape v e l o c i t y d e s c r i b e d 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 l e a d e r 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 o f 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 MEASURE dot/dt  DAY 1 j  n  4  s  2  .099  .00143  4 14.01  n 5  DAY 10 X .175  S  2  .00167  -  ]  t a i l  2.862  < .05  22.6341  5 14.98 11.4743 0.359  >.25  55.8079  5  >.25  T o t a l escape V e l o c i t y (cm/sec)  180°-away escape V e l o c i t y (cm/sec) 4  8.54  8.15 28.9499  0.091  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 a t the time o f  reaction 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 Discussion P r i o r t o 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 r e s e a r c h , a few words o f e x p l a n a t i o n w i l l be given f o r u s i n g two types o f experimental apparatus.  Some o f 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 c o n s i d e r e d , w i l l a l s o be mentioned. 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 o f the d i s t u r b a n c e on the r a t e 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 i m p o s s i b l e 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 o f 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 l e a r n e d response to the v i s u a l q u a l i t i e s o f the model.  The cinematographic p r e d a t o r 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 p r e s e n t a t i o n s o f 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 . In both types o f apparatus, however, i t was necessary to c o n f i n e the f i s h to a small area i n order t h a t 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 w a l l s 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 d a t a , 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 h a b i t u a t e d to i n i t i a l l y frightening stimuli.  Other authors have a l s o r e p o r t e d  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 t h a t 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 h a b i t u a t e d 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 a l (1955) found t h a t f e a r responses o f chickens t o predator models can be e x t i n g u i s h e d with repeated s t i m u l a t i o n . In a l l cases where rates o f p r e s e n t a t i o n have been r e p o r t e d , however, these were g r e a t l y i n excess o f the r a t e s 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 t h a t during h a b i t u a t i o n o f o v 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 & M e l v i n , 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 presentation.  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.  T h i s 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 o f 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 c o n s i d e r e d to be a l e a r n e d change i n the behaviour o f the d a n i o s , a c c o r d i n g t o 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 e x p e r i e n c e " .  An i n c r e a s e d d i s t a n c e o f reac-  t i o n t o an approaching predator i s assumed to be a d a p t i v e , an assump-  57  t i o n which i s supported by the data o f 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 g r 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 in 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 p e r c e p t i o n o f 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 o f .21 seconds would be r e q u i r e d to account f o r the observed change o f dot/dt a t the time o f 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 p e r c e p t i o n and response would have t o exceed t h i s amount.  Although  lags o f even g r e a t e r magnitude have been r e p o r t e d 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 t h a t j a c k 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 v a r y i n g from 1 to 2.5 s e c ) i t i s u n l i k e l y t h a t such a l a r g e l a g operated i n the 2 2 p r e s e n t 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  ( S e c t i o n I I I ) would have a pronounced p o s i t i v e c u r v a t u r e which i s not e v i d e n t from the data. The second p o s s i b i l i t y i s t h a t k ( t h r e s h o l d da/dt) a c t u a l l y decl i n e s with e x p e r i e n c e . 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 s t r o n g 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 a l s o be e x p l a i n e d by the f o l l o w i n g one. T h i s 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 c o n s i d e r e d t o be the most l i k e l y one, i s t h a t 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 o f the approaching p r e d a t o r 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 w e l l known  i n psychology, however, and i s termed "secondary reinforcement". Deese (1958) d e f i n e d 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 o r 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 ; c o n s i s t e n t arousal o f [withdrawal-processes] may s e t up  "a 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 p r e d a t o r i n c r e a s e s 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 o f prey by predators has a l s o been observed to i n c r e a s e w i t h experience. Rate o f 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 a t the time o f response t o the cinematographic predator appeared t o 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 n o t t o t a l l y n a i v e , 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 theref 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 t o s e t an upper l i m i t t o r e a c t i v e d i s tance i s n o t known.  I t i s possible that objects a t greater distances  were n o t p e r c e i v e d owing t o the f a c t t h a t 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 , t o c a l c u l a t e the  maximum s i g h t i n g range without some i n f o 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 t h e background and the s p e c t r a l volume a t t e n u a t i o n c o e f f i c i e n t o f the water. [ I t should be noted t h a t 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 learning curves).  A second p o s s i b i l i t y i s t h a t the maximum d i 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.  Visual acuity is 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 1948).  [Senders,  In o t h e r words, oc a t the maximum d i 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 t o 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). are not independent,  These two e x p l a n a t i o n s  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  i n c r e a s e s 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 o b j e c t s a t g r e a t e r d i s t a n c e s , and hence lower rates o f i n c r e a s e o f da/dt, were p e r c e i v e d but not r e a c t e d t o . S t i m u l i with da/dt below some o t h e r 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 l e a r n e d change i n response could be demons t r a t e d a f t e r 10 days without experience o f the cinematographic predator.  T h i s 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 a t l e a s t t h i s f r e q u e n t l y i n nature. f i s h g e n e r a l l y appear q u i t e long.  Retention times i n  M a n t e i f e l 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 a c q u i r e d , 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 l e a r n e d 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 t h a t a c o 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 t o 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 o b j e c t s (whether predators o r 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 t h r e s h o l d s (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 t h r e s h o l d s 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 t h a t i t i s p o s s i b l e  to reduce an animal's f l i g h t d i s t a n c e to some s t i m u l i through t r a i n i n g . Ware (1971), however, showed t h a t 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 colors. do so.  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 Hinde (1966) reported t h a t "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 i n c r e a s e d 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". "pseudo-conditioning".  This t r a n s f e r i s called  On the other hand, Kramer and von S t . Paul  (1951) found t h a t 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 o n l y to other members o f 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 general 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 r e p o r t e d 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 o f the pike with f r i g h t substance r e l e a s e d from the s k i n o f a schoolmate t h a t had been a t t a c k e d .  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 shock.  1  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 cons p e c i f i c s (Thines and Vandenbussche, 1966).  Lescheva (1968) has  even reported t h a t 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 p r e d a t i o n than the o r i g i n a l performers.  The p o s s i b i l i t y t h a t 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.  Similarly,  G i r s a ( i 9 6 2 ) and Veselov (1962), found t h a t 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  less susceptible.  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 a t 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 s p e c u l a t e 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 ) ,  t h 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 response.  fright  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 predator.  and not d i r e c t l y to the  approaching  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, V e r h e i j e n (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 s a r d i n e s (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 d i s c u s s e d 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 p r e d a t o r s , 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 o f 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 a t t a c k occurred with the f a c t o f 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  p r e d a t o r , would be i d e n t i c a l .  64  5  Conclusions (i)  The r a t e o f change o f v i s u a l angle  a t 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 o f previous experiences o f t h a t predator, (ii)  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 o f the p r e d a t o r 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 (iii)  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 t o an asymptote, (iv)  The change o f da/dt a t the time o f response i s not due t o growth, maturation, o r 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 d u r i n g 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 o f the l e a r n e d response i s e v i d e n t a f t e r 10 days without experience o f the predator,  (vi) (vii)  The angle o f escape i s not a f f e c t e d by experience, Escape v e l o c i t y d e c l i n e s with experience o f the cinematographic p r e d a t o r , but not with experience o f the model p r e d a t o r .  65 V  THE EFFECT OF HUNGER ON THE THRESHOLD RATE OF CHANGE OF VISUAL ANGLE 1  Introduction H o l l i n g ( i n prep) has shown that the d i s t a n c e from which the  mantid (Hierodula crassa) w i l l begin t o s t a l k prey i s dependent upon the accuracy o f the mantid's estimate o f d i s t a n c e (<$)•  The process  o f d i s t a n c e e s t i m a t i o n i n the mantid i s a b i n o c u l a r one, and the r a t e 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 d i s t a n c e from the eye o f the mantid t o the prey (RP) determines the accuracy o f the process.  H o l l i n g showed t h a t  d/3 = 2 (ES + L) dRP 2 4 R p  where  +  +  L )  ...(18)  2  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 a t 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 t h r e s h o l d  £ .. ^mi n  This e q u a t i o n , c o n c e p t u a l i z e d  i n a totally different fashion, i s  analogous to equation (2) d e r i v e d i n S e c t i o n I I I above. dRP = -V dt therefore  Since  ...(19)  d/3 = -2V(ES + L) 4RP +(ES+L)  d t  2  ...(20) 2  When D and S a r e 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) 4D +(ES+S) d t  2  2  ... (21)  66  I f ES i s ignored as being small r e l a t i v e t o 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 4D + S d t  2  ...(22) 2  Equation (22) i s n e a r l y i d e n t i c a l t o equation ( 2 ) .  I t therefore  appears t h a t 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 b f 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 o b j e c t s 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 t h a t § was a f f e c t e d by hunger i n such a way t h a t the h u n g r i e r 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 p r e d a t o r would be "more w i l l i n g " t o accept the r i s k t h a t 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 o f the  danios i s so s i m i l a r , i t seemed l o g i c a l t o 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 t h a t the h u n g r i e r 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 t o a p r e d a t o r o f constant s i z e and approach v e l o c i t y .  T h i s i s based  upon the reasoning t h a t 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 a t 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 o r d e r 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 t o d e f i n e hunger  67  i n terms o f a v a r i a b l e which c o u l d be e a s i l y c o n t r o l l e d e x p e r i m e n t a l l y 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 p l a c e d 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 a c c l i m a t e d t o the j a r s f o r a p e r i o d o f three days, d u r i n g which time they were f e d t w i c e . 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 d u r i n g a 25 minute period.  Excess food was then siphoned from the j a r s .  Three danios  each were then r e f e d a t 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 o f food (Tetramtn  f l a k e s ) accepted by  each danio was recorded. T h i s procedure was repeated with a new group o f 24 d a n i o s , to g i v e a t o t a l o f 6 r e p l i c a t e s a t each o f the 8 dep r i v a t i o n times. The danios averaged 29.6 mm fork l e n g t h (range 27.0-32.0). The water temperature throughout the experiment was 2324°C. The f l a k e s o f food were presented one a t 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 o f the d i s h , was c o r r e c t e d as f o l l o w s to g i v e the actual weight o f 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 p o s t - f e e d i n g weights o f t h i s d i s h were never the same, a p p a r e n t l y because o f d i f ferences i n humidity between the rooms used f o r weighing and f e 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 f e e d i n g and a p p l i e d t o the pre-weights of the food i n the experimental d i s h e s . The weight o f food eaten by the danio c o u l d then be a c c u r a t e l y determined.  68  Two o t h e r procedural p o i n t s 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 a t  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 s t o c k o f f i s h (hatchery-reared).  Secondly, the danios were not i n v i s u a l c o n t a c t  with each o t h e r d u r i n g the f e e d i n g s . Thus the amount o f food was a measure o f hunger, and was not confounded with any s o c i a l facilitation effect. Having d e f i n e d hunger as a f u n c t i o n o f time o f food d e p r i v a t i o n , the next s t e p 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 r a t e o f change o f v i s u a l angle a t 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 h o l d i n g aquarium were f e d to s a t i a t i o n and the excess food removed. S i x danios each were removed from the tank a t 1, 3, 5, 8 and 11 hours a f t e r f e e d i n g 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.  T h i s 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 o f 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 l e n g t h (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 o f response was recorded f o r each f i s h t h a t responded to the cinematographic p r e d a t o r .  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 o f 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 w i t h 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 a t each o f 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 TIME 1 2 4 8 12 24 36 48  n  4 .6 4 5 5 5 5 5  ,  WEIGHT EATEN (grams) X S£ .0031 .0049 .0062 .0077 .0086 .0065 .0061 .0081  .0010 .0008 .0009 .0014 .0012 .0012 .0015 .0012  During the f i r s t 12 hours the hunger rose smoothly an apparent asymptote.  towards  A f t e r t h i s time, however, hunger appear-  ed t o 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 , t h e r e -  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 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 (mean ± one standard error).  70  DEPRIVATION TIME  (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 o f a number o f 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.  to t h i s model:  dH dTF Where  According  (23)  = AD (HK - H)  H = hunger (weight o f food eaten) TF = d e p r i v a t i o n time AD = constant, instantaneous r a t e o f digestion HK = maximum gut c a p a c i t y (maximum weight o f food i n t a k e p o s s i b l e )  Thus:  H = HK (1  e-ADCTF),  .(24)  and, t r a n s f o r m i n g , In  HK HK-H  AD(TF)  ..(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 o f the s l o p e 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 a t p<.005.  The best estim-  ates o f HKand AD were .0089 grams and .2773 h r  - i  respectively.  Figure 16  Hunger data transformed to t e s t equation i n the t e x t .  C25)  72  DEPRIVATION  TIME  (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 - - - 2 7 7 3 ( T F ) e  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 o f 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 r a t e o f change o f 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 - " ' ) 2773  T F  e  TF (hrs)  n  HUNGER (gms)  2 4 6 9 12  4 8 6 7 7  .0038 .0060 .0072 .0082 .0086  THRESHOLD da/dt (rad/sec) X Sj .129 .181 .146 .193 .172  .030 .022 .015 .035 .025  A r e g r e s s i o n a n a l y s t s o f t h r e s h o l d da/dt (k) a g a i n s t hunger d i d not i n d i c a t e the e x i s t e n c e o f a s l o p e s i g n i f i c a n t l y d i f f e r e n t from zero a t p = .05. Further, i n d i v i d u a l t - t e s t s between the mean k a t 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 o f 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 4 HUNGER  1  I  6 (mg)  I  I  8  L  75 I t must t h e r e f o r e be concluded t h a t 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 o f 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 o f 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 o f the danios o r 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 s c r e e n .  The danios tended to escape at a v e l o c i t y  o f 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 " (10.8/19.1) = 124°. 1  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 u n a f f e c t e d by hunger. 4 Discussion For the purposes o f 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 d e f i n e d as the amount o f food accepted by the f i s h during an ad l i b i d u m f e e d i n g s e s s i o n . The amount o f food consumed by the danios a f t e r v a r i o u s d e p r i v a t i o n times was d e s c r i b e d very w e l l by a model which assumes t h a t the maximum amount eaten represents the maximum stomach c a p a c i t y (HK) and t h a t the instantaneous r a t e at which food consumpt i o n i n c r e a s e s with d e p r i v a t i o n time i s the same r a t e 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 H i e r o d u l a c r a s s a and Mantis r e l i g i o s a , and the b l o w f l y Phormia r e g i n a ( H o l l i n g , 1966).  However,  i n none o f 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 e x p l a n a t o r y , 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 o f parameter v a l u e s .  76  There i s some evidence t h a t 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 . an over- or underestimate.  Overesttmation  I t may be e i t h e r  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 t h a t 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 a t 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). 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. Beukema (1968) concluded  Despite  Similarly,  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 d i s t a n c e s 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 o f prey a t 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 p l a t e a u .  Beukema  (1968) reported t h a t 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 p r e d a t i o n 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 o f 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. Ci bid)  Hence, hunger, as d e f i n e d by H o l l i n g  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 o f a prey being d i s c o v e r e d 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 a t low hunger levels.  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 e x t e n s i v e enough to allow r e j e c t i o n o f the hypothesis.  In the  absence o f 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 I n c r e a s i n g 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 d i s t a n c e s 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 h e r b i v o r e s 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. are both s i m u l t a n e o u s l y :  Most animals  f e e d i n g on some organisms and being f e d  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 a t 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 s u g g e s t i v e o f the .existence o f 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 flight.  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 n o t i o n o f 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 w h i l e 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 c o n v i n c i n g . A few r e f e r e n c e s 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 o t h e r c o n t e x t s ) . Breder and Halpern (1946) found t h a t an a r t i f i c i a l f i s h ( p a i n t e d 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. t n , t n area, but caused i n c r e a s i n g f r e q u e n c i e s o f advance with d e c r e a s i n g s t z e down to 4 s q . t n . T h i s 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 o b j e c t s 4-7 mm. long  provoked p u r s u i t t n perch, w h i l e longer o b j e c t s provoked  flight.  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) r e p o r t e d 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 h i g h e r 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 r a t e o f change o f 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 c o u l d be d e t e c t e d .  There was some s u g g e s t i o n 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 d e c r e a s i n g 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 a t 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 t o accept h i g h e r r i s k s o f p r e d a t i o n i n the hope t h a t 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 t o o b j e c t s t n i t s v i s u a l f i e l d .  80  5  Conclusions (t)  Hunger, o p e r a t i o n a l l y d e f i n e d as the amount o f food eaten by an i n d i v i d u a l i n an ad l i b i d u m f e e d i n g 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.  (ii)  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 p r e d a t o r .  81  VI  ADDITION OF THE AVOIDANCE LEARNING COMPONENT TO A GENERALIZED MODEL OF THE PREDATION PROCESS 1 Introduction The experiments d e s c r i b e d above have 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 to an approaching predator may be p r e d i c t e d from the equation RD = / VS - S^ J k 4  ....(3)  Where V = approach v e l o c i t y o f 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 (rad/sec).  I t has a l s o been shown t h a t k decreases as a f u n c t i o n  o f e x p e r i e n c e , according to an equation o f the form  ^  ...07)  n  Where E = number o f past experiences with the p r e d a t o r ; and k ^ , EC and EONK are p o s i t i v e c o n s t a n t s .  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 p l a t e a u 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 s e v e r a l l i n e s o f argument support the c o n t e n t i o n t h a t they have g e n e r a l i t y , a t 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 t h a t 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 s e a r c h i n g predator can be p r e d i c t e d from equation ( 3 ) , and t h a t equation (17) d e s c r i b e s 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 e x p r e s s i o n o f the avoidance component o f the p r e d a t i o n process and make p o s s i b l e i t s a d d i t i o n t o H o l l i n g ' s (1965, 1966) g e n e r a l i z e d p r e d a t i o n model.  This  w i l l be done by e x p e r i m e n t a l l y 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 o f the model (Table X I V ) . Table XIV The components o f p r e d a t i o n and t h e i r subcomponents as c o n c e p t u a l i z e d 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  2 Time prey are exposed to predators 3 Handling time per prey  4 Hunger  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 Time spent i n non-attack (a) activities (b) Time a v a i l a b l e f o r attack Time spent pursuing and (a) 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 Digestive rate Ca) (b) Maximum stomach c a p a c i t y (a)  5 Exploitation 6 7 8 9  I n t e r f e r e n c e between predators Learning by predator I n h i b i t i o n by prey Social 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 v e 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 c o n c e p t u a l i z e d mathematically and added t o 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 o f avoidance l e a r n i n g has been c o n c e p t u a l i z e d suggests t h a t 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 subd 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  f u 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 t o 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 t o a f f e c t p u r s u i t time i s shown d i a g r a m m a t i c a l l y i n F i g . 18. The p r e d a t o r s i g h t s the prey a t a d i s t a n c e ROp^ and begins to approach i t a t a given v e l o c i t y (AV).  Once the p r e d a t o r has  approached t o RPp^rryj the prey begins t o f l e e . c l o s e the d i s t a n c e R p r D  Rf  D  -  R  D  P R E Y  ^  S  T  H  E  A  P P  R  The time taken t o O  A  C  N  T  I  M  E  (  T  A  )  A  N  D  i s expressed a s : TA =  RD  PRED " PREY. '. .' AV RD  ,, * ...Uo; c  Once the prey has begun t o f l e e (with escape v e l o c i t y EV), the p r e d a t o r 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 o r d e r t o s t r i k e a t 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 a t 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 funct 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 o t h e r escape t r a jectory.  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 t o be  Figure 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 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 e x p l a n a t i o n .  84  w  I1%  wttitflnm,t i i — •  *-RD RD,PRED  PREY  DS^.>capture ?  «  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 ...(29)  TP = TA + TC  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 w i t h 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 x p e r i m e n t a l l y were added to the  model o f the p r e d a t i o n 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 p r e d a t i o n arena. The bass was allowed to consume a maximum o f f i v e prey per day and the experiment was run over a p e r i o d o f three months ( A p r i l 15 to J u l y 10, 1971).  The bass, however, d i d not  grow d u r i n g 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 o f a t r i a l , the bass was a l r e a d y i n the arena. When i t was i n a p o s i t i o n on the o p p o s i t e s i d e o f the arena  86  from the s l i d i n g doors, a s t n g l e prey was i n t r o d u c e d . 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 s u r f a c e 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.  F i l m i n g 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.  Fifteen  minutes separated c o n s e c u t i v e 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 r e c o r d i n g the f o l l o w i n g parameters o f t h e i n t e r a c t i o n :  p r e d a t o r 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 t o approach (TA), prey escape v e l o c i t y , p r e d a t o r 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 t o c l o s u r e (TC), and whether o r 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 u s e f u l data. Cb) Results and d i s c u s s i o n The observed p r e d a t o r and prey r e a c t i v e d i s t a n c e s and the approach v e l o c i t y o f the predator were used t o p r e d i c t an approach time f o r each encounter a c c o r d i n g t o 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). s i o n was h i g h l y s i g n i f i c a n t ( F ^ ^  The r e g r e s -  ~ 1074.13) and the i n t e r -  cept and the s l o p e d i d n o t 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  a c c u r a t e l y p r e d i c t e d from R D to equation (26).  pRf£D>  RD  , and  A v  p R E Y  according  Figure 19 R e l a t i o n s h i p between observed approach time (TA) and p r e d i c t e d approach t i m e ( ( R D p - pRr£Y)/ Rr£ ) ^ 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 . RD  RED  V  o r  L  87  •5  1.0  1.5  PREDICTED TA (sec)  2.0  2.5  88  S i m i l a r l y , the observed prey r e a c t i v e d i s t a n c e s and escape v e l o c i t i e s , and the p r e d a t o r s t r i k e d i s t a n c e s 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 a c c o r d i n g to equations (27) and (28). These were then compared with the observed c l o s u r e times by means o f 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 o f V ^  L  between 20 and 90 cm/sec.  The r e g r e s s i o n  was c o n d i t i o n e d 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 o f the s l o p e 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 t h a t the value  o f "a" i n equation (27) i s g r e a t e r than 1.0. i s 1.0/.79 o r about 1.27.  The best estimate  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 p r e d a t o r s ) and because the p r e d a t o r d i d not t r a c k 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 o r 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 t h a t  f i l m i n g at a h i g h e r speed ( i m p o s s i b l e 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 ^ ) ^ ^ ^ '° 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 . or  e  ass  d a n i  89  PREDICTED TC (sec)  90  p r a c t i c a l reasons) would show t h a t 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 t h a t 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-  e v e r , 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 = PREY " 1.27 (PV - EV) RD  ...(30)  DS  Schoener (1969) used a s i m i l a r equation to r e p r e s e n t 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 sizes f o r predators.  The e x p l a n a t i o n f o r t h i s conceptual  d i s c r e p a n c y l i e s i n Schoener s t a c i t assumption t h a t the 1  predator and prey begin to respond to"each other at the same instant.  Thus, TA would be zero i n the e x p r e s s i o n TP = TA + TC.  I f DS, PV and EV were c o n s t a n t s , 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 s l o p e o f .79/(PV - EV).  A p l o t o f the  observed TC and RDp £y values ( F i g . 21) f i t s such a r e l a t i o n R  s h i p very p o o r l y . A p p a r e n t l y , one or more o f the parameters assumed to be constants were not. examined i n two ways.  The data were t h e r e f o r e  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 distance.  91  PREY  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 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 AV  analysis.  AV 1.000  PREY EV PV DS RD  RD  PREY  PARAMETER EV  0.441* 1.000  0.164 -0.198 1.000  PV  DS 0.042 0.513*  0.749** 0.566** 0.096 1.000  0.037 -0.112 1.000  Table XV shows that both DS and PV were s i g n i f i c a n t l y correlated with pR£Y'  P  RD  r e y  i " t i v e distances e a c  tended to  be associated 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 distance 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  correlation  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 ship v e r i f i e d i n Sec I I I .  relation-  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 control o f the same i n t e r n a l motivational  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 r e g r e s s i o n s on experience (E) o r on E were about the same. Maldonado (1963) has reported t h a t the approach phase o f 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 o f 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 o r 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 g r e a t e r d i s t a n c e at a prey with a g r e a t e r "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 t h a t 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 success (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 d i s t a n c e s l e s s than or g r e a t e r than 6.4 cm (mean DS observed). N  DS  ~SS  15 10  < X > X  .80 .50  F i s h e r exact p r o b a b i l i t y = .106 The t r u e 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 success 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 t h a t the s t r i k e d i s t a n c e s 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 , w i t h s t r i k e s i n i t i a t e d at g r e a t e r o r 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 i n c r e a s e d 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 a t the r a t e at which the mouth opened was constant and independent o f the bass v e l o c i t y .  If  the v e l o c i t y i n the l a s t .02 sec before jaw opening i n c r e a s e s 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. DS.  There was a l s o no apparent e f f e c t o f hunger on  In c o n t r a s t , Maldonado (1964) found t h a t both experience  and hunger caused an i n c r e a s e 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 i n c r e a s e d i n inexperienced octopuses, but not i n experienced ones.  More  experimental s t u d i e s w i l l be r e q u i r e d 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 t n Sec VI.3, DS w t l l be assumed t o be constant. 3 The S i m u l a t i o n Model The b a s i s f o r the present model i s the one d e 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 o f avoidance l e a r n i n g w i l l be d i s c u s s e d 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 t o each o f t e n 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 p r e d a t o r , a c c o r d i n g t o 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 s u b r o u t i n e 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 t o 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 o t h e r c l a s s e s are s e t t o z e r o .  ADCOM  then c a l l s s u b r o u t i n e FR t o c a l c u l a t e a s t a b l e a t t a c k r a t e , A, instantaneous w i t h r e s p e c t t o p r e d a t o r d e n s i t y P. Subroutine FR i s i d e n t i c a l t o 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 a t t a c k , with the e x c e p t i o n o f the m o d i f i c a t i o n s d e s c r i b e d below.  97  Search time (TS) was d e f i n e d by H o l l i n g (1965) as the time taken f o r the area swept by the s e a r c h i n g 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 cont 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  in  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 o f prey with r e a c t i v e d i s t a n c e s l e s s than t h a t of the predator.  Prey with higher r e a c t i v e d i s t a n c e s are  assumed to take e v a s i v e 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 p r o p o r t i o n s o f v u l n e r a b l e 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 o c c u r s , 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 a c c o r d i n g 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. prey may o n l y reach cover i f TC exceeds TR, the time to refuge.  The TR  i s determined by s e l e c t i n g a random number between 0 and 1, and mult i p l y i n g t h i s by twice the mean TR (an i n p u t 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  RN1 = TANO * FRAND(O)  1= 1.NMAX  RN1 = RNl-ANO(I). 11 = I  YES  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 XTP = XTP + TP1 + TGAIN XTR = XTR - TC - TGAIN TC = MAN*(GAIN-DS)/VR TP1 = TC  VO 00  TPMAX = PAR1*(H1 - HTP) (1+PAR2(H1-HTP)J  HI = HK + (H1-HK)*EXP(-AD+TP1) P.N = FRAND(O)  ir-^^  NO  TUP = TA + TC  H> HTC  STUP = STUP + TUP + XTP HI = HK+(H11-HK*EXP(-AD*STUP)) ESCAP(II) = ESCAP(II) + 1  YES  TUP =  0  Wl = W  .  EATEN(II) = 1+EATEN(II) TP1 •= TP1 + XTP JJ = 2 RETURN^^-  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 o b s e r v a t i o n s r e p o r t e d i n the l i t e r a t u r e . Estes and Goddard (1967), f o r example, found t h a t A f r i c a n hunting dogs w i l l not attempt t o 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 y a r d s .  I t i s not known however whether t h i s i s  based on past experience t h a t a g a z e l l e with such a long head s t a r t w i l l always escape o r whether the dogs are unable t o 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 t h a t i f a moose  stayed more than 100 yards ahead o f pursuing wolves f o r 10 o r 15 s e c , 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 p r e d a t o r gets c l o s e enough t o the prey t o 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 t o FR  under one o f two c o n d i t i o n s : (1)  J J = 1, STUP has a v a l u e , TP = 0, and the number o f escapes from the c l 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 .  T h i s process  continues u n t i l a prey has been captured ( J J = 2 ) , the STUP's and TS's being accumulated. (2)  J J = 2, STUP = 0, TP has a v a l u e , and the number o f 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 s u b r o u t i n e , SUMRY.  100  SUMRY, shown as a flow diagram t n Figure 24, c a l c u l a t e s the a t t a c k r a t e , A, as meals p e r u n i t time, where: MEAL = X E A T E N ( I ) TIME = 2TI = £ ( T D + TS + STUP + TP + T E ) . The s u b r o u t i n e r e t u r n s to FR with e i t h e r a s t a b l e a t t a c k r a t e (JJ=2) o r 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 o f 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 d u r i n g 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 p r o p o r t i o n o f s u c c e s s f u l ( S P ( I ) ) , and u n s u c c e s s f u l ( F P ( I ) ) a t t a c k s by the p r e d a t o r and the r a t e s o f a t t a c k (AA(I)) and escape (AESC(I)). Subroutine FR then c a l c u l a t e s A from the average o f the l a s t two values given by SUMRY and r e t u r n s t o ADCOM ( F i g . 25).  This  s u b r o u t i n e 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 o f 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 e l a p s e d .  To do so  i t uses the estimates o f a t t a c k and escape r a t e s generated by SUMRY. Note t h a t prey a r e not only removed from a c l a s s by being eaten, b u t a l s o by being u n s u c c e s s f u l l y a t t a c k e d . 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 .  In the l a t t e r case, they are 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 t o be removed from a c l a s s may exceed the number present.  When t h i s o c c u r s , T i s a d j u s t e d downward so t h a t 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 a d j u s t e d ,  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 o f subroutine SUMRY.  101 FREE  = 0.  M E A L = 0. T I M E = T I M E + T1 MEAL = ^  EATEN  (I)  www  F R E E = ^> E S C A P (I) A = MEAL/TIME A D I F F = |A-XA|/A XA =A  YES  TSP = M E A L / ( M E A L + FREE) JJ=  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 AA(I)^  X1/TIME  AESC(I)=  SP(I) = FP(I) =  X2/TIME  0. 0.  SP(1) =X1/  F P ( I ) = X2/ A T T A C K  YES  AA(I) SP(I) FP(I)  ATTACK  = 0. = 0.> I=NMAX+1,10 = 0. J  <3-  Figure 25  Flow diagram o f subroutine ADCOM.  TANO = 0 IN = 0  SUMT = 0 T = 0 TANOX=TANO AHA = 0 •at——  <I>—  ATT= TNA(I) OUT= ESC(I) AND(I)=ANO(I)-ATT-OUT+IN  Z=TAN0/(TAN0-.02TAN0X) Z-Z**(1.0/AK) T=TAN0*AK*(Z-1)/(A*P) INDEX = 1 SUMTR = SUMT  1.NMAX  ANO(I) = 0  SUMT = SUMTR + T YES  ANHA(I)=ANHA(I)+ATT TANO = TANO + ANO(I) IN = OUT  T = TAG - SUMTR SUMT = TAG  O  ro TOTNA = A*T*P  T=ANO(I)/DEN0M  YES  YES  1= 1,10 TNA(I) = AA(I)*T*P ESC(l) = AESC(I)*T*P  ANO(I) * 0 TNA (I) = 0 ESC(l) ' 0  EATEN(I) = 0 ESCAP(I) - 0  1 = 1.NMAX CALL FR  YES  I = K.10  INOEX = 1 + 1 DENOM = P*(AA(I)+AESC(I))  REMOVE=TNA(I)+ESC(I) I = INOEX.NMAX  YES  NMAX  TANHA = TANHA + ANHA(I)  103  c a l l made to subroutine FR.  T h i s continues u n t i l a l l o f 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 o f the  d e n s i t i e s o f 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 ,  t h a t changes i n the frequency d i s t r i b u t i o n o f prey 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 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 o f 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 i n c o r p o r a t e d 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 o f the s i m u l a t i o n s . The meanings and values o f a l l parameters used i n these s i m u l a t i o n s are given i n T a b l e 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 o c c u r r e d , 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 a t t a c k e d . In a l l o t h e r 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 m o d i f i e d v e r s i o n o f 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 t h a t 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 s i m u l a t i o n model.  PARAMETER  VALUE . UNITS  AD  0.2  AK  3.0  AKE  .00001  CAPT DS EC  1.0 5.8 1.9845  EONK  0.5  EYE  2.0  GAIN  16.0  HK HONP  1.8  HOPT  0.3  KA  KMIN  LOPT LPAR  1.0  3.1416  ,2349  MEANING  hr"  Instantaneous r a t e o f d i g estion. Dispersion c o - e f f i c i e n t of negative binomial hr Time t o e a t one gram o f prey Ratio between t h r e s h o l d hungers f o r ' c a p t u r e and for pursuit cm Strike distance 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 unsuccessful s t r i k e gm Maximum gut c a p a c i t y cm/gm Constant r e l a t i n g purs u i t d i s t a n c e t o 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 reaction to distance o f r e a c t i o n s t r a i g h t ahead rad/sec  3.0  cm  Minimum p o s s i b l e da/dt threshold Prey length  4.0 1.5  cm rad/sec  Optimum prey length Naive dw/dt t h r e s h o l d  SOURCE Glass (1971) Griffiths & 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  Hypothetical Measured  Measured  105  PARAMETER MAN  VALUE  UNITS ..  0.8  MYOP  16.56  gm/cm  P PARI  0.2 0.222  -1 sq. m hrs/gm  PAR2  0.02  gm"  SIZE SR SS TAG  2.65 0.8 0.8 24  cm  hrs  TR  .00007  hrs  VP VR  5600 3600  m/hr m/hr  W  4  1  0.27  gm  .  MEANING  Relative manoeuverability o f prey Constant r e l a t i n g dHTP/dL to (LOPT-L) Predator d e n s i t y Parameter i n TPMAX c a l c u lation Parameter i n TPMAX c a l c u lation Predator diameter Recognition success S t r i k e success Time a v a i l a b l e f o r generating a t t a c k s Mean time f o r prey t o reach cover Predator's v e l o c i t y Predator's r e l a t i v e velocity Weight o f one prey  SOURCE Sec VI.2 Mantid ( H o l l i n g , i n prep) Hypothetical Hypothetical Hypothetical Measured Hypothetical Table XIII Hypotheti cal Hypothetical Measured Measured Measured  Results and D i s c u s s i o n The r e s u l t s o f s i m u l a t i o n s o f 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 a t t a c k s 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 explanat 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 t o e a t n e a r l y a l l o f the prey i n l e s s than 24 hours; a t d e n s i t i e s g r e a t e r 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  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 predators to prey with, and without the a b i l i t y t o 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 a t t a c k e d .  106  5 TANO  10  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 a t t a c k s remained n e a r l y constant.  Thus a type I response can occur when predator r e a c t i v e d i s -  tance i n c r e a s e s 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 r e q u i r e d somewhat  longer to consume a l l o f 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 o f encountering an experienced prey was low, s i n c e there were such a l a r g e number o f 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 o f e f f e c t , and even here i t was s m a l l . The maximum advantage to the prey p o p u l a t i o n o c c u r r e d 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 o f t r e b l i n g the s u r v i v a l r a t e (from .85 to 2.52%) a t t h a t d e n s i t y . It 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 p r e d a t o r feeding on non-learning prey spent 19.8 hours d i g e s t i n g prey and 4.2 hours s e a r c h i n g f o r and c a p t u r i n g them. The predator f e e d i n g 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 m e t a b o l i c r a t e s o f 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 ( a t 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 p r e d a t o r . These were converted to c a l o r i e s a c c o r d i n g to the r e l a t i o n s h i p cal = mg0 x ?  1 ml 1.428 mg  x 4.85 c a l m!0 2  The c a l o r i c expenditure o f the p r e d a t o r f e e d i n g on n o n - l e a r n i n g prey was 7105 c a l , w h i l e t h a t f o r the predator f e e d i n g on prey capable o f l e a r n i n g was 7548, an i n c r e a s e o f 6.2%.  Since the number o f prey  captured per p r e d a t o r (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 i n c r e a s e o f 8%.  Consequently,  a p r e d a t o r f e e d i n g on prey capable o f l e a r n i n g would have a lower net energy gain than one f e e d i n g 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 p r e d a t o r 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 (Solomon, 1949).  response to prey d e n s i t y  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 c o n f e r r e d 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 o f each o f the 10 c l a s s e s were  run. through s u b r o u t i n e CHASE and the number o f s u c c e s s f u l captures recorded.  A number o f 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 o f prey about e q u a l l y . Only changes i n p r e d a t o r 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), c o n f e r r e d d i f f e r e n t to each prey c l a s s .  advantages  Changing the d i s t r i b u t i o n o f time t o refuge  from uniform t o 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 i n c r e a s e d 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 c o n f e r r e d was .116 prey/sq. m. (cf.085/sq. :m) and o c c u r r e d at a d e n s i t y o f 6 prey/sq. m. The model was a l s o used t o 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 t o 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 t o predator d e n s i t y was maximal a t i n t e r m e d i a t e predator d e n s i t i e s .  A t low predator  d e n s i t i e s , there was a s u r p l u s 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 o f v a r i o u s behavioural and environmental parameters 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 o f previous e x p e r i e n c e , as simulated by the model. Refer to Table XVII f o r an e x p l a n a t i o n o f the meaning and u n i t s o f the various parameters.  no  P R E YC L A S S  Figure 28 S i m u l a t i o n o f the d e n s i t y o f 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.  Ill  6r  1  2  3 4 P R E Y / S Q . M.  5  6  7  8  Figure 29  S i m u l a t i o n o f the number o f prey attacked p e r predator per day (FRNHA) as a f u n c t i o n o f 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 o f .50 and .75. VP = 4000, VR = 2000.  112  •  .1  1  1  I  .15 .2 .25 PREDATORS/SQ.M.  L.  .3  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 n e a r l y a l l the prey were eaten, r e g a r d l e s s 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 o f l i t t l e consequence.  The maximum e f f e c t o f 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 e x p e c t a t i o n o f G r i f f i t h s and H o l l i n g (1969) t h a t "the g r e a t e r the p r e d a t o r d e n s i t y , the g r e a t e r the chance t h a t each prey w i l l have a c q u i r e d 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 a t t a c k r a t e " was v e r i f i e d . I n c r e a s i n g the l e a r n i n g r a t e (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 a t i n t e r m e d i a t e p r e d a t o r 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 p r e d a t o r 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 p r e d a t o r prey i n t e r a c t i o n on the predator's a b i l i t y to r e g u l a t e the prey p o p u l a t i o n was a l s o e x p l o r e d using the model.  The curves o f  actual m o r t a l i t y shown i n F i g . 30 are those generated by the model in s i t u a t i o n s where the prey are i n c a p a b l e (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 o f prey destroyed i s i n i t i a l l y constant (ACT), o r n e a r l y so (ACT'), and then becomes i n v e r s e l y prop 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 n e a r l y c o n s t a n t , 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 p o p u l a t i o n from generation t o g e n e r a t i o n . 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 t o 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 popul a t i o n ; ACT and ACT' = actual percent predation when prey are incapable and capable o f 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 charact 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 p r e d a t i o n m o r t a l i t y r e q u i r e d t o 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;  (ii)  as d e 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 p r o p o r t i o n a t e i n c r e a s e i n pred a t i o n m o r t a l i t y i f the prey population i s to remain s t a b l e ;  (iii)  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 . P o p u l a t i o n e q u i l i b r i a occur a t a l l points where ACT = NEC. may be o f three kinds:  These  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) o r escape (ES).  A stable equilibrium  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 p o p 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 t o t h a t 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), o r 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 i n c 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 p o p u l a t i o n are considered unwarranted.for s e v e r a l reasons.  regulation  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 o f 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 o f 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 e n v i s i o n e d 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 o f 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 p o p u l 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 o f 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 i n c l u d 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 o f p o p u l 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 relationships:  117  TP = TA + TC TA = ( R D  p R E D  -  TC = ( R D  p R E Y  - DS)/1.27 V  r  d  )/ PRED V  p  r  e  y  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 (ii)  process.  The o p p o r t u n i t y 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).  (iii)  Data c o l l e c t e d from f i l 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. (iv)  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 a)  l e a r n i n g component i n c l u d e d :  M o d i f i c a t i o n s o f 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 o f prey to account f o r those whose r e a c t i v e d i s t a n c e s exceed that o f 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 o f 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 ) a c c o r d i n g 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 r e f u g e , and the predator's s t r i k e s u c c e s s .  (v)  S i m u l a t i o n s t u d i e s using s u b r o u t i n e CHASE show t h a t 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 i n c r e a s e s 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 c o n f e r r e d 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 p r e d a t o r behaviour. (vi)  A t the l e v e l o f the p o p u l a t i o n , the a d d i t i o n o f 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 o f 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 o f predators to prey d e n s i t y i s a l s o suggested.  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