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UBC Theses and Dissertations

Competitive exclusion of ostracod species in a temporary environment McLay, Colin Lindsay 1970

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COMPETITIVE EXCLUSION OF OSTRACOD SPECIES' IN A TEMPORARY ENVIRONMENT by COLIN LINDSAY MCLAY BoSCo(Hons), U n i v e r s i t y o f Otago, N.Z., 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY I n t h e Department o f Z o o l o g y We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA March, 19 70 In presenting t h i s thesis in p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t f r e e l y available for reference and study. I further agree tha permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis f o r f i n a n c i a l gain shall not be allowed without my written permission. Department of The University of B r i t i s h Columbia Vancouver 8, Canada Date if 7 O i ABSTRACT Two s p e c i e s o f o s t r a c o d s ( C y p r i n o t u s c a r o l i n e n s i s F e r g u s o n , 1958 and H e r p e t o c y p r i s r e p t a n s ( B a i r d , 18 35) l i v i n g i n a t emporary p u d d l e were s t u d i e d t o f i n d o ut whether one s p e c i e s c o u l d cause t h e e x t i n c t i o n o f t h e o t h e r . The t i m e d u r i n g w h i c h t h e a n i m a l s can r e p r o d u c e i s l i m i t e d because t h e p u d d l e s a r e t e m p o r a r y . W h i l e t h e p u d d l e i s wet each s p e c i e s may be p r e s e n t a t any t i m e as b o t h a n i m a l s and eggs. The p u d d l e i n w h i c h t h e a n i m a l s l i v e d was a l o n g (31.1 m), harrow (34.0 cm) and s h a l l o w (2.5 cm) r u t on a g e n t l y s l o p i n g f i e l d . I t was s u p p l i e d w i t h w a t e r from r u n - o f f and seepage. The p u d d l e f i l l e d i n t h e f a l l and d r i e d up i n t h e s p r i n g ; d u r i n g t h i s i n t e r v a l t h e eggs p r e s e n t i n t h e f a l l had t o become more eggs by t h e s p r i n g f o r t h e s p e c i e s t o s u r v i v e . The p r e s e n c e o r absence of a s p e c i e s was a s s e s s e d a f t e r d r y i n g - u p i n t h e s p r i n g . The e f f e c t o f one s p e c i e s upon a n o t h e r i s e x p r e s s e d by a s i n g l e q u a n t i t y - t h e number o f eggs o f t h e s p e c i e s t h a t a r e p r e s e n t a t t h i s t i m e . One s p e c i e s o f o s t r a c o d c a n a f f e c t a n o t h e r by a l t e r i n g t h e number o f a n i m a l s w h i c h h a t c h i n any u n i t o f t i m e , t h e number and l e n g t h o f time r e q u i r e d f o r them t o r e a c h m a t u r i t y and t h e l e n g t h o f t i m e which t h e y spend l a y i n g eggs. A computer model was b u i l t w h i c h was c a p a b l e o f s i m u l a t i n g t h e p o p u l a t i o n s o f eggs and a n i m a l s o f b o t h s p e c i e s when a l o n e and t o g e t h e r . The model was b u i l t up from o b s e r v a -t i o n s and e x p e r i m e n t s on t h e o s t r a c o d s . Where p o s s i b l e t h e models o f p r o c e s s e s which were d e v e l o p e d were t e s t e d upon th e i i n a t u r a l p o p u l a t i o n . A f t e r t h e a d d i t i o n o f w a t e r t o t h e p u d d l e t h e r e i s a d e l a y o f f r o m 6 - 7 d a y s b e f o r e t h e e g g s o f e a c h s p e c i e s b e g i n t o h a t c h . The e g g s a r e c a p a b l e o f h a t c h i n g a t any t i m e a f t e r t h e a d d i t i o n o f w a t e r . A s i m p l e m o d e l , i n w h i c h t h e m o r t a l i t y i n an i n t e r v a l o f t i m e r e l a t e d o n l y t o t h e numbers p r e s e n t , was f o u n d t o be s a t i s f a c t o r y . The m o r t a l i t y o f H e r p e t o c y p r i s was l e s s t h a n t h a t o f C y p r i n o t u s when b o t h w e r e a l o n e . C y p r i n o t u s a f f e c t e d t h e m o r t a l i t y o f H e r p e t o c y p r i s i n t h e same way as d i d t h e members o f H e r p e t o c y p r i s , b u t t h e r e was an a d d i t i o n a l e f f e c t o f H e r p e t o c y p r i s u p o n C y p r i n o t u s . The number o f d a y - d e g r e e s r e q u i r e d f o r t h e a n i m a l s t o r e a c h m a t u r i t y was c o n s t a n t , r e g a r d l e s s o f t h e t i m e a t w h i c h t h e a n i m a l s h a t c h e d . The number f o r C y p r i n o t u s was h a l f t h a t r e q u i r e d f o r H e r p e t o c y p r i s , a n d i t i n c r e a s e d l i n e a r l y w i t h t h e t o t a l i n i t i a l i n p u t o f a n i m a l s . The e g g - l a y i n g r a t e o f b o t h s p e c i e s i s a l m o s t t h e same and was f o u n d t o d e c r e a s e i n an e x p o n e n t i a l manner as t h e t e m p e r a t u r e d e c r e a s e d a n d / o r t h e d e n s i t y i n c r e a s e d . T h e r e i s a d e l a y b e t w e e n t h e l a y i n g a n d h a t c h i n g o f t h e e g g s , w h i c h i n c r e a s e s as t h e t e m p e r a t u r e -d e c r e a s e s . The d e l a y f o r H e r p e t o c y p r i s e g g s i s much s h o r t e r t h a n i t i s f o r C y p r i n o t u s e g g s . The f i n a l number o f e g g s l e f t i n t h e mud when t h e p u d d l e d r i e s i s g i v e n b y t h e sum o f t h e o l d e g g s t h a t r e m a i n a nd t h e new e g g s w h i c h h a v e b e e n a d d e d . The number o f new e g g s i s t h e d i f f e r e n c e b e t w e e n t h e t o t a l number w h i c h h a v e b e e n l a i d and t h e t o t a l number o f t h e s e w h i c h h a v e h a t c h e d . G i v e n an i n p u t o f e g g s , t h e t i m e s t h a t t h e p u d d l e f i l l e d a n d d r i e d up and t h e t e m p e r a t u r e d u r i n g t h e i i i w e t - p e r i o d , t h e o u t p u t o f e g g s i n t h e s p r i n g c o u l d be p r e d i c t e d . The a b i l i t y o f t h e m o d e l t o i m i t a t e t h e r e a l p o p u l a t i o n s was t e s t e d . G i v e n t h e same i n p u t o f e g g s t h e o u t p u t o f e g g s by t h e m o d e l was c o m p a r e d w i t h t h e n a t u r a l o u t p u t i n t h e f o l l o w -i n g s p r i n g . The e x p e c t e d n u m bers a g r e e d c l o s e l y w i t h t h e o b s e r v e d . D u r i n g f i l l i n g a n d d r y i n g - u p n o t a l l p a r t s o f t h e p u d d l e c o v e r e d o r d r i e d a t t h e same t i m e ; h e n c e t h e mean d a i l y p u d d l e - l e n g t h f l u c t u a t e s . A s i m p l e m o d e l o f t h e f l u c t u a t i o n s i n l e n g t h was c o n s t r u c t e d . I t u s e d o n l y t h e r e c o r d o f r a i n -f a l l d u r i n g e a c h p e r i o d . U s i n g t h e mean t i m e s o f f i l l i n g and d r y i n g a nd mean t e m p e r a t u r e s f o r t h e y e a r s 1 9 6 1 - 6 9 , f o r s e l e c t e d p o i n t s i n t h e p u d d l e , t h e e f f e c t o f e a c h s p e c i e s u p o n t h e o t h e r was i n v e s t i g a t e d o n t h e c o m p u t e r . The o u t c o m e d e p e n d e d u p o n t h e i n i t i a l n u m b e r s o f e g g s . H e r p e t o c y p r i s c o u l d c a u s e t h e e x t i n c t i o n o f C y p r i n o t u s o v e r m o s t o f t h e r a n g e o f i n p u t s . C y p r i n o t u s c o u l d o n l y become t h e d o m i n a n t s p e c i e s when i t s i n i t i a l n umbers w e r e 7 - 8 t i m e s l a r g e r t h a n t h o s e o f t h e o t h e r s p e c i e s . The number o f ' s e a s o n s ' r e q u i r e d t o a r r i v e a t t h e s e r e l a t i v e p o s i t i o n s d e p e n d e d u p o n t h e i n i t i a l n u m b e r s . The m o d e l was u s e d t o s i m u l a t e t h e p o p u l a t i o n s o f b o t h s p e c i e s f o r t h e y e a r s 1 9 6 2 - 6 9 . The c o n d i t i o n s f l u c t u a t e d f r o m y e a r t o y e a r . I n i t i a l c o n c e n t r a t i o n s o f f r o m 0.1 -2 1.0 e g g s / c m f o r e a c h s p e c i e s w e r e t r i e d a n d t h e o u t c o m e was f o u n d t o be e x t r a o r d i n a r i l y s e n s i t i v e t o t h e i n i t i a l d e n s i t y . A n a r r o w r a n g e o f i n p u t s l e d t o t h e o b s e r v e d c o e x i s t e n c e i n 1 9 6 9 . Below t h i s r a n g e o n l y C y p r i n o t u s r e m a i n e d and a b o v e i t i v o n l y H e r p e t o c y p r i s c I t i s t h e r e f o r e c o n c l u d e d t h a t c o m p e t i t i v e e x c l u s i o n i s i n d e e d p o s s i b l e f o r t h e s e a n i m a l s , even when t h e e n v i r o n m e n t f l u c t u a t e s from y e a r t o y e a r . TABLE OF CONTENTS PAGE ABSTRACT i TABLE OF CONTENTS V L I S T OF TABLES v i i L I S T OF FIGURES i x ACKNOWLEDGEMENT x i v PREFACE. x v i INTRODUCTION 1 THE OSTRACODS STUDIED 7 PART I a) The h a t c h i n g o f o l d s t o r e d e g g s . 10 b) M o r t a l i t y o f r e c r u i t s . 17 c ) The amount o f t i m e r e q u i r e d t o r e a c h m a t u r i t y . 36 d) The a c c u m u l a t i o n o f d a y - d e g r e e s b y t h e a n i m a l s . 41 e) The m e c h a n i s m o f t h e e f f e c t o f d e n s i t y o f t h e a n i m a l s u p o n one a n o t h e r . 50 f ) The number o f a n i m a l s o f t h e same age r e a c h i n g m a t u r i t y . 6 3 g j The e g g - l a y i n g by m a t u r e a n i m a l s . 71 h) The h a t c h i n g o f new e g g s . 78 i ) The e f f e c t s o f d e s i c c a t i o n u p o n t h e a n i m a l s . 90 j ) The number o f e g g s l e f t i n a u n i t o f s p a c e a t t h e t i m e o f d r y i n g - u p . 9 3 k ) The e f f e c t s o f f r e e z i n g u p o n t h e p u d d l e a n i m a l s . 96 1) E x p e r i m e n t s u p o n t h e d i s p e r s a l o f o s t r a c o d s f r o m a p o i n t s o u r c e i n t o a s h a l l o w p o o l . 97 PART I I a) The t y r e - t r a c k p u d d l e and i t s w a t e r - s u p p l y . 114 b ) A m o d e l o f w a t e r - l e v e l f l u c t u a t i o n s i n t h e p u d d l e . 124 v i PAGE c) The e f f e c t s of sub-zero temperatures upon the puddle„ 134 d) Immigration by ostracods from other puddles. 137 PART I I I a) A summary of p o p u l a t i o n processes. 141 b) A s y n t h e s i s of p o p u l a t i o n processes f o r s i m u l a t i o n on a computer. 142 c) Test of the a b i l i t y of the synthesized model to p r e d i c t the number of eggs i n the puddle at the time of drying-up. 146 d) E x p l o r a t i o n of the consequences of changes i n d e n s i t y of each s p e c i e s . 154 e) S i m u l a t i o n of the p o p u l a t i o n i n the puddle f o r the years 1961-1969, and c o n c l u s i o n * 165 DISCUSSION 170 BIBLIOGRAPHY 179 APPENDICES 1. The feeding appendages of o s t r a c o d s . 181 2. A l i s t of animals which have been found i n the puddle. 184 3. The s i m u l a t i o n model CRUST. 185 v i i L IST OF TABLES TABLE PAGE I V a l u e s of t h e i n t e r c e p t , s l o p e and c o r r e l a t i o n c o e f f i c i e n t f o r t h e r e l a t i o n -s h i p between t h e e x p e c t e d and o b s e r v e d c u m u l a t i v e number o f day-degrees f o r each y e a r from 1961-1969., 48 I I The t i m e s o f o c c u r r e n c e o f maximum d e v i a t i o n s i n d a y - d e g r e e s 0 49 I I I V a l u e s o f t h e mean numbers p e r sample, the v a r i a n c e on t h e mean and v a l u e s o f the n e g a t i v e b i n o m i a l d i s p e r s i o n c o -e f f i c i e n t ( k:) , f o r p o p u l a t i o n s o f C y p r i n o t u s <> 55 IV V a l u e s o f t h e mean numbers p e r sample, the v a r i a n c e on t h e mean and v a l u e s o f th e n e g a t i v e b i n o m i a l d i s p e r s i o n c o e f f i c i e n t ( k ), f o r p o p u l a t i o n s o f H e r p e t o c y p r i s . 5 6 V The e f f e c t o f t h e p r e s e n c e o f b o t h s p e c i e s upon t h e d i s p e r s i o n o f each s p e c i e s . 57 VI The o b s e r v e d and e x p e c t e d p r o p o r t i o n s o f l a r g e and s m a l l C y p r i n o t u s a n i m a l s p r e s e n t i n t h e p u d d l e . 69 V I I V a l u e s o f t h e i n s t a n t a n e o u s r a t e o f h a t c h -i n g (RH) o f C y p r i n o t u s eggs a t a range o f t e m p e r a t u r e s . 82 V I I I The p r o p o r t i o m : o f t h e number o f C y p r i n o t u s eggs i n each sample l a i d a t each t e m p e r a t u r e , which h a t c h d u r i n g t h e f i r s t and second p e r i o d s . 83 IX The mean v e l o c i t i e s a t whi c h t h e a n i m a l s move when c r a w l i n g , b u r r o w i n g and swimming, f o r b o t h s p e c i e s o f o s t r a c o d . 100 X The p r o p o r t i o n o f sample a r e a s o f t h e p u d d l e , o c c u p i e d by u n c o v e r e d mud and g r a s s a t d i f f e r e n t p o i n t s a l o n g i t s l e n g t h . 120 X I A summary o f the v a l u e s o f t h e c o n s t a n t s o b t a i n e d from t h e e x p e r i m e n t a l work, w h i c h a r e used i n the F o r t r a n program, CRUST. 14 7 I n p u t d a t a f o r t h e CRUST program used t o t e s t t h e a b i l i t y o f t h e s y n t h e s i z e d model t o p r e d i c t t h e numbers o f C y p r i n o t u s eggs a t v a r i o u s p o i n t s a l o n g t h e l e n g t h o f t h e t y r e - t r a c k puddle,, C o n t a i n i n g t h e a n n u a l mean and maximum monthly mean a i r t e m p e r a t u r e (°F) f o r th e y e a r s 1961-69, measured a t t h e UBC M e t e r o l o g i c a l S t a t i o n ; t h e t i m e s o f f i l l i n g and d r y i n g f o r t h e t y r e - t r a c k p u d d l e a t t h e p o i n t s 5,0, 12 o0 and 22„0 m from t h e s o u t h end, f o r the y e a r s 1961-69 and t h e mean v a l u e s f o r t h e a n n u a l mean and maximum monthly mean t e m p e r a t u r e , and t h e t i m e s o f f i l l i n g and d r y i n g f o r each p o i n t d u r i n g t h e s e y e a r s . i x L I S T OF FIGURES FIGURE PAGE 1 I l l u s t r a t i o n o f t h e s e q u e n c e o f e v e n t s w h i c h must o c c u r f o r e g g s t o p r o d u c e more egg s d u r i n g t h e p e r i o d when t h e p u d d l e i s wet, 3 2 The s h a p e and c h a n g e s i n s h a p e o f t h e v a l v e s o f t h e two s p e c i e s o f o s t r a c o d , b e t w e e n h a t c h i n g f r o m t h e egg and e g g -l a y i n g , 8 3 The h a t c h i n g o f o l d e g g s o f b o t h s p e c i e s f r o m s o i l c o r e s t a k e n f r o m t h e p u d d l e , 11 4 The r e l a t i o n s h i p b e t w e e n t h e t i m e s u b -m e r g e d t i l l t h e a p p e a r a n c e o f t h e l a r v a e , a n d t h e number o f d a y s t h a t t h e s o i l h a d b e e n d r i e d , 15 5 C o m p a r i s o n o f t h e way i n w h i c h t h e s t o r e o f e g g s o f e a c h s p e c i e s p r e s e n t i n t h e f a l l , i s e r o d e d as t h e t i m e s u b m e r g e d i n c r e a s e s . 16 6 The r e l a t i o n s h i p b e t w e e n t h e p r o p o r t i o n o f t h e i n i t i a l n u m b ers a l i v e a f t e r 49 days and t h e i n i t i a l d e n s i t y , f o r C y p r i n o t u s a l o n e . 22 7 The s h a p e o f t h e r e l a t i o n s h i p b e t w e e n t h e n u m bers p r e s e n t (N) and t h e t i m e a f t e r t h e a d d i t i o n o f w a t e r ( T ) , f o r b o t h s p e c i e s . 24 8 T e s t o f t h e m o r t a l i t y m o d e l f o r C y p r i n o t u s by c o m p a r i n g t h e e x p e c t e d and o b s e r v e d numbers a t s e l e c t e d p o i n t s a l o n g t h e l e n g t h ' o f t h e p u d d l e a f t e r 38 and 78 d a y s o f 2 7 s u b m e r g e n c e . 9 The r e l a t i o n s h i p b e t w e e n t h e p r o p o r t i o n o f t h e i n i t i a l n u mbers a l i v e a f t e r 49 d a y s and t h e i n i t i a l d e n s i t y , f o r H e r p e t o c y p r i s a l o n e . 28 10 The t e s t o f t h e m o r t a l i t y m o d e l f o r H e r p e t o c y p r i s i n t h e p u d d l e . 29 11 The e f f e c t o f e a c h s p e c i e s u p o n t h e m o r t a l i t y o f t h e o t h e r , when g r o w n i n s m a l l p e t r i - d i s h e s . 31 The manner.in which the mature animals of both species d i e - o f f w i t h i n c r e a s i n g time (days) s i n c e maturation,, The number of day-degrees (°F) which the animals were exposed to before reaching m a t u r i t y , as a f u n c t i o n of the number of days a f t e r August 1st t h a t they hatched. The e f f e c t of the i n i t i a l d e n s i t y of ,v animals upon the number of day-degrees (°F) r e q u i r e d f o r the animals to reach m a t u r i t y . The shape of the r e l a t i o n s h i p between the mean monthly temperature i n the P o i n t Grey area and the number of days a f t e r August 1 s t . The e f f e c t of s t a r t i n g at d i f f e r e n t times a f t e r August 1s t , to accumulate, a given number of day-degrees (from 500 to 15,000), upon the length of time r e q u i r e d to achieve the v a l u e . Demonstrating the l i n e a r nature of the r e l a t i o n s h i p between the expected and the observed cumulative number of day-degrees (°C)„ Comparison of the observed d i s t r i b u t i o n ( s o l i d l i n e s ) of the frequency of samples w i t h d i f f e r e n t numbers of o s t r a c o d s , w i t h the expected f r e q u e n c i e s (dashed l i n e s ) generated from the negative b i n o m i a l d i s t r i b u t i o n . The lengths of time t h a t each species can withstand t o t a l food d e p r i v a t i o n . The p r o p o r t i o n of the o r i g i n a l number al i v e , i s given f o r each i n t e r v a l of time. I l l u s t r a t i o n of the method of p a r t i t i o n -i n g the m o r t a l i t y i n each i n t e r v a l of time, among the age-classes. Changes i n the p r o p o r t i o n s of each age-class of Cyprinotus represented, at d i f f e r e n t values of time a f t e r the beginning of r e c r u i t m e n t . x i 74 FIGURE PAGE 22 The r e l a t i o n s h i p between the egg-l a y i n g r a t e of C y p r i n o t u s , the water temperature (°C) and the d e n s i t y of animals. 2 3 The a b i l i t y of the simple r e l a t i o n s h i p between the egg-lay i n g r a t e of C y p r i n o t u s , the water temperature and d e n s i t y , to p r e d i c t the cumulative number of eggs l a i d per cm^9 by small p o p u l a t i o n s of animals i n p e t r i - d i s h e s of mud. 24 Test of the egg-laying model f o r Herpetocypris to p r e d i c t the cumulative numbers of eggs l a i d by small p o p u l a t i o n s l i v i n g on mud i n p e t r i - d i s h e s at ambient temperature. 76 77 25 The delay i n the beginning of hat c h i n g of the eggs of both species as a func-t i o n of the water temperature (°C). ^0 26 The r e l a t i o n s h i p between the time of l a y i n g ( i n days a f t e r the animal matured), and the time of hatching f o r Cyprinotus eggs l a i d at 24°C. 8 5 2 7 Tests of the egg-hatching model f o r Herpetocypris eggs. 88 28 The decrease i n the percentage of Cyprinotus a l i v e i n mud-samples taken from the puddle as the length of the p e r i o d of desiccation.' i n c r e a s e d . 91 29 An example f o r each species of the observed r e l a t i o n s h i p between the cumulative numbers of eggs l a i d and the cumulative number of these eggs which have hatched. 95 30 The e f f e c t s of f r e e z i n g upon both species of o s t r a c o d and some other animals i n the puddle. 93 31 The p r o p o r t i o n s of each o b s e r v a t i o n p e r i o d spent by the animals e i t h e r s t a t i o n a r y or moving f o r both s p e c i e s . 102 32 D i s p e r s a l of the ostracods i n a l a b o r a t o r y puddle from a p o i n t source. 104 x i i F I G U R E 3 3' 34 35 36 37 38 39 40 41 42 43 P A G E Test of the random d i f f u s i o n model f o r the d i s p e r s a l of both species of ostracods from a p o i n t source i n an a r t i f i c i a l puddle, 108 P h y s i c a l dimensions of the t y r e - t r a c k puddle, 11-7 The d i s t r i b u t i o n of open (Lo) and grassed ( L c ) u n i t s of the puddle along i t s l e n g t h , 118 A map of the f i e l d on the J e r i c h o Army Base c o n t a i n i n g the t y r e - t r a c k puddle, 121 The i n c i d e n c e of the lengths of dry and wet periods and the a s s o c i a t e d mean d a i l y temperature (°F) during each p e r i o d as taken from the UBC C l i m a t o l o g i c a l S t a t i o n Records f o r the years 1961-69, 126 The d i u r n a l f l u c t u a t i o n i n the le n g t h of the t y r e - t r a c k puddle during the p e r i o d 4th May to 1st June, 19 68, 12 8 The r e l a t i o n s h i p s between the decrement i n length ( i n metres) and the number of days s i n c e r a i n , and the increment i n length ( i n metres) per u n i t r a i n f a l l , used to generate the expected lengths of the puddle, 130 Test of the a b i l i t y of the puddle-model to p r e d i c t length of the t y r e - t r a c k puddle during the p e r i o d s of d r y i n g and f i l l i n g , 131 The i n c r e a s e i n depth of i c e i n the t y r e -t r a c k puddle with i n c r e a s i n g numbers of consecutive days on which the d a i l y minimum a i r temperature was l e s s than or equal to 0°C r e g a r d l e s s of the amount by which i t went below t h i s v a l u e , 136 A F o r t r a n f l o w - c h a r t of the operations performed by the computer during each c i r c u i t through the program, 144 The observed and expected output of eggs i n the t y r e - t r a c k puddle f o r the winter of 1967-68,' 153 The o u t p u t o f eggs i n t h e s p r i n g f o r b o t h s p e c i e s o f o s t r a c o d as a f u n c t i o n o f t h e i n p u t of eggs i n t h e f a l l , when the s p e c i e s are a l o n e and t h e c o n d i -t i o n s r e m a i n c o n s t a n t . The e f f e c t on each s p e c i e s o f a range o f s i m u l t a n e o u s i n p u t numbers o f eggs o f t h e o t h e r s o e c i e s upon t h e o u t p u t o f eggs p e r cm"- a t 12.0 m from t h e s o u t h end o f t h e p u d d l e . A.phase-diagram showing t h e consequences o f s t a r t i n g w i t h d i f f e r e n t r e l a t i v e numbers o f eggs p e r cm^ ( c r o s s e s ) f o r each s p e c i e s . Lo 2 The e x p e c t e d numbers o f eggs p e r cm f o r each s p e c i e s a t 12.0 m from t h e s o u t h end o f t h e p u d d l e , i n t h e s p r i n g o f each y e a r from 1962-69, when t h e c o n d i t i o n s f l u c t u a t e . The appendages o f C y p r i d o p s i s v v i d u a . x i v ACKNOWLEDGEMENT During t h i s study I have received assistance from many people whom I wish to thank. I am very g r a t e f u l to Professor Peter Larkin f o r his consistent and patient help, f o r the provi s i o n of funds, and f o r supervision of the work. Don McQueen has assisted i n many ways with both f i e l d and experimental work and I wish to thank him f o r his able advice. From Mr. Steven Borden and Mr. N e i l G i l b e r t I often sought help with mathematics and B i l l Webb has provided very able assistance with writing programs f o r the computer. At various times Barbara Coward, Nita Jensen and S y l v i a Behrens have worked as research a s s i s t a n t s . Colonel H.N. McKenzie and Mr. D. Hummings of the Department of National Defence, Jericho Army Base, Vancouver, helped to preserve the state of the tyre-track puddle and f r e e l y provided information about the h i s t o r y of the Jericho area. For i d e n t i f i c a t i o n of the ostracods I wish to thank Dr. E. Ferguson and Dr. Dennis Delorme. Mr. J.H. Wallis, a member of the U.B.C. Cl i m a t o l o g i c a l Station Committee, provided copies of meterological records on many occasions. Dr. W.B. Schofield of the Department of Botany, U.B.C. i d e n t i f i e d the plants from the f i e l d . I also wish to thank Mr. J . S.chonfield of the Geography Department, U.B.C. for providing a e r i a l photographs of the Point Grey area. Dr. D.H. Chitt y and Dr. G. Scudder have provided valuable c r i t i c i s m of the manuscript. I wish to thank Mrs. W„ McQueen fo r typing t h i s t h e s i s . XV F o r h e r i n v a l u a b l e h e l p w i t h a l l a s p e c t s o f t h e work and p r e p a r a t i o n o f t h i s m a n u s c r i p t , and f o r h e r c o n s t a n t c o m p a n i o n s h i p , I w i s h t o thank M a r g a r e t McLay. x v i PREFACE The contents of t h i s thesis are arranged i n the customary order of Introduction, Materials, Results and Discussion, A l l the 'methods' used are not described separately, but appear along with the r e s u l t s . No one section has been l a b e l l e d 'Results'. A f t e r the Introduction and Ostracods Studied there are three sections which con s t i t u t e the r e s u l t s . Part I presents the r e s u l t s of the i n v e s t i g a t i o n of some of the e f f e c t s of each species upon each other, the models of the way i n which they act, and where possible, tests of the models. In Part II the p a r t i c u l a r d e t a i l s of the tyre-track puddle are presented. Part I I I contains a d e s c r i p t i o n and summary of the computer program written to synthesize a l l the processes, and the conclusions about the r e s u l t s of the e f f e c t s of the species upon one another. Parts I - III consist of a number of sections, each terminated by a summary. Some consequences of the model are explored i n the Discussion. Understanding of the way i n which each section i s linked to others w i l l be assisted by reference to Figures 1 and 42„ When the term 'animals' appears, i t r e f e r s to a l l ages of a species but not to the eggs. The properties of the eggs are so e n t i r e l y d i f f e r e n t that they are treated separately. F r o n t i s p i e c e The t y r e - t r a c k p u d d l e (Drawn by R a c h e l G o u r l e y ) 1 INTRODUCTION One consequence of competition between animals i s competitive exclusion. This i s the e x t i n c t i o n of a species •at the hands' of another, as opposed to e x t i n c t i o n r e s u l t i n g from catastrophes or gradual change i n the environment. I t i s important since i t i s the means by which evolutionary replace-ment of one species by another might occur. Stated i n t h i s way, 'competitive exclusion' could include predation or parasitism. Many authors have i m p l i c i t l y assumed that the term had a meaning that was every e f f e c t other than predation or parasitism (see review by Milne, 1961). In the l i t e r a t u r e the term 'competitive e f f e c t ' has been used as though i t were equivalent to 'predation e f f e c t ' , without saying p r e c i s e l y what happens. There does not e x i s t any acceptable general theory about the mechanism of competitive exclusion. But a single p r i n c i p l e about i t s supposed e f f e c t has been proposed. This i s the competitive exclusion p r i n c i p l e (Gause;'s Law, G r i n n e l l ' s Law are other names), which states that "complete competitors cannot coexist" (Hardin, I 9 6 0 ) . This study was conducted because of my i n t e r e s t i n the p o s s i b i l i t y of competitive exclusion of one species of animal by another i n a temporary environment. In previous studies of the e f f e c t s of competition between species of f r e s h -water animals (e.g. Frank, 1957) two fundamental phenomena have been neglected. These are that a species may be present 2 i n more than one independent form at the same time and i n the same un i t of space, and that reproductive time f o r fresh-water animals (and many others) i s usually not continuous. Besides the animal i t s e l f , the a l t e r n a t i v e form(s) i s usually an i n a c t i v e stage and i t i s t h i s form which e x i s t s during non-reproductive periods. S.uch a species e x i s t s at one point of time s o l e l y i n one form and has a f i n i t e length of time i n which to return to that form. This study was begun with the suspicion that t h i s d i s c o n t i n u i t y might allow the coexistence of some species of animals by preventing any competitive process from ever reaching a conclusion. Many animals, e s p e c i a l l y the non-vertebrates, have l i f e - h i s t o r y stages which perpetuate the species when the environment, i n which they are l i v i n g , becomes unfavourable. One reason f o r the change i n the f a v o u r a b i l i t y of the environment may be the presence of another species. To study t h i s problem I chose ostracods which l i v e i n puddles. The ostracod fauna of puddles i s noted for the large number of species often present (Hoff 1943, Barclay 1966). The puddle environment becomes unfavourable at c e r t a i n times by drying-up. During the dry-period the animals p e r s i s t as eggs and during the wet-period, eggs coexist with the animals. The eggs of some species of ostracod have shown a remarkable a b i l i t y to withstand long periods of des i c c a t i o n . Sharpe (1917) (c i t e d by Kesling 1951), t e l l s of Cypris sp. being obtained from dried mud 24 - 30 years o l d . The e f f e c t s of one species of ostracod upon the other which have been found are (see F i g . 1) to change: the number F i g u r e 1 I l l u s t r a t i o n o f t h e sequence o f e v e n t s w h i c h must o c c u r f o r eggs t o produce more eggs d u r i n g t h e p e r i o d when t h e p u d d l e i s wet. The amount o f t i m e w h i c h t h e y have t o do t h i s i s l i m i t e d , b u t c o n t i n u o u s , T^ i s the t i m e i n days a f t e r August 1 s t t h a t a group o f a n i m a l s h a t c h e s , T m i s t h e t i m e t h a t t h e y mature, i s t h e i n i t i a l number i n t h e group and N i s the number o f them wh i c h r e a c h m a t u r i t y . WATER ADDED ANIMALS Nh=Ne N, m EGGS STORED EGG-STORE. DECREMENTED EGGS EGG-STORE REPLENISHED i WATER . REMOVED TIME 4 of the species which hatch from eggs i n any increment of time (N,), the number of these which reach maturity (N ), the h ' m ' length of time required f o r them to reach maturity (T - ), the rate at which they lay eggs, and the length of time which they spend laying eggs. These e f f e c t s of the species upon one another may be influenced by the removal of water by evapora-t i o n or when the animals are k i l l e d by freezing of the puddle. Since each species begins a wet-period as a number of eggs, the e f f e c t s of another species w i l l be upon the number of eggs remaining at the end of t h i s period. During the wet-period the species may become extinct and r e - e s t a b l i s h a number of times i n a uni t of space, but only the state of the egg-populations at the time of drying-up need be considered. The exclusion which might occur i s of a species which had enough time to lay some eggs before the wet-period ended, but because of the other species i t f a i l e d to do so. The excluded species could have been present v/hen the puddle f i l l e d or could have entered the unit of space at some time during the period. Therefore, 'having enough time' depends upon the i n i t i a l state of the representative of the species. The time required could range from some maximum for an egg to zero for an animal already mature. The ostracods were studied i n the laboratory and i n t h e i r natural environment. Experiments were performed upon the animals under c o n t r o l l e d conditions, and the r e s u l t s tested upon the natural populations. The populations which were studied l i v e d i n a temporary pool i n a f i e l d located on the Jericho Army Base i n suburban Vancouver. The temperature of the water i n the puddle was recorded continuously and the populations examined at regular i n t e r v a l s . Frequent v i s i t s were made merely to record the water l e v e l , e s p e c i a l l y during the f a l l and spring. The puddle i s a long, t h i n , shallow body of water, barely distinguishable from the pasture i n which i t l i e s , occupying an old. truck tyre-track which runs down the grassy slope of the f i e l d (see Frontispiece) and which f i l l e d with water during the f a l l and dried up during the spring. Water from the surrounding land entered at the upper end and flowed gently through the grass occupying the rut and f i l l i n g the whole length of the depression. During the winter the puddle often froze. The ecology of freshwater ostracods i s v i r t u a l l y un-known, there being, to my knowledge, only two studies directed s o l e l y to the ostracods (Ferguson 1944, Hoff 1942) and only a small number of studies i n which the animals received more: than a passing mention (e.g. Barclay 1966). However, t h e i r taxonomy has not been neglected and many of the species described were obtained from packets of mud posted from many parts of the world to the taxonomist who merely had to add water to obtain his animals, which hatched from the r e s i s t a n t eggs (STars 1889, 1901). The freshwater ostracods of Canada-have been c l o s e l y studied by Dobbin (1942), T r e s s l e r (1957) and Delorme (1967, 1970 and others). This work has been stimulated by the importance of ostracod remains to paleontol-ogy and the stratigraphy of l a c u s t r i n e sediments. The most e x h a u s t i v e r e v i e w o f t h i s f i e l d has been w r i t t e n by Van Morkhoven ( 1 9 6 2 ) . O s t r a c o d s have r e c e i v e d a s m a l l amount o f a t t e n t i o n from g e n e t i c i s t s because o f t h e i r p a r t h e n o g e n e t i c mode o f r e p r o d u c t i o n and t h e i r p o l y p l o i d chromosomes. T h i s work has: been r e v i e w e d by Suomalainen ( 1 9 5 3 ) . S p e c i a t i o n of" o s t r a c o d s i n l a r g e l a k e s has a l s o been s t u d i e d and t h e work done i n Lake O h r i d has been r e v i e w e d by S t a n k o v i c ( 1 9 6 0 ) . A~n i m p o r t a n t s t u d y o f a c o n c h o s t r a c a n , ( L i m n a d i a s t a n l e y a n a ) l i v i n g i n some A u s t r a l i a n t e m p o r a r y p o o l s , has been done by B i s h o p ( 1 9 6 7 ) . 7 THE OSTRACODS STUDIED Along the length of the tyre-track puddle there occurred four species of ostracods, only tv/o of which were common and which were studied i n t e n s i v e l y . The two species are Cyprinotus c a r o l i n e n s i s Ferguson, 1958, and Herpetocypris reptans (Baird), 1835 (hereafter r e f e r r e d to by t h e i r generic names onl y ) . Both species reproduce parthenogenetically. No males of ei t h e r species were found during the study. The f i r s t species i s a small ostracod growing to 1.5 mm i n length, whose carapace valves are coloured a l i g h t orange; the second species grows to the greater length (2.0 mm) and i s coloured a dark green (see F i g . 2A). Kesling (1951) states that a l l species of ostracods pass through nine moults, but only f i v e were recorded f o r these species and no animals became mature before completing the f i n a l moult. The sizes of the valves of each species at and between each moult are shown i n F i g . 2B. Cyprinotus i s the shorter and f a t t e r and Herpetocypris the longer and thinner of the p a i r . The animals hatch from the eggs with only three p a i r s of appendages and during the f i r s t few moults gain one new pa i r with each change, u n t i l there are seven pairs (refer to Appendix I ) : these are a pa i r of foliaceous antennae used f o r swimming, a. second p a i r of antennae a s s i s t i n g i n the swimming but also used f o r feeding and grubbing i n the mud, a pa i r of stout mandibles, a p a i r of maxillae for rasping o f f the food p a r t i c l e s , the f i r s t p a i r of legs which are hardly noticeable but a.ssist i n feeding, a large second p a i r of forward-pointing legs used f o r locomotion Figure 2 The shape and changes i n shape of the valves of the two species of ostracods, between hatching from the egg and egg-laying, F i g , 2A (upper l e f t ) a Cyprinotus adult. The appendages shown are i n order from the anterior end, the f i r s t antennae, second antennae and second pair of legs, (lower r i g h t ) a Herpetocypris adult. The same appendages are shown. F i g . 2 B The changes i n depth and length of the valves (in mm) during the l i f e of the animals. The s t r a i g h t l i n e i s depth = length and the closed c i r c l e s are measurements fo r Cyprinotus and crosses are for Herpetocypris, D E P T H OF VALVE (mm) 9 over f l a t surfaces and grass sterns, and a t h i r d pair of legs of doubtful function. There i s also a pair of stout rods terminating the body which point forward and can be used to move the body when they are dug down into the mud. These furcae are not considered to be appendages equivalent i n o r i g i n to the others (Van Morkhoven 1962). During the summer when the tyre-track puddle i s dry, Cyprinotus and Herpetocypris are present i n the s o i l i n the form of eggs because the other l i f e - h i s t o r y stage cannot withstand long periods of des i c c a t i o n . At the time that the puddle i s covered with water each species has a store of eggs which w i l l hatch i f the puddle remains wet. Between t h i s time and when the puddle dries the species must produce more eggs to survive the next dry-period, since the addition of water i s a. s u f f i c i e n t stimulus to i n i t i a t e hatching of the eggs. The amount of time which they have to do t h i s each year i s not the same because the puddle can f i l l or dry-up at d i f f e r e n t times, depending upon the d i s t r i b u t i o n of r a i n f a l l and the a i r temperature during the f a l l and spring. Also each part of the puddle need not f i l l or dry-up at the same time as other parts, depending upon the supply of water. Furthermore, t h i s time between f i l l i n g and drying need not be continuous because in mid-winter the puddle may freeze, k i l l i n g a l l the animals. 10 PART I a) The hatching of old stored eggs In the f a l l ostracods are present i n the sediment of the puddle as eggs which have survived from the previous w i n t e r , The addition of water to the s o i l i s a s u f f i c i e n t stimulus- to i n i t i a t e the hatching of Cyprinotus a.nd Herpetocypris eggs. For a period of 6 - 7 days a f t e r the addition of water there i s no response from the eggs and then suddenly they begin to hatch, the rate of the process becoming large very quickly (Fig , 3). But not a l l of the eggs of each species hatch soon af t e r the water i s added: the process continues for a very long period of time afterwards. The manner i n which t h i s hatching rate changes i s d N M —-r- = - r • N dt where N i s the number of eggs hatching per day and i s given by N H e " r " T (1) t o where H i s the i n i t i a l rate of hatching and r i s the i n s t a n t -o aneous rate of change of the process. Cores of s o i l (radius = 0.95, depth = 10.0 cm) from the tyre-track puddle and others nearby (see map i n F i g . 37) were taken during the f a l l of 1967 and 1968. They were kept i n 8 oz„ jars and water was added to them at the same time that the puddles f i l l e d with water. These were examined at approx-imately weekly i n t e r v a l s and a l l the animals which had hatched during the period were removed. The hatching of the old eggs of both species, from s o i l cores taken from the puddle. P r i o r to the addition of water the s o i l had been dried, during the summer, for a period of approximately 3 months. The natural logarithm of the egg hatching rate (numbers per day) i s p l o t t e d against the time a f t e r the addition of water (The i n i t i a l values have been corrected for the delay i n beginning of hatching). E i g . 3A - the f i r s t hatch of Cyprinotus eggs, slope = - 0.033, c o r r e l a t i o n c o e f f i c i e n t = 0.874. F i g . 3B - the second hatch of Cyprinotus eggs, slope = - 0.039, c o r r e l a t i o n c o e f f i c i e n t = 0.83. F i g . 3C - the f i r s t hatch of Herpetocypris eggs, slope - 0.055, c o r r e l a t i o n c o e f f i c i e n t - 0.97. A TIME (DAYS) SINCE WATER WAS ADDED 12 The hatching of the eggs of both species from s o i l cores occurs i n two stages. There was an i n i t i a l large hatch which continued f o r longer than one hundred days a f t e r the addition of water and t h i s was followed by a second smaller hatch. The proportions of the t o t a l number of eggs which hatched during the two times was not the same for each species. The hatching of the f i r s t group of animals for Cyprinotus i s shown i n F i g . 3A. The decrease of the process i s c l e a r l y of the form i n equation (1) and the points f o r each hatch f a l l along the st r a i g h t l i n e InN = InH - r-T o where T i s the number of days since water was added. The slope of the l i n e (r) i s -0.03317. At 204 days a f t e r the addition of water there was a. sudden increase i n the number of Cyprinotus hatching from s o i l cores. This was the mean time before the s t a r t of the second hatch i n cores which were kept at ambient outdoor temperature throughout the winter. During the winter of 1967-68 a small number of cores from the same puddle were kept at room temperature (18 - 20°C) and the second hatch appeared a f t e r 120 days, suggesting that the timing of the hatch may be temperature-dependent. But since the annual mean temperature i n the Vancouver area i s remark-ably constant* and since no further information' 5 i s a v a i l a b l e * The annual mean a i r temperature i s usually very close to 50.0°F. See the "Monthly Record of Meterological Observa-tions i n Canada" prepared by the Canada Department of Transport and Meterological Branch. The UBC Main Library has the information i n annual volumes whose c a l l number i s QC,985,A21. Also r e f e r to Table XII. 13 I assume t h a t the t i m i n g of the second hatch w i l l be the same each year. The change of the r a t e of h a t c h i n g w i t h time of the second hatch i s apparently s i m i l a r to that of the f i r s t , F i g , 3B. The slope of t h i s l i n e i s -0.03882„ The hatching of Herpetocypris eggs occurred i n the same way as Cyprinotus but the r a t e of decrease of the process i s much more r a p i d w i t h the r e s u l t t h a t the hatching r a t e tended to zero much more q u i c k l y . Almost a l l of the l a r v a e appeared w i t h i n the f i r s t 40 days.. The instantaneous r a t e of change of the process i s 0.055, which i s the slope of the l i n e i n F i g . 3C. A s m a l l number of l a r v a e of t h i s species appeared at a time w e l l a f t e r equation (1) p r e d i c t s t h a t a l l of the f i r s t hatch of Herpetocypris has already appeared. These animals appeared i n s o i l samples at or a f t e r 130 days of sub-mergence at ambient temperature, but the number was so s m a l l as to make i m p o s s i b l e measuring the r a t e of change of the h a t c h i n g . But f o l l o w i n g the s i m i l a r i t y of the value of r f o r the two hatches of Cyprinotus t h i s r a t e i s assumed to be the same as t h a t of the f i r s t hatch f o r H e r p e t o c y p r i s . The two species d i f f e r e d , i n the p r o p o r t i o n of eggs hatc h i n g during the two p e r i o d s , being f o r C y p r i n o t u s , 0.621 and 0.379 (the means of 62 c o r e s ) , and f o r Herpetocypris 0.929 and 0.071 (means of 5 c o r e s ) . The eggs of both Herpetocypris and Cyprinotus which are present i n the s o i l during the summer are able to respond to the a d d i t i o n of water at any time during t h i s p e r i o d . During the summer of 1967 small samples of s o i l were removed 14 from the puddle and water was added. The time t i l l the appear-ance of the f i r s t animals o f each s p e c i e s i n each sample was r e c o r d e d and i s shown i n F i g . 4. The mean l e n g t h of the d e l a y i s a p proximately 6 days f o r C y p r i n o t u s and 7 days f o r H e r p e t o c y p r i s . There i s no tendency f o r the d e l a y between the a d d i t i o n of water and the h a t c h i n g of the o s t r a c o d s to change wit h i n c r e a s i n g l e n g t h of d e s i c c a t i o n . F o r these s p e c i e s t h e r e i s no r e s t r i c t i o n upon the time d u r i n g the d r y - p e r i o d at which they might hatch i f water was p r e s e n t . The i n i t i a l s t o r e o f eggs o f each s p e c i e s p r e s e n t at the time of submergence w i l l decrease i n two stages so t h a t the t o t a l number (H) l e f t at any time l a t e r (T) w i l l be g i v e n by a combination o f two e q u a t i o n s . F o r C y p r i n o t u s t h i s i s H T = E - c - ^ U - e - - 0 3 3 1 7 ' T ) f Q r T ^ 2 0 4 H T = E . C l . (1 - e - * 0 3 3 1 7 " T ) + E . c 2 - ( 1 - e * " - 0 3 8 8 2 ' T ) f o r T ^ 2 0 4 ( I A ) where E i s the t o t a l i n i t i a l number of eggs, c-^  and c 2 are the p r o p o r t i o n s of the eggs which w i l l h a t c h d u r i n g the f i r s t and second p e r i o d s and T the number of days s i n c e water was added. The shape of t h i s f u n c t i o n i s shown i n F i g . 5 f o r both C y p r i n o t u s and H e r p e t o c y p r i s . The number of o l d eggs i n any u n i t o f space h a t c h i n g i n any increment of time, A T w i l l be NH " N e T - AT " N e T where the r i g h t - h a n d s i d e i s o b t a i n e d by s u b s t i t u t i n g from the p r e v i o u s e q u a t i o n . F i g u r e 4 The r e l a t i o n s h i p between t h e t i m e submerged t i l l t h e appearance o f t h e l a r v a e and t h e number' o f days t h a t t h e s o i l had been d r i e d . C y p r i n o t u s and H e r p e t o c y p r i s h a t c h i n g from s o i l - c o r e s t a k e n from t h e t y r e - t r a c k p u d d l e d u r i n g t h e summer o f 1967. F o r C y p r i n o t u s t h e mean d e l a y i s 6 days ( F i g . 4A) and f o r H e r p e t o c y p r i s ( F i g . 4B)~', 7 days. APPEARED 15 -A ARVAE 10 -MEAN • 5.9 o o n n,. o 0 0 0 o 0 0 0 o o 0 0 FIRST L 5- o o 0 o o 00 TILL i 1 1 1 1 B DAYS 15-°F 10 -or UJ CD MEAN • 6.6 X XXX X X X X S Z 5-X X X X XX X X 20 40 60 l 80 1 1 -100 120 1 140 i • • •  —1 160 NUMBER OF DAYS OF DESICCATION F i g u r e 5 Comparison o f t h e way i n wh i c h t h e s t o r e o f eggs o f each s p e c i e s , p r e s e n t i n t h e f a l l , i s e r o d e d as t h e t i m e submerged i n c r e a s e s . The i n s t a n t a n e o u s r a t e o f d e c r e a s e o f t h e number o f C y p r i n o t u s (C) eggs i s 0.0 332 ( f i r s t ) and 0.0 39 (secondTT F o r b o t h groups o f H e r p e t o c y p r i s (H) eggs t h e r a t e i s 0.055. TIME (DAYS) SINCE WATER WAS ADDED 17 Summary 1, D u r i n g t h e d r y - p e r i o d t h e eggs o f b o t h s p e c i e s can h a t c h at any t i m e a f t e r t h e a d d i t i o n o f water„ 2, There i s a d e l a y o f 6 - 7 days a f t e r t h e a d d i t i o n o f w a t e r t i l l t h e eggs b e g i n t o h a t c h . T h i s d e l a y does not change w i t h t h e l e n g t h o f time t h a t t h e eggs - have been d e s i c c a t e d , 3. The eggs h a t c h i n two d i s t i n c t groups each a p p e a r i n g o v e r a l o n g p e r i o d o f t i m e . The r a t e a t whi c h t h e y h a t c h de-c r e a s e s i n a n e g a t i v e e x p o n e n t i a l manner w i t h t i m e s i n c e t h e s t a r t of h a t c h i n g , 4. The p r o p o r t i o n s o f C y p r i n o t u s eggs i n each group are 0,621 and 0,379 and o f H e r p e t o c y p r i s eggs 0,929 and 0,071, The second group o f C y p r i n o t u s eggs b e g i n s t o h a t c h 2 04 days a f t e r t h e a d d i t i o n o f w a t e r ; i n H e r p e t o c y p r i s t h e d e l a y i s o n l y 130 d a y s , b) M o r t a l i t y o f r e c r u i t s Of t h o s e a n i m a l s w h i c h h a t c h i n a u n i t o f t i m e i n t o a u n i t a r e a o f the p u d d l e n o t a l l w i l l s u r v i v e t o l a y eggs a t some t i m e l a t e r . Some of t h e a n i m a l s w i l l d i e w i t h i n t h e a r e a and o t h e r s w i l l be l o s t as a r e s u l t o f t h e i r moving o u t o f the a r e a . Of t h e a n i m a l s w h i c h d i e w i t h i n t h e a r e a two p o s s i b l e c a u s e s have been t e s t e d t o see whether t h e y can ac c o u n t f o r t h e l o s s . These a r e t h a t p a r t o f t h e l o s s i s a t t r i b u t a b l e t o p r e d a t i o n by c y c l o p o i d s , which l i v e t h r o u g h o u t t h e p u d d l e , and t h a t p a r t o f i t i s t h e r e s u l t o f a p r o c e s s which i s d e n s i t y 18 dependent and which r e s u l t s i n an i n c r e a s e i n t h e m o r t a l i t y r a t e as t h e numbers p r e s e n t i n c r e a s e . The c y c l o p o i d l i v i n g i n t h e p u d d l e has been i d e n t i f i e d a s C y c l o p s b i s e t o s u s Rehberg 1863, and t h e a d u l t s grow up t o 1,0 mm i n l e n g t h . Both i n t h e p u d d l e s and i n l a b o r a t o r y d i s h e s t h e s e a n i m a l s were o b s e r v e d g r a s p i n g dead o r n e a r l y - d e a d s m a l l o s t r a c o d s l e s s t h a n 0,5 mm i n l e n g t h , and l a r g e r dead a n i m a l s such as o l i g o c h a e t e s , c h i r o n o m i d l a r v a e , h a r p a c t i c o i d s and o t h e r c y c l o p o i d s . From t h e s e o b s e r v a t i o n s i t was not p o s s i b l e t o t e l l whether t h e c y c l o p o i d s had k i l l e d t h e a n i m a l s o r had f o u n d them a l r e a d y dead. T h e r e f o r e some i n i t i a l e x p e r i m e n t s 2 were p e r f o r m e d i n s m a l l p e t r i d i s h e s o f a r e a 20 cm , w i t h 3 w a t e r 0,7 cm deep (volume = 14 cm ) and w i t h a. l a y e r o f s e d i -ment on t h e bottom. F i v e s m a l l C y p r i n o t u s and one c y c l o p o i d were p l a c e d i n each d i s h (6 r e p l i c a t e s ) and were l e f t f o r 24 h o u r s a t room t e m p e r a t u r e . A f t e r t h i s t i m e no l a r v a e were f o u n d which were damaged i n any way. The e x p e r i m e n t was r e p e a t e d w i t h t h e sediment removed b u t t h e r e s u l t s were t h e same. I n o r d e r t o i n c r e a s e t h e chances o f c o n t a c t between t h e c y c l o p o i d and t h e o s t r a c o d s t h e numbers were i n c r e a s e d t o 10, 20, 30 and 40 per d i s h (3 r e p l i c a t e s o f each d e n s i t y ) b u t t h e a n i m a l s were s t i l l unharmed. Then t h e number of c y c l o p o i d s was i n c r e a s e d t o 3 p e r d i s h under t h e same c o n d i t i o n s w i t h o u t any o s t r a c o d s b e i n g t a k e n . Next t h e volume o f w a t e r h o l d i n g t h e a n i m a l s was r e d u c e d t o 1 ml i n t h e c e n t r e o f a p e t r i d i s h and s t i l l a f t e r a p e r i o d o f 24 hou r s C y p r i n o t u s young remained unharmed i n t h e p r e s e n c e o f a s i n g l e c y c l o p o i d a d u l t (6 r e p l i -1 9 c a t e s ) . F i n a l l y newly h a t c h e d young which had n o t y e t m o u l t e d f o r t h e f i r s t t i m e were p l a c e d w i t h t h e c y c l o p o i d , 5 young per' drop o f water and i n 3 o f t h e 6 r e p l i c a t e s some o f t h e l a r v a e were e a t e n . The same s e r i e s o f e x p e r i m e n t s was pe r f o r m e d w i t h H e r p e t o c y p r i s young w i t h t h e same r e s u l t s . The o n l y c o n d i t i o n s under w h i c h o s t r a c o d s were t a k e n were t h o s e o f c l o s e c o n f i n e -ment and v e r y young a n i m a l s . O b s e r v a t i o n s on t h e young o f b o t h s p e c i e s h a t c h i n g from eggs i s t h e l a b o r a t o r y show t h a t d u r i n g t h e p e r i o d between emergence and t h e second m o u l t , d u r i n g which t h e o s t r a c o d s do n o t f e e d , t h e y r e m a i n c l o s e t o th e s i t e a t wh i c h t h e eggs were l a i d , which c o u l d be i n s i d e an o l d g r a s s stem o r c u r l e d l e a f o r on sand g r a i n s i n t h e s e d i m e n t . At t h i s t i m e t h e y w ould, t h e r e f o r e , be u n a v a i l a b l e t o c y c l o p o i d s . T h e r e f o r e i t i s c o n c l u d e d t h a t C y c l o p s b i s e t o s u s c o u l d n o t c o n t r i b u t e t o t h e m o r t a l i t y of t h e young b u t t h a t i t may d i s p o s e o f a n i m a l s d y i n g from o t h e r c a u s e s . The e f f e c t upon t h e m o r t a l i t y o f i n c r e a s i n g t h e numbers o f o s t r a c o d s p r e s e n t was i n v e s t i g a t e d f o r b o t h s p e c i e s . S m a l l p l a s t i c p e t r i - d i s h e s were f i l l e d w i t h p r e p a r e d mud*, f r e e o f o s t r a c o d s , t o a depth o f 0,5 cm and t o each d i s h was r added some members o f t h e n a t u r a l f a u n a o f t h e p u d d l e ( c y c l o -p o i d s and h a r p a c t i c o i d s ) and 2 o r 3 p i e c e s o f d r i e d g r a s s stem * P r e p a r e d mud was used t o f i l l t h e d i s h e s because t h e n a t u r a l mud c o u l d c o n t a i n eggs o f t h e o s t r a c o d s . S u r f a c e s o i l was t a k e n from t h e l a n d i m m e d i a t e l y a l o n g s i d e t h e p u d d l e and was s i e v e d t o remove t h e s m a l l p e b b l e s , g r a s s r o o t s and stems and s t i c k s . The r e m a i n i n g mud. was t h e n p l a c e d i n l a r g e d i s h e s , under w a t e r and ' i n n o c u l a t e d ' w i t h water f r o m " t h e p u d d l e t o e s t a b l i s h p o p u l a t i o n s o f t h e a l g a e , p r o t o z o a and b a c t e r i a t h a t n o r m a l l y o c c u r i n t h e mud. These were l e f t f o r a p e r i o d o f 4 weeks, p r i o r t o t h e e x p e r i m e n t . 20 i n an attempt to i m i t a t e the n a t u r a l s i t u a t i o n . To each d i s h was added a number of young ostracods of one or other or both species and i t was then covered by a piece of b o l t i n g s i l k (mesh s i z e = .0029 i n c h e s ) , fastened to the d i s h by a t i g h t rubber band. These dishes were then placed i n a l a r g e , shallow p l a s t i c d i s h (depth = 5 cm) which contained both the mud and n a t u r a l fauna of the puddle and clumps of grass. Each l a r g e d i s h h e l d some 30 p e t r i dishes and they were placed i n an enclosure exposed to the n a t u r a l l i g h t and at ambient temperature. By t h i s means f r e e - f l o w of water between the s m a l l e r u n i t s and the a r t i f i c i a l puddle was allowed but the experimental animals remained separate from the ' f r e e ' p a r t of the p o p u l a t i o n i n the l a r g e d i s h . Large numbers of animals were r e q u i r e d f o r the ex-periment and so i n order to preserve the s t a t e of the TT puddle they were obtained from another puddle nearby. This puddle was very s i m i l a r i n shape to the TT puddle and had the same fauna. Because of i t s l a r g e r s i z e l a r g e numbers of animals c o u l d be c o l l e c t e d from i t . The animals were c o l l e c t e d f o r the experiment w i t h i n the f i r s t s i x weeks a f t e r f i l l i n g when there were p l e n t y present, and were used w i t h i n a few days of c o l l e c t i o n . The p e t r i dishes were stocked w i t h animals over a p e r i o d of 2 weeks and a f t e r an i n t e r v a l of 49 days the numbers l e f t were recorded over a s i m i l a r i n t e r v a l . In the dishes to which Cyprinotus animals had been added the p r o p o r t i o n of the i n i t i a l numbers added th a t were a l i v e a f t e r the i n t e r v a l of time, decreased as the i n i t i a l 21 n u m b e r s i n c r e a s e d . T h e d e c r e a s e w a s l i n e a r l y r e l a t e d t o t h e i n i t i a l i n p u t s o t h a t t h e p r o p o r t i o n a l i v e w a s g i v e n b y PA = C - B • N (2) 2 w h e r e N i s t h e i n i t i a l n u m b e r p e r cm ( F i g , 6 ) . V a l u e s o f C a n d B w e r e o b t a i n e d b y r e g r e s s i o n . A s t h e v a l u e o f N d e c r e a s e s t h e v a l u e o f PA s h o u l d a p p r o a c h t h e v a l u e o f C w h i c h s h o u l d b e 1,0, T h e v a l u e o b t a i n e d f o r t h e i n t e r c e p t w a s 1,035 w h i c h w a s n o t s i g n i f i c a n t l y d i f f e r e n t f r o m 1,0 a n d t h e s l o p e o f t h e l i n e i s 0 , 0 8 8 92. T h e m o r t a l i t y r a t e d u r i n g t h e e x p e r i m e n t a l p e r i o d a t e a c h o f t h e d e n s i t i e s i s g i v e n b y MR = N_Z*LPA t w h e r e A t = 49 d a y s . T h e i n s t a n t a n e o u s m o r t a l i t y r a t e i s I n N - l n ( N . P A ) I M R 2 l n M - l n ( N - B « N ) = r - I n (1 - B.N)«D t h e v a l u e o f B b e i n g t h e i n c r e a s e i n IMR p e r o s t r a c o d p r e s e n t a n d w h e r e D = . D u r i n g a n y i n t e r v a l o f t i m e t h e r e l a t i o n -s h i p b e t w e e n t h e n u m b e r s p r e s e n t a t t h e end. o f t h e i n t e r v a l a n d t h e n u m b e r s p r e s e n t a t t h e b e g i n n i n g o f t h e i n t e r v a l w i l l b e N T = NT-I " NT-I ( 1 ~ B , N T _ i } ' D a n d r e m o v i n g b r a c k e t s N T = N T _ 1 - D - N ^ - B . D - N , ^ 2 The r e l a t i o n s h i p between t h e p r o p o r t i o n o f t h e i n i t i a l numbers a l i v e a f t e r 49 days and t h e i n i t i a l d e n s i t y , f o r C y p r i n o t u s a l o n e . The s l o p e o f t h e l i n e i s 0.0889, There a r e t h r e e r e p l i c a t e s f o r each d e n s i t y and each d a t a v a l u e i s g i v e n . I 2 3 4 5 6 7 8 INITIAL NUMBERS (NO PER cm 2 23 T h i s r e l a t i o n s h i p has been t e s t e d f o r t h e p o p u l a t i o n o f C y p r i n o t u s i n t h e p u d d l e . I n t h e n a t u r a l p o p u l a t i o n r e c r u i t -ment f r o m t h e egg s t o r e c o n t i n u e s and so i n each i n t e r v a l o f t i m e t h e r e w i l l be an a d d i t i o n t o t h e number which has a l r e a d y been shown t o be p r o p o r t i o n a l t o t h e i n i t i a l number o f eggs and t h e number o f days s i n c e t h e w a t e r was added. The number o f C y p r i n o t u s added d u r i n g a day soon a f t e r f i l l i n g w i l l be H e o w i t h R = 0.03317 and t h e change i n number d u r i n g a day w i l l be N T " N T - 1 " H o e * R ' T " °' NT-1 " K ' N T - 1 2 where K = B«D. As t h e i n t e r v a l becomes s m a l l e r t h e d e r i v a t i v e w i l l be ^ = H e - R * T - D.N - K.N 2 (3) d t o I n o r d e r t o o b t a i n a v a l u e o f N f o r some ti m e ( t ) i t i s n e c e s s a r y t o i n t e g r a t e t h i s e q u a t i o n from T = 0 t o T = t . S i n c e t h e exponent o f a term c o n t a i n i n g N i s g r e a t e r t h a n 1 on t h e r i g h t - h a n d s i d e an e x p l i c i t s o l u t i o n f o r t h e i n t e g r a l i s no t e a s i l y o b t a i n e d . Such an e q u a t i o n i s o f t h e form o f a R i c c a t i - e q u a t i o n ( D a v i s 1962, p. 59) and so an e x p l i c i t s o l u -t i o n i s p o s s i b l e b u t t h e amount o f m a n i p u l a t i o n n e c e s s a r y t o o b t a i n i t would be v e r y g r e a t and so t h i s was n o t a t t e m p t e d . I n s t e a d a p p r o x i m a t e v a l u e s o f N f o r v a r i o u s v a l u e s o f t were o b t a i n e d by i n t e g r a t i n g t h e e q u a t i o n n u m e r i c a l l y u s i n g the IBM s u b r o u t i n e RKGS. The g e n e r a l shape o f N as a f u n c t i o n o f T i s shown i n P i g . 7. I n i t i a l l y t h e numbers p r e s e n t s h o u l d F i g u r e 7 The shape o f t h e r e l a t i o n s h i p between the numbers p r e s e n t and t h e time a f t e r t h e a d d i t i o n o f water ( T ) , f o r b o t h species". V a l u e s o f N a t i n t e r v a l s o f T were o b t a i n e d by n u m e r i c a l i n t e g r a t i o n of- e q u a t i o n s (3) f o r C y p r i n o t u s (C) and (4) f o r H e r p e t o c y p r i s ( H ) . The dashed l i n e s are t h e number o f days a f t e r f i l l i n g t h a t the p u d d l e - p o p u l a t i o n s were sampled d u r i n g t h e 1968-69 w i n t e r . NUMBER OF ANIMALS PER cm 2 N 01 * OI 0 ) 25 i n c r e a s e v e r y r a p i d l y r e a c h i n g a peak soon a f t e r h a t c h i n g has begun and t h e n d e c r e a s i n g a t an i n c r e a s i n g l y s l o w e r r a t e as t h e r e c r u i t m e n t becomes s m a l l e r and s m a l l e r and l e s s t h a n t h e m o r t a l i t y . T h i s r e l a t i o n s h i p between N and T ha.s been t e s t e d i n t h e p u d d l e by c o m p a r i n g t h e e x p e c t e d and o b s e r v e d numbers o f C y p r i n o t u s p r e s e n t a t v a r i o u s p o i n t s i n t h e p u d d l e on two days-a f t e r t h e p u d d l e f i l l e d . D u r i n g t h e w i n t e r o f 1968-69 C y p r i n o t u s was a l m o s t t h e s o l e o c c u p a n t o f t h e n o r t h end o f t h e p u d d l e up t o 17 m from t h e s o u t h end. S o i l c o r e s had been t a k e n from t h e p u d d l e a t 1 m i n t e r v a l s (2 samples p e r p o i n t ) a l o n g i t s l e n g t h and so the i n p u t o f C y p r i n o t u s a n i m a l s from s t o r e d eggs was known. The e x p e c t e d number f o r t h e s e p o i n t s i n t h e p u d d l e was o b t a i n e d by i n t e g r a t i n g e q u a t i o n (3) n u m e r i c -a l l y u s i n g t h e p a r a m e t e r v a l u e s o b t a i n e d from t h e e x p e r i m e n t and where H Q i s g i v e n by . H q = -E • 0.621 • 0.03317 and : .E i s t h e t o t a l e g g - i n p u t f o r C y p r i n o t u s f o r t h e whole w i n t e r . 'The e x p e c t e d v a l u e s o f M were o b t a i n e d f o r T = 38 and T = 78 days a f t e r f i l l i n g . These a r e compared w i t h t h e o b s e r v e d v a l u e s o b t a i n e d by s a m p l i n g t h e p u d d l e p o p u l a t i o n * on t h e s e * The samples of a n i m a l s were t a k e n from t h e p u d d l e u s i n g a' s m a l l c y l i n d e r o f r a d i u s 1.1 cm and l e n g t h 18 cm and a t u b e w i t h a l a r g e r u b b e r - b u l b on t h e end. The c y l i n d e r was pushed i n t o t h e s o f t s u r f a c e sediment as f a r as i t would go, e n c l o s i n g an a r e a o f mud and w a t e r . S i n c e t h e r e was n o t enough wa t e r p r e s e n t t o a l l o w r e m o v a l o f the mud and a n i m a l s t h e c y l i n d e r was f i l l e d w i t h water w h i c h was t h e n s t i r r e d up t o put t h e s e i n t o s u s p e n s i o n . A l l t h e l i q u i d was t h e n r e -moved from t h e c y l i n d e r u s i n g t h e r u b b e r - b u l b e d s u c t i o n d e v i c e . 26 days i n F i g . 8. At both times the expected and the observed agree q u i t e c l o s e l y but the expected r e s u l t s are c o n s i s t e n t l y h i g h e r f o r most p o i n t s . There i s very l i t t l e d i f f e r e n c e at e i t h e r end of the area of the puddle c o n s i d e r e d , but i n the r e g i o n between 18 m and 24 tn from the south end the o v e r -e s t i m a t i o n i s l a r g e s t . The m o r t a l i t y of H e r p e t o c y p r i s animals i n d i s h e s by themselves was r e l a t e d to the i n i t i a l number i n the same way as f o r C y p r i n o t u s ( e q u a t i o n ( 2 ) ) . The i n t e r c e p t on the y - a x i s o b t a i n e d by r e g r e s s i o n was 1.006 and the s l o p e of the l i n e was 0.0592, F i g . 9. The s l o p e i s somewhat l e s s than t h a t f o r C y p r i n o t u s , showing t h a t the e f f e c t of each i n d i v i d u a l H e r p e t o c y p r i s upon the m o r t a l i t y of the p o p u l a t i o n i s l e s s than t h a t f o r C y p r i n o t u s . The complement t o e q u a t i o n (3) f o r H e r p e t o c y p r i s i s ~ : = H e o U O D - ,0204-N - ,001215'N (4) dt o U s i n q these v a l u e s and v a l u e s f o r H o b t a i n e d i n a s i m i l a r 3 o manner from s o i l - c o r e s , v a l u e s o f N were o b t a i n e d by n u m e r i c a l i n t e g r a t i o n f o r v a r i o u s p o i n t s i n the puddle where H e r p e t o c y p r i s was p r e s e n t . E x c e l l e n t agreement was o b t a i n e d f o r the ex-p e c t e d and observed v a l u e s , F i g . 10, at the times 46 and 60 days a f t e r f i l l i n g . At the f i r s t time the model tends to u n d e r e s t i m a t e the d e n s i t y but l a t e r the correspondence i s c l o s e r . F i g u r e 8 T e s t of the m o r t a l i t y model f o r C y p r i n o t u s by comparing the expected and observed numbers at s e l e c t e d p o i n t s along the l e n g t h o f the puddle a f t e r 38 ( F i g . 8A) and 78 ( F i g . 8B) days o f submergence. The i n p u t s of eggs to g i v e the expected numbers o f animals, were o b t a i n e d from the numbers of animals h a t c h i n g from sample s o i l -c o r e s taken at each p o i n t i n the puddle. (Observed v a l u e s - c l o s e d c i r c l e s and s o l i d l i n e s ; expected v a l u e s - open c i r c l e s and dashed l i n e s ) . DISTANCE (m) FROM SOUTH END OF PUDDLE F i q u r e 9 The r e l a t i o n s h i p between t h e p r o p o r t i o n o f t h e i n i t i a l numbers a l i v e a f t e r 49 days and t h e i n i t i a l d e n s i t y , f o r H e r p e t o c y p r i s a l o n e . The s l o p e o f t h e l i n e i s 0.059, The p r o p o r t i o n a l i v e i n each o f t h e t h r e e r e p l i c a t e s i s shown, PROPORTION ALIVE F i g u r e 10 The t e s t o f t h e m o r t a l i t y model f o r H e r p e t o c y p r i s i n the p u d d l e . The e x p e c t e d ( s q u a r e s ) and o b s e r v e d ( c r o s s e s ) numbers a t t h e p o i n t s a t which t h e s p e c i e s was p r e s e n t and t h e e g g - i n p u t a t t h a t p o i n t was known, a r e g i v e n . The t i m e s a f t e r f i l l i n g a r e 46 days ( F i g . 10A) and 60 days ( F i g . 10B). E u ce UJ CL CO CE Ul CD 5 •=> z 2H D I S T A N C E (m) F R O M S O U T H E N D O F P U D D L E 30 When both the species are grown together the mortality-increases i n a s i m i l a r way to that for the single-species, as the i n i t i a l density increases. As the number of Cyprinotus increases the proportion of Herpetocypris a l i v e i s less than that for the species by i t s e l f at the same density, F i g . 11A and so the addition of Cyprinotus c l e a r l y had some e f f e c t upon t h i s species. But the e f f e c t i s the same as i f the extra i n d i v i d u a l s added had belonged to Herpetocypris i t s e l f since the intercept and slope, of the l i n e PA = C -B(NH + NC) are not s i g n i f i c a n t l y d i f f e r e n t from those of the species by i t s e l f , F i g . 11B. The values obtained were 1.043 (alone, 1.006) and 0.05973 (alone, 0.05952) r e s p e c t i v e l y . Where PA i s i n t h i s case the proportion of the i n i t i a l number of Herpetocypris a l i v e and NH + NC the t o t a l number added. In any i n t e r v a l of time the mortality of Herpetocypris w i l l be proportional to the : t o t a l number of the two species, NT, and equation (4) w i l l become = H e ~ ° 0 5 5 ' T - . 02 04 * NT - .001215'NT2 dt o But the e f f e c t of Herpetocypris animals upon the mortality of Cyprinotus i s not the same as the. e f f e c t of Cyprinotus upon i t s e l f . The proportion a l i v e i s s u b s t a n t i a l l y less when Herpetocypris i s added than .when i t i s alone ( F i g . 11C). However, the square-root of the proportion of Cyprinotus a l i v e i s given by JPA. = C - B ' NT (5 ) F i g u r e 11 The e f f e c t o f e a c h s p e c i e s u p o n t h e m o r t a l i t y o f t h e o t h e r , when g r o w n i n s m a l l p e t r i d i s h e s . F i g . 11A - t h e p r o p o r t i o n o f H e r p e t o c y p r i s a l i v e when g r o w n w i t h a r a n g e o f d e n s i t i e s o f C y p r i n o t u s , i n r e l a t i o n t o t h e i n i t i a l d e n s i t y o f H e r p e t o c y p r i s a l o n e . The l i n e r e l a t i n g t h e s e q u a n t i t i e s when t h e s p e c i e s i s g r o w n a l o n e ( s e e F i g . 9) i s a l s o shown (NC = 0 ) . F i g . 11B - t h e same d a t a as i n F i g . 11A, p l o t t e d a g a i n s t t h e t o t a l i n i t i a l d e n s i t y . The c o r r e l a t i o n c o e f f i c i e n t f o r t h e l i n e shown i s 0 . 6 6 . E i g . 1 1 C - t h e p r o p o r t i o n o f C y p r i n o t u s a l i v e when g r o w n w i t h H e r p e t o c y p r i s a t a r a n g e o f d e n s i t i e s , a n d t h e i n i t i a l d e n s i t y o f t h e s p e c i e s i t s e l f . The l i n e f o r t h e r e l a t i o n s h i p when t h e s p e c i e s i s a l o n e i s a l s o shown (NH = 0 ) . E i g . 11D - t h e s q u a r e - r o o t o f t h e p r o p o r t i o n o f C y p r i n o t u s a l i v e p l o t t e d a g a i n s t t h e t o t a l i n i t i a l n u m b ers o f b o t h s p e c i e s . The c o r r e l a t i o n c o e f f i c i e n t i s 0.82„ 32 which i s l i n e a r although the values of C and B are larger than for Cyprinotus alone, F i g , 11D0 These are 1,12 and 0.1018 and by rearranging the previous equation we have PA = C 2 - 2-C-B-NT + (B•NT) 2 The e f f e c t of the addition of Herpetocypris i s small u n t i l a 2 density of about 3 per cm i s reached when i t becomes quite large. In the presence of Herpetocypris equation (3) for Cyprinotus becomes = H e o U J J X ' 1 _ O0256-NT - ,0047-NT - .00021-NT dt o The shape of the r e l a t i o n s h i p between N and T f o r each species by i t s e l f f o r a standard input of eggs i s shown i n F i g . 7. The number of Herpetocypris should increase most r a p i d l y at f i r s t because of the greater rate of recruitment but then they begin to decrease almost as r a p i d l y as the r e c r u i t -ment quickly tends to zero. Cyprinotus,on the other hand,is i n i t i a l l y less abundant but i t s continued recruitment f o r a. longer period should cause i t to eventually have large numbers present„ After both species have reached the mature size and begun to lay eggs, there i s a r a d i c a l change i n the rate at which the proportion of these animals a l i v e changes with time. During the i n i t i a l part of the post-maturation period the decrease i s very small and then i t accelerates f o r a short period and f i n a l l y decreases with a very small proportion of the animals l i v i n g long a f t e r the majority have died. The 3 3 p r o p o r t i o n o f mature a n i m a l s r e m a i n i n g a l i v e as t h e number o f days s i n c e t h e y matured i n c r e a s e s , d e c r e a s e s i n a sigmoid, f a s h i o n . T h e r e f o r e t h e p r o p o r t i o n a l i v e (PA) a t any t i m e (T) a f t e r m a t u r a t i o n w i l l be g i v e n by V a l u e s o f c and s were o b t a i n e d by r e g r e s s i o n o f the d a t a f o r PA, t r a n s f o r m e d so t h a t a l i n e a r e q u a t i o n r e s u l t e d - I n ( ~ - 1) = C - S»T and so t h e v a l u e o f C s h o u l d be p o s i t i v e and t h e s l o p e o f t h e l i n e , S, n e g a t i v e . Such a r e l a t i o n s h i p g i v e s a v e r y good d e s -c r i p t i o n o f t h e o b s e r v a t i o n s , F i g , 12, A f t e r m a t u r i n g , t h e H e r p e t o c y p r i s a n i m a l s a r e l o n g e r - l i v e d t h a n a r e C y p r i n o t u s , The r a t e a t w h i c h t h e d e c r e a s e o c c u r s , S, i s 0.03856 f o r H e r p e t o c y p r i s and 0,05 f o r C y p r i n o t u s so t h a t i t i s 12 0 days u n t i l h a l f t h e i n i t i a l number of t h e f i r s t s p e c i e s have d i e d b u t o n l y 90 days f o r t h e s econd. The p r o p o r t i o n s o f t h e mature p o p u l a t i o n s d y i n g e i t h e r b e f o r e o r a f t e r t h e s e t i m e s i s a p p a r e n t l y n o r m a l l y d i s t r i b u t e d because o f t h e symmetry o f t h i s f u n c t i o n . The mean l e n g t h o f l i f e o f C y p r i n o t u s was v e r y much l e s s t h a n t h a t o f H e r p e t o c y p r i s because t h e y r e a c h e d m a t u r i t y much s o o n e r . U s u a l l y t h e l a t t e r s p e c i e s w i l l l i v e about h a l f as l o n g a g a i n as t h e f o r m e r . I t i s not known whether t h e r a t e o f d e c r e a s e o f t h e p r o p o r t i o n a l i v e a f t e r m a t u r i t y (S) i s dependent upon t h e number wh i c h r e a c h m a t u r i t y o r t h e number o f a n i m a l s p r e s e n t . The o n l y change i n numbers o f a n i m a l s p r e s e n t i n t h e e x p e r i m e n t a l p o p u l a t i o n s r e s u l t e d F i g u r e 12 The manner i n w h i c h t h e mature a n i m a l s o f b o t h s p e c i e s d i e o f f . The t r a n s f o r m e d p r o p o r t i o n o f t h e a n i m a l s a l i v e a t m a t u r a t i o n i s p l o t t e d a g a i n s t t h e l e n g t h o f t i m e s i n c e m a t u r a t i o n (H - H e r p e t o c y p r i s , C - C y p r i n o t u s ) . TIME (DAYS) SINCE MATURATION (T-TM) 35 from d e a t h o f some o f t h e i n i t i a l members. Some a n i m a l s d i e a f t e r l a y i n g o n l y a. few eggs b u t some c o n t i n u e t o l a y eggs f o r a l o n g t i m e a f t e r . T h i s does not seem t o r e s u l t from t h e a n i m a l s r u n n i n g o u t o f eggs s i n c e a l l t h e dead a n i m a l s f rom t h e s e p o p u l a t i o n s t h a t were examined s t i l l had from 2 - 2 5 eggs s t o r e d i n t h e abdomen, a p p a r e n t l y r e a d y f o r r e l e a s e and t h e i r o v a r i e s c o n t a i n e d eggs not y e t s u p p l i e d w i t h y o l k and t h e h a r d o u t e r c o v e r i n g . Summary 1. The c y c l o p o i d C y c l o p s b i s e t o s u s was not found t o c o n t r i b u t e t o t h e m o r t a l i t y o f e i t h e r s p e c i e s o f o s t r a c o d . 2. The e x p e c t e d numbers o f each s p e c i e s p r e s e n t i n t h e p u d d l e soon a f t e r f i l l i n g g i v e n by a s i m p l e model i n which t h e m o r t a l i t y i n any i n t e r v a l o f t i m e was' r e l a t e d o n l y t o the numbers p r e s e n t were c l o s e t o t h e o b s e r v e d numbers. The m o r t a l i t y r a t e o f H e r p e t o c y p r i s i s s m a l l e r t h a n t h a t f o r C y p r i n o t u s when each s p e c i e s i s a l o n e , 3. The e f f e c t o f C y p r i n o t u s upon t h e m o r t a l i t y o f H e r p e t o c y p r i s i s t h e same as i f t h e a n i m a l s b e l o n g e d t o t h a t s p e c i e s . There i s an a d d i t i o n a l e f f e c t o f H e r p e t o c y p r i s upon t h e m o r t a l i t y o f C y p r i n o t u s . 4. The p r o p o r t i o n o f a n i m a l s o f b o t h s p e c i e s which r e a c h m a t u r i t y d e c r e a s e s a f t e r t h i s t ime i n a s i g m o i d manner. The r a t e o f d e c r e a s e i s g r e a t e r f o r C y p r i n o t u s t h a n f o r H e r p e t o c y p r i s . 36 c) The amount of time required, to reach m a t u r i t y The amount of time r e q u i r e d to reach m a t u r i t y i s not the same f o r both s p e c i e s . Cyprinotus animals r e q u i r e much l e s s time than do Herpetocypris animals hatching at the same time. Furthermore the amount of time i s l e s s v/hen the temperature i s higher than when i t i s lower. S t a r t i n g at d i f f e r e n t times during the w i n t e r , newly hatched Cyprinotus animals were grown on prepared mud i n small enclosed p e t r i d ishes beginning with a small number (5 per d i s h ) . These were grown at ambient temperature i n dishes of water, the temper-ature of which was recorded c o n t i n u o u s l y . The number of day-degrees to which each p o p u l a t i o n of animals was exposed was computed from the records of the mean d a i l y temperature. The r e l a t i o n s h i p between these values and the number of days a f t e r the previous August 1st i s shown i n F i g . 13. There i s a s l i g h t tendency f o r those animals beginning at around 1 9 0 days to r e q u i r e more than the others but at the other times the q u a n t i t y i s q u i t e constant. The mean number of day-degrees (°F) r e q u i r e d i s 3632.0 and the standard e r r o r on the mean i s 90.8. The number of day-degrees r e q u i r e d i n c r e a s e s as the i n i t i a l number of animals i n c r e a s e s . The e f f e c t of beginning w i t h l a r g e r numbers of animals i s t o slow the growth of each of the animals, thereby d e l a y i n g the beginning of e g g - l a y i n g . The i n c r e a s e i n the number of day-degrees r e q u i r e d (HURQ) to reach m a t u r i t y i s l i n e a r w i t h i n the range of d e n s i t i e s which I have i n v e s t i g a t e d . , For Cyprinotus grown alone the r e l a t i o n -F i g u r e 13 The number of day-degrees ( F) which the animals were exposed to before reaching m a t u r i t y , as a f u n c t i o n of the number of days after- August• 1 s t t h a t they hatched (*- _ Cyprinotus , H - Herpetocypris ) . 6000 -5000-NUMBER OF DAYS AFTER AUGUST I st 38 s h i p i s HURQ = 3310.0 + 433. 7 . NC As t h e i n i t i a l number i n c r e a s e d so d i d t h e m o r t a l i t y , b u t a t no d e n s i t y was t h i s l a r g e enough t o r e s u l t i n m a t u r a t i o n o f t h e p o p u l a t i o n sooner t h a n one b e g i n n i n g a t a lo w e r d e n s i t y ( F i g . 14A). Such a r e s u l t may be p o s s i b l e b u t t h e number o f a n i m a l s r e a c h i n g m a t u r i t y would be v e r y s m a l l . The a n i m a l s may be so i m p a i r e d by exposure t o t h e l a r g e d e n s i t y t h a t t h e y d i e w i t h o u t m a t u r i n g . The e f f e c t on C y p r i n o t u s o f a d d i n g some H e r p e t o c y p r i s a n i m a l s i s t o i n c r e a s e t h e v a l u e o f HURQ. Assuming an e q u i v a l e n c e i n t h e e f f e c t o f a n i m a l s o f b o t h s p e c i e s upon C y p r i n o t u s t h e r e l a t i o n s h i p i s s t i l l l i n e a r b u t t h e s l o p e and i n t e r c e p t a r e a l t e r e d , F i g . 14B. The i n t e r c e p t i s now 3855.0, wh i c h i s c l o s e t o t h e o r i g i n a l v a l u e , b u t t h e s l o p e i s m a r k e d l y d e c r e a s e d . The a s s u m p t i o n o f i n d i v i d u a l e q u i v a l e n c e i s n o t met by t h e d a t a . A p p a r e n t l y t h e r e i s a tendency f o r t h e e f f e c t p e r i n d i v i d u a l H e r p e t o c y p r i s t o be l e s s t h a n the e f f e c t o f i n d i v i d u a l C y p r i n o t u s upon t h e m s e l v e s . V/hen t h e b o t h s e t s o f d a t a a r e combined t h e r e l a t i o n s h i p becomes HURQ = 3568.0 + 341.7 'NT where NT i s t h e t o t a l i n i t i a l number r e g a r d l e s s o f s p e c i e s ( F i g . 14C). Only t h e v a l u e o f HURQ f o r a m i n i m a l d e n s i t y o f H e r p e t o c y p r i s has been d e t e r m i n e d because i n t h e e x p e r i m e n t d e s i g n e d t o measure t h e e f f e c t o f d e n s i t y t h e d i s h e s were a c c i d e n t a l l y f r o z e n . The mean v a l u e o f HURQ f o r H e r p e t o c y p r i s 2 grown a t 5 a n i m a l s p e r p e t r i d i s h (0.25/cm ) i s 7753.0 day-Fiqure 14 The e f f e c t of the i n i t i a l density of animals upon the number of day-degrees (°F) required for the animals to reach maturity. F i g , 14A - showing that the rate of increase of day-degrees required i s l i n e a r over the range of i n i t i a l d e n s i t i e s of Cyprinotus that were used. The slope of the l i n e i s 433,7 and the c o r r e l a t i o n c o e f f i c i e n t , r = 0,93. F i g , 14B - the e f f e c t of adding Herpetocypris animals to Cyprinotus, upon the increase i n day-degrees required. This i s p l o t t e d against the t o t a l i n i t i a l numbers regardless of species. C o r r e l a t i o n c o e f f i c i e n t = 0,72, F i g , 14C - the l i n e r e l a t i n g the number of day-degrees required for Cyprinotus to reach maturity and the t o t a l i n i t i a l number regardless of species. (This i s the data from F i g . 14A and B, combined). Co r r e l a t i o n c o e f f i c i e n t = 0.82, 5 0 0 0 \-4 0 0 0 3 0 0 0 2 0 0 0 1 0 0 0 LU D C Z> t-< O h -5 0 0 0 _L U J L. . 8 — e -co UJ LU CE e> LU Q I >-< 4 0 0 0 3 0 0 0 2 0 0 0 CE LU m z 1 0 0 0 5 0 0 0 4 0 0 0 3 0 0 0 2 0 0 0 1 0 0 0 .8—8-° C -1 L. INITIAL NUMBERS PER cm 2 40 d e g r e e s ( F i g . 1 3 ) . T h i s i s more t h a n t w i c e t h e v a l u e o f C y p r i n o t u s . The d i f f e r e n c e seems t o be p a r t i a l l y a c c o u n t e d f o r by t h e n e c e s s i t y o f H e r p e t o c y p r i s t o grow t o a l a r g e r s i z e b e f o r e m a t u r i n g , b u t t h i s s i z e i s n o t t w i c e t h e mature s i z e o f C y p r i n o t u s . Not enough i s known about the r e l a t i v e volume o f t i s s u e which must be b u i l t up i n o r d e r t o l a y eggs, o r t h e e f f i c i e n c i e s o f t h e two s p e c i e s i n o b t a i n i n g and c o n v e r t i n g f o o d i n t o such t i s s u e , t o a l l o w c a l c u l a t i o n o f whether t h e d i f f e r e n c e i s e n t i r e l y a t t r i b u t a b l e t o the l a r g e r s i z e . (When a l l t h e p r o c e s s e s and e f f e c t s o f t h e s p e c i e s upon one a n o t h e r a r e b r o u g h t t o g e t h e r i n a model i t i s assumed t h a t t h e r a t e o f i n c r e a s e o f d ay-degrees r e q u i r e d per i n p u t - e g g i s t h e same f o r each s p e c i e s , i . e . 341.7). The same d e l a y ( i n days) has been o b s e r v e d f o r t h e l e n g t h o f the l a r v a l p e r i o d o f D r o s o p h i l a grown on a r t i f i c i a l media, (reviewed!'by M i ' l l e r 1967). But u n l i k e t h e o s t r a c o d s , as t h e i n i t i a l l a r v a l d e n s i t y was i n c r e a s e d t h e o n l y e f f e c t o b s e r v e d was an i n c r e a s e i n t h e l e n g t h o f time s p e n t as a l a r v a e and a d e c r e a s e i n t h e f i n a l s'lze o f t h e a n i m a l . Only a t v e r y h i g h d e n s i t i e s d i d s e v e r e m o r t a l i t y b e g i n t o o c c u r . Summary 1. The amount o f t i m e r e q u i r e d f o r t h e a n i m a l s t o r e a c h m a t u r i t y can be measured i n d a y - d e g r e e s . 2. The number o f day-degrees r e q u i r e d by C y p r i n o t u s i s 3568 day-degrees F„ and by H e r p e t o c y p r i s 7753 day-degrees F„ 3. As t h e i n i t i a l numbers of a n i m a l s are i n c r e a s e d t h e number 41 o f day-degrees r e q u i r e d f o r each a n i m a l t o r e a c h m a t u r i t y a l s o i n c r e a s e s . F o r C y p r i n o t u s t h e i n c r e a s e was l i n e a r o v e r t h e range o f i n i t i a l numbers t h a t were used. The r a t e 2 o f i n c r e a s e p e r egg per cm f o r C y p r i n o t u s i s 341,7, d) The a c c u m u l a t i o n o f day-degrees by t h e a n i m a l s I t has a l r e a d y been shown i n t h e p r e v i o u s s e c t i o n t h a t t h e amount o f t i m e between the h a t c h i n g o f a group o f animals-and t h e i r m a t u r a t i o n i s a t l e a s t a f u n c t i o n o f t h e i n i t i a l number o f a n i m a l s and a l s o depends upon t h e s p e c i e s i t s e l f . T h i s I s the q u a n t i t y HURQ, t h e minimum v a l u e s o f which a r e 3568,0 day-degrees F, f o r C y p r i n o t u s and 775 3,0 f o r H e r p e t o c y p r i s , T h i s i s a measure, o f t h e a b i l i t y o f t h e s p e c i e s t o ac c u m u l a t e enough energy i n o r d e r t o be a b l e t o b e g i n t o l a y eggs. D u r i n g t h i s p e r i o d t h e a n i m a l must c o m p l e t e a f i x e d number o f m o u l t s (5) each marked by an i n c r e a s e i n s i z e . A l l days a re not t h e same t o t h e a n i m a l s - t h e y can grow more on some t h a n on others-. T h e r e f o r e r e a l t i m e i s r e p l a c e d by d a y - d e g r e e s . D u r i n g t h e p e r i o d when t h e puddle i s wet t h e number o f day-degrees from any i n i t i a l t i m e T^ t o t h e p r e s e n t , T 2 , w i l l be g i v e n by \ t dT HUAC = J T 1 I n t h e a r e a o f Vancouver t h e mean monthly a i r t e m p e r a t u r e as measured by t h e UBC C l i m a t o l o g i c a l S t a t i o n f o l l o w s a. r e g u l a r c o u r s e , d e c l i n i n g from a maximum i n August t o a minimum i n J a n u a r y and t h e n a s c e n d i n g a g a i n i n t h e shape o f a s i n e wave ( F i g , 15A,). The mean d a i l y a i r t e m p e r a t u r e on any day T, F i g u r e 15 The shape o f t h e r e l a t i o n s h i p between t h e mean monthly t e m p e r a t u r e i n t h e P o i n t Grey a r e a and t h e number o f days a f t e r August 1 s t f o r t h e y e a r s 1961-69„ The change o f t e m p e r a t u r e w i t h t i m e i s c l e a r l y t h e same as a s i n e wave which i s a f u n c t i o n o f t i m e and no f i t t i n g o f t h e f u n c t i o n i s r e q u i r e d : t h e v a l u e s o f t h e a n n u a l mean and maximum mean monthly t e m p e r a t u r e , and l e t t i n g t he v a l u e o f T e q u a l z e r o on August 1 s t o f each y e a r , were s u f f i c i e n t C o n s e q u e n t l y t h e t e m p e r a t u r e i s a minimum on J a n u a r y 31st „ Fig„ 15A - t h e mean monthly t e m p e r a t u r e f o r t h e y e a r s 1961-Fig„ 15B - t h e model r e l a t i o n s h i p between t e m p e r a t u r e and t i m e u s i n g t h e mean v a l u e s from F i g , 15A and i l l u s t r a t i n g t he method o f f i n d i n g t h e i n t e g r a l o f t e m p e r a t u r e w i t h r e s p e c t t o time d u r i n g an i n t e r v a l T, t o T p„ WATER TEMPERATURE ( ° F ) 43 measured i n days a f t e r August 1s t , i s given by t = (tmax - tba r )• cos (—•*TT'F~ ) + t b a r 3bb where tmax i s the maximum monthly temperature f o r the year, t b a r the mean annual temperature and where the cosine f u n c t i o n has been converted to r a d i a n s . S u b s t i t u t i n g f o r t i n the previous i n t e g r a t i o n we have t h a t T 2 • 2K HUAC = ^  (tmax - tb a r ) • cos ( - r ^ ) + tbar dT / m O D D 1 l T2 (tmax - t b a r ) • (^~) • s i n (2L_*__^_IL) + t b a r • T 2 TT 365 x l T herefore i f a group of animals hatches on a day T^ and has to accumulate a s p e c i f i e d number of day-degrees, HURQ, the amount of time r e q u i r e d to do t h i s (T 2 - T^) can be obtained from the exp r e s s i o n 365 ^2 * 2 (tmax - t b a r ) • (T—-) • s i n ) + tba r • T Q = 2 Tf 365 2 •sec T, • 2T( (tmax - tbar) • C 2 ^ ) • s i n ( — — ) + t b a r • T± + HURQ (7) where the value of the unknown i n t e g r a l at T 2 i s obtained by s e t t i n g i t equal to the value of the i n t e g r a l at the lower l i m i t p l u s the necessary number and then i t e r a t i v e l y s o l v i n g f o r T 2 ( F i g . 15B). The q u a n t i t y (T 2 -,T^) as a f u n c t i o n of the number of days a f t e r August 1st of T-^  behaves i n an i n t e r e s t i n g and s i g -n i f i c a n t way when a l t e r n a t i v e values of HURQ are considered. 44 For small values there i s v i r t u a l l y a constant length of time required (TRQU) but as HURQ i s increased the s t a r t i n g time (TSTRT) becomes very important„ With d i f f e r e n t values of HURQ t h i s r e l a t i o n s h i p i s explored i n F i g , 16„ The length of time required i s i n i t i a l l y small but quickly ascends to a maximum value. The de r i v a t i v e of the time required with respect to the time of s t a r t i n g i s not a constant and i t s value i s dependent upon the value of HURQ, Furthermore the point i n time at which the de r i v a t i v e changes from p o s i t i v e to negative i s not constant but changes with HURQ, The approximate times of maximum TRQU are marked i n F i g , 16 and as can be seen t h e i r p o s i t i o n changes r a p i d l y as- HURQ i s increased and the time seems to tend to a particular- value of TSTRT. The p a r t i c u l a r l i n e s f o r HURQ for Cyprinotus and Herpetocypris are also shown i n F i g . 16. The consequences f o r animals hatching at d i f f e r e n t times aft e r August 1st are e n t i r e l y d i f f e r e n t f o r the two species as r e s u l t of the large d i f f e r e n c e i n the values of HURQ. For both species the following r e l a t i o n must hold: TRQU •< (TSTP - TSTRT) (8) or else the species w i l l become ex t i n c t , where TSTP i s the number of days a f t e r August 1st that drying up occurs. The value of TSTRT can be any number of days a f t e r August 1st when there i s water present. S u r p r i s i n g l y small errors are involved i n using t h i s r e l a t i o n s h i p to predict the temperature, when only the mean F i q u r e 16 T h e e f f e c t o f s t a r t i n g a t d i f f e r e n t t i m e s a f t e r A u g u s t 1 s t , t o a c c u m u l a t e a g i v e n n u m b e r o f d a y - d e g r e e s ( f r o m 5 0 0 t o 1 5 , 0 0 0 ) , u p o n t h e l e n g t h o f t i m e r e q u i r e d t o a c h i e v e t h e v a l u e . T h e s m a l l s q u a r e o n e a c h l i n e m a r k s t h e t i m e o f s t a r t i n g w h e n t h e t i m e r e q u i r e d i s a m a x i m u m . T h e t w o d a s h e d l i n e s a r e f o r C y p r i n o t u s (HURQ = 3 5 6 8 ) a n d H e r p e t o c y p r i s (HURQ = 7 7 5 3 ) . T h e sum o f t h e c o o r d i n a t e s o f t h e d o t t e d l i n e , e q u a l 3 6 4 d a y s . T o t h e l e f t o f t h e l i n e t h e p u d d l e i s t e m p o r a r y a n d t o t h e r i g h t i t i s p e r m a n e n t „ 500 ~1 1 1 ^ 1 1 1 1 1 1 1 30 60 90 120 150 180 210 240 270 300 330 TIME OF START 46 a n n u a l t e m p e r a t u r e and t h e maximum m o n t h l y t e m p e r a t u r e a r e u s e d . T h e e x p e c t e d a c c u m u l a t e d d a y - d e g r e e s f r o m t h e f i r s t d a y o f A u g u s t t o any d a y T i s EXP = (tmax - t b a r ) • ( I ™ - ) • s i n ( T* 2^-) + t b a r • T The o b s e r v e d number o f d a y - d e g r e e s was a p p r o x i m a t e d b y summing t h e s u c c e s s i v e mean d a i l y t e m p e r a t u r e s c a l c u l a t e d f r o m t h e d a i l y maximum and minimum. The r e l a t i o n s h i p b e t w e e n t h e s u c c e s s i v e v a l u e s on e a c h day o f t h e e x p e c t e d and t h e o b s e r v e d s h o u l d b e l i n e a r t h r o u g h t h e o r i g i n a n d h a v e a s l o p e e q u a l t o 1.0. T h i s r e l a t i o n s h i p was t e s t e d f o r t h e y e a r s 1961 t o 1 9 6 9 . As c a n be s e e n i n F i g . 17 t h e r e i s an e x c e l l e n t l i n e a r r e l a t i o n -s h i p b e t w e e n t h e e x p e c t e d a n d o b s e r v e d w i t h v e r y l i t t l e t e n d e n c y f o r t h e p o i n t s t o w a n d e r f a r : f r o m t h e l i n e o f e q u a l i t y . The v a l u e o f t h e i n t e r c e p t , t h e s l o p e and c o r r e l a t i o n c o e f f i c i e n t s o b t a i n e d b y r e g r e s s i o n a r e g i v e n i n T a b l e I f o r e a c h year. The c o m p a r i s o n o f e x p e c t e d and o b s e r v e d v a l u e s when s t a r t i n g t i m e s o t h e r t h a n A u g u s t 1 s t a r e u s e d , h a v e n o t b e e n a t t e m p t e d s i n c e t h e p r o b l e m i s q u i t e l a r g e ; , , e v e n f o r a c o m p u t e r . The maximum d e v i a t i o n s i n d a y - d e g r e e s o f t h e e x p e c t e d f r o m t h e o b s e r v e d a n d t h e t i m e o f t h e maximum a r e shown i n T a b l e I I . T h e s e v a l u e s h a v e a l s o b e e n c o n v e r t e d i n t o d a y s b y d i v i d i n g b y t h e mean a n n u a l t e m p e r a t u r e . T h e s e p e r i o d s a r e q u i t e s m a l l . Summary 1. The mean m o n t h l y t e m p e r a t u r e i n t h e V a n c o u v e r a r e a d e c r e a s e s f r o m a maximum i n A u g u s t t o a minimum i n J a n u a r y and i n -c r e a s e s a g a i n as a. c o s i n e f u n c t i o n o f t h e number o f d a y s F i g u r e 17 D e m o n s t r a t i n g t h e l i n e a r n a t u r e o f the r e l a t i o n s h i p between t h e e x p e c t e d and t h e o b s e r v e d c u m u l a t i v e number o f day-degrees (°'C). Each p o i n t shown i s t h e w e e k l y c u m u l a t i v e number t h r o u g h o u t t h e y e a r . T h e r e f o r e s i n c e t h e a c c u m u l a t i o n i s s l o w e r i n t h e w i n t e r , when t h e t e m p e r a t u r e i s l o w e r , t h e p o i n t s a re c l o s e r t o g e t h e r i n t h e c e n t r e o f each g r a p h . The l i n e shown on each graph i s t h e s t r a i g h t - l i n e y = C + Bx i n which C = 0.0 and B = 1.0. T e s t s o f t h e l i n e a r i t y o f the d a t a may be found i n T a b l e I , and T a b l e I I r e c o r d s t h e maximum d e v i a t i o n s o f t h e e x p e c t e d from t h e o b s e r v e d . TABLE I V a l u e s o f t h e i n t e r c e p t , s l o p e and c o r r e l a t i o n c o e f f i c i e n t f o r t h e r e l a t i o n s h i p between t h e e x p e c t e d and o b s e r v e d c u m u l a t i v e number o f day-degrees f o r each y e a r from 1961-69, The v a l u e s which would i n d i c a t e no d i f f e r e n c e between the e x p e c t e d and the o b s e r v e d a r e when t h e i n t e r c e p t I s 0,0, t h e s l o p e e q u a l t o 1,0 and t h e c o r r e l a t i o n c o e f f i c i e n t i s 1.0. Yea r I n t e r c e p t S l o p e C o r r e l a t i o n c o e f f i c i e n t 1961-62 126.1 0.9469 0.9909 1962-63 25.86 1.001 0.9990 1963-64 -15.20 0.9847 0.9986 1964-65 163.8 0.9158 0.9903 1965-66 45 .9 3" 0.9677 0.9987 1966-67 66.43 0.9334 0.9985 1967-68 80.12 0.9530 0.9961 1968-69 105.5 0.9396 0.9970 49 TABLE I I The times of occurrence ( i n clays a f t e r August 1st) of the maximum d e v i a t i o n i n day-degrees ( ° C ) and days of the expected from the observed cumulative number of day-degrees f o r each year from 1961-69, Max, d e v i a t i o n Max, d e v i a t i o n Time of i n day-degrees i n days occurrence 1961-62 238,9 24,7 140 1962-63 144,5 14,18 185 1963-64 137,1 13,5 256 1964-65 175,9 19,6 160 1965-66 102, 7 10, 7 285 1966-67 195,3 20,3 365 1967-68 155,5 14,8 254 1968-69 159,0 17,3 365 50 a f t e r August 1 s t , I n a d d i t i o n i t was n e c e s s a r y t o use t h e maximum monthly and t h e mean a n n u a l t e m p e r a t u r e , 2, The number o f day-degrees between any two p o i n t s i n ' t i m e can be o b t a i n e d by i n t e g r a t i n g t h e c o s i n e f u n c t i o n o v e r t h e i n t e r v a l , 3, The e x p e c t e d c u m u l a t i v e number o f day-degrees d i d n o t d i f f e r g r e a t l y from t h e o b s e r v e d number a t any t i m e d u r i n g each o f t h e y e a r s 1961-1969, 4, To o b t a i n any g i v e n number o f d a y - d e g r e e s , the time r e q u i r e d i n c r e a s e s as t h e number o f days a f t e r August 1 s t t h a t t h e a c c u m u l a t i o n i s begun i s i n c r e a s e d , e ) The mechanism o f the e f f e c t s of. d e n s i t y o f t h e a n i m a l s upon one a n o t h e r , I n t h e puddle, s m a l l clumps o f a n i m a l s a re c o n t i n u a l l y b e i n g formed and b r o k e n down, i n some c a s e s t h e a n i m a l s a r e m e r e l y c l o s e r t o g e t h e r , l e a v i n g a r e a s o f v a c a n t mud s u r f a c e , and i n o t h e r s t h e y e n c o u n t e r one a n o t h e r by d i r e c t c o n t a c t and r e a c t t o t h e p r e s e n c e o f each o t h e r by each c r a w l i n g o v e r t h e o t h e r as though i t were a. fragme n t o f g r a s s t o u c h i n g t h e v a l v e s o f t h e a n i m a l w i t h t h e i r antennae. When t h e r e i s a l a r g e number o f a n i m a l s p r e s e n t t h e number o f m u t u a l - i n s p e c t -i o n s o c c u r r i n g a t one t i m e w i t h i n t h e group can be q u i t e l a r g e . These lumps o f a n i m a l s may form f o r o t h e r r e a s o n s . The p r e s e n c e o f a dead a n i m a l such as' a c h i r o n o m i d l a r v a , o l i g o c h a e t o r sometimes a f r e s h g r e e n f r a g m e n t o f a. g r a s s o r t r e e l e a f , 5 1 w i l l u s u a l l y draw a crowd o f t h e a n i m a l s . They c r a w l o v e r t h e o b j e c t d e m o l i s h i n g a l l s o f t p a r t s , l e a v i n g i n t h e c a s e o f a l e a f o n l y t h e h a r d e r s t r u c t u r a l t i s s u e . T h e r e f o r e some o f t h i s c l u m p i n g a c t i v i t y r e s u l t s i n t h e a n i m a l s o b t a i n i n g f o o d b u t even i n t h e absence o f any such n u c l e i o f c o n t a g i o n t h e c l u m p i n g s t i l l o c c u r s . T h e r e f o r e one p o s s i b l e means o f t h e a n i m a l s i n f l u e n c i n g one a n o t h e r as t h e d e n s i t y i n c r e a s e s i s by i n c r e a s i n g t h e amount of t i m e s p e n t i n t h i s a c t i v i t y a t t h e expense o f o b t a i n i n g f o o d . T h i s e f f e c t h a s been i n v e s t i g a t e d u s i n g n a t u r a l mud whi c h had' been r e d u c e d t o a u n i f o r m f i n e p a r t i c l e s i z e by s i e v i n g o u t t h e l a r g e r o r g a n i c and i n o r g a n i c f r a g m e n t s . S i n c e t h e a n i m a l s e x h i b i t a g g r e g a t i o n b e h a v i o u r i t was a n t i c i p a t e d t h a t t h e q u a n t i t y , number o f a n i m a l s p e r sample, would be d i s t r i b u t e d i n t h e manner o f t h e n e g a t i v e b i n o m i a l so t h a t t h e p r o b a b i l i t y o f a sample c o n t a i n i n g x a n i m a l s would be g i v e n by _ i _ r i x-s-K ( K + x - 1 ) ' , x ,x p x = ( 1 + K ) - X T - T K " T T T ( — x - K where x, i s t h e mean number p e r sample and K, i s the d i s p e r s i o n c o e f f i c i e n t , w h i c h when l a r g e r e s u l t s i n a s e r i e s o f terms a p p r o x i m a t i n g t h e P o i s s o n s e r i e s and when s m a l l a u n i f o r m s e r i e s o f t e r m s . A c c o r d i n g t o B e r t h e t and G e r a r d ( 1 9 6 5 ) an e f f i c i e n t e s t i m a t o r o f t h e v a l u e o f K i s . x ( S 2 - x) 52 When th e v a r i a n c e i s g r e a t e r t h a n t h e mean and d e c r e a s e s t o w a r d s i t K w i l l t e n d t o + o o and c o n v e r s e l y , when i t i s l e s s t h a n t h e mean and b e g i n s t o approach i t K tend s ' t o -«». I f t h e d i s p e r s i o n o f the a n i m a l s changes w i t h d e n s i t y so t h a t t h e y become more clumped and spend more time i n c l o s e a s s o c i a t i o n w i t h o t h e r a n i m a l s t h a n t h e y would a t lo w e r d e n s i t i e s , t h e n t h e v a l u e o f K s h o u l d have some i n v e r s e r e l a t i o n s h i p w i t h t h e d e n s i t y . P o p u l a t i o n s o f each s p e c i e s were s e t up at d i f f e r e n t d e n s i t i e s i n s m a l l o b l o n g (7 x 12 cm) p l a s t i c boxes w i t h b l a c k s i d e s w i t h a"'layer o f s i e v e d mud 0,5 cm deep on t h e bottom a t 20°C, A n i m a l s 1,0 - 1,5 mm i n l e n g t h were us e d . The d e p t h o f t h e water was 2,0 cm. The t o t a l p o p u l a t i o n was t h e n sampled by d r o p p i n g a s m a l l p l a s t i c g r i d on t o the mud, t h e r e b y sub-d i v i d i n g t h e whole a r e a and i t s p o p u l a t i o n i n t o 18 samples 2 each o f a r e a 4,6 cm „ The number o f a n i m a l s i n each u n i t was t h e n r e c o r d e d . Between a d d i t i o n t o t h e mud and s a m p l i n g , each p o p u l a t i o n was l e f t u n d i s t u r b e d f o r from 2 t o 4 h o u r s . A t each d e n s i t y from 108 t o 650 samples were o b t a i n e d , more a t t h e low d e n s i t i e s . F o r C y p r i n o t u s t h e f i t o f t h e n e g a t i v e b i n o m i a l was f i r s t o f a l l t e s t e d w i t h a p o p u l a t i o n o f 50 a n i m a l s ( i , e , 2 0.60 animals/cm ), The o b s e r v e d and e x p e c t e d number o f a n i m a l s per sample are shown i n F i g , 18, I t can be seen t h a t t h e f i t o f t h e e x p e c t e d t o t h e o b s e r v e d i s v e r y good. T h e r e -f o r e f o r the d a t a f o r each d e n s i t y t h e same d i s t r i b u t i o n was used t o c a l c u l a t e t h e v a l u e o f K from the v a r i a n c e and t h e mean and t h e e x p e c t e d and o b s e r v e d f r e q u e n c i e s compared. For a l l d e n s i t i e s the v a r i a n c e was g r e a t e r than t h e mean and so a F i g u r e 18 Comparison o f t h e o b s e r v e d d i s t r i b u t i o n ( s o l i d l i n e s . ) o f t h e f r e q u e n c y o f samples w i t h d i f f e r e n t numbers of o s t r a c o d s , w i t h t h e e x p e c t e d f r e q u e n c i e s (dashed l i n e s ) g e n e r a t e d from the n e g a t i v e b i n o m i a l d i s t r i b u t i o n . There were f i f t y a n i m a l s i n each p o p u l a t i o n . F i g , 18A - C y p r i n o t u s , c h i - s q u a r e = 21,18, number of samples = 216, F i g , 18B - H e r p e t o c y p r i s , c h i - s q u a r e = 22,15, number o f samples = 144, 20 16 12 UJ _ l 0. < CO UL o 'T " '-T>u,u i H ! >-o LU s B 20 16 12 8 -4 -10 12 14 16 IB NUMBER OF OSTRACODS PER SAMPLE 54 p o s i t i v e v a l u e o f K was. o b t a i n e d ( T a b l e I I I ) 0 As t h e d e n s i t y i n c r e a s e d t h e v a l u e K remained s m a l l even when p o p u l a t i o n s o f 2 500 a n i m a l s per box (6,0/cm ) were u s e d . But i n t h e s m a l l e s t 2 p o p u l a t i o n (5 per box, 0.06/cm ) K was q u i t e l a r g e s i n c e the v a r i a n c e was v e r y c l o s e t o t h e mean. N e g l e c t i n g t h i s l a r g e v a l u e t h e mean v a l u e o f K i s 1.059. I t t h e r e f o r e seems t h a t t h e d i s p e r s i o n o f t h e a n i m a l s i s not changed by I n c r e a s i n g t h e i r number t o h i g h d e n s i t i e s . A t v e r y low d e n s i t i e s C y p r i n o t u s a n i m a l s t e n d t o assume a random d i s t r i b u t i o n . The v a l u e o f K a l s o r e m a i n e d unchanged as t h e d e n s i t y o f H e r p e t o c y p r i s changed e x c e p t a t t h e l o w e s t d e n s i t y where K was n e g a t i v e because th e v a r i a n c e was; l e s s t h a n t h e mean ( T a b l e I V ) . E x c l u d i n g t h i s n e g a t i v e v a l u e , t h e mean v a l u e o f K f o r H e r p e t o c y p r i s i s 1.84, w h i c h i s s l i g h t l y l a r g e r t h a n t h e mean f o r C y p r i n o t u s , s u g g e s t i n g t h a t the s p e c i e s i s u s u a l l y l e s s clumped. However, as i n t h e c a s e o f C y p r i n o t u s t h e v a l u e o f K i s i n d e p e n d e n t o f t h e mean e x c e p t a t l o w e s t d e n s i t i e s . The e f f e c t o f each s p e c i e s upon the d i s p e r s i o n o f t h e o t h e r was t h e n i n v e s t i g a t e d by making up mixed p o p u l a t i o n s o f e q u a l number of each s p e c i e s o v e r a range o f d e n s i t i e s . V a l u e s o f K were t h e n o b t a i n e d f o r d e n s i t i e s o f each s p e c i e s i n t h e p r e s e n c e o f an e q u a l number of t h e o t h e r s p e c i e s and f o r t h e d i s t r i b u t i o n of a l l a n i m a l s among samples r e g a r d l e s s o f s p e c i e s . I f t h e r e i s no e f f e c t o f t h e p r e s e n c e o f the. o t h e r s p e c i e s t h e n the mean v a l u e o f K s h o u l d r e m a i n unchanged. The r e s u l t s are shown i n T a b l e V. Most v a l u e s o f K a r e sub-s t a n t i a l l y r e d u c e d , showing t h a t each s p e c i e s i s much more TABLE I I I V a l u e s o f t h e mean numbers per sample, t h e v a r i a n c e on t h e mean and t h e v a l u e s o f t h e n e g a t i v e b i n o m i a l d i s p e r s i o n c o e f f i c i e n t (K) f o r p o p u l a t i o n s o f C y p r i n o t u s a l o n e i n s m a l l d i s h e s . The number o f samples used t o c a l c u l a t e t h e s e p a r a m e t e r s i s a l s o g i v e n f o r each d e n s i t y . Mean number ..  . Number o f , V a r i a n c e K n p e r sample samples 0.27 0.28 10.68 648 0.55 0. 74 1.63 648 0.98 1. 78 1.2.1 216 1. 3"7 4.2 7 0.64 216 2.76 7. 74 1.53 216 4.18 33.18 0.60 216 5.59 33.37 1.12 288 11.16 194.38 0.68 216 27.34 522.19 1.51 108 TABLE IV V a l u e s o f t h e mean numbers p e r sample, t h e v a r i a n c e on t h e mean and t h e v a l u e s o f the d i s p e r s i o n c o e f f i c i e n t (K) f o r p o p u l a t i o n s o f H e r p e t o c y r p i s a l o n e i n s m a l l d i s h e s - The number o f samples upon which t h e s e p a r a m e t e r s a re based i s a l s o g i v e n f o r each d e n s i t y . Mean numbers pe r sample V a r i a n c e K Number o f samples 0.56 0.44 -2. 75 216 1.31 2.35 1. 66 216 2. 79 6. 38 2. 17 144 4. 73 15.55 2. 07 90 11.22 86.42 1. 67 162 57 TABLE V The e f f e c t o f t h e p r e s e n c e o f b o t h s p e c i e s u p o n t h e d i s -p e r s i o n o f e a c h s p e c i e s . F o r e a c h s p e c i e s t h e v a r i a n c e a n d t h e v a l u e o f K a r e g i v e n f o r e a c h v a l u e o f t h e m e a n . The number o f s a m p l e s t a k e n a t e a c h d e n s i t y i s a l s o i n d i c a t e d (C - C y p r i n o t u s , H - H e r p e t o c y p r i s ) , Mean number V a r i a n c e K Number o f s a m p l e s • s a m p l e C H C H f o r e a c h 0,29 0.33 0.28 1. 78 -11.57 706 1,20 2.95 2 .44 1.22 0.93 365 2,80 13.02 7.48 0. 79 1.59 162 7,60 5.40 164.99 18. 75 0.37 217 180 s p e c i e s 58 clumped when on i t s own o v e r t h e same range o f d e n s i t i e s . The v a l u e o f K f o r t h e p r e s e n c e o f 5 H e r p e t o c y p r i s was n e g a t i v e w i t h t h e s p e c i e s a l o n e b u t i t i s now even more n e g a t i v e , s u g g e s t i n g t h a t a t t h i s low d e n s i t y , t h e a n i m a l s a r e more u n i f o r m l y d i s t r i b u t e d than b e f o r e . Both o f t h e s e s p e c i e s o f o s t r a c o d s t a k e i n s m a l l  p a r t i c l e s o f mud and d e b r i s o b t a i n e d by s c r a p i n g them o f f l a r g e r o r g a n i c o r i n o r g a n i c f r a g m e n t s . The c o n t e n t s o f t h e g u t s o f b o t h s p e c i e s t a k e n from t h e p u d d l e c o n s i s t e d o f b a c t e r i a . , a l g a e , p r o t o z o a , t h e o c c a s i o n a l r o t i f e r and a l a r g e mass o f u n i d e n t i f i a b l e o r g a n i c f r a g m e n t s w h i c h were p r o b a b l y p i e c e s o f g r a s s . The appendages which t h e a n i m a l uses are d e s c r i b e d i n d e t a i l i n Appendix I . There do not seem t o be any d i f f e r e n c e s i n t h e s t r u c t u r e o r s i z e o f t h e i r f o o d - g a t h e r i n g appendages. M a t e r i a l can a l s o be g a t h e r e d from f l a t s u r f a c e s such as g r a s s stems and l e a v e s . I n t h e e x p e r i m e n t a 1 d i s h e s used t o measure t h e m o r t a l i t y some s i g n i f i c a n t changes occurred, i n t h e sediment. and t o t h e a n i m a l s . A t t h e low d e n s i t i e s ( l e s s t h a n 0,3 2 animals/cm ) o f C y p r i n o t u s t h e r e was a v i s i b l e growth o f p e r i p h y t i c and f i l a m e n t o u s a l g a e upon t h e s u r f a c e o f t h e sedim e n t and d i s h , and on t h e g r a s s stems, d e s p i t e t h e p r e s e n c e o f t h e a n i m a l s . A t d e n s i t i e s g r e a t e r t h a n t h i s no such v i s i b l e g r o w t h was m a i n t a i n e d s i n c e t h e a n i m a l s were a p p a r e n t l y u t i l i z i n g i t as f a s t as i t was g r o w i n g . The m a j o r i t y o f t h e t i m e s p e n t f e e d i n g by H e r p e t o c y p r i s a t low d e n s i t y i s when i t i s b e n e a t h t h e s u r f a c e l a y e r s o f mud. At d e n s i t i e s up t o 59 0.7 animals/cm t h e a n i m a l s r a r e l y appeared on t h e s u r f a c e and the' upper l a y e r o f t h e sediment and w a l l s o f t h e d i s h e s became g r e e n w i t h t h e growth o f a l g a e . But a t h i g h e r d e n s i t i e s t h e a l g a e d i s a p p e a r e d and t h e s u r f a c e l a y e r s were d i s t u r b e d by t h e c o n t i n u a l emergence and r e - b u r r o w i n g o f t h e a n i m a l s . The i n t r o d u c t i o n o f a second s p e c i e s d i d not i n e i t h e r c a s e p roduce changes i n t h e s e phenomena o t h e r t h a n t h o s e w h i c h r e s u l t e d " f r om t h e i n t r o d u c t i o n o f members o f t h e same s p e c i e s . As t h e d e n s i t y i n c r e a s e d t h e r e was a d e c r e a s e i n t h e darJcness o f t h e c o l o u r o f t h e c a r a p a c e o f t h e s u r v i v o r s o f b o t h s p e c i e s . T h e r e f o r e a p a r t i a l e x p l a n a t i o n o f t h e d i f f e r e n c e i n t h e m o r t a l i t y e x p e r i e n c e d by t h e two s p e c i e s may be t h a t C y p r i n o t u s , w h i c h i s t h e most a f f e c t e d , i s u n a b l e t o o b t a i n enough f o o d . A t h i g h d e n s i t i e s t h e a n i m a l s would have t o be a b l e t o w i t h s t a n d a low r a t e o f f o o d i n t a k e . T h i s p o s s i b i l i t y has been i n v e s t i g a t e d by o b s e r v i n g t h e r e s p o n s e o f b o t h s p e c i e s t o t h e extreme c o n d i t i o n o f t o t a l f o o d d e p r i v a t i o n by m e a s u r i n g t h e l e n g t h o f t i m e s i n c e d e p r i v a l and t h e d e a t h o f i n d i v i d u a l a n i m a l s . The e x p e c t a t i o n f o r t h e outcome was t h a t H e r p e t o c y p r i s s h o u l d be a b l e t o w i t h s t a n d a l o n g e r p e r i o d w i t h o u t f o o d i n t a k e t h a n c o u l d C y p r i n o t u s . Rates o f s u p p l y o f f o o d o t h e r t h a n none a t a l l were not a t t e m p t e d . The a n i m a l s used f o r t h e e x p e r i m e n t were c o l l e c t e d f r o m t h e p u d d l e a l o n g w i t h some mud and were k e p t l i v i n g on t h i s mud f o r 2 weeks p r i o r t o t h e e x p e r i m e n t . S i n g l e a n i m a l s were added t o s m a l l p e t r i d i s h e s o f d i s t i l l e d t a p water and were k e p t a t 20°C. F o r t h e f i r s t few hou r s each d i s h was 60 i n s p e c t e d c l o s e l y so t h a t t h e f a e c a l p e l l e t s c o u l d be removed t o p r e v e n t reingestion„ F o r C y p r i n o t u s the a n i m a l s were s e g r e g a t e d i n t o t h r e e s i z e s a c c o r d i n g t o t h e i r c a r a p a c e l e n g t h -0 - 0,5 mm, 0„5 - 1=0 mm, and 1.0 - 1.5 mm. The i n i t i a l numbers v a r i e d b u t f o r each s i z e c l a s s t h e r e were 2 o r 3 r e p l i c a t e s e t s o f d i s h e s (see F i g . 1 9 ) . D u r i n g t h e f i r s t 20 hours no a n i m a l s d i e d b u t a f t e r t h i s t i me t h e number a l i v e began t o d e c r e a s e , a t an a l m o s t c o n s t a n t r a t e . The 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 a l i n e a r r e l a t i o n s h i p between t h e p r o p o r t i o n a l i v e and l e n g t h o f d e p r i v a t i o n which a r e g i v e n i n t h e l e g e n d t o F i g . 20 a r e not l e s s t h a n 0.92. Only i n a few o f t h e e x p e r i m e n t s was t h e r e any c o n s i s t e n t t r e n d o f the p o i n t s about t h e l i n e . F u r t h e r m o r e , t h e s i z e o f t h e a n i m a l made no d i f f e r e n c e a t a l l : l a r g e r a n i m a l s w h i c h had been e x p e c t e d t o have g r e a t e r r e s e r v e s and thus r e s i s t a n c e t o d e p r i v a t i o n l a s t e d no l o n g e r t h a n t h e s m a l l e s t ones. The mean o b s e r v e d l e n g t h o f t i m e was 64 h o u r s . The maximum t i m e was 128 h o u r s . The r e s u l t f o r H e r p e t o c y p r i s were s u b s t a n t i a l l y d i f f e r e n t from t h o s e f o r t h e o t h e r s p e c i e s ( F i g . 19D). The s m a l l e s t a n i m a l s (0 - 0.5 mm i n l e n g t h ) l i v e d as l o n g as a l l s i z e s o f C y p r i n o t u s , t h e i r d e c r e a s e b e i n g a l m o s t i d e n t i c a l . But t h e two l a r g e r s i z e s 0.5 - 1.0 mm and 1.5 - 2.0 mm l i v e d f o r a mean l e n g t h o f t i m e o f 160 t o 186 hours r e s p e c t i v e l y . I n a l l c a s e s t h e r a t e o f d e c r e a s e was c o n s t a n t . The e x p e c t e d g r e a t e r r e s i s t a n c e o f H e r p e t o c y p r i s a n i m a l s was found t o be t h e c a s e . I n t h e e x p e r i m e n t f o r b o t h s p e c i e s t h e l o s s o f i n t e n s i t y o f c o l o u r t h a t had been o b s e r v e d i n p r e v i o u s m o r t a l i t y e x p e r i m e n t s Figure 19 The lengths of time that each species can withstand t o t a l food deprivation. The proportion of the o r i g i n a l number-a l i v e i s given f o r each i n t e r v a l of time, (The c o r r e l a -t i o n c o e f f i c i e n t , r, i s given) F i g , 19A - Cyprinotus, 0 - 0,5 mm i n length. The equation of the l i n e i s y = 114,1 - 0„994X,r = 0,92, F i g , 19B - Cyprinotus, 0,5 - 1,0 mm i n length. The equation of the l i n e i s y = 121,0 - l,0X,r = 0,95, F i g , 19C - Cyprinotus, 1=0 - 1,5 mm i n length. The equa-tio n of the l i n e i s y = 131,3 - l„45X,r = 0,97. F i g . 19D - Herpetocypris, 0 - 0.5 mm long (closed c i r c l e s ) , 0.5 - 1.0 mm long (open c i r c l e s ) and 1.5 - 2.0 mm long (crosses). The respective equations and c o r r e l a t i o n c o e f f i c i e n t s are, y = y = y = 113.5 - 1.2 6X,r = 143.6 - 0.59X,r = 159.7 - 0.57X,r = 0 . 9 6 , 0 . 9 9 , 0 . 9 8 . PERCENTAGE ALIVE 62 was foundo As t h e t i m e o f d e p r i v a t i o n i n c r e a s e d so the i n t e n s i t y o f t h e c o l o u r o f t h e pigment i n t h e c a r a p a c e v a l v e s o f b o t h s p e c i e s d e c r e a s e d . Some p a r t s o f t h e body o f t h e H e r p e t o c y p r i s a n i m a l s became a l m o s t t r a n s p a r e n t , I t h e r e f o r e c o n c l u d e t h a t H e r p e t o c y p r i s a n i m a l s are more a b l e t o w i t h s t a n d f o o d d e p r i v a t i o n t h a n C y p r i n o t u s and t h a t t h i s i s a p a r t i a l e x p l a n a t i o n o f t h e o b s e r v e d s m a l l e r e f f e c t o f i n c r e a s i n g d e n s i t y upon H e r p e t o c y p r i s , A f u r t h e r consequence o f i n c r e a s i n g t h e d e n s i t y was c a n n i b a l i s m o f o t h e r o s t r a c o d s by members o f i t s own and t h e o t h e r s p e c i e s . T h i s o n l y seemed t o o c c u r v/hen an a n i m a l was i n t h e p r o c e s s o f m o u l t i n g , i m m e d i a t e l y a f t e r w h i c h t h e new v a l v e s a re v e r y s o f t and can be chewed by t h e o t h e r a n i m a l s . However, I was not a b l e t o e s t a b l i s h whether t h e e a t e n a n i m a l s were dead p r i o r t o the ev e n t o r d i e d as a r e s u l t o f i t . Many a n i m a l s were i n v o l v e d i n t h e e a t i n g , swarming o v e r t h e v i c t i m and q u i c k l y d e m o l i s h i n g i t . Summary 1. Both s p e c i e s o f o s t r a c o d have a c o n t a g i o u s d i s t r i b u t i o n o v e r t h e mud s u r f a c e . T h i s d i s t r i b u t i o n i s a d e q u a t e l y d e s c r i b e d by t h e n e g a t i v e b i n o m i a l d i s t r i b u t i o n at a l l d e n s i t i e s . 2. When t h e s p e c i e s were p l a c e d t o g e t h e r t h e d i s p e r s i o n c o -e f f i c i e n t , K, f o r each s p e c i e s was l e s s t h a n f o r t h e s p e c i e s a l o n e a t each d e n s i t y , i n d i c a t i n g t h a t t h e i r d i s t r i b u t i o n s were more' clumped. 63 3. Herpetocypris i s more able to survive a period of t o t a l food deprivation than i s Cyprinotus. 4 . At high d e n s i t i e s cannibalism of each species by the other can occur. f) The number of animals of the same age reaching maturity The number of animals of the same age i n any unit of space present at the time when they reach maturity w i l l depend upon t h e i r i n i t i a l number, the length of time required to reach that state and the manner i n which the mortality dictated by equation (3) during each i n t e r v a l of time i s d i s t r i b u t e d among the age c l a s s e s . This length of time i s dependent upon the i n i t i a l number of eggs present and upon the time at which the p a r t i c u l a r group of animals hatched. Each of these has been dealt with separately except f o r the d i s t r i b u t i o n of mortality among the age c l a s s e s . The model used and tested f o r t h i s i s presented i n t h i s section. Only an approximation to the r e a l answer has been attempted, primarily because the formal a n a l y t i c a l s o l u t i o n i s so formidable and numerical evaluation i s a quite reasonable s u b s t i t u t e . The r e l a t i o n s h i p between the t o t a l number present at any time, obtained from equation (3) and the present quantity i s most exactly stated as follows: V N (t, a) da. = N (t) =\ H e " R T - D • N - B-N2 dt Jo ^o where at time T the maximum number of ages present (a) i s T. 6 4 The change i n N, A N, d u r i n g a s m a l l u n i t o f t i m e , A t , p r i o r t o t h e m a t u r a t i o n o f t h e a n i m a l s , i s A N = H o e ~ R ' T - D-N - B-N 2 where t h e c o e f f i c i e n t s a r e a p p r o p r i a t e t o t h e u n i t o f t i m e . I f each l o t o f r e c r u i t s a p p e a r i n g d u r i n g A t i s d enoted as an a g e - c l a s s t h e n t h e maximum number o f age c l a s s e s t h a t can be p r e s e n t a t t i m e T i s T / A t and so t h e m o r t a l i t y d u r i n g t h e i n t e r v a l T t o T + A t w i l l be d i s t r i b u t e d among t h i s number o f ages. The f o l l o w i n g d i s t r i b u t i o n model has been t e s t e d . That t h e p a r t o f t h e t o t a l m o r t a l i t y i n f l i c t e d upon an age c l a s s d u r i n g an i n t e r v a l o f t i m e i s dependent upon t h e age o f t h e c l a s s a t t h a t t i m e and t h e number o f o t h e r c l a s s e s p r e s e n t . F o r a c l a s s whose- age i s A , t h i s i s g i v e n by x l v v -.0115 • X YN • e dx where YN =AN • 0.0115 and X- = A X = A + A x Y L • A T X = — The q u a n t i t y L i s t h e maximum v a l u e o f X which was 400. T h i s . v a l u e was used because t h e v a l u e o f •400 V M -.0115 • X , YN-e dx 'o i s c l o s e t o A N . I t i s i n f a c t e q u a l t o (0.988 x A N ) . T h i s e r r o r i s s m a l l and i s not s u b s t a n t i a l l y r e d u c e d by i n c r e a s i n g L, The a c c u r a c y was f u r t h e r i m p r o v e d by u s i n g a r e a l v a l u e o f Xo T h i s p a r t i t i o n i n g model i s i l l u s t r a t e d i n Fig„ 20, The number o f a n i m a l s p r e s e n t a t m a t u r i t y can be c a l c u l a t e d from t h e v a r i a b l e s l i s t e d i n i t i a l l y , p r o v i d e d t h a t t h e t i m e i s c o n t i n u o u s because t h e o n l y s o u r c e o f r e c r u i t m e n t i s t h e s t o r e o f eggs w h i c h was i n i t i a l l y p r e s e n t . A f t e r m a t u r i t y t h i s need not be t r u e . The p r o c e s s e s o f r e c r u i t m e n t from s t o r e d eggs, c a l c u l a t i o n o f t o t a l m o r t a l i t y and p a r t i t i o n i n g and a p p l i c a t i o n o f m o r t a l i t y among t h e a g e - c l a s s e s were combined i n a computer program. The v a l u e o f t was 1 day and the newly r e c r u i t e d a g e - c l a s s o f t h e day was immune t o m o r t a l i t y . The program was r u n so t h a t each of t h e s e was e x e c u t e d once e v e r y time around and t h e numbers of each age-c l a s s l e f t were s t o r e d i n an a r r a y . A t r e g u l a r i n t e r v a l s o f t i m e t h e p r o p o r t i o n o f t h e t o t a l numbers p r e s e n t t h a t b e l o n g e d t o a p a r t i c u l a r " a g e - c l a s s was c a l c u l a t e d . T h i s p r o p o r t i o n i s a l t e r e d by" t h e d e n s i t y o f t h e i n i t i a l i n p u t , so i n o r d e r t o t e s t t h e t h e o r y a g a i n s t the o b s e r v e d t h e mean i n p u t o f 2 C y p r i n o t u s eggs p e r cm f o r 1968-69 was used and t h e e x p e c t e d p r o p o r t i o n o f t h e t o t a l number b e l o n g i n g t o each a g e - c l a s s was c a l c u l a t e d f o r t h o s e t i m e s a t which t h e p o p u l a t i o n had been sampled. The way i n w h i c h t h e l i n e s r e l a t i n g t h e p e r c e n t age o f t h e t o t a l number b e l o n g i n g t o an a g e - c l a s s and t h e day o f r e c r u i t m e n t o f t h a t ' a g e - c l a s s f o r d i f f e r e n t v a l u e s o f T i s shown i n F i g , 21A, A p p a r e n t l y a l l r e c r u i t e d a g e - c l a s s e s have members u n t i l about T = 40 but t h e n a g e - c l a s s e s r e c r u i t -ed a f t e r about day 2 0 b e g i n t o become e x t i n c t so t h a t t h e r e s h o u l d be an i n c r e a s i n g p r e p o n d e r a n c e of o l d e r ages. The F i q u r e 20 I l l u s t r a t i o n o f the method o f p a r t i t i o n i n g t h e m o r t a l i t y i n each i n t e r v a l o f t i m e , among t h e a g e - c l a s s e s . The f u n c t i o n f ( x ) i s g i v e n by e-°<> : I- : L 5 X, L = 4 0 0 , A T = 1 and T i s t h e number o f days s i n c e the p u d d l e f i l l e d , t h a t t h e p a r t i t i o n i n g i s p e r f o r m e d . There a re as many i n t e r v a l s o f x as t h e r e a r e da y s . F i g u r e 21 Changes i n the p r o p o r t i o n s o f each a g e - c l a s s o f C y p r i n o t u s r e p r e s e n t e d , a t d i f f e r e n t v a l u e s o f t i m e a f t e r t h e b e g i n n i n g o f r e c r u i t m e n t . The shapes o f t h e s e r e l a t i o n s h i p s f o l l o w f r o m t h e way i n which t h e r a t e o f r e c r u i t m e n t changes w i t h t i m e and t h e way I n wh i c h t h e m o r t a l i t y i s p a r t i t i o n e d among t h e a g e - c l a s s e s p r e s e n t . A l l v a l u e s have been o b t a i n e d n u m e r i c a l l y . F i g . 21 (upper) - t h e p e r c e n t a g e of t h e t o t a l number p r e s e n t a t d i f f e r e n t t i m e s (T) which b e l o n g t o p a r t i c u l a r a g e - c l a s s e s . F i g . 21 ( l o w e r ) - t h e p e r c e n t a g e o f t h e i n i t i a l number r e c r u i t e d t o each a g e - c l a s s which r e m a i n a l i v e a t d i f f e r e n t t i m e s ( T ) . DAY RECRUITED 68 p r o p o r t i o n s o f t h e t o t a l b e l o n g i n g t o t h e f i r s t - r e c r u i t e d c l a s s e s , i n f a c t , b e g i n t o i n c r e a s e because t h e y are becoming I n c r e a s i n g l y immune t o m o r t a l i t y w i t h i n c r e a s i n g age. The t h e o r y g i v e s p r e d i c t i o n s o f a. f i n e n e s s t h a t c o u l d n o t be approached by t h e f i e l d samples s i n c e i n t h e s e i t was n o t p o s s i b l e t o d i s t i n g u i s h between a n i m a l s whose age d i f f e r e d by an o r d e r o f a day. The a n i m a l s i n t h e samples were d i v i d e d i n t o t h r e e s i z e c l a s s e s , (0 - 0.5, 0.5 - 1.0, 1.0 - 1.5 mm i n l e n g t h ) , and t h e number i n each c l a s s f o r a l l samples i n t h e p u d d l e on t h e sample d a t e were combined. I n t h e s e samples i t was p o s s i b l e t o d i s t i n g u i s h a c l e a r d i f f e r e n c e between l a r g e r a n i m a l s and the s m a l l ones. S i n c e t h e a n i m a l s moult a t r e g u l a r s i z e s i t i s s a f e t o assume t h a t t h e s e can be t r e a t e d as d i f f e r e n t ages. T h i s f i r s t p r e d i c t i o n by t h e t h e o r y o f t h e e x i s t e n c e o f two c l e a r l y s e p a r a b l e age-groups a f t e r a c e r t a i n t i m e was i n f a c t f o u n d . The p r o p o r t i o n s o f t h e t o t a l numbers t h a t s h o u l d b e l o n g t o each of t h e s e has been t e s t e d and t h e r e s u l t s a r e g i v e n i n T a b l e V I . On b o t h sample d a t e s t h e ex-p e c t e d and. t h e o b s e r v e d p r o p o r t i o n s agree v e r y n i c e l y . The consequence o f t h e model i s t h a t o n l y t h e f i r s t few r e c r u i t c l a s s e s e v e r r e a c h m a t u r i t y because a l l t h e l a t e r ones a p p a r e n t l y do not have enough members. The manner i n w h i c h t h e p e r c e n t a g e o f t h e i n i t i a l number i n a c l a s s changes w i t h i n c r e a s i n g t i m e i s shown i n F i g . 2 IB. I t s h o u l d be n o t e d t h a t t h e p r o p o r t i o n a l i v e o f t h e most r e c e n t a g e - c l a s s on t h a t day i s 100.0% b e c a u s e , i n t h e model, i t i s not s u b j e c t e d t o m o r t a l i t y u n t i l t h e f o l l o w i n g day. The number o f a g e - c l a s s e s 69 TABLE VI The observed (0) and expected (E) numbers of l a r g e (L) and s m a l l (S) C y p r i n o t u s animals p r e s e n t i n the sample from the puddle on the dates - 26/10/68 (T = 38), 5/12/68 (T = 78) o (The expected p r o p o r t i o n s are shov/n i n the upper p a r t of F i g . 21). T = 38 S L E 51 81 0 38 96 2 df ° > .05 = 5.99 Accept h y p o t h e s i s o f no d i f f e r e n c e between expected and observed numbers. T = 78 S E 4 0 5 L 52 92 * 2 c a l c . - ° ' 2 5 4 Accept h y p o t h e s i s of no d i f f e r e n c e . 70 present with members as a. function of time increases l i n e a r -ly at f i r s t , reaching a maximum of about 40 when T = 40 and then begins to decrease as vacant classes appear. This theory appears to be adequate f o r Cyprinotus i n the puddle. Unfortunately ?the same theory cannot be tested for Herpetocypris because I do not have the information concerning the input of eggs f o r the species during the winter of 1968-69. The number of Cyprinotus animals belonging to a p a r t i c u l a r age-class which reach maturity can now be obtained as follows: Tm N (t) dt = N T Th where Th i s the time a f t e r f i l l i n g of the puddle that the age-c l a s s was r e c r u i t e d and Tm i s that number of days required (TRQU) to accumulate the number of day-degrees given previous-l y . The proportion of the t o t a l number present at that time, which belong to the class can then be obtained from F i g . 21A. Summary 1. When the mortality i n any i n t e r v a l of time i s d i s t r i b u t e d i n a negative exponential manner among the age-classes so that the youngest receive the most 7 the r e s u l t i n g expected age-classes present i n the puddle at d i f f e r e n t times were found to agree c l o s e l y with the observed. 2. The only animals which reach maturity are the survivors of the f i r s t - f e w - r e c r u i t e d age-classes. Later classes do not 71 have enough members t o s u r v i v e t h e p e r i o d , cf_) The e g g - l a y i n g by mature a n i m a l s D u r i n g t h e growth o f t h e a n i m a l s from moult t o moult t h e o v a r i e s , which a r e p l a c e d on t h e s i d e s o f t h e body and a g a i n s t t h e i n n e r s u r f a c e o f t h e v a l v e s , g r a d u a l l y i n c r e a s e d i n s i z e , but l a r g e y o l k e d eggs d i d not appear u n t i l a f t e r the l a s t moult= P r i o r t o t h e l a y i n g of t h e f i r s t egg as many as 25 may b u i l d up i n t h e abdomen i n two masses, each produced by t h e o v a r y o f one s i d e . The eggs l a i d by b o t h s p e c i e s are b r i g h t l y c o l o u r e d , t h o s e of C y p r i n o t u s b e i n g a l i g h t orange and t h o s e o f H e r p e t o c y p r i s a. l i g h t y e l l o w . Both are c i r c u l a r , and 0,14 -0,18 mm i n d i a m e t e r . Each egg i s e n c l o s e d i n a t o u g h , t r a n s -p a r e n t , p r o t e c t i v e c a s e . When l a i d , t h e egg c a s e o f C y p r i n o t u s i s a p p a r e n t l y q u i t e s t i c k y because eggs are f o u n d a d h e r i n g t o one a n o t h e r . T h i s s p e c i e s p l a c e s i t s eggs i n t h e c r a c k s and c r e v i c e s o f s t i c k s , l e a v e s and g r a s s stems o r i n t h e minute s u r f a c e i n d e n t a t i o n s o f sand g r a i n s . I f t h e r e are a l a r g e number of mature anima.ls p r e s e n t and t h e y can g e t t o g e t h e r , t h e n th e e g g - l a y i n g i s u s u a l l y communal and each a n i m a l w i l l c o n t r i b u t e eggs t o a common s t i c k o r s t o r e . Eggs are o f t e n l a i d r e l a t i v e t o eggs a l r e a d y p r e s e n t because th e c o n t r i b u t i o n s o f many a n i m a l s a r e o r g a n i z e d so t h a t b e g i n n i n g a t one p o i n t on a rough g r a s s stem, the eggs a r e l a i d o ut from t h a t p o i n t i n one o r more d i r e c t i o n s so t h a t each egg i s packed t i g h t l y a g a i n s t i t s n e i g h b o u r s and l a y i n g i s o c c u r r i n g a l o n g a f r o n t 72 a t any t i m e . The o u t e r c o v e r i n g must be s o f t and a d h e s i v e a t l a y i n g because,when i n d i v i d u a l eggs are removed from a mass, t h e y a r e shaped so as t o f i t s n u g l y a g a i n s t t h e o t h e r s . H e r p e t o c y p r i s eggs a r e , on t h e o t h e r hand, not a d h e s i v e . The a n i m a l s l a y them i n t h e h o l l o w o f c u r l e d g r a s s stems o r poke them i n t o t h e s o f t t i s s u e o f a stem. Both s p e c i e s w i l l c o n t i n u e t o l a y eggs even a l t h o u g h t h e r e are no s o l i d o b j e c t s t o w h i c h t h e y may be a t t a c h e d . I n p e t r i - d i s h e s o f s i e v e d mud i n w h i c h t h e a n i m a l s were grown, eggs were f o u n d l y i n g l o o s e i n t h e s e d i m e n t . The eggs o f C y p r i n o t u s were sometimes l a i d upon t h e smooth p l a s t i c s u r f a c e o f the d i s h . The e f f e c t s o f t h e numbers o f e g g - l a y i n g a n i m a l s p r e s e n t and the t e m p e r a t u r e upon t h e e g g - l a y i n g r a t e have been i n v e s t i g a t e d . Mature a n i m a l s were grown a t a range o f d e n s i t i e s and t e m p e r a t u r e s upon p r e p a r e d mud from t h e p u d d l e i n s m a l l p e t r i - d i s h e s . The d i s h e s were p l a c e d under f l u o r e s c e n t lamps, wh i c h were t u r n e d on f o r 9 out o f 24 hours and l e f t f o r two weeks p r i o r t o t h e a d d i t i o n o f t h e a n i m a l s . The r a t e s o f e g g - l a y i n g p e r a n i m a l were th e n measured o v e r p e r i o d s o f from 7 - 2 0 d a y s . As t h e t e m p e r a t u r e i n c r e a s e d t h e e g g - l a y i n g r a t e i n c r e a s e d s l o w l y at f i r s t and t h e n v e r y r a p i d l y as the temper-a t u r e approached 2 0°C. As t h e numbers o f a n i m a l s p r e s e n t i n c r e a s e d t h e e g g - l a y i n g r a t e d e c r e a s e d q u i c k l y a t f i r s t and t h e n more s l o w l y . T h i s s u g g e s t e d the f o l l o w i n g e q u a t i o n which was f i t t e d by r e g r e s s i o n : l n ELR = InC + CT • T - CN • Nt (9) where T i s t h e t e m p e r a t u r e , CT t h e r a t e o f i n c r e a s e o f t h e egg-7 3 2 l a y i n g r a t e w i t h t e m p e r a t u r e and NT t h e number p r e s e n t p e r cm and CN t h e r a t e o f c h a n g e w i t h i n c r e a s i n g n u m b e r s , F i g , 22A a n d B o T r a n s f o r m i n g e q u a t i o n ( 9 ) and p u t t i n g i n t h e v a l u e s f o r C, CT and CN o b t a i n e d f r o m t h e r e g r e s s i o n we h a v e „ T O n n n i ( 0 o l 3 7 7 • T - 0,1902-NT) ELR = 0,071e The e f f e c t o f i n c r e a s i n g b o t h t e m p e r a t u r e and t h e number p r e s e n t was a p p a r e n t l y a b o u t t h e same t h o u g h d i f f e r e n t i n s i g n . The v a r i a n c e o f t h e o b s e r v e d v a l u e s was n o t c o n s t a n t t h r o u g h o u t : i t i n c r e a s e d as t h e t e m p e r a t u r e i n c r e a s e d and as t h e d e n s i t y d e c r e a s e d s o t h a t t h e e x p e c t e d e g g - l a y i n g r a t e was more u n -c e r t a i n u n d e r t h e s e c o n d i t i o n s , A'n e q u a t i o n o f t h e same f o r m p r o v e d t o be a d e q u a t e f o r t h e d e s c r i p t i o n o f t h e e g g - l a y i n g r a t e b y H e r p e t o c y p r i s (number o f d a t a v a l u e s = 4 9 , c o r r e l a t i o n c o e f f i c i e n t = 0 , 7 5 ) , The r e g r e s s i o n v a l u e s o b t a i n e d w e r e , „ T - „ n c ( 0 , 1 3 0 8 • T - 0 . 3 5 9 8 - N T ) E L R = u,0be T h e s e v a l u e s a r e v e r y s i m i l a r t o t h o s e o b t a i n e d f o r C y p r i n o t u s e x c e p t t h a t t h e e f f e c t o f i n c r e a s i n g t h e number p r e s e n t was a l i t t l e g r e a t e r . F o r b o t h s p e c i e s much v a r i a b i l i t y r e s u l t e d f r o m t h e a n i m a l s s t o r i n g e g g s i n t h e abdomen and t h e n l a y i n g more i n a s h o r t e r t i m e t h a n w o u l d be e x p e c t e d by t h e a b o v e e q u a t i o n . B u t f o r p e r i o d s o f a week o r more t h e e g u a t i o n s s h o u l d g i v e an a c c u r a t e p r e d i c t i o n a b o u t t h e r a t e o f e g g - l a y i n g p e r d a y . B e s i d e s t h e n e c e s s i t y o f h a v i n g t o s h a r e among more i n d i v i d u a l s t h e a v a i l a b l e f o o d , p a r t o f t h e e f f e c t o f i n c r e a s i n g t h e n u m bers p r e s e n t i s one o f i n t e r f e r e n c e d u r i n g e g g - l a y i n g s i n c e t h e a n i m a l s a t h i g h d e n s i t y s p e n d a l o t o f t i m e c r a w l i n g F i g u r e 22' The r e l a t i o n s h i p between the egg-laying r a t e of C y p r i n o t u s , the water temperature (°C) and the d e n s i t y of the animals. The only data shown are f o r the egg-l a y i n g r a t e at a range of temperature, when the d e n s i t y i s 0,1 per crrr ( F i g , 22A) , and at a range of d e n s i t i e s when the temperature i s 18°C ( F i g , 22B), The l i n e s are from equation ( 9 ) whose c o e f f i c i e n t s were obtained by m u l t i p l e r e g r e s s i o n u s i n g these and a. small number" of other measurements of the egg-laying r a t e , which are not shown. The number of data values i s 120 and the m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t i s 0,74, 75 o v e r one a n o t h e r and d i s t u r b i n g o t h e r s t r y i n g t o l a y eggs. Owing t o a s h o r t a g e o f a n i m a l s t h e e f f e c t s o f t h e p r e s e n c e o f members o f t h e o t h e r s p e c i e s upon t h e o t h e r c o u l d n o t be s t u d i e d . I n t h e s y n t h e s i z e d model p r e s e n t e d l a t e r i t w i l l be assumed t h a t t h e members o f t h e o t h e r s p e c i e s a f f e c t t h e egg-l a y i n g o f t h e s p e c i e s as though t h e y were members of t h a t s p e c i e s . N e i t h e r s p e c i e s seems t o be c a p a b l e o f e a t i n g eggs o f i t s own o r o f t h e o t h e r . Loose eggs o f each s p e c i e s s u p p l i e d t o b o t h k i n d s o f a n i m a l s were n o t e a t e n . I t was n o t p o s s i b l e t o t e s t the model f o r e g g - l a y i n g i n t h e p u d d l e s i n c e t h e eggs are e x t r a o r d i n a r i l y d i f f i c u l t t o f i n d . However, the models have been t e s t e d upon t h e e g g - l a y i n g by s m a l l p o p u l a t i o n s of a n i m a l s g r o w i n g i n p e t r i - d i s h e s i n w h i c h t h e water t e m p e r a t u r e and d e n s i t y changed w i t h t i m e . There were 4 r e p l i c a t e s o f each s p e c i e s g r o w i n g by i t s e l f a t ambient t e m p e r a t u r e . A t . i n t e r v a l s o f 7 days t h e number o f a n i m a l s p r e s e n t and numbers o f eggs l a i d were r e c o r d e d . The w a t e r t e m p e r a t u r e was r e c o r d e d c o n t i n u o u s l y . T h e r e f o r e t h e e q u a t i o n s f o r each s p e c i e s by i t s e l f c o u l d be t e s t e d u s i n g as i n p u t s t h e d e n s i t y and w a t e r t e m p e r a t u r e and comparing t h e e x p e c t e d w i t h t h e o b s e r v e d c u m u l a t i v e number o f eggs l a i d as a f u n c t i o n o f t i m e . F o r C y p r i n o t u s t h e r e s u l t s o f t h i s t e s t a r e g i v e n i n F i g . 23. The p r e d i c t e d a c c u m u l a t e d number of eggs a g r e e s w i t h t h e o b s e r v e d a t most t i m e s and i n a l l r e p l i -c a t e s . The r e s u l t s o f t h e same t e s t f o r H e r p e t o c y p r i s are shown i n F i g . 24. Here t h e agreement i s not so good and some F i g u r e 2 3 T e s t o f t h e a b i l i t y o f t h e s i m p l e r e l a t i o n s h i p between t h e e g g - l a y i n g r a t e o f C y p r i n o t u s , t h e wa t e r t e m p e r a t u r e and t h e d e n s i t y , t o p r e d i c t t h e c u m u l a t i v e number o f eggs l a i d p e r cm^ by s m a l l p o p u l a t i o n s o f a n i m a l s i n p e t r i - d i s h e s o f mud. F o r each r e p l i c a t e , A - D, t h e d e n s i t y o f a n i m a l s and t h e o b s e r v e d c u m u l a t i v e number o f eggs l a i d o v e r t i m e ( c l o s e d c i r c l e s ) a re shown. The e x p e c t e d c u m u l a t i v e number o f eggs p e r cm^ (open c i r c l e s ) accompany each r e p l i c a t e . The wa t e r temper-ature" i s shown a l o n g t h e bottom o f t h e f i g u r e - . WATER CUMULATIVE DENSITY CUMULATIVE DENSITY CUMULATIVE DENSITY CUMUATIVE DENSITY OF OF OF OF TEMPERATURE CO NUMBER OF EGGS ANIMALS NUMBER OF EGGS ANIMALS NUMBER OF EGGS ANIMALS NUMBERS OF EGGS ANIMALS F i g u r e 24 T e s t o f t h e e g g - l a y i n g model f o r H e r p e t o c y p r i s t o p r e d i c t t h e c u m u l a t i v e number o f eggs l a i d by s m a l l p o p u l a t i o n s l i v i n g on mud i n p e t r i - d i s h e s a t ambient t e m p e r a t u r e o F o r each r e p l i c a t e , A - D, t h e d e n s i t y o f a n i m a l s and t h e e x p e c t e d (open c i r c l e s ) , and o b s e r v e d ( c l o s e d c i r c l e s ) c u m u l a t i v e number of eggs l a i d a r e shown. A l o n g t h e bottom o f t h e f i g u r e t h e mean d a i l y w a t e r t e m p e r a t u r e (°C.) f o r each i n t e r v a l o f t i m e i s shown. WATER CUMULATIVE NUMBER CUMULATIVE NUMBER CUMULATIVE NUMBER CUMULATIVE NUMBER OF OF OF Or TEMPERATURE(C) NUMEER OF EGGS LAID ANIMALS NUMBER OF EGGS LAID ANIMALS NUMBER OF EGGS LAID ANIMALS NUMBER OF EGGS LAID ANIMALS 3 , 3 3 o p p 3 3 p O p i O t S p 9 y i p w S p 78 q u i t e wide d e v i a t i o n s o f the o b s e r v e d from t h e e x p e c t e d were f o u n d . The r e a s o n s f o r t h i s a re unknown b u t i t s h o u l d be n o t e d t h a t t h e t e s t was p e r f o r m e d under t h e c o n d i t i o n s when t h e e g g - l a y i n g r a t e i s most s e n s i t i v e t o change o f t h e v a r i a b l e s . Summary 1. The e g g - l a y i n g r a t e o f b o t h s p e c i e s i s v e r y s i m i l a r and d e c r e a s e s w i t h i n c r e a s i n g d e n s i t y and d e c r e a s i n g t e m p e r a t u r e . 2. The b r i g h t l y - c o l o u r e d eggs a r e a t t a c h e d or poked i n s i d e s o l i d o b j e c t s i n t h e e n v i r o n m e n t . 3 . I t i s unknown whether t h e e f f e c t s o f a n i m a l s o f t h e o t h e r s p e c i e s upon t h e e g g - l a y i n g r a t e o f t h e s p e c i e s would be any g r e a t e r t h a n members o f t h a t s p e c i e s . 4. When t e s t e d upon s m a l l p o p u l a t i o n s o f each s p e c i e s g r o w i n g a l o n e t h e r e l a t i o n s h i p between e g g - l a y i n g , t e m p e r a t u r e and d e n s i t y gave p r e d i c t i o n s c l o s e t o t h e o b s e r v e d . h) The h a t c h i n g o f new eggs Between t h e time of l a y i n g and o f h a t c h i n g o f each egg t h e r e i s a d e l a y which i s f o r b o t h s p e c i e s a f u n c t i o n o f t h e t e m p e r a t u r e a t w h i c h t h e eggs were l a i d , though t h e r e l a t i o n s h i p s w i t h t h i s v a r i a b l e are e n t i r e l y d i f f e r e n t f o r each s p e c i e s . A s m a l l number o f a n i m a l s o f each s p e c i e s were grown a t a range o f t e m p e r a t u r e s and t h e eggs which t h e s e a n i m a l s l a i d were k e p t a t t h e same t e m p e r a t u r e . The eggs were c o l l e c t e d o v e r a p e r i o d o f a few days and removed from t h e d i s h e s . The t i m e between t h e i r c o l l e c t i o n and b e g i n n i n g o f 79 h a t c h i n g was measured f o r each t e m p e r a t u r e . The eggs o f C y p r i n o t u s h a t c h e d i n an u n u s u a l manner s i n c e t h e r e were two d i s t i n c t g r o u p s , each o f which began t o h a t c h at d i f f e r e n t t i m e s and whose h a t c h i n g c o n t i n u e d f o r a l o n g t i m e . The r e l a -t i o n s h i p between th e t i m e o f l a y i n g and t h e t i m e o f b e g i n n i n g o f h a t c h i n g f o r C y p r i n o t u s eggs i s shown i n F i g , 25. F o r b o t h h a t c h e s t h e d e l a y (HDL1 and HDL2) i s s h o r t e s t a t the h i g h e s t t e m p e r a t u r e but b e g i n s t o i n c r e a s e r a p i d l y as t h e t e m p e r a t u r e i s d e c r e a s e d . The manner o f t h i s i n c r e a s e i s f o r the f i r s t h a t c h HDL1 = 6 2 7 . 0 e ~ ° ° 1 5 8 7 ' T (10) and f o r t h e second h a t c h -0 111 - T HDL2 = 1159.8e U ° ± ± - L ( H ) These l i n e s a r e a l m o s t p a r a l l e l , w hich s u g g e s t s t h a t t h e d e l a y -i n g e f f e c t o f t e m p e r a t u r e upon each o f t h e k i n d s o f eggs i s a l m o s t t h e same. The d e l a y f o r h a t c h i n g o f t h e second group a t 4°C was l o n g e r t h a n t h e l e n g t h o f t h e e x p e r i m e n t and so was not o b s e r v e d . F o r H e r p e t o c y p r i s t h e e f f e c t o f t h e t e m p e r a t u r e was t o cause a c o n s t a n t change i n t h e d e l a y . As t h e temper-a t u r e i n c r e a s e d t h e r e was a l i n e a r d e c r e a s e i n t h e d e l a y , F i g . 25. The r e l a t i o n s h i p o b t a i n e d by r e g r e s s i o n was HDL = 105.4 - 5.45-T (12) The v a l u e o f T when HDL = 0 i s 19.34°C„ I t i s known t h a t above a w a t e r t e m p e r a t u r e o f 21°C a l l t h e eggs l a i d by t h i s s p e c i e s a r e i n v i a b l e so t h a t h i s i n t e r c e p t i s a p p r o p r i a t e s i n c e o n l y p o s i t i v e v a l u e s o f HDL a r e u s e d . C y p r i n o t u s l a y s v i a b l e eggs a t l e a s t up t o 26°C b u t t h i s i s o f l i t t l e use s i n c e t h e p u d d l e F i g u r e 2 5 The delay i n beginning of hatching of the eggs of both species as a f u n c t i o n of the water temperature (°C)„ F i g . 2 5 A - the delay i n the beginning of hatching of both hatches of Cyprinotus eggs. The f u n c t i o n s are equations (10) and (11), and the 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 each l i n e are, r e s p e c t i v e l y , 0.88 and 0.99. F i g . 25B - the delay of hatching of Herpetocypris eggs as a f u n c t i o n of the water temperature. The i n t e r c e p t and slope appear i n equation (12) and the c o r r e l a t i o n c o e f f i c i e n t i s 0.95. 81 would d r y up q u i c k l y a t t h i s t e m p e r a t u r e . A f t e r t h e i n i t i a t i o n o f h a t c h i n g o f each group of C y p r i n o t u s eggs i t c o n t i n u e s f o r l o n g p e r i o d s o f time and t h e i n i t i a l f a s t r a t e o f h a t c h i n g g r a d u a l l y t a p e r s o f f t o z e r o . The r a t e o f h a t c h i n g as a f u n c t i o n o f time a f t e r i n i t i a t i o n has been measured a t each o f t h e t e m p e r a t u r e s and i s o f t h e form In EHR = In C - RH • T (13)' The d a t a f o r each r e p l i c a t e o f eggs at each t e m p e r a t u r e and f o r b o t h t h e f i r s t and second h a t c h e s has been t e s t e d and found t o be o f t h e above k i n d . There does not appear t o be any r e l a t i o n -s h i p between th e v a l u e o f the RH and the t e m p e r a t u r e and nor does i t v a r y between t h e two h a t c h e s ( T a b l e V I I ) . The mean o f a l l t h e s e v a l u e s i s 0.04 73. The H e r p e t o c y p r i s eggs a l l seem t o h a t c h a f t e r a c o n s t a n t p e r i o d o f t i m e so t h a t t h e r e i s no c o r r e s p o n d i n g v a l u e t o RH f o r t h i s s p e c i e s . Of t h e H e r p e t o c y p r i s eggs l a i d a t each t e m p e r a t u r e t h e r e were a v e r y s m a l l number-l e f t a t t h e end o f t h e e x p e r i m e n t ( l e s s t h a n 5 % ) . These were c o n s i d e r e d t o be i n v i a b l e b u t i t c o u l d be t h a t t h e y were eggs t h a t would h a t c h a t a much l a t e r d a t e . T h e r e f o r e t h e r e c o u l d p o s s i b l y be l a t e h a t c h i n g eggs l a i d by t h i s s p e c i e s . The p r o p o r t i o n o f t h e t o t a l number of C y p r i n o t u s eggs h a t c h i n g i n each group a t a range of t e m p e r a t u r e s i s shown i n T a b l e V I I I . The mean p r o p o r t i o n s a r e 0.202 and 0.798. The a n i m a l s do not seem t o a l t e r t h e s e p r o p o r t i o n s as the temper-a t u r e changes w h i c h would be u s e f u l f o r e x i s t e n c e i n an e n v i r o n -ment wh i c h becomes more l i a b l e t o v a n i s h as t h e t e m p e r a t u r e i n c r e a s e s . 8 2 TABLE V I I V a l u e s o f t h e i n s t a n t a n e o u s r a t e o f h a t c h i n g (RH) o f C y p r i n o t u s eggs at a range o f t e m p e r a t u r e s (°C)„ The v a l u e s o f RH f o r b o t h h a t c h e s were o b t a i n e d by r e g r e s s i o n o f In (egg h a t c h i n g r a t e ) on t h e t i m e (days) a f t e r i n i t i a t i o n o f hatching„ Temperature RH RH (°C) H a t c h 1 H a t c h 2 4 0 o 0 5 2 -9 0 o 0 4 0 0 , 0 2 1 2 0 0 , 0 7 0 0 , 0 4 3 2 4 0 , 0 7 1 0 , 0 2 7 2 6 0 , 0 3 8 0 . 0 5 1 TABLE V I I I The p r o p o r t i o n o f t h e number o f C y p r i n o t u s eggs i n each sample, l a i d a t each t e m p e r a t u r e - T ° C ) , which h a t c h d u r i n g t h e f i r s t and second p e r i o d s . P r o p o r t i o n Temperature Hat c h 1 Hatc h 2 9 0,225 0. 775 20 0, 357 0, 64 3 24 0.194 0,806 26 0,151 0.849 Means 0.202 0, 798 84 F o r each s p e c i e s t h e r e l a t i o n s h i p s between the v a r i o u s p r o c e s s e s o f egg h a t c h i n g and the v a r i a b l e s which were found t o m o d i f y them have been t e s t e d . A l a r g e number o f samples o f C y p r i n o t u s eggs was c o l l e c t e d o v e r p e r i o d s o f 3 - 4 days from p o p u l a t i o n s of mature f e m a l e s g r o w i n g upon mud from t h e p u d d l e i n l a r g e p l a s t i c t u b s . These eggs were k e p t a t ambient t e m p e r a t u r e and t h e r e s u l t s o f t h e i r h a t c h i n g used t o t e s t t h e models d e r i v e d from data, o b t a i n e d from a n i m a l s grown under c o n t r o l l e d c o n d i t i o n s . The e x p e c t e d s e g r e g a t i o n o f t h e eggs i n t o two h a t c h e s was f o u n d . The o b s e r v e d p r o p o r t i o n o f t h e eggs h a t c h i n g i n each group was 0.196 f o r t h e f i r s t and 0.804 f o r t h e second w h i c h compares v e r y f a v o u r a b l y w i t h t h e ex-p e c t e d v a l u e s (0.202, 0.798). S i n c e t h e eggs were l a i d a t 20°C the e x p e c t e d d e l a y s f o r each group o f eggs were 26 and 130 days r e s p e c t i v e l y . The o b s e r v e d mean d e l a y s were 10.3 and 67.5 days w h i c h b o t h d i f f e r v e r y s i g n i f i c a n t l y from t h e e x p e c t e d v a l u e s . T h i s d i f f e r e n c e i s a t p r e s e n t i n e x p l i c a b l e b u t may r e s u l t from a s p e e d i n g of development when t h e eggs a r e i n a f l u c t u a t i n g ambient t e m p e r a t u r e as c o n t r a s t e d t o t h e c o n s t a n t t e m p e r a t u r e f o r the e x p e r i m e n t a l eggs. The e x p e c t e d c u m u l a t i v e number o f eggs h a t c h e d as a. f u n c t i o n o f t i m e a f t e r i n i t i a t i o n o f h a t c h i n g s h o u l d be, from e q u a t i o n ( 1 3 ) , f o r b o t h h a t c h e s o f eggs —RH • T TH = Neg•(1 — e 1 ) where Neg i s t h e t o t a l i n i t i a l number of eggs t h a t w i l l h a t c h ' i n t h e group. T h i s can be r e a r r a n g e d i n a l i n e a r f orm, 85 The d a t a f o r each h a t c h o f eggs from each sample was t h e n t r a n s -formed a c c o r d i n g l y and v a l u e s o f RH o b t a i n e d by r e g r e s s i o n o f t h e t r a n s f o r m e d d a t a upon t h e c o r r e s p o n d i n g v a l u e s o f T 0 The mean o b s e r v e d v a l u e o f RH was 0„063 whi c h i s s l i g h t l y l a r g e r t h a n t h e model v a l u e b u t t h e l a t t e r does n o t d i f f e r s i g n i f i c a n t -l y from i t s i n c e t h e o b s e r v e d v a l u e s ranged from 0.028 t o 0.093. There r e m a i n s t h e q u e s t i o n o f whether the eggs l a i d by a p a r t i c u l a r a n i m a l on each day i t spends l a y i n g eggs a r e l i a b l e t o h a t c h a t a p a r t i c u l a r t i m e a f t e r l a y i n g , o r whether t h e eggs l a i d on each day are s i m i l a r and h a t c h o v e r t h e same ran g e o f t i m e . T h i s was i n v e s t i g a t e d f o r C y p r i n o t u s by grow-i n g 37 a n i m a l s a t 24°C, s i n g l y upon mud and c o l l e c t i n g t h e eggs l a i d each day u n t i l t h e a n i m a l d i e d . The t i m e o f h a t c h i n g was t h e n r e c o r d e d f o r each o f t h e eggs. I f t h e r e i s no r e l a t i o n -s h i p between t h e ti m e o f l a y i n g and t h e time o f h a t c h i n g t h e n t h e d a t a s h o u l d be s c a t t e r e d o v e r t h e g r a p h . The r e s u l t s shown i n F i g . Z6 d e m o n s t r a t e q u i t e c l e a r l y t h a t t h e r e i s no m o d i f i c a t i o n by t h e a n i m a l o f the h a t c h i n g p r o p e r t i e s o f t h e eggs as e g g - l a y i n g c o n t i n u e s . The eggs l a i d d u r i n g any ti m e o f t h e e g g - l a y i n g p e r i o d a r e e q u a l l y l i k e l y t o h a t c h a t any t i m e a f t e r t h e y have been l a i d . Each p o i n t i n F i g . 26 does not r e p r e s e n t t h e l a y i n g and h a t c h i n g o f o n l y one egg. The numbers o f eggs t h a t gave r i s e t o each p o i n t v a r i e d from 1 t o as many as 50. I t f o l l o w s from e q u a t i o n s (10) and (11) t h a t t h e g r e a t e s t number o f l a r v a e s h o u l d have h a t c h e d a t t h o s e F i g u r e 26 The r e l a t i o n s h i p between t h e t i m e o f l a y i n g ( i n days a f t e r t h e a n i m a l m a t u r e d ) , and t h e t i m e o f h a t c h i n g (age o f t h e e g g s ) , f o r C y p r i n o t u s eggs l a i d a t 24°C„ The e x p e c t e d t i m e s o f b e g i n n i n g o f t h e two h a t c h e s o f eggs a r e shown by t h e two l i n e s , (T) - f i r s t h a t c h (2) - second h a t c h . 100 • 90-80 -Z 7 0 -X ' o < X 60-C0 50 • >-< t A. 30-2 0 -10-* • • • -CD-10 15 I— 20 25 30 I 35 —I— 4 0 T I M E (DAYS) O F LAYING 87 p o i n t s a l o n g t h e l i n e s Th = 6 2 7 . 0 e ~ ° 1 5 8 7 ' 2 4 14 days and Th = 1 1 5 9 „ 8 e ~ o 1 1 1 ' 2 4 81 days T h i s i s not i n d i c a t e d i n t h e f i g u r e but t h e i n -a c c u r a c y o f t h e h a t c h i n g d e l a y model i s d e m o n s t r a t e d by t h e o c c u r r e n c e o f many p o i n t s n e a r e r t o t h e x - a x i s t h a n t h e f i r s t l i n e . By t h e model no p o i n t s s h o u l d f a l l i n t h i s a r e a . (The sum o f t h e c o o r d i n a t e s o f each p o i n t i s t h e age o f t h e egg a t t h e t i m e o f h a t c h i n g , r e l a t i v e t o t h e day on which t h e p a r e n t a n i m a l m a t u r e d ) . The manner i n which H e r p e t o c y p r i s eggs s h o u l d h a t c h depends upon t h e number o f eggs l a i d on each day some days p r e v i o u s l y and t h e t e m p e r a t u r e a t w h i c h t h e y were l a i d . The r e l a t i o n s h i p between t h e d e l a y and h a t c h i n g and t h e a s s u m p t i o n t h a t a l l eggs l a i d on one day h a t c h a t a c o n s t a n t t i m e l a t e r have been t e s t e d upon t h e h a t c h i n g o f eggs a c c u m u l a t e d by 4 p o p u l a t i o n s o f mature a n i m a l s g r o w i n g on n a t u r a l mud i n s m a l l p e t r i - d i s h e s . The eggs l a i d p e r u n i t time and t h e t e m p e r a t u r e o f t h e w a t e r were known and so were used t o p r e d i c t t h e c u m u l a t i v e number of l a r v a e h a t c h e d as a. f u n c t i o n o f t i m e . These e x p e c t e d v a l u e s a r e compared w i t h t h e o b s e r v e d i n F i g . 2 7. The p o p u l a t i o n s o f a n i m a l s were grown d u r i n g t h e summer months and t h e t e s t s a r e c o m p l i c a t e d by t h e f a c t t h a t d u r i n g p e r i o d s when t h e w a t e r t e m p e r a t u r e exceeded 21°C t h e eggs l a i d were i n v i a b l e . F o r some o f the r e p l i c a t e s t h e shape and f i n a l v a l u e t h a t t h e e x p e c t e d v a l u e s assume are not c l o s e t o the o b s e r v e d . F i g u r e 27 Test of the egg-hatching model f o r Herpetocypris eggs. The eggs l a i d by the animals i n each r e p l i c a t e , during each p e r i o d of time, are shown as a histogram and the observed cumulative number of eggs hatched ( c l o s e d c i r c l e s ) i s shown below. The expected cumulative number hatched ( l a r g e r , open c i r c l e s ) i s given f o r each r e p l i c a t e . CUMULATIVE NUMBER NUMBER OF CUMULATIVE NUMBER NUMBER OF CUMULATIVE NUMBER NUMBER OF CUMULATIVE NUMBER NUMBER OF OF LARVAE HATCHED EGGS LAID OF LARVAE HATCHED EGGS LAID OF LARVAE HATCHED EGGS LAID OF LARVAE HATCHED EGGS LAID gi 3 t? £j • _. ro rji 3 <5 O _ M cn Q t? S3 _ ro ' 5 3 5! — ro b O O O O Q o o o o o o o o o o o o o o o o o o 89 The l a c k o f c o r r e s p o n d e n c e o f t h e l a s t p a i r o f v a l u e s i s a r e s u l t o f i n a c c u r a c i e s r e s u l t i n g f r om t h e r e j e c t i o n o f a l l eggs l a i d above t h e maximum l i m i t . A p p a r e n t l y not a l l o f them were i n v i a b l e . I n o t h e r c a s e s t h e e x p e c t e d d e l a y i n h a t c h i n g seems t o o v e r e s t i m a t e t h e o b s e r v e d r e s u l t i n g i n t h e model l a g g i n g behind, t h e o b s e r v e d v a l u e s . The i n v i a b i l i t y o f H e r p e t o c y p r i s eggs l a i d a t h i g h t e m p e r a t u r e s i s i n n a t u r e u n i m p o r t a n t because a t t h a t t e m p e r a t u r e t h e p u d d l e soon d r i e s up. Summary 1 , The d e l a y between l a y i n g and h a t c h i n g o f H e r p e t o c y p r i s eggs i n c r e a s e s l i n e a r l y as the t e m p e r a t u r e d e c r e a s e s , 2, The C y p r i n o t u s eggs h a t c h i n two groups o v e r a l o n g p e r i o d o f t i m e . The d e l a y between l a y i n g and h a t c h i n g o f each group d e c r e a s e d e x p o n e n t i a l l y as t h e t e m p e r a t u r e i n c r e a s e d . A t a l l t e m p e r a t u r e s the d e l a y was g r e a t e r f o r C y p r i n o t u s t h a n f o r H e r p e t o c y p r i s eggs, 3 = There i s o n l y one k i n d o f H e r p e t o c y p r i s eggs. A l l eggs l a i d on one day h a t c h a t a c o n s t a n t t i m e l a t e r , C y p r i n o t u s eggs o f each k i n d a r e l a i d on any day d u r i n g t h e l a y i n g p e r i o d . A f t e r t h e d e l a y t h e r a t e o f h a t c h i n g o f each group i s t h e s ame. 4 , T e s t s o f t h e e x p e r i m e n t a l r e l a t i o n s h i p s upon a n i m a l s g r o w i n g under n a t u r a l c o n d i t i o n s were not v e r y s u c c e s s f u l . The model o v e r e s t i m a t e d t h e d e l a y f o r C y p r i n o t u s eggs and f o r H e r p e t o c y p r i s was o n l y an a p p r o x i m a t i o n . 9 0 i ) The e f f e c t s o f d e s i c c a t i o n upon t h e a n i m a l s When t h e wa t e r r e c e d e s from a p a r t o f t h e p u d d l e t h e a n i m a l s a re l e f t s t r a n d e d upon t h e mud s u r f a c e and c o l l e c t i n minor d e p r e s s i o n s and c r a c k s and a l o n g s i d e g r a s s stems on t h e s u r f a c e . Q u i t e l a r g e numbers o f them can be c o n c e n t r a t e d when a s m a l l a r e a o f t h e p u d d l e i s c u t o f f from t h e r e m a i n d e r and t h e n s h r i n k s t o i t s l o w e s t p o i n t t h r o u g h e v a p o r a t i o n . The s t r a n d e d a n i m a l s l i e upon t h e s u r f a c e w i t h . t h e i r v a l v e s t i g h t l y c l o s e d and some may burrow i n t o t h e s u r f a c e l a y e r s o f t h e mud w h i l e i t i s s t i l l m o i s t . The a n i m a l s r e m a i n e n t i r e l y i n a c t i v e . D u r i n g t h e s p r i n g o f 1969 when the t y r e - t r a c k p u d d l e d r i e d up, samples o f a n i m a l s from t h e p u d d l e were t a k e n a t r e g u l a r i n t e r v a l s f r om mid-way a l o n g i t s l e n g t h f o r a p e r i o d o f 17 da y s . Water was added t o t h e samples o f d r i e d mud and t h e numbers o f a n i m a l s which responded w i t h i n 24 hour s were r e c o r d e d . These are e x p r e s s e d as a. p r o p o r t i o n o f t h e t o t a l numbers i n each sample f o r C y p r i n o t u s i n F i g , 28, The a n i m a l s were n o t s e p a r a t e d a c c o r d i n g t o t h e i r s i z e . There was no e f f e c t a t a l l o f t h e l o s s o f wa t e r u n t i l 3 da y s , a f t e r w hich t h e p r o p o r t i o n dead i n c r e a s e d c o n s t a n t l y r e a c h i n g 1,0 a t about 12 d a y s . The t i m e a t which 50% o f t h e a n i m a l s were dead was a p p r o x i m a t e l y 7 da y s . Only s m a l l numbers o f H e r p e t o c y p r i s were p r e s e n t a t t h i s t i m e and t h e r e were not enough t o c o n s t r u c t t h e same r e l a t i o n s h i p f o r t h i s s p e c i e s . D u r i n g t h e p e r i o d o f d e s i c c a t i o n t h e a n i m a l s a r e u n a b l e t o f e e d and so must be a b l e t o w i t h s t a n d n o t o n l y w a t e r -l o s s b u t s t a r v a t i o n . From t h e s t a r v a t i o n e x p e r i m e n t s done w i t h F i g u r e 28 The d e c r e a s e i n t h e p e r c e n t a g e o f C y p r i n o t u s a l i v e i n mud-samples t a k e n from t h e p u d d l e as t h e l e n g t h o f t h e p e r i o d o f d e s i c c a t i o n i n c r e a s e d . The samples were t a k e n d u r i n g t h e s p r i n g o f 1969. The t i m e a t wh i c h 50% of t h e a n i m a l s a r e dead i s shown by t h e dashed l i n e . PERCENTAGE DEAD 92 C y p r i n o t u s i t was e x p e c t e d t h a t t h e mean l e n g t h o f t i m e t h a t the a n i m a l s c o u l d s u r v i v e w i t h o u t f e e d i n g would be a p p r o x i m a t e l y 62 h o u r s o r 2.5 da y s . But t h e o b s e r v e d mean t i m e i n t h e p u d d l e was 7 days o r 172 h o u r s . The o n l y e x p l a n a t i o n t h a t I can o f f e r f o r t h i s c o n t r a d i c t i o n i s t h a t t h e e x p e r i m e n t a l a n i m a l s had been k e p t w i t h o u t f o o d i n s m a l l volumes o f w a t e r and so were a b l e t o move around. C o n t i n u e d swimming and s e a r c h i n g by t h e a n i m a l s must have used up energy r e s e r v e s much more r a p i d l y t h a n s i t t i n g upon t h e mud s u r f a c e . The m e t a b o l i c r a t e o f t h e a n i m a l s i n t h e p u d d l e may have been a l i t t l e l e s s s i n c e t h e mean d a i l y t e m p e r a t u r e was l e s s t h a n t h e 20°C t h a t t h e s t a r v a -t i o n e x p e r i m e n t was c o n d u c t e d a t . But t h e p u d d i e a n i m a l s would be f u l l y exposed t o t h e sun upon a dark a b s o r p t i v e s u r f a c e and" so t h e maximum t e m p e r a t u r e which t h e y e x p e r i e n c e d may have been much h i g h e r . I t i s unknown whether t h e g r e a t e r r e s i s t a n c e t o f o o d d e p r i v a t i o n shown by H e r p e t o c y p r i s i n t h e l a b o r a t o r y e x p e r i m e n t a l s o o c c u r r e d i n t h e pu d d l e when i t d r i e d up. Summary 1° C y p r i n o t u s i s a b l e t o s u r v i v e 3 days o f d e s i c c a t i o n . A f t e r t h i s t i m e t h e p r o p o r t i o n o f t h e o r i g i n a l number a l i v e d e c r e a s e s l i n e a r l y w i t h i n c r e a s i n g e x p o s u r e . A t a p p r o x i -m a t e l y 7 days 50% were dead". 2. D u r i n g t h e p e r i o d o f e x p o s u r e t h e a n i m a l s were i m m o b i l e and u n a b l e t o f e e d . They s u r v i v e d t h r e e t i m e s as l o n g as a n i m a l s d e p r i v e d o f food, b u t a b l e t o move around i n w a t e r . 93 3 0 I n s u f f i c i e n t i n f o r m a t i o n about t h e a b i l i t y o f H e r p e t o c y p r i s t o s u r v i v e d e s i c c a t i o n was o b t a i n e d b u t i t seems t o be s i m i l a r t o C y p r i n o t u s . i ) The number o f eggs l e f t i n a u n i t o f space a t the t i m e o f d r y i n g - u p . The t o t a l number o f eggs t h a t t h e s p e c i e s has i n s t o r e a t t h e t i m e t h a t t h e wa t e r v a n i s h e s from a. u n i t o f a space i s g i v e n by NEL = NE T + NNE T (14) where T i s t h e t i m e a f t e r submergence t h a t d r y i n g - u p o c c u r s , NE T i s t h e t o t a l number of un h a t c h e d o l d eggs from t h e p r e v i o u s w i n t e r and NNE^, i s t h e t o t a l number o f new eggs t h a t have r e s u l t e d from t h e e g g - l a y i n g by t h e c u r r e n t c r o p o f a d u l t s . The v a l u e o f WE^ i s g i v e n by e q u a t i o n (1A ) and depends upon t h e i n i t i a l number o f eggs and t h e l e n g t h o f submergence o f t h e u n i t o f sp a c e . The shape o f t h e f u n c t i o n i s shown i n F i g . 5. F o r t h e u s u a l v a l u e s o f T t h e number o f H e r p e t o c y p r i s eggs l e f t w i l l u s u a l l y be z e r o u n l e s s t h e r e i s a v e r y l a r g e number t o b e g i n w i t h . T h i s i s because t h e o l d eggs o f t h i s s p e c i e s h a t c h so r a p i d l y a f t e r the a d d i t i o n o f wa t e r and t h e p r o p o r t i o n o f them h a t c h i n g i n t h e second group i s v e r y s m a l l . W h i l e the v a l u e o f NE^ i s o b t a i n e d q u i t e s i m p l y t h i s i s n o t t r u e f o r NNE T s i n c e i t i s dependent upon a s e r i e s o f e v e n t s w h i c h have been p r e s e n t e d p r e v i o u s l y . C e r t a i n l y no s i n g l e e x p r e s s i o n can be w r i t t e n f o r i t s v a l u e . However, i t i s e a s i l y seen t h a t i t i s dependent i m m e d i a t e l y upon two 94 q u a n t i t i e s which a re i n t h e m s e l v e s v e r y complex. That i s NNE T = NNG - NEH (15) where NNG i s the t o t a l number o f new eggs l a i d and NEH t h e t o t a l number o f new eggs h a t c h e d up t i l l t h e p r e s e n t . No at t e m p t i s made h e r e t o e x p l o r e t h e p o s s i b l e shapes o f NNE^ as a f u n c t i o n o f time, because t h e r e seem t o be an i n f i n i t e number, none o f which has a s p e c i a l meaning and each d i f f e r i n g , f o r example, o n l y i n t h e t i m e a f t e r f i l l i n g t h a t the egg-a c c u m u l a t i o n began which would depend upon many o t h e r v a r i a b l e s , p a r t i c u l a r l y t h e t e m p e r a t u r e . However, t h e consequences o f t h e two d i f f e r e n t k i n d s o f e g g - h a t c h i n g shown by each s p e c i e s upon t h e v a l u e o f NNE T as a f u n c t i o n o f t i m e a re i l l u s t r a t e d by two examples i n F i g u r e 29„ No att e m p t i s made t o . i m i t a t e ' t h e s e r e s u l t s w i t h t h e model. They s h o u l d be r e g a r d e d as o n l y two o f many p o s s i b l e shapes f o r NNE T as a f u n c t i o n of T„ F o r C y p r i n o t u s i n t h e example t h e r e was a most f a v o u r a b l e t i m e t o s t o p because t h e h a t c h i n g o f t h e eggs l a g g e d w e l l b e h i n d t h e l a y i n g , a l l o w i n g a l a r g e b u i l d - u p , b u t t h i s was g r a d u a l l y e r o d e d as t h e r a t e o f h a t c h i n g a c c e l e r a t e d . F o r H e r p e t o c y p r i s i t would have made v e r y l i t t l e d i f f e r e n c e when t h e d r y i n g - u p had o c c u r r e d because t h e r a t e o f e g g - l a y i n g and e g g - h a t c h i n g approached an e q u i l i b r i u m . I t can be seen t h a t NNE^ i s t h e q u a n t i t y upon w h i c h a l l t h e c o m p e t i t i v e e f f e c t s of t h e o t h e r s p e c i e s must be focused:... I t f u r t h e r f o l l o w s from t h e c o m p l e x i t y o f the r e l a t i o n s h i p s and range o f p o s s i b i l i t i e s o f c o m b i n a t i o n s o f v a r i a b l e s such as s t a r t i n g and s t o p p i n g t i m e s , t e m p e r a t u r e F i g u r e 2 9 An example o f t h e o b s e r v e d r e l a t i o n s h i p between t h e c u m u l a t i v e ' numbers o f eggs l a i d and the c u m u l a t i v e number o f t h e s e eggs which have h a t c h e d . F o r each s p e c i e s t h e s e are shown i n t h e upper boxes o f t h e f i g u r e . The shape o f t h e r e l a t i o n s h i p between t h e t o t a l number o f eggs a v a i l a b l e t o be s t o r e d and t h e t i m e a f t e r t h e b e g i n n i n g o f e g g - l a y i n g i s shown be n e a t h each example. F i g . 29A and B - example f o r C y p r i n o t u s . F i g . 29C and D - example f o r H e r p e t o c y p r i s . NUMBERS OF EGGS CUMULATIVE NUMBERS 96 and d e n s i t i e s o f t h e s p e c i e s t h a t o b t a i n i n g t h e answer as t o the p o s s i b i l i t y o f c o m p e t i t i v e e x c l u s i o n i s b e s t l e f t t o t h e computer. T h i s i s l e f t t o a l a t e r s e c t i o n where th e manner i n w h i c h a l l t h e p r o c e s s e s were assembled t o g e t h e r i n t o a program and t h e answer o b t a i n e d i s p r e s e n t e d . Summary 1. The t o t a l number o f eggs l e f t i n t h e sediment a t t h e t i m e of d r y i n g - u p i s t h e sum o f t h e number of o l d eggs t h a t d i d n o t h a t c h and t h e number of new eggs. 2 . The number of new eggs i s t h e d i f f e r e n c e between t h e t o t a l number l a i d and t h e t o t a l number h a t c h e d . 3. The e f f e c t o f one s p e c i e s upon t h e number o f new eggs produce d by t h e o t h e r s p e c i e s i s not s i m p l e because t h e r e a r e many o t h e r v a r i a b l e s i n v o l v e d . k) The e f f e c t s o f f r e e z i n g upon th e pudd'le a n i m a l s The c o n t i n u o u s p r e s e n c e o f water i n t h e p u d d l e can be b r o k e n by f r e e z i n g . The a n i m a l s a r e o n l y k i l l e d i f t h e y are f r o z e n i n t o t h e i c e . T h i s means t h a t t h e i c e must e x t e n d down from t h e s u r f a c e t o i n c l u d e t h e s e d i m e n t . I n t h e p u d d l e b o t h s p e c i e s o f o s t r a c o d have been o b s e r v e d t o r e m a i n v e r y a c t i v e , moving around on t h e mud, when t h e t e m p e r a t u r e was as low as 1 - 2°C o r i n water beneath a l a y e r o f i c e . The eggs of o s t r a c o d s seem t o be u n a f f e c t e d by f r e e z i n g . The e f f e c t s o f f r e e z i n g upon b o t h s p e c i e s o f o s t r a c o d s and upon th e 97 c y c l o p o i d s and h a r p a c t i c o i d s o f t h e p u d d l e have been i n v e s t -i g a t e d by f r e e z i n g them i n t h e i c e - b o x o f a r e f r i g e r a t o r . F o r each s p e c i e s 10 a n i m a l s were p l a c e d i n each c e l l o f an i c e -cube t r a y w h i c h was f i l l e d w i t h mud and w a t e r . These were t h e n f r o z e n f o r v a r i o u s l e n g t h s o f t i m e and t h e n m e l t e d i n wa t e r and t h e e f f e c t s upon t h e a n i m a l s r e c o r d e d . I n a l l c a s e s t h e e f f e c t s were d i s a s t r o u s . None o f t h e a n i m a l s was a b l e t o s u r v i v e l o n g e r t h a n 5 hour s f r o z e n s o l i d , F i g . 30. F o r - b o t h s p e c i e s o f o s t r a c o d s t h e l a r g e r a n i m a l s l a s t e d t h e l o n g e s t . The p r o p o r t i o n a l i v e o f t h e s m a l l e s t a n i m a l s was z e r o a f t e r o n l y 0.5 hour s f r e e z i n g and t h i s was the s h o r t e s t p e r i o d u s e d . These r e s u l t s c o n f i r m o b s e r v a t i o n s o f t h e f r o z e n a r e a s o f the puddle„ Summary 1. None o f t h e o s t r a c o d s , c y c l o p o i d s o r h a r p a c t i c o i d s c o u l d s u r v i v e l o n g e r t h a n a few hour s when f r o z e n . 1) E x p e r i m e n t s upon t h e d i s p e r s a l o f o s t r a c o d s from a. p o i n t soiarce i n t o a s h a l l o w p o o l The two s p e c i e s of o s t r a c o d s d i f f e r i n t h e i r l o c o -motory b e h a v i o u r . Both s p e c i e s a r e u s u a l l y q u i t e a c t i v e , moving around o v e r t h e s u r f a c e o f t h e mud. The p e r i o d s o f movement a r e p u n c t u a t e d by p e r i o d s when t h e a n i m a l s s t o p and e x p l o r e s m a l l a r e a s o r b e g i n t o burrow i n t o t h e mud. As a d u l t s , o n l y C y p r i n o t u s a n i m a l s a re c a p a b l e o f swimming. H e r p e t o c y p r i s a n i m a l s a re l a r g e r b u t do n o t seem t o have antennae ( t h a t F i g u r e 30 The e f f e c t s o f f r e e z i n g upon b o t h s p e c i e s o f o s t r a c o d and some o t h e r a n i m a l s i n t h e p u d d l e . The p r o p o r t i o n o f a n i m a l s r e c o v e r i n g when the i c e m e l t e d i s p l o t t e d a g a i n s t t h e number o f hours f r o z e n . F i g . 30A - C y p r i n o t u s , 0 - 0.5 mm l o n g ( c l o s e d c i r c l e s ) , and 1.0 - 1.5 mm l o n g (open c i r c l e s ) . F i g . 30B - H e r p e t o c y p r i s , 0 - 0.5 mm l o n g (open c i r c l e s ) , and 1.5 - 2.0 mm l o n g ( s q u a r e s ) . F i g . 30C - C y c l o p s b i s e t o s u s ( c l o s e d c i r c l e s ) and A t t h e y e l l a n o r d e n s k i o l d i i ( t r i a n g l e s ) . A 0.73 -\\ 0.50 H 0.2 5 H ~i —I l , , 1 I r -5 10 15 20 25 30 35 40 TIME (HOURS) FROZEN 99 would be used f o r swimming) g r e a t e r i n s i z e i n p r o p o r t i o n t o t h e body s i z e t h a n t h o s e of C y p r i n o t u s . T h e r e f o r e when moving l o n g e r d i s t a n c e s (5 - 10 m)- C y p r i n o t u s swims b u t H e r p e t o c y p r i s must c r a w l . On t h e o t h e r hand H e r p e t o c y p r i s i s p r i m a r i l y a b u r r o w e r , i t s l o n g and narrow shape b e i n g - v e r y s u i t a b l e , b u t C y p r i n o t u s o n l y r a r e l y burrows and does not u s u a l l y move h o r i z o n t a l l y when b u r r o w i n g . I t burrows down i n t o t h e mud and u s u a l l y emerges a t or v e r y near t h e p o i n t a t which i t e n t e r e d . Inasmuch as t h e shape o f H e r p e t o c y p r i s i s s u i t e d f o r b u r r o w i n g so t h e shape o f C y p r i n o t u s i s u n s u i t e d because i t i s s h o r t e r i n l e n g t h and w i d e r . L i k e a wedge i t t a p e r s from b e i n g n a r r o w e s t i n f r o n t t o b r o a d e s t a t t h e r e a r and so p r e s e n t s a. l a r g e s u r f a c e a r e a t o t h e s e d i m e n t . The v e l o c i t i e s o f c r a w l i n g on t h e mud s u r f a c e ( V c ) , swimming (Vs)and o f b u r r o w i n g (Vb) have been measured f o r b o t h s p e c i e s . The bottom o f a s h a l l o w d i s h was c o v e r e d w i t h mud and t h e a n i m a l s timed o v e r measured d i s t a n c e s f o r each o f t h e a c t i v i t i e s . The measurements were made a t t h e l e i s u r e o f t h e a n i m a l as i t was not f o r c e d t o move. The mean v e l o c i t i e s f o r each a c t i v i t y a r e shown i n T a b l e IX f o r b o t h s p e c i e s . The h i g h e s t v e l o c i t y was f o r C y p r i n o t u s when swimming and was 1.04 cm/sec. The l o w e s t v e l o c i t y was a l s o f o r t h e same s p e c i e s , when i t was burro w i n g ' - 0.028 cm/sec. H e r p e t o c y p r i s burrowed f a s t e r b u t not by a g r e a t amount and C y p r i n o t u s was the f a s t e s t c r a w l e r on the s u r f a c e . Under t h e same c o n d i t i o n s t h e p r o p o r t i o n s o f ti m e s p e n t by a n i m a l s o f each s p e c i e s e i t h e r swimming, c r a w l i n g on 1 0 0 TABLE I X The mean v e l o c i t i e s a t which t h e a n i m a l s move when c r a w l i n g ( V c ) , b u r r o w i n g (Vb) and swimming ( V s ) , f o r b o t h s p e c i e s o f o s t r a c o d o Each v e l o c i t y ( i n cm/sec) i s t h e mean o f a t l e a s t 17 measurementso S p e c i e s Vc Vb Vs mean O o 5 3 0 o 0 2 8 l o 0 4 C y p r i n o t u s v a r i a n c e 0 „ 0 3 3 " 0 . 0 0 0 2 0 o 0 2 6 mean 0 . 2 2 0 „ 0 3 4 H e r p e t o c y p r i s v a r i a n c e O o 0 0 4 0 . 0 0 0 2 -101 t h e s u r f a c e , b u r r o w i n g o r s t o p p e d ( e i t h e r on o r below t h e s u r f a c e ) were measured by r e c o r d i n g t h e b e h a v i o u r c o n t i n u o u s l y . The e v e n t s were r e c o r d e d f o r a n i m a l s by t h e m s e l v e s and t h e l e n g t h o f each o b s e r v a t i o n p e r i o d was from 5 - 1 2 minutes (20 o b s e r v a t i o n p e r i o d s were made f o r each s p e c i e s ) . The d i f f e r e n c e i n t h e t i m e - p r o p o r t i o n s f o r each s p e c i e s a r e shown i n F i g . 31. The p r o p o r t i o n s o f t h e time s p e n t s t a t i o n a r y ( u s u a l l y when t h e a n i m a l was f e e d i n g ) was a l m o s t i d e n t i c a l f o r each s p e c i e s , b e i n g c l o s e t o 0.31. S i m i l a r l y t h e time s p e n t c r a w l i n g was a l m o s t i d e n t i c a l , 0.40 - 0.45, and t h e r e m a i n d e r o f t h e time was s p e n t by H e r p e t o c y p r i s w h i l e b u r r o w i n g and by C y p r i n o t u s b u r r o w i n g and swimming. S u r p r i s i n g l y , t h e t i m e s p e n t below t h e s u r f a c e by C y p r i n o t u s was f o u n d t o be s l i g h t l y l o n g e r t h a n t h a t by H e r p e t o c y p r i s . The r e s u l t s o f b o t h t h e s e s e t s o f o b s e r v a t i o n s s u g g e s t t h a t C y p r i n o t u s s h o u l d be t h e f a s t e s t t o d i s p e r s e from a p o i n t o f r e l e a s e l a r g e l y f o r t h e r e a s o n t h a t i t i s c a p a b l e o f swim-ming and can c r a w l t h e f a s t e r . But from t h i s work i t i s not p o s s i b l e t o say how f a s t a group o f a n i m a l s o f e i t h e r s p e c i e s w i l l move out from a p o i n t o f r e l e a s e s i n c e t h e d i r e c t i o n and r e s p o n s e s i n movements by each a n i m a l t o t h e p r e s e n c e o f o t h e r a n i m a l s has n o t been i n c l u d e d . Some e x p e r i m e n t s were c o n d u c t e d t o see whether t h e movement by t h e a n i m a l s from a p o i n t o f r e l e a s e was a d i f f u s i o n p r o c e s s i n which t h e a n i m a l s moved randomly and t h e r e f o r e i n d e p e n d e n t l y , and t h e i r mean d i s t a n c e f r o m t h e p o i n t o f r e l e a s e i n c r e a s e d w i t h t i m e a f t e r r e l e a s e . A l o n g , narrow and s h a l l o w t a n k was b u i l t upon a. t a b l e F i g u r e 31 The p r o p o r t i o n s o f each o b s e r v a t i o n p e r i o d s p e n t by t h e a n i m a l s e i t h e r s t a t i o n a r y (STP) o r moving (MU) f o r b o t h s p e c i e s . F i g . 31A - C y p r i n o t u s , F i g . 3113 -H e r p e t o c y p r i s . F o r each s p e c i e s t h e p r o p o r t i o n o f t i m e s p e n t moving i s d i v i d e d among swimming (SW), b u r r o w i n g (BR) and c r a w l i n g (CR). F o r each p r o p o r t i o n t h e 95% c o n f i d e n c e l i m i t s are g i v e n . There were 20 o b s e r v a t i o n p e r i o d s f o r each s p e c i e s . PROPORTION OF T O T A L TIME — o b b i I on H "0 03 JO o TO CD 103 and s u r r o u n d e d by a b l a c k p l a s t i c c o v e r i n g and some f l u o r e s c e n t t u b e s a r r a n g e d end t o end were suspended 1 m above t h e w a t e r . The l i g h t s and t h e c o v e r i n g m a i n t a i n e d an even i l l u m i n a t i o n o f t h e t a n k which was 2.52 m l o n g and 0.63 m wide. The d e p t h o f t h e w a t e r was 3 - 4 cm. The a n i m a l s used f o r the e x p e r i m e n t s were t h e l a r g e s t s i z e f o r each s p e c i e s so t h a t t h e y c o u l d be more e a s i l y r e c o v e r e d . The a n i m a l s were r e l e a s e d by p l a c i n g them i n a s m a l l c y l i n d e r ( r a d i u s = 3 cm) s t a n d i n g v e r t i c a l l y i n t h e mud a t t h e c e n t r e o f the tank and l e a v i n g them f o r 15 m i n u t e s p r i o r t o l i f t i n g t h e c y l i n d e r and a l l o w i n g t h e a n i m a l s t o move o f f . T h e i r p o s i t i o n s were r e c o r d e d by p l a c i n g p a r t i t i o n s 21 cm a p a r t a c r o s s t h e w i d t h o f t h e tank and t h e n c o u n t i n g t h e a n i m a l s i n each a r e a . The a n i m a l s were r e c o r d e d as coming from t h e mean d i s t a n c e o f t h e c e n t r e o f t h a t a r e a from t h e p o i n t o f r e l e a s e . Each e x p e r i m e n t was p a i r e d because u s u a l l y about h a l f of t h e a n i m a l s moved o f f i n each d i r e c t i o n and so a f t e r each r e l e a s e the mean d i s t a n c e o f each group i n b o t h d i r e c t i o n s c o u l d be c a l c u l a t e d . The mud. i n t h e tank was p r e p a r e d from s o i l n e a r t h e p u d d l e i n t h e p r e v i o u s l y d e s c r i b e d manner. (See P a r t I ( b ) ) . I n i t i a l l y a s t a n d a r d number o f 140 a n i m a l s was r e l e a s e d and t h e mean d i s t a n c e which t h e y had moved was o b t a i n e d . Then f o r C y p r i n o t u s o n l y , a h i g h e r (300) and. a l o w e r (40) number were used t o see whether t h i s had any e f f e c t upon th e r a t e a t w h i c h t h e a n i m a l s moved o u t . There was no a p p a r e n t d i f f e r e n c e between t h e r e s u l t s f o r each i n i t i a l number and so a l l t h e d a t a have been combined and a r e p r e s e n t e d i n F i g . 32A and B f o r b o t h s p e c i e s . As a n t i c i p a t e d , t h e r a t e o f F i g u r e 32 D i s p e r s a l o f t h e o s t r a c o d s i n a l a b o r a t o r y p u d d l e from a p o i n t s o u r c e . The i n c r e a s e o f t h e mean i n d i v i d u a l d i s t a n c e from t h e p o i n t o f r e l e a s e as a f u n c t i o n o f t h e number o f h o u r s a f t e r r e l e a s e a r e shown i n F i g . 32A ( H e r p e t o c y p r i s ) and B ( C y p r i n o t u s ) . The v a l u e s i n F i g . 32A are f o r H e r p e t o c y p r i s moving o v e r an open mud s u r f a c e . The number i n i t i a l l y r e l e a s e d f o r each measurement was c o n s t a n t (140 a n i m a l s ! . I n F i g . 32B t h e v a l u e s f o r C y p r i n o t u s moving o v e r an open mud s u r f a c e - number r e l e a s e d = 40 ( c l o s e d c i r c l e s ) , number r e l e a s e d = 140 ( c r o s s e s ) , number r e l e a s e d = 300 (open c i r c l e s ) . F o r C y p r i n o t u s moving o v e r a s u r f a c e w i t h g r a s s p r e s e n t when t h e number r e l e a s e d was 140 - s q u a r e s . A 100 • 80 • Q U l Ul > < ui 60 40 20 • —r-10 20 30 - 1 — 40 ^— 50 —r— 60 70 TIME (HOURS) SINCE RELEASE — i — 80 O z < U l 100 r 8 10 12 14 TIME (HOURS) SINCE RELEASE 16 105 movement o f C y p r i n o t u s was l a r g e r t h a n t h a t f o r H e r p e t o c y p r i s ( n o t e t h e d i f f e r e n t s c a l e s f o r t h e x - a x i s i n Fig,, 3 2 ) . But t h e magnitude o f t h e o b s e r v e d d i f f e r e n c e had not been a n t i c -i p a t e d . A f t e r t h e d i s p e r s a l had begun t h e r a t e o f i n c r e a s e f o r t h e d i s t a n c e from t h e s o u r c e became a p p r o x i m a t e l y c o n s t a n t _ 3 and f o r C y p r i n o t u s i t was- 30.3 x 10 cm/sec, b u t f o r _ 3 H e r p e t o c y p r i s i t was o n l y 0.29 x 10 ' cm/sec. The maximum mean d i s t a n c e t h a t c o u l d be measured was h a l f way between t h e s o u r c e and t h e end o f t h e t a n k . T h i s d i s t a n c e was 63.0 cm and as t i m e i n c r e a s e d the mean d i s t a n c e t e n d e d t o t h i s v a l u e , as a n i m a l s e n c o u n t e r e d t h e e n d - w a l l and began t o r e t u r n . I f t h e a n i m a l s were moving randomly t h e n t h e mean d i s t a n c e from t h e s o u r c e s h o u l d be r e l a t e d t o t h e square r o o t o f t h e t i m e s i n c e r e l e a s e . The shape o f t h i s r e l a t i o n i s an i n i t i a l r a p i d i n c r e a s e and a g r a d u a l d e c r e a s e o f the r a t e w i t h t i m e . F o r b o t h s p e c i e s t h e r e appeared t o be an i n i t i a l p e r i o d o f r a p i d movement f o l l o w e d by a d e c r e a s e i n t h e r a t e b u t t h e d a t a i s so v a r i a b l e as t o n o t a l l o w r u l i n g o u t the. s i m p l e r e x p l a n a t i o n o f a c o n s t a n t r a t e o f i n c r e a s e i n d e p e n d e n t o f t h e t i m e ( F i g . 3'2) . However an a l t e r n a t i v e t e s t of t h e random d i f f u s i o n model can be made because i t i s p o s s i b l e t o make p r e d i c t i o n s about t h e p r o p o r t i o n s o f t h e i n i t i a l numbers a t t h e s o u r c e t h a t a re t o be f o u n d a t each d i s t a n c e from t h e s o u r c e a t a. p a r t i c u l a r t i m e . F o r movement o f p a r t i c l e s i n an i s o -t r o p i c medium t h e r a t e o f t r a n s f e r o f t h e d i f f u s i n g p a r t i c l e s t h r o u g h a u n i t a r e a o f a s e c t i o n i s p r o p o r t i o n a l t o t h e c o n c e n t r a t i o n g r a d i e n t measured normal t o t h e s e c t i o n so t h a t 106 R - -i n w h i c h R i s t h e r a t e o f t r a n s f e r p e r u n i t a r e a o f s e c t i o n , C t h e c o n c e n t r a t i o n o f the d i f f u s i n g p a r t i c l e s and x t h e d i m e n s i o n a l o n g w h i c h t h e t r a n s f e r i s o c c u r r i n g , , The g u a n t i t y , D, i s t h e d i f f u s i o n c o e f f i c i e n t . The n e g a t i v e s i g n appears because t h e d i f f u s i o n i s i n t h e d i r e c t i o n o p p o s i t e t o t h a t o f i n c r e a s i n g c o n c e n t r a t i o n . S i n c e t h e r e were no o b s t a c l e s around w h i c h t h e o s t r a c o d s had t o move,the e x p e r i m e n t a l tank can be s a f e l y r e g a r d e d as b e i n g i s o t r o p i c . I t i s i m p o r t a n t t h a t t h e o p p o r t u n i t y f o r movement i n any d i r e c t i o n i n t h e n e i g h b o u r h o o d o f any p o i n t be t h e same. Because o f t h i s symmetry about any p o i n t t h e f l o w o f d i f f u s i n g p a r t i c l e s i s a l o n g t h e normal t o t h e s u r f a c e o f c o n s t a n t c o n c e n t r a t i o n t h r o u g h t h e p o i n t . T h i s w i l l n o t be t r u e i n an a n i s o t r o p i c medium. F o r a d i f f u s i v e p r o c e s s i n one d i m e n s i o n and i n w h i c h t h e d i f f u s i o n c o e f f i c i e n t r e m a i n s c o n s t a n t t h e f o l l o w i n g i s t h e e x p r e s s i o n f o r t h e p a r t i a l d e r i v a t i v e o f c o n c e n t r a t i o n o f t h e d i f f u s i n g p a r t i c l e s w i t h r e s p e c t t o t i m e : 3 c _ B 2 c O x f r o m which we can o b t a i n a n i e x p r e s s i o n f o r C C - A e - * 2 / 4 ' D - t where A i s an a r b i t r a r y c o n s t a n t . T h i s e x p r e s s i o n i s s y m m e t r i c a l about x = 0 and approaches z e r o as x t e n d s t o p l u s o r minus i n f i n i t y f o r a c o n s t a n t v a l u e o f t . When M i s t h e number o f 107 d i f f u s i n g p a r t i c l e s and when i t remains c o n s t a n t and e q u a l t o t h e amount o r i g i n a l l y d e p o s i t e d , t h e n the p r e v i o u s e q u a t i o n c a n be r e a r r a n g e d (Crank 1956) so we g e t M -x 2/4-D't r T: e c ~ 2 ( IT * D - t ) ^ Now f o r d i f f u s i o n from a s o u r c e i n t h e e a r l y s t a g e s b e f o r e t h e p a r t i c l e s have r e a c h e d t h e boundary and have begun t o be r e -f l e c t e d t h e n t h i s e q u a t i o n can be r e a r r a n g e d as f o l l o w s : C l t . k . e - ^ 4 ^ where k = m/( TC • D)" 2, and from w h i c h we can g e t 2 I n (C J t ) = g - ^ p-1 2 where g = I n k - 477577:° P l o t t i n g t h e I n (C J/t) a g a i n s t x / t s h o u l d g i v e a s t r a i g h t l i n e w i t h n e g a t i v e s l o p e . I t s h o u l d be n o t e d t h a t C i s t h e q u a n t i t y o f a n i m a l s a t t h e d i s t a n c e x from t h e s o u r c e a t t i m e t . D u r i n g t h e f i r s t 9 h o u r s o f t h e move-ment o f C y p r i n o t u s l i t t l e c o n t a c t was made w i t h t h e end o f t h e t a n k and so t h e d a t a from t h i s p e r i o d has been used t o t e s t t h e r e l a t i o n s h i p ( F i g . 33A). The r e l a t i o n s h i p c o u l d be l i n e a r and c o u l d a l s o be n o n - l i n e a r . The s p r e a d o f the v a l u e s i s q u i t e l a r g e . The n o n - l i n e a r i t y i n d i c a t e s t h a t t h e r e were more a n i m a l s c l o s e t o t h e s o u r c e and more a n i m a l s f u r t h e r from t h e s o u r c e t h a n e x p e c t e d by t h e model. A p p a r e n t l y t h e r e were a s m a l l number o f v e r y a d v e n t u r o u s a n i m a l s w h i c h s p r e a d out q u i c k l y from t h e bunch w h i l e t h e r e s t were s t i l l g e t t i n g underway. The same seems t o be t r u e f o r H e r p e t o c y p r i s (Fig„33B) F i g u r e 33 T e s t of t h e random d i f f u s i o n model f o r t h e d i s p e r s a l o f b o t h s p e c i e s o f o s t r a c o d s from a p o i n t s o u r c e i n an a r t i f i c i a l p u d d l e . The n a t u r a l l o g a r i t h m o f t h e numbers (C) a t a d i s t a n c e (x) from t h e p o i n t of r e l e a s e t i m e s t h e s q u a r e r o o t of t h e t i m e a f t e r r e l e a s e ( t ) i s p l o t t e d a g a i n s t t h e d i s t a n c e s q u a r e d d i v i d e d by t h e t i m e . The e x p e c t a t i o n f o r f i t o f t h e model was t h a t t h e p o i n t s s h o u l d f a l l a l o n g a s t r a i g h t l i n e w i t h n e g a t i v e s l o p e . F i g . 3 3A - C y p r i n o t u s F i g . 3 3 B - H e r p e t o c y p r i s (Note t h e d i f f e r e n c e i n t h e s c a l e o f t h e x - a x i s f o r t h e two g r a p h s ) . 3000 6000 9000 12,000 15,000 18000 21,000 24,000 27,000 o 200 400 600 800 1000 1200 1400 1600 1800 109 a l t h o u g h t h e r e i s more n e a r l y a. s i m p l e l i n e a r r e l a t i o n s h i p . There a r e a few low v a l u e s o f c l o s e t o t h e x - a x i s w h i c h a g a i n r e p r e s e n t p r e c o c i o u s a n i m a l s b e i n g a l o n g way from t h e s o u r c e when t i s s m a l l . I f f u r t h e r d a t a were a v a i l a b l e f o r t h i s s p e c i e s t h e s p r e a d o f t h e v a l u e s c o u l d w e l l be as l a r g e as f o r C y p r i n o t u s . There seem t o be two e x p l a n a t i o n s o f t h e l a r g e number o f a n i m a l s n e a r e r t h e r e l e a s e - p o i n t t h a n e x p e c t e d . That t h e o s t r a c o d s a r e not e n t i r e l y o b l i v i o u s o f t h e i r f e l l o w s i s a l r e a d y known because c l u m p i n g o f members o f s m a l l p o p u l a t i o n s has a l r e a d y been d e m o n s t r a t e d . T h e r e f o r e some o f t h e a n i m a l s c o u l d be t h o s e w h i c h k e p t c l o s e r c o n t a c t w i t h o t h e r s f o r m i n g groups c l o s e t o t h e p o i n t o f r e l e a s e . The o t h e r p o s s i b i l i t y i s t h a t p a r t o f t h e o v e r - r e p r e s e n t a t i o n r e s u l t s from t h e f a c t t h a t t h e a n i m a l s were r e l e a s e d from a s m a l l a r e a and some spen t t h e time between r e l e a s e and r e t r i e v a l moving m a i n l y t o t h e s i d e s o f t h e tank r a t h e r t h a n towards t h e ends. I t i s c o n c l u d e d t h a t t h e d i f f u s i o n model i s o n l y a v e r y a p p r o x i m a t e d e s c r i p t i o n o f the movement o f t h e o s t r a c o d s . I n t h e n a t u r a l p u d d l e t h e o s t r a c o d s must move i n t h e w a t e r , r e l a t i v e t o dense clumps o f g r a s s stems, which p a r t i t i o n t h e l e n g t h o f t h e p u d d l e , i n some p a r t s c o m p l e t e l y and i n o t h e r s o n l y p a r t i a l l y . T h e r e f o r e t h e same e x p e r i m e n t as above was p e r f o r m e d ( f o r C y p r i n o t u s o n l y ) when g r a s s t a k e n from t h e f i e l d had been added t o t h e w a t e r . S h o r t g r a s s stems and r o o t s were c u t from t h e p a s t u r e and p l a c e d i n t h e e x p e r i m e n t a l t a n k , some l y i n g h o r i z o n t a l l y and o t h e r s v e r t i c a l l y and a r r a n g e d so as t o s i m u l a t e what t h e g r a s s i n t h e p u d d l e l o o k e d 110 l i k e . ' No measurements of t h e d e n s i t y o f stems i n e i t h e r t h e p u d d l e o r t h e tank were made. The r e s u l t s o f t h e s e measure-ments o f r a t e o f movement t h r o u g h g r a s s a r e shown i n F i g , 32B, S u r p r i s i n g l y , t h e v a l u e s f o r mean d i s t a n c e moved a t b o t h 1 and 3 h o u r s are n o t a t a l l d i f f e r e n t from t h o s e o b t a i n e d w i t h o u t g r a s s . The a d d i t i o n o f t h e g r a s s d i d n o t seem t o impede th e movement o f t h e a n i m a l s . I f t h i s were t r u e and t h e c o n d i t i o n s f a i t h f u l l y i m i t a t e d the n a t u r a l p u d d l e t h e n t h e members o f b o t h s p e c i e s s h o u l d be t h o r o u g h l y mixed and t h e r e c o u l d be no s p a t i a l s e g r e g a t i o n . I n t h e t y r e - t r a c k p u d d l e t h i s i s not t h e c a s e , A s p a t i a l s e p a r a t i o n was m a i n t a i n e d d u r i n g t h e p e r i o d o f s t u d y , w i t h C y p r i n o t u s o c c u p y i n g m a i n l y t h e n o r t h e r n end w i t h s c a t t e r e d a n i m a l s a l o n g t h e r e m a i n i n g l e n g t h and w i t h H e r p e t o c y p r i s o n l y i n t h e s o u t h e r n end. The d i s t r i b u t i o n o f g r a s s i n t h e p u d d l e was t h e n examined more c l o s e l y (see F i g , 35 ) and i t was n o t i c e d t h a t a t i n t e r v a l s a l o n g t h e p u d d l e s ' l e n g t h t h e r e are v e r y dense a r e a s o f g r a s s o These are much d e n s e r than t h a t used i n t h e t a n k . T h e r e f o r e i f t h e s e dense a r e a s o f g r a s s were i m p e d i n g t h e s p r e a d o f t h e a n i m a l s and i f a l l t h e a n i m a l s were removed from a p a r t o f t h e p u d d l e t h e n we would not e x p e c t i t t o be c o l o n i z e d from a d j a c e n t a r e a s s e p a r a t e d by t h e g r a s s . F u r t h e r , i f t h e w a t e r l e v e l o f t h e p u d d l e were r a i s e d so t h a t t h e r e was open-water above th e clumps of g r a s s t h e n t h e a n i m a l s s h o u l d move out on t o t h e a d j a c e n t a r e a . Two n a t u r a l e v e n t s a l l o w e d t e s t i n g o f b o t h t h e s e i d e a s . D u r i n g t h e months o f J a n u a r y and F e b r u a r y 19 69 an e x t r e m e l y c o l d p e r i o d o f weather caused I l l t h e n o r t h e r n end o f t h e p u d d l e t o f r e e z e , k i l l i n g a l l t h e a n i m a l s , b u t w h i c h l e f t t h e r e m a i n d e r o f t h e p u d d l e unchanged. D u r i n g t h e s u c c e e d i n g months t i l l t h e p u d d l e d r i e d up i n t h e s p r i n g t h e v a c a t e d 9 m o f l e n g t h was watched c l o s e l y f o r t h e appearance of a n i m a l s . A p p a r e n t l y no a n i m a l s moved i n from t h e o t h e r end. The o n l y a n i m a l s w h i c h appeared were s m a l l C y p r i n o t u s whose p r e s e n c e c o u l d be a c c o u n t e d f o r by t h e h a t c h i n g o f eggs, l e f t unharmed by t h e f r e e z i n g . L a r g e C y p r i n o t u s and H e r p e t o c y p r i s a n i m a l s l i v i n g b u t a few y a r d s away t h r o u g h t h e g r a s s d i d not move i n t o t h e a r e a . The second n a t u r a l e x p e r i m e n t o c c u r r e d i n a n o t h e r p u d d l e n e a r b y * , v e r y s i m i l a r i n shape though w i t h a deeper p r o f i l e and w i t h t h e same s p e c i e s p r e s e n t . D u r i n g t h e f i l l i n g o f t h i s p u d d l e t h e water l e v e l d i d not e n c r o a c h upon t h e whole s u r f a c e o f t h e p u d d l e , w h i c h a l l o w e d t h e a n i m a l s i n t h e wet a r e a t o h a t c h and grow. L a t e r t h e w a t e r l e v e l moved f u r t h e r o v e r t h e s u r f a c e a f t e r a p e r i o d o f wet->weather so as t o i n c l u d e a g r a s s e d a r e a t o t h e west. The l e v e l was m a i n t a i n e d and t h e eggs i n t h e new a r e a h a t c h e d b u t t h e members o f t h e o l d e r p o p u l a t i o n d i d n o t move on t o t h e newly c o v e r e d a r e a which was s e p a r a t e d by a dense a r e a o f g r a s s 3 m l o n g and f i l l i n g t h e w i d t h o f t h e p u d d l e . T h e r e f o r e f o r a p e r i o d o f one month, two p o p u l a t i o n s of d i f f e r e n t ages remained a d j a c e n t t o one * The p u d d l e r e f e r r e d t o i s t o be found a l o n g s i d e 4th Avenue, on t h e s o u t h e r n s i d e , o p p o s i t e some o f t h e J e r i c h o Army Base b u i l d i n g s which a r e o p p o s i t e t h e c o r n e r of W a l l a c e and. 4 t h . I t i s a d r a i n a g e c h a n n e l c a r r y i n g w a t e r from t h e h i g h e r l a n d t o a. d r a i n b e s i d e t h e r o a d . 112 a n o t h e r and y e t s e p a r a t e d by t h e g r a s s . F i n a l l y i n e a r l y December a heavy r a i n s t o r m o c c u r r e d which r e s u l t e d i n more wa t e r b e i n g d e l i v e r e d from t h e s u r r o u n d i n g lawn t h a n t h e d r a i n c o u l d h a n d l e , w i t h t h e r e s u l t t h a t t h e l e v e l o f t h e p u d d l e r o s e above t h e a r e a o f dense g r a s s . W i t h i n 2 days l a r g e r a n i m a l s from t h e o l d e r p o p u l a t i o n were found i n among t h e o t h e r s on t h e o t h e r s i d e o f t h e g r a s s . I t seems c l e a r t h a t t h e dense g r a s s p r e s e n t i n b o t h t h e s e p u d d l e s p r e v e n t e d t h e d i s p e r s a l o f t h e a n i m a l s . T h i s e x p l a n a t i o n seems t o a c c o u n t f o r t h e f a i l u r e o f the e x p e c t e d m i x i n g o f t h e s p e c i e s t o be ob-s e r v e d . However th e e x p l a n a t i o n i s not e n t i r e l y s a t i s f a c t o r y because t h e r e r e m a i n s no way o f e x p l a i n i n g how the a n i m a l s m i g h t r e c o l o n i z e a r e a s i n which t h e y become e x t i n c t . A t p r e s e n t i t seems t h a t such r e c o l o n i z a t i o n would be a c c i d e n t a l and t h e r e s u l t o f f o r t u i t o u s e v e n t s t h a t would r e s u l t i n a change i n t h e w a t e r l e v e l , change i n the s u r f a c e o f t h e l a n d o r the d e a t h and decay o f a clump of g r a s s . The a n i m a l s may or may not move i n a random manner w i t h i n t h e unimpeded a r e a s b u t t h e manner o r f r e q u e n c y w i t h which t h e y n e g o t i a t e b a r r i e r s o f dense g r a s s r e m a i n s unknown. Summary 1, The p r o p o r t i o n s o f t h e t i m e s p e n t moving and s t a t i o n a r y a r e a l m o s t i d e n t i c a l f o r b o t h s p e c i e s . The t i m e spent c r a w l i n g and b u r r o w i n g a r e a l s o s i m i l a r , b u t C y p r i n o t u s i s t h e o n l y s p e c i e s which i s c a p a b l e o f swimming. O v e r a l l C y p r i n o t u s moves f a s t e r t h a n does H e r p e t o c y p r i s . 113 2. The r a t e o f movement from a p o i n t o f r e l e a s e i n an _3 e x p e r i m e n t a l t a n k was 30.3 x 10 cm/sec f o r C y p r i n o t u s _3 and 0.29 x 10 cm/sec f o r H e r p e t o c y p r i s , 3o The d i s p e r s a l o f b o t h s p e c i e s from a p o i n t o f r e l e a s e was t e s t e d t o see i f i t conformed t o a random d i f f u s i o n model i n w h i c h t h e d i f f u s i o n c o e f f i c i e n t r emained c o n s t a n t . More a n i m a l s o f b o t h s p e c i e s were found f u r t h e r from the p o i n t o f r e l e a s e t h a n e x p e c t e d by t h e model. 4 . D i s p e r s a l o f t h e o s t r a c o d s i n t h e p u d d l e was found t o be p r e v e n t e d by dense clumps o f g r a s s . The means and f r e q u e n c y w i t h w h i c h t h e y c o u l d n e g o t i a t e t h e s e clumps are unknown. 114 PART II a) The tyre-track puddle and i t s water supply The tyre-track puddle i s located i n a f i e l d belong-ing to the Department of National Defence west of an access road running north o f f 4th Avenue to Jericho Beach, The f i e l d , surrounded by a formidable looking fence, i s covered i n short grass and rushes with a large clump of trees (Red Alders, Alnus rubra) on i t s western side and i t slopes gently towards the sea (see the map i n F i g , 36 and F r o n t i s p i e c e ) , The puddle i s located i n m i d - f i e l d some 20 m east of the trees. P r i o r to about 1940 the area north of 4th Avenue and behind the beach was a well treed golf-course and a i r photos taken i n 1932 and 1938 show well-kept lawns dotted with those week-end hazards of the a r i s t o c r a c y , sand-traps, (One low-level oblique photo shows a parking l o t near what may have been the 19th occupied with sleek black Buicks carrying t h e i r spare tyres on the mud-guard). The g o l f course seems to have been made by c l e a r i n g the trees since the only c l e a r areas are lawned. The s i t e of the present puddle was a long fairway running north-west from near 4th Avenue, After the area was taken over by the Depart-ment of National Defence and the Jericho Base erected, the f i e l d l y i n g to the east of the buildings seems to have been unused.. In 1946 an important landmark appeared. This i s a tunnel carrying steam li n e s to outlying buildings and which was covered by concrete slabs wide enough to show on a i r photos. Alongside the tunnel was l e f t a small group of trees 115 (Red A'lders) and b o t h t h e t u n n e l and t h e t r e e s a r e p r e s e n t t o d a y . The p r e s e n t p u d d l e l i e s some 50 m due s o u t h o f t h e p o i n t where t h e steam l i n e e n c o u n t e r s t h e t r e e s and so can be l o c a t e d a c c u r a t e l y upon a i r p h o t o s * t a k e n s i n c e t h e n . U n t i l 1959 t h e r e i s no e v i d e n c e o f t h e p r e s e n c e o f t h e t y r e - t r a c k s i n w hich t h e p u d d l e now l i e s b u t i n t h a t y e a r t h e r e appear some d i s t i n c t t r a c k s i n t h e g r a s s . These a re d i s c e r n a b l e under an o r d i n a r y power s t e r e o s c o p e . A c c o r d i n g t o J e r i c h o Base Army a u t h o r i t i e s t h e s e t r a c k s were p r o b a b l y made by heavy t r u c k s c a r r y i n g s o i l i n t o b u i l d up a low l y i n g a r e a b e h i n d t h e bea c h . The t r u c k s e n t e r e d from 4 t h Avenue about 100 y a r d s e a s t o f th e p r e s e n t a c c e s s r o a d and dr o v e a c r o s s t h e f i e l d and o v e r t h e steam l i n e . The t r a c k s i n whi c h t h e p u d d l e l i e s do not go back t o t h e r o a d on t h e 1959 a i r photo and seem t o be an o f f - s h o o t o f the main t r a c k , perhaps used t o t u r n t h e t r u c k s around. A deep r u t i s p r e s e n t now where t h e s i d e t r a c k s l e f t t h e main one s u g g e s t i n g t h a t t h e t r u c k s may have become s t u c k i n t h e mud q u i t e o f t e n . D u r i n g 1960-61 t h e t r a c k was used t o c a r t s o i l from t h e H i g h b u r y Sewage T u n n e l P r o j e c t and dump i t b e h i n d t h e beach. F u r t h e r a i r photos t a k e n up t o t h e p r e s e n t show t h a t t h e a r e a has remained u n d i s t u r b e d . I ca n n o t e s t a b l i s h t h e e x i s t e n c e o f t h e p r e s e n t p a t t e r n o f d r a i n a g e on t h e l a n d , v i t a l t o t h e e x i s t e n c e o f t h e p u d d l e , b u t t h e pu d d l e as i t e x i s t s t o d a y p r o b a b l y d i d n o t appear u n t i l 1962 when t h e t r u c k s dumping t h e s o i l no l o n g e r drove o v e r t h e a r e a . * A i r p h o t o s used t o t r a c e t h e h i s t o r y o f t h e a r e a were t a k e n by b o t h P r o v i n c i a l and F e d e r a l Departments and c o p i e s b e l o n g i n g t o t h e UBC Geography Department were s t u d i e d . 116 The p r e s e n t p u d d l e i s 31,1 m l o n g and has a. mean w i d t h of 0„34 m. The n o r t h e r n h a l f t e n d s t o be w i d e r t h a n t h e r e m a i n d e r and a l s o s l i g h t l y deeper ( F i g , 34A., B)„ The mean dep t h i s 0.97 on. The l a n d s l o p e s g e n t l y (1:30) a t an a l m o s t c o n s t a n t r a t e (see F i g . 34C) and t h e water whose f l o w i s b r o k e n by clumps o f g r a s s t r i c k l e s down t h e r u t . Owing t o i t s s h a l l o w n a t u r e and the p r e s e n c e o f g r a s s the p u d d l e i s o n l y d i s c e r n a b l e a t a s h o r t d i s t a n c e . The a r e a w i t h i n t h e p u d d l e i s b r o k e n up by p a t c h e s o f g r a s s g r o w i n g i n t h e s o i l o f t h e p u d d l e and emerging t h r o u g h t h e s u r f a c e o f t h e w a t e r . Stems from t h e s e clumps and g r a s s g r o w i n g a l o n g t h e edges l i e h o r i z o n t a l l y below and o v e r t h e s u r f a c e o f t h e p u d d l e and impede the f l o w o f w a t e r . A l o n g t h e l e n g t h t h e r e a re r e c o g n i z a b l e 'open' and ' c o v e r e d ' a r e a s , t h e f o r m e r b e i n g m o s t l y water and mud bounded by t h e l a t t e r . F o r most o f t h e l e n g t h t h e y r u n a l t e r n a t e l y from s i d e t o s i d e o f t h e p u d d l e . I n some p l a c e s t h e r e a re a d j a c e n t u n i t s . The maximum l e n g t h o f t h e s e u n i t s p a r a l l e l t o t h e main a x i s o f t h e p u d d l e were measured on March 3 r d , 1969. The d i s t r i b u t i o n a l o n g t h e l e n g t h i s shown i n F i g . 35A and B„ The mean o f t h e open u n i t l e n g t h s , L q , i s 11.64 cm and o f t h e c o v e r e d u n i t s , L , 14.57 cm. c' These measurements do n o t g i v e an a c c u r a t e i d e a o f t h e p r o p o r t i o n o f t h e a r e a o c c u p i e d by each k i n d o f u n i t . P a r t i c u l a r a r e a s a l o n g t h e l e n g t h were mapped by p l a c i n g a s h e e t o f p l e x i g l a s s o v e r sample a r e a s o f t h e p u d d l e and t r a c i n g around t h e open a r e a s . The l i n e s were t h e n t r a c e d on t o s h e e t s F i q u r e 34 P h y s i c a l d i m e n s i o n s o f t h e t y r e - t r a c k p u d d l e . F i g , 3 4 A - t h e w i d t h o f t h e p u d d l e i n c e n t i m e t r e s a t v a r i o u s d i s t a n c e s from i t s s o u t h e r n end. F i g , 34B - t h e maximum d e p t h ( u s u a l l y i n t h e c e n t r e o f t h e w i d t h ) a t t h e same d i s t a n c e s . F i g . 34C - a p r o f i l e o f t h e s l o p e on which t h e p u d d l e l i e s . The v e r t i c a l d i s t a n c e i n c e n t i -metres below t h e l e v e l o f t h e s o u t h e r n end a re g i v e n f o r each d i s t a n c e i n metres from t h a t end (Note t h e d i f f e r e n c e i n s c a l e between t h e y and x - a x i s f o r t h i s g r aph which e x a g g e r a t e s the s l o p e ) . VERTICAL DISTANCE (cm) MAXIMUM DEPTH (cm) WIDTH O F PUDDLE (cm) g I z: o m m J3 O O c —i m z o o -n n c o o r~ m F i g u r e 35 The d i s t r i b u t i o n o f open (L ) and g r a s s e d (L ) u n i t s of t h e p u d d l e a l o n g i t s l e n g t h . The g r e a t e s t l e n g t h o f each u n i t o f a r e a a l o n g t h e n o r t h - s o u t h a x i s o f t h e p u d d l e i s shown f o r each d i s t a n c e from t h e s o u t h e r n end. F i g , 35A - open ( n o n - g r a s s e d ) a r e a s F i g , 3 5 B - g r a s s e d a r e a s . A 40 30 20 ft ft • 10 • • ft ft • • » * • • ft • • • ft • • - • ft • • • B 80 70 60 50 40 30 20 10 • ft • ft * 12 15 18 21 24 27 30 DISTANCE (m) FROM THE SOUTH END OF PUDDLE 119 o f p a p e r . The s i z e o f each a r e a sampled was 48 x 30 cm. The a r e a s o f each k i n d o f s u r f a c e were t h e n d e t e r m i n e d by d i v i d i n g t h e maps up / i n t o s q u a r e s and c o u n t i n g t h e number i n each a r e a . The mean p r o p o r t i o n o f o p e n - s u r f a c e was 0,25 and o f g r a s s e d s u r f a c e 0.75 (see T a b l e X.) „ The range o f v a l u e s was from 0.15 t o 0.39. The e x i s t e n c e o f t h e t y r e - t r a c k p u d d l e i s dependent upon t h e c o n t i n u e d s u p p l y o f wa t e r from t h e s u r r o u n d i n g l a n d because r a i n f a l l i n c i d e n t upon t h e p u d d l e ' s s u r f a c e i s n o t s u f f i c i e n t t o m a i n t a i n t h e wa t e r l e v e l . The a r e a o f s u r r o u n d -i n g l a n d from w h i c h t h e p u d d l e r e c e i v e s w a t e r s h a l l be c a l l e d t h e catchment a r e a o f t h e p u d d l e . The t y r e - t r a c k r e c e i v e s w a t e r from t h r e e main a r e a s o f l a n d . These a r e a s (see F i g . 36) a r e a b a s i c catchment a r e a i m m e d i a t e l y above and t o t h e e a s t o f t h e p u d d l e , a s m a l l a r e a a d j o i n i n g t h e w e s t e r n s i d e a l o n g t h e f i r s t 9 m o f t h e p u d d l e and f i n a l l y a l a r g e area, o f l a n d a p p r o x i m a t e l y 100 m s o u t h o f t h e p u d d l e . The wa t e r f l o w s a l o n g s u r f a c e c h a n n e l s as shown i n t h e map. The m a j o r i t y o f w a t e r d e l i v e r e d t o t h e p u d d l e e n t e r s v i a t h e c h a n n e l on t h e e a s t e r n s i d e 13 m from t h e s o u t h e r n end. The l i m i t s o f t h e a r e a o f l a n d c o n t r i b u t i n g w a t e r were d e t e r m i n e d by o b s e r v i n g t h e d i r e c t i o n o f f l o w o f wa t e r o v e r t h e s u r f a c e when i t was r a i n i n g , f o l l o w i n g minor s u r f a c e f l o w s t o see i f t h e y c o n t r i b u t e d t o t h e f i n a l c h a n n e l . The a r e a s o f each p i e c e o f l a n d a r e 2 2 2 483 m ( b a s i c ) , 32 m ( s m a l l ) , and a p p r o x i m a t e l y 500 m ( l a r g e ) . N o r m a l l y a c o n t i n u o u s f l o w o f w a t e r i s m a i n t a i n e d from t h e b a s i c and s m a l l catchment a r e a s , t h e l a r g e one o n l y c o n t r i b u t i n g a f t e r p e r i o d s o f heavy r a i n f a l l . I f t h e r e i s no r a i n f o r a TABLE X The p r o p o r t i o n o f s a m p l e - a r e a s o f t h e p u d d l e (0.146 m ) o c c u p i e d by u n c o v e r e d mud and g r a s s a t d i f f e r e n t p o i n t s a l o n g i t s l e n g t h . The d i s t a n c e i s measured from t h e c e n t r e o f each sample a r e a t o t h e s o u t h end. D i s t a n c e (m) P r o p o r t i o n open P r o p o r t i o n c o v e r e d 5,60 0.235 0.765 14, 33 0.393 0.607 20,29 0.154 0.846 22 ,40 0.288 0. 712 23.87 0.350 0.650 25.14 0.159 0.841 28.42 0.184 0.816 29.62 0.167 0.833 30.85 0.350 0.648 Means 0.254 0. 74 7 F i q u r e 36 A map of the f i e l d on the Jericho Army Base containing the tyre-track puddle. The f i e l d i s bounded on the east and south sides by a high fence and on the west side by a large clump of trees. The tyre-track puddle (TT) and others mentioned i n the text are l a b e l l e d - SP, RLP, BPTT, TP, BTP. The areas of land near some of the puddles which contribute water to the puddle are also indicated. Basic catchment area, small catchment area and large catchment area for the TT puddle; and the areas for BPTT and RLP' are also shown. Arrows with s o l i d l i n e s i n d i c a t e the d i r e c t i o n of flow of water when i t i s present and those with dashed l i n e s i n d i c a t e the d i r e c t i o n of flow when there i s a sudden down-pour. The p a i r of trees below the puddle, mentioned i n the text are shown beside the path. This foot-path runs along the top of the under-ground steam-line also mentioned. The point where the path passes the p a i r of trees was used to locate the s i t e of the puddle i n the air-photos. 122 p e r i o d g r e a t e r t h a n about 2 weeks the o n l y w a t e r e n t e r i n g t h e p u d d l e comes from th e s m a l l a r e a . I t seems t h a t some o f t h e w a t e r e n t e r i n g t h e p u d d l e does not o r i g i n a t e from r a i n f a l l i n c i d e n t d i r e c t l y upon t h e catchment a r e a s . A f t e r l o n g p e r i o d s w i t h o u t r a i n d u r i n g t h e w i n t e r a s m a l l f l o w i s m a i n t a i n e d by u n derground seepage from a s t r i p o f l a n d t h a t i s p a r t o f b o t h t h e s m a l l and b a s i c catchment a r e a s . I t i s r e c o g n i z a b l e because i t s u p p o r t s the growth of p a t c h e s o f r e e d s (Juncus effusus.) ] and i s u s u a l l y more m o i s t . D u r i n g p e r i o d s not p r e c e d e d by r a i n f a l l i n t h e p r e v i o u s 3 days t h e volume o f w a t e r e n t e r i n g t h e p u d d l e d u r i n g 3 t h e w i n t e r i s o f t h e o r d e r o f 1 - 2 m per day. A f t e r a p e r i o d o f heavy r a i n t h i s amount can be 10 t i m e s as l a r g e and t h e r e i s v e r y l i t t l e d e l a y between th e d e p o s i t i o n o f t h e r a i n and i n c r e a s e i n r a t e o f f l o w . Heavy d e l u g e s do n o t have d i s -a s t e r o u s e f f e c t s because t h e e x t r a water f l o w s o f f a l o n g a l t e r n a t i v e c h a n n e l s , b y - p a s s i n g t h e p u d d l e . E x c e s s w a t e r d e l i v e r e d t o t h e p u d d l e o v e r f l o w s t h r o u g h t h e g r a s s t o an a d j a c e n t p u d d l e . N o r m a l l y t h e r e i s a c o n t i n u o u s b u t s m a l l o v e r f l o w . The most common p l a n t s i n t h e t y r e - t r a c k p u d d l e a r e : J uncus acumenatus - a s h o r t g r e e n r u s h whose stems p r o t r u d e t h r o u g h t h e s u r f a c e o f t h e p u d d l e f o r 10 - 15 cm and which i s e s p e c i a l l y dense i n t h e n o r t h e r n 6 m and a l m o s t t h e s o l e o c c u p a n t o f t h e s o u t h e r n 15 m o f t h e p u d d l e ; A g r o s t i s sp. (? s t o l o n i f e r a ) - a s h o r t , s p r e a d i n g g r a s s w i t h many stems below t h e s u r f a c e o f t h e w a t e r and which i s most common i n the 12 3 c e n t r a l p a r t o f t h e pu d d l e between t h e two a r e a s o f r u s h e s ; Anthoxanthum o r d o r a t u m - a n o t h e r s h o r t g r a s s , more e r e c t i n h a b i t t h a n t h e A g r o s t i s s p. and o c c u r r i n g w i t h i t i n t h e c e n t r a l p a r t ; and P l a n t a g o l a n c e o l a t a - o c c a s i o n a l p l a n t s a l o n g w i t h A g r o s t i s s p. and whose r o s e t t e shape o f growth f o r c e s open a r e a s i n among t h e g r a s s . The s u r r o u n d i n g p a s t u r e i s composed p r i m a r i l y o f A g r o s t i s s p . , A. o r d o r a t u m , f i e l d c l o v e r ( T r i f - o l i u m a r y e n e s e ) , s h o r t r u s h e s (Juncus t e n i u s ) and t h e o c c a s i o n a l b u r c h - p l a n t ( H y p o c h o r i s r a d i c a t a ) . I n t h e w e t t e r a r e a s , where t h e underground seepage a p p e a r s , a re l a r g e p a t c h e s o f t a l l r u s h e s Juncus e f f u s u s . There are a l s o some s m a l l (4 f e e t h i g h ) t r e e s j u s t t o t h e west o f t h e p u d d l e : s m a l l r e d a l d e r s and p o p l a r s o r cottonwoods ( P o p u l u s t r i c h o c a r p a ) . Summary 1. The t y r e - t r a c k p u d d l e i s l o c a t e d on an unused f i e l d o f t h e J e r i c h o Army Base, P o i n t Grey, Vancouver. The a r e a was used f o r a g o l f c o u r s e up u n t i l 1940 and by f o l l o w i n g t h e h i s t o r y o f t h e a r e a i n a e r i a l p h otos i t was e s t a b l i s h e d t h a t the p u d d l e was p r o b a b l y formed i n 1962. 2. The l e n g t h o f t h e p u d d l e i s 31.1 m, i t s mean w i d t h i s 34.2 7 cm and mean maximum d e p t h i s 0.97 cm. The s l o p e o f t h e p u d d l e i s 1:30. The p u d d l e i s f i l l e d w i t h g r a s s . 3= Some o f t h e w a t e r e n t e r i n g t h e p u d d l e i s r u n - o f f from t h e s u r r o u n d i n g l a n d and some i s from underground seepages which emerge on t o t h e s u r f a c e o f t h e s l o p e above the p u d d l e . 124 4 o D u r i n g p e r i o d s w i t h o u t r a i n t h e p u d d l e - l e v e l i s m a i n t a i n e d by t h e seepage. 5. P e r i o d s o f heavy r a i n do n o t have d i s a s t r o u s , e f f e c t s upon t h e p u d d l e because t h e wa t e r f l o w s o f f t h e l a n d by a l t e r n a t i v e c h a n n e l s . b) A model o f w a t e r - l e v e l f l u c t u a t i o n s i n t h e p u d d l e S i n c e each p a r t o f t h e p u d d l e does n o t d r y up a t t h e same t i m e and s i n c e i t i s n e c e s s a r y t o know a t what t i m e s p a r t i c u l a r p o i n t s i n t h e p u d d l e become d r y i n t h e p a s t , i t i s e s s e n t i a l t o have some means o f s i m u l a t i n g t h e f l u c t u a t i o n s i n wa t e r l e v e l d u r i n g t h e c r i t i c a l f i l l i n g and d r y i n g - u p p e r i o d s . Between t h e t i m e s when t h e f u l l l e v e l had been e s t a b l i s h e d , i n t h e f a l l and when t h e l e v e l had begun t o d e c r e a s e i n t h e s p r i n g t h e r e were, d u r i n g t h e p e r i o d o f s t u d y , no f l u c t u a t i o n s i n t h e l e v e l . T h e r e f o r e i f the t i m e s o f i n i t i a t i o n o f f i l l i n g and of d r y i n g - u p i n t h e p a s t can be r e c o g n i z e d t h e n o n l y t h e t r a n s i t i o n a l l e v e l s need be s i m u l a t e d . The t i m e when t h e l e n g t h b e g i n s t o i n c r e a s e i s t h a t t i m e a t whi c h t h e catchment a r e a s s u p p l y i n g t h e wa t e r a r e a b l e t o m a i n t a i n a f l o w o f w a t e r g r e a t e r t h a n t h e l o s s e s from t h e p u d d l e r e s u l t i n g from e v a p o r a t i o n , t r a n s p i r a t i o n and soakage. C o n v e r s e l y , t h e t i m e o f i n i t i a t i o n of d e c r e a s e i n l e n g t h i s when t h e a r e a s c a n n o t m a i n t a i n t h e f u l l l e n g t h . o f t h e p u d d l e . The o b s e r v e d c o n d i t i o n s a s s o c i a t e d w i t h t h e s e e v e n t s d u r i n g t h e y e a r s 1967, 1968 and 1969 were f o r f i l l i n g an amount o f r a i n f a l l o f g r e a t e r t h a n 1.5" i n a pe r i o d , o f l e s s t h a n 4 days 1 2 5 ( w h i c h i s a r a i n f a l l i n t e n s i t y o f 0 o 4 " / d a y ) , and f o r d r y i n g , r a i n - f r e e p e r i o d o f a t l e a s t 5 days a s s o c i a t e d w i t h a mean d a i l y t e m p e r a t u r e of g r e a t e r t h a n 1 0°C„ A p p a r e n t l y t h e f i l l i n g i s i n d e p e n d e n t o f t h e d a i l y temperature. Some i d e a of t h e i n c i d e n c e o f t h e s e c o n d i t i o n s i n t h e P o i n t Grey a r e a i s g i v e n i n F i g , 3 7 where t h e r e i s shown t h e l e n g t h s o f p e r i o d s o f c o n s e c u t i v e d r y days and t h e mean d a i l y t e m p e r a t u r e d u r i n g . t h o s e days as w e l l as t h e l e n g t h s o f p e r i o d s o f c o n s e c u t i v e wet days ( r e g a r d l e s s o f the amount o f r a i n f a l l ) and mean d a i l y t e m p e r a t u r e . There were two v a l u e s f o r t h e l e n g t h s o f d r y p e r i o d s and t e m p e r a t u r e w h i c h were r e c o r d e d f o r a p e r i o d when t h e p u d d l e was known t o be f u l l b u t a c c o r d i n g t o t h e c r i t e r i a i t s h o u l d have been empty. Both o f t h e s e o c c u r r e d d u r i n g t h e f i l l i n g o f t h e p u d d l e i n 1 9 6 8 a f t e r t h e p u d d l e had f i l l e d and t h e u n d e r g r o u n d w a t e r was enough t o m a i n t a i n t h e l e v e l . There were no e x c e p t i o n s t o the c r i t e r i a f o r f i l l i n g . The r e g i o n s o f t h e g r a p h s o c c u p i e d by v a l u e s r e c o r d e d when t h e p u d d l e was f u l l o r empty a r e , as e x p e c t e d , f u l l when t h e wet p e r i o d s a r e l o n g and f r e q u e n t and t h e t e m p e r a t u r e low; and empty* when t h e d r y p e r i o d s were l o n g and f r e q u e n t and the t e m p e r a t u r e h i g h . D u r i n g t h e p e r i o d s o f f i l l i n g and d r y i n g - u p t h e l e n g t h o f t h e p u d d l e c o v e r e d w i t h water f l u c t u a t e s d u r i n g each day. At n i g h t t h e leng'th tends t o i n c r e a s e , r e a c h i n g a maximum d u r i n g t h e e a r l y morning and d u r i n g t h e day i t d e c r e a s e s The term i s used h e r e t o mean no t c o m p l e t e l y f u l l . V a l u e s f o r t i m e s when t h e p u d d l e was i n the p r o c e s s o f r e c e d i n g are i n c l u d e d i n t h e 'empty'-group, F i g u r e 37 The i n c i d e n c e o f t h e l e n g t h s o f d r y and wet p e r i o d s and t h e a s s o c i a t e d mean d a i l y t e m p e r a t u r e (°C) d u r i n g .each p e r i o d as t a k e n from t h e U.B.C. C l i m a t -o l o g i c a l S I t a t i o n Records f o r t h e y e a r s 1961-69. I t was not p o s s i b l e t o put a l l t h e p o i n t s on t h e graphs because of t h e l a r g e number ne a r t h e x - a x i s b u t t h e r e l a t i v e o c c u r r e n c e o f each k i n d o f p e r i o d i s s t i l l a c c u r a t e l y i n d i c a t e d . F i g , 37A and C. - d r y and wet p e r i o d s f o r t h e y e a r s 1961-69 Fig„ 37B and D - d r y and wet p e r i o d s r e s p e c t i v e l y when t h e s t a t e o f t h e p u d d l e was known. C l o s e d c i r c l e s - p u d d l e f u l l , l a r g e r open c i r c l e s - p u d d l e s n o n - f u l l . The arrows i n F i g . 37B p o i n t t o two p e r i o d s when t h e p u d d l e was f u l l b u t by t h e c r i t e r i a , m e ntioned i n t h e t e x t , i t s h o u l d have been d r y i n g - u p . LL o A B • • • • • • •• | j « «M * * • • i' i - n h i r i " i « » • C D • • • * • \ . St.', <• . M V i - . l . - ' - l l l . fl< !•£%• ..t. . _ i f i ' / ' i m ' - i i / l - i J l i | i i ; t l i i i i i i l M i l i - l •! I , c 1 • !• I - . — . , . l t . I 'j 10 2 0 3 0 4 0 5 0 6 0 10 2 0 3 0 4 0 5 0 6 0 M E A N DAILY T E M P E R A T U R E . ( ° F ) 12 7 because t h e warmer t e m p e r a t u r e s dry-up t h e s u p p l y o f w a t e r from t h e catchment a r e a b e f o r e i t can f l o w i n t o t h e p u d d l e . The minimum l e v e l i s r e a c h e d d u r i n g t h e e a r l y e v e n i n g a f t e r w h i c h t h e c y c l e i s r e p e a t e d . Each e v e n i n g t h e i n f l o w c h a n n e l was f o u n d t o be empty and each morning i t was c a r r y i n g some w a t e r . The f l u c t u a t i o n s , measured between 0900 - 1000 hours and 1700 - 1800 h o u r s d u r i n g t h e s p r i n g o f 1968, are shown i n F i g . 38. A f t e r each r e s p o n s e t o t h e r a i n f a l l ' t h e l e v e l s g r a d u a l l y d e c r e a s e , each morning and e v e n i n g l e v e l b e i n g l e s s t h a n t h e day b e f o r e . . I n c r e m e n t s i n l e n g t h i n r e s p o n s e t o r a i n f a l l r e m a i n f o r a s h o r t e r p e r i o d when t h e d r y i n g - u p has' been p r o c e e d i n g f o r a few days t h a n d u r i n g the I n i t i a l p e r i o d . T h i s i s because as t h e l e n g t h o f t i m e t h a t a p a r t o f t h e p u d d l e has been v a c a t e d i n c r e a s e s , t h e s o i l i n t h a t a r e a becomes d r i e r and so a b s o r b s more of any new c o v e r a g e . The w a t e r l e v e l i n t h e p u d d l e i s l i k e t h e t i d e on a sandy beach whose a b s o r b e n c y i n c r e a s e s w i t h t i m e e x c e p t t h a t t h e w a t e r r e c e d e s up t h e s l o p e i n s t e a d o f down i t . D u r i n g t h e p e r i o d o f d r y i n g - u p t h e l e n g t h o f t h e p u d d l e r e s p o n d s t o two m e t e r o l o g i c a l c o n d i t i o n s . These a r e t h e o c c u r r e n c e o f r a i n and the o c c u r r e n c e o f r a i n - f r e e p e r i o d s . O n l y t h e o b s e r v a t i o n s o f changes i n l e n g t h d u r i n g t h e s p r i n g o f 1968 were used t o b u i l d a s i m p l e , e m p i r i c a l model. T h i s i s as f o l l o w s : on days on which t h e r e i s no r a i n t h e r e w i l l be a. decrement o f l e n g t h whose s i z e i s p r o p o r t i o n a l o n l y t o t h e number of days s i n c e the l a s t r a i n o c c u r r e d r e g a r d l e s s o f i t s amount, and on days w i t h r a i n t h e r e w i l l be an i n c r e m e n t F i g u r e 38 The d i u r n a l f l u c t u a t i o n i n t h e l e n g t h o f t h e t y r e -t r a c k p u d d l e d u r i n g the p e r i o d 4 t h May t o 1 s t J u n e , 1968. The o c c u r r e n c e and amount o f each r a i n f a l l i s g i v e n i n a h i s t o g r a m a l o n g t h e top o f t h e g r a p h . The morning w a t e r l e v e l i s i n d i c a t e d by a c r o s s and t h e e v e n i n g water l e v e l by a c l o s e d c i r c l e . .PUDDLE LENGTH (m) RAINFALL (inches) ro ro to V p yi o 01 o p 6 6 - 6 6 6 6 6\ 129 i n l e n g t h whose s i z e i s l i n e a r l y r e l a t e d t o t h e amount o f r a i n f a l l on t h a t day a l o n e . The v a l u e s f o r t h e r a t e s o f t h e s e r e l a t i o n s h i p s were o b t a i n e d by r e g r e s s i o n . The r e l a t i o n s h i p between t h e l e n g t h , L, and t h e number o f days s i n c e r a i n NDSR i s T T -0,2018 • NDSR ,__, L = L Q e (16) where L q i s t h e l e n g t h a f t e r t h e l a s t p e r i o d o f r a i n (see F i g , 39A)„ The r e s p o n s e t o r a i n , & L, i s g i v e n by A L = -0,517 + 26, 32 • RNFL (17) where RNFL i s t h e d a i l y r a i n f a l l i n i n c h e s ( F i g , 39B) The model was the n t e s t e d by r e a d i n g i n t o t h e computer t h e d a i l y r a i n f a l l f o r t h e t r a n s i t i o n p e r i o d f o r t h e s p r i n g o f 1969 and t h e n comparing t h e o b s e r v e d w i t h t h e e x p e c t e d w a t e r l e v e l s . S i n c e t h e o b s e r v a t i o n s f o r t h i s p e r i o d i n no way c o n t r i b u t e d t o t h e p a r a m e t e r s t h i s i s an adeguate t e s t o f t h e t h e o r y and t h e agreement i s v e r y good ( F i g , 4 0 ) . But a much more p o t e n t t e s t can be p e r f o r m e d , by t a k i n g the model d e v e l o p e d f o r t h e d r y i n g - u p p e r i o d and o b t a i n i n g t h e e x p e c t e d l e v e l s f o r t h e p e r i o d i n t h e f a l l when t h e p u d d l e was f i l l i n g . As can be seen t h e agreement between e x p e c t e d and o b s e r v e d f o r t h e f a l l o f 1967 and 1968 i s q u i t e good ( F i g , 4 0 ) , The e x p e c t e d l e n g t h s o f the p u d d l e were c o n s t r a i n e d between 0,0 and 31,1 m„ I t has a l r e a d y been shown t h a t the o s t r a c o d s a r e u n a b l e t o w i t h s t a n d d e s i c c a t i o n and t h a t the p r o p o r t i o n o f t h e numbers a l i v e d e c r e a s e s l i n e a r l y as a f u n c t i o n o f t i m e F i q u r e 39 The r e l a t i o n s h i p s between t h e decrement i n l e n g t h ( i n m e t r e s ) and t h e number o f days s i n c e r a i n , and t h e i n c r e m e n t i n l e n g t h ( i n m e t r e s ) p e r u n i t r a i n -f a l l , used t o g e n e r a t e the e x p e c t e d l e n g t h s o f the p u d d l e . The d a t a i s t a k e n from o b s e r v a t i o n s o f t h e r e s p o n s e o f t h e p u d d l e t o t h e s e v a r i a b l e s d u r i n g t h e s p r i n g o f 1968, F i g , 39A - t h e n a t u r a l l o g a r i t h m o f t h e decrement i n metres o f t h e l e n g t h o f the p u d d l e on days w i t h o u t r a i n d u r i n g t h e t r a n s i t i o n a l p e r i o d , p l o t t e d a g a i n s t t h e number o f days s i n c e i t l a s t r a i n e d r e g a r d l e s s o f t h e amount o f r a i n . The s l o p e o f t h e l i n e i s -0,2018 and c o r r e l a t i o n c o -e f f i c i e n t i s 0,70, F i g , 39B - t h e i n c r e m e n t i n p u d d l e l e n g t h i n metres on days w i t h r a i n p e r u n i t o f r a i n f a l l . The s l o p e o f t h e l i n e i s 26,32 and t h e c o r r e l a t i o n c o e f f i c i e n t i s 0.91, RAINFALL PER DAY (INCHES) F i g u r e 40 T e s t o f t h e a b i l i t y o f t h e puddle-model t o p r e d i c t t h e l e n g t h o f t h e t y r e - t r a c k p u d d l e d u r i n g t h e p e r i o d s o f d r y i n g and f i l l i n g . The o b s e r v e d mean d a i l y l e n g t h ( v e r t i c a l l i n e s and c l o s e d c i r c l e s ) on each day d u r i n g t h e p e r i o d and t h e e x p e c t e d l e n g t h ( c r o s s e s ) a r e shown f o r d i f f e r e n t t i m e s on t h e l e f t - h a n d s i d e o f t h e f i g u r e . O p p o s i t e each o f t h e s e i s t h e number o f days s i n c e t h e b e g i n n i n g o f d r y i n g o r f i l l i n g , t h a t p o i n t s s p a c e d a t 0,5 m i n t e r v a l s a l o n g t h e l e n g t h o f t h e p u d d l e were d r y ( f o r 7 days) o r wet ( f o r 5 d a y s ) , w h i c h e v e r i s a p p r o p r i a t e . F i g , 40A - s p r i n g 1969, F i g , 40B - f a l l 1967, F i g , 40C - f a l l 1968 F i g , 40D - s p r i n g 1968, TIME (DAYS) DISTANCE (m) FROM SOUTH END OF PUDDLE 132 (see Fig„ 28)„ S i n c e the c o m p a r t m e n t a l i z a t i o n o f t h e p u d d l e p r e v e n t s t h e r e s i d e n t s o f an a r e a from r e c e d i n g w i t h t h e water, t h e p r o p o r t i o n o f them l e f t a l i v e a f t e r a g i v e n number o f days of d e s i c c a t i o n can be c a l c u l a t e d . T h e r e f o r e , by knowing t h e a b i l i t y o f t h e a n i m a l s t o s t a n d d e s i c c a t i o n , the number o f days a f t e r t h e b e g i n n i n g o f d r y i n g - u p t h a t a c e r t a i n p r o p o r t i o n o f . t h e a n i m a l s i s dead a t a p a r t i c u l a r p o i n t i n t h e p u d d l e , can be c a l c u l a t e d . Both t h e o b s e r v e d and e x p e c t e d l e n g t h s o f t h e p u d d l e a t d i f f e r e n t t i m e s d u r i n g the s p r i n g o f 1968 and 1969 were f e d I n t o t h e computer program. Then, p i c k i n g a p o i n t i n t h e space o f t h e s i m u l a t e d p u d d l e t h e program scanned a l o n g the t i m e a x i s t o f i n d t h a t p o i n t i n t i m e w h i c h had been p r e c e d e d by d e s i c c a t i o n o f a g i v e n number o f d a y s . These r e s u l t s are shown i n F i g , 40 where f o r d r y i n g -up t h e number of d r y days i s 7 s i n c e a t t h i s t ime 50% o f t h e C y p r i n o t u s a n i m a l s were dead. S i m i l a r l y , f o r t h e f i l l i n g - u p o f 1967 and 1968 where t h e number of days t i l l a p o i n t was submerged f o r a p e r i o d e q u a l t o the h a t c h i n g d e l a y (5 days) o f old. eggs i s shown. The p r o x i m i t y o f t h e e x p e c t e d v a l u e s t o t h e o b s e r v e d i s e x c e l l e n t . I t can be seen t h a t depending upon t h e t o l e r a n c e s o f t h e s p e c i e s t h e l e n g t h s o f time a v a i l -a b l e t o them would be e n t i r e l y d i f f e r e n t . These t o l e r a n c e s a r e e x t r e m e l y i m p o r t a n t t o t h e a n i m a l because time i s v e r y v a l u a b l e a t t h e t e m p e r a t u r e s a t which changes i n l e n g t h o c c u r . A l t e r n a t i v e t o l e r a n c e s f o r d e s i c c a t i o n and h a t c h i n g d e l a y have been i n v e s t i g a t e d b u t t h e r e s u l t s a r e n o t p r e s e n t e d h e r e . As can be i m a g i n e d , t h e a l t e r n a t i v e f u n c t i o n s are l i a b l e t o be e n t i r e l y d i f f e r e n t i n s l o p e because of t h e f l u c t u a t i o n s i n 133 w a t e r l e v e l . W i t h t h i s model and t h e r a i n f a l l d a t a f o r the a p p r o p r i a t e p e r i o d s o f t h e y e a r s 1961-6,7, t h e e x p e c t e d l e n g t h s o f t he p u d d l e a t t h e s e t i m e s have been c a l c u l a t e d and t h e number o f days t i l l a c e r t a i n c r i t e r i o n i s met have been obtained» Summary 1. D u r i n g t h e w i n t e r t h e t y r e - t r a c k p u d d l e remains f u l l . Each p a r t o f t h e p u d d l e does n o t f i l l - u p o r dry-up a t t h e same t i m e d u r i n g t h e f a l l and s p r i n g r e s p e c t i v e l y , 2. The t i m e a t whi c h t h e p u d d l e b e g i n s t o f i l l i s when t h e catchment area, i s a b l e t o m a i n t a i n a s u p p l y o f water t o t h e p u d d l e . The t i m e a t w h i c h i t b e g i n s t o dry-up i s when a. s u f f i c i e n t s u p p l y o f w a t e r cannot be m a i n t a i n e d , 3. The c o n d i t i o n s a s s o c i a t e d w i t h t h e s e t i m e s a r e : f o r f i l l i n g , an amount o f r a i n o f g r e a t e r t h a n 1,5" i n a p e r i o d o f l e s s t h a n 4 days and f o r d r y i n g , a r a i n - f r e e p e r i o d o f a t l e a s t 5 days w i t h a mean d a l l y t e m p e r a t u r e o f g r e a t e r t h a n 10°C, 4. D u r i n g t h e s e t r a n s i t i o n a l p e r i o d s t h e l e n g t h o f t h e p u d d l e f l u c t u a t e s d i u r n a l l y . I t i s l o n g e s t i n t h e morning and s h o r t e s t a t n i g h t . 5. A s i m p l e model wh i c h used t h e r a i n f a l l r e c o r d f o r each p e r i o d was v e r y s u c c e s s f u l a t p r e d i c t i n g t h e l e n g t h o f t h e p u d d l e on each day. On each r a i n - f r e e day t h e r e was 134 a. decrement i n l e n g t h p r o p o r t i o n a l t o t h e number o f days s i n c e i t l a s t r a i n e d and on each r a i n y day t h e r e was an i n c r e m e n t i n l e n g t h t h a t was l i n e a r l y r e l a t e d t o t h e amount of r a i n . 6 0 From t h e o b s e r v e d and e x p e c t e d p u d d l e - l e n g t h t h e number o f days a f t e r t h e b e g i n n i n g o f f i l l i n g o r d r y i n g t i l l s e l e c t e d p o i n t s i n t h e p u d d l e had been submerged o r d r i e d c o n s e c u t i v e -l y f o r a g i v e n p e r i o d o f d a y s , was c a l c u l a t e d . c) The e f f e c t s o f s u b - z e r o t e m p e r a t u r e s upon the p u d d l e S i n c e t h e volume o f w a t e r i n the p u d d l e a t any one 3 t i m e i s v e r y s m a l l ( a p p r o x i m a t e l y 0.11 m ) and i s s p r e a d out i n such a t h i n l a y e r , t h e a i r t e m p e r a t u r e does not have t o r e m a i n below 0°C v e r y l o n g t i l l f r e e z i n g o c c u r s . Because o f t h e d r a s t i c e f f e c t o f f r e e z i n g upon th e a n i m a l s i t i s n e c e s s a r y t o know what t h e e f f e c t of a g i v e n f r o s t w i l l be upon each p a r t of t h e p u d d l e and what c o n d i t i o n s w i l l k i l l t h e a n i m a l s . I t has a l r e a d y been shown t h a t t h e a n i m a l s cannot s u r v i v e b e i n g f r o z e n f o r more t h a n a few h o u r s . T h e r e f o r e t h e c o n d i t i o n s i n t h e p u d d l e t h a t w i l l r e s u l t i n d e a t h o f t h e a n i m a l s w i l l be when t h e i c e t h i c k n e s s i n c r e a s e s t o where i t b e g i n s t o i n c l u d e t h e sediment and t h e a n i m a l s . There i s f o r t h i s p u d d l e an e x c e l l e n t l i n e a r r e l a t i o n -s h i p between t h e t h i c k n e s s o f i c e and t h e number of c o n s e c u t i v e days upon wh i c h t h e minimum a i r t e m p e r a t u r e was l e s s t h a n 0°C, r e g a r d l e s s o f t h e v a l u e o f t h e minimum. D e s p i t e t h e v a r i a b i l i t y t h a t c o u l d r e s u l t f r om h i g h day t e m p e r a t u r e s m e l t i n g o r 135 p a r t i a l l y , m e l t i n g t h e i c e o r t h e o c c u r r e n c e o f r a i n o r snow, t h e r e i s a l i n e a r i n c r e a s e o f i c e - d e p t h ( I D ) i n cm a c c o r d i n g t o I D = 0.26 + 0.564 • NCD ( s e e Fig„ 4 1 ) . The number o f c o n s e c u t i v e d a y s (NCD) o f f r e e z i n g t h a t r e s u l t s i n t h e i n c l u s i o n i n t o t h e i c e o f t h e s e d i m e n t i s n i n e . N o r m a l l y d u r i n g t h e f i r s t f e w d a y s o f i c e - f o r m a t i o n a i r s p a c e s w i l l f o r m u n d e r t h e l a y e r o f i c e , l e a v i n g t h e m o i s t s e d i m e n t w i t h t h e a n i m a l s l y i n g o n t h e s u r f a c e . I f t h e r e i s snow d u r i n g t h i s p e r i o d , i t w i l l p r o t e c t t h e a n i m a l s u n d e r -n e a t h f r o m b e i n g f r o z e n . B u t i n f l o w i n g s e e p a g e - w a t e r now becomes t h e i n d i r e c t c a u s e o f t h e i r d e a t h , b e c a u s e i t i s f r o z e n i n t o t h e l a y e r o f i c e . I f c o l d w e a t h e r c o n t i n u e s t h e i c e -l a y e r t h i c k e n s a n d b e g i n s t o i n c l u d e t h e s e d i m e n t . Some C y p r i n o t u s a n i m a l s h a v e b e e n r e c o r d e d f r o m s u r f a c e l a y e r s o f i c e s u g g e s t i n g t h a t t h e y h a d become c a u g h t w h i l e n o t on t h e s e d i m e n t . The e x p e c t e d i c e t h i c k n e s s when d e a t h o f t h e p o p u l a t i o n o c c u r s i s 5.4 cm w h i c h i s s u b s t a n t i a l l y t h i c k e r t h a n t h e p r o f i l e o f t h e p u d d l e . T h i s r e s u l t s f r o m t h e a d d i t i o n o f i c e t o t h e s u r f a c e l a y e r s a n d f r o m b e n e a t h . N o t a l l t h e l e n g t h o f t h e TT p u d d l e h a s b e e n o b -s e r v e d t o f r e e z e s o l i d l y . The a r e a f r o m t h e s o u t h e n d t o 22.4 m f r o m t h a t e n d h a s n o t b e e n ^ o b s e r v e d t o f r e e z e s o l i d l y . T h i s o c c u r r e n c e c a n n o t be e n t i r e l y e x p l a i n e d b u t i t seems t o r e s u l t f r o m t h e d e l i v e r y o f u n d e r g r o u n d w a t e r f r o m t h e s m a l l c a t c h m e n t a r e a t o t h e p u d d l e when a l l o t h e r i n f l o w s a r e f r o z e n . F i g u r e 41 The i n c r e a s e i n depth of i c e i n the t y r e - t r a c k puddle w i t h i n c r e a s i n g numbers of consecutive days on which the d a i l y minimum a i r temperature was l e s s than or equal to 0°C r e g a r d l e s s of the amount by which i t went below t h i s v a l u e . The slope of the s t r a i g h t l i n e i s 0,564 and the c o r r e l a t i o n c o e f f i c i e n t i s 0,93, NUMBER OF CONSECUTIVE DAYS 137 T h i s w a t e r f l o w s down the l e n g t h o f t h e p u d d l e , benea.th t h e i c e and s t o p s a t t h i s p o i n t . Summary 1„ There i s a l i n e a r i n c r e a s e o f i c e - d e p t h i n t h e t y r e - t r a c k p u d d l e w i t h an i n c r e a s i n g number o f c o n s e c u t i v e days on whi c h t h e minimum a i r t e m p e r a t u r e i s l e s s t h a n 0°C. 2 0 Only t h e l a s t 9 m o f t h e t y r e - t r a c k p u d d l e have been o b s e r v e d t o f r e e z e l o n g enough t o k i l l t h e animals'. d) I m m i g r a t i o n by o s t r a c o d s from o t h e r p u d d l e s That a r e a o f l a n d w h i c h i n c l u d e s t h e p u d d l e and i t s catchment a r e a has a. c e r t a i n i ndependence because o f t h e f l o w o f t h e wa t e r i n t h a t a r e a . T h i s i s t h e s i m p l e s t e n v i r o n m e n t a l u n i t s i n c e t h e r e c o u l d be such u n i t s w i t h i n t h e same u n i t o c c u p y i n g a l a r g e r a r e a and c o m b i n a t i o n s o f p a r t s o f t h e s e . The wa t e r e n t e r i n g one p u d d l e c o u l d have p a s s e d t h r o u g h a number o f o t h e r s i f t h e y are l o c a t e d i n the catchment a r e a . I t i s p r o b a b l e t h a t t h e number o f i n c l u s i o n s w i t h i n one i n d e p e n d e n t system i s q u i t e s m a l l . From my o b s e r v a t i o n s o f p u d d l e s i n f i e l d s I would guess t h a t t h i s i s c e r t a i n l y l e s s t h a n t e n . * I n t h e J e r i c h o f i e l d , t h e maximum number o f * I n f l a t f o r e s t a r e a s o f P o i n t Grey t h e o b s e r v e d number o f i n c l u s i o n s i s v e r y s m a l l because t h e p o o l s are deep and th e p r e s e n c e o f t r e e r o o t s and u n d e r g r o w t h p r e v e n t s s u r f a c e r u n - o f f from f l o w i n g v e r y f a r . But on f o r e s t s l o p e s t h i s i s p r o b a b l y n o t t r u e . 138 i n c l u s i o n s i s s i x . (The o r d e r o f t h e s e f r o m t h e m o s t i n -d e p e n d e n t t o t h e m o s t i n c l u s i v e i s - SMP1, SMP2, TT, BPTT, RLP, SP - s e e t h e map i n F i g . 36 f o r t h e i r l o c a t i o n ) . B u t t h i s i s n o t t h e o n l y o r d e r i n w h i c h t h e y may be a r r a n g e d , s i n c e , f o r e x a m p l e , t h e r e i s one p o o l ( T P ) whose w a t e r may o c c a s i o n -a l l y r e a c h t h e TT p u d d l e b u t w h i c h d o e s n o t e n t e r SMP1 o r SMP2 . The f l o w o f w a t e r f r o m one p u d d l e t o a n o t h e r c o u l d p r o v i d e t h e o p p o r t u n i t y f o r t h e c a r r i a g e o r e x c h a n g e o f o s t r a c o d s b e t w e e n p o o l s o r a r e a s . A l t h o u g h t h e m a i n i n f l o w t o t h e TT p u d d l e was n o t m o n i t o r e d f o r l o n g p e r i o d s , no l i v e o s t r a c o d s w e r e c a u g h t i n s a m p l e s o f w a t e r e n t e r i n g t h e p u d d l e . D u r i n g J a n u a r y and F e b r u a r y , 1 9 6 8 , 8 s a m p l e s o f w a t e r e a c h 2 000 c c i n v o l u m e w e r e c o l l e c t e d a t t h e p o i n t w h e r e t h e w a t e r f r o m t h e b a s i c c a t c h m e n t a r e a e n t e r s t h e p u d d l e . Some o f t h e s e s a m p l e s w e r e t a k e n d u r i n g p e a k p e r i o d s o f r u n - o f f , d u r i n g o r a f t e r r a i n f a l l . O n l y a s m a l l number o f l i v e h a r p a c t i c o i d s and c y c l o p o i d s w e r e f o u n d i n t h e w a t e r , and one d e a d s p e c i m e n o f a n o t h e r s p e c i e s o f o s t r a c o d . O b s e r v a t i o n s o f C y p r i n o t u s and H e r p e t o c y p r i s a n i m a l s i n t h e TT p u d d l e showed t h a t when t h e y w ere c a u g h t b y a w a t e r c u r r e n t and r o l l e d a l o n g t h e o p e n b o t t o m t h e y i n v a r i a b l y came t o r e s t a g a i n s t a g r a s s s t e m , s t o p p e d and b e g a n t o move a r o u n d a g a i n , o f t e n t o w a r d w h e r e t h e y h a d come f r o m . T h e s e movements seemed t o r e s u l t i n them s t a y i n g i n t h e same g e n e r a l a r e a i n 139 w h i c h t h e y were i n i t i a l l y o b s e r v e d . * These o b s e r v a t i o n s s u g g e s t t h a t t h e a n i m a l s would n o t be r e a d i l y moved by w a t e r f l o w i n g t h r o u g h t h e g r a s s - f i l l e d d r a i n a g e c h a n n e l s . A d r a i n -age c h a n n e l would have t o r e m a i n f i l l e d l o n g enough f o r an a n i m a l t o d i s p e r s e ( p r o v i d e d t h e r e were no b a r r i e r s ) r a t h e r t h a n be t r a n s p o r t e d from one p o o l t o a n o t h e r . T h e r e f o r e , u n l e s s t h e numbers l e a v i n g a p u d d l e are l a r g e and t h e d i s t a n c e s between p u d d l e s s m a l l , i m m i g r a t i o n w i l l be r a r e i f o c c u r r i n g a t a l l . L i t t l e i s known about t h e o c c u r r e n c e o f i m m i g r a t i o n by o t h e r means o f t r a n s p o r t and f rom more d i s t a n t s o u r c e s . On a s i n g l e o c c a s i o n ( F e b r u a r y 1 3 t h , 1969 a t 9.00 a.m.) a. p a i r o f M a l l a r d ducks were seen w a l k i n g over t h e g r a s s near t h e t y r e - t r a c k p u d d l e . These and. o t h e r ducks have been shown t o c a r r y v i a b l e eggs o f a number o f c r u s t a c e a n s i n t h e i r g u t s . The o s t r a c o d s p e c i e s C y p r i d o p s i s v i d u a , C y p r i n o t u s d e n t a t u s , 9." i n c o n q r u e n s , P h y s o c y p r i a . s p . and P o t a m o c y p r i s sp. have been r e c o v e r e d from t h e l a r g e i n t e s t i n e and d r o p p i n g s of m a l l a r d s , g r e e n - w i n g t e a l and g a d w a l l ducks by P'roctor ( 1 9 6 4 ) . T r a n s -p o r t o f t h e o s t r a c o d s upon the o u t s i d e s o f ducks o r o t h e r b i r d s w h i c h d r i n k f rom t h e p u d d l e might a l s o o c c u r . D u r i n g t h e d r y - p e r i o d t h e eggs might be s u s c e p t i b l e t o t r a n s p o r t by w ind c a r r y i n g dead f r a g m e n t s o f g r a s s o r d u s t on which eggs * Some o b s e r v a t i o n s of an extreme example o f t h i s k i n d o f b e h a v i o u r by some C y p r i n o t u s a n i m a l s i n the p u d d l e a l o n g 4 t h Avenue have been o b s e r v e d . Very l a r g e numbers moving up a g a i n s t t h e f l o w o f t h e w a t e r and t h e n b e i n g washed down f o r 1 - 2 m, r e g a i n i n g a f o o t h o l d and s t a r t i n g u pstream a g a i n . 140 had' been l a i d . A- s m a l l ( u n i d e n t i f i e d ) f i e l d mouse l i v e s i n t h e f i e l d and t h e s e a n i m a l s c o u l d t r a n s p o r t o s t r a c o d eggs by removing g r a s s from t h e p u d d l e when i t i s d r y . ( A f t e r t h e f i e l d had been snow-covered f o r a l m o s t s i x weeks i n J a n u a r y -F e b r u a r y , 1969, t h e a c t i v i t i e s o f t h e s e a n i m a l s o f chewing up t h e g r a s s under t h e snow, were v e r y e v i d e n t . ) Summary 1. No o s t r a c o d s were r e c o r d e d from samples o f t h e water f l o w -i n g i n t o t h e t y r e - t r a c k p u d d l e . 2. The chances o f i m m i g r a t i o n by t h i s o r o t h e r means r e m a i n unknown. 141 PART I I I a) A summary of p o p u l a t i o n p r o c e s s e s 1. The eggs p r e s e n t i n the f a l l ' ' d o n ot a l l h a t c h a t t h e same t i m e . They h a t c h i n two g r o u p s , t h e f i r s t soon a f t e r t h e a d d i t i o n o f w a t e r and the second f o r H e r p e t o c y p r i s a f t e r 130 days submergence, and f o r C y p r i n o t u s a f t e r 2 04 d a y s . The r a t e o f r e c r u i t m e n t d u r i n g t h e s e p e r i o d s i s g r e a t e r f o r H e r p e t o c y p r i s t h a n f o r C y p r i n o t u s . 2. The m o r t a l i t y i n each i n t e r v a l o f t i m e i s r e l a t e d o n l y t o t h e numbers o f a n i m a l s p r e s e n t . I f t h e s p e c i e s are a l o n e t h e n i t i s g r e a t e r f o r C y p r i n o t u s t h a n f o r H e r p e t o c y p r i s . When t o g e t h e r t h e e f f e c t o f C y p r i n o t u s upon H e r p e t o c y p r i s i s t h e same as i f i t b e l o n g e d t o t h a t s p e c i e s b u t H e r p e t o c y p r i s has an a d d i t i o n a l e f f e c t upon C y p r i n o t u s . 3. A c o n s t a n t number o f day-degrees i s r e q u i r e d f o r each age-c l a s s t o r e a c h m a t u r i t y . The minimum number f o r C y p r i n o t u s i s 35 68 (°F) and f o r H e r p e t o c y p r i s 775 3 (°F)„ The number r e g u i r e d f o r each a g e - c l a s s i n c r e a s e s as t h e t o t a l i n i t i a l number o f eggs i n c r e a s e s . 4. The e g g - l a y i n g r a t e d e c l i n e s r a p i d l y as t h e t e m p e r a t u r e d e c r e a s e s and/or t h e d e n s i t y i n c r e a s e s . F o r a l l temper-a t u r e s and d e n s i t i e s t h e e g g - l a y i n g r a t e f o r each s p e c i e s i s s i m i l a r . 5. The d e l a y between l a y i n g and h a t c h i n g o f eggs d e c r e a s e s as t h e t e m p e r a t u r e i n c r e a s e s . The d e l a y i s much s h o r t e r f o r 142 H e r p e t o c y p r i s t h a n f o r C y p r i n o t u s eggs. b) A s y n t h e s i s o f p o p u l a t i o n p r o c e s s e s f o r s i m u l a t i o n on a computer G i v e n an i n p u t o f eggs f o r e i t h e r s p e c i e s o f o s t r a c o d a t t h e b e g i n n i n g o f a wet p e r i o d , the o u t p u t o f eggs a t the end o f t h e p e r i o d can be o b t a i n e d by c o m b i n i n g a l l t h o s e p r o c e s s e s w h i c h have been o u t l i n e s p r e v i o u s l y , , Because i t i s n e c e s s a r y t o know the s t a t e o f b o t h the egg and a n i m a l p o p u l a -t i o n s on any day a f t e r the p u d d l e f i l l s , t h e changes i n t h e p o p u l a t i o n s must be computed from day t o day. T h e r e f o r e a computer model* was b u i l t w h i c h p e r f o r m e d t h e s e o p e r a t i o n s and o b t a i n e d t h e f i n a l answer. The sub-models were o r d e r e d i n such a way t h a t once t h r o u g h t h e program r e p r e s e n t e d a day and t h e o p e r a t i o n s p e r f o r m e d depended upon t h e number o f days s i n c e t h e s i m u l a t i o n was s t a r t e d . I n i t i a l l y t h e p r o c e s s e s which ar e o c c u r r i n g a r e few s i n c e t h e r e i s o n l y r e c r u i t m e n t and m o r t a l i t y b u t as t i m e i n c r e a s e s t h e p r o c e s s e s i n c r e a s e i n number and t h e amount o f work wh i c h t h e computer has t o do e s c a l a t e s e n o r m o u s l y . The number o f a n i m a l s o f each s p e c i e s i s k e p t t r a c k o f by a g e - c l a s s i n s e p a r a t e a r r a y s and t h e changes t o each s p e c i e s a r e made by m o d i f y i n g each c l a s s i n t u r n . I t i s n o t n e c e s s a r y t o use a r r a y s f o r t h e i n p u t eggs because * A l t h o u g h a s i n g l e - s p e c i e s model was b u i l t f o r an IBM 113D computer, because o f the l a r g e amount o f s t o r a g e space r e q u i r e d , t h e t w o - s p e c i e s model had t o be r u n on t h e IBM 360 machine. T h i s program was g i v e n t h e name CRUST ( s h o r t f o r ' C r u s t a c e a ' ) and w i l l be r e f e r r e d t o by t h i s t i t l e . 143 t h e number o f them h a t c h i n g i n each i n t e r v a l o f time can be c a l c u l a t e d from e q u a t i o n ( 1 ) , F o r each s p e c i e s t h e number o f mature a g e - c l a s s e s p r e s e n t on each day i s r e c o r d e d and a l s o t h e number o f a n i m a l s i n each a g e - c l a s s which r e a c h m a t u r i t y . The new eggs l a i d by t h e mature a n i m a l s a r e s t o r e d i n s e p a r a t e a r r a y s i n a p o s i t i o n i n t h e a r r a y which denotes t h e t i m e a t w h i c h t h e y w i l l h a t c h , o r b e g i n t o h a t c h . The young o f new eggs, when t h e y appear, a re s t o r e d i n t h e same a r r a y as t h e young o f o l d eggs. The g u a n t i t y o f a n i m a l s o r eggs p r e s e n t d u r i n g any i n t e r v a l o f time can be c a l c u l a t e d by summing o v e r a l l e l e m e n t s i n t h e p a r t i c u l a r a r r a y . A- d i agram o f the sequence o f o p e r a t i o n s ( i n g e n e r a l t e r m s ) w h i c h i s p e r f o r m e d by t h e program i s g i v e n i n F i g , 42, The e n v i r o n m e n t a l i n p u t s f o r the program a r e number o f days a f t e r August 1 s t t h a t t h e u n i t of space had been submerged f o r 5 days (TSTRT), t h e numbers o f days t i l l d r y i n g - u p o c c u r r e d , t h e t i m e s o f o c c u r r e n c e o f any f r e e z e - u p s and t h e mean an n u a l and maximum monthly t e m p e r a t u r e f o r t h e y e a r . Each s p e c i e s b e g i n s as an i n p u t o f eggs and t h e f i n a l v a l u e o b t a i n e d i s t h e number o f eggs l e f t when d r y i n g - u p o c c u r s . T h i s number i s t h e sum o f t h e number o f the i n p u t - e g g s t h a t d i d not h a t c h d u r i n g t h e p e r i o d and t h e number o f new-eggs l a i d d u r i n g t h e p e r i o d t h a t r e m a i n u n h a t c h e d . The program c o n s i s t s o f t h e main program and t h e 17 s u b r o u t i n e s which i t u s e s . The f u n c t i o n o f the main program i s t o o r g a n i z e t h e o p e r a t i o n s o f t h e sub-programs. One sub-program d e a l s w i t h t h e h a t c h i n g o f t h e i n p u t - e g g s o f each s p e c i e s and c a l c u l a t e s t h e number o f F i g u r e 42 A f o r t r a n f l o w - c h a r t o f the o p e r a t i o n s p e r f o r m e d by t h e computer d u r i n g each c i r c u i t ( i . e . 'day') t h r o u g h t h e program. T i s t h e number o f days s i n c e t h e s i m u l a t i o n began and TWET i s t h e number o f days t h a t w i l l be s i m u l a t e d ( i . e . TSTP - TSTRT). The ' f l a g s ' r e f e r r e d t o are i n d e x e s whose s i g n o r v a l u e r e c o r d t h e o c c u r r e n c e and/or t i m e o f o c c u r r e n c e o f e v e n t s d u r i n g t h e s i m u l a t e d s e a s o n . ^ START )^ INPUT OF EGGS. DATA OH TIME OF START, STOP, FREEZE-UPS, TEMPERATURE. SET FLAGS WIPE-OUT ALL NON-EGGS RESET FLAGS NEGATIVE HATCHING OF OLD EGGS YES YES HATCHING OF NEW EGGS-ADDED TO OLD-EGG RECRUITS MORTALITY APPLIED TO IMMATURE ANIMALS YES RECRUITMENT TO THE MATURE POPULATION MORTALITY APPLIED TO MATURE ANIMALS 145 input-eggs l e f t at any time,, Another sub-program c a l c u l a t e s the t o t a l number of animals l e f t at any time, a q u a n t i t y used to determine the m o r t a l i t y . Two sub-programs apply the m o r t a l i t y to the immature animals d i s t r i b u t i n g i t among the age-classes of each s p e c i e s . Two sub-programs deal with the maturing of each age, c a l c u l a t i n g the number of day-degrees t h a t have been accumulated by each c l a s s and then t e s t i n g to see i f t h i s i s enough to reach m a t u r i t y . The m o r t a l i t y of animals a f t e r they become mature i s handled by f i v e sub-programs. The f i r s t of these i s merely an o r g a n i z e r and each of the others r e c o r d the a c q u i s i t i o n of immature age-classes by the mature p o p u l a t i o n , the number i n each c l a s s at m a t u r i t y , the i n t e r v a l i n days between a d d i t i o n s and the decrement of each age during the time i n t e r v a l . For Cyprinotus two sub-programs handle the l a y i n g of new eggs, t h e i r storage t i l l h a t ching and the hat c h i n g i t s e l f . For Herp e t o c y p r i s t h i s i s done by a s i n g l e sub-program t h a t has two p a r t s , e q u i v a l e n t i n f u n c t i o n to the ones f o r the other s p e c i e s , A s i n g l e sub-program deals w i t h the occurrence of a freeze-up and the r e s u l t i n g r e o r g a n i z a t i o n of the remainder of the program. The f i n a l two sub-programs produce the out-put of the r e s u l t s which i s the number of animals which matured, the t o t a l number present when exe c u t i o n terminated, the number of o l d eggs l e f t and the number new eggs accumulated f o r each s p e c i e s , A l i s t i n g of the complete program with d e t a i l e d e x p l a n a t i o n of i t s s t r u c t u r e may be found i n the Appendix. A summary of a l l the constants t h a t go i n t o the 146 model and t h e i r v a l u e s i s g i v e n i n T a b l e XI„ The symbols' u sed f o r t h e p a r a m e t e r s are t h o s e used i n t h e F o r t r a n program. Q u a n t i t i e s which were a s y m p t o t i c t o z e r o were t r u n c a t e d and s e t e q u a l t o z e r o when th e y become l e s s t h a n 10 4„ T h i s i s l e s s t h a n one p e r s q u a r e metre o f p u d d l e s u r f a c e . Summary 1. The computer program s y n t h e s i z i n g a l l t h e p r o c e s s e s w h i c h have been found t o a f f e c t t h e number o f eggs produc e d d u r i n g a w e t - p e r i o d i s d e s c r i b e d . 2. The o p e r a t i o n s p e r f o r m e d by the computer depend upon t h e day d u r i n g the w e t - p e r i o d w h i c h i s b e i n g s i m u l a t e d . A g e n e r a l f l o w - c h a r t f o r any day i s p r e s e n t e d . c ) T e s t o f t h e a b i l i t y o f t h e s y n t h e s i z e d model t o p r e d i c t the number o f eggs i n t h e p u d d l e a t t h e time o f d r y i n q - u p . F o r t h e w i n t e r o f 1967-68 t h e i n p u t o f C y p r i n o t u s eggs a t s e l e c t e d p o i n t s i n t h e pu d d l e was known. A l s o t h e t i m e s a t which t h e s e p o i n t s were submerged and d r i e d - u p were known so t h e s y n t h e s i z e d model c o u l d be t e s t e d by comparing t h e o b s e r v e d o u t p u t (measured i n t h e f o l l o w i n g w i n t e r ) and t h e e x p e c t e d o u t p u t o f eggs g i v e n by t h e model. The same i n p u t s were known f o r H e r p e t o c y p r i s but t h e o u t p u t was not measured and so t h e model c a n n o t be t e s t e d f o r t h i s s p e c i e s . However t h e e f f e c t o f H e r p e t o c y p r i s upon C y p r i n o t u s can be t e s t e d . TABLE X I A summary of t h e v a l u e s o f t h e c o n s t a n t s o b t a i n e d from t h e e x p e r i m e n t a l work, which a r e used i n t h e F o r t r a n program, CRUST, Symbol Meaning V a l u e B The r a t e o f i n c r e a s e o f t h e m o r t a l i t y o f C y p r i n o t u s immatures p e r t h e s q u a r e o f t h e t o t a l numbers p r e s e n t 0,001812 BH The same as B but f o r H e r p e t o c y p r i s 0,001319 CC The y - i n t e r c e p t f o r the egg-l a y i n g r a t e o f H e r p e t o c y p r i s 0.05 CCPT The y - i n t e r c e p t f o r t h e l i n e a r t r a n s f o r m e d d e c r e a s e i n t h e p r o p o r t i o n o f a mature C y p r i n o t u s a q e - c l a s s a l i v e a f t e r m a t u r i t y . 4,5 74 CDYDG The minimum number o f day-degrees (°F) w h i c h C y p r i n o t u s must a c c u m u l a t e 3568.0 CEPTI The h a t c h i n g - d e l a y ( i n days) o f C y p r i n o t u s h a t c h - 1 new-eggs when t h e t e m p e r a t u r e i s 0.0°C. 627.0 CEPT2 The same as CEPTI bu t f o r C y p r i n o t u s h a t c h - 2 new-eggs 1159.8 CPT The h a t c h i n g - d e l a y ( i n days) o f H e r p e t o c y p r i s eggs, when th e t e m p e r a t u r e .is 0,0°C, 105.4 CSLP The r a t e o f d e c r e a s e of t h e t r a n s f o r m e d p r o p o r t i o n o f mature C y p r i n o t u s a l i v e as a f u n c t i o n o f time ( i n days) a f t e r m a t u r i t y 0.05 148 TABLE X I cont„ Symbol Meaning V a l u e The r a t e o f d e c r e a s e o f t h e t r a n s -CSLP formed p r o p o r t i o n o f mature C y p r i n o t u s a l i v e as a f u n c t i o n o f t i m e ( i n days) a f t e r m a t u r i t y Oo 05 The r a t e o f i n c r e a s e o f t h e D m o r t a l i t y o f C y p r i n o t u s immatures 0„ 0204 pe r t h e t o t a l number o f o s t r a c o d s p r e s e n t DH Same as D b u t f o r H e r p e t o c y p r i s 0„ 0204 The r a t e o f d e c r e a s e o f t h e m o r t a l i t y DISTR r a t e i n any i n t e r v a l o f ti m e as t h e age o f t h e a n i m a l s p r e s e n t i n c r e a s e s Oo 0115 The r a t e o f i n c r e a s e p e r i n p u t - e g g DNS IT o f t h e number o f day-degrees r e q u i r e d t o r e a c h m a t u r i t y 341 o 7 EMX The y - i n t e r c e p t f o r t h e e g g - l a y i n g r a t e o f C y p r i n o t u s Oo 071 The r a t e o f i n c r e a s e o f t h e m o r t a l i t y F o f C y p r i n o t u s immatures i n t h e p r e s e n c e o f H e r p e t o c y p r i s p e r t h e cube o f t h e t o t a l numbers p r e s e n t Oo 00021 G The same as D b u t f o r C y p r i n o t u s w i t h H e r p e t o c y p r i s Oo 0204 H The same as B b u t f o r C y p r i n o t u s i n t h e p r e s e n c e o f H e r p e t o c y p r i s Oo 0042 HCPT The same as CCPT b u t f o r H e r p e t o c y p r i s 4„ 153 HDYDG The same as CDYDG b u t f o r H e r p e t o c y p r i s 775 3 o 0 149 TABLE X I c o n t . Symbol Meaning V a l u e HDL The d e l a y ( i n days) a f t e r the a d d i t i o n o f water t h a t o l d eggs b e g i n t o h a t c h 6 7 ( C y p r l n . ) (Herpo ) HSEH The ti m e o f i n i t i a t i o n o f t h e s e c o n d - h a t c h o f o l d s t o r e d eggs o f H e r p e t o c y p r i s i n days a f t e r f i l l i n g o f t h e p u d d l e 130.0 HSLP The same as CSLP but f o r H e r p e t o c y p r i s mature a n i m a l s 0.0386 HUMAX The maximum i n c r e a s e i n number o f day-degrees r e q u i r e d t o r e a c h m a t u r i t y 10 -INPUT P The p r o p o r t i o n o f n e w l y - l a i d C y p r i n o t u s eggs t h a t w i l l h a t c h i n the f i r s t group 0.202 PCI The p r o p o r t i o n o f o l d s t o r e d C y p r i n o t u s eggs which h a t c h i n the f i r s t group 0.621 PC2 The p r o p o r t i o n o f o l d s t o r e d C y p r i n o t u s eggs which h a t c h i n t h e second group 0. 379 PHI The same as PCI but f o r H e r p e t o c y p r i s 0.929 PH2 The same as PC2 b u t f o r H e r p e t o c y p r i s 0.071 Q The p r o p o r t i o n o f n e w l y - l a i d C y p r i n o t u s eggs a p p e a r i n g i n t h e second group 0.7985 R The i n s t a n t a n e o u s r a t e o f change o f th e h a t c h i n g r a t e o f t h e f i r s t group o f C y p r i n o t u s o l d eggs as a f u n c t i o n o f t i m e a f t e r HDL 0.0 3 32 RH The same as R b u t f o r H e r p e t o c y p r i s 0.0549 150 TABLE X I c o n t . S'ymbo 1 Meaning V a l u e RHR The i n s t a n t a n e o u s r a t e o f change o f the h a t c h i n g r a t e o f n e w l y - l a i d C y p r i n o t u s eggs o f b o t h t h e f i r s t and second groups O o 0473 RHXP The r a t e o f d e c r e a s e o f t h e egg-l a y i n g r a t e o f H e r p e t o c y p r i s p e r mature a n i m a l p r e s e n t O o 360 RNXP The same as RHXP b u t f o r C y p r i n o t u s O o 1902 RT The i n s t a n t a n e o u s r a t e o f change o f t h e h a t c h i n g r a t e o f t h e second group o f C y p r i n o t u s o l d eggs as a f u n c t i o n o f t i m e a f t e r SEH 0„ 0338 SEH The number o f days a f t e r f i l l i n g t h a t t h e second group o f o l d C y p r i n o t u s eggs b e g i n t o h a t c h 204 SLP1 The i n s t a n t a n e o u s r a t e o f d e c r e a s e o f t h e h a t c h i n g d e l a y (days) o f C y p r i n o t u s h a t c h - 1 eggs p e r °C 0 0„ 15.8 7 SLP2 The same as SLP1 b u t f o r t h e ha t c h - 2 O o 111 TEXP The r a t e o f i n c r e a s e o f - t h e e g g - l a y i n g r a t e f o r H e r p e t o c y p r i s p e r °C O o 1308 TSLP' The r a t e o f d e c r e a s e o f t h e h a t c h i n g d e l a y ( i n days) o f n e w l y - l a i d H e r p e t o c y p r i s eggs p e r C 5 o 45 TXP The same as TEXP b u t f o r C y p r i n o t u s egg l a y i n g O o 1377 WIDTH The mean w i d t h ( i n cm) o f t h e t y r e -t r a c k p u d d l e 3 4 o 2 7 151 A. summary o f the v a l u e s o f the i n p u t v a r i a b l e s i s shown i n T a b l e I I I . The t i m e s a t which the p u d d l e d r i e d - u p and t h e e g g - i n p u t f o r each s p e c i e s were d i f f e r e n t f o r each p a r t of t h e p u d d l e . The e f f e c t o f each s p e c i e s on t h e o t h e r o f i n c r e a s i n g t h e number o f day-degrees r e q u i r e d t o r e a c h m a t u r i t y was r e s t r i c t e d i n t h e model. The e f f e c t had been o b s e r v e d i n the e x p e r i m e n t s (see F i g , 14) t o be l i n e a r up t o 2 an i n p u t d e n s i t y o f 5 a n i m a l s p e r cm and p o p u l a t i o n s o f 2 C y p r i n o t u s whose i n i t i a l numbers were 10 p e r cm had n o t r e a c h e d m a t u r a t i o n when the e x p e r i m e n t was a c c i d e n t a l l y t e r m i n a t e d . None had r e a c h e d t h e mature s i z e . The e f f e c t i s 2 t h e r e f o r e assumed t o be l i n e a r up t o an .input o f 10 per cm and t h e r e a f t e r c o n s t a n t . The a l t e r n a t i v e o f assuming t h e r e l a t i o n s h i p t o be l i n e a r o v e r a l l e g g - d e n s i t i e s beyond t h e o b s e r v e d range q u i c k l y l e a d s t o t h e c o n c l u s i o n t h a t a l t h o u g h t h e r e a r e many a n i m a l s p r e s e n t t h e y s h o u l d never be a b l e t o l a y eggs and t h i s i s u n s a t i s f a c t o r y because i t seems l i k e l y t h a t t h e r e w i l l be some l i m i t upon t h e l e n g t h o f t i m e t h a t t h e a n i m a l s can w a i t t o r e a c h m a t u r i t y . The e x p e c t e d and t h e o b s e r v e d o u t p u t s o f C y p r i n o t u s eggs are shown i n F i g , 43, The agreement between the e x p e c t e d and t h e o b s e r v e d numbers o f eggs i s v e r y good. I n most c a s e s t h e e x p e c t e d i s a t l e a s t w i t h i n the range o f t h e o b s e r v e d and. o f t e n c l o s e t o t h e mean o b s e r v e d v a l u e . I n the s o u t h end o f t h e p u d d l e where b o t h s p e c i e s are p r e s e n t t h e r e s u l t s a r e v e r y c l o s e , b u t toward t h e o t h e r end where o n l y C y p r i n o t u s i s p r e s e n t t h e model seems t o o v e r - e s t i m a t e t h e numbers o f eggs. I n t h e l a s t 5 m o f t h e p u d d l e t h e r e i s a t h i r d s p e c i e s o f o s t r a c o d p r e s e n t , 152 TABLE X I I I n p u t d a t a f o r t h e CRUST-program used t o t e s t t h e a b i l i t y o f t h e s y n t h e s i z e d model t o p r e d i c t the numbers o f C y p r i n o t u s eggs a t v a r i o u s p o i n t s a l o n g t h e l e n g t h o f t h e t y r e - t r a c k p u d d l e . D i s t a n c e S l t a r t Stop L e n g t h o f Number o f Number o f from s o u t h t i m e * t i m e * p e r i o d C y p r i n o t u s H e r p e t o c y p r i s end (m) (days) eggs** eggs** 10, 7 71 317 246 7,07 9,41 12,5 71 291 220 16,50 2,75 15, 7 71 291 2Z0 18,45 -18,6 71 289 218 46,74 3.14 20,4 71 289 218 51,06 2,35 22,2 71 288 218 63,63 3,92 24,0 71 288 217 6,68 -26,9 71 287 217 2,75 -27, 7 71 287 217 13,35 -Measured as t h e number o f days a f t e r August 1 s t , : Number o f eggs 2 p e r cm , F i g u r e 4 3 The o b s e r v e d and e x p e c t e d o u t p u t o f eggs i n the t y r e - t r a c k p u d d l e f o r t h e w i n t e r o f 1967-68. The v a l u e s o f numbers o f eggs/cm 2 are p l o t t e d f o r p o i n t s measured i n metres from t h e s o u t h end o f t h e p u d d l e . The range o f the o b s e r v e d v a l u e s ( c l o s e d c i r c l e s ) , and t h e e x p e c t e d v a l u e ( c r o s s e s ) a r e g i v e n . N U M B E R S O F E G G S P E R C M 2 - j L t O G O A O I O - v l C D C O o o o o o o o o o ~l S 1 . 9 « — i ' I T 154 (C y p r i c e r c u s r e t i c u l a t u s ) , which i s known to have the e f f e c t of i n c r e a s i n g the m o r t a l i t y r a t e of Cyprinotus and so may p a r t i a l l y e x p l a i n t h i s o v e r - e s t i m a t i o n , (The i n f o r m a t i o n obtained from an i n v e s t i g a t i o n of t h i s species was i n s u f f i c i e n t to i n c l u d e i t i n the model). In the r e g i o n of the puddle where both species were present Cyprinotus always managed to produce some eggs before the puddle dried-up. Summary 1 , The synt h e s i z e d model has been t e s t e d f o r the p o p u l a t i o n of Cyprinotus l i v i n g i n the t y r e - t r a c k puddle. The p r e d i c t e d 2 numbers of eggs per cm present i n the s o i l when the puddle d r i e d up were very c l o s e to the observed numbers f o r a l l p o i n t s w i t h i n the puddle which were t e s t e d . At some p o i n t s t h e r e was a simultaneous i n p u t of Her p e t o c y p r i s eggs, d) E x p l o r a t i o n of the conseguences of changes i n d e n s i t y of each s p e c i e s . The r e l a t i o n s h i p between the output of eggs i n the s p r i n g and the i n p u t of eggs i n the f a l l when the temperature and l e n g t h of wet p e r i o d are held constant has been obtained f o r each species u s i n g the CRUST-model, The r e l a t i o n s h i p has been obtained f o r each species by i t s e l f and then f o r each species i n the presence of the other whose i n p u t numbers are v a r i e d . From t h i s a n a l y s i s i t should be p o s s i b l e to reach a t h e o r e t i c a l c o n c l u s i o n about the p o s s i b i l i t y of e x c l u s i o n ; one or other or both species ending the wet p e r i o d without any eggs 155 as a r e s u l t o f t h e p r e s e n c e o f t h e o t h e r s p e c i e s . S i n c e t h e shape o f t h i s r e l a t i o n s h i p changes a l o n g t h e l e n g t h o f t h e p u d d l e t h e i n p u t v a l u e s f o r s i n g l e p o i n t s i n space were u s e d . F o r each s p e c i e s d i f f e r e n t p o i n t s i n space were s e l e c t e d b ecause H e r p e t o c y p r i s c a n n o t produce any eggs a t many o f t h e p o i n t s t h a t C y p r i n o t u s c a n . The temperaturesuiased were mean a n n u a l t e m p e r a t u r e s f o r t h e y e a r s 1961-69 and th e mean maximum mon t h l y t e m p e r a t u r e f o r t h e same p e r i o d ( T a b l e X I I I ) . U s i n g t h e w a t e r - l e v e l f l u c t u a t i o n model d e v e l o p e d p r e v i o u s l y , t h e w a t e r - l e v e l s i n t h e pu d d l e d u r i n g t h e f a l l and s p r i n g f o r t h e y e a r s 1961-69 were s i m u l a t e d . The d a t e s were t h e n o b t a i n e d f r om t h e s i m u l a t e d p u d d l e , on which t h e p a r t i c u l a r p o i n t s i n space had been submerged and d r i e d - u p f o r t h e r e q u i r e d p e r i o d s . These v a l u e s a r e shown i n T a b l e X I I I . The p o i n t s i n t h e p u d d l e w h i c h were used were 22.0 m from t h e s o u t h end (which i s j u s t beyond t h e a r e a i n which f r e e z i n g m ight o c c u r ) , f o r C y p r i n o t u s and 5.0 m f o r H e r p e t o c y p r i s . F o r any a g e - c l a s s (a) o f C y p r i n o t u s , t h e q u a n t i t y o f ' t e m p e r a t u r e - t i m e ' under t h e c o n s t a n t c o n d i t i o n s i s g i v e n by TT = V (63. 37 - 49.55 )• cos (--^-J---) + 49.55 d t a \ j _ Q c 365 85 + a and f o r any a g e - c l a s s (a) o f H e r p e t o c y p r i s , TT = ( (63. 37 - 49.55 )-cos ( ~ ^ ~ — - ) + 49.55 dt. a Jt = 61+a As t h e number o f i n p u t eggs o f C y p r i n o t u s i n c r e a s e s so does t h e t o t a l o u t p u t number o f eggs, F i g . 44A. The 156 TABLE X I I I C o n t a i n i n g t h e a n n u a l mean (TBAR) and maximum monthly mean (TMAX) a i r t e m p e r a t u r e (°F) f o r t h e y e a r s 1961-69, measured a t t h e UBC M e t e r o l o g i c a l S t a t i o n ; t h e t i m e s o f f i l l i n g (F) and d r y i n g - u p (D) o f t h e t y r e - t r a c k p u d d l e a t t h e p o i n t s 5o0, 12oO and 22 o0 m from t h e s o u t h end f o r t h e y e a r s 1961-69; and. t h e mean v a l u e s f o r t h e a n n u a l mean and maximum monthly mean t e m p e r a t u r e , and t h e t i m e s o f f i l l i n g and d r y i n g f o r each p o i n t d u r i n g t h e s e y e a r s . 5,0 12, 0 22. 0 YEAR TBAR TMAX p * D* p * D* p * D* 1961-62 49.42 66.0 38 361 39 346 73 309 1962-63 50,33 61.-0 79 305 79 299 111 296 1963-64 50,33 64.0 87 343 88 337 88 334 1964-65 48,17 64.0 54 313 57 297 102 304 1965-66 49,33 62 .0 82 365 84 365 95 299 1966-67 49,33 62.0 50 327* * 50 310**' 87 287* * 1967-68 50.88 66.3 71** 344** 40** 317* * 7 ]_ * * 319** 1968-69 48,5 7 61,65 28* * 318** 51** 304* * 51** 288** Means 49.55 63,37 61.0 335 61 322 85 305 Measured as t h e number o f days a f t e r August 1st t h a t t h e e v e n t o c c u r r e d , F - f i l l i n g , D - d r y i n g . Observed v a l u e s . F i g u r e 44 The o u t p u t o f eggs i n t h e s p r i n g f o r b o t h s p e c i e s o f o s t r a c o d , as a f u n c t i o n o f t h e i n p u t o f eggs i n the f a l l , when t h e s p e c i e s a re a l o n e and t h e c o n d i t i o n s r e m a i n c o n s t a n t . F i g , 44A - the o u t p u t o f C y p r i n o t u s eggs p e r cm-' as a f u n c t i o n o f t h e i n p u t number a t t h e p o i n t 22,0 m from t h e s o u t h end o f t h e p u d d l e when t h e s t a r t i n g - t i m e (85 days a f t e r August 1 s t ) and s t o p p i n g - t i m e < (305 days) and t e m p e r a t u r e p a r a m e t e r s (TBAR = 49.6 and TMAX = 63„4°F) a r e c o n s t a n t . The s t r a i g h t l i n e i n each graph i s t h e l i n e a l o n g which t h e o u t p u t e q u a l s t h e i n p u t . F i g , 44B - t h e same r e l a t i o n s h i p f o r H e r p e t o c y p r i s w i t h t h e same t e m p e r a t u r e v a l u e s as above b u t f o r t h e p o i n t 5,0 m from the s o u t h end o f t h e p u d d l e . T h e r e f o r e t h e t i m e s o f s t a r t i n g and s t o p p i n g a re d i f f e r e n t (61 days and 335 d a y s ) . >0 20 30 <0 50 CO 70 60 SO I N P U T N U M B E R O F E G G S P E R C M ? 158 d e r i v a t i v e i s g r e a t e s t when t h e i n p u t i s v e r y s m a l l and as t h i s i n c r e a s e s t h e d e r i v a t i v e d e c r e a s e s . But I n s t e a d o f the d e r i v a -t i v e becoming n e g a t i v e i t becomes c o n s t a n t a t about 0.10, The number o f i n p u t eggs wh i c h e x a c t l y r e p l a c e t h e m s e l v e s a t t h i s p o i n t i n t h e p u d d l e i s a p p r o x i m a t e l y 54, o f which 43 s h o u l d be new eggs and t h e r e m a i n d e r l e f t o v e r from t h e i n p u t . As the i n p u t I n c r e a s e s t h e l e f t - o v e r eggs a l s o i n c r e a s e and even a l t h o u g h t h e number o f new eggs s t o r e d c o n t i n u e s t o d e c l i n e t h e s l o p e o f t h e t o t a l o u t p u t remains p o s i t i v e . An i m p o r t a n t consequence o f t h i s a n a l y s i s i s t h e u n i m p o r t a n c e o f t h e e f f e c t o f t he s i z e o f t h e i n p u t o f eggs upon the r e s u l t a n t o u t p u t . T h i s i s because the e x t r a t i m e r e q u i r e d t o mature was o f l i t t l e use f o r e g g - l a y i n g anyway because t h e t e m p e r a t u r e was s t i l l q u i t e low. The a n i m a l s more t h a n make up f o r t h e l o s s o f time by l a y i n g t h e i r eggs a t h i g h e r t e m p e r a t u r e s . But t h i s un-i m p o r t a n c e need not be t r u e f o r o t h e r p o i n t s i n t h e p u d d l e , e s p e c i a l l y t h o s e w h i c h f i l l - u p l a t e r and dry-up e a r l i e r t h a n t h i s p a r t i c u l a r p o i n t . The main r e a s o n f o r t h e d e c l i n e i n t h e number o f new eggs s t o r e d by C y p r i n o t u s i s t h e g r e a t e r number o f a n i m a l s t r y i n g t o . l a y eggs a t t h e same t i m e . Even a l t h o u g h H e r p e t o c y p r i s had a v a i l a b l e a much l o n g e r t i m e i n wh i c h t o mature a n d . l a y eggs t h e r e s u l t s o f i t s e f f o r t s a re meagre i n d e e d . T h i s i s m a i n l y because a much l a r g e r p o r t i o n o f t h e t i m e was needed t o mature, l e a v i n g l e s s t i m e t o l a y eggs. But t h e number o f eggs l a i d by t h e o s t r a c o d s was much g r e a t e r than i s shown i n F i g . 44B. Many o f t h e eggs h a t c h e d because t h e y were l a i d a t a t i m e when the h a t c h i n g 159 d e l a y was s h o r t and so were l o s t . The e q u i l i b r i u m i n p u t f o r H e r p e t o c y p r i s i s a p p r o x i m a t e l y 11 eggs and as the i n p u t i n c r e a s e s t h e o u t p u t tends t o z e r o because t h e r e a r e no o l d eggs l e f t and because o f t h e d e n s i t y dependent e f f e c t on t h e e g g - l a y i n g r a t e o f t h e numbers wh i c h r e a c h m a t u r i t y . The e f f e c t s o f the p r e s e n c e o f each s p e c i e s upon t h e o t h e r has been i n v e s t i g a t e d f o r a p o i n t 12.0 m from t h e s o u t h end o f t h e p u d d l e , a l m o s t mid-way between the p r e v i o u s two p o i n t s . The mean t i m e s o f f i l l i n g and d r y i n g - u p a re shown i n T a b l e X I I I and t h e amount o f t e m p e r a t u r e - t i m e f o r an age-c l a s s (a) o f e i t h e r s p e c i e s i s g i v e n by TT = C (63.37 - 49.55 ) cos ( — ^ ) + 49.55 d t a L n 365 >Jt = 61 + a U s i n g s e v e r a l l e v e l s o f i n p u t o f H e r p e t o c y p r i s eggs w i t h a range o f d e n s i t i e s o f C y p r i n o t u s eggs the e f f e c t o f each s p e c i e s upon t h e o t h e r ' s o u t p u t o f eggs i n t h e s p r i n g , under c o n s t a n t c o n d i t i o n s , was d e t e r m i n e d . T h i s i s shown i n F i g . 45.- As t h e i n p u t o f t h e o t h e r s p e c i e s i s i n c r e a s e d the shape o f t h e o u t -p u t / i n p u t r e l a t i o n s h i p f o r each s p e c i e s by i t s e l f i s m o d i f i e d so as t o d e c r e a s e t h e o u t p u t . I n i t i a l l y f o r b o t h s p e c i e s t h e o u t p u t i s g r e a t e r t h a n t h e i n p u t . The maximum o u t p u t f o r C y p r i n o t u s i s a p p a r e n t l y l i m i t l e s s though f o r l a r g e i n p u t s t h e o u t p u t w i l l always be l e s s t h a n t h e i n p u t w h i c h produced i t . On t h e o t h e r hand t h e o u t p u t o f H e r p e t o c y p r i s r e a c h e s a 2 maximum o f 15.0 eggs/cm and i f l a r g e i n p u t s o f eggs are used t h e o u t p u t becomes v e r y s m a l l . The r e a s o n f o r t h i s d i f f e r e n c e F i g u r e 45 The e f f e c t o f a range o f s i m u l t a n e o u s i n p u t numbers o f eggs o f t h e o t h e r s p e c i e s upon the o u t p u t o f eggs p e r cm^ a t 12.0 m from t h e s o u t h end o f each s p e c i e s o The s t a r t i n g t i m e (61 days) and s t o p p i n g t i m e (322 days) and t h e t e m p e r a t u r e v a l u e s remained c o n s t a n t (49.6 and 63.4°F). F i g . 45A - t h e o u t p u t o f H e r p e t o c y p r i s eggs f o r each i n p u t a t a range o f i n p u t s o f C y p r i n o t u s eggs ( C ) . F i g , 45B - t h e o u t p u t of C y p r i n o t u s eggs f o r each i n p u t a t a range o f i n p u t s o f H e r p e t o c y p r i s eggs (H)„ OUTPUT NUMBER OF EGGS (per cm 2) 161 I s t h e r e t e n t i o n o f a s i z e a b l e p r o p o r t i o n o f t h e i n p u t eggs by C y p r i n o t u s so t h a t w h i l e t h e number o f new eggs l a i d may be v e r y s m a l l t h e number o f o l d eggs l e f t i n c r e a s e s as t h e i n p u t i n c r e a s e s . I f the i n p u t o f H e r p e t o c y p r i s eggs i s g r e a t e r t h a n 2 about 6 0 0 p e r cm the n o u t p u t o f C y p r i n o t u s eggs i s l e s s t h a n any i n p u t . I n one t i m e - p e r i o d ( w i n t e r ) as r e p r e s e n t e d i n F i g . 45 t h e e x t i n c t i o n o f e i t h e r s p e c i e s can r e s u l t i f t h e i n p u t o f t h e o t h e r s p e c i e s i s made l a r g e . However, t h e i n p u t s n e c e s s a r y t o produce t h i s r e s u l t a r e e n o r m o u s , r e l a t i v e t o n a t u r e . E x t i n c t i o n o f one s p e c i e s can o c c u r under t h e s e c o n s t a n t c o n d i t i o n s i n more t h a n one t i m e - p e r i o d . The number o f t i m e - p e r i o d s and whi c h o f t h e s p e c i e s becomes e x t i n c t depends upon t h e i n i t i a l r e l a t i v e d e n s i t i e s o f eggs. P l a y i n g the game of ' b l i n d mans b l u f f ' ( H o l l i n g and Ewing 1969) a wide range o f r e l a t i v e d e n s i t i e s were chosen and the consequences o f each c o m b i n a t i o n were o b t a i n e d where t h e o u t p u t s f o r each s p e c i e s f o r each t i m e - p e r i o d become t h e i n p u t s t o t h e n e x t t i m e - p e r i o d . These consequences a r e shown i n F i g . 46 which i s a phase-d i a g r a m i n which t h e s u c c e s s i v e c o m b i n a t i o n s o f d e n s i t i e s o f each s p e c i e s a t the ti m e t h a t the u n i t o f space was d e s i c c a t e d a r e p l o t t e d and c o n n e c t e d by a s t r a i g h t - l i n e . T h i s i s t h e same as a s t o c k - r e c r u i t r e l a t i o n s h i p ( R i c k e r 1954) i n which t h e ' r e c r u i t s ' f o r each s p e c i e s at s u c c e s s i v e t i m e s a re t h e c o o r d i n a t e s o f each p o i n t . When l a r g e i n i t i a l d e n s i t i e s o f e i t h e r s p e c i e s a re chosen t h e s t r o n g d e n s i t y - d e p e n d e n t e f f e c t s r e s u l t i n b o t h s p e c i e s h a v i n g v e r y s m a l l i n p u t numbers f o r t h e n e x t p e r i o d . F i g u r e 46 A p h a s e - d i a g r a m showing t h e consequences o f s t a r t i n g w i t h d i f f e r e n t r e l a t i v e numbers o f eggs p e r cm 2 ( c r o s s e s ) f o r each s p e c i e s . The o u t p u t number o f eggs p e r cm 2 f o r each s p e c i e s a t 5.0 m from the s o u t h end o f t h e p u d d l e a t t h e end of each season I n s u c c e s s i v e y e a r s have been p l o t t e d and t h e sequence o f p o i n t s j o i n e d by s t r a i g h t - l i n e s . F o r c l a r i t y o n l y a s i n g l e l i n e i s shown i n t h e r e g i o n o f t h e d i a g r a m where t h e s u c c e s s i v e v a l u e s t e n d t o y = 14, x = 0. The dashed l i n e s e p a r a t e s i n i t i a l c o n c e n t r a t i o n s which have d i f f e r e n t outcomes. P o i n t s above t h e l i n e l e a d t o t h e e x c l u s i o n o f C y p r i n o t u s and t h o s e below t h e l i n e l e a d t o an e q u i l i b r i u m i n w h i c h C y p r i n o t u s i s t h e dominant s p e c i e s but H e r p e t o c y p r i s manages t o p e r s i s t . (Note: t h e s e a r e r e s u l t s f o r c o n s t a n t e n v i r o n m e n t a l c o n d i t i o n s . ) 163 These l i n e s go d i r e c t l y t o the v i c i n i t y o f t h e o r i g i n and t h e y bounce back out i n one o r o t h e r d i r e c t i o n . There a r e t h r e e k i n d s o f outcome t h a t can r e s u l t , o n l y one o f which i s t h e e x t i n c t i o n o f one s p e c i e s . I f t h e d e n s i t y o f eggs o f H e r p e t o c y p r i s i s g r e a t e r t h a n 1/7 - 1/8 o f t h e d e n s i t y o f C y p r i n o t u s eggs th e H e r p e t o c y p r i s w i l l e x c l u d e C y p r i n o t u s and w i l l t e n d towards i t s e q u i l i b r i u m egg d e n s i t y o f 13 - 14 eggs/ 2 cm . I f t h e d e n s i t y o f C y p r i n o t u s eggs i s g r e a t e r t h a n 7 -8 t i m e s t h a t o f H e r p e t o c y p r i s t h e n C y p r i n o t u s w i l l become t h e more numerous s p e c i e s b u t a p p a r e n t l y i t c annot r e s u l t i n t h e e x t i n c t i o n o f H e r p e t o c y p r i s . C y p r i n o t u s t e n d s t o i t s 2 e q u i l i b r i u m egg d e n s i t y o f 46 p e r cm b u t a t t h i s d e n s i t y H e r p e t o c y p r i s can s t i l l p roduce a s m a l l number o f eggs 2 ( a p p r o x i m a t e l y 0.3 - 0.4 p e r cm ). T h i s c o m b i n a t i o n i s a s t a b l e p o i n t and once t h e s p e c i e s have a r r i v e d a t i t t h e y c a n n o t change t h e i r r e l a t i v e numbers. The t h i r d p o s s i b l e outcome i s t h a t t h e c o o r d i n a t e s o f t h e p o i n t i n F i g . 46 s h o u l d p l a c e i t on t h e d o t t e d l i n e d i v i d i n g t h e two a r e a s o f d i f f e r e n t outcome. A p p a r e n t l y once t h e y a r r i v e a t t h i s p o i n t t h e r e l a t i v e numbers c a n n o t change because any p o i n t on t h i s l i n e i s an. e q u i l i b r i u m . F u r t h e r m o r e t h e r e i s a p p a r e n t l y no r e s t r i c t i o n upon the p o i n t a t w h i c h t h i s e q u i l i b r i u m might be s e t up. They a r e any p o i n t s a t w h i c h t h e e q u i l i b r i u m numbers o f C y p r i n o t u s eggs are 7 - 8 t i m e s g r e a t e r t h a n t h o s e o f H e r p e t o c y p r i s . T h i s i s a s i g n i f i c a n t r e s u l t because i t s u g g e s t s t h a t a p o p u l a t i o n o f t h e s e s p e c i e s , a t t h i s p o i n t i n t h e p u d d l e , might p e r m a n e n t l y r e f l e c t t h e i r r e l a t i v e c o n c e n t r a -t i o n s when the p o p u l a t i o n s began some time i n the p a s t . I t 164 I s n o t known whether t h i s i s t r u e f o r o t h e r p a r t s o f the puddle„ When the l e n g t h o f t h e w e t - p e r i o d , t e m p e r a t u r e and p r o p e r t i e s o f the s p e c i e s a r e h e l d c o n s t a n t the e x t i n c t i o n o f o n l y one s p e c i e s ( C y p r i n o t u s ) can r e s u l t , even a l t h o u g h t h i s i s t h e s p e c i e s w h i c h i s t h e most c o n s e r v a t i v e i n t h a t i t c o n t i n u a l l y h o l d s t h e g r e a t e s t p r o p o r t i o n o f i t s eggs i n s t o r e . I t now r e m a i n s t o f i n d o ut whether t h i s e x c l u s i o n can o c c u r i n t h e p u d d l e when the p o p u l a t i o n i s s i m u l a t e d from y e a r t o y e a r and t h e c o n d i t i o n s change. Summary 1. The r e l a t i o n s h i p between t h e o u t p u t and i n p u t o f eggs f o r a wet p e r i o d o f . c o n s t a n t l e n g t h and t e m p e r a t u r e i s g i v e n f o r each s p e c i e s . F o r s m a l l numbers o f eggs th e o u t p u t i s g r e a t e r t h a n t h e i n p u t but as t h e l a t t e r i n c r e a s e s the two become e q u a l and w i t h f u r t h e r i n c r e a s e t h e o u t p u t i s t h e s m a l l e r . The e q u i l i b r i u m e g g - d e n s i t i e s f o r t h e s e t o f 2 c o n s t a n t c o n d i t i o n s are 54 p e r cm f o r C y p r i n o t u s ( a t 22„0 m 2 from t h e s o u t h end o f t h e puddle)" and 11 p e r cm f o r H e r p e t o c y p r i s ( a t 5.0 m from t h e s o u t h e n d ) . 2, Under c o n s t a n t c o n d i t i o n s c o m p e t i t i v e e x c l u s i o n can o c c u r . The outcome depends upon t h e r e l a t i v e i n i t i a l d e n s i t i e s b u t f o r most s t a r t i n g v a l u e s H e r p e t o c y p r i s i s t h e o n l y r e m a i n i n g s p e c i e s a f t e r 5 o r 6 w e t - p e r i o d s . C y p r i n o t u s c annot cause t h e e x t i n c t i o n o f t h e o t h e r s p e c i e s but f o r i n i t i a l v a l u e s where C y p r i n o t u s i s 7 - 8 t i m e s more abundant t h a n H e r p e t o c y p i t c a n b e c o m e t h e dominant s p e c i e s . 165 e) S i m u l a t i o n o f t h e p o p u l a t i o n i n t h e p u d d l e f o r the y e a r s 1961-69, and c o n c l u s i o n The f i n a l s t e p , f o r which g r a d u a l p r e p a r a t i o n has been made, can now be t a k e n and the p o s s i b i l i t y o f c o m p e t i t i v e e x c l u s i o n , o f one s p e c i e s from an a r e a o f t h e p u d d l e d u r i n g t h e known l i f e o f t h e p u d d l e , be e s t a b l i s h e d . The t i m e a t w h i c h th e p u d d l e p r o b a b l y began and t h e t i m e s a t which v a r i o u s p o i n t s w i t h i n t h e p u d d l e s h o u l d have been submerged and d e s i c c a t e d each y e a r have been e s t a b l i s h e d i n p r e v i o u s s e c t i o n s . F o r t h e p o i n t 12.0 m from t h e s o u t h end o f t h e p u d d l e t h e s e are shown i n T a b l e X I I I . The a b i o t i c q u a n t i t y f o r each a g e - c l a s s (a) w h i c h f l u c t u a t e s f r om y e a r t o y e a r i s t h e ' t e m p e r a t u r e - t i m e ' g i v e n by r t = D ? TT = \ (TMAX - TBAR) «COS + TBAR dt a 4 = F + a 3 6 5 Each s p e c i e s was i n i t i a l i z e d w i t h a s m a l l number o f eggs and b e g i n n i n g w i t h the w i n t e r of 1961-62 th e o u t p u t o f eggs f o r each s p e c i e s was o b t a i n e d . The o u t p u t o f t h i s y e a r became t h e i n p u t o f t h e f o l l o w i n g y e a r when the t i m e s o f f i l l i n g and d r y i n g , and t h e t e m p e r a t u r e were d i f f e r e n t . T h i s was r e p e a t e d u n t i l t h e o u t p u t s f o r each s p e c i e s f o r t h e w i n t e r o f 1968-69 were o b t a i n e d . The mean t e m p e r a t u r e f o r each y e a r were c l o s e t o 50°F and t h e maximum monthly t e m p e r a t u r e v a r i e d from 61 - 66°F. The l e n g t h o f t h e w e t - p e r i o d v a r i e d from 220 -30 7 days and t h e b l o c k s o f time began as e a r l y as 39 days a f t e r August 1 s t (1961-62). 166 The numbers o f a n i m a l s f o u n d i n g t h e p o p u l a t i o n were 2 assumed t o be s m a l l and t h a t v a l u e s o f 1 egg p e r cm would be r e a s o n a b l e . I t i s assumed t h a t t h e i n p u t o f each s p e c i e s a t t h i s t i m e would be e q u a l . S i n c e the means by w h i c h t h e y c o u l d have a r r i v e d i n t h e p u d d l e are unknown t h e r e i s no r e a s o n t o make any o t h e r a s s u m p t i o n . The outcome o f t h e e f f e c t s o f each s p e c i e s upon t h e o t h e r t u r n e d out t o be e x t r a o r d i n a r i l y s e n s i t i v e t o t h e i n i t i a l d e n s i t y o f eggs. When the i n i t i a l numbers a r e e q u a l , by t h e s p r i n g o f 1969 C y p r i n o t u s s h o u l d be t h e o n l y s p e c i e s r e m a i n i n g i f t h e i n i t i a l numbers were l e s s 2 t h a n or e q u a l t o 0.65 eggs/cm , b u t i f t h e v a l u e was g r e a t e r 2 t h a n o r e q u a l t o 0.8 eggs/cm t h e n o n l y H e r p e t o c y p r i s s h o u l d be l e f t . F o r any v a l u e w i t h i n t h i s range th e two s p e c i e s s h o u l d be f o u n d c o e x i s t i n g by t h e s p r i n g o f 1969 b u t w i t h C y p r i n o t u s t h e more abundant s p e c i e s ( F i g . 4 7 ) . No i n i t i a l v a l u e s w i t h i n t h i s range l e a d t o a s t a t e o f c o e x i s t e n c e i n w h i c h H e r p e t o c y p r i s i s t h e most abundant s p e c i e s a t t h i s t i m e . I f t h e i n i t i a l i n t r o d u c t i o n had been s m a l l as has been assumed t h e n t h e r e s u l t s o f t h e computer s i m u l a t i o n ( F i g . 47) s u g g e s t t h a t up t o t h e s p r i n g o f 1965 t h e r e s h o u l d have been v e r y l i t t l e d i f f e r e n c e between the abundance o f b o t h s p e c i e s b u t i n t h e f o l l o w i n g f o u r w i n t e r s t h e r e s h o u l d have been v e r y r a d i c a l i n c r e a s e s o f one o f the s p e c i e s . The t h e o r e t i c a l i n v u l n e r a b i l i t y o f H e r p e t o c y p r i s t o e x t i n c t i o n w h i c h was f o u n d i n t h e c a s e o f c o n s t a n t c o n d i t i o n s (see p r e v i o u s s e c t i o n ) , was n o t f o u n d t o be t r u e f o r t h i s s e r i e s o f y e a r s . The f l u c t u a t i n g c o n d i t i o n s improved th e chances of C y p r i n o t u s t o be t h e most abundant o r o n l y s p e c i e s l e f t . A l s o t h e 1 6 7 iNUMBER OF E G G S p e r c m 2 168 i n v i n c i b i l i t y o f C y p r i n o t u s o n l y when 7 - 8 t i m e s more abundant t h a n H e r p e t o c y p r i s was not f o u n d t o h o l d under t h e s e c o n d i t i o n s . C y p r i n o t u s c o u l d q u i t e q u i c k l y ( i n o n l y 3 - 4 w i n t e r s ) o u s t t h e o t h e r s p e c i e s when the r a t i o o f t h e i n i t i a l numbers was o n l y 2:1. (Note t h a t when t h e r a t i o i s 1:1 t h e r e v e r s e i s t r u e ) . A f u r t h e r i n t e r e s t i n g r e s u l t o f g i v i n g C y p r i n o t u s an i n i t i a l a dvantage was t h e f a c t t h a t w i t h i n t h e range o f 8:1 - 4:1 eggs 2 p e r cm n o t o n l y was t h i s s p e c i e s t h e o n l y one r e m a i n i n g b u t r e g a r d l e s s o f t h e i n i t i a l numbers i n t h e range i t s d e n s i t y by t h e s p r i n g o f 1969 was e x a c t l y t h e same. T r a c e s o f t h e e f f e c t o f t h e s i z e o f t h e i n i t i a l i n t r o d u c t i o n were d i s c e r n a b l e f o r t h e f i r s t few y e a r s . The o b s e r v e d s t a t e o f the p o p u l a t i o n s i n t h e s p r i n g o f 1969 a t t h i s p o i n t i n t h e p u d d l e (12 m from t h e s o u t h end) i s w i t h C y p r i n o t u s t h e most abundant s p e c i e s by a f a c t o r o f about f i v e , a s t a t e which t h e model s u g g e s t s c o u l d o n l y have been r e a c h e d f r o m an i n i t i a l i n t r o d u c t i o n o f between 0.6 and 0.8 2 eggs/cm of b o t h s p e c i e s i n t h e f a l l o f 1961. A l t h o u g h t h e t i m e and magnitude o f the i n i t i a l i n t r o d u c t i o n a r e not known f o r c e r t a i n , t h i s c o r r e s p o n d e n c e o f t h e o b s e r v e d and r e a s o n -a b l e e x p e c t e d r e l a t i v e numbers does n o t c ause me t o r e j e c t t h e model. T h e r e f o r e I c o n c l u d e t h a t c o m p e t i t i v e e x c l u s i o n o f e i t h e r s p e c i e s can o c c u r i n t h i s r e g i o n o f t h e p u d d l e even a l t h o u g h t h e c o n d i t i o n s shown by t h e model t o i n f l u e n c e t h e p o p u l a t i o n s , f l u c t u a t e from y e a r t o y e a r . Other e x p l a n a t i o n s o f the c u r r e n t s t a t e o f t h e p o p u l a t i o n s w h i c h assume o t h e r t i m e s and s i z e s o f the i n t r o d u c t i o n can be p r o p o s e d but each w o u l d r e q u i r e s p e c i a l a s s u m p t i o n s . 169 Summary I t i s c o n c l u d e d from t h e i n v e s t i g a t i o n o f t h e model t h a t when t h e l e n g t h o f t h e wet p e r i o d and t e m p e r a t u r e s f l u c t u a t e from y e a r t o y e a r c o m p e t i t i v e e x c l u s i o n can s t i l l o c c u r . V a l u e s f o r t h e mean a n n u a l and maximum monthly t e m p e r a t u r e s , and t i m e s o f f i l l i n g and d r y i n g f o r t h e y e a r s 1962-1969 were u s e d . The outcome o f t h e s i m u l a t i o n was e x t r e m e l y s e n s i t i v e t o t h e i n i t i a l egg d e n s i t y used f o r each s p e c i e s . When t h e i n i t i a l v a l u e s f o r each s p e c i e s were e q u a l and l e s s t h a n 2 0.7 per cm C y p r i n o t u s was the o n l y s p e c i e s r e m a i n i n g i n 2 1969; when t h e y were g r e a t e r t h a n 0.8 p e r cm" H e r p e t o c y p r i s was t h e o n l y s p e c i e s t o s u r v i v e . V a l u e s between 0,7 and 2 0.8 eggs p e r cm l e d t o c o e x i s t e n c e i n 1969, which i s t h e o b s e r v e d s t a t e . 170 DISCUSSION T h i s s t u d y o f t h e o s t r a c o d s began from an i n t e r e s t i n t h e p o s s i b i l i t y o f c o m p e t i t i v e e x c l u s i o n (a term c o i n e d by H a r d i n i 9 6 0 ) t h a t was s u g g e s t e d by r e a d i n g t h e 'paradox o f t h e p l a n k t o n ' paper o f H u t c h i n s o n ( 1 9 6 1 ) , I t was s u s p e c t e d t h a t t h e c o e x i s t e n c e of many s p e c i e s o f o s t r a c o d s i n p u d d l e s m i g h t have been a consequence of t h e t e m p o r a r y e x i s t e n c e o f t h e environmento That one s p e c i e s might n o t have enough t i m e , when the p u d d l e was wet, t o cause t h e e x t i n c t i o n o f a n o t h e r s p e c i e s = But what had not been r e a l i z e d was t h a t when the p u d d l e r e f i l l e d i n t h e f o l l o w i n g y e a r t h e a n i m a l s ivould e s s e n t i a l l y t a ke-up where t h e y l e f t - o f f . More i m p o r t a n t was t h e f i n d i n g t h a t t h e consequences o f the e f f e c t s o f t h e a n i m a l s upon one a n o t h e r a r e complex. The b a s i c e f f e c t s o f t h e s p e c i e s upon one a n o t h e r a r e t o m o d i f y t h e number o f eggs h a t c h i n g i n any u n i t o f t i m e , t o r e d u c e t h e p r o p o r t i o n o f any day's r e c r u i t s r e a c h i n g m a t u r i t y , t o i n c r e a s e t h e l e n g t h o f t i m e r e q u i r e d t o r e a c h m a t u r i t y , t o d e c r e a s e the e g g - l a y i n g r a t e o r t o s h o r t e n the l e n g t h o f t i m e s p e n t l a y i n g eggs. These form the b a s i s f o r the model w h i c h has been d e v e l o p e d f o r t h e changes i n t h e p o p u l a t i o n o f eggs i n t h e p u d d l e . The consequence, o f changes i n t h e e n v i r o n m e n t , f o r t h e eggs a r e many and p a r t i c u l a r t o t h e s e t o f c o n d i t i o n s . The p r i n c i p l e which g i v e s r i s e t o t h e 'paradox' does not t a k e i n t o a c c o u n t t h e e x i s t e n c e o f t h e s e phenomena. F u r t h e r m o r e t h e p r i n c i p l e t h a t e c o l o g i c a l s i m i l a r i t y (whether r e c o g n i z e d by taxonomic s i m i l a r i t y o r n o t ) s h o u l d r e s u l t i n e x t i n c t i o n o f one s p e c i e s , 171 i s as y e t u n t e s t e d , l a r g e l y because th e ' e c o l o g i c a l s i m i l a r i t y ' t h a t i s s p e c i f i e d by t h e p r i n c i p l e c a nnot be i d e n t i f i e d i n n a t u r e . I t i s f o r t h i s r e a s o n t h a t I r e j e c t t h e e x i s t e n c e o f a 'paradox', A l t h o u g h t h e model t h a t has been d e v e l o p e d g i v e s a p p a r e n t l y a c c e p t a b l e r e s u l t s , t h e r e a r e a number o f ar e a s i n w h i c h i n f o r m a t i o n i s l a c k i n g and where ' r e a s o n a b l e ' a s s u m p t i o n s have t o be made about th e way i n which t h e p r o c e s s e s might o c c u r . F o r o t h e r a r e a s e x p e r i m e n t a l i n f o r m a t i o n was o b t a i n e d , b u t f o r one r e a s o n o r a n o t h e r c o u l d n o t be t e s t e d . Two o f t h e s e a r e a s o f u n c e r t a i n t y t u r n e d out t o be q u i t e c r i t i c a l t o t h e model. These are t h e e f f e c t s o f each s p e c i e s upon t h e e g g - l a y i n g r a t e o f the o t h e r s p e c i e s (assumed t o be the same as t h o s e o f members o f the s p e c i e s ) and t h e e f f e c t o f t h e s i z e o f t h e i n p u t o f eggs upon t h e number o f day-degrees f o r t h e a n i m a l s t o r e a c h m a t u r i t y . F o r t h e f i r s t o f t h e s e no i n f o r m -a t i o n was o b t a i n e d and f o r t h e second o n l y p a r t i a l e x p e r i m e n t a l e v i d e n c e ( F i g , 14) was o b t a i n e d . The e f f e c t was found t o be l i n e a r o v e r the range of i n p u t s e x p l o r e d , b u t t h e s e t u r n e d o u t t o be n e a r e r t h e l o w e r end o f t h e n a t u r a l r a n g e . F o r C y p r i n o t u s b o t h the o b s e r v e d and e x p e c t e d e q u i l i b r i u m i n p u t s were of t h e o r d e r o f 5 - 6 t i m e s l a r g e r t h a n t h e h i g h e s t e x p e r i m e n t a l i n p u t d e n s i t y . F u r t h e r m o r e , i t was assumed t h a t t h e r a t e o f d e c r e a s e o f t h e p r o p o r t i o n o f mature • a n i m a l s a l i v e as a f u n c t i o n o f t i m e a f t e r m a t u r i t y , was a c o n s t a n t f o r each s p e c i e s . T h i s might be s a t i s f a c t o r y i f t h e m o r t a l i t y o f immatures r e s u l t e d i n t h e e f f e c t s o f l a r g e i n p u t s o f eggs 1 7 2 b e i n g dampened - a s i m i l a r number r e a c h i n g m a t u r i t y r e g a r d l e s s o f t h e i n p u t . However, t h i s does not o c c u r and t h e p r o p o r t i o n r e a c h i n g m a t u r i t y i s a p p r o x i m a t e l y l i n e a r and has a s m a l l p o s i t i v e s l o p e . I t i s p o s s i b l e t h a t the e x c e l l e n t agreement between the e x p e c t e d and o b s e r v e d o u t p u t of eggs i n t h e p u d d l e o v e r t h e l a r g e range o f i n p u t s o f eggs (some o f which exceeded t h e range o f e x p e r i m e n t a l d a t a ) r e s u l t s p a r t i a l l y from a c o m p e n s a t i o n o f e r r o r s , some p o s i t i v e and o t h e r s n e g a t i v e . The model t r e a t s t h e o s t r a c o d s emerging from t h e eggs w i t h i n a u n i t o f space as though t h e y r emained w i t h i n t h a t u n i t d u r i n g t h e time t h a t i t i s wet o r , a l t e r n a t i v e l y , t h a t any l o s s e s from the u n i t o f space are equated by g a i n s . I t s h o u l d be e s p e c i a l l y n o t e d t h a t t h e g a i n s are o f t h e same k i n d as t h e l o s s e s , i n t h a t a n i m a l s o f t h e same 'age' w i t h r e s p e c t t o the t i m e of m a t u r i t y a r e exchanged. W i t h i n t h e s m a l l ' p o c k e t s ' o f t h e p u d d l e , where movement i s r e l a t i v e l y unimpeded, t h i s i s g u i t e s a t i s f a c t o r y b u t , as has a l r e a d y been n o t e d ( 1 ( 1 ) ) , t h e manner and f r e q u e n c y w i t h which impediments t o movement ( e . g . bunches o f g r a s s ) a r e n e g o t i a t e d i s unknown. The r e l e v a n t q u a n t i t i e s t h a t need t o be known ar e t h e d i s t a n c e f r o m t h e p o i n t o f emergence from th e egg t h a t an a n i m a l b e g i n s t o l a y eggs, and t h e a r e a o v e r w h i c h i t moves w h i l e l a y i n g eggs. I n t h e s y n t h e s i z e d model, when a s p e c i e s becomes e x t i n c t , t h e r e i s no way o f knowing how i t s r e - e s t a b l i s h m e n t might o c c u r . The e f f e c t s o f f r e e z i n g o f t h e p u d d l e upon t h e outcome o f t h e c o m p e t i t i v e p r o c e s s e s has not been i n v e s t i g a t e d , p r i m a r i l y because H e r p e t o c y p r i s c a n n o t l i v e i n t h e r e g i o n o f 1 7 3 t h e p u d d l e where f r e e z i n g o c c u r s r e g u l a r l y . I t i s t h e same r e g i o n o f the p u d d l e w h i c h i s wet f o r t h e s h o r t e s t t ime and a-nY H e r p e t o c y p r i s eggs h a t c h i n g a f t e r a p e r i o d o f f r e e z i n g would n ot have enough time t o r e a c h m a t u r i t y b e f o r e t h i s p a r t o f t h e p u d d l e d r i e d - u p . , F u r t h e r m o r e , t h e c o n c l u s i o n s t o be drawn from c o m p u t e r - t r i a l s o f d i f f e r e n t t i m e s o f f r e e z i n g a r e q u i t e p a r t i c u l a r , t h e r e b e i n g one f o r each d i f f e r e n t t r i a l . The e f f e c t s o f f r e e z i n g a r e c a t a s t r o p h i c t o the p o p u l a t i o n i n t h o s e r e g i o n s o f t h e p u d d l e , b u t 'minor c a t a s t r o p h i e s ' may r e s u l t from s e v e r e f l o o d i n g o f t h e p u d d l e . As has been n o t e d ( 1 K b ) ) , none was r e c o r d e d d u r i n g t h e p e r i o d o f t h e s t u d y , heavy r a i n f a l l r u n n i n g o f f t h e l a n d by a l t e r n a t i v e c h a n n e l s . Such e v e n t s would, u n l i k e t h e f r e e z i n g , a f f e c t t h e whole l e n g t h o f t h e p u d d l e and c o u l d r e s u l t i n t h e r e m o v a l o f a l a r g e p r o p o r t i o n o f t h e p o p u l a t i o n s o f each s p e c i e s , c a r r y i n g t h e a n i m a l s out onto a r e a s o f t h e f i e l d , which do not r e m a i n wet l o n g enough f o r the a n i m a l s t o mature and l a y eggs. The f r e q u e n c y w i t h which f l o o d i n g might o c c u r , and t h e amount o r i n t e n s i t y o f r a i n f a l l which would produce f l o o d i n g , i s un-known. I t i s p o s s i b l e t h a t such ' p e r i o d i c - d i l u t i o n s ' * m i g h t a l l o w f o r t h e c o e x i s t e n c e o f t h e two s p e c i e s o f o s t r a c o d s when t h e c o n c l u s i o n from t h e model 1 would be t h e e x t i n c t i o n o f one o r o t h e r s p e c i e s . The d e n s i t y - d e p e n d e n t c o n t r o l s o p e r a t i n g upon t h e o s t r a c o d s a re n o t o f t h e same i m p o r t a n c e t h r o u g h o u t t h e l e n g t h * I s h o u l d l i k e t o note t h a t t h i s term and i d e a f o r t h e c o e x i s t e n c e o f t h e o s t r a c o d s was pr o p o s e d by P,A» L a r k i n , 174 o f t h e p u d d l e . I n t h e n o r t h e r n end the d e l a y i n t h e b e g i n n i n g o f e g g - l a y i n g i s t h e most i m p o r t a n t because t h i s p a r t o f t h e p u d d l e f i l l s - u p l a s t and d r i e s - u p f i r s t , and t h e o s t r a c o d s c o u l d be caught w i t h a l l o r p a r t o f t h e i n i t i a l e g g - s t o r e i n t h e form o f a n i m a l s w h i c h have not y e t begun t o r e p l a c e t h e i n i t i a l i n v e s t m e n t . The consequences o f t h e d e l a y are not s i m p l e because t h e l a t e r t h a t t h e e g g - l a y i n g b e g i n s , the h i g h e r i s t h e t e m p e r a t u r e and a l t h o u g h t h e e g g - l a y i n g r a t e w i l l be h i g h e r , t h e eggs which a r e l a i d a re more l i a b l e t o h a t c h , A l s o , the h i g h e r t h e t e m p e r a t u r e t h e more l i k e l y i s t h e d i s a p p e a r a n c e o f t h e w a t e r from t h e a r e a . Towards t h e o t h e r end o f t h e p u d d l e t h e d e n s i t y - d e p e n d e n t e f f e c t o f t h e mature a n i m a l s upon t h e e g g - l a y i n g r a t e becomes e f f e c t i v e and t h e d e l a y i n b e g i n n i n g e g g - l a y i n g becomes u n i m p o r t a n t because t h e a n i m a l s more th a n make up f o r the d e l a y by l a y i n g t h e i r eggs at a h i g h e r t e m p e r a t u r e . However, a b u i l t - i n c o n t r o l b e g i n s t o o p e r a t e i n t h i s r e g i o n because o f t h e l o s s e s from t h e e g g - s t o r e due t o h a t c h i n g . I f t h e a r e a remains wet l o n g enough, an e q u i l i b r i u m w i l l be s e t - u p between th e s t o r a g e o f eggs and l o s s e s from the s t o r e (see F i g , 3 0 ) , T h i s l o s s o n l y a c t s as a c o n t r o l because of the t i m i n g o f t h e d r y i n g - u p and t h e e g g - l a y i n g . These p r o c e s s e s a r e l a r g e l y r e s p o n s i b l e f o r the d i f f e r e n c e between t h e outcomes o f t h e c o m p e t i t i v e e f f e c t s under c o n s t a n t c o n d i t i o n s (see t h e phase diagram of F i g , 46) and t h e r e s u l t s when the c o n d i t i o n s f l u c t u a t e from y e a r t o y e a r ( F i g , 4 7 ) , The model d e v e l o p e d f o r t h e t y r e - t r a c k p u d d l e s h o u l d be e n t i r e l y adequate f o r a n o t h e r p u d d l e w i t h t h e same q u a l i t i e 175 b u t o f d i f f e r e n t shape and perhaps w a t e r - s u p p l y , The g r o s s shape o f t h e p u d d l e i s not r e c o g n i z e d by t h e p r e s e n t t h e o r y because t h e s e p a r a t e p o i n t s i n space are t r e a t e d as b e i n g i n d e p e n d e n t . The model o n l y t a k e s i n t o a c c o u n t t h e changes i n t i m i n g o f t h e e v e n t s a t d i f f e r e n t p o i n t s i n s p a c e , * I f a l l e v e n t s o c c u r r e d a t t h e same t i m e a t a l l p o i n t s o v e r t h e s u r f a c e , t h e n t h e p r e s e n t model would be e n t i r e l y adequate, and so f o r a s m a l l c i r c u l a r ( f o r e.g.) p u d d l e , which d r i e d - u p e n t i r e l y o v e r a s h o r t p e r i o d o f t i m e , t h e w a t e r r e c e d i n g t o t h e d e e p e s t p o i n t , t h e s i m u l a t i o n o f t h e outcome a t one p o i n t would s u f f i c e f o r a l l o t h e r p o i n t s . C o n s e g u e n t l y , t h e t o t a l number o f eggs (TE) i n t h e s o i l a t d r y i n g - u p , f o r such s p e c i e s ' would be g i v e n by TE = A • f ( a ) 2 where A. i s t h e a r e a o f the p u d d l e ( r f o r t h i s example) and f ( a ) t h e t o t a l number o f eggs per u n i t a r e a o b t a i n e d from t h e s i m u l a t i o n . I n a p u d d l e i n w h i c h t h e r e was a g r a d u a l change i n t h e c o n d i t i o n s o v e r t h e s u r f a c e t h e t o t a l number o f eggs would be g i v e n by f y 2 f x 2 TE = \ V f ( x , y ) d x d y (18) Jy1 J x 1 where x and y are the two s p a t i a l axes o f t h e s u r f a c e . F o r t h e t y r e - t r a c k p u d d l e i n w h i c h t h e change o c c u r s g r a d u a l l y * The shape o f t h e p u d d l e may i n f l u e n c e t h e manner i n which t h e a n i m a l s d i s p e r s e from t h e p o i n t at w h i c h t h e y l e f t t h e eggs. 176 a l o n g a s i n g l e a x i s t h e t o t a l number o f eggs can be o b t a i n e d f r o m _ /*x = 31.1 TE = w V f ( x ) d x (19) J x ^ 0 where w i s t h e mean w i d t h o f t h e p u d d l e . The v a l u e o f f ( x ) can be o b t a i n e d n u m e r i c a l l y and i t has been e v a l u a t e d f o r t h e p o i n t s 5.0, 12.0, 22.2 metres from t h e s o u t h end o f t h e p u d d l e (see F i g s . 45A, 45B, 46) f o r a range o f i n p u t s o f C y p r i n o t u s . The use o f t h e i n t e g r a l i n e q u a t i o n (19) t o o b t a i n t h e v a l u e o f TE, r a t h e r t h a n a summation o f terms i s , f o r t h e t y r e - t r a c k p u d d l e , an a p p r o x i m a t i o n because t h e change i n t h e t i m i n g o f t h e e v e n t s i s n o t e n t i r e l y gr.adual (see F i g . 4 1 ) . But t h e r e i s no a l t e r n a t i v e because t h e d i s t r i b u t i o n o f t h e t i m i n g o f t h e e v e n t o v e r t h e space i s a t each p o i n t i n space t h e consequence o f two i n d e p e n d e n t l y d e t e r m i n e d e v e n t s . These ar e t h e t i m e o f f i l l i n g and t h e t i m e o f d r y i n g o f t h e p o i n t . S i n c e b o t h t h e s e p r o c e s s e s a re i n t h e m s e l v e s d i s c o n t i n u o u s t h e t i m i n g d u r i n g f i l l i n g i n t h e f a l l need not c o r r e s p o n d t o t h e same s p a t i a l d i s c o n t i n u i t i e s d u r i n g t h e s p r i n g . F u r t h e r m o r e , t h e d i s t r i b u t i o n o f t h e d i s c o n t i n u i t i e s o v e r t h e s u r f a c e i s n o t c o n s t a n t so t h a t t h e summation would have t o be o v e r terms o f v a r y i n g s i z e . T h e r e f o r e t h e i n t e r v a l a l o n g t h e a x i s i s assumed t o be i n f i n i t e l y s m a l l and so t h e i n t e g r a l i s us e d . I n r e a l i t y t h e p u d d l e ends a t 31.1 m from i t s s o u t h end because t h e l a n d b e g i n s t o s l o p e i n t h e o p p o s i t e d i r e c t i o n and t h e wa t e r can t r i c k l e no f u r t h e r . But a t t h i s p o i n t we can d e p a r t from t h e r e s t r i c t i o n o f t h e i n v e s t i g a t i o n t o t h e 177 s p a t i a l l i m i t s o f the p u d d l e , and e n q u i r e about e v e n t s w h i c h m i g h t o c c u r i f t h e l a n d c o n t i n u e d i t s g r a d u a l downward s l o p e Beyond 31.1 m. F o r m a l l y we can e x p l o r e t h e consequences o f e x t e n d i n g t h e l i m i t o v e r w h i c h t h e i n t e g r a l i n e q u a t i o n (19) i s t a k e n so as t o i n c l u d e t h e i m a g i n a r y p a r t s o f t h e p u d d l e . Because o f t h e d e c r e a s i n g l e n g t h o f t h e w e t - p e r i o d towards t h e n o r t h e r n end o f t h e p u d d l e , i t s h o u l d be found t h a t a p o i n t i n t h e i n t e g r a t i o n w i l l be r e a c h e d where none o f t h e o s t r a c o d s c a n l i v e and o n l y t h o s e a n i m a l s such as c y c l o p o i d s and h a r p a c t i c o i d s , w h i c h do not r e q u i r e v e r y l o n g t o r e a c h m a t u r i t y , s h o u l d be f o u n d . The v a l u e o f t h e i n t e g r a l from any a r b i t r a r y p o i n t a l o n g t h e a x i s w i l l be a s y m p t o t i c i n t h i s r e g i o n . I n r e a l i t y t h i s i m a g i n a r y p a r t o f t h e t y r e - t r a c k p u d d l e does, i n f a c t , e x i s t , a l t h o u g h i t i s p r o b a b l y not t h e same as would be fo u n d by i n t e g r a t i o n . I t e x i s t s as t h e p u d d l e s BPTT, RLP and SP (see t h e map o f t h e f i e l d i n F i g . 3 7 ) . These p u d d l e s a r e n o t t h e same as t h e i m a g i n a r y p a r t f o r two r e a s o n s . F i r s t l y , t h e y a re n o t e n t i r e l y dependent upon o v e r f l o w from t h e t y r e -t r a c k p u d d l e f o r t h e i r w a t e r s u p p l y and s e c o n d l y , t h e y have d i f f e r e n t s h apes, b e i n g s m a l l , o b l o n g and dee p e r . (Deep enough so t h a t f r e e movement o f t h e o s t r a c o d s w i t h i n t h e s p a t i a l b o u n d a r i e s o f t h e p u d d l e can o c c u r . ) Because o f t h e g r e a t e r depth t h e y c o u l d o n l y be c o n s i d e r e d as s i n g l e p o i n t s a l o n g t h e i m a g i n a r y p a r t of t h e t y r e - t r a c k a x i s . * * The same e x t e n s i o n c o u l d be made a t the s o u t h e r n end o f t h e p u d d l e , t h e i m a g i n a r y p a r t o f whi c h would l a s t l o n g e r because i t i s n e a r e r t h e s o u r c e o f s u p p l y o f t h e w a t e r . No r e a l p a r t s a re i n f a c t p r e s e n t . 178 The s t u d y o f the c o m p e t i t i v e e f f e c t s o f a n i m a l s upon each o t h e r has had a l o n g h i s t o r y because o f t h e i m p o r t a n c e o f t h e o b s e r v a t i o n t h a t 'the f i t t e s t ( i n d i v i d u a l s o r s p e c i e s ) s u r v i v e ' and t h e means by wh i c h t h i s c o u l d o c c u r has been s o u g h t . I n t h i s t h e s i s I do n o t i n t e n d t o r e v i e w t h i s l o n g and d i v e r s e h i s t o r y . But t h e r e i s one o b s e r v a t i o n t h a t I s h o u l d l i k e t o make. I t seems t h a t t o y i n g w i t h t h e s i m p l e e q u a t i o n s o f L o t k a , V o l t e r a and N i c h o l s o n i s b u t i d l e f o l l y i n t h e f a c e o f t h e a l m o s t b e w i l d e r i n g change o f t e m p o r a l and s p a t i a l q u a l i t i e s w i t h i n a s i n g l e p u d d l e . The e x p r e s s i o n f o r t h e d e r i v a t i v e o f numbers w i t h r e s p e c t t o t i m e , s a i d t o be t r u e f o r any p e r i o d o f t i m e i s (from L a r k i n • 1963), d N i 2 _ = r . • N. - a. • N ± - b ± . N ±- N j The e q u a t i o n e x p r e s s e s t h e i d e a t h a t the d e r i v a t i v e i s a p r o d u c t o f t h o s e ' f o r c e s ' t e n d i n g t o i n c r e a s e t h e numbers p r e s e n t and t h o s e t e n d i n g t o d e c r e a s e them. S p e c i f i c a l l y t h a t t h e i n c r e a s e i s l i n e a r l y r e l a t e d t o t h e number p r e s e n t and t h e d e c r e a s e i s made up o f two p a r t s , one p r o p o r t i o n a l t o t h e s q u a r e o f t h e numbers o f t h e s p e c i e s , and t h e o t h e r b e i n g p r o p o r t i o n a l t o t h e j o i n t p r o d u c t o f the numbers o f the two s p e c i e s . A t no time d u r i n g t h e w e t - p e r i o d o f the p u d d l e can I f i n d a t i m e a t which t h i s e x p r e s s i o n might h o l d . F u r t h e r m o r e I can f i n d no s c a l e o f t i m e f o r which t h i s e x p r e s s i o n might a p p r o x i m a t e t h e i n s t a n t a n e o u s r a t e o f change o f e i t h e r o f t h e numbers o f eggs or a n i m a l s . The c o m p l e x i t y o f t h e c o m p e t i t i v e p r o c e s s e s i s f a r i n e x c e s s o f t h e 'e l e m e n t a r y p r o c e s s ' e n v i s a g e d by Cause ( 1 9 3 4 ) . 179 B I B L I O G R A P H Y B a r c l a y , M„ (1966) An e c o l o g i c a l s t u d y o f a temporary pond near A u c k l a n d , New Z e a l a n d . A u s t . J , Mar. Freshw. 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(1943) S e a s o n a l changes i n t h e o s t r a c o d f a u n a o f t e mporary ponds. E c o l o g y 24:116-118. H o l l i n g , C.S. and S, Ewing (1969) B l i n d - m a n ' s - b l u f f -e x p l o r i n g t h e r e s p o n s e space g e n e r a t e d by r e a l i s t i c e c o l o g i c a l s i m u l a t i o n models, P r o c , I n t e r n . S'ymp. S t a t i s t i c a l E c o l o g y ( i n p r e s s ) . 180 H u t c h i n s o n , G.E:„ (1961) The paradox o f t h e p l a n k t o n . Am. Nat, 95:137-145, K e s l i n g , R.V. (1951) The morphology o f o s t r a c o d moult s t a g e s , I l l i n o i s B i o l , Monogr, 21:1-324, L a r k in - , . P . A . ( 1963) I n t e r s p e c i f i c c o m p e t i t i o n and e x p l o i -t a t i o n , J , E i s h , Res, Bd, Canada, 20:647-678, M i l l e r , R.S. (1967) P a t t e r n and p r o c e s s i n c o m p e t i t i o n , Adv, E c o l , Res, 4:1-74, M i l n e , A, (1961) D e f i n i t i o n s o f c o m p e t i t i o n among a n i m a l s . Symp, Exp. B i o l . 15:40-61. R i c k e r , W.E. (1954) S t o c k and r e c r u i t m e n t . J . F i s h . Res. Bd. Canada. 11:559-62 3. S a r s , G.O. (1889) On some f r e s h w a t e r O s t r a c o d a and Copepoda r a i s e d from d r i e d A u s t r a l i a n Mud. C h r i s t . V i d e n s -S e l s . F o r h a n d , 8:1-79. S a r s , G.O. (1901) C o n t r i b u t i o n s t o t h e knowledge o f t h e f r e s h w a t e r E n t o m o s t r a c a o f South A m e r i c a as shown by h a t c h i n g from d r i e d m a t e r i a l . A r c h i v . Math. Naturo 24(1) -.1-52. S h a r p e , R.W. (1917) The O s t r a c o d a . I n Ward and W h i p p l e , F r e s h w a t e r B i o l o g y , pp. 790-827. S I t a n k o v i c , S. (1960) The B a l k a n Lake O h r i d and i t s l i v i n g w o r l d . Monogr. B i o l . 9:1-357. Suoma.la.inen, E„ (195 3) P a r t h e n o g e n e s i s i n a n i m a l s . Advan. G e n e t i c s 3:193-253. T r e s s l e r , W.L. (1957) The O s t r a c o d a o f t h e G r e a t S l a v e L a k e . J . Wash. Acad. S c i . 47:415-423. Van Morkhoven,F.P. (1962) P o s t - p a l a e o z o i c O s t r a c o d a , t h e i r morphology, taxonomy and economic u s e . V o l . 1 G e n e r a l E l s e v i e r P u b l . Co. London. A P P E N D I C E S 181 APPENDIX 1 The f e e d i n g appendages o f t h e o s t r a c o d s The f e e d i n g appendages o f b o t h C y p r i n o t u s and H e r p e t o c y p r i s c o n s i s t o f t h r e e p a i r s o f appendages. These a r e t h e m a n d i b l e s , m a x i l l a e and t h e f i r s t p a i r o f l e g s . The s t r u c t u r e and arrangement o f t h e s e i s i l l u s t r a t e d i n F i g , 48. The d r a w i n g s t a k e n from Van Morkhoven (1962) a r e o f C y p r i d o p s i s v i d u a whose appendages are a l m o s t i d e n t i c a l t o t h e two s p e c i e s t h a t were s t u d i e d . The a n i m a l g r a s p s t h e fragment u s i n g t h e o p p o s a b l e p a i r s o f second antennae d i r e c t e d backwards from i n f r o n t and second l e g s d i r e c t e d f o r w a r d from b e h i n d t o h o l d i t b e n e a t h t h e c e n t r a l m a r g i n s o f t h e c a r a p a c e . The v a l u e s are p a r t e d and t h e fragment b r o u g h t c l o s e t o t h e mouth w h i c h i s s u r r o u n d e d by t h e s m a l l appendages. The mouth i s b o r d e r e d i n f r o n t by an u p p e r - l i p w h i c h does n o t c a r r y any appendages and b e h i n d by t h e hypostome l y i n g between t h e f e e d i n g appendages. Both have a c h i t i n o u s s k e l e t a l s u p p o r t . Between t h e s e , l y i n g i n a narrow s l o t , a r e t h e m a n d i b l e s f a c i n g each o t h e r a c r o s s t h e o p e n i n g t o t h e gut so t h a t t h e i r t o o t h e d edges can be opposed and used f o r c h e w i n g . S p r i n g i n g from t h e e x t e r i o r and c e n t r a l end o f each m a n d i b l e i s a s t r o n g p a l p s u p p l i e d ' w i t h s e t a e a l o n g i t s s i d e s and t e r m i n a t e d by s t r o n g c l a w s . These hook around t h e ends o f t h e m a n d i b l e s and l y i n g o u t s i d e t h e s l o t c an move back and f o r t h w i t h a s c r a p i n g a c t i o n . L y i n g b e h i n d t h e m a n d i b l e s , p a r a l l e l t o them are t h e m a x i l l a e w h i c h a r e Figure 48 The appendages of Cypridopsis vidua- The upper l e f t i l l u s t r a t i o n shows the arrangement of the appendages and the upper r i g h t the i n t e r n a l organs within the enclosing carapace. In each drawing the l e f t valve has been removed. Along the lower edge are arranged i n Order, magnified drawings of the three feeding appendages - outer face of the r i g h t mandible, outer face of the l e f t maxilla and outer face of the f i g h t f i r s t thoracic leg, (Note that these enlargements are not a l l from the same side of the animal and are not oriented to t h e i r natural position.) 1 8 3 s u p p l i e d w i t h s t r o n g , c l a w e d ends ( m a s t i c a t o r y p r o c e s s e s ) w h i c h can a c t w i t h t h e m a n d i b u l a r p a l p t o s c r a p e a t a s u r f a c e . A s s i s t i n g t h e m a x i l l a e are a p a i r o f f l i m s y appendages, w h i c h l i e a l m o s t h o r i z o n t a l and e x t e n d f o r w a r d on t h e c e n t r a l s u r f a c e o f t h e hypostome, w h i c h are d enoted as t h e f i r s t p a i r o f legs. They may a i d i n h o l d i n g o r g u i d i n g f o o d p a r t i c l e s . A l t h o u g h t h e r e a r e b r a c h i a l p l a t e s s u p p l i e d w i t h many s e t a e , e x t e n d i n g from t h e d o r s a l ends of b o t h t h e m a n d i b l e s and m a x i l l a e t h e y seem t o be p u r e l y r e s p i r a t o r y i n f u n c t i o n s i n c e t h e r e does n o t seem t o e x i s t i n C y p r i n o t u s o r H e r p e t o c y p r i s any means by which f i v e p a r t i c l e s p a s s i n g t h r o u g h t h e . l a t e r a l chamber b e n e a t h t h e v a l v e s and on e i t h e r s i d e o f the body, c o u l d be caught and t r a n s f e r r e d t o the mouth f o r i n g e s t i o n . These p l a t e s are i n c o n s t a n t m o t i o n i n t h e r e s t i n g a n i m a l and an a d d i t i o n a l r e s p i r a t o r y f u n c t i o n may be t h e maintenance o f a f l o w o f w a t e r i n t o and out o f t h i s space and f o s t e r i n g gaseous exchange between t h e body s u r f a c e and t h e w a t e r . 184 APPENDIX 2 A l i s t o f a n i m a l s which have been found i n the t y r e - t r a c k pudd'le The most common o f t h e l a r g e r a n i m a l s t h r o u g h o u t t h e t y r e - t r a c k p u d d l e d u r i n g t h e p e r i o d of s t u d y were t h e c y c l o p o i d s and h a r p a c t i c o i d s . They were u n i f o r m l y abundant a l o n g t h e 2 whole l e n g t h w i t h d e n s i t i e s up t o 20 p e r cm . T h e i r d i s t r i b u -t i o n was not r e s t r i c t e d t o any one p a r t o f t h e pud d l e - A p a r t from t h e o s t r a c o d s t h e a n i m a l s r e c o r d e d from the p u d d l e a r e as f o l l o w s : R o t i f e r s (many s p e c i e s ) O l i g o c h a e t e s ( u n i d e n t i f i e d ) Nematodes ( u n i d e n t i f i e d ) C a d d i s - f l y l a r v a e ( L i m n o p h i l u s sp.) C h i r o n o m i d l a r v a e (2 s p e c i e s ) Water b e e t l e (one specimen) C y c l o p o i d ( C y c l o p s b i s e t o s u s ) H a r p a r t i c o i d ( A t t h e y e l l a n o r d e n s k i o l d i i ) The o s t r a c o d s r e c o r d e d f rom t h e p u d d l e i n a d d i t i o n t o C y p r i n o t u s c a r o l i n e n s i s and H e r p e t o c y p r i s r e p t a n s a r e two o t h e r , l e s s common s p e c i e s Candona d e c o r a ( i n t h e s o u t h e r n end) and C y p r i c e r c u s r e t i c u l a t u s ( i n the n o r t h e r n e n d ) . 185 APPENDIX 3 The s i m u l a t i o n model CRUST The computer model o f t h e c o m p e t i t i v e e f f e c t s o f t h e two s p e c i e s upon each o t h e r i s e s s e n t i a l l y a model d e v e l o p e d f o r one s p e c i e s and t h e n e x t e n d e d t o i n c l u d e t h e second s p e c i e s . T h i s was done s i m p l y by c r e a t i n g s e p a r a t e a r r a y s f o r s t o r a g e o f t h e i n f o r m a t i o n about t h e second s p e c i e s and so i t w i l l be s u f f i c i e n t t o d e s c r i b e t h e model f o r one s p e c i e s o n l y . Some p a t t e r n was adhered t o when naming t h e v a r i a b l e s and c o n s t a n t s i n t h e model: most q u a n t i t i e s b e g i n n i n g o r e n d i n g w i t h C. are f o r C y p r i n o t u s and H, are f o r H e r p e t o c y p r i s and t h o s e f o r a n i m a l s a p p e a r i n g i n t h e second h a t c h a re t e r m i n a t e d by the l e t t e r S. A c o m p l e t e l i s t o f q u a n t i t i e s and t h e i r meanings accompanies t h e l i s t i n g o f t h e program i n t h i s a p p e n d i x . The two b a s i c a r r a y s i n t h e model a r e t h o s e s t o r i n g t h e h a t c h e d - a n i m a l s and t h o s e s t o r i n g t h e n e w l y - l a i d eggs. These are REC and EGN ( f o r C y p r i n o t u s ) and RECH and EGNH ( f o r H e r p e t o c y p r i s ) . A l l o t h e r a r r a y s a re a s s o c i a t e d w i t h t h e use o f e i t h e r o f t h e s e two. Those a s s o c i a t e d w i t h REC are NRM and NRMS ( r e c o r d i n g t h e number o f mature a g e - c l a s s e s p r e s e n t on a day d u r i n g t h e m a t u r a t i o n p e r i o d ) , TNR ( r e c o r d i n g t h e t o t a l number o f a n i m a l s r e c r u i t e d on a day a f t e r t h e new-eggs have begun t o h a t c h ) , RNTMF, RNTMS ( r e c o r d i n g t h e number o f a n i m a l s i n each a g e - c l a s s on t h e day t h a t t h e y m a t u r e ) , and TMT (an a r r a y c o n t a i n i n g t h e i n t e r v a l s i n days o r parts o f days between t h e m a t u r a t i o n o f a g e - c l a s s e s ) . The 186 a r r a y s a s s o c i a t e d w i t h EGN a r e MTDY and MTDYS ( r e c o r d i n g t h e day a f t e r August 1 s t t h a t t h e o l d e s t a g e - c l a s s w i t h members r e a c h e s m a t u r i t y ) and HTDY ( r e c o r d i n g t h e day on which t h e f i r s t new eggs b e g i n t o h a t c h ) . S i m i l a r l y f o r RECH and EGNH. There a r e s e v e n t e e n sub-programs i n t h e model and t h e f u n c t i o n o f each i s e x p l a i n e d i n t h e f o l l o w i n g s e c t i o n . S u b r o u t i n e HTCOE ( s h o r t f o r ' h a t c h i n g o f o l d eggs') h a n d l e s the h a t c h i n g o f t h e i n p u t ( o r ' o l d ' ) eggs f o r each s p e c i e s and c a l c u l a t e s t h e t o t a l number r e m a i n i n g on any day. I t a s s i g n s t h e a n i m a l s t o the a p p r o p r i a t e a r r a y . S u b r o u t i n e TARND ( s h o r t f o r ' t o t a l number around') c a l c u l a t e s t h e t o t a l number o f a n i m a l s b e l o n g i n g t o one s p e c i e s o r any p a r t o f t h a t t o t a l (RNUM) and a l s o the number o f a g e - c l a s s e s o v e r w h i c h i t summed t h a t had members. S u b r o u t i n e IMMATR ( s h o r t f o r 'immature') was o r i g i n a l l y a sub-program t h a t h a n d l e d most o f t h e a p p l i c a t i o n o f m o r t a l i t y t o immature a n i m a l s bu t i t g r a d u a l l y e v o l v e d i n t o a p u r e l y o r g a n i z i n g s u b r o u t i n e f o r t h e same work. S u b r o u t i n e MORTY ( s h o r t f o r ' m o r t i s youngus') a p p l i e s t h e m o r t a l i t y t o t h e immature a n i m a l s o f e i t h e r s p e c i e s (SOMA) a t t h e same t i m e p a r t i t i o n i n g t h e t o t a l m o r t a l i t y among t h e a g e - c l a s s e s . Of a l l t h e sub-programs t h i s one p r o b a b l y does t h e most work s i n c e each t i m e i t i s c a l l e d i t must c r e a t e an a r r a y (PD) which can be up t o 400 elements l o n g , t h e n s u b t r a c t each element from th e a p p r o p r i a t e element of SOMA D u r i n g any s i m u l a t e d day t h i s sub-program might be c a l l e d up t o f o u r t i m e s . S u b r o u t i n e MORTO ( s h o r t f o r ' m o r t i s o l d u s ' ) o r g a n i z e s 187 t h e m o r t a l i t y a p p l i e d t o t h e mature a g e - c l a s s e s and i s t h e c o u n t e r p a r t o f t h e sub-program IMMATR. S u b r o u t i n e MATURD ( s h o r t f o r , ? t o t a l number which matured!) c a l c u l a t e s the number o f a n i m a l s i n each a g e - c l a s s ( o f e i t h e r s p e c i e s ) which were p r e s e n t when t h e c l a s s was r e c r u i t e d t o t h e mature p o p u l a t i o n . S u b r o u t i n e MATREC ( s h o r t f o r ' r e c o r d o f m a t u r i t y ' ) r e c o r d s the a c c q u i s i t i o n o f an a g e - c l a s s by t h e mature p o p u l a t i o n . S u b r o u t i n e INTMAT ( s h o r t f o r ' i n t e r v a l s between m a t u r i n g ' ) c a l c u l a t e s t h e i n t e r v a l s between t h e m a t u r a t i o n o f an a g e - c l a s s . S u b r o u t i n e MAMRT ( s h o r t f o r 'mature m o r t a l i t y ' ) a p p l i e s t h e m o r t a l i t y t o t h e mature a g e - c l a s s e s a c c o r d i n g t o t h e age o f t h e c l a s s . S u b r o u t i n e MTSIN ( s h o r t f o r 'matures i n ' ) r e c o r d s t h e i n c r e a s e i n the number of mature a g e - c l a s s e s which s t i l l have members. S u b r o u t i n e ADLTS ( s h o r t f o r ' a d u l t s ' ) c a l c u l a t e s t h e number o f d a y - d e g r e e s , ( n o t e t h a t t h e s e a r e i n degrees f a h r e n h e i t and t h a t t h e r e s t o f t h e program o p e r a t e s i n degrees c e n t i g r a d e ) , a c c u m u l a t e d by each a g e - c l a s s and whether o r not an a g e - c l a s s i s r e a d y t o mature. T h i s i s done by comparing HUAC w i t h HURQ and i f t h e f i r s t i s g r e a t e r t h a n o r e q u a l t o t h e second t h e n K O M X i s i n c r e m e n t e d . L a t e r , K O M X i s i n s p e c t e d by a n o t h e r s u b r o u t i n e f o r any i n c r e m e n t w h i c h when i t o c c u r s , e x t e n d s t h e number o f a g e - c l a s s e s t r e a t e d by t h e mature sub-programs 188 and s h r i n k s t h e number t r e a t e d by t h e immature ones. S u b r o u t i n e DYDG ( s h o r t f o r 'day-degrees') o b t a i n s t h e i n t e g r a l o f t e m p e r a t u r e w i t h r e s p e c t t o t i m e from some i n i t i a l day (DYONE) t o t h e p r e s e n t (DYTWO). S u b r o u t i n e EGLY ( s h o r t f o r ' e g g - l a y i n g ' ) c a l c u l a t e s t h e number o f eggs l a i d by t h e mature C y p r i n o t u s p r e s e n t and a s s i g n s them t o a p o s i t i o n i n t h e a r r a y EGN c o r r e s p o n d i n g t o t h e day on which t h e i r h a t c h i n g w i l l b e g i n . S u b r o u t i n e HTCNE' ( s h o r t f o r ' h a t c h i n g o f new eggs') i n s p e c t s t h e C y p r i n o t u s e g g - a r r a y t o see i f any are r e a d y t o h a t c h . I f so the element i s decremented by an a p p r o p r i a t e amount and t h e decrement p a s s e d o u t s i d e t h e sub-program where i t i s a s s i g n e d t o t h e REC a r r a y . S u b r o u t i n e HEGHT ( s h o r t f o r ' H e r p e t o c y p r i s e g g - l a y i n g and h a t c h i n g ' ) does t h e same work as t h e s u b r o u t i n e EGLY and HTCNE do f o r C y p r i n o t u s . I t has s e p a r a t e a r e a s and the one used depends upon t h e v a l u e o f L I P . S u b r o u t i n e I C I K L ( s h o r t f o r ' i c e - k i l l ' ) w i p e s - o u t any non-eggs and r e o r g a n i z e s t h e program when f r e e z i n g o c c u r s . S u b r o u t i n e SCRBL ( s h o r t f o r ' s c r i b e o r s c r i b b l e ' ) i s an o u t p u t s u b r o u t i n e r e p o r t i n g upon t h e s t a t e o f t h e a n i m a l o r egg p o p u l a t i o n s o f e i t h e r s p e c i e s when c a l l e d by t h e main program, CRUST. C o m p i l a t i o n o f t h i s program by an IBM 360 computer t o o k 50 seconds and e x e c u t i o n o f an average l e n g t h o f t h e season r e q u i r e d a p p r o x i m a t e l y 16.0 seconds o f cpu t i m e . 189 P e r f o r m a n c e was c o n s i d e r a b l y enhanced by e x e c u t i n g an o b j e c t program ( s t o r e d i n a f i l e i n t h e computer) each t i m e t h e program was u s e d . The program w i l l p roduce upon i n s t r u c t i o n any o f t h e f o l l o w i n g g u a n t i t i e s a t any time d u r i n g t h e s i m u l a t i o n : the t o t a l number o f a s p e c i e s p r e s e n t , t h e t o t a l number o f mature a n i m a l s , t h e number of any a g e - c l a s s , t h e p e r c e n t a g e of t h e i n i t i a l r e c r u i t m e n t t o any a g e - c l a s s which r e m a i n , t h e p e r c e n t a g e o f the t o t a l number p r e s e n t t h a t any a g e - c l a s s c o n s t i t u t e s , the t o t a l number o f each a g e - c l a s s p r e s e n t when t h e y matured, the t o t a l number o f i n p u t - e g g s r e m a i n i n g , t h e t o t a l number o f new eggs r e m a i n i n g and t h e t o t a l number o f young r e c r u i t e d from new eggs on any day. Most o f t h i s i n f o r m a t i o n i s o b t a i n e d v i a t h e s u b r o u t i n e S'CRBL whi c h has a c c e s s t o t h e s e g u a n t i t i e s . 190 THE G R U S T PROGRAM C C DATA T I T L 1 / ' C I N C ' / D A T A T I T L 2 / ' H E R P • / D A T A T I T L 3 / ' K O M X ' / D A T A T I T L 4 / ' K M H S 1 / D A T A T I T L 5 / • H L A R • / D A T A T I T L 6 / ' C L R V V D A T A T I T L 8 / ' K M T H ' / D A T A T I T L 9 / • K M A T ' / D A T A T I T L A / ' K M T S ' / D A T A T I T L B / 1 M T D Y * / D A T A T I T L C / ' M T D S 1 / DATA T I T L D / ' M H D Y • / D A T A T I T L E / ' M H D S ' / COMMON R E C ( 4 0 0 ) » N R M ( 9 0 ) • E G N ( 9 0 0 ) » T N R ( 9 0 ) • R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) » M T D Y S ( 4 ) » H T D Y ( 4 ) » F S T R T ( 4 ) » F S T O P ( 4 ) » R N T M S ( 9 0 ) COMMON R O » R » D » B » T O E G » T N E G » R O T » R T » T O E G G » S E H » N F R E Z » W I D T H » W I N D » I F R E Z COMMON J S T » K M A T » K M A T S » N F R Z S » N R M S ( 9 0 ) » M H D Y S ( 4 ) » N R M H S ( 9 0 ) » H T D Y H ( 4 ) COMMON R E C H ( 4 0 0 ) » E G N H ( 9 0 0 ) » T N R H ( 3 0 0 ) » M T H D Y ( 4 ) » N R M H ( 9 0 ) » K M A T H » K M T H S COMMON R O H * R H » D H » B H » T O G H F » T N E G H # R O H S » H S E H • T O G H S » TNGHS COMMON H N T M F ( 9 0 ) # H N T M S ( 9 0 ) COMMON / C O N S T / R N O F i R N O S » H N O F . H N O S » C N S T 1 » C N S T 2 • C O N V . K H L D • 8 TMXC » T B R C R E A D ( 2 » 2 6 9 ) Y E A R 2 6 9 F O R M A T ( F 6 » 0 ) I F ( Y E A R ) 6 0 0 » 6 0 0 . 6 2 0 6 2 0 C O N T I N U E R E A D ( 2 i 2 8 9 ) I R I T E 2 8 9 F O R M A T ( 1 4 ) R E A D ( 2 » 5 0 2 ) T B A R i T M A X 5 0 2 F O R M A T ( 2 F 1 0 . 0 ) R = 0 . 0 3 3 1 7 D = 0 . 0 2 0 4 1 B = 0 . 0 0 1 8 1 2 R T = 0 . 0 3 8 8 2 R H * 0 . 0 5 4 9 2 D H = 0 . 0 2 0 4 B H = 0 . 0 0 1 3 1 9 W I D T H = 3 4 . 2 7 S E H = 2 0 4 . 0 W I N D = 3 0 0 « 0 H S E H = 1 3 0 . 0 H U M A X = 1 0 . 0 C C P T = 4 . 5 7 4 C S L P = 0 . 0 5 H C P T = 4 . 1 5 3 H S L P = 0 . 0 3 8 5 6 C D Y D G = 3 5 6 8 . 0 H D Y D G = 7 7 5 3 . 0 D N S I T = 3 4 1 . 7 P C 1 = 0 . 6 2 0 9 PC2=0.379 1 9 1 PH1=0.929 PH2=0.071 CONV=0.5556 CNSTl=365./6.283 CNST2=6.283/365.0 KHLD*900 TMXC= <TMAX-32.0)*CONV TBRC=(TBAR-32.0)*CONV WRITE( 3»30 J. 30 FORMAT(1H1 ) WRITE(3»201)YEAR . 201 FORMAK/»40X »'THIS IS THE WINTER OF SF5.0.//) WRITE(3»301)WIDTH 301 FORMAK10X#'MEAN WIDTH OF TT PUDDLE = 'tF6.2.' CM.') WRITE(3»302)WIND 302 FORMAKlOXt'EXIT-LIMIT IN DAYDEGREES * '»F5.0) WRITE(3»303 >TITL1»SEH 303 FORMAT!10X»'TIME OF BEGINNING OF »»A4»' SECOND-HATCH IS '•FS.O.' D 5AYS AFTER FILLING.•) WRITE(3»303)TITL2»HSEH WRITE(3»307)TITLliCDYDG 307 FORMAT(10X * * FOR '»A4>' THE MINIMUM NUMBER OF DAYDEGREES = '»F8.2) WRITE(3»307)TITL2»HDYDG WRITE(3»308)DNSIT 308 FORMAK10X» 'RATE OF INCREASE OF DYDG. PER EGG-INPUT = «»F6.2) WRITE(3#3111HUMAX 311 FORMAK10X»'HUMAX = «»F6.2»» TIMES DNSIT PLUS MINIMUM.') WRITE(3»50)TITL1.R»D»B»RT 50 FORMAT(1 OX *'FOR ».A4.' R = »»F7.5»' D = »»F7.5»' B = '.F8.6.' RT = 7 «»F7.5) WRITE(3#304)CCPT»CSLP 304 FORMAT(10X»'CCPT = '»F7.3»' CSLP = >»F8.5) WRITE(3»306)PC1*PC2 306 FORMAKlOXi 'PROPORTION OF EGG-INPUT IN HATCH-ONE = '»F6.4»/» 4 10X»'PROPORTION OF EGG-INPUT IN HATCH-TWO = '»F6.4t//) WRITE(3»51 )TITL2»RH.DH.BH 51 FORMAT(10X»'FOR »*A4»' RH = »»F7.5»' DH = '»F7.5t' BH = '»F8.6) WRITE(3»305 )HCPT.HSLP 305 FORMAK10X»'HCPT = '»F7.3»' HSLP = '»F8.5) WRITE(3«306)PH1»PH2 700 READ(2 #223)IFREZ•TST#TSTP•DI ST.CEGG»HEGG 223 FORMAK I4.5F10.0) IF(IFREZ)600»342»343 343 READ(2 »344)(FSTRT(I) .FSTOPtI)»1 = 1»IFREZ) 344 FORMAT(2F6 • 2 ) GO TO 346 342 DO 345 J0=l#4 FSTRTUO) = 0.0 345 FSTOPIJ0)=0.0 346 DO 520 J0=l»4 MTDY(JO)=0 MTDYS(JO)=Q MTHDY(JO ) = 0 MHDYS(JO)=0 HTDY(JO)=0 HTDYH(JO)=0 520 CONTINUE KEXP=2 JEXP=2 IF(CEGG)280»280»81 81 IF(HEGG)280»280t281 281 CONTINUE KEXP=3 280 CONTINUE R0=CEGG*PC1*R ROT=CEGG*PC2*RT R0H=HEGG#PH1*RH ROHS=HEGG*PH2*RH RN0F*CEGG*PC1 RNOS=CEGG*PC2 HN0F=HEGG*PH1 HNOS=HEGG*PH2 KRCR=400 IMLIM=90 EXWRT=20.0 LT=TSTP-TST KT=(LT/EXWRT)+l TTMT=0.0 TTMTH=0.0 RLRV=0#0 TOTLV=0.0 HLARV=0.0 TTLVH=0.0 TNEG=0.0 TNEGH=0•0 TNGHS=0.0 EGAC=0.0 NFREZ=1 NFRZS=1 NFZHS=1 KOMX=0 KOMXS=0 KOMXH=0 KMXHS=0 KFIND=0 I HFND = 0 KMAT=1 KMATS=1 KMATH=1 KMTHS=1 IMFIX=0 MTFIX=0 MHFIX=0 MHFXS=0 CIN1=0.0 CIN2=0.0 HP1=0.0 HP2=0.0 EGAH=0.0 JST = 1 DO 509 JO=l»IMLIM RNTMF(J0)=0.0 RNTMS(JO)=0.0 H N T M F ( J O ) = 0 » 0 193 H N T M S U O ) = O e O T M T ( J O ) = 0 . 0 N R M S l J O ) = 0 N R M H ( J O ) = 0 N R M H S ( J O ) = 0 5 0 9 N R M ( J O ) = 0 DO 3 4 0 J O = l . K R C R R E C C J O ) = 0 . 0 3 4 0 R E C H ( J O ) = 0 . 0 DO 1641 J O = l . K H L D E G N H ( J O ) = 0 • 0 1 6 4 1 E G N ( J O ) = 0 . 0 W R I T E ( 3 » 3 1 ) 31 F O R M A T ! / / / ) W R I T E ( 3 . 2 3 5 ) T B A R . T M A X 2 3 5 F O R M A T { 1 0 X » ' M E A N MONTHLY T E M P . - ' . F 6 . 2 . ' MAXIMUM M O N T H L Y T E M P . -8 ' . F 6 . 2 ) W R I T E ( 3 * 2 2 4 ) D I S T . T S T » T S T P 2 2 4 F O R M A T t 1 Q X . ' D I S T A N C E FROM THE SOUTH END OF T H E P U D D L E OF THE U N I T 7- * » F 6 . 2 » ' M . 1 • / » l O X i ' S T A R T I N G T I M E - ' . F 4 . 0 . ' S T O P P I N G T I M E - ' . F 4 7 . 0 » • A F T E R AUGUST 1 S T . •) W R I T E ( 3 » 1 6 3 1 ) L T 1 6 3 1 F 0 R M A K 1 0 X . ' L E N G T H OF THE WET P E R I O D = « t 14 » 1 D A Y S . ' ) I F ( C E G G ) 4 0 . 4 0 , 4 1 41 C O N T I N U E W R I T E ( 3 . 5 2 ) T I T L 1 » R N 0 F * R N 0 S » C E G G 4 0 I F ( H E G G ) 4 2 . 4 2 . 4 3 4 3 C O N T I N U E W R I T E ( 3 . 5 2 ) T I T L 2 . H N 0 F . H N 0 S » H E G G 52 F O R M A T ( 1 0 X » ' F O R ' » A 4 . ' THE EGG INPUT FOR H A T C H ONE WAS ' » F 7 . 3 » ' P E 4R S Q C M . ' » / . 1 0 X . ' AND FOR H A T C H TWO ' . F 7 . 3 . ' PER S Q C M . ' • / » l O X t * T O T A 7L EGGS = ' . F 7 . 3 . ' PER S Q C M . * ) 4 2 C O N T I N U E I F ( I F R E Z ) 2 3 2 * 2 3 2 . 2 3 3 2 3 3 W R I T E < 3 » 2 3 1 ) I F R E Z 2 3 1 F O R M A T ( 1 0 X » ' T H E NUMBER OF F R E E Z E - U P S T H I S YEAR = ••I 3 • / . 2 0 X . ' F R O M 8 T O . ' ) W R I T E ( 3 » 2 3 4 ) ( F S T R T ( K ) . F S T O P ( K ) » K = 1 . I F R E Z ) 2 3 4 F O R M A T C 2 0 X . F 6 . 2 . 4 X . F 6 . 2 ) GO TO 2 4 7 2 3 2 W R I T E ( 3 . 2 4 8 ) 2 4 8 F O R M A T t 1 0 X » ' N O F R E E Z E - U P S T H I S Y E A R . ' ) 2 4 7 C O N T I N U E K = 0 DO 96 J O = l » K T DO 97 K R = 1 » 2 0 K = K+1 I F ( K - L T ) 7 0 3 . 7 0 3 . 7 0 4 7 0 3 C O N T I N U E I F ( I F R E Z ) 5 1 0 » 5 1 0 » 1 1 7 1 1 1 7 1 K F R Z = K - F S T R T ( N F R E Z J + l I F ( K F R Z ) 5 1 0 . 5 1 0 . 5 1 3 5 1 3 L N G F R = F S T O P ( N F R E Z ) - F S T R T ( N F R E Z ) + l I F U F R Z - L N G F R ) 5 1 4 . 5 1 5 . 5 1 5 5 1 4 C A L L I C I K L ( K » L N G F R » E G S U P . K F R Z . K O M X . K O M X S » K O M X H . E G H U P . K M X H S ) E G A C = E G A C + E G S U P 194 E G A H = E G A H + E G H U P C I N l = 0 . 0 C I N 2 = 0 . 0 H P 1 = 0 . 0 HP2 = 0 . 0 T T M T H = 0 . 0 T T M T a O . O M T F I X = 0 I M F I X = 0 M H F I X = 0 MHFXS=0 GO TO 97 5 1 5 I F ( I F R E Z - N F R E Z ) 5 1 7 . 5 1 7 * 5 1 6 5 1 6 N F R E Z = N F R E Z + 1 J S T = K I F t F S T O P ( N F R E Z - 1 ) - S E H ) 4 3 0 . 4 3 0 . 4 3 1 4 3 1 N F R Z S - N F R Z S + 1 4 3 0 C O N T I N U E I F ( F S T O P ( N F R E Z - 1 ) - H S E H ) 2 9 » 2 9 » 2 8 28 N F Z H S = N F Z H S + 1 2 9 GO TO 5 1 0 5 1 7 I F R E Z = 0 N F R E Z = N F R E Z + 1 J S T = K I F ( F S T O P ( N F R E Z - 1 ) - S E H ) 5 1 0 • 5 1 0 * 4 3 2 4 3 2 N F R Z S = N F R Z S + 1 5 1 0 C A L L H T C O E ( K » 1 ) R E C ( K ) = R E C < K ) + E G A C E G A C = 0 . 0 C A L L H T C O E ( K . 2 ) R E C H ( K ) a R E C H ( K , ) + E G A H E G A H = 0 . 0 K L = K - 1 I F ( K L - J S T ) 9 9 1 » 9 9 1 » 9 9 2 9 9 1 R N = R E C ( K ) N O = l R N H = R E C H ( K ) N0H=1 GO TO 9 9 3 9 9 2 C O N T I N U E C A L L T A R N D ( R E C » S E H » R N » K L » l » N O ) C A L L T A R N D f R E C H . H S E H . R N H . K L . l . N O H ) 9 9 3 C O N T I N U E RNTOT=RN+RNH TNOW=K KO = 0 KOS = 0 S T N O = R N O F + H N O F E X R T T = 1 . 0 - E X P ( - R T * J S T ) E X R J T = 1 . 0 - E X P ( - R * J S T ) E X R H S = 1 . 0 - E X P ( - R H * S E H ) S T N O S = R N O S + H N O S - ( H N O S * E X R H S ) I F ( J S T - 1 ) 1 2 0 . 1 2 0 . 1 2 3 1 2 3 I F ( J S T - S E H ) 1 2 6 . 1 2 6 . 1 2 7 1 2 6 S T N O = R N O F - R N O F * E X R J T E X R H T = 1 . 0 - E X P ( - R H * J S T ) S T N O = S T N O + H N O F - (HNOF-&EXRHT ) GO TO 1 2 0 1 2 7 S T N O S = R N O S - ( R N O S * E X R T T ) S T N O S = S T N O S + H N O S - ( H N O S * E X R H T ) 1 2 0 HURQ=CDYDG+DNS IT*STNG H U R Q S = C D Y D G + D N S I T * S T N O S I F ( H U M A X ) 3 1 4 . 3 1 4 . 3 1 5 3 1 5 U M X = C D Y D G + D N S I T * H U M A X H U R Q = A M I N 1 ( H U R Q . U M X ) H U R Q S = A M I N 1 ( H U R Q S » U M X ) 3 1 4 C O N T I N U E • C A L L A D L T S ( T S T .KOMX . K . K O . K O M X S . T B A R . TMAX • KOS »S EH »HURQ » H U R Q S • R EC ) KOH = 0 KOHS=0 STNO=HNOF+RNOF E X R H S = 1 . 0 - E X P ( - R * H S E H ) S T N O S = H N O S + R N O F - ( R N O F # E X R H S ) I F ( J S T - 1 ) 1 3 4 » 1 3 4 . 1 3 5 1 3 5 I F ( J S T - H S E H ) 1 3 6 . 1 3 6 . 1 3 7 1 3 6 S T N O = H N O F - ( H N O F * E X R H T ) S T N O = S T N O + R N O F - ( R N O F * E X R J T ) GO TO 1 3 4 1 3 7 S T N O S = H N O S - ( H N O S * E X R H T ) S T N O S = S T N O S + R N O F - ( R N O F * E X R J T ) 1 3 4 H U R Q = H D Y D G + D N S I T * S T N O HURQS=HDYDG+DNS IT*S TNOS I F ( H U M A X ) 3 1 6 . 3 1 6 . 3 1 7 3 1 7 U M X = H D Y D G + D N S I T * H U M A X H U R Q = A M I N 1 ( H U R Q t U M X ) H U R Q S = A M I N I ( H U R Q S . U M X ) 3 1 6 C O N T I N U E C A L L A D L T S ( T S T . K O M X H . K . K O H . K M X H S . T B A R . T M A X . K O H S . H S E H . H U R Q . H U R Q S . R E 7 C H ) F R D Y = J S T - S E H I F ( F R D Y ) 2 6 4 » 2 6 5 . 2 6 5 2 6 4 F R D Y = 0 . 0 2 6 5 C O N T I N U E C A L L I M M A T R ( K . S E H . F R D Y . K O M X . K O M X S . R N T O T . R E C . D . B . K E X P ) C A L L I M M A T R ( K . H S E H . F R D Y . K O M X H . K M X H S . R N T O T . R E C H . D H . B H . J E X P ) I F ( M T F I X ) 1 4 2 . 1 4 2 . 1 4 6 142 I F ( K O M X ) 9 5 » 9 5 . 1 4 5 1 4 5 M T D Y ( N F R E Z ) = K W R I T E ( 3 . 2 2 2 ) T I T L B . M T D Y ( N F R E Z ) 2 2 2 FORMAT ( 1 OX • A 4 . ' = S I 4 ) M T F I X = 1 W R I T E ( 3 . 2 2 2 ) T I T L 3 . K O M X 1 4 6 C A L L M T S I N ( K O . K O M X . R E C . K M A T . N R M . T I T L 9 ) C A L L T A R N D ( R E C . S E H . C I N I . K O M X . I . N C L ) H T T = C I N 1 + C I N 2 + H P 1 + H P 2 C A L L E G L Y ( T M A X . T B A R . T S T . T N O W . H T T . C I N l . l ) I F ( I M F I X ) 1 1 0 0 . 1 1 0 0 . 2 4 2 1 1 0 0 I F ( K O M X S ) 2 4 0 . 2 4 0 . 1 1 0 1 1 1 0 1 M T D Y S ( N F R Z S ) = K I M F I X = 1 WR ITE I 3 . 2 2 2 J T I T L C . M T D Y S ( N F R Z S ) 2 4 2 C A L L M T S I N ( K O S . K O M X S » R E C . K M A T S » N R M S . T I T L A ) C A L L T A R N D ( R E C . S E H . C I N 2 . K O M X S . 2 . N C L ) H T T = C I N 1 + C I N 2 + H P 1 + H P 2 ' 196 C A L L E G L Y ( T M A X . T B A R . T S T . T N O W . H T T . C I N 2 . 2 ) C A L L M O R T O ( R E C i K O S » K »KOMXS . R N T M S . N R M S . M T D Y S . K M A T S » S E H . C C P T . C S L P . 2 4) 2 4 0 K M = K - M T D Y ( 1 ) + 1 C A L L M O R T O ( R E C . K O . K . K O M X » R N T M F » N R M . M T D Y . K M A T . S E H » C C P T » C S L P . 1 ) 95 C O N T I N U E T T M T = C I N 1 + C I N 2 C A L L H T C N E ( T N O W » T M A X . T B A R . T S T » R L R V , T O T L V ) T O T L V = T O T L V + R L R V I F ( K F I N D ) 1 0 » 1 0 » 20 10 I F ( R L R V ) 2 Q » 2 Q » 2 2 5 2 2 5 H T D Y ( N F R E Z ) = K K F I N D = 1 2 0 I F ( H T D Y ( 1 ) 1 6 2 . 6 2 . 2 2 8 2 2 8 KMH=K-HTDY ( 1) +1 T N R ( K M H ) = R E C ( K ) W R I T E ( 3 . 5 5 5 ) T I T L 6 » R L R V 6 2 C O N T I N U E E L = T O E G + T N E G + T O E G G I F ( M H F I X ) 5 6 . 5 6 . 5 7 56 I F 1 K 0 M X H 1 6 3 . 6 3 . 5 8 58 M T H D Y ( N F R E Z ) = K W R I T E ( 3 . 2 2 2 ) T I T L D . M T H D Y ( N F R E Z ) M H F I X = 1 57 C A L L M T S I N ( K O H . K O M X H > R E C H . K M A T H . N R M H • T I T L 8 ) C A L L M O R T O ( R E C H » K O H » K . K O M X H . H N T M F . N R M H . M T H D Y . K M A T H . H S E H . H C P T . 8 H S L P . l ) K M M = K - H T D Y H ( 1 ) + 1 C A L L TARNDJ R E C H . H S E H . H P 1 . K O M X H . 1 . N C L ) H T T = C I N 1 + C I N 2 + H P 1 + H P 2 C A L L H E G H T ( T M A X . T B A R . T S T . T N O W . K O M X H . H L A R V . H P 1 . l . H T T ) GO TO 1 5 5 6 3 C O N T I N U E C A L L H E G H T ( T M A X . T B A R . T S T . T N O W . K O M X H . H L A R V . H P 1 . 2 » H T T ) 1 5 5 I F ( K M X H S ) 2 1 . 2 1 . 1 5 4 1 5 4 C A L L T A R N D ( R E C H » H S E H . H P 2 . K M X H S . 2 . N C L ) H T T = C I N 1 + C I N 2 + H P 1 + H P 2 C A L L H E G H T ( T M A X . T B A R . T S T . T N O W . K M X H S . H L A R V » H P 2 . 3 » H T T ) 21 T T M T H = H P 1 + H P 2 I F ( M H F X S ) 2 2 . 2 2 . 2 3 22 I F ( K M X H S ) 2 4 . 2 4 . 2 5 25 M H D Y S ( N F Z H S ) B K W R I T E ( 3 . 2 2 2 ) T I T L E . M H D Y S ( N F Z H S ) MHFXS=1 2 3 C A L L M T S I N ( K O H S . K M X H S . R E C H . K M T H S . N R M H S . T I T L 4 ) C A L L M O R T O ( R E C H . K O H S . K . K M X H S . H N T M S . N R M H S . M H D Y S . K M T H S . H S E H . H C P T . 8 H S L P . 2 ) 2 4 C O N T I N U E ' I F ( I H F N D ) 3 2 . 3 2 . 3 3 32 I F ( H L A R V ) 3 3 . 3 3 . 3 4 34 H T D Y H ( N F R E Z ) = K IHFND=1 33 I F ( H T D Y H ( 1 ) ) 3 5 . 3 5 . 3 6 36 K H H = K - H T D Y H ( 1 ) + l T N R H ( K H H ) * R E C H ( K ) W R I T E ( 3 . 5 5 5 ) T I T L 5 . H L A R V 5 5 5 F O R M A T ( 1 O X . ' T H E NUMBER OF ' . A 4 . ' * ' . F 7 . 3 ) 35 CONTINUE T TLVH = TT LVH+HLARv ELH=TOGHF+TOGHS+TNEGH+TNGHS 97 CONTINUE IF(IRITE)96.96.287 287 CONTINUE IF(CEGG)44,44,45 45 CONTINUE CALL SCRBL(TNOW »RN»TTMT»1»EL»TST*TITL1) 44 IF(HEGG)96»96.46 46 CONTINUE CALL SCRBL(TNOWiRNH»TTMTH»3»ELH*TST»TITL2) 96 CONTINUE 704 CONTINUE IF(CEGG)71»71»72 72 CONTINUE CALL SCRBL(TNOW »RN »TTMT»1»EL»TST»TITL1) CALL MATURD(KOMX »TOTAL»RNTMF.TITL1»1) CALL MATURD(KOMXS »T0TAL»RNTMS»TITL1*2) WRITE(3.31 ) 71 IF(HEGG)73 »73»74 74 CONTINUE CALL SCRBL{TNOW »RNH»TTMTH»3»ELH»TST»TITL2) CALL MATURD(KOMXH»TOTAL»HNTMF•TITL2»1) CALL MATURD(KMXHS»TOTAL»HNTMF.TITL2»2 ) 73 CONTINUE WRITE(3#30 ) GO TO 700 600 CALL EXIT END 198 C Q tt tt tt tttt tt tt tt tt tt tt tt tt tt tt tt tt tt tt- tt * tt tt tt tt tt tt tt tt tt tt * tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt- Or tt tt tt tt tt tt tt tt tt C tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt- tt tt tt tt tt tt tt tt tt tt -tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt * tt tt tt tt tt tt tt tt tt tt tt * tt tt tt tt C SUBROUTINE HTCOE(K» ISPP) COMMON REC( 400) iNRMl 90 ! »E6N ( 900 ) »TNR ( 90 } <> RNTMF ( 90 ) » TMT { 9 0 ) COMMON MTDY(4)»MTDYS(4)>HTDY(4!*FSTRT(4) *FST0P(4) »RNTMS(90) COMMON RO » R » D » B iTOEG * TNEG i ROT »RT * TOEGG « SEH > NFREZ »'WIDTH »W I ND »IFREZ , COMMON J ST » KMAT t KMA TS » NFRZS » NRMS ( 9 0 ! *MHDYS ( 4 ) *.NRMHS ! 90 ) * HTDYH ( 4) COMMON R ECU(400)* EGNH(90 0 ) »TNRH(300)»MTHDY(4)*NRMH(90) »KMA TH»KMTHS COMMON ROH »RH•DH »BH tTOGHF » TNEGH•ROHS »HSEH > T OGHS> TNGHS C0MMON HNTMF ( 90 ) »HNTMS ( 90 ) COMMON /CONST/ RNOF* RNOS »HNOF > HNOS * CNST1» CNST 2 » CONV »KHLD » 8 TMXCtTBRC GO TO (50*60).ISPP 50 CONTINUE T0EGG=RNOS EXRK=EXP(~R#K) EXR=EXP(R) IF(K-SEH)lOOilOOtlOl 100 REC(K)=((RO*EXRK)/R)#(EXR-1.0) GO TO 105 101 RK=K-SEH EXRT = EXP ( RT ) ... . . . . EXRTK=EXP(-RT#RK) REC (K ) = I (ROT*EXRTK )./RT )* ( EXRT-1.0 ) TOEGG=RNOS-(RNOS*<loQ-EXRTK)) IF((WIDTHSTOEGG)-1.0)94»105*105 94 TOEGG=OoO 105 TOEG=RNOF-(RNOF*(1.0-EXRK)) IF((WIDTH*TOEG)-1.0)95»96»96 95 TOE6=0«0 96 CONTINUE RETURN 60 CONTINUE TOGHS=HNOS EXRH=EXP(RH) EXRHK=EXP(-RH*K) IF(K-HSEH)200.»200»201 ""'" " •" 200 RECH(K)=(<ROH*EXRHK)/RH)*(EXRH-1.0> GO TO 205 201 RK=K-HSEH EXRHR=-EXP(-RH*RK) . RECH(K) = ( (ROHS*EXRHR)/RH)*(EXRH-1.0) TOGHS = HNOS-(HNOS*( 1.0-EXRHR.) > IF((WIDTH*TOGHS)-1«0)294.205*205 294 TOGHS=0»0 205 TOGHF = HNOF-(HNOF*(1e 0-EXRHK) ) IF((WIDTH*TOGHF)-1.0)295*296*296 29 5 TO'G'HF = 0.0 296 CONTINUE RETURN END 199 C. C tt tt tt tt tt tt tt tt tt tt tt tt tt * -if tt # # * *• tt * tt tt -if * tt * tt tt tt tt tt tt tt tt tt tt * 4:- tt tt «• tt * tt -if tt tt * * tt * tt tt * * * tt # tt 4;- tt * * C tttt tt tt tt tt tt •«- tt -it * tt tt- tt ->;- tt tt * tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt -;<• tt tt tt tt tt tt- tt tt tt tt tt tt * tt tt tt tt tt tt tt tt tt tt tt tt c SUBROUTINE TARND(SOMA»TIME»RNUM•ICLAS•LL»NCL) DIMENSION SOMA( l) COMMON RECI400)»NRM(90J.EGN1900)»TNR(90)»RNTMF(90)»TMT(90) COMMON MTDY(4) »MTDYS(4)» HTDY(4 )»FSTRT(4) .FST0P14) »RNTMS(90) COMMON R O . R » D »B »TOEG* TNEG * ROT »RT•TOEGG»SEH .NFREZ.WIDTH.WIND*IF R E Z COMMON JST »KMAT .KMATS»NFRZSoNRMS(90) »MHDYS14) »NRMHS(90 ) .HTDYH(4J COMMON RECH(400)»EGNH(900)»TNRH(300)»MTHDY(4)»NRMH(90). K.MATH?KMTHS COMMON ROH.RH.DH.BH.TOGHF.TNEGH.ROHS.HSEH.TOGHS.TNGHS COMMON HNTMF(90)» HNTMS(90) GO TO (100 »200) »LL 100 CONTINUE NCL=0 ILOWRaJST IUPPR^ICLAS IF(IUPPR-ILOWR)50»50»51 5 0 RNUM-SOMA(ILOWR) GO TO 5 5 51 CONTINUE RNUM=0«0 DO. 21 J = ILOWR* IUPPR IF(SOMA(J) )2 1 »21i20 2 0 RNUM=RNUM+SOMA(J) NCL=NCL+1 21 CONTINUE 5 5 CONTINUE RETURN 200 . CONTINUE NCL = 0 JX»JST-TIME I F ( J X ) 1 1 . 1 1 . 1 2 11 ILOWR=TIME J X = 0 G O TO 40 12 I L ' O W R B J S T 40 IUPPR=TIME+ICLAS+JX IF( IUPPR-ILOWR160.60 .61 60 RNUM=SOMA(ILOWR) GO T O 75 61 CONTINUE RNUM=0o0 . D O 31 J=ILOWR.IUPPR I F( S O M A ( J ) J31.31.30 3 0 RNUM=RNUM+SOMA(J) NCL=NCL+1 31 CONTINUE 7 5 CONTINUE RETURN • • • • END 2 00 C C * # * * -it -rr # # -it -it -it -it- -it -if # -;t -it # * * # -if -ii- * -;t * * # * * -K- * * # * -it -it -it -it -st -it -it •» -st * # C ###•!(•# *- -5f # -if -if * * -it * * -j,- * * -if * * * -if it * -!f -X- * tt -if tt -it -it -if # -ir tt * * * * -it -it * -it -it * tt -if -if -it -if -if tt * -if -it -if -it tt * tt tt * tt * r SUBROUT I NE IMMATR(NTIM•TI ME t FRDY » JMTR»JMT RS•RNTT »SOMA•DD t BB » I X P ) DIMENSION S O M A ( l ) COMMON RECt 40 0) »NRM(90)»EGN(900) »TNR(90) »RNTMF(90) >TMT(90) COMMON M T D Y ! 4 ) » M T D Y S ( 4 ) * H T D Y ( 4 ) * F S T R T ( 4 ) » F S T O P ( 4 ) s R N T M S ( 9 0 ) COMMON RO»R»D»B»TOEG»TNEG»RQT»RT»TOEGG»SEH*NFREZ*WIDTH»WIN D »IF R E Z COMMON JST»KMAT*KMATS»NFRZS»NRMS(90) »MHDYS ( 4 ) sNRViHS{90) 5 HTDYH ( 4 ) COMMON R E C H 1 4 0 0 ) t E G N H ( 9 0 0 > » TNRH(300)»MTHDY(4)*NRMH(90) tKMATH tKMTHS COMMON ROH »RH* DH > BM•TOGHF1TNEGH»ROMS » HSEH »TOGHS•TNGHS COMMON HNTMF(90)»HNTMS(90> I F ( i \T IM-T IME)l»l»2 2 KYNG-NTIM-TIME-FRDY . I F ( J S T - T I M E ) 1 6 0 0 * 1 6 0 0 * 1 6 0 1 16 01 NMA=JST GO TO 1602 1600 NMA-TIME+JMTR+1 1602 CALL MORTY(RNTT »KYNG»NTIM»JMTR »1»SOMA»DD*B3»NMA*IXP) • GO TO 8 1 KYNG=NTIM-JMTR-JST NMA=JST+JMTR CALL MORTY(RNTT»KYNG»NTIM«JMTRS*1*SOMA *DD »BB »NMA»IXP) 8 CONTINUE RETURN END '01 C *- * tt tt tt •» tt tt tt tt •«• tt tt tt tt tt * tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt- tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt * tt tt C tt tt- tt •«• tt tt tt- tt tt tt- tt tt tt tt tt- tt •«- tt tt tt- tt tt tt tt tt- tt tt tt tt tt tt tt tt tt tt tt *- tt * tt tt tt tt tt tt- tt tt tt tt * tt tt tt- tt tt tt tt tt tt- tt tt tt tt tt c SUBROUT I NE MORTY ( R.N » KA » I T » KOMX t M * SOMA * DD »BB »NMA » I XP ) DIMENSION PD(400) «SOMA( 1) COMMON RECt 400).»NRM( 90 ) *EGN( 900 J »TNR (90 J »RNTMF( 90) *TMT (90) COMMON MTDY(4) »MTDYS(4)»HTDY(4 ) » F S T R T(4) » F STOP (4 ) » RNTMS!90 ) COMMON RO»R»D»B»TOEG»TNEG»ROT»RT»TOE GG»S EH »NFR EZ•WID TH»W I ND*IF R E Z COMMON JST »KMAT»KMATS »NFRZS* NRMS(90) »MHDYS(4) »NRMHS(90! sHTDYH(4) COMMON RECHt 400) » E G N H(9 0 0) »TNRHt 300 )> M T H D Y (4 ) *MRMHt90) »KMATH* KMTHS COMMON ROH * RH »DH » BH * TOGHF* TNEGH* ROMS * HSEH* T OGHS *TNGHS COMMON HNTMF(90) * HNTMS(90) DATA D I S T R / . 0 1 1 5 / DATA G / o 0 2 0 4 / DATA H / . 0 0 4 2/ DATA F / . 0 0 0 2 1 / I F ( I XP-2 ) 1*1*2 2 DN=(G*RN )+ (H*RN**2 ) + ( F * R N * * 3 ) GO TO 3 1 DN=((DD*RN)+BB*(RN##IXP)) 3 CONTINUE KN = 0 I F ( K A ) 2 0 1 » 2 0 1 * 2 0 2 201 R I C L = 4 0 0 6 0 GO TO 203 202 ' R I C L = 4 0 0«0 / K A STRT=0o0 RX=0e0 DO 99 I=1*KA RX=RX+RICL XXM = D N * ( 1 . 0 - E X P ( ~ D I S T R * R X ) ) PD ( I )=XXM-STRT 99 CONTINUE 203 KB=IT-1 IF (KB-NMA)208»208*209 209 CONTINUE ' ~ — KN=1 • . KBNMA=KB+NMA . . . DO 96 IK = NMA « KB JM = KBNMA-IK I F ( S O M A ( J M ) - 1 . 0 E - 4 ) 9 2 * 9 2 > 9 3 9 2 S O M A ( J M ) = 0 . 0 GO TO 96 9 3 SOMA( JM)=SOMA( JM)-PD(KN) 96 KN=KN+1 208 RETURN END 202 C c *#*#*#***###**######•«•# c S U B R O U T I N E M O R T O ( S O M A » K A . I T » J M A T • R M A T » I N R A M » M D A Y • L M A T » T I M E * Y C P T » 7 O S L P t M ) D I M E N S I O N S O M A ( 1 ) » R M A T ( 1 ) » I N R A M ( 1 ) * M D A Y ( 1 ) COMMON R E C ( 4 0 0 ) » N R M ( 9 0 ) • E G N ( 9 0 0 ) * T N R ( 9 0 ) . R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) » M T D Y S ( 4 ) » H T D Y ( 4 ) » F S T R T ( 4 ) * F S T 0 P ( 4 ) » R N T M S ( 9 0 ) COMMON R O * R » D » B » T O E G » T N E G » R O T » R T » T O E G G * S E H * N F R E Z * W I D T H » W l N D * I F R E Z COMMON J S T » K M A T » K M A T S » N F R Z S » N R M S ( 9 0 ) » M H D Y S ( 4 ) t N R M H S ( 9 0 ) » H T D Y H ( 4 ) COMMON R E C H ( 4 0 0 ) » E G N H ( 9 0 0 ) » T N R H ( 3 0 0 ) * M T H D Y ( 4 ) • N R M H ( 9 0 ) • K M A T H . K M T H S COMMON R O H * R H * D H » B H » TOGHF » T N E G H * R O H S » H S E H » T O G H S » T N G H S COMMON H N T M F ( 9 0 ) i H N T M S ( 9 0 ) GO TO ( 1 2 0 * 1 3 0 ) * M 120 C O N T I N U E C A L L M A T R E C f K A » J M A T • R M A T » S O M A ) K M = ( I T - M D A Y ( N F R E Z ) ) + l I U P P R » L M A T - 1 LWR=2 INT = 1 IDD=2 C A L L I N T M A T ( I U P P R » L W R » I N R A M » I N T » I D D ) TM = KM M D = J S T - 1 MND = 0 C A L L M A M R T ( 1 • J M A T • T M . S O M A • M D » M N D » Y C P T » O S L P » R M A T ) R E T U R N 1 3 0 C O N T I N U E F R D Y = J S T - T I M E I F ( F R D Y ) 1 1 0 . 1 1 1 * 1 1 1 1 1 0 F R D Y = 0 . 0 111 C O N T I N U E C A L L M A T R E C ( K A » J M A T » R M A T » S O M A ) K M = I T - M D A Y ( N F R Z S ) +1 LWR = 2 I U P P R = L M A T INT = 1 IDD=2 C A L L I N T M A T ( I U P P R » L W R • I N R A M » I N T » I D D ) TM = KM M D = T I M E + F R D Y MND=0 C A L L M A M R T ( 1 » J M A T » T M » S O M A • M D * M N D » Y C P T » O S L P * R M A T ) R E T U R N END 2 0 3 C c ###•*•******* ********************************************* ************* C *********************************#*********************************** c SUBROUTINE MATURD(KLAS .TOTAL.ARRAY.TITLE »ITCH) DIMENSION ARRAY(1) COMMON REC(400).NRM190)»EGN(900)»TNR(90).RNTMF(90)»TMT(90) COMMON MTDY(4).MTDYS(4).HTDY(4)•FSTRT(4).FST0P(4).RNTMS(90) COMMON RO.R.D.B.TOEG»TNEG.ROT.RT.TOEGG.SEH.NFREZ.WIDTH .WIND.IFREZ COMMON JST»KMAT»KMATS»NFRZS.NRMS(90) »MHDYS(4) »NRMHS<90) .HTDYH ( 4 ) COMMON RECHJ400).EGNH(900) »TNRH(300).MTHDY(4).NRMHt 90) .KMATH.KMTHS COMMON ROH tRH.DH.BH.TOGHF.TNEGH.ROHS.HSEH.TOGHS.TNGHS COMMON HNTMF(90)»HNTMS(90) TOTAL=0.0 IF(KLAS-1)1160.1161.1162 1161 TOTAL=ARRAY(KLAS) GO TO 1160 1162 CONTINUE DO 1153 JTM=1.KLAS 1153 TOTAL=TOTAL+ARRAY(JTM) 1160 CONTINUE IF(ITCH-1)1000.1000.1100 1000 WRITE(3.10)TITLE.TOTAL 10 FORMA K/.10X."TOTAL FIRST-HATCH '.A4»' WHICH MATURED ».F7.3) RETURN 1100 W R I T E O . l l )TITLE,TOTAL 11 FORMAK/»1 OX t'TOTAL SECOND-HATCH '.A4»' WHICH MATURED '.F7.3) RETURN END 2 0 4 C c S U B R O U T I N E M A T R E C ( M I N C . M A T T t A R R A Y » X L I N E ) D I M E N S I O N A R R A Y ( 1 ) » X L I N E ( 1 ) COMMON R E C ( 4 0 0 ) » N R M ( 9 0 ) » E G N ( 9 0 0 ) » T N R ( 9 0 ) » R N T M F ( 9 0 ) » T M T ( 9 0 ) COMMON M T D Y ( 4 ) . M T D Y S ( 4 ) » H T D Y ( 4 ) . F S T R T U > . F S T 0 P ( 4 ) . R N T M S ( 9 0 ) COMMON RO.R.D.B.TOEG » T N E G » R O T . R T . T O E G G . S E H . N F R E Z . W I D T H . W I N D . I F R E Z COMMON J S T » K M A T » K M A T S » N F R Z S » N R M S ( 9 0 ) » M H D Y S ( 4 ) . N R M H S ( 9 0 ) . H T D Y H ( 4 ) COMMON R E C H ( 4 0 0 ) . E G N H ( 9 0 0 ) . T N R H ( 3 0 0 ) . M T H D Y ( 4 ) . N R M H ( 9 0 ) . K M A T H . K M T H S COMMON ROH .RH.DH.BH.TOGHF.TNEGH.ROHS.HSEH.TOGHS.TNGHS COMMON H N T M F J 9 0 ) . H N T M S ( 9 0 ) J S T 1 = J S T - 1 I F ( M I N C ) 1 . 2 . 3 3 C O N T I N U E I F ( M I N C - 1 ) 1 . 2 . 6 6 C O N T I N U E MTC=MATT-MINC DO 4 J A M = 1 .MINC KKK=MTC+JAM K K = K K K + J S T 1 4 A R R A Y ( K K K ) = X L I N E ( K K ) GO TO 1 2 K K = M A T T + J S T 1 A R R A Y ( M A T T ) = X L I N E ( K K ) 1 C O N T I N U E RETURN END 2 0 5 C c S U B R O U T I N E I N T M A T ( K M . K K J » N M T » I N T . I D D ) D I M E N S I O N N M T ( 1 ) COMMON R E C ( 4 0 0 ) » N R M ( 9 0 ) » E G N ( 9 0 0 ) » T N R ( 9 0 ) • R N T M F ( 9 0 ) » T M T ( 9 0) COMMON M T D Y ( 4 ) . M T D Y S ( 4 ) * H T D Y ( 4 ) » F S T R T ( 4 ) » F S T 0 P ( 4 ) . R N T M S ( 9 0 ) COMMON R O * R » D » B » T O E G » T N E G > R O T » R T » T O E G G . S E H » N F R E Z » W I D T H » W I N D » I F R E Z COMMON J S T » K M A T » K M A T S . N F R Z S » N R M S ( 9 0 ) » M H D Y S ( 4 ) »NRMHS(90) .HTDYH(4) COMMON RECH(400)» E G N H ( 9 0 0 ) »TNRH(30 0 ) » M T H D Y ( 4 ) • N R M H ( 9 0 ) »KMATHiKMTHS COMMON ROH .RH.DH.BH. T O G H F » T N E G H • R O H S * H S E H i T O G H S i T N G H S COMMON H N T M F ( 9 0 ) » H N T M S ( 9 0 ) I F ( K M - K K J ) 2 2 0 . 2 2 0 . 2 2 1 2 2 1 CONTINUE DO 158 K I = K K J .KM J D I F F = N M T ( K I ) - N M T ( K I - l ) I F ( J D I F F - l ) 1 5 9 . 1 5 7 . 1 6 0 157 T M T ( I D D ) = I N T IDD=IDD+1 GO TO 1 5 6 16 0 X D I F F = 1 . 0 / J D I F F DO 3 0 0 I = 1 . J D I F F T M T ( I D D ) = X D I F F 3 0 0 IDD=IDD+1 1 5 6 INT=1 GO TO 15 8 15 9 I N T = I N T + 1 158 CONTINUE GO TO 161 2 2 0 T M T ( K M ) = 1 1 6 1 RETURN END 2 0 6 C C c SUBROUTINE MAMRT<JJK.KMO.TM.SOMA.MM I.MNI•YCPT•OSLP.RRMAT) DIMENSION SOMA(1)»RRMAT ( 1) COMMON REC I 4-00) »NRM(90) »EGN(900) .TNR(90) .RNTMF (90) .TMT (90) COMMON MTDY(4).MTDYS(4).HTDY(4)»FSTRT(4)»FST0P(4)»RNTMS(90) COMMON RO.R»D.B»TOEG.TNEG.ROT.RT.TOEGG.SEH.NFREZ.WIDTH .WIND.IFREZ COMMON JST »KMAT.KMATS»NFRZS.NRMS(90).MHDYS(4).NRMHS(90) .HTDYH(4) COMMON RECHI 400).EGNH(900) »TNRH(300)»MTHDY(4)»NRMH(90) .KMATH.KMTHS COMMON ROH.RH.DH.BH.TOGHF.TNEGH.ROHS.HSEH.TOGHS.TNGHS COMMON HNTMF(90)»HNTMS(90) MM = MM I MN=MNI DO 150 LL=JJK.KMO TMETM-TMT(LL) MM=MM+1 MN=MN+1 SOMA(MM)=RRMAT(MN)/(1.0+EXP(-YCPT+(OSLP#TM))) IF(SOMA(MM)•LT•1•OE-4)SOMA(MM)=0.0 150 CONTINUE RETURN END 2 0 7 C c S U B R O U T I N E M T S I N ( N U M B » M M X . S O M A » K M T . J O M A T » T I T L E ) D I M E N S I O N S O M A ! 1 ) • J O M A T ( 1 ) COMMON REC I 4 0 0 ) »NRM(90) » E G N ( 9 0 0 ) # T N R ( 9 0 ) » R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) » M T D Y S ( 4 ) » H T D Y ( 4 ) » F S T R T ( 4 ) » F S T O P ( 4 ) » R N T M S < 9 0 ) COMMON R O » R » D » B . T O E G . T N E G . R O T . R T » T O E G G . S E H , N F R E Z . W I D T H . W I N D . I F R E Z COMMON J S T . K M A T . K M A T S . N F R Z S . N R M S ( 9 0 ) . M H D Y S ( 4 ) . N R M H S ( 9 0 ) . H T D Y H ( 4 ) COMMON R E C H ( 4 0 0 ) . E G N H ( 9 0 0 ) . T N R H ( 3 0 0 ) . M T H D Y ( 4 ) . N R M H ( 9 0 ) . K M A T H . K M T H S COMMON R O H . R H . D H . B H . T O G H F » T N E G H t R O H S » H S E H • T O G H S . T N G H S COMMON H N T M F ( 9 0 ) . H N T M S ( 9 0 ) I F ( N U M B - l ) 8 0 0 . 6 0 0 . 7 0 0 7 0 0 CONTINUE KNST=MMX-NUMB+JST DO 59 J J = 1 . N U M B K H = K N S T + J J I F ( S O M A ( K H ) ) 5 9 . 5 9 . 6 0 60 JOMAT(KMT)=MMX W R I T E ( 3 . 2 2 2 ) T I T L E . K M T 2 2 2 F O R M A T ( 1 0 X »A4»• = ' . 1 4 ) W R I T E ( 3 » 2 2 0 ) N U M B 2 2 0 FORMAT(10X.'NUMB= ' . 1 4 ) KMT=KMT+1 59 CONTINUE GO TO 8 0 0 6 0 0 KH=(MMX-NUMB)+1+JST I F ( S O M A ( K H ) ) 7 1 . 7 1 . 7 2 7 2 JOMAT(KMT)=MMX W R I T E ( 3 . 2 2 2 ) T I T L E » K M T W R I T E ( 3 . 2 2 0 ) N U M B 7 1 CONTINUE KMT=KMT+1 RETURN 8 0 0 CONTINUE RETURN END 208 C c S U B R O U T I N E A D L T S ( T S T » K O M X . K . K O . K O M X S . T B A R , T M A X • K O S • T M E . H U R Q . H U R Q S , 1SOMA) D I M E N S I O N S O M A ( 1 ) COMMON R E C ( 4 0 0 ) » N R M ( 9 0 ) . E G N ( 9 0 0 ) , T N R ( 9 0 ) i R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) . M T D Y S ( 4 ) . H T D Y ( 4 ) . F S T R T U ) » F S T 0 P ( 4 ) . R N T M S ( 9 0 ) COMMON R O . R . D . B . T O E G . T N E G . R O T . R T . T O E G G » S E H . N F R E Z . W I D T H . W I N D . I F R E Z COMMON J S T .KMAT.KMATS.NFRZS »NRMS< 9 0 ) » M H D Y S ( 4 ) . N R M H S ( 9 0 ) . H T D Y H ( 4 ) COMMON R E C H ( 4 0 0 ) . E G N H ( 9 0 0 ) . T N R H ( 3 0 0 ) . M T H D Y ( 4 ) . N R M H t 9 0 ) .KMATH.KMTHS COMMON ROH.RH.DH.BH.TOGHF.TNEGH.ROHS.HSEH.TOGHS.TNGHS COMMON H N T M F ( 9 0 ) » H N T M S ( 9 0 ) COMMON /CONST/ R N O F » R N O S » H N O F . H N O S . C N S T 1 . C N S T 2 . C O N V . K H L D . 8 TMXC.TBRC K L = K - 1 TNOW=K PX=K-TME AGE=TST+KOMX+JST HQND=HURQ-WIND TCALC=TBAR-TMAX I F ( J S T - T M E ) 1 2 6 . 1 2 6 . 4 1 2 1 2 6 LNMC=KOMX+JST I F ( K L - L N M C ) 3 5 0 » 3 5 0 » 3 5 1 3 5 1 CONTINUE DO 1 0 1 K E = L N M C » K L C A L L D Y DGITBAR.TCALC.HUAC.AGE.TNOW.TST) I F ( H U R Q - H U A C ) 4 0 0 . 4 0 0 . 1 0 7 4 0 0 RM=SOMA(KE) I F ( R M ) 1 0 8 . 1 0 8 . 1 0 2 1 0 2 KO=KO+l GO TO 1 0 1 1 0 7 I F ( H Q N D - W I N D ) 1 0 1 » 1 0 1 . 1 0 8 1 0 1 AGE=AGE+1 108 KOMX=KOMX+KO GO TO 4 1 2 3 5 0 KOMX=0 KO = 0 4 1 2 I F ( P X ) 4 1 0 . 4 1 0 . 4 1 3 4 1 0 CONTINUE RETURN 4 1 3 LNMC=KOMXS+TME+l AGE=TST+TME+KOMXS I F ( K L - L N M C ) 3 5 5 . 3 5 5 . 3 5 6 3 5 6 CONTINUE HQNDS=HURQ5-WIND DO 308 KE=LNMC.KL C A L L DYDG(TBAR.TCALC.HUAC.AGE.TNOW.TST) I F ( H U R Q S - H U A C ) 3 0 3 » 3 0 3 . 3 0 5 303 RM = SOMA(KE ) IF(RM)311.311*309 309 K0S=K0S+1 GO TO 308 305 I F ( H Q N D S - W I N D ) 3 0 8 » 3 0 8 » 3 1 1 308 AGE=AGE+1 311 KOMXS=KOMXS+KOS GO TO 35 7 355 KOMXS=0 KOS = 0 357 CONTINUE RETURN END 210 C c c SUBROUTINE D Y D G ( T B A R » T C A L C • H U A C » D Y O N E > T N O W » T S T ) COMMON /CONST/ R N O F » R N O S • H N O F t H N O S » C N S T 1 . C N S T 2 » C O N V . K H L D * 8 TMXCiTBRC DYTWO=TST+TNOW YHU=TCALC#CNST1*SIN(DYTWO*CNST2>+(TBAR*DYTWO) XHU=TCALC*CNST1*SIN(DYONE*CNST2>+(TBAR*DYONE) HUAC=YHU-XHU RETURN END 211 C C C S U B R O U T I N E EGLY(TMAX.TBAR•TST.TNOW.RN.TMTM.KEG) COMMON R E C ( 4 0 0 ) »NRM(90 ) »EGN(900)» T N R ( 9 0 ) . R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) » M T D Y S ( 4 ) . H T D Y ( 4 ) . F S T R T ( 4 ) » F S T 0 P ( 4 ) . R N T M S ( 9 0 ) COMMON R O . R . D . B . T O E G . T N E G . R O T . R T . T O E G G » S E H . N F R E Z . W I D T H . W I N D . I F R E Z COMMON J S T . K M A T . K M A T S » N F R Z S » N R M S ( 9 0 ) » M H D Y S ( 4 ) . N R M H S ( 9 0 ) .HTDYH t 4 ) COMMON R E C H ( 4 0 0 ) . E G N H ( 9 0 0 ) . T N R H ( 3 0 0 ) . M T H D Y ( 4 ) « N R M H ( 9 0 ) .KMATH.KMTHS COMMON R O H . R H . D H . B H . T O G H F . T N E G H » R O H S . H S E H . T O G H S . T N G H S COMMON H N T M F ( 9 0 ) » H N T M S ( 9 0 ) COMMON /CONST/ RNOF.RNOS.HNOF•HNOS.CNST1.CNST2.CONV.KHLD. 8 TMXC.TBRC DATA RNXP / . 1 9 0 2 / DATA EMX / . 0 7 1 / DATA TXP / . 1 3 7 7 / DATA P / . 2 0 1 5 / DATA Q / . 7 9 8 5 / DATA C E P T 1 / 6 2 7 . 0 / DATA S L P 1 / . 1 5 8 7 / DATA C E P T 2 / 1 1 5 9 . 8 / DATA S L P 2 / . 1 1 1 / KTM=TNOW-MTDY{1)+l T=<TST+TNOW)*CNST2 TEMP= <TMXC-TBRC>*COS(T)+TBRC E G G = T M T M * ( E M X * E X P ( T X P * T E M P - R N X P * R N ) ) I 0 N E = ( C E P T 1 * E X P ( - S L P 1 * T E M P ) ) + K T M I F ( I O N E - K H L D ) 8 0 . 8 0 . 8 1 80 E G N < I O N E ) = E G N < I O N E ) + P * E G G GO TO 82 81 E G N ( K H L D ) = E G N ( K H L D ) + P * E G G 82 I T W O = ( C E P T 2 * E X P ( - S L P 2 * T E M P ) ) + K T M I F ( I T W O - K H L D ) 8 3 . 8 3 .84 8 3 E G N ( I TWO)«EGN(I TWO)+Q*EGG GO TO 85 84 E G N ( K H L D ) = E G N ( K H L D ) + Q * E G G 85 CONTINUE RETURN END 212 C c S U B R O U T I N E H T C N E ( T N O W » T M A X » T B A R . T S T . R L R V » T O T L V 1 COMMON R E C ( 4 0 0 ) t N R M ( 9 0 ) » E G N ( 9 0 0 ) . T N R ( 9 0 ) » R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) . M T D Y S ( 4 ) . H T D Y ( 4 ) . F S T R T ( 4 ) . F S T O P t 4 ) . R N T M S ( 9 0 ) COMMON R O . R . D . B . T O E G . T N E G . R O T . R T » T O E G G . S E H . N F R E Z . W I D T H . W I N D . I F R E Z COMMON J S T . K M A T . K M A T S . N F R Z S . N R M S ( 9 0 ) . M H D Y S t 4 ) . N R M H S ( 9 0 ) . H T D Y H ( 4 ) COMMON R E C H ( 4 0 0 ) . E G N H ( 9 0 0 ) . T N R H ( 3 0 0 ) . M T H D Y ( 4 ) » N R M H ( 9 0 ) .KMATH.KMTHS COMMON ROH » R H . D H . B H . T O G H F . T N E G H . R O H S » H S E H . T O G H S . T N G H S COMMON H N T M F ( 9 0 ) » H M T M S ( 9 0 ) COMMON /CONST/ R N O F . R N O S . H N O F , H N O S . C N S T 1 » C N S T 2 . C O N V . K H L D • 8 TMXC.TBRC DATA RHR / . 0 4 7 3 / NT=TNOW KTM=TNOW-MTDY<11+1 RLRV=0.0 I F ( K T M - 1 ) 1 0 . 1 0 . 1 1 11 CONTINUE E X P V = E X P ( - R H R * K T M ) E X P T = E X P ( - R H R ) DO 3 0 0 JHTCH=1.KTM I F ( E G N ( J H T C H ) 1 3 0 0 . 3 0 0 . 2 2 2 2 R L R v = R L R V + ( E G N ( J H T C H ) # R H R ! # E X P v E X P V = E X P V / E X P T 3 0 0 CONTINUE 10 R E C ( N T ) = R E C ( N T ) + R L R V TNEG=0.0 DO 29 J E = 1 .KHLD 2 9 T N E G = T N E G + E G N ( J E ) TNEG=TNEG-TOTLV RETURN END 213 C c S U B R O U T I N E H E G H T ( T M A X » T B A R . T S T • T N O W . K O M X H . H L A R V , T O M A T . L I P • T A N IM) COMMON R E C ( 4 0 0 ) .NRM(90) . E G N ( 9 0 0 ) » T N R ( 9 0 ) . R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) » M T D Y S ( 4 ) . H T D Y ( 4 ) » F S T R T ( 4 ) » F S T O P ( 4 ) » R N T M S ( 9 0 ) COMMON RO.R.D.B.TOEG.TNEG.ROT.RT.TOEGG.SEH.NFREZ.WIDTH.WIND.IFREZ COMMON J S T . K M A T . K M A T S . N F R Z S . N R M S ( 9 0 ) » M H D Y S ( 4 ) . N R M H S ( 9 0 ) . H T D Y H ( 4) COMMON R E C H ( 4 0 0 ) . E G N H ( 9 0 0 ) . T N R H ( 3 0 0 ) . M T H D Y ( 4 ) . N R M H ( 9 0 ) . K M A T H . K M T H S COMMON ROH . R H . D H . B H . T O G H F . T N E G H • R O H S . H S E H . T O G H S » T N G H S COMMON H N T M F ( 9 0 ) . H N T M S ( 9 0 ) COMMON /CONST/ R N O F » R N O S . H N O F » H N O S . C N S T 1 . C N S T 2 . C O N V • K H L D . 8 TMXC.TBRC DATA CC / . 0 5 / DATA T E X P / . 1 3 0 8 / DATA RNXP / . 3 5 9 8 Z DATA CPT / 1 0 5 . 4 / DATA T S L P / 5 . 4 5 / T=(TST+TNOW)*CNST2 T E M P = ( T M X C - T B R C ) * C O S ( T ) + T B R C H D L = C P T - T S L P * T E M P KMDAY=TNOW-MTHDY(1)+1 JHTDY=HDL+KMDAY I F ( J H T D Y - K H L D ) 1 4 . 1 4 . 13 13 JHTDY=KHLD 14 CONTINUE GO T O I 2 0 0 . 3 0 0 . 4 0 0 ) . L I P 2 0 0 CONTINUE E G G S = T O M A T * ( C C * E X P ( T E X P * T E M P - R N X P * T A N I M ) ) E G N H ( J H T D Y ) = E G N H ( J H T D Y ) + E G G S 3 0 0 CONTINUE I F ( K M D A Y - 1 ) 5 7 0 . 5 7 0 . 5 7 2 5 7 2 CONTINUE HLARV=0.0 DO 4 9 9 IJ=1»KMDAY I F ( E G N H ( I J ) ) 4 9 9 . 4 9 9 . 4 9 0 4 9 0 H L A R V = H L A R v + E G N H ( I J ) E G N H ( I J ) = 0 . 0 4 9 9 CONTINUE 5 7 0 TNEGH=0.0 DO 4 5 0 ISRCH=KMDAY.300 I F ( E G N H ( I S R C H ) ) 4 5 0 . 4 5 0 . 4 4 9 4 4 9 TNEGH=TNEGH+EGNH(ISRCH) 4 5 0 CONTINUE RETURN 4 0 0 CONTINUE E G G S = T O M A T * ( C C # E X P ( T E X P * T E M P - R N X P # T A N I M ) ) E G N H ( J H T D Y ) = E G N H ( J H T D Y ) + E G G S RETURN END 214 C C ########### c S U B R O U T I N E I C I K L ( I T N . L N G F R . E G S U P » K F R Z » K O M X . K O M X S . K O M X H »EGHUP.KMXHS 2) COMMON R E C ( 4 0 0 ) » N R M ( 9 0 ) » E G N ( 9 0 0 ) » T N R ( 9 0 ) » R N T M F ( 9 0 ) . T M T ( 9 0 ) COMMON M T D Y ( 4 ) » M T D Y S ( 4 ) t H T D Y ( 4 ) » F S T R T ( 4 ) » F S T 0 P ( 4 ) » R N T M S ( 9 0 ) COMMON RO.R.D.B.TOEG.TNEG.ROT.RT.TOEGG.SEH.NFREZ.WIDTH.WIND.IFREZ COMMON J S T »KMAT »KMA T S . N F R Z S • N R M S ( 9 0 ) » M H D Y S ( 4 ) » N R M H S ( 9 0 ) • H T D Y H ( 4 ) COMMON R E C H ( 4 0 0 ) t E G N H ( 9 0 0 > » T N R H ( 3 0 0 ) » M T H D Y ( 4 ) » N R M H ( 9 0 ) .KMATH.KMTHS COMMON ROH.RH.DH.BH.TOGHF.TNEGH.ROHS.HSEH.TOGHS »TNGHS COMMON H N T M F ( 9 0 ) » H N T M S ( 9 0 ) DATA I M L I M / 9 0 / IF(K F R Z - 1 ) 2 0 . 2 1 » 2 2 2 1 DO 23 J J = 1 . I T N R E C H ( J J ) = 0 « 0 23 R E C ( J J ) = 0 . 0 DO 24 J J = l f I M L I M N R M H S ( J J ) = 0 N R M H ( J J ) = 0 N R M S ( J J ) = 0 T M T ( J J ) = 0 . 0 R N T M F ( J J ) = 0 . 0 R N T M S ( J J ) = 0 . 0 H N T M F ( J J ) = 0 • 0 H N T M S ( J J ) = 0 . 0 24 N R M ( J J ) = 0 KMAT=1 KMATS<=1 KMATH=1 KMTHS=1 K0MX=0 KOMXS=0 KOMXH=0 KMXHS=0 22 C A L L H T C O E ( I T N . l ) E G S U P = R E C ( I T N ) R E C ( I T N ) = 0 . 0 C A L L H T C O E ( I T N . 2 ) E G H U P = R E C H ( I T N ) R E C H ( I T N > = 0 . 0 20 CONTINUE RETURN END 215 C c S U B R O U T I N E S C R B L ( R K » T O Y N G » T T M T » N W » E L » T S T » S P E C S ) COMMON R E C ( 4 0 0 ) » N R M ( 9 0 ) , E G N ( 9 0 0 ) » T N R ( 9 0 ) » R N T M F ( 9 0 ) » T M T ( 9 0 ) COMMON M T D Y ( 4 ) » M T D Y S ( 4 ) # H T D Y ( 4 ) » F S T R T ( 4 ) » F S T 0 P ( 4 > i R N T M S ( 9 0 ) COMMON R O , R » D » B » T O E G • T N E G , R O T » R T » T O E G G » S E H » N F R E Z » W I D T H » W I N D , I F R E Z COMMON J S T »KMAT »KMATS»NFRZS » N R M S ( 9 0 ) » M H D Y S ( 4 ) , N R M H S ( 9 0 ) » H T D Y H ( 4 1 COMMON R E C H ( 4 0 0 ) » E G N H ( 9 0 0 ) , T N R H ( 3 0 0 ) t M T H D Y ( 4 ) » N R M H < 9 0 ) , K M A T H . K M T H S COMMON R Q H » R H » D H » B H » T O G H F » T N E G H » R O H S » H S E H »TOGHS•TNGHS COMMON H N T M F 1 9 0 ) » H N T M S ( 9 0 ) • K = RK WIDTT=5.0*WIDTH GO T O ( 8 6 » 8 8 » 8 9 » 9 0 ) » N W 86 CONTINUE W R I T E ( 3 , 5 3 ) 53 F O R M A K / / / / ) W R I T E ( 3 » 4 5 ) S P E C S 45 F O R M A T ( 1 0 X # ' S P E C I E S - '»A4) W R I T E ( 3 » 6 0 ) R K . T O Y N G 6 0 F O R M A T ( 1 OX•'AT '»F4.0»' D A Y S . T H E R E WERE ' . F 9 o 3 . ' A N I M A L S P R E S E N T . ' 3) W R I T E ( 3 . 4 0 ) T T M T » T O E G » T O E G G 4 0 F O R M A T ( 1 0 X » ' N O . M A T U R E A N I M A L S = »»F9.3»/»10X • 'NO.OLD EGGS OF HATCH 2 ONE= ••F7.3»' AND OF HATCH TWO= ' . F 7 . 3 ) W R I T E ( 3 . 4 1 ) T N E G »EL 4 1 F O R M A T ( 1 OX *'THE NUMBER OF NEW EGGS= ».F7.3»' TOTAL EGGS= ' , F 8 . 3 ) W R I T E ( 3 » 7 5 ) 75 F O R M A T ( / / ) RETURN 88 CONTINUE W R I T E ( 3 » 7 0 ) 70 F O R M A K 1 0 X * ' T H I S TOTAL NUMBER HAD THE FOLLOWING AGE C O M P O S I T I O N - ' , 5/) I F ( ( R E C ( J S T ) * W I D T T 1 - 1 . 0 ) 1 0 9 , 2 4 , 2 4 2 4 W R I T E ( 3 » 7 1 ) 7 1 F O R M A K 1 0 X , » DAY NUMBER P R E S E N T P E R C E N T A G E R E C R U I T S P 6ERCENT OF T O T A L ' , / , 1 0 X » • R E C R U I TED. ' *9X , 'NOW.',9X,'ST I L L A L I V E . ' , 8 X 6, 'NUMBER PRESENT.« ) 10 9 I F ( K - S E H ) 1 0 0 , 1 0 0 , 1 0 1 1 0 0 KWR=K GO TO 1 0 5 10 1 KWR=SEH 10 5 I F ( J S T - K W R ) 1 0 6 » 1 0 6 , 2 8 1 1 0 6 DO 81 IG=JST»KWR PCNT= R E C < I G ) / ( ( R 0 # E X P ( - R # I G ) l / R * ( E X P ( R 1 - 1 . 0 ) 1 * 1 0 0 . 0 P N T = ( R E C ( I G ) / T O Y N G 1 * 1 0 0 . 0 I F ( P N T ) 7 4 , 8 3 , 8 3 7 4 PNT=0.0 83 I F ( ( R E C ( I G ) * W I D T T 1 - 1 . 0 ) 8 1 , 8 1 , 8 2 216 82 WRITE(3»85)IG»REC(IG)»PCNT »PNT 8 5 F O R M A T ( 1 2 X . I 3 . 1 0 X . F 8 . 3 . 1 0 X . F 7 . 3 . 1 3 X . F 7 . 3 ) 81 CONTINUE 281 CONTINUE WRITE(3.75) I F (K-SEH )108 .108 .104 104 JX=SEH+1 WR ITEO .71 ) DO 102 KH=JX.K I F (HTDY (1 ) )10*10 .20 20 I F (KH-HTDY(1 ) )10 .66 .66 10 PCNT=REC(KH)/ ( (ROT*EXP(-RT* (KH-SEH) ) )/RT*tEXP (RT)-1.0 ) ) *100.0 GO TO 67 66 KHT=KH-HTDY(1)+l PCNT = REC(KH)/TNR(KHT)* 100 . 0 67 PNT=(REC(KH)/TOYNG)*100.0 I F ( PNT )102 .102 .110 110 WR ITEO . 8 5 ) KH »REC ( KH) .PCNT.PNT 102 CONTINUE 108 CONTINUE RETURN 89 CONTINUE WRITE(3.45 JSPECS WRITE(3.60)RK»TOYNG WRITE(3.40)TTMT.TOGHF.TOGHS WRITE(3.41JTNEGH.EL WRITE(3.75) RETURN 90 CONTINUE WRITE(3.70) I F ( (RECH( JST ) *WIDTT1-1 .0 )309 .324 .324 324 WRITE(3.71) 309 I F (K-HSEH)300.300.301 300 KWR=K GO TO 305 301 KWR=HSEH 305 IF ( JST-KWR)306.306.481 306 DO 381 IG=JST.KWR PCNT = RECH( IG)/( (ROH*EXP(-RH*IG) )/RH*(EXP(RH)-1.0 ) ) *100 .0 PNT=(RECH(IG)/TOYNG)*100.0 I F ( PNT )374 .383 .383 374 PNT=0.0 38 3 IF( (RECH ( IG ) *WIDTT)-1 .0 )381 .38 1»382 382 WRITE(3»85)IG»RECH(IG).PCNT.PNT 381 CONTINUE 481 CONTINUE WRITE(3»75 ) I F (K-HSEH)308.308 .304 304 JX=HSEH+1 WRITE(3.71) DO 302 KH=JX»K I F (HTDYH(1 ) )310 .310 .320 320 IF(KH-HTDYH(1))310»366.366 310 PCNT=RECH(KH)/( (ROHS*EXP(-RH*(KH-HSEH)) )/RH*(EXP(RH)-1.0)1*10 0.0 GO TO 367 366 KHT=KH-HTDYH(1)+l PCNT=RECH(KH)/TNRH(KHT)*100.0 217 367 PNT=(RECH(KH)/TOYNG)#100.0 IF(PNT)302*302*410 410 WRITE(3*85)KH»RECH(KH)»PCNT»PNT 302 CONTINUE 308 CONTINUE RETURN END C 9 • a o i y 3 d Niazoyj v O N i y n a 9 SiydA90X3dy3H dO S993 (33H9XVHNn a3iVinwnjDV dO y39W0N - HV93 9 •aoiysd 9 N3zoyj v 9Niyna snxoNiydA9 d o SDOS Q3H9XvHNn a s x v m w r m v - 9V93 9 9 •993 lOdNI y3d 9 a3yino3y (jj»y93a-Ava d o •ON SHX J O 3svsa9Ni 30 s x v y 3Hi - J L I S N Q 9 9 •siaarid >9vyx-3yAX 3Hi 9 30 aN3 Hinos 3HX woyd 39vds do XIIMH SHX do S D N V I S I Q 3 H I - xsia 9 9 •3WIX 30 1VAH31NI SHX 9 N I lN3S3Hd "1VWINV y3d SIydA90X3dy3H dO AXIIVXyOW 3 H 1 HQ 3 9 •3WI1 dO IVAySlNI 9 3HX IM I iN3S3yd 1VWINV y3d SnX0IMiydA9 dO AIIIVIUOW 3 H 1 0 9 9 •SSV19-39V NV NI 9 •NiydA9 3ynivw d o Mouyodoyd 3Hi d o 3SV3y93a d o 3ivy SHX - d i S 9 9 9 •lN3S3yd H91VH-C1N093S 3Hi dO SrUONIHdAD a d f U V W dO ysaWPN 3HI - ZNI9 9 9 •iN353yd H91VH-iSyid 3 H 1 dO SrUONIHdAD 3yniVW dO y38WHN 3H1 - INI9 9 9 •39VdS dO UNO 3H1 0 1 9 y31!MIM sn0IA3yd 3Hi WOyd S993 Sni0NiydA9 dO indlMI I V l O i 3 H 1 - 9939 9 9 •Aiiyruvw 9 H9V3y 01 »NiydA9 yOd (d)S33y93a-AVa dO 'ON WnwINIW 3Hi -OCIACO 9 9 • i w i i Ava 3 H I NO synxvw 9 SSV19-39V SniONiydA9 V dO 39VlN33y3d 3HX dO •001 » 1 V N 3H1 «* id99 9 9 •SiydA90i3dy3H yOd XN3S3yd 9 n v n a i A i a N i y3d s i v y A i n v x y o w S H I d o 3sv3y9Ni do 3ivy S H I He 9 9 •smoNiydA9 yod XN3S3yd 9 i v n a i A i a N i y3d s i v y A i n v x y o w 3HX d o 3sv3y9Ni d o 3xvy 3HX 9 9 • A I N O wvyooyd NIVW 3HX N I 9 yf1990 H9IHM S3IXIXNVD0 3HX dO XSI1 V 9 SI N0IX93S SIHX 9 tttt#tttt###tttt## tt*tttttt#tt#*tt##tt#tttttttt 9 • i xsny9 i w v y o o y d 3HX N I SSWVN 3HX d o NoixvNvidxs 9 ##tttttt**tttttttt#tt#tttt*tttt*#^ 9 a * * * * * * * * * a-**-***-** #tttttt#*tt#tttttt^# 9 812 C E G H U P - S A M E A S ' E G S U P ' B U T F O R H E R P E T O C Y P R I S . C C E G N - A N A R R A Y T O W H I C H T H E S U B R O U T I N E 1 E G L Y • A S S I G N S E G G S L A I D C B Y C Y P R I N O T U S A C C O R D I N G T O T H E T I M E A T W H I C H H A T C H I N G O F T H E E G G S S H O U L D B E G I N . C C E G N H - T H E S A M E A S E G N B U T F O R H E R P E T O C Y P R I S ( S U B R O U T I N E ' H E G H T ' ) . C C E G S U P - I S T H E N U M B E R O F C Y P R I N O T U S E G G S W H O S E H A T C H I N G O N T H E D A Y C W A S S U P P R E S S E D B Y F R E E Z I N G . C C E L - I S T H E T O T A L N U M B E R O F U N H A T C H E D C Y P R I N O T U S E G G S P R E S E N T C O N A D A Y R E G A R D L E S S O F T H E I R A G E . C C E L H - T H E T O T A L N U M B E R O F H E R P E T O C Y P R I S E G G S U N H A T C H E D . C C E X P O S - T H E N U M B E R O F D A Y S W I T H O U T W A T E R W H I C H R E S U L T S I N T H E C D E A T H O F H A L F T H E A N I M A L S . C C E X W R T - T H E I N T E R V A L I N D A Y S B E T W E E N W R I T I N G O U T C U R R E N T S T A T E C O F T H E P O P U L A T I O N . C C F R D Y - I S T H E N U M B E R D A Y S F R O M ' S E H ' T H A T T H E L A S T P E R I O D O F C F R E E Z I N G O C C U R R E D . I T C A N B E B O T H N E G A T I V E A N D P O S I T I V E . C C F S T O P - T H E T I M E I N D A Y S S I N C E F I L L I N G T H A T A P E R I O D O F F R E E Z I N G C W I L L E N D . C C F S T R T - T H E T I M E I N D A Y S S I N C E F I L L I N G T H A T A P E R I O D O F F R E E Z I N G C W I L L B E G I N . C C H C P T - T H E S A M E A S C C P T B U T F O R H E R P E T O C Y P R I S . C C H D L Y - T H E N U M B E R O F C O N S E C U T I V E D A Y S O F S U B M E R G E N C E T I L L T H E E G G S C B E G I N T O H A T C H . C C H D Y D G - T H E S A M E A S C D Y D G B U T F O R H E R P . . C C H E G G - T H E T O T A L I N P U T O F H E R P E T O C Y P R I S E G G S F R O M T H E P R E V I O U S C W I N T E R T O T H E U N I T O F S P A C E . C C H L A R V - T H E N U M B E R O F H E R P E T O C Y P R I S H A T C H I N G F R O M N E W L Y - L A I D C E G G S O N T H E D A Y . C C H N O F - S A M E A S F O R • R N O F ' B U T F O R H E R P E T O C Y P R I S . C C H N O S - S A M E A S F O R ' R N O S ' B U T F O R H E R P E T O C Y P R I S . C C H N T M F - S A M E A S ' R N T M F ' B U T F O R H E R P E T O C Y P R I S . C C H N T M S - S A M E A S ' R N T M S ' B U T F O R H E R P E T O C Y P R I S . C C HP1 - T H E N U M B E R O F M A T U R E H E R P E T O C Y P R I S O F T H E F I R S T - H A T C H C P R E S E N T N O W . C C HP2 - S A M E A S 'HP1' B U T F O R H E R P E T O C Y P R I S S E C O N D - H A T C H . C 2 2 0 C HSEH - THE TIME I N DAYS A F T E R 'TST' OF I N I T I A T I O N OF THE SECOND-C HATCH OF THE OLD STORED H E R P E T O C Y P R I S EGGS. C C H S L P - THE SAME AS C S L P BUT FOR H E R P . . C C HTDY - THE F I R S T DAY ON WHICH N E W L Y - L A I D C Y P R I N O T U S EGGS B E G I N C TO H A T C H . C C HTDYH- THE F I R S T DAY ON WHICH N E W L Y - L A I D H E R P E T O C Y P R I S EGGS B E G I N C TO HATCH. C C HTT - THE TOTAL NUMBER OF MATURE A N I M A L S OF BOTH S P E C I E S P R E S E N T C ON A P A R T I C U L A R DAY. C C HURQ - THE NUMBER OF DAY-DEGREES R E Q U I R E D FOR THE MATURATION OF C EACH A G E - C L A S S OF F I R S T - H A T C H A N I M A L S OF BOTH S P E C I E S . C C HURQS- THE SAME AS 'HURQ' BUT FOR THE SECOND-HATCH. C C I F R E Z - THE NUMBER OF T I M E S THAT THE PART OF THE PUDDLE W I L L BE C FROZEN DURING THE 'YEAR'. C C I H F N D - SAME AS ' K F I N D ' BUT FOR H E R P E T O C Y P R I S . C C I M F I X - SAME AS 'MTFIX* BUT FOR C Y P R I N O T U S SECOND-HATCH. C C I M L I M - THE LENGTH OF S E V E R A L ARRAYS S T O R I N G THE NUMBER OF MATURE C A G E - C L A S S E S ON EACH DAY DURING THE P E R I O D OF M A T U R A T I O N . C C I R I T E - A CONSTANT WHOSE S I G N CONTROLS THE OUTPUT OF R E S U L T S . C C J S T - I S THE DAY ON WHICH THE L A S T FROZEN P E R I O D E N D E D . I F ' I F R E Z • C I S ZERO THEN 'JST'=1. C C K - I S THE.NUMBER OF DAYS S I N C E THE UNIT OF S P A C E WAS SUBMERGED C AND I T S MAXIMUM V A L U E I S ' L T ' . C C K F I N D - AN INDEX USED TO F I N D THE F I R S T DAY ON WHICH N E W L Y - L A I D C C Y P R I N O T U S EGGS HATCH. C C K F R Z - I S AN INTEGER V A R I A B L E WHICH WHEN P O S I T I V E I N D I C A T E S THE C OCCURRENCE OF A FROZEN P E R I O D AND I N I T I A T E S THE R E S U L T I N G C R E O R G A N I Z A T I O N OF THE P O P U L A T I O N S . I T I S THE NUMBER DAYS C THAT THE U N I T HAS B E E N F R O Z E N . C C KHH - I S THE SAME AS 'KMH' BUT FOR H E R P E T O C Y P R I S . C C KHLD - THE LENGTH OF THE A R R A Y S I N WHICH NEW-EGGS ARE P L A C E D . C C K L - THE NUMBER OF DAYS S I N C E SUBMERGENCE MINUS ONE. C C K L K - I S THE NUMBER OF A G E - C L A S S E S OF H E R P E T O C Y P R I S P R E S E N T C R E G A R D L E S S OF WHETHER THEY HAVE MEMBERS OR ARE MATURE. C C KM - I S THE NUMBER OF DAYS S I N C E THE F I R S T C Y P R I N O T U S AGE C MATURED. 2 2 1 C C KMH - I S THE NUMBER OF DAYS S I N C E THE. F I R S T OF THE N E W L Y - L A I D C C Y P R I N O T U S EGGS HATCHED. C C KMM - I S THE NUMBER OF DAYS S I N C E THE F I R S T H E R P E T O C Y P R I S C A G E - C L A S S MATURED. C C KMAT - THE NUMBER OF DAYS REQUIRED FOR C Y P R I N O T U S F I R S T - H A T C H A G E -C C L A S S E S TO MATURE UP TO THE P R E S E N T . C C KMATH- THE NUMBER OF DAYS REQU I R E D FOR H E R P E T O C Y P R I S F I R S T - H A T C H C AGE*-CLASSES TO MATURE UP TO THE P R E S E N T . C C KMATS- SAME AS 'KMAT• FOR SECOND-HATCH C Y P R I N O T U S . C C KMTHS- SAME AS 'KMATH • BUT FOR H E R P E T O C Y P R I S SECOND-HATCH. C C KMXHS- SAME AS 'KOMXH' BUT FOR SECOND-HATCH H E R P E T O C Y P R I S . C C KO - THE NUMBER OF AGES OF F I R S T - H A T C H C Y P R I N O T U S MATURING ON A C P A R T I C U L A R D A Y . I T I S C A L C U L A T E D BY THE S U B R O U T I N E ' A D L T S * . C C KOH - THE SAME AD 'KO' BUT FOR H E R P E T O C Y P R I S . C C KOHS - THE SAME AS 'KOS' BUT FOR H E R P E T O C Y P R I S . C C KOMX - THE NUMBER OF MATURE F I R S T - H A T C H C Y P R I N O T U S A G E - C L A S S E S UP C T I L L THE P R E S E N T . C C KOMXH- THE TOTAL NUMBER OF MATURE F I R S T - H A T C H H E R P E T O C Y P R I S AGE-C C L A S S E S UP T I L L THE P R E S E N T . C C KOMXS- SAME AS 'KOMX' BUT FOR SECOND-HATCH C Y P R I N O T U S . C C KOS - SAME AS 'KO» BUT FOR SECOND-HATCH C Y P R I N O T U S . C C KRCR - THE NUMBER OF E L E M E N T S IN THE ARRAY S T O R I N G THE R E C R U I T S C FOR EACH DAY. C C KT THE NUMBER OF T I M E S THAT THE S T A T E OF THE P O P U L A T I O N I S C R E P O R T E D . C C KY - I S THE TOTAL NUMBER OF NON-MATURE A G E - C L A S S E S OF C Y P R I N O T U S C R E G A R D L E S S OF WHETHER THEY HAVE MEMBERS. C C L N G F R - THE NUMBER OF DAYS THAT THE UNIT OF S P A C E W I L L BE F R O Z E N . C C LT - THE LENGTH I N DAYS BETWEEN SUBMERGENCE AND D E S I C C A T I O N OF C THE UNIT OF S P A C E . C C M H F I X - AN INDEX USED TO F I N D THE DAY ON WHICH THE F I R S T A G E - C L A S S C OF H E R P E T O C Y P R I S F I R S T - H A T C H A N I M A L S REACHES M A T U R I T Y . C C MHFXS- SAME AS 'MHFIX' BUT FOR H E R P E T O C Y P R I S SECOND-HATCH. C C MTDY - THE T I M E I N DAYS S I N C E F I L L I N G THAT THE MEMBERS OF F I R S T -C HATCH C Y P R I N O T U S W I L L B E G I N TO MATURE. 222 C C M T F I X - AN INDEX USED TO F I N D THE DAY ON WHICH THE F I R S T A G E - C L A S S C OF C Y P R I N O T U S F I R S T - H A T C H A N I M A L S REACHES M A T U R I T Y . C C MTDYS- THE TIME I N DAYS S I N C E F I L L I N G THAT MEMBERS OF C Y P R I N O T U S C HATCH-TWO W I L L B E G I N TO MATURE . C C MTHDY- AS FOR 'MTDY' BUT FOR H E R P E T O C Y P R I S . C C MHDYS- AS FOR 'MTDYS' BUT FOR H E R P E T O C Y P R I S . C C NCL - THE NUMBER OF A G E - C L A S S E S OF A P A R T I C U L A R PART OF THE C P O P U L A T I O N OF ONE S P E C I E S . C A L C U L A T E D BY THE S U B R O U T I N E C •TARND'• C C N F R E Z - THE NUMBER OF FROZEN P E R I O D S THAT HAVE OCCURRED UP T I L L THE C P R E S E N T TO THE F I R S T - H A T C H A N I M A L S ( M I N U S O N E ) . C C N F R Z S - SAME AS 'NFREZ' FOR SECOND-HATCH C Y P R I N O T U S . C C N F Z H S - SAME AS 'NFREZ * FOR SECOND-HATCH H E R P E T O C Y P R I S . C C NMA - I S THE DAY ON WHICH THE OLDEST MATURE A G E - C L A S S WAS C R E C R U I T E D . C C NO THE TOTAL NUMBER OF C Y P R I N O T U S A G E - C L A S S E S WHICH HAVE C MEMBERS. C C NOH - THE TOTAL NUMBER OF P O S I T I V E A G E - C L A S S E S OF H E R P E T O C Y P R I S . C C NRM - I S THE NUMBER OF MATURE A G E - C L A S S E S WITH MEMBERS OF THE C C Y P R I N O T U S F I R S T - H A T C H P R E S E N T ON A DAY DURING THE C MATURATION P E R I O D . THE V A L U E S ARE A S S I G N E D BY THE S U B R O U T I N E C • M T S I N ' AND THE MAXIMUM LENGTH OF THE ARRAY USED I S C DETERMINED BY THE NUMBER OF DAYS R E Q U I R E D FOR A L L THE C A N I M A L S TO MATURE. C C NRMH SAME AS 'NRM' BUT FOR H E R P E T O C Y P R I S . C C NRMHS- SAME AS 'NRMS' BUT FOR H E R P E T O C Y P R I S . C C NRMS SAME AS 'NRM* BUT FOR C Y P R I N O T U S SECOND-HATCH. C C P C I - THE PROPORTION OF CEGG IN THE F I R S T H ATCH. C C PC2 - THE PROPORTION OF CEGG IN THE SECOND H A T C H . C C P H I - THE PROPORTION OF HEGG IN THE F I R S T HATCH. C C PH2 - THE PROPORTION OF HEGG IN THE SECOND H A T C H . C C R THE INSTANTANEOUS RATE OF H A T C H I N G OF F I R S T - H A T C H C C Y P R I N O T U S EGGS. C C REC - THE ARRAY IN WHICH EACH DAYS C Y P R I N O T U S R E C R U I T S ARE C STORED.THE LENGTH OF THE ARRAY USED IS G I V E N BY C ( 1 T S T P ' - ' T S T ' ) . T H E A N I M A L S R E M A I N ORDERED ACCORDING TO THE 223 C DAY A F T E R F I L L I N G THAT THEY WERE R E C R U I T E D AND DURING EACH C I N T E R V A L OF TIME EACH P O S I T I V E ELEMENT I S DECREMENTED C BY AN AMOUNT G I V E N BY ONE OF THE M O R T A L I T Y S U B R O U T I N E S C A F T E R THE B E G I N N I N G OF A P E R I O D OF F R E E Z I N G THE WHOLE ARRAY C I S C L E A R E D . C C RECH - THE SAME AS ' REC ' BUT FOR H E R P E T O C Y P R I S . C C RH THE INSTANTANEOUS H A T C H I N G RATE OF OLD STORED C H E R P E T O C Y P R I S EGGS. C C RLRV - THE NUMBER OF C Y P R I N O T U S HATCHING FROM N E W L Y - L A I D EGGS ON C THE DAY. C C RN THE TOTAL NUMBER OF C Y P R I N O T U S PRESENT ON A P A R T I C U L A R DAY. C C RNH - THE TOTAL NUMBER OF H E R P E T O C Y P R I S PRESENT ON A P A R T I C U L A R C D A Y S . C C RNOF - THE NUMBER OF THE C Y P R I N O T U S EGG-INPUT THAT A P P E A R C I N THE F I R S T EGG-HATCH. C C RNOS - THE NUMBER OF THE C Y P R I N O T U S EGG-INPUT THAT A P P E A R C I N THE SECOND EGG-HATCH. C C RNTMF- THE NUMBER OF A N I M A L S IN EACH C Y P R I N O T U S A G E - C L A S S WHICH C M A T U R E D ( F I R S T - H A T C H ) . C C RNTMS- THE NUMBER OF A N I M A L S IN EACH C Y P R I N O T U S A G E - C L A S S WHICH C M A T U R E D ( S E C O N D - H A T C H ) . C C RNTOT- THE TOTAL NUMBER OF OSTRACODS P R E S E N T ON A P A R T I C U L A R DAY. C C RO - THE NUMBER OF F I R S T - H A T C H C Y P R I N O T U S EGGS H A T C H I N G C I N I T I A L L Y . C C ROH - THE NUMBER OF F I R S T - H A T C H H E R P E T O C Y P R I S EGGS H A T C H I N G C I N I T I A L L Y . C C ROHS - THE NUMBER OF SECOND-HATCH H E R P E T O C Y P R I S EGGS HATCHING C I N I T I A L L Y . C C ROT - THE NUMBER OF SECOND-HATCH C Y P R I N O T U S EGGS H A T C H I N G C I N I T I A L L Y . C C RT THE INSTANTANEOUS H A T C H I N G RATE OF SECOND-HATCH C C Y P R I N O T U S EGGS. C C SEH - THE TIME I N DAYS A F T E R 'TST' OF I N I T I A T I O N OF SECOND-HATCH C OF THE OLD STORED C Y P R I N O T U S EGGS C C STNO - THE INPUT OF F I R S T - H A T C H EGGS OF BOTH S P E C I E S TO THE C I C E - F R E E P E R I O D OF T I M E . C C STNOS- SAME AS 'STNO' BUT FOR THE SECOND-HATCH OF BOTH S P E C I E S . C C TBAR - THE MEAN ANNUAL TEMPERATURE IN DEGREES FAHRENH. 3 9 9 •ie A i n r 01 i onv woyj y v 3 A 3NO JO a o i y s d v - y v 3 A 9 3 • , S l i a V i NI dOOl 3H1 WOyj 1IX3 N I SnnS3W 030339X3 N3HM 0 HDIH/V, ioynH,.woyj IDVOH, 30 sss y o s a A v a NI NOIIVIAHO 3Hi - GNIM 3 3 •W3 NI 3iaand .ll, 3H1 dO H10 IM NV3W 3H1 -HJ.OIM 3 °iN3S3yd s i y d A 3 o i 3 d y 3 H 3ynxvw do ysgwrw i v i o i SHI -HIWII 3 3 • s i N 3 S 3 y d snioNiydAD 3ynivw do ysgwrw i v i o i 3HI - i w i i 3 " " "" 3 •S993 0IVI-A1M3N 3 woyj a 3 i i n y 3 3 y s i y d A 3 o i 3 d 3 H JO ysswnN S A i i y m w n o SHI - H M U 3 3 'SAVO iS0dX3i Hod 031V33IS3a SVM 3 3"iaond 3nx do i y v d 3 Hi IVHI I onv y s i d v SAVO do ysawnw SHI - d i s i 3 3 • S A V a - i A I O H I yod asbyswans SVM 3 3naand SHI do i y v d 3Hi IVHI I onv y s i s v SAva NI 3WU 3,HI - i s i 3 3 °S993 0IV1-A1M3N 3 WOyd 9NIH31VH SniOMiydA3 dO ySSWDN 1V101 3AUVinwn3 3H1 -A1101 3 3 NIVWSy IVHI S'993 SI ydA90i 3d«3H H91VH-aN033S dO y38Wf1N 3H1 -SH901 9 9 NIVW3« IVHI S993 SiydA0O13dy3H H91VH~lSyId dO y39WflN 3H1 -3H901 9 9 •NIVW3y I V H i S993 SDiONiydAD H9J.VH-0NOD3S dO y33WnN 3H1 -99301 9 9 •NIVW3y IVHI S993 SfUONiydAD HjJ.VH-J.Sy I d dO y39WHN 3H1 - 9301 9 9 °s iydA9oi3dy3H yod m a sv 3WVS - Hywi 9 9 •ci3idn330 l w s s s y d i v Avyyv- 3H1 do HIONSI 9 3H1 SI II ONV IW>I AB N3AI9 SI A VC] 3H18NH93G SVH S993 9 M3N do 9NIH31VH'SHI y s i d v AVO v NO a 3 i i n y 3 3 y Sni0NiydA9 9 30 y39Wni\J "1V101 3H1 SI 1N3W313 H3V3 HDIHW NI AVyyV MV S I - y N l ' 9 9 • i w y o j nvsy) 3DN3oy3W9ns 39NIS SAVO do y3awnN 3Hi - MONI 9 9 •S1VWINV M91VH-CJN033S yOd ih'93Nii SV 3WVS -SH9N1 9 9 "S1VWINV HjJ.VH-J.Sy Id A3 0IVT.N339 3AVH 9 IVHI S 9 9 3 SiydA3013dy3H 03H31VHNin M3N dO y3aWflM 1V101 3H1 -H93N1 9 9 •S093 SniONiydAD 03H31VHNn M3N dO dSQWON 1V101 3H1 - 93N1 9 9 •SH2aW3W 9 SVH m i IS H9IHK SSV13-39V ' NV 30 NOUVyniVW 3H1 N33MJ.39 SAVO 9 do s r y v d yo SAVO NI s 1VAy3j.Ni SHI SNIVINOS HDIHM OSTIVD 9 s i i ivwi . N i i S N i i n o y a n s 3Hi BWIJ. HJVS asivyaNSO Avyyv NV SI - IWI 3 3 •asynivw 9 SSV"13-39V 3H1 1VW1 9NIH91VH y31dV SAVQ dO ysaWDN 3H1 Wl 9 9 0HNSyHVd s s a y o s a NI 3ynivy3dW3i AIHINOW wnwixvw SHI - xvwi 9 9 vzz 

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