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Of flies, fitness and fluctuating environments Roff, Derek A. 1976

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OF FLIES, FITNESS &.N.D FLUCTUATING ENVIRONMENTS E Y DEREK A. EOFF B.Sc.(Hons.), Sydney U n i v e r s i t y , 1971 A THESIS SUBMITTED IN PARTIAL FULFILLMENT O.F THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Zoology He accept t h i s t h e s i s as conforming to the r e g u i r e d standard THE UNIVERSITY OF B R I T I S H COLUMBIA NOVEMBER?, „ 19267 (T) Derek A. Roff, 1976 In presenting th is thesis in par t ia l fu l f i lment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shal l make i t f reely avai lable for reference and study. I further agree that permission for extensive copying of th is thesis for scholar ly purposes may be granted by the Head of my Department or by h is representatives. It i s understood that copying or publ icat ion of th is thesis for f inanc ia l gain shal l not be allowed without my written permission. Department of 2 Q OL O C^W The University of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date \X /l/tyvt^LtW /f7/£ i ABSTRACT Environmental h e t e r o g e n e i t y may be important i n determining the amount of g e n e t i c v a r i a t i o n w i t h i n a p o p u l a t i o n . P r e v i o u s t h e o r e t i c a l s t u d i e s have an a l y s e d the importance of s p a t i o - t e m p o r a l v a r i a b l i t y f o r e c o l o g i c a l g e n e t i c s w i t h i n a very general framework. The present study attempts to analyse the consequences of environmental h e t e r o g e n e i t y f o r a p a r t i c u l a r e c o l o g i c a l l y important c h a r a c t e r . The study i s concerned with the e v o l u t i o n of body s i z e i n an ' r - s e l e c t e d * p o i k i l o t h e r m . Is body s i z e . The measure of f i t n e s s , r , i s determined by the f e c u n d i t y of the organism and i t s development time. These two l i f e h i s t o r y c h a r a c t e r s are c o r r e l a t e d to body s i z e and hence the l a t t e r may be used as a measure of changes i n l i f e h i s t o r y parameters, whether or not s e l e c t i o n a c t s d i r e c t l y upon body s i z e . A model i s presented that r e l a t e s the e f f e c t o f s p a t i a l and temporal v a r i a t i o n on body s i z e . T h i s e f f e c t may be due to d i r e c t e f f e c t s on body s i z e as with s i z e s e l e c t i v e p r e d a t i o n or due t o e f f e c t s upon other c h a r a c t e r s such as development time. To demonstrate that the behaviour .of the model does not r e s u l t from i m p l a u s i b l e assumptions or parameter values the model i s developed with r e f e r e n c e to an organism f o r which these f a c t o r s have been reasonably well s t u d i e d . T h i s group i s the D r o s o ^ h i l a and most p a r t i c u l a r l y , D£Osop_hila melafi03astern The c o n c l u s i o n s drawn from the model i i are t h a t s p a t i a l and temporal v a r i a b i l i t y can determine both the optimum body s i z e and the range i n body s i z e and t h a t ' r a r e ' events may have s i g n i f i c a n t l y more e f f e c t on the e v o l u t i o n of body s i z e than the most f r e q u e n t l y o c c u r r i n g c o n d i t i o n s . i i i TABLE OF CONTENTS LIST OF FIGURES i v XiIST OF T A BXE S • • • • • • • * • • • » • • • • • • • * • • • * *••*•• *'••••• • > • • *1 • • • • v x X FX R ST T HO UGHTS • • • • • • * • • • • • • • • • • • ••••#"* • •• * * • 1 I NT ROD OCTXO H « • • • • • • •••••• • • • • •«• • * • • • • • • • • • • * • • • # • • • • • • • • 2 THB LIFB-HISTORY CHAR ACTERISTICS OF DROSOPHXLA . . . . . . . . . . . 6 DEFINING THE ENVIRONMENT- . . . . . . , ......... ... .......... . . .12 CASE 1 : NO EE PRODUCTIVE COST TO DISPERSAL . . . . . . . . . . . . . . . 1 4 CASE 2 : DISPERSAL REDUCES FECUNDITY . . . . . . . . . . . . . . . . . . . . . 27 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 FXGURES • • • •'•«•• • * • » " * ' « * ' • ' • " » • • • • » : " « . • # • -56 T A BTi ES • * • • « • •'•'«••• « • •' -• • m- •" • •'••;•'§ •. * ' * ' • • ' •''••'•/ • •• •• 7 U REFERENCES • • • • • •• • • • * * • • • * » • • * • • • ••-=• » » • • • • * • • • # • # • .80 i v LIST OF FIGURES Fi g u r e Pagje 1. The l a r v a l development f u n c t i o n s used i n t h i s study. These are i d e a l i z e d v e r s i o n s of those a c t u a l l y observed i n • D r o s o p h i l a . .. .-. .... .. .. .. ...., .•yv>VvVVrvv..-.57 2. The growth curves of D r o s o p h i l a l u l l e r i l a r v a e on the d i f f e r e n t y e a s t s found i n t h e i r host p l a n t , Ofiuntia v Data from Wagner (1944). 58 3. The e f f e c t of changes i n a d u l t s i z e on the r a t e of i n c r e a s e when o v i p o s i t i o n s i t e s a l l c o n t a i n the same yeast type a t any given time. The p r o b a b i l i t y of a l l s i t e s c o n t a i n i n g Type S yeasts i s p and the p r o a b i i i t y of a l l s i t e s -,, c o n t a i n i n g Type F yeasts i s 1-p. >--.w.v.Vy>-v^ 4. The e f f e c t o f changes i n a d u l t s i z e on the r a t e o f i n c r e a s e . ,.< «hen o v i p o s i t i o n s i t e s may c o n t a i n e i t h e r type F yeasts or S type S ye a s t s a t some given time. The p r o b a b i l i t y of a s i t e c o n t a i n i n g Type ...s yeasts i s f and the p r o b a b i l i t y of a s i t e c o n t a i n i n g Type F yeasts i s 1-f 60 5. S u r v i v a l of D ^ ? r a u i l e r i l a r v a e as a f u n c t i o n of the development time and the yeast s p e c i e s . Data from Bagner (1944) . ,•• •.•••.^.^.^ v»->. 61 6. Map showing the average percentage of Type S y e a s t s per : cactus f r u i t i n the 5 l o c a l i t i e s sampled by Wagner (1944). . . . . ... .. . . .. •w-v.vi-vyy .-Vr.!V* .. 62 7. The frequency d i s t r i b u t i o n o f Type S y e a s t s i n A u s t i n and C r e s t o n i o , Data from Wagner(1944) . 63 8. The e f f e c t of f l i g h t on egg production confidence l i m i t s shown are + 2 standard e r r o r s . 64 9. D i f f e r e n c e s between egg p r o d u c t i o n on adjacent days f o r f l i e s flown and not flown. The x a x i s shows the days co n s i d e r e d and the y a x i s the d i f f e r e n c e i n egg production between these days. Note t h a t a f t e r f l i g h t (day 3) the drop i n egg production between days 3 and 4 i s s i g n i f i c a n t l y g r e a t e r f o r the flown group than the unflown group. Confidence l i m i t s shown are + 2 standard e r r o r s . , 10. The estimated ' r e p r o d u c t i v e c o s t * o f a one hour f l i g h t i n D r o s o p h i l a mel anqga s t e r 7:- See t e x t f o r method of c a l c u l a t i n g t h i s c o s t . Confidence l i m i t s shown are + 1 s^cincLciircl ©irjror* .;• ••• '»'•• • «'v:*^ »v/«'-».• • •/•'••••••'•,»;>v,-»: 11...The e f f e c t of f l i g h t d u r a t i o n on egg-production on the day -, proceeding f l i g h t . / 67 12. The e f f e c t of f l i g h t d u r a t i o n on the combined egg production of the two days proceeding f l i g h t . ........ 68 1 3 . . R e s p i r a t i o n r a t e as a f u n c t i o n of wingbeat frequency. Data from Chadwick and Gilmour 1940 and Chadwick 1947, 14. The e f f e c t of changes i n a d u l t s i z e on the r a t e of i n c r e a s e when f l i g h t reduces f e c u n d i t y . T h i s r e d u c t i o n was c a l c u l a t e d on the b a s i s t h a t a f l y of thorax l e n g t h 1mm has a decrease i n egg production o f 20 eggs per day v i 15. The size d i s t r i b u t i o n of non-dispersing f l i e s (n=17) compared to a control sample (n=36) .measurements made from , the junction of longitudinal veins 1 and 2 to the end of Ion Qf u cLxn&X in 2 •. • • * * •.• ••>•••; ••••>vvv v>'- »:-»>••••••: • v:vvv>':y''*-:'«:':'»> ,.: 7 'I 16. The size d i s t r i b u t i o n of non-dispersing f l i e s (n=38) compared to a control sample (n=44) . . • . : \ ^ / , , , r , , « ; v v v t v , i . ' . , . , 7 2 17. Size d i s t r i b u t i o n of natural and 1st generation laboratory stocks of D ^ l i m i c a . Data from Kambysellis and Heed (1971) .) dU 73 v i i LIST OF TABLES Table Pag^e 1. Parameter e s t i m a t e s f o r D. melanoqaster . .. 74 2. E f f e c t of cage s i z e on egg production i n D.yme 1 anoga:ster.n Egg production of 15 females i n a l a r g e cage compared to the egg production of 15 females i n 15 v i a l s . ........ 75 3. E f f e c t o f cage s i z e on egg p r o d u c t i o n i n D.. raelanoo^ster*. Comparison between egg p r o d u c t i o n i n one g a l l o n c o n t a i n e r s 4. E f f e c t of l a r v a l d e n s i t y on the s i z e and number of emerging 9.clu Xi-S• • • • • • • • • • •• • • "* • • • •-• • * •"•'•*•• • • • > 77 5. Comparison of the d i s p e r s a l r a t e s of f l i e s r e a r e d under clx£•£©ir€H^ cl^ sn s x 11 ss • • * ••••«••••«•••*•••••*••«*•• * 73 6. The mean number of males and females remaining a f t e r 3 IJSST THODGHTS 'The t h i n g can be done,' s a i d the Butcher, '.I t h i n k . The t h i n g must be done, I am sure. The t h i n g s h a l l be done! Bring me paper and i n k , The best there i s time to procure.» The Beaver brought p a p e r , p o r t f c l i o , p e n s . And ink i n u n f a i l i n g s u p p l i e s : While strange creepy c r e a t u r e s came out of t h e i r dens And watched them with wondering eyes. So engrossed was the. Butcher, he heeded them not., As he wrote with a pen i n each hand, And e x p l a i n e d a l l the while i n a popular s t y l e Which the Beaver could well understand, 't a k i n g Three as the s u b j e c t to reason about-A convenient number to s t a t e -We add Seven, and Ten, and then m u l t i p l y out By One Thousand di m i n i s h e d by E i g h t . 'The r e s u l t we proceed to d i v i d e , as you see, By Nine Hundred and Ninety and Two: Then s u b t r a c t Seventeen, and the answer must be E x a c t l y and p e r f e c t l y t r u e . •The method employed I would g l a d l y e x p l a i n , While I have i t so c l e a r i n my head, I f I had but the time and you had but the b r a i n -But much yet remains to be s a i d . Mn one moment I've seen what has h i t h e r t o been Enveloped i n a b s o l u t e mystery, And without e x t r a charge I w i l l g i ve you at l a r g e A l e s s o n i n N a t u r a l H i s t o r y . ' from "The Beaver's Lesson" XlaS. Hunting of The Sjiark by Lewis C a r r o l l 2 INTBODUCTION I t i s a clear and obvious fact that the world i s both s p a t i a l l y and temporally variable. Yet early attempts to formulate mathematical models i n ecology and e c o l o g i c a l genetics ignored t h i s v a r i a b i l i t y . This was not done because of oversight or because i t was thought that such v a r i a b i l i t y was unimportant. Rather i t was a pragmatic necessity ; a mathematical model , just l i k e an experimental investigation must proceed from the simple to the complex. In t h i s way the importance and significance of each component may be most ea s i l y analysed and understood. However, the assumption of environmental homogeneity i n time and space has increasingly been considered a s i m p l i f i c a t i o n that cannot be made without grossly d i s t o r t i n g our picture of how the natural world functions (Andrewartha and Birch 1954, den Boer 1968, May 1973, Holliag 1973). In this thesis I w i l l present a model that demonstrates that s p a t i a l and temporal variations in environmental conditions may be of considerable importance i n determining the Darwinian f i t n e s s of an organism. The importance of s p a t i a l and temporal v a r i a b i l i t y in ecological genetics has been discussed i n a general way by Dickinson and Antonovics (1973), den Boer (1968), Levins (1968) and others. The model that w i l l be presented in t h i s thesis i s general i n the sense that i t may apply to a wide range of organisms but s p e c i f i c i n that a l l functional relationships have a b i o l o g i c a l meaning 3 and r e f e r to p a r t i c u l a r l i f e h i s t o r y c h a r a c t e r i s t i c s . The case to be considered i s the e v o l u t i o n of body s i z e i n a c o l o n i z i n g p o i k i l o t h e r m . The s p e c i f i c q u e s t i o n to be analysed i s 'what s i z e w i l l maximise the average r a t e of i n c r e a s e over time ?' I t w i l l be shown t h a t t h i s question cannot be answered by c o n s i d e r i n g the average or most f r e g u e n t l y o c c u r r i n g environmental c o n d i t i o n s . F u r t h e r , i t w i l l be shown t h a t s p a t i a l and temporal are capable of determining not only the optimum s i z e but a l s o the range i n s i z e s . The reason f o r l i m i t i n g the scope of t h i s study to c o l o n i z i n g organisms, or more g e n e r a l l y • r - s e l e c t e d ' organisms, i s to avoid the very d i f f i c u l t problems imposed by i n t r a - s p e c i f i c i n t e r a c t i o n s . Such problems are not amenable to the a n a l y t i c treatment o u t l i n e d i n t h i s t h e s i s and are probably best t a c k l e d by computer s i m u l a t i o n . The i n c r e a s e i n the number of parameters i n v o l v e d under such circumstances may be very great and i t i s probably best to c o n s i d e r such s i t u a t i o n s with r e f e r e n c e to p a r t i c u l a r case s t u d i e s . The r a t e of i n c r e a s e , r , i s determined by the number of o f f s p r i n g t h a t s u r v i v e t o reproduce and the l e n g t h of time between b i r t h and r e p r o d u c t i o n . I t w i l l be shown t h a t these two parameters are c o r r e l a t e d with s i z e ; i n c r e a s i n g s i z e i n c r e a s e s f e c u n d i t y but a l s o i n c r e a s e s the age at f i r s t r e p r o d u c t i o n . Thus s e l e c t i o n a c t i n g upon some l i f e h i s t o r y c h a r a c t e r such as the developmental r a t e w i l l r e s u l t i n a 4 change i n body s i z e . I n t h i s t h e s i s I w i l l show how e n v i r o n m e n t a l h e t e r o g e n e i t y may a c t as a s e l e c t i o n agent e i t h e r d i r e c t l y on s i z e o r i n d i r e c t l y t h r ough some l i f e h i s t o r y c h a r a c t e r which i n f l u e n c e s body s i z e . An a b s t r a c t model w h i l e b e i n g m a t h e m a t i c a l l y c o r r e c t may be i n a p p r o p r i a t e t o any ' r e a l w o r l d ' s i t u a t i o n because e i t h e r the f u n c t i o n a l forms of the submodels or t h e parameter v a l u e s may be b i o l o g i c a l l y u n r e a l i s t i c . To a v o i d t h i s problem I w i l l p r e s e n t the model w i t h r e f e r e n c e t o a p a r t i c u l a r group of o rganisms f o r which th e r e q u i r e d r e l a t i o n s h i p s and parameter v a l u e s are r e a s o n a b l y w e l l known. T h i s group i s t h e genus D£osop.hilai The genus D r o s o p h i l a i s s u i t a b l e f o r s e v e r a l e t h e r r e a s o n s , 1 ) t h e r e i s c o n s i d e r a b l e i n t e r - s p e c i f i c v a r i a t i o n i n body s i z e , f o r example, the Hawaiian s p e c i e s D., c ^ r t o l o m a has a body l e n g t h f i v e t i m e s f a m i l i a r s p e c i e s D.. m e l a n o g a s t e r (Carson e t a l 1970). 2) body s i z e v a r i e s w i t h i n a s p e c i e s , such v a r i a t i o n may be a s s o c i a t e d w i t h g e o g r a p h i c l o c a t i o n ( S t a l k e r and Carson 1947, P r e v o s t i 1955, Heed 1962, S o k o l o f f 1965, David 1971,1973, David and Bocguet 1972,1973,1974,1975), a l t i t u d e ( S t a l k e r and Carson 1948) o r season ( S t a l k e r and C a r s o n 1949, Tantawy 1964). These d i f f e r e n c e s have been shown t o be g e n e t i c and not a r e s u l t o f e n v i r o n m e n t a l c o n d i t i o n s i n t h e l a r v a l s t a g e ( a l t h o u g h c o n d i t i o n s i n t h e l a r v a l s t a g e do i n f l u e n c e body s i z e ) . 5 3) the h e r i t a b i l i t y of body s i z e i s r e l a t i v e l y high, l y i n g between 0.2 and 0.4, and , more i m p o r t a n t l y , the response to s e l e c t i o n under a v a r i e t y of environmental c o n d i t i o n s produces a s i g n i f i c a n t d e v i a t i o n d e t e c t a b l e w i t h i n 3 or 4 generations (Robertson and Reeve 1952, Robertson 1960, Druger 1962, Tantawy e t a l 1964, Tantawy and Rafcha 1964, Frahm and Kojima 1966, Tantawy and T a y e l 1970). F l i e s r e t a i n e d i n the l a b o r a t o r y f o r a number of years a l s o show changes i n body s i z e (Anderson 1966,1973, David and Bocguet 1975). Thus body s i z e i n Drosojohila i s a c h a r a c t e r which i s v a r i a b l e , has a high g e n e t i c component and w i l l respond to s e l e c t i o n . The p o p u l a t i o n dynamics of d i f f e r e n t s p e c i e s of ££oso£hila have not been well s t u d i e d . The i n f o r m a t i o n t h a t i s a v a i l a b l e suggests t h a t , i n g e n e r a l , Drgsojahila p o p u l a t i o n s do not f u l l y u t i l i s e a v a i l a b l e r e s o u r c e s and are t h e r e f o r e ' r -s e l e c t e d * organisms ( B i r c h and B a t t a g l i a 1957, Da Cunha et a l 1957, Tantawy 1964, P i p k i n 1965). 6 2111 MIIz SIS TORY CH1RACTERS OF DHQSOJiflliA--I n t h i s s e c t i o n I s h a l l d e f i n e t h e l i f e h i s t o r y c h a r a c t e r i s t i c s o f a t y p i c a l s p e c i e s o f fir o s o p _ h i l a / £ i fflglgnggasterA I n d e f i n i n g t h e f u n c t i o n a l r e l a t i o n s h i p s a n d a s s i g n i n g p a r a m e t e r v a l u e s I h a v e b e e n c o n c e r n e d o n l y w i t h o b t a i n i n g f u c t i o n s a n d v a l u e s t h a t a r e ' r e a s o n a b l e ' a n d h a v e n o t a t t e m p t e d t o a c h i e v e a d e g r e e o f a c c u r a c y t h a t w o u l d be n e c e s s a r y i f , f o r e x a m p l e , we were a t t e m p t i n g t o m o d e l t h e a c t u a l p o p u l a t i o n g r o w t h o f | K m e l a n o q a s t e r . I t i s n o t i n t e n d e d , i n t h i s s t u d y , t o d e s c r i b e t h e f a c t o r s t h a t l i m i t b o d y s i z e i n D A m e l a n o a a s t e r : t h e p u r p o s e o f t h e s t u d y i s t o show what f a c t o r s may l i m i t b o d y s i z e i n an o r g a n i s m t h a t h a s t h e c h a r a c t e r i s t i c s e x e m p l i f i e d by D,_ m e l a n o a a s t e r > T h e d a t a o n t h e l i f e h i s t o r y c h a r a c t e r i s t i c s o f t h i s s p e c i e s a r e u s e d s i m p l y t o d e m o n s t r a t e t h a t t h e h y p o t h e s i s c o n c e r n i n g t h e i n f l u e n c e o f e n v i r o n m e n t a l v a r i a b i l t y on body s i z e d o e s n o t r e s u l t f r o m b i o l o g i c a l l y u n r e a l i s t i c a s s u m p t i o n s o r p a r a m e t e r v a l u e s . T h e f e a t u r e s o f t h e l i f e h i s t o r y c h a r a c t e r i s t i c s t h a t a r e n e c e s s a r y f o r t h e i n i t i a l d e v e l o p m e n t o f t h e m o d e l a r e , 1) f e c u n d i t y i n c r e a s e w i t h b o d y s i z e 2) body s i z e a n d d e v e l o p m e n t t i m e a r e c o r r e l a t e d . 3) t h e r e e x i s t a t l e a s t t w o s e t s o f c o n d i t i o n s u n d e r w h i c h t h e g r o w t h o f l a r v a e i s m a r k e d l y d i f f e r e n t . I n o n e i n s t a n c e t h e g r o w t h . c u r v e i s c u r v i l i n e a r s u c h t h a t t h e r a t e o f i n c r e a s e i n s i z e i n c r e a s e s w i t h t i m e . I n t h e s e c o n d i n s t a n c e t h e g r o w t h c u r v e i s more o r l e s s l i n e a r ; t h e r a t e o f i n c r e a s e 7 i n s i z e i s independent of time. 4 ) the p r o p o r t i o n of l a r v a e s u r v i v i n g t o pupation decreases with time such t h a t t h e r e i s some developmental time beyond which no l a r v a e s u r v i v e . In p o i k i l o t h e r m s an i n c r e a s e i n body s i z e i s g e n e r a l l y accompanied by an i n c r e a s e i n f e c u n d i t y ( C l i f f o r d and boerger 1 9 7 4 , Mackerras 1 9 3 3 , Green 1 9 5 6 , Bagenal 1 9 6 6 , S a l t h e 1 9 6 9 , T i n k l e et a l 1 9 7 0 , Hadley 1 9 7 1 ) . The r e l a t i o n s h i p between f e c u n d i t y and s i z e can be d e s c r i b e d by an equation of the g e n e r a l form, Nocx^ ( 1 ) where N i s the number of young, x i s some body measurement such as body l e n g t h or weight and m i s a constant depending on the organism and the body dimension x. Measurements of f e c u n d i t y i n p.. melanomaster and Ih £seudoobscura• i n d i c a t e t h a t i f x i s some l i n e a r dimension such as thorax l e n g t h m i s approximately egual to 3 (Robertson 1 9 5 7 , Tantawy and Vetukhiv 1 9 6 0 , Barker and Podger 1 9 7 0 ) . The d a i l y egg production has been s t u d i e d i n d e t a i l by McMillan et a l ( 1 9 7 0 a,b). They developed the f o l l o w i n g equation t o d e s c r i b e the d a i l y egg p r o d u c t i o n i n p._ melano^asterx N (t) = M(1.-e ) e (2) where N (t) : the egg production on day t to '.the day upon which egg production begins M : the p o t e n t i a l maximum d a i l y egg production €jOL : constants depending upon the s t r a i n Equation (2) does not c o n s i d e r the e f f e c t of changes i n body s i z e . Eguation (1) may be used to extend e q u a t i o n (2) to the case of v a r i a b l e body s i z e . T h i s can be done by r e p l a c i n g H by M = H'X"* (3) where M'J.S a constant depending upon the s p e c i e s and s t r a i n . The next l i f e h i s t o r y parameter that we r e q u i r e i s the growth f u n c t i o n of the l a r v a e . I n t u i t i v e l y i t seems reasonable to suppose t h a t the l a r v a l development time w i l l ba a f u n c t i o n of the a d u l t s i z e . Fenchel {1974) has shown t h a t , f o r the animal kingdom i n g e n e r a l , body s i z e and the age at f i r s t r e p r o d u c t i o n are r e l a t e d ; the l a r g e r the animal the l o n g e r i t takes to reach sexual maturity. The r e l a t i o n s h i p between s i z e and development time has been measured f o r p.. me l a nog a s t e r bY s e v e r a l workers. David and Bocquet (1974) measured the a d u l t 9 weight and d u r a t i o n of development of 47 Japanese s t r a i n s of P.. I§l§nogaster x 31 French s t r a i n s and 19 t r o p i c a l s t r a i n s . They found a s i g n i f i c a n t c o r r e l a t i o n between development time and body weight i n both males and females of the Japanese s t r a i n s and i n the females of the t r o p i c a l s t r a i n s but no s i g n i f i c a n t c o r r e l a t i o n f o r the males of the t r o p i c a l s t r a i n s o r i n e i t h e r sex of the French s t r a i n s . Robertson (1960 a,b) s t u d i e d the r e l a t i o n s h i p between s i z e and development time i n d i f f e r e n t l y s e l e c t e d s t r a i n s of p A melanogasteri. He found a s i g n i f i c a n t c o r r e l a t i o n between these parameters, o v e r - a l l , t h e r e f o r e , there i s s u f f i c i e n t evidence to j u s t i f y the assumption that body s i z e and development time are g e n e r a l l y c o r r e l a t e d . The developmental p e r i o d can be d i v i d e d i n t o three phases, the time from o v i p o s i t i o n to hatching, the p e r i o d of growth and the pupal p e r i o d . P r i o r to the a c t u a l time of pupation growth slows and there i s a p e r i o d where l i t t l e or no i n c r e a s e i n s i z e occurs. Thus we can d e f i n e two p e r i o d s between hatching and pupation, a p e r i o d i n which the r a t e of i n c r e a s e i s constant or i n c r e a s i n g with time and a p e r i o d i n which i t i s d e c r e a s i n g to z e r o . During the the f i r s t p e r i o d the l e n g t h of the l a r v a e may i n c r e a s e e x p o n e n t i a l l y with time (Bakker 1959, Robertson et a l 1968) or l i n e a r l y with time (Chiang and Hodson 1950). These two growth f u n c t i o n s can be d e s c r i b e d by the eguations 10 T = ae (4) T = a + ct (5) where T i s the thorax length of the adult (assumed to be proportional to the length at pupation), t i s the time between hatching and the moment the growth rate slows down, and a,b and c are constants. I have assumed that the duration of the second phase of growth ( that i n which the increase in size decreases) , the period from oviposition to hatching and the pupal period are constant. Although not perfect mathematical descriptions of the growth curves equations (4) and (5) do embody the general c h a r a c t e r i s t i c s and are s u f f i c i e n t l y accurate for the present study. The general shapes of these two functions are shown in f i g 1. The differences in the form of the growth curves may be attr i b u t a b l e to differences in the type of yeast upon which the larvae are fed. This i s shown by the growth of D.. mulleri larvae on the nine yeasts found on the l a r v a l host plant, c a c t i of the genus, Ojsuntia (Wagner 1944) . The growth curves vary from being more or less l i n e a r to being highly c u r v i l i n e a r ( f i g 2). The f i n a l parameters necessary to cal c u l a t e r are the s u r v i v a l rates of larvae and adults. There i s only one study 11 on the s u r v i v a l of l a r v a e during development, t h a t o f Chiang and Hodson (1950) on the d a i l y s u r v i v a l of l a r v a e . The p r o p o r t i o n of l a r v a e s u r v i v i n g d e c l i n e s l i n e a r l y with time, the slope of the l i n e depending on the i n i t i a l d e n s i t y of l a r v a e . Under optimal c o n d i t i o n s i n the l a b o r a t o r y the s u r v i v a l of l a r v a e i s g e n e r a l l y about 90 percent, a l t h o u g h i n s e v e r a l cases the s u r v i v a l has been found to be much lower. The s u r v i v a l under l a b o r a t o r y c o n d i t i o n s may, or may not, bear any resemblance to the s u r v i v a l r a t e s i n the w i l d . In t h i s paper I have assumed that the p r o p o r t i o n of l a r v a e s u r v i v i n g i s determined by the l e n g t h of time i n which l a r v a e are ' a c t i v e l y growing', that i s the time determined from equations (4) and (5). The p r o p r t i o n s u r v i v i n g d e c l i n e s l i n e a r l y with t h i s time such t h a t e l y there i s approximately an 80 percent p r o b a b a b i l i t y of s u r v i v i n g a day of ' a c t i v e growth'. T h i s s u r v i v a l r a t e i s lower than the best s u r v i v a l r a t e s observed i n the l a b o r a t o r y but I do not t h i n k t h a t i t i s u n r e a l i s t i c a l l y low f o r the w i l d . The s u r v i v a l of a d u l t s has been e x t e n s i v e l y s t u d i e d under l a b o r a t o r y c o n d i t i o n s but there i s no r e l i a b l e data on s u r v i v a l under n a t u r a l c o n d i t i o n s . The e f f e c t of changes i n the a d u l t s u r v i v a l r a t e on r i s very s m a l l because r i s determined l a r g e l y by the very e a r l y p e r i o d of r e p r o d u c t i o n (Lewontin 1965). For t h i s reason I have assumed a constant d a i l y s u r v i v a l p r o b a b i l i t y . The v a l u e s of the parameters d e s c r i b e d above are given i n Table 1. The 12 Having d e f i n e d the l i f e - h i s t o r y c h a r a c t e r i s t i c s of our organism we must now d e f i n e the environmental s i t u a t i o n . The s i t u a t i o n I wish to c o n s i d e r i s one i n which s i t e s s u i t a b l e f o r o v i p o s i t i o n and l a r v a l growth are s c a t t e r e d through space as ' i s l a n d s ' . T h i s s i t u a t i o n s u i t a b l y d e s c r i b e s the d i s t r i b u t i o n of resources of w i l d D r o s o p h i l a . The a d u l t s and l a r v a e of D r o s o p h i l a feed upon y e a s t s . In the temperate zones the breeding s i t e s of s e v e r a l s p e c i e s of D r o s o p h i l a have been found to be the fermenting exudates from v a r i o u s tree s p e c i e s (Carson and S t a l k e r 1951, Carson 1951, Carson 1952, Carson 1958) w h i l s t i n the t r o p i c s l a r v a e may be found i n fermenting p l a n t m a t e r i a l ( B i r c h and B a t t a g l i a 1957, Heed 1968, P i p k i n 1965) or w i t h i n l i v i n g p l a n t p a r t s ( P i p k i n et a l 1966). Breeding s i t e s are thus s c a t t e r e d over space as ' i s l a n d ' h a b i t a t s . The composition of yeast f l o r a i n each patch w i l l , i n g e n e r a l , vary. As a f i r s t approximation I s h a l l assume that a t each s i t e only one type of yeast occurs. The growth r a t e of l a r v a e w i l l depend upon the type of yeast upon which they are f e e d i n g . For the sake of the present d i s c u s s i o n we can broadly c l a s s i f y yeasts i n t o two types, d e f i n e d with r e s p e c t to t h e i r e f f e c t on the l a r v a l growth r a t e . Those yeasts upon which the i n c r e a s e i n length i s c u r v i l i n e a r with time I s h a l l c a l l Type F (or ' f a s t growth') yeasts. Those yeasts upon which l a r v a e grow a t a more or l e s s constant r a t e I s h a l l c a l l Type S (or 1 3 •slow growth') y e a s t s . The s i z e of l a r v a e growing on Type F yeasts i s c a l c u l a t e d from equation (4) and the s i z e o f l a r v a e growing on Type S yeasts by equation (5). In the next two s e c t i o n s I s h a l l c o n s i d e r two cases. F i r s t l y I s h a l l c o n s i d e r the consequences of v a r i a t i o n i n yeast types i n time and space where d i s p e r s a l between patches does not reduce f e c u n d i t y . D i s p e r s a l i n v o l v e s a c t i v e f l i g h t which uses energy. I f energy f o r f l i g h t and egg p r o d u c t i o n come from the same s t o r e f l i g h t may reduce egg p r o d u c t i o n . In the second case I s h a l l c o n s i d e r to what extent the c o n c l u s i o n s of the f i r s t case are modified i f d i s p e r s a l e n t a i l s a r e d u c t i o n i n f e c u n d i t y . 14 CASE J 2 NO BEPBODUCTIVE COST TO DISPEBSAL I t i s assumed i n t h i s s e c t i o n that energy f o r f l i g h t and energy f c r egg production are separate so that d i s p e r s a l does not reduce the number of eggs a female i s capable of l a y i n g . The most simple s p a t i a l and temporal d i s t r i b u t i o n of yeast types i s t h a t i n which a l l h a b i t a t s t h a t become s u i t a b l e at any point i n time c o n t a i n the same type o f yeast. For example, a l l new patches t h a t a r i s e at time t might c o n t a i n only Type S y e a s t s . The s u i t a b l i t y of patches f o r o v i p o s i t i o n i s assumed to be very s h o r t so t h a t at any given time f l i e s can only o v i p o s i t e on 'newly a r i s e n ' s i t e s . Thus alt h o u g h at any mGment i n time the h a b i t a t i s composed of both types of yeast, patches s u i t a b l e f o r o v i p o s i t i o n a l l c o n t a i n the same type of yeast. Let r^(T) be the r a t e of i n c r e a s e of f l i e s with thorax l e n g t h s T on Type I yeasts and r(T) the mean r a t e of i n c r e a s e . The number o f f l i e s at time t i s given by ?Lr)t Nfc (T) = N^ (T) e (6) where N^(T) i s the number of f l i e s o f l e n g t h T a t time t . Now assume that time may be d i v i d e d i n t o d i s c r e t e i n t e r v a l s , with the p r o b a b i l i t y o f Type S yeasts o c c u r r i n g being p and the p r o b a b i l i t y of Type F yeasts o c c u r r i n g being 1-p. The time i n t e r v a l must be of s u f f i c i e n t d u r a t i o n that the m a j o r i t o r y of a female's eggs are l a i d w i t h i n t h i s i n t e r v a l . In 15 2i jelSHSa^ster t h i s l e n g t h would be of the order o f a week or two. Equation (6) can now be w r i t t e n as where r^ (T) i s the r a t e of i n c r e a s e per txme increment. Combining eguations {6} and (7) we o b t a i n The r e s u l t s c f s o l v i n g eguation (8) f o r v a r i o u s values of p are shown i n f i g 3. In the absence of Type S yeasts (p=0) the optimum thorax l e n g t h i s gr e a t e r than 10mm, a l e n g t h which may not be p o s s i b l e f o r Dro s o p h i l a because of p h y s i o l o g i c a l c o n s t r a i n t s . However, the maximum thorax length that can be achieved when onl y Type S yeasts are present i s l e s s than 2.5mm. T h i s maximum, l a b e l l e d T i n f i g 3, i s determined by the s u r v i v a l r a t e of l a r v a e . The time r e g u i r e d to r e a c h a s i z e g r e a t e r than T^ on Type S yeasts i s so great that t h e r e i s a n e g l i g i b l e p r o b a b i l i t y of a l a r v a s u r v i v i n g . T h i s maximum, T^, might a l s o r e s u l t from the n u t r i t i o n a l q u a l i t y of Type S yeasts being so low that l a r v a e of l e n g t h g r e a t e r than T cannot meet maintenance c o s t s . In the l a t t e r case the s u r v i v a l Vt (T) = $ o (T) e (7) (8) 16 of l a r v a e would be a f u n c t i o n of s i z e r a t h e r than time. I f the p r o b a b i l i t y of Type S yeasts o c c u r r i n g i s g r e a t e r than 0 then the maximum p o s s i b l e thorax l e n g t h i s T because Cat any f l i e s t h a t exceed t h i s s i z e w i l l not leave progeny when a v a i l a b l e o v i p o s i t i o n s i t e s c o n t a i n only Type S yeast s . F l i e s with thorax lengths g r e a t e r than T^may be generated by g e n e t i c recombination, and during p e r i o d s i n which Type F y e a s t s occur s e l e c t i o n w i l l favour an i n c r e a s e i n thorax length above T c (provided t h a t other c o n s t r a i n t s do not set a lower l i m i t ; an assumption i m p l i c i t i n the above argument). Note t h a t when o n l y Type S yeasts occur (p=1) the optimum thorax l e n g t h i s c o n s i d e r a b l y f u r t h e r from T^ . than when there i s a non zero p r o b a b i l i t y of Type F yeasts o c c u r r i n g . I f the p r o b a b i l i t y of Type S yeasts o c c u r r i n g i s very low then the p r o b a b i l i t y of a lo n g s e r i e s o f time i n t e r v a l s i n Type F yeasts occur i s high. Under these circumstances there i s a chance t h a t the average le n g t h of f l i s s i n the p o p u l a t i o n w i l l exceed T . However, e v e n t u a l l y Type S yeasts w i l l dominate the o v i p o s i t i o n s i t e s and the progeny of f l i e s l a r g e r than T^ w i l l not s u r v i v e . T h i s may l e a d t o a l a r g e p o p u l a t i o n crash due to massive l a r v a l m o r t a l i t y . Thus i f the p r o b a b i l i t y of Type S yeasts o c c u r r i n g i s very low i t s e f f e c t may be not only to g r e a t l y reduce the optimum body s i z e but a l s o to cause l a r g e f l u c t u a t u i o n s i n po p u l a t i o n numbers. Although i n the ' r e a l ' world' there may e x i s t a p r o b a b i l i t y of only one type of yeast o c c u r i n g at a g i v e n time 17 the more usual s i t u a t i o n i s undoubtably one i n which the p r o p o r t i o n of each type v a r i e s over time. Assume t h a t at each o v i p o s i t i o n s i t e t here e x i s t s only one type of yeast. Let the p r o b a b i l i t y of Type S yeasts o c c u r i n g be f and the p r o b a b i l i t y of Type F yeasts T-f. F u r t h e r assume that, f l i e s do not d i s c r i m i n a t e between s i t e s . Then the number of o f f s p r i n g a f l y of thorax l e n g t h T produces per time increment i s given by e = fe s J+ (1-f) e t (9) Hence r(T) = l o g ^ ( f e +{1-f)e 4 ) (10) Equation (10) i s p l o t t e d i n f i g 4 f o r d i f f e r e n t values of f . rtt?) For f l i e s of thorax length g r e a t e r than T^ , e equals 0 and equation (10) reduces t o 'r(T) = l o g ^ d - f ) + r^(T) (11) Even a low frequency of Type S yeasts s i g n i f i c a n t l y reduces A /\ r (T): a t a frequency of 10 per cent Type S y e a s t s reduce r (T) by 0.105. I f Type S yeasts comprise 40 per cent of the A . a v a i l a b l e yeasts r(T) i s reduced by 0.51. Furthermore, the A presence of Type S yeasts produces a l o c a l maximum o f r(T) at a value below T . The presence o f r e l a t i v e l y low percentages of Type S 18 yeasts may s e v e r e l y r e t a r d the r a t e at which the mean thorax l e n g t h o f the po p u l a t i o n i n c r e a s e s . The o c c a s i o n a l presence of a very high frequency of Type S yeasts w i l l reduce the p o p u l a t i o n mean to a value below T^. The optimum thorax l e n g t h i s determined very l a r g e l y by the presence of Type S yeasts even when the s p a t i o - t e m p o r a l frequency of such yeasts i s low. The extent to which the assumption of a random d i s p e r s a l of f l i e s between qener a t i o n s i s v a l i d w i l l depend upon the p e r s i s t e n c e time of a patch and the s p a t i a l d i s t r i b u t i o n of yeast types. I f the p e r s i s t e n c e time of a patch i s g r e a t e r than one ge n e r a t i o n we miqht expect some f l i e s t o remain at the s i t e . Experiments suggest t h a t the p r o b a b i l i t y of d i s p e r s i n g from a s i t e i s p o s i t i v e l y c o r r e l a t e d with s i z e (Roff 1976). In a s i t e t h a t p e r s i s t s f o r many g e n e r a t i o n s t h e r e may t h e r e f o r e be a d e c l i n e i n the average s i z e of a f l y from t h i s s i t e . There are i n s u f f i c i e n t data to g i v e any es t i m a t e of the p e r s i s t e n c e time of s u i t a b l e o v i p o s t i o n s i t e s f o r any Drosqphila s p e c i e s . I f s i t e s do not remain s u i t a b l e between seasons or there i s a mixing o f f l i e s between seasons the tendency f o r l o c a l d i f f e r e n t i a t i o n with r e s p e c t t o s i z e may be of l i t t l e consequence i n the l o n g term. Loc a l c l u s t e r i n g of s i t e s c o n t a i n i n g p a r t i c u l a r yeast types may a l s o produce l o c a l d i f f e r e n t i a t i o n . The s p a t i o - t e m p o r a l d i s t r i b u t i o n of h a b i t a t patches and the movement of f l i e s between them r e q u i r e s more study. The t e c h n i c a l d i f f i c u l t i e s 19 i n v o l v e d i n such a study are extreme although a study of those D r c s o ^ h i l a s p e c i e s which axe h i g h l y s p e c i a l i z e d i n t h e i r o v i p o s i t i o n s i t e s might be f r u i t f u l . A t e s t of the h y p o t h e s i s developed above r e q u i r e s i n f o r m a t i o n on (a) the l a r v a l growth f u n c t i o n s (b) s u r v i v a l as a f u n c t i o n of time and s i z e (c) the s p a t i o - t e m p o r a l d i s t r i b u t i o n of the yeast types. Such data are.very d i f f i c u l t to c o l l e c t . The study of the n u t r i t i o n a l requirements of D A m u l l e r i by Wagner (1944) comes c l o s e to p r o v i d i n g the necessary i n f o r m a t i o n . Dj. j u l l e r i l a y s i t s eggs on c a c t i of the genus Q£ujrtia. High numbers of the f l y are a s s o c i a t e d with the f r u i t i n g season of Oguntia and i t i s b e l i e v e d that the c a c t u s f r u i t are the major or s o l e source of food f o r the l a r v a e . Wagner i d e n t i f i e d 9 d i f f e r e n t yeasts from the c a c t i and measured the growth of D ± m u l l e r i l a r v a e on each ( f i g 2). From these data the yeasts can be c l a s s i f i e d i n t o Type F or Type S. Under what c o n d i t i o n s w i l l the presence of Type S yeasts i n f l u e n c e the optimum s i z e of Dj. m u l l e r i ? F i r s t l y , i t i s necessary that the s u r v i v a l r a t e of l a r v a e on Type S yeasts i s very low. Wagner d i d not measure the s u r v i v a l of l a r v a e during development but he d i d measure the p r o p o r t i o n of l a r v a e s u r v i v i n g to pupation. There i s a h i g h l y s i g n i f i c a n t n e g a t i v e c o r r e l a t i o n between the percentage s u r v i v a l to pupation and the time taken to pupate (r--0.906, P<.01). T h i s r e l a t i o n s h i p 20 i s shown i n f i g 5. The s i z e at pupation i s dependant on the type of yeast upon which the l a r v a e are f e d . Larvae f e d on Type S yeasts (Y-1, Y-3) pupate at a smal l e r s i z e than those f e d on Type F ye a s t s . Why do l a r v a e grown on Type S yeasts f a i l t o reach the s i z e achieved on Type F yeasts? The most l i k e l y e x p l a n a t i o n i s that they cannot do so because these yeasts are n u t r i t i o n a l l y inadeguate. Larvae t h a t attempt to grew u n t i l they reach the s i z e achieved on Type F ye a s t s probably do not s u r v i v e . From the above argument we may conclude t h a t T^, the maximum s i z e p o s s i b l e on Type S yeasts i s very c l o s e to t h a t observed f o r growth on Type F yeas t s . F l i e s grown upon Type F yeasts could most l i k e l y i n c r e a s e t h e i r r a t a of i n c r e a s e upon such yeasts by i n c r e a s i n g t h e i r s i z e . Such an i n c r e a s e would be prevented by the o c c a s i o n a l occurrence of high f r e g u n c i e s of Type S yeasts i n t h e i r environment. The next g u e s t i o n we must, t h e r e f o r e ask i s 'do Type S y e a s t s , at l e a s t o c c a s i o n a l l y dominate the o v i p o s i t i o n s i t e s ?' Wagner c o l l e c t e d Oguntia f r u i t from 5 areas i n Texas ( A u s t i n , Hoore, D i l l e y , C o t u l l a and Crestonio) and analysed the f r u i t f o r the d i f f e r e n t s p e c i e s of yeast. The average percentages of Type S yeasts f o r the 5 areas sampled are given i n f i g 6. The growth curves f o r yeasts Y-8 and Y-9 are not given by Wagner: on the b a s i s of the time taken to pupate and the percentage s u r v i v a l I have c l a s s i f i e d Y-8 as Type F and Y-9 as Type S. In three areas Type S yeasts make up onl y a very 21 s m a l l percentage of the t o t a l yeasts present. In two areas, C r e s t o n i o and A u s t i n , they comprise approximately of the yeasts present. The d i s t r i b u t i o n s of Type S yeasts per c a c t u s f r u i t f o r these two areas are shown i n f i g 7. The sample s i z e s a r e , u n f o r t u n a t e l y , very s m a l l . In C r e s t o n i o 30ft of the c a c t i f r u i t c o n t a i n e d only Type S yeasts w h i l s t i n A u s t i n 15% of the the c a c t i f r u i t contained only Type S y e a s t s . There are i n s u f f i c i e n t data to c a l c u l a t e the d i s t r i b u t i o n f u n c t i o n from which t o estimate the p r o b a b i l i t y that Type S yeasts w i l l be the only y e a s t s present. The f a c t t h a t i n one area out of f i v e 30% of the c a c t i f r u i t contained only Type S y e a s t s suggests t h a t t h i s p r o b a b i l i t y i s not n e g l i g i b l e . Thus the h y p o t h e s i s t h a t the s i z e of D t m u l l e r i i s l i m i t e d by the s p a t i o - t e m p o r a l d i s t r i b u t i o n of Type S yeasts appears t o be a tenable one. I t has been assumed that Dj_ m u l l e r i l a r v a e c o u l d grow l a r g e r upon Type F yeasts. T h i s assumption c o u l d be t e s t e d by s e l e c t i n g f o r i n c r e a s e d s i z e upon Type F y e a s t s . I t would a l s o be i n t e r e s t i n g t o s e l e c t f o r l a r g e s i z e upon the Type S y e a s t s . I t i s i m p l i c i t i n the above model t h a t e i t h e r the s p a t i o - t e m p o r a l d i s t r i b u t i o n of Type S yeasts w i l l n ot s e l e c t fox an i n c r e a s e d a b i l i t y t o use these yeasts or t h a t such an i n c r e a s e would d e t r a c t from the a b i l i t y of the l a r v a e to use the Type F yeasts. The l a t t e r p o s s i b i l i t y could be t e s t e d by experiment. I f the former reason was c o r r e c t would i t s t i l l be p o s s i b l e f o r the s i z e to be determined by the s p a t i o - t e m p o r a l d i s t r i b u t i o n o f Type S yeasts ? The a b i l i t y to u t i l i z e a 22 p a r t i c u l a r v a r i e t y of yeasts i n v o l v e s an array of b i o c h e m i c a l a d a p t a t i o n s . The r a r e t y of Type S yeasts may prevent the a s s i m i l a t i o n of such an a r r a y . The s i z e at pupation, however, may be governed by a simple device such as a s t r e t c h r e c e p t o r ; when a l a r v a e reaches a c e r t a i n s i z e the r e c e p t o r f i r e s and i n i t i a t e s the processes l e a d i n g to pupation and metamorphosis. S e l e c t i o n f o r a change i n the t h r e s h o l d at which the r e c e p t o r f i r e s may be much more e a s i l y achieved than s e l e c t i o n f o r the m u l t i p l e changes necessary to i n c r e a s e the a b i l i t y of the l a r v a e to u t i l i z e d i f f e r e n t y e a s t s . For t h i s reason the s p a t i o - t e m p o r a l d i s t r i b u t i o n of Type S yeasts may be capable of s i g n i f i c a n t l y i n f l u e n c i n g the a d u l t body s i z e without being at a frequency t h a t i s s u f f i c i e n t l y high to s e l e c t f o r i n d i v i d u a l s capable of b e t t e r u t i l i z i n g these yeasts. The model and a n a l y s i s o u t l i n e d i n t h i s s e c t i o n may be extended to s i t u a t i o n s other than those i n which t h e r e are v a r i a t i o n s i n the l a r v a l growth r a t e . Suppose, f o r example, t h a t o n l y one type of yeast occurred i n the environment, that i s l arvae were able to u t i l i z e a l l a v a i l a b l e s p e c i e s of yeast with equal f a c i l i t y . The environmental c o n d i t i o n s at each patch are not l i k e l y to be i d e n t i c a l . Some patches may be more exposed than o t h e r s and r e c e i v e more s u n l i g h t thereby i n c r e a s i n g the p r o b a b i l i t y t h a t temperatures w i t h i n the patch may reach l e t h a l l i m i t s f o r e i t h e r the yeast or the l a r v a e . Other patches may be c l o s e to the ground and s u b j e c t to p e r i o d i c f l o o d i n g . These d i f f e r e n c e s i n environmental 2 3 c o n d i t i o n s may r e s u l t i n a l a r v a l s u r v i v a l r a t e t h a t v a r i e s with l o c a t i o n and time. In some patches c o n d i t i o n s may remain h o s p i t a b l e f o r a long p e r i o d of time and permit a l o n g developmental p e r i o d . In other patches environmental d e t e r i o r a t i o n may be r a p i d s e l e c t i n g f o r a s h o r t developmental p e r i o d . I t i s a simple matter to apply the above a n a l y s i s to t h i s s i t u a t i o n . Instead of d e f i n i n g d i f f e r e n t yeast types we d e f i n e d i f f e r e n t types of patches. In the s i m p l e s t case we can c l a s s i f y patches i n t o twc groups, those which p e r s i s t f o r only a ' s h o r t ' p e r i o d and those which p e r s i s t f o r a 'long' p e r i o d . These types correspond mathematically to patches c o n t a i n i n g Type S yeasts and those c o n t a i n i n g Type F yeasts. The a n a l y s i s may now be done i n the same manner as f o r t h i s l a t t e r s i t u a t i o n . The c o n c l u s i o n that can be drawn i s t h a t the optimum development time , and hence the optimum body s i z e , can be governed by the s p a t i o - t e m p o r a l frequency of patches t h a t remain s u i t a b l e f o r growth f o r the l e a s t amount of time. Even a very low frequency of these 'poor r i s k ' patches may a c t as important s e l e c t i v e f o r c e s on body s i z e . We might expect, t h e r e f o r e , t h a t organisms w i l l show a degree of d i s c r i m i n a t i o n i n t h e i r c h o i ce of o v i p o s i t i o n s i t e s . C e r t a i n cues, such as the degree of exposure may i n d i c a t e 'poor r i s k ' patches and such s i t e s may be avoided. The degree of d i s c r i m i n a t i o n w i l l depend upon the s p a t i o - t e m p o r a l freguency of the v a r i o u s c a t e g o r i e s of patches. In s i t u a t i o n s where s i t e s are s c a r c e , s i t e s which have a very low p r o b a b i l i t y of p e r s i s t i n g may be 24 s e l e c t e d because the probability of f i n d i n g a b e t t e r s i t e i s very much lower. I f the a b i l i t y to d i s c r i m i n a t e between the s u i t a b i l i t y o f o v i p o s i t i o n s i t e s has a g e n e t i c component, d i f f e r e n t p o p u l a t i o n s may show d i f f e r e n t t e n d e n c i e s t o accept or r e j e c t a s i t e depending upon the s p a t i o - t e m p o r a l d i s t r i b u t i o n of s i t e s . Another s i t u a t i o n to which the model developed i n t h i s s e c t i o n may be a p p l i e d i s t h a t i n which there i s s i z e -s e l e c t i v e p r e d a t i o n . In t h i s i n s t a n c e s e l e c t i o n a c t s d i r e c t l y upon s i z e r a t h e r than i n d i r e c t l y through the development f u n c t i o n . S i z e s e l e c t i v e p r e d a t i o n has been i m p l i c a t e d as a major f a c t o r i n the composition of zoopla.nk.tcn communities (Brooks and .Dodson 1965, Dodson 1974). In these s t u d i e s p r e d a t i o n has been shown to r e s u l t i n a change i n s p e c i e s composition. F u r t h e r , s i z e s e l e c t i v e p r e d a t i o n has been suggested as being important i n the e v o l u t i o n of s i z e i n such d i v e r s e organisms as the c l a d o c e r a n , Da£hnia l u m h o l t z i (Green 1967) and a f i s h , the t h r e e - s p i n e d s t i c k l e b a c k (Moodie 1972). The question f o r which the model presented i n t h i s s e c t i o n can be used i s 'how frequent and how severe must such p r e d a t i o n be i n order t o s i g n i f i c a n t l y e f f e c t the s i z e d i s t r i b u t i o n of a p o p u l a t i o n or community ?' Suppose t h a t the p r o b a b i l i t y of being eaten i n c r e a s e s with s i z e . As b e f o r e , we may d e f i n e two types of patch or circumstance. In the f i r s t case the p r o b a b i l i t y of being eaten i s only weakly i n f l u e n c e d by s i z e and i n the second t h i s 25 p r o b a b i l i t y i n c r e a s e s r a p i d l y with s i z e . The former case corresponds mathematically to the patch c o n t a i n i n g Type F yeasts and the second to the patch c o n t a i n i n g Type S y e a s t s . F o l l o w i n g the same method of a n a l y s i s we can show t h a t even a very low i n c i d e n c e of s i z e - s e l e c t i v e p r e d a t i o n may be important i n determining the s i z e d i s t r i b u t i o n of a p o p u l a t i o n or community. I t i s i n t e r e s t i n g to note that s p a t i a l v a r i a t i o n i n the i n t e n s i t y of s i z e s e l e c t i v e p r edation may g i v e r i s e to a bimodel f i t n e s s curve ( f i g 4 ), and hence a bimodal d i s t r i b u t i o n i n the s i z e spectrum of the community, although a l l eguations d e s c r i b i n g the v a r i o u s l i f e h i s t o r y parameters are monotonic. I t i s , t h e r e f o r e , unecessary to invoke d i f f e r e n t mechanisms to account f o r b i m o d a l i t i e s w i t h i n the s i z e spectrum of a community or t o assume that p r e d a t i o n i s n e c e s s a r i l y most i n t e n s e upon s p e c i e s of an i n t e r m e d i a t e s i z e . Bather more complicated s i t u a t i o n s may r e s u l t i f the p r o b a b i l i t y of being eaten i s not a f u n c t i o n t h a t changes monotonically with s i z e . Another f a c t o r that must be taken i n t o c o n s i d e r a t i o n i s the stage i n the l i f e c y c l e of the organism dur i n g which s i z e s e l e c t i v e p r e d a t i o n i s happening. S i z e s e l e c t i v e p r e d a t i o n of a d u l t animals may have l i t t l e e f f e c t , i n g e n e r a l , upon the optimum s i z e because changes i n a d u l t s u r v i v a l have r e l a t i v e l y minot impact upon r compared to changes i n immature s u r v i v a l or generation l e n g t h . S i z e s e l e c t i v e p r e d a t i o n of j u v e n i l e s may be a s i g n i f i c a n t e v o l u t i o n a r y f a c t o r because i f happens before r e p r o d u c t i o n and 26 hence before animals have made any c o n t r i b u t i o n to the next g e n e r a t i o n . In summary, the average s i z e o f i n d x v i d u a l s of a p o p u l a t i o n ,measured over time may be determined by the r a r e occurence of a s e t of c o n d i t i o n s i n which there i s s i g n i f i c a n t time-dependent or size-dependent m o r t a l i t y . The degree to which a p o p u l a t i o n w i l l d e v i a t e from the long term mean i s determined by the frequency with which these c o n d i t i o n s occur and the r a t e at which •l a r g e * animals are generated by g e n e t i c recombination. 27 CASE 2 i DISPERSAL REDUCES FECUNDITY In the p r e v i o u s s e c t i o n i t was assumed t h a t the energy s t o r e s f o r f l i g h t and egg p r o d u c t i o n were s e p a r a t a . In t h i s s e c t i o n I s h a l l c o n s i d e r how the r e s u l t s of case 1 are e f f e c t e d i f f l i g h t and egg production share a common energy s t o r e . I s t h i s assumption a reasonable one ? Diptarans produce t h e i r eggs a f t e r emergence, from the pupa and l a y them e i t h e r i n batches or s e q u e n t i a l l y . Rygg(1966) s t u d i e d the r e p r o d u c t i v e cost of f l i g h t i n a d i p t e r a n which l a y s i t s eggs i n batches, the f r i t f l y , O s c i n e l l a f r i t : "the t o t a l number of eggs l a i d was not i n f l u e n c e d by a s i n g l e f l i g h t i n e a r l y adult l i f e , nor was the p a t t e r n of egg l a y i n g or l o n g e v i t y eggs were l a i d more o f t e n when i n s e c t s flew every second day, but there were fewer eggs i n each batch. As these f l i e s l i v e d f o r a s h o r t e r time, they l a i d fewer eggs" (Rygg 1966) . D r o s o p h i l a l a y t h e i r eggs s e q u e n t i a l l y , a l t h o u g h the p a t t e r n of egg l a y i n g does show a c i r c a d i a n rhythm (Reusing and Hardeland 1967) . I f the same energy r e s e r v e s are used f o r f l i g h t a c t i v i t y and egg p r o d u c t i o n , as i s suggested by the work of Rygg, then egg production ( measured as the number of eggs l a i d ) i n D r o s o p h i l a should be decreased a f t e r a period of f l i g h t . To t e s t t h i s hypothesis I d i d the f o i l o w i n g experiment: f l i e s ( D.. me/lanoqaster ) were attached to p i n s by means of a l a t e x g l u e , permitted t o f l y f o r a given period of 28 time and then removed by g e n t l y t a p p i n g the pin. I then measured the egg production of these f l i e s over the next few days. I had c o n s i d e r a b l e d i f f i c u l t y i n g e t t i n g i n d i v i d u a l s to f l y f o r a predetermined time; f r e q u e n t l y a f l y would stop and c o u l d not be made to r e s t a r t f l i g h t . I f g e n t l e p e r s u a t i o n by tapping and blowing was i n s u f f i c i e n t t o r e s t a r t an i n d i v i d u a l i t was removed from the pin and i t s f l i g h t time scored as the time up to t h i s p o i n t . To a s c e r t a i n i f f l i g h t a f f e c t e d egg p r o d u c t i o n one group of f l i e s was flown f o r one hour and another stuck onto pins but not permitted t o f l y . Of the f l i e s i n the 'flown' group two flew l e s s than one hour (22 mins and 36 mins). Except where s t a t e d these two f l i e s have been i n c l u d e d i n the a n a l y s i s : the two treatments are thus 'flown' and 'unflown'. Counts of the d a i l y egg production of each f l y were begun one day a f t e r e c l o s i o n and the experiment performed on the f o u r t h day a f t e r e c l o s i o n . F i g 8 shows the d a i l y egg p r o d u c t i o n of the two groups. Both groups show a drop i n egg p r o d u c t i o n f o l l o w i n g the experimental manipulation but the drop of the flown group i s g r e a t e r than that of the unflown group. T h i s d i f f e r e n c e i s not, however, s i g n i f i c a n t . A problem with the f o r e g o i n g a n a l y s i s i s t h a t the w i t h i n group v a r i a n c e i n egg production i s very l a r g e compared to the sample s i z e s (10 i n the 'flown' group, 8 i n the 'unflown'). T h i s problem may be p a r t i a l l y overcome by comparing the d i f f e r e n c e i n egg production between days f o r i n d i v i d u a l s (Fig 9). This a n a l y s i s 29 shows t h a t there i s s i g n i f i c a n t d i f f e r e n c e between the flown group and the unflown group (t=2.72 P<0.01, o n e - t a i l e d t e s t ) even with the removal of the two i n d i v i d u a l s which flew l e s s than one hour (t= 2.0, P<0.05, o n e - t a i l e d t e s t ) . An estimate of the decrease i n egg production t days a f t e r f l i g h t , C f t ) , can be obtained using the formula <t) = N;{0) - <t) - D (0,t) where (t) : the estimated c o s t f o r the i t h f l y t days a f t e r f l i g h t . N • (t) : the number of eggs l a i d by the i t h f l y t days c a f t e r f l i g h t . N• (0) : the number of eggs l a i d by the i t h f l y on the day preceeding the f l i g h t . D(0,t) : the mean d i f f e r e n c e between the number of eggs l a i d on day 0 and day t by the group of f l i e s not flown. The p l o t cf C • (t) on t i s shown i n f i g 10. The two f l i e s v which d i d not f l y f o r one hour are excluded from t h i s a n a l y s i s . The r e g r e s s i o n of (t) on t i s s i g n i f i c a n t (r=-0.390, p<0.05 ) and i n d i c a t e s t h a t egg production i s reduced f o r 3 to 4 days a f t e r a one hour f l i g h t . To demonstrate a c o r r e l a t i o n between f l i g h t time and egg p r o d u c t i o n more sample p o i n t s are needed than obtained i n the 30 p r e v i o u s experiment. Because of the time taken zo a n a e t h e t i s e the f l i e s and glue them onto the p i n s i t proved i m p r a c t i c a l to use the same procedure as before. T h e r e f o r e , i n t h i s experiment the n o n - f l i g h t group were a n a e t h e t i s e d and placed i n v i a l s . Four of the f l i e s attached t o pin s d i d not f l y and t h e i r egg p r o d u c t i o n was no d i f f e r e n t from the group not att a c h e d to pins ( f i g 11) i n d i c a t i n g t h a t the o p e r a t i o n of g l u e i n g f l i e s t o the p i n s has no i l l e f f e c t s . The drop i n egg pr o d u c t i o n of the unflown group i n t h e previous experiment can be a s c r i b e d to the a n a e s t h e t i c . I measured the egg p r o d u c t i o n of a l l f l i e s on the f i r s t day a f t e r the experiment and f o r two days a f t e r the experiment f o r about one h a l f of the sample. There i s a s i g n i f i c a n t c o r r e l a t i o n between f l i g h t time and egg production on the day f o l l o w i n g the f l i g h t (r=-0.378 P<0.05, f i g 11 ). There i s a l s o a s i g n i f i c a n t c o r r e l a t i o n between f l i g h t time and the egg p r o d u c t i o n of the two days f a l l o w i n g f l i g h t (r=-0.471, P<0.05, f i g 12 ). The v i a l s used i n the previous experiments are not l a r g e enough to permit much f l i g h t a c t i v i t y (4.5 cms i n diameter x 10 cms i n h e i g h t ) . I f f l i g h t s i g n i f i c a n t l y reduces egg pr o d u c t i o n then f l i e s i n l a r g e r cages, where i n c r e a s e d f l i g h t a c t i v i t y i s p o s s i b l e , may produce fewer eggs. To t e s t t h i s I placed 15 females i n a s i n g l e l a r g e cage (measuring 32 x 32 x 32 cms) i n which were a v a i l a b l e 15 food caps f o r o v i p o s i t i o n . The egg production o f t h i s group was compared with t h a t of a 31 group of 15 females i n 15 of the v i a l s used i n the previous experiments. The r e s u l t s of t h i s experiment are given i n Table 2. On a l l three days the egg production of the f l i e s i n the l a r g e cage was s i g n i f i c a n t l y l e s s than those i n the v i a l s . To ensure that t h i s r e s u l t was not obtained because of i n t e r a c t i o n between females i n the l a r g e cage I repeated the experiment t h i s time p l a c i n g s i n g l e females i n one g a l l o n c o n t a i n e r s . The r e s u l t s are the same as before; f l i e s i n the l a r g e cages produced s i g n i f i c a n t l y fewer eggs than f l i e s i n the v i a l s (Table 3) . F l i g h t a c t i v i t y reduces the number of eggs a female can l a y . The next g u e s t i c n to be c o n s i d e r e d i s M s the r e d u c t i o n i n the number of eggs l a i d dependent upon the s i z e of the female ?' I t f o l l o w s from simple aerodynamic c o n s i d e r a t i o n s t h a t the e n e r g e t i c cost of f l i g h t w i l l decrease as the s i z e of the f l y i s i n c r e a s e d ( D. Ludwig pers. comm.). Thus given t h a t i t r e g u i r e s a c e r t a i n number of c a l o r i e s to produce an egg then the ' r e p r o d u c t i v e c o s t ' of d i s p e r s a l w i l l decrease as the s i z e of the f l y i n c r e a s e s . To o b t a i n the f u n c t i o n a l r e l a t i o n s h i p between s i z e and ' r e p r o d u c t i v e c o s t ' we r e q u i r e the consumption r a t e of c a l o r i e s and the speed of f l i g h t as f u n c t i o n s of s i z e . From these two equations we can o b t a i n the c o s t per u n i t d i s t a n c e as a f u n c t i o n of s i z e . The r a t e of consumption of c a l o r i e s i s p r o p o r t i o n a l to the r a t e of r e s p i r a t i o n . The r a t e of r e s p i r a t i o n d u r i n g f l i g h t 32 depends upon the wingbeat frequency which i s i t s e l f a f u n c t i o n of the s i z e of the f l y . From t h e o r e t i c a l c o n s i d e r a t i o n s the r e s p i r a t i o n r a t e of a f l y of thorax l e n g t h i s r e l a t e d t o the wingbeat frequency a c c o r d i n g t o the equation, B(T)oc (W (T) j * (12) where R(T) i s the r e s p i r a t i o n r a t e of a f l y of thorax l e n g t h T and W(T) the wingbeat freguency. The exponent x should be l e s s than or egual to 3 (Chadwick 1947). The a c t u a l value of x f o r D r o s o p h i l a ^ obtained u s i n g data from Chadwick and Gilmour (1940) and Chadwick (1947), i s . 2.4 (see f i g 13). Heed, Wi l l i a m s and Chadwick (1942) measured the wingbeat frequency and body dimensions of v a r i o u s D r o s o p h i l a s p e c i e s . Using t h i s data the r e l a t i o n s h i p between wingbeat frequency and thorax l e n g t h i s found to be, log^W (T) = 9.4 - 0.431og^T (13) Equations (12) and (13) s p e c i f y the r a t e o f energy consumption during f l i g h t as a f u n c t i o n of s i z e . To f i n d the amount o f energy consumed i n f l y i n g some u n i t d i s t a n c e we need to know the time taken to f l y t h a t d i s t a n c e , ae thus r e q u i r e i n f o r m a t i o n on the speed of f l i g h t as a f u n c t i o n of body s i z e . In the sheep b l o w f l y , P h a e n i c i a s e r i c a t a , f l i g h t speed 33 and wingbeat frequency both i n c r e a s e l i n e a r l y with temperature (Yurkicwicz and Smyth 1966a,b). As an approximation, t h e r e f o r e , we can assume t h a t f l i g h t speed i s p r o p o r t i o n a l to wingbeat fraguency. The e n e r g e t i c c o s t of f l y i n g some d i s t a n c e d, may now be computed. The r e l a t i o n s h i p between t h i s cost and s i z e i s given by x\j (T) oc d/T (14) where n^(T) i s the c o s t i n c a l o r i e s or eggs. As the thorax l e n g t h i n c r e a s e s the r e p r o d u c t i v e c o s t of f l i g h t decreases. The wingbeat frequency and hence the r e s p i r a t i o n r a t e decrease with an i n c r e a s e i n thorax l e n g t h but f l i g h t speed a l s o decreases . However, the r e s p i r a t i o n r a t e d i m i n i s h e s more r a p i d l y with i n c r e a s i n g thorax l e n g t h than f l i g h t speed; hence the r e s u l t t h a t l a r g e r f l i e s i n c u r a lower c o s t . Two asssumptions made i n d e r i v i n g equation (14) r e q u i r e experimental v e r i f i c a t i o n . The f i r s t assumption i s t h a t the number of c a l o r i e s r e q u i r e d to produce an egg i s independent of s i z e . I t i s well e s t a b l i s h e d that i n animals i n g e n e r a l the r e s p i r a t i o n r a t e , measured as c a l o r i e s consumed par u n i t body weight per u n i t time, i n c r e a s e s as body weight decreases 34 (Fenchel 1 9 7 4 ) . However, Hunter ( 1 9 6 4 , 1965) found no r e l a t i o n s h i p between oxygen consumption/mg wet weight and weight i n e i t h e r male or female D._ fi'seudoobscura or JQi v i r a c o c h i , or i n male D\ melanogaster. She d i d f i n d a s i g n i f i c a n t c o r r e l a t i o n between these parameters i n female D i g e l a n g g a s t e r T h e d i s c r e p e n c y between the r e s u l t s r e p o r t e d f o r animals i n g e n e r a l and D r o s o p h i l a i n p a r t i c u l a r may be due to the s c a l e of change i n body weight. The v a r i a t i o n between animals i n t h e i r consumption r a t e s may be so great t h a t a c r o s s the range i n weight encompassed by a s i n g l e s p e c i e s no r e l a t i o n s h i p between consumption r a t e and weight i s d e t e c t a b l e without very l a r g e sample s i z e s . An i n c r e a s e i n r e s p i r a t i o n r a t e with decreased s i z e suggests that the number of c a l o r i e s consumed i n the production of an egg may depend upon the s i z e of the f l y . The •cos t ' of p r o d u c t i o n may, t h e r e f o r e , i n c r e a s e with d e c r e a s i n g s i z e . The use of e q u i v a l e n t amounts of c a l o r i e s i n f l i g h t by two f l i e s of d i f f e r e n t s i z e s may not be e q u i v a l e n t to the same number of eggs. In the s m a l l e r f l y where more c a l o r i e s are r e g u i r e d to produce an egg than i n the l a r g e r f l y the r e d u c t i o n i n egg p r o d u c t i o n w i l l be l e s s . Thus the exponent i n equation (14) may be an overestimate. The second assumption t h a t r e q u i r e s f u r t h e r examination i s the assumption t h a t f l i g h t speed i n c r e a s e s l i n e a r l y with wingbeat frequency. The o b s e r v a t i o n s by Yurkiewicz and Smyth, quoted above, suggest t h i s r e l a t i o n s h i p . More d i r e c t evidence 35 i s r e a l l y necessary. Hocking (1953) measured the f l i g h t speed and weight of 10 D ± melanggaster. These data i n d i c a t e no s i g n i f i c a n t c o r r e l a t i o n between f l i g h t speed and body weight. The s m a l l sample s i z e and the method of f l y i n g the specimens (t e t h e r e d f l i g h t ) might be r e s p o n s i b l e f o r the l a c k of a c o r r e l a t i o n . I f f l i g h t speed i s independent o f s i z e the exponent i n equation (14) i s an underestimate. For the present l e t us assume that equation i s a reasonable d e s c r i p t i o n of the ' r e p r o d u c t i v e c o s t ' of f l i q ' h t i n r e l a t i o n t o s i z e . To estimate the e f f e c t of f l i g h t on r I assumed that a f l y of thorax l e n g t h 1.0mm f l i e s on average f o r one hour per day and t h i s f l i g h t c o s t s i t 20 eggs on the day f o l l o w i n g f l i g h t . T h i s estimate of the c o s t i s an underestimate s i n c e egg production i s reduced f o r a t l e a s t 3 days f o l l o w i n g a one hour f l i g h t . I f u r t h e r assumed t h a t f l i g h t s which c o s t f l i e s more eggs than they are capable of producing does not decrease t h e i r s u r v i v a l . Knowing the c o s t f o r a f l y of a given s i z e the c o s t f o r a f l y of any o t h e r s i z e may be c a l c u l a t e d by simple a l g e b r a . The r e s u l t of i n c o r p o r a t i n g t h i s r e p r o d u c t i v e cost i n t o the c a l c u l a t i o n s of r i s shown i n f i g 14. I assumed a l i n e a r l a r v a l growth f u n c t i o n (eguation (5)) and to ensure that any s h i f t s i n o p t i m a l body s i z e were d e t e c t a b l e I set the l a r v a l m o r t a l i t y at a constant (10%). A f l i g h t of one hour per day g r e a t l y i n c r e a s e s the thorax l e n g t h f o r which r i s g r e a t e r than zero and, to a much l e s s e r extent, the optimum thorax l e n g t h . T h i s 36 r e s u l t does not depend g r e a t l y upon the exact form.of equation (14). Compare , f o r example, the case i n which f l i g h t does not reduce f e c u n d i t y with t h a t i n which f l i g h t reduces f e c u n d i t y but t h i s r e d u c t i o n i s independent of body s i z e . Suppose t h a t i n the l a t t e r case the r e d u c t i o n due to f l i g h t i s 2 0 eggs. F l i e s which l a y twenty eggs or l e s s may have a r a t e of i n c r e a s e i n excess of zero when egg number and f l i g h t are u n r e l a t e d but they cannot maintain t h e i r numbers when f l i g h t reduces f e c u n d i t y by 2 0 eggs. In the l a t t e r circumstance these genotypes w i l l be maintained i n the p o p u l a t i o n only by g e n e t i c recombination. The thorax l e n g t h f o r which r i s g r e a t e r than zero w i l l be i n c r e a s e d even i f the c o s t of f l i g h t i n c r e a s e d with s i z e . The importance of the mathematical r e l a t i o n s h i p between egg p r o d u c t i o n , f l i g h t , and body s i z e i s t h a t i t determines the c u r v a t u r e o f the f i t n e s s f u n c t i o n . I t i s the d e c r e a s i n g c o s t with s i z e that causes the very steep d e c l i n e i a r with d e c r e a s i n g s i z e shown i n f i g 14. The frequency o f d i s p e r s a l w i l l depend upon both the p e r s i s t e n c e time of a patch and the d i s t a n c e between patches. As the patches become more and more unstable with r e s p e c t to t h e i r p e r s i s t e n c e time the advantaqes of spreading o f f s p r i n g over a number of patches w i l l i n c r e a s e . On the o t h e r hand, a decrease i n the d e n s i t y of patches w i l l favour a r e d u c t i o n i n d i s p e r s a l because of the i n c r e a s i n g ' r e p r o d u c t i v e c o s t ' of d i s p e r s i n g between s i t e s . Because of the size-dependence of 37 t h i s ' r e p r o d u c t i v e c o s t ' the t r a d e - o f f between i n c r e a s i n g the number of patches i n which eggs are l a i d versus the conseguent decrease i n f e c u n d i t y w i l l a l s o be size-dependent. For example, i f d i s p e r s a l between patches reduces a f l y ' s egg production t o zero t h e r e i s no point i n d i s p e r s i n g . I t may, however, be advantageous f o r a f l y of a l a r g e r s i z e to d i s p e r s e because i t ' s f e c u n d i t y w i l l not be reduced to zero and i t w i l l leave progeny i n two l o c a t i o n s , thereby p o s s i b l y I n c r e a s i n g i t s f i t n e s s . The above arguments suggest t h a t the p r o b a b i l i t y of d i s p e r s a l , i f i t i s under g e n e t i c c o n t r o l , w i l l be a d j u s t e d a c c o r d i n g to the s p a t i o - t e m p o r a l nature of the h a b i t a t and to the s i z e of the f l y . The a v a i l a b l e evidence suggests t h a t the l e v e l of a c t i v i t y and t h e r e f o r e the r a t e of d i p s e r s a l i s under g e n e t i c c o n t r o l . Sakai et al(1958) have shown that d i f f e r e n t s t r a i n s of p melanogaster show d i f f e r e n t l e v e l s of a c t i v i t y . In f u r t h e r experiments Narise (1969) showed t h a t the l e v e l of a c t i v i t y i s dependent upon the genotype of the f l y . attempts to s e l e c t f o r d i f f e r e n t a c t i v i t y r a t e s i n D roe, l a n og a s t e r have not been very s u c c e s s f u l , p r i m a r i l y because o f e x p e r i m e n t a l problems; f o r example, s e l e c t i o n f o r low a c t i v i t y r a t e r e s u l t e d i n animals that were u n w i l l i n g to move through the t u n n e l s of the experimental apparatus (Ewing 1963,1967). These r e s u l t s c a s t some doubt upon the r e s u l t s of N a r i s e and h i s coworkers because they used s i m i l a r apparatus t o measure a c t i v i t y . 38 There i s no i n f o r m a t i o n on the r a t e s of a c t i v i t y and the s p a t i o - t e m p o r a l d i s t r i b u t i o n c f o v i p o s i t i o n s i t e s f o r any s p e c i e s of D r o s o p h i l a . Southwood (1962) g i v e s evidence t h a t , f o r i n s e c t s i n g e n e r a l , the l e v e l of d i s p e r s a l a c t i v i t y i s c o r r e l a t e d with h a b i t a t s t a b i l i t y . At t h i s l e v e l ,however, the o b s e r v a t i o n i s almost t r i v i a l : f o r example, i t i s obvious t h a t a newly formed pond w i l l , i n g e n e r a l be c o l o n i z e d by i n s e c t s capable of f l i g h t r a t h e r than those without wings. The e f f e c t of s i z e upon d i s p e r s a l r a t e i s a much e a s i e r problem to i n v e s t i g a t e . I attempted to s o l v e t h i s problem i n the f o l l o w i n g manner. The s i z e of a f l y i s dependent upon the degree of crowding i t experiences as a l a r v a e . Thus d i f f e r e n t s i z e d f l i e s may be obtained by r e a r i n g l a r v a e at d i f f e r e n t d e n s i t i e s . Reed (1938) showed t h a t s m a l l f l i e s , produced by r a i s i n g at higher than optimal d e n s i t i e s , are l e s s a c t i v e than l a r g e f l i e s . . To generate two s i z e d i s t r i b u t i o n s of f l i e s I allowed e i t h e r 2 or 12 females to o v i p o s i t i n a v i a l f o r 24 hours. J u s t p r i o r to emergence of the r e s u l t i n g f l i e s I placed the v i a l s o u t s i d e i n boxes supported on stakes and open at the bottom to permit d i s p e r s a l . I f the hypothesis above i s c o r r e c t the f l i e s emerging frcm the low d e n s i t y c o n d i t i o n s should d i s p e r s e more r a p i d l y than those from the high d e n s i t y c o n d i t i o n s . To c o n t r o l f o r the e f f e c t of the d e n s i t y of emerging f l i e s w i t h i n these v i a l s I put out t h r e e boxes c o n t a i n i n g ; 39 1) 15 v i a l s of l a r v a e at the low density 2) 30 v i a l s of l a r v a e a t the low density, 3) 15 v i a l s of l a r v a e at the high d e n s i t y Each box a l s o c o n t a i n e d 20 v i a l s of f r e s h food and mashed banana. To estimate numbers emerging I placed out 10 s e a l e d v i a l s at each d e n s i t y . I c o l l e c t e d the remaining f l i e s a f t e r 4 days. The number of f l i e s emerging does not d i f f e r with d e n s i t y (Table 4) and hence the counts f o r the two boxes c o n t a i n i n g the f l i e s reared a t low d e n s i t i e s can be pooled f o r the purpose of a n a l y s i s . The f l i e s r e a r e d at the higher d e n s i t y are ,however, s m a l l e r than these reared at the lower d e n s i t y (Table 4). The number of f l i e s remaining within the v i a l s from which they were reared i n c r e a s e s s i g n i f i c a n t l y with an i n c r e a s e i n the l a r v a l d e n s i t y (Table 5). T h i s c o n c l u s i o n i s not a f f e c t e d by the i n c l u s i o n of f l i e s w i t h i n the other v i a l s or on the s i d e w a l l s (see Table 5). Table 6 g i v e s the means f o r the two sexes: u n f o r t u n a t e l y the sexes were not separated as they were removed from the v i a l s and hence no standard e r r o r s can be given. I t can be seen t h a t i n both sexes there i s a r e d u c t i o n i n the p r o b a b i l i t y of d i s p e r s a l with a r e d u c t i o n i n body s i z e . Thus the r a t e of d i s p e r s a l of f l i e s decreases as the d e n s i t y at which they are reared i s i n c r e a s e d . There remains the p o s s i b i l i t y t h a t f l i e s r e a red under high d e n s i t y c o n d i t i o n s are s t a r v e d upon emergence from the pupa and t h i s 40 f a c t o r , not s i z e , determines the d i s p e r s a l r a t e . T h i s h y p o thesis can be t e s t e d by comparing the d i s p e r s a l r a t e s of well f ed f l i e s of v d i f f e r e n t s i z e s , produced by r e a r i n g a t d i f f e r e n t d e n s i t i e s . F l i e s used i n experiments designed t o study the e f f e c t of temperature on d i s p e r s a l r a t e (Roff 1976) had been r e t a i n e d and c o u l d thus be used to determine i f s i z e and d i s p e r s a l r a t e are c o r r e l a t e d . These f l i e s were a l l well f ed bef o r e being placed o u t s i d e . The a n a l y s i s c o n s i s t s of comparing the s i z e d i s t r i b u t i o n of the remaining (non-dispersing) f l i e s with t h a t of a c o n t r o l sample. In s e l e c t i n g s u i t a b l e samples i t i s necessary t o ensure that the number of f l i e s d i s p e r s i n g i s s u f f i c i e n t l y l a r g e to make a d i f f e r e n c e i n s i z e d e t e c t a b l e ; but i t must not be so l a r g e that the sample of remaining f l i e s i s e x c e s s i v e l y s m a l l . Without any a p r i o r i e s t i m a t e s of these c o n d i t i o n s I c o n s e r v a t i v e l y s e l e c t e d only one experiment, t h a t i n which 17 of the 50 females r e l e a s e d remained. No males were measured. The s i z e d i s t r i b u t i o n s of these f l i e s and the c o n t r o l sample are shown i n f i g 15. The n o n - d i s p e r s i n g females are s i g n i f i c a n t l y s m a l l e r than the c o n t r o l sample (t=2.25 P<0.025, o n e - t a i l e d t e s t ) . To t e s t t h i s r e s u l t f u r t h e r I r e l e a s e d about 220 females i n the same manner as before and c o l l e c t e d the remaining f l i e s t h r e e days a f t e r the r e l e a s e . Approximately 70 f l i e s remained. The s i z e d i s t r i b u t i o n s of these f l i e s and the c o n t r o l sample are shown i n f i g 16. There i s a h i g h l y s i g n i f i c a n t d i f f e r e n c e 41 i n the v a r i a n c e s , ( F=3.14, P<0.001) due to the presence of a group of very s m a l l f l i e s i n the non d i s p e r s i n g sample. T h i s experiment was repeated 2 more times and i n both cases the r e s u l t s were n o n - s i g n i f i c a n t (such i s the e r r o r of r e p e a t i n g experiments). The evidence, although h i g h l y s u g g e s t i v e , i s i n c o n c l u s i v e . More experiments are r e q u i r e d not only using f l i e s of d i f f e r e n t s i z e s r e s u l t i n g from d i f f e r e n t l a r v a l c o n d i t i o n s but a l s o using f l i e s o f g e n e t i c a l l y d i f f e r e n t s i z e s . The t r a n s i e n t nature of o v i p o s i t i o n s i t e s makes i t e s s e n t i a l f o r D r o s o p h i l a to d i s p e r s e . The general arguments given above suggest t h a t the s p a t i o - t e m p o r a l d i s t r i b u t i o n of s i t e s may be an important parameter i n determining the r a t e of d i s p e r s a l . T h i s r a t e may a l s o be s i z e dependent. To what extent w i l l the s p a t i o - t e m p o r a l d i s t r i b u t i o n of s i t e s e f f e c t the s i z e d i s t r i b u t i o n of the p o p u l a t i o n ? I s h a l l consider f i r s t the consequences of temporal v a r i a b i l i t y i n the d e n s i t y of s i t e s . Two s i m p l i f i i n g assumptions w i l l be made. The f i r s t i s t h a t patches upon which l a r v a e have fed are not s u i t a b l e f o r o v i p o s i t i o n . T h i s assumption i s not a l t o g e t h e r u n r e a l i s t i c because i t has been found t h a t D r o s o p h i l a s p e c i e s that o v i p o s i t e on s l i m e f l u x e s a v o i d f l u x e s c o n t a i n i n g l a r v a e or pupae (Cole e t a l 1970). The second assumption i s that s i t e s are evenly d i s t r i b u t e d i n space so t h a t there i s l i t t l e v a r i a t i o n i n the d i s t a n c e 42 between adjacent s i t e s ( a l t e r n a t i v e l y we might choose to accept the average d i s t a n c e between s i t e s as a reas o n a b l e approximation of the average d i s p e r s a l d i s t a n c e and i g n o r e the degree of c o n t a g i o n ) . In t h i s case r(T) can be c a l c u l a t e d by means of equation ( 8 ) . Let' r^(T) be the r a t e of i n c r e a s e of f l i e s c f thorax l e n g t h s T when the d e n s i t y of s i t e s i s D^. . Let p be the p r o b a b i l i t y of a d e n s i t y , a t which the d i s p e r s a l c o s t i s c (T) eggs per day f o r a f l y of s i z e T, and (1-p) the p r o b a b i l i t y of a d e n s i t y at which the d i s p e r s a l c o s t i s n e g l i g i b l e . Then r(T) i s given by, ^ ( T ) = p r 5 (T) + (1-p)rp(T) (15) Equation (15) has e x a c t l y the same form as equation (8) . However, in t h i s i n s t a n c e the optimum thorax l e n g t h w i l l not be e f f e c t e d very g r e a t l y by changes i n the d e n s i t y of s i t e s because the optimum thorax l e n g t h does not depend t o any great extent upon the r e p r o d u c t i v e cost of d i s p e r s a l (see f i g 14). What w i l l be e f f e c t e d , however, i s the minimum thorax s i z e The minimum thorax s i z e w i l l be determined by the d e n s i t y of s i t e s at which the co s t of d i s p e r s a l i s hi g h e s t , t h a t i s , the lowest d e n s i t y ( h e r e a f t e r c a l l e d D c ) . F l i e s t h a t are so small t h a t a r e d u c t i o n of c (T) eggs per day reduces t h e i r r a t e of i n c r e a s e below zero w i l l be e l i m i n a t e d from the p o p u l a t i o n during the p e r i o d when s i t e s are s p a r s e l y d i s t r i b u t e d ( d e n s i t y D c ) . The p r o b a b i l i t y of f i n d i n g f l i e s i n the p o p u l a t i o n t h a t 4 3 are s m a l l e r than the l i m i t s et by D w i l l depend upon the p r o b a b i l i t y of such low d e n s i t i e s o c c u r r i n g and the degree of contagion of patches. I f d e n s i t i e s g r e a t e r than D occur with a high frequency f l i e s s m a l l e r than those t h a t can p e r s i s t when the d e n s i t y of s i t e s approaches D may be found i n numbers gre a t e r than could be produced by g e n e t i c recombination alone. These numbers w i l l depend i n part upon the d i s t a n c e between the optimum body s i z e and the s m a l l e s t s i z e p o s s i b l e at the d e n s i t y D c, and the f u n c t i o n a l r e l a t i o n s h i p between / r (T) and T. A very steep decrease i n y r ( T ) as T decreases below i t s optimum w i l l favour animals very c l o s e to the optimum w h i l s t a very slow d e c l i n e w i l l f a v o u r a wider range. The s p a t i a l d i s t r i b u t i o n of s i t e s i s u n l i k e l y to be as even as assumed so f a r . S i t e s w i l l probably be c o n t a g i o u s l y d i s t r i b u t e d so t h a t there w i l l be areas i n which s i t e s are densely packed and the c o s t of d i s p e r s a l i s low; i n other areas s i t e s may be f a r apart and the d i s p e r s a l c o s t consequently h i g h e r . Within areas i n which the d e n s i t y of patches i s higher than average, f l i e s which are s m a l l e r than the l i m i t s e t by the average d i s p e r s a l d i s t a n c e may p e r s i s t . G e n o t y p i c a i l y s m a l l f l i e s may p e r s i s t f o r a peri o d i n such l o c a l c o n c e n t r a t i o n s of patches but t h e i r p r o b a b i l i t y of long term s u r v i v a l w i l l be n e g l i g i b l e because e v e n t u a l l y the d e n s i t y of patches i n t h i s area w i l l decrease. Sexual r e p r o d u c t i o n with i t s consequent g e n e t i c recombination may 44 c o n t i n u a l l y produce a s m a l l number o f f l i e s t h a t are below the minimum s i z e determined by D^. L o c a l d i f f e r e n c e s i n s i t e d e n s i t y may tend to generate l o c a l d i f f e r e n c e s i n s i z e d i s t r i b u t i o n s but i f s i t e s do not p e r s i s t from one breeding season to another the mixing of f l i e s between seasons w i l l counterbalance such d i f f e r e n t i a t i o n . The mixing of f l i e s between seasons may a l s o prevent l o c a l d i f f e r e n t i a t i o n due to v a r i a t i o n i n the p e r s i s t e n c e times of patches. I f h a b i t a t patches are evenly d i s t r i b u t e d the lowest s i z e a f l y should pupate at i s determined by the average re productive cost of d i s p e r s i n g between s i t e s , assuming that the patch upon which i t has grown i s u n s u i t a b l e f o r f u r t h e r o v i p o s i t i o n . I f s i t e s are c o n t a g i o u s l y d i s t r i b u t e d a f l y which pupates at a s i z e below that set by D c may s t i l l have a chance of r e p r o d u c i n g s u c c e s s f u l l y i f i t i s w i t h i n an area or at a time i n which s i t e s are not at t h i s lowest d e n s i t y . As the d i s t r i b u t i o n of s i t e s becomes more contagious we should expect to see an i n c r e a s e i n the a b i l i t y of an organism to metamorphose at a s i z e below t h a t at which i t metamorphoses under optimal c o n d i t i o n s . Thus w i t h i n a p o p u l a t i o n we should f i n d a range of 'small' phenotypes t h a t are not represented by ' s m a l l ' genotypes. T h i s has been observed i n P r o s o p h i l a ^ McFarguhar and Robertson (1963) measured the s i z e d i s t r i b u t i o n of a n a t u r a l p o p u l a t i o n of D_j. subobscura and that of the f i r s t g e n e r a t i o n l a b o r a t o r y stock. S i m i l a r measurements were made f o r a Hawaiian s p e c i e s , D_j_ mimica x by Kambysellis and Heed 45 (1971) ( f i g 17 ). In both s p e c i e s t h e r e i s a l a r g e percentage of p h e n o t y p i c a l l y s m a l l f l i e s which are not r e p r e s e n t e d by any • s m a l l ' genotypes. The absence of ' s m a l l ' genotypes i n d i c a t e s t h a t although ' s m a l l ' phenotypes may p e r s i s t over a s h o r t p e r i o d of time i n the long term g e n e t i c a l l y 'small* f l i e s cannot p e r s i s t . I t would be i n t e r e s t i n g to study the d i s t r i b u t i o n and s t a b i l i t y of s i t e s i n r e l a t i o n to the a b i l i t y t o pupate at a reduced s i z e . Myers (1976) has shown t h a t i n the cinnabar moth, l i r i a jacobaeae , the r e l a t i o n s h i p between l a r v a l weight and s u c c e s s f u l pupation d i f f e r s both between p o p u l a t i o n s and between years w i t h i n a p o p u l a t i o n . In these experiments l a r v a e were reared under i d e n t i c a l c o n d i t i o n s suggesting t h a t . the r e l a t i o n s h i p between s i z e and s u c c e s s f u l pupation i s , i n part at l e a s t , g e n e t i c a l l y determined and hence can be acted upon by n a t u r a l s e l e c t i o n . To summarize the r e s u l t s of t h i s s e c t i o n , 1) In D r o s o p h i l a f l i g h t reduces f e c u n d i t y . 2) The t r a n s i e n t nature of o v i p o s i t i o n s i t e s makes i t e s s e n t i a l f o r D r o s o p h i l a to d i s p e r s e between h a b i t a t s . 3) Because of 1) and 2) the f i t n e s s of a f l y w i l l depend i n p a r t upon i t s s i z e i n r e l a t i o n to the s p a t i o - t e m p o r a l d i s t r i b u t i o n of patches. 4) The e f f e c t on r (T) of changes i n the d e n s i t y o f s i t e s i s to i n c r e a s e the s i z e at which r (T) i s g r e a t e r than zero. There i s l i t t l e e f f e c t upon the optimum s i z e . 46 5) The s i z e a t which r{T) i s g r e a t e r than zero may be g r e a t l y i n f l u e n c e d by the lowest d e n s i t y of s i t e s t h a t occurs (D ). T h i s d e n s i t y does not have a s i g n i f i c a n t e f f e c t upon the optimum s i z e . 6) The p e r s i s t e n c e time of a patch and the amount of c o n t agion of patches are f a c t o r s that i n f l u e n c e the p r o b a b i l i t y of f l i e s s m a l l e r than determined by D p e r s i s t i n g i n the p o p u l a t i o n . 7) The two f a c t o r s mentioned i n 6) may a l s o be important i n the e v o l u t i o n of the a b i l i t y of a f l y to pupate at a s i z e much below t h a t at which i t pupates under optimal c o n d i t i o n s . 47 DISCUSSION The g e n e r a l message of t h i s paper i s that the s i z e d i s t r i b u t i o n of a c o l o n i z i n g p o i k i l o t h e r m can be determined by the s p a t i o - t e m p o r a l v a r i a b i l i t y of i t s environment. Furthermore, the f i t n e s s of a p a r t i c u l a r genotype cannot be estimated from the average environmental c o n d i t i o n s ; 'poor' c o n d i t i o n s when they occur have a p r o p o r t i o n a t e l y l a r g e r e f f e c t than 'good' c o n d i t i o n s . Consider f i r s t the c o n d i t i o n s necessary t o make environmnental c o n d i t i o n s an important determinant o f the upper s i z e l i m i t of an • r - s e l e c t e d ' p o i k i l o t h e r m . I t i s r e g u i r e d t h a t an organism i s subjected to one or more time-dependent or size-dependent m o r t a l i t y f u n c t i o n s . In the f o r e g o i n g a n a l y s i s t h i s c o n d i t i o n i s obtained by the presence of d i f f e r e n t growth r a t e s and a s i n g l e m o r t a l i t y f u n c t i o n ( l a r v a l s u r v i v a l decreases with time to pupa t i o n ) . Given a p a r t i c u l a r growth r a t e , s e l e c t i o n w i l l favour some p a r t i c u l a r s i z e . When two or more growth r a t e s are p o s s i b l e s e l e c t i o n w i l l favour not a s i z e which i s the average o f the p o s s i b l e optimum s i z e s obtained under the d i f f e r e n t constant c o n d i t i o n s but a s i z e c l o s e r to that o b t a i n e d under the l e a s t f a v o u r a b l e c o n d i t i o n s . I f at any i n s t a n c e i n time the whole p o p u l a t i o n i s s u b j e c t e d to the same environmental c o n d i t i o n s , i n t h i s i n s t a n c e the same food s u b s t a t e , then i t i s the temporal changes i n the environmental c o n d i t i o n s that w i l l determine the upper l i m i t . Under these circumstances i t i s not necessary 48 t h a t the h a b i t a t be d i s t r i b u t e d p a t c h i l y i n space. There are probably few circumstances ,however, i n which the food source or other r e l e v e n t environmental f a c t o r i s the same over a p o p u l a t i o n ' s domain. More g e n e r a l l y the h a b i t a t w i l l be a mosaic of c o n d i t i o n s . The d i s t r i b u t i o n of food and o v i p o s i t i o n s i t e s of D r o s o p h i l a are an example,, as are the d i s t r i b u t i o n of host p l a n t s of many l e p i d o t e r a n s p e c i e s . The upper s i z e l i m i t i n a 'mosaic environment' depends upon both the temporal and s p a t i a l frequency of resources. The important f a c t o r i s how o f t e n unfavourable c o n d i t i o n s occur over a l a r g e part p a r t of the environment. I t should be noted t h a t the emphasis i s upon the c o n d i t i o n s t h a t p e r t a i n to the l a r v a l s t a t e . Varying m o r t a l i t y r a t e s i n the a d u l t stage w i l l have r e l a t i v e l y l i t t l e i n f l u e n c e upon the upper l i m i t or optimum a d u l t s i z e because r i s determined l a r g e l y by the e a r l y o f f s p r i n g p r o d u c t i o n , the r e p r o d u c t i v e value of an i n d i v i d u a l d e c l i n i n g very r a p i d l y with a d u l t age (Lewontin 1965). T h i s may not, however, be t r u e of the lower l i m i t to s i z e . I n d i v i d u a l s of a p a r t i c u l a r genotype must ba a b l e to at l e a s t r e p l a c e themselves i n order f o r that genotype to p e r s i s t . In p o i k i l o t h e r r a s f e c u n d i t y i s a f u n c t i o n of s i z e . Thus given some p a r t i c u l a r m o r t a l i t y r a t e there i s some minimum s i z e that i s necessary t o ensure t h a t b i r t h s egual deaths, any environmental f a c t o r t h a t reduces f e c u n d i t y w i l l r a i s e the lower l i m i t to s i z e . I t has been shown that energy 49 i n D rosqphila i s not s e p a r a t e l y p a r t i t i o n e d i n t o s t o r e s f o r f l i g h t and s t o r e s f o r r e p r o d u c t i o n . Thus f l i g h t reduces the number of eggs t h a t a f l y can l a y . Since the o v i p o s i t i o n s i t e s are d i s t r i b u t e d i n space, part of a f l y ' s energy r e s e r v e s must be seguestered f o r d i s p e r s a l between patches. T h i s means t h a t the s i z e at which f e c u n d i t y i s at l e a s t s u f f i c i e n t t o meet m o r t a l i t y i s a f u n c t i o n of the s p a t i a l d i s t r i b u t i o n of the o v i p o s i t i o n s i t e s . The f u r t h e r the patches are ap a r t the higher w i l l be the lower l i m i t to s i z e . The f a c t t h a t the ab s o l u t e r e p r o d u c t i v e cost i n c r e a s e s as s i z e decreases r a i s e s t h i s l i m i t even f u r t h e r . As noted above, these c o n s t r a i n t s do not a f f e c t the optimum body s i z e to any great degree. The g e n e r a l i t y of the phenomenum of r e d u c t i o n i n egg pro d u c t i o n as a r e s u l t of d i s p e r s a l can only be a s c e r t a i n e d by experimental a n a l y s i s . C e r t a i n f l y i n g p o i k i l o t h e r m s make long m i g r a t i o n s or d i s p e r s a l f l i g h t s upon emergence from the pupa. In such groups we might expect to f i n d t h a t egg pr o d u c t i o n and f l i g h t are p a r t i t i o n e d i n time as indeed they seam t o be. Dysdercus ni.grofaciatus , f o r example, make f l i g h t s a f t e r emergence from the pupa but h i s t o l y s e the f l i g h t muscles when egg production begins. H i s t o l y s i s of the f l i g h t muscles and the onset of egg p r o d u c t i o n w i l l not occur i f the female i s st a r v e d (Dingle and Arora 1973). In t h i s s p e c i e s s u i t a b l e o v i p o s i t i o n s i t e s are p a t c h i l y d i s t r i b u t e d i n space but the patches are s u f f i c i e n t l y p r o d u c t i v e and s t a b l e that they can support a l l the o f f s p r i n g of the female. In Br-osophila,. 50 o v i p o s i t i o n patches are probably very unstable and t h e r e i s a high p r o b a b i l i t y t h a t a patch w i l l become u n s u i t a b l e before the l a r v a e are a b l e to pupate. I t i s , t h e r e f o r e advantageous f o r a female t o spread her eggs over a number of patches. I t would be i n t e r e s t i n g to examine the r e l a t i o n s h i p between h a b i t a t d i s p e r s i o n and h a b i t a t s t a b i l i t y and the e f f e c t of f l i g h t i n a v a r i e t y of d i p t e r a n s p e c i e s . P r e d i c t i o n s about i n t e r - s p e c i f i c d i f f e r e n c e s i n body s i z e as they r e l a t e to changes i n h a b i t a t d e n s i t y cannot be made unles s other l i f e - h i s t o r y c h a r a c t e r i s t i c s are taken i n t o account. I n t r a - s p e c i f i c comparisons are much e a s i e r to make but even i n these cases one should bear i n mind that changes i n h a b i t a t d e n s i t y are symptomatic c f more general changes i n environmental c o n d i t i o n s . A proper i n v e s t i g a t i o n of t h i s e f f e c t should i n v o l v e a reasonably thorough study of the l i f e -h i s t o r y of the organism, h o p e f u l l y ending i n a s i m u l a t i o n model t h a t can s u c c e s s f u l l y p r e d i c t the p o p u l a t i o n dynamics of the s p e c i e s . The g r e a t e s t stumbling block to any p r e d i c t i o n s at present i s the simple l a c k of case h i s t o r i e s . Even to c l a s s i f y a s p e c i e s as sedentary or h i g h l y mobile i s extremely, d i f f i c u l t , p a r t i c u l a r l y i n d i p t e r a n s where the presence of wings may i n c o r r e c t l y suggest high a c t i v i t y (Southwood 1962). A f u r t h e r c o m p l i c a t i o n i s t h a t the l e s s d i s p e r s e d the h a b i t a t and the l e s s mobile the animal, the more l i k e l y i t i s t h a t the s p e c i e s i s not a c o l o n i z i n g s p e c i e s . Under c o n d i t i o n s of strong density-dependent c o n t r o l of p o p u l a t i o n numbers the 51 q u a l i t y of o f f s p r i n g r a t h e r than the number may be- of o v e r r i d i n g s i g n i f i c a n c e . The e f f e c t of s p a t i a l and temporal events on the optimum and maximum body s i z e are l i k e l y to have wider g e n e r a l i t y than the e f f e c t of d i s p e r s a l on the minimum body s i z e . The important c o n s i d e r a t i o n i s t h a t the s u r v i v a l r a t e i s a f u n c t i o n of s i z e and t h i s r a t e i s v a r i a b l e i n space and time. Even i n v e r t e b r a t e p o i k i l o t h e r m s t h i s c o n d i t i o n may h o l d . For example, the time-dependent m o r t a l i t y of l a r v a l amphibians may vary from pond t o pond and year t o year (Savage 19**, B e l l 1974) . Other f a c t o r s such as com p e t i t i o n f o r food may s e t an upper l i m i t below the l i m i t s et by the v a r i a b i l i t y i n environmental c o n d i t i o n s . There are a h i e r a r c h y of upper l i m i t s . At the extreme there are p h y s i o l o g i c a l l i m i t s to s i z e . Below t h i s l i m i t , e c o l o g i c a l and behav i o u r a l f a c t o r s set l i m i t s . The f a c t o r that s e t s the lowest l i m i t w i l l be of predominating s i g n i f i c a n c e . In some i n s t a n c e s t h i s could be size-dependent mating success, i n others the p r o b a b i l i t y of s u r v i v a l i n crowded c o n d i t i o n s and i n others i t c o u l d be the success i n s u r v i v i n g a v a r i e t y of environmental c o n d i t i o n s . In an ' r - s e l e c t e d ' organism, by d e f i n i t i o n , t h e r e i s a very great chance that the success of a p a r t i c u l a r s i z e d i n d i v i d u a l w i l l depend upon how well i t can cope with environmental f a c t o r s ether than members of i t s own s p e c i e s . Such organisms are not l i k e l y to reach l a r g e p o p u l a t i o n s i z e s 52 i n r e l a t i o n to t h e i r resources and hence a study of t h e i r p o p u l a t i o n dynamics i s r a t h e r more d i f f i c u l t than with a 'k-s e l e c t e d ' organism. Despite the success of r e a r i n g D r o s o p h i l a i n the l a b o r a t o r y t h e r e has been l i t t l e success i n l o c a t i n g i t s o v i p o s i t i o n s i t e s or understanding the p o p u l a t i o n dynamics of a p a r t i c u l a r s p e c i e s i n the f i e l d . The most f r u i t f u l approach i s most l i k e l y to i n v o l v e a study of a ' k - s e l e c t e d ' organism. The l e p i d o p t e r a n s are a t t r a c t i v e i n t h i s r e s p e c t . Many s p e c i e s have m u l t i p l e host p l a n t s and a study of l a r v a l s u r v i v a l on these p l a n t s i n c o r p o r a t i n g c o n s i d e r a t i o n s of the e f f e c t s of l a r v a l crowding would be rewarding. The e f f e c t of i n t r a - s p e c i f i c c o m p e t i t i o n upon the c o n c l u s i o n s reached i n t h i s t h e s i s w i l l depend upon whether such c o m p e t i t i o n i s 'scramble' or 'contest'. In the former case the r e s o u r c e s are d i v i d e d more or l e s s e q u a l l y between l a r v a e having the same growth r a t e : as a r e s u l t m o r t a l i t y w i l l i n c r e a s e with s i z e . Backer (1951) has shown t h a t c o m p e t i t i o n between d i f f e r e n t s t r a i n s of p^ melanoqaster l a r v a e i s of t h i s form. The e f f e c t of t h i s type of competition i s to decrease the p r o b a b i l i t y t h a t the average body s i z e of the p o p u l a t i o n w i l l exceed T and hence i t w i l l reduce the f l u c t u a t i o n s i n p o p u l a t i o n numbers. I f the d e n s i t y becomes very high r e s o u r c e s may be so t h i n l y d i s t r i b u t e d t h a t the s u r v i v a l r a t e i s very low and p o p u l a t i o n numbers may be s e v e r e l y reduced. Thus a low i n t e n s i t y of competition may s t a b i l i z e p o p u l a t i o n numbers and hence decrease the p r o b a b i l i t y of e x t i n c t i o n but a high 53 i n t e n s i t y of c o m p e t i t i o n w i l l i n c r e a s e the p r o b a b i l i t y of e x t i n c t i o n because few l a r v a e o b t a i n s u f f i c i e n t f o o d . The l a t t e r p r o b a b i l i t y would be decreased i f under severe crowding the competition changed from the 'scramble' type to the 'c o n t e s t ' type i n which there was i n t e r f e r e n c e between l a r v a e and some animals obtained more than t h e i r ' f a i r share'. There i s some i n d i c a t i o n t h a t t h i s does occur i n D.. melanogaster : the s i z e a t pupation d e c l i n e s i n i t i a l l y with i n c r e a s i n g d e n s i t y but i n c r e a s e s s l i g h t l y at very high d e n s i t i e s (Chiang and fiodscn 1950). By d e f i n i t i o n , an • r - s e l e c t e d ' organism i s one which maximizes i t s r a t e of i n c r e a s e , r . I t has been suggested t h a t i n some i n s t a n c e s r may not be an a p p r o p r i a t e measure of f i t n e s s even when density-dependent processes are unimportant. In some i n s t a n c e s s e l e c t i o n may favour a l i f e - h i s t o r y t h a t ensures t h a t a female l e a v e s at l e a s t two o f f s p r i n g i n the next ge n e r a t i o n (assuming a male mates with only one female). T h i s s t r a t e g y has been c a l l e d 'bet-hedging' (Stearns 1976). In essence, however, i t i s an argument based on r , but with a long time h o r i z o n . By adopting the 'bet-hedging' s t r a t e g y an organism ensures t h a t many genera t i o n s hence i t w i l l have descendants. Thus over the long term such an organism has the hi g h e s t r. Two examples from t h i s t h e s i s i l l u s t r a t e t h i s p o i n t q u i t e c l e a r l y . F i r s t , l e t us c o n s i d e r case 1 of t h i s t h e s i s . The optimum body s i z e i s a c t u a l l y the one t h a t maximizes r over the long 54 term. F l i e s of t h i s s i z e can always complete development. In the s h o r t term s e l e c t i o n may favour a l a r g e r body s i z e because when the p r o b a b i l i t y of Type S yeasts dominating the environment i s very s m a l l there i s a high p r o b a b i l i t y of a l o n g p e r i o d i n which almost a l l s i t e s c o n t a i n Type F y e a s t s . The s i z e d i s t r i b u t i o n of f l i e s t h a t we might f i n d i n such a p o p u l a t i o n w i l l depend upon the p e r i o d over which we observe i t . We cannot speak of a 'best* development time or s i z e unless we d e f i n e the time h o r i z o n . The second example i s drawn from case 2 of t h i s t h e s i s . Suppose t h a t the p r o b a b i l i t y of a patch p e r s i s t i n g f o r the developmental peri o d o f a f l y l a r v a i s g (0<g<1) . L e t the t o t a l f e c u n d i t y of a f l y be F and the • c o s t 1 of moving from one patch to another be c. I f a f l y does not d i s p e r s e but l a y s a l l i t s eggs i n the same patch i n which i t grew the expected number of o f f s p r i n g t h a t i t w i l l leave i s Fg. Now suppose the f l y d i s t r i b u t e s i t s eggs e g u a l l y amongst n patches, 'what i s the expected number of o f f s p r i n g t h at i t w i l l l e a v e ?' The answer i s (F-nc)g. C l e a r l y , on average, the f l y t h a t does not d i s p e r s e w i l l leave more o f f s p r i n g than the one t h a t does d i s p e r s e . Thus no animal should d i s p e r s e ! The f a l l a c y i n t h i s argument i s t h a t i t i g n o r e s the p r o b a b i l i t y of an organism l e a v i n g descendents more than one g e n e r a t i o n hence. I f a f l y does not d i s p e r s e the p r o b a b i l i t y t h a t i t w i l l l e a v e no o f f s p r i n g i s 1-q w h i l s t the p r o b a b i l i t y t h at a f l y t h a t d i s t r i b u t e s eggs amongst n patches leaves no o f f s p r i n g i s 55 rv (1-q) . The n c n - d i s p e r s e r although i t has a higher expected production of progeny than the d i s p e r s e r a l s o has a very much highe r p r o b a b i l t y of l e a v i n g no o f f s p r i n g . In an a s s e x u a l l y reproducing organism the s t r a t e g y t h a t has the longest p e r s i s t e n c e time w i l l be the one t h a t w i l l e v e n t u a l l y p r e v a i l . Sexual r e p r o d u c t i o n , with i t s recombination of genotypes may a l t e r t h i s r e s u l t and a s t r a t e g y t h a t g i v e s a lower p e r s i s t e n c e time than another but which might produce t e m p o r a r i l y very l a r g e p o p u l a t i o n s i z e s may p r e v a i l . The trend towards such a s t r a t e g y may r e s u l t i n the premature e x t i n c t i o n of the p o p u l a t i o n , as demonstrated i n the s i m u l a t i o n s t u d i e s of Roff (1975) or to l a r g e p o p u l a t i o n f l u c t u a t i o n s as i n case 1 of t h i s study. In p r a c t i s e , t h e r e f o r e , w h i l s t we might be able t o p r e d i c t the 'optimal' s t r a t e g y the one t h a t we a c t u a l l y observe may be r a t h e r d i f f e r e n t . The r e l a t i o n s h i p between 'simple' theory and •complex' r e a l i t y can only be u l t i m a t e l y r e s o l v e d whan we have some good case h i s t o r i e s t o compare p r e d i c t e d and observed p a t t e r n s . 56 FIGOJES 57 F i g 1 : Tha l a r v a l development functions, used i n t h i s study. These ar? i d e a l i z e d v=rsions of those a c t u a l l y ooserved i n D r o s p p h i l a . TIME -t 5 8 F i q 2 : The growth curves of Droso£hi2a m u l l e r i l a r v x e on the d i f f e r e n t yeasts found i n t h e i r host p l a n t , Opu^tia.. Data from Wagner (1944). X r-o z L U i i i i i i < i i i i i i i i i i • • Y-7 i i i i i i I I I 0 3 0 6 6 102. 1 3 8 174 3 0 6 6 102 138 174-T I M E - H O U R S 5 9 F i q 3 : The e f f e c t of changes i n a d u l t s i z e on -cue r a t e of i n c r e a s e when o v i p o s i t i o n s i t e s a l l con t a i n t i e same yeast type at any given time. The p r o b a b i l i t y of a l l s i t e s c o n t a i n i n g Type S yeasts i s p and the probability of a l l s i t e s A c o n t a i n i n g Type F yeasts i s 1-p. THORAX LENGTH 6 0 P i g 4 : The e f f e c t of changes i n ad u l t s i z e on u e ra t e of i n c r e a s e when o v i p o s i t i o n s i t e s may c o n t a i n e i t h e r type F yeasts or T y p e S yeasts at some given time. The p r o b a b i l i t y of a s i t e c o n t a i n i n g Type S yeasts i s f and the p r o b a b i l i t y of a s i t e c o n t a i n i n g Type F yeasts i s 1-f. THORAX LENGTH 61 F i g 5 : S u r v i v a l of p.. m u l l e r i l a r v a e as a f u n c t i o n of the development time and the yeast s p e c i e s . Data from Wagner(1944). 100 80 60 < ^ 40-cr Y - 4 © Y " 6 © Y - 5 ©Y-2 ©Y-7 ®Y-8 Y= 144 - -61X r - -«91 <Y-1 Y -3 © Y -9 0 100 140 180 220 L A R V A L PERIOD ( H O U R S ) 62 F i g 6 : Map showing the average percentage of Type S yeasts per c a c t u s f r u i t i n the 5 l o c a l i t i e s sampled by Wagner (1944). 6 0 m i l e s 63 F i g 7 : The frequency d i s t r i b u t i o n of Type S y e a s t s i n A u s t i n and C r e s t o n i o . Data frcm Wagner (1944) * In all cases Type S yeasts comprise 100% of the yeasts present CO DC 111 CQ Z) z 5 4 3 2 1 8 6 2 0 C r e s t o n i a N = 9 T r 1 1—"—r A u s t i n N=20 T 1—"—r T 1 1 1 — — i — — r 5 2 5 45 65 8 5 P E R C E N T T Y P E S Y E A S T S 6 4 F i g 8 : The e f f e c t o f f l i g h t cn egg p r o d u c t i o n • net f l o w n O flown 1 2 3 4 5 6 7 DAY 65 F i g 9 : D i f f e r e n c e s between eqg pro d u c t i o n on adjacent days f o r f l i e s flown and not flown. The x a x i s shows the days c o n s i d e r e d and the y a x i s the d i f f e r e n c e i n <=gg p r o d u c t i o n between these days. Note t h a t a f t e r f l i g h t (day 3) tne drop i n egg p r o d u c t i o n between days 3 and 4 i s s i g n i f i c a n t l y greater f o r the flown group than the unflown group. Confidence l i m i t s shewn are + 2 standard e r r o r s . \ • NOT FLOWN 0 FLOWN T , T + 1 6 6 Fig 10 : The estimated 'reproductive cost* of a one hour f l i g h t in Drosgphila melanocjaster A Sae text ror method of c a l c u l a t i n g t h i s cost. Confidence l i m i t s shown are + 1 standard error. Y - 21.0 - 5.7X I •. . • # . " ' « 1 2 3 4 DAY AFTER FLIGHT 6 7 F i g 11 : Th* e f f e c t of f l i g h t d u r a t i o n on egg p r o d u c t i o n on the day proceeding f l i g h t . • • - f l i e s stuck on pins which d i d not f l y . Y = 5 5 . 6 - 0 . 4 3 X 9 ' 8-7-6 -' o T — X _r 4 2-1 0 • © o o © ° « 0 0 1 3 4 5 6 - I FLIGHT TIME-MINSx10 F i g 12 : The e f f e c t of f l i g h t d u r a t i o n on the combined pr o d u c t i o n of the two days proceeding f l i g h t . Y = 127. 9 - 0. 74X 69 F i g 13 : R e s p i r a t i o n r a t e as a f u n c t i o n of wingbeat. frequency, Data from Chadwick and Gilraour 1940 and Chadwic* 1947. SYMBOL SPECIES SEX t D. AMERICANA MALE 0 D. VIRILIS MALE X C. REPLETA FEMALE D. 5 EPLETA MALE Y = -22.8+2.4X r =. 0. 89 £ £ £ O CD -(—• Q. U d * o • 5 i • 2 5 0 -- • 2 5 -- 5 —75-I - 1 - 0 - 1 - 2 5 - 1 - 5 x • X • • o 8-7 8-9 —i r 9-1 9-3 Loge(Wingbeat Frequency) 9 - 5 70 F i g 14 : The e f f e c t of changes i n a d u l t s i z e on tae r a t e of i n c r e a s e when f l i g h t reduces f e c u n d i t y . T h i s r e d u c t i o n was c a l c u l a t e d on the b a s i s that a f l y of thorax l e a g t h 1mm has a decrease i n eqg pr o d u c t i o n of 20 eggs per day due to d i s p e r s a l . MAXIMA * i i 1 1 1 1 1 1 0 1 2 3 4 THORAX LENGTH 71 F i g 15 : Th-5 s i z e d i s t r i b u t i o n of n o n - d i s p e r s i n g f l i e s (n=17) compared to a c o n t r o l sample (n=36).measurements made from the j u n c t i o n of l o n g i t u d i n a l v e i n s 1 and 2 to the end of l o n g i t u d i n a l vein 2. CO DC LU CD z: 8-j 6-4-2 0 6 4-c o n t r o l n o n d i s p e r s e r s ° 68 70 72 74 76 78 80 82 84 WING LENGTH-MICROMETER UNITS F i g 16 : the s i z e d i s t r i b u t i o n of n o n - d i s p e r s i n g f i l e s (n compared to a c o n t r o l sample (n=44). CO DC LU CQ 12 8 12! 8 i A-CONTROL I 1 i i I I 1 r - " — j — — I I 1 I i l 1 I > ' NON DISPERSERS r n . / 64 66 68 70 72 74 76 78 80 82 WING LENGTH-MICROMETER UNITS 7 3 F i g 17 : S i z e d i s t r i b u t i o n of n a t u r a l and 1st g e n e r a t i o n l a b o r a t o r y s t o c k s of p.. s i l i c a . Data from K d m b y s e l l i s and Heed (1971). 5 0 4 4 0 30-20-UJ 10 < z 111 o . cc 22 111 18 14 6 L A B . F 1 N = 3 4 7 WILD N = 325 • •__ i _ 1-3 1-5 1-7 1-9 2-1 2-3 THORAX L E N G T H - M M . TABLE 1 Parameter values used i n calculating r. Values based on data for Drosophila melanogaster from a number of sources. EQUATION PARAMETER VALUE EGG PRODUCTION At ( i - -t y-e A t 5 5 -2. O-IX LARVAL GROWTH EQUATIONS 44. a +• ct c LARVAL SURVIVAL (%)• ±Cro - st 21.C ADULT SURVIVAL (% DAILY SURVIVAL) * t : time i n days # t : hatching time + pupation time + time i n l a s t phase of growth MAJOR REFERENCES i . Alpatov 1929, Bakker 1959, Chiang and Hodson 1950, David et a l 1974, David and Clavel 1967, M M i l l a n et a l 1970 a,b, Prowsner 1935. 75 E f f e c t of cage s i z e on egg pr o d u c t i o n i n D.. meianoaa-ster. Egg production of 15 females i n a l a r g e cage compared t o the egg pr o d u c t i o n of 15 females i n 15 v i a l s . DAY LARGE CAGE X SD 1 4.20 3.74 2 23.73 13.04 3 31.60 18.92 VIALS T X SD 9. 93 9.29 2. 21* 38.00 19. 82 2. 32* 46.06 25.03 1.78+ * P<0.025 ONE-TAILED TEST + P<0.05 ONE-TAILED TEST 76 TABLE 3 E f f e c t of cage s i z e on egg production i n EL. melanogasteri. Comparison between egg production one g a l l o n c o n t a i n e r s and v i a l s . » LARGE CAGES VIALS X SD X SD 14 37.07 14.20 49.15 10.62 t=2.48, P<0.025 o n e - t a i l e d t e s t 77 TAELj! 4 e f f e c t of l a r v a l d e n s i t y on the s i z e and number of emerging a d u l t s . 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