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Studies on the genetics of the sex-ratio trait in the two sibling species of Drosophila : D. Pseudoobscura… Wu, Chung-I 1982

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STUDIES ON THE GENETICS OF THE SEX-RATIO TRAIT IN THE TWO SIBLING SPECIES OF DROSOPHILA: D. PSEUDOOBSCURA AND D. PERSIMILIS by CHUNG-I WU B . S c , Tunghai U n i v e r s i t y , Taiwan, 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Genet ics Programme) We accept t h i s t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA 7 March 1982 (c) Chung-I Wu, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the,Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Bepa-r-fcmcnt--€>£ Q^lW /' c > \ Frt friw f The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) i i ABSTRACT Many spec ies of D r o s o p h i l a have an X chromosome i n v e r s i o n polymorphism: the Standard arrangement and the Sex-Rat io (SR) arrangement. Male c a r r i e r s of SR t ransmi t predominantly X-bear ing sperm and hence produce n e a r l y a l l - f e m a l e progeny. In the absence of s t rong c o u n t e r a c t i n g s e l e c t i o n , SR would be m e i o t i c a l l y d r i v e n to f i x a t i o n , caus ing p o p u l a t i o n e x t i n c t i o n . In PART I , the r o l e of v i r i l i t y s e l e c t i o n i n m a i n t a i n i n g the SR polymorphism in D. pseudoobscura i s examined by p a r t i t i o n i n g i t i n t o two components. The SR males are found to s u f f e r s u b s t a n t i a l v i r i l i t y r e d u c t i o n which would not be detected i f the d i f f e r e n c e s between the two components are not heeded. The s i g n i f i c a n c e of t h i s f i n d i n g i s d i scus sed i n l i g h t of two s p e c i f i c observa t ions u s u a l l y a s s o c i a t e d w i t h the Sex-R a t i o polymorphism i n t h i s s p e c i e s . One i s the absence of suppressor m o d i f i e r s of " s e x - r a t i o " expres s ion and the other i s the temperature-dependent d i s t r i b u t i o n of the s e x - r a t i o t r a i t . In PART I I , a model i s proposed to de sc r ibe the behavior of the autosomal suppressor m o d i f i e r s of " s e x - r a t i o " m e i o t i c d r i v e . These m o d i f i e r s , i f n e u t r a l i n other r e s p e c t s , should increase because they tend to be a s s o c i a t e d w i t h the rare sex (males) . However, s e l e c t i o n opera t ing on the s e x - l i n k e d d r i v e locus w i l l sometimes act aga ins t autosomal m o d i f i e r s as w e l l because the two l o c i are always i n gametic phase d i s e q u i l i b r i u m . C o n d i t i o n s under which m o d i f i e r s w i l l not increase are presented i n terms of the f i t n e s s e s of d i f f e r e n t genotypes at the sex-l i n k e d d r i v e l o c u s . To prevent an increase i n m o d i f i e r a l l e l e s , the f i t n e s s of Sex-Rat io males r e l a t i v e to Standard males has to be no greater than 0 . 3 . Th i s r e s u l t i s i n good agreement w i t h that of PART I . PART I I I dea l s w i t h " s e x - r a t i o " genes, t i g h t l y l i n k e d w i t h i n the Sex-Rat io i n v e r s i o n . By t a k i n g advantage of the fac t that the Sex-Rat io chromosome of D. p e r s i m i l i s (SR(B)) i s homosequential to the Standard chromosome of D. pseudoobscura (ST(A) ) , two r e c i p r o c a l i n t r o g r e s s i o n experiments were c a r r i e d ou t . I n d i v i d u a l segments of SR(B) or ST(A) were i n t r o g r e s s e d i n t o the genome of D. pseudoobscura or D. p e r s i m i l i s , r e s p e c t i v e l y . Males possess ing a h y b r i d SR(B)-ST(A) X chromosome and a genet ic background d e r i v e d from e i t h e r of the two species were te s ted for f e r t i l i t y and " s e x - r a t i o " e x p r e s s i o n . I t was found t h a t , i n terms of the me io t i c d r i v e genes, the Sex-Rat io chromosome d i f f e r s e x t e n s i v e l y from the Standard chromosome. Because recombinat ions of these genes r e s u l t i n a complete l o s s of s e x - r a t i o e x p r e s s i o n , t h i s f i n d i n g lends s t rong support to the hypothes i s of gene c o a d a p t a t i o n . Coadapta t ion , i n t h i s c o n t e x t , i s the advantage of being t r a n s m i t t e d p r e f e r e n t i a l l y . In l i g h t of t h i s f i n d i n g , e v o l u t i o n of the s e x - r a t i o system in these two s i b l i n g species i s d i s c u s s e d . I n t r o g r e s s i o n experiments a l s o y i e l d e d i n f o r m a t i o n about h y b r i d s t e r i l i t y . Four types of s t e r i l i t y i n t e r a c t i o n s were i d e n t i f i e d ; one of them i n v o l v e d at l e a s t three genet i c elements . With r e c i p r o c a l i n t r o g r e s s i o n , s t e r i l i t y i n t e r a c t i o n s were found to be "a symmetr ic " . The asymmetry i s f u l l y expected from the v iewpoint of e v o l u t i o n of postmating r e p r o d u c t i v e i s o l a t i o n . V TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS i x PROLOGUE 1 PART I - ON VIRILITY SELECTION 9 A b s t r a c t 10 I n t r o d u c t i o n 11 M a t e r i a l s and methods 19 R e s u l t s 28 The t h r e s h o l d hypothes i s on male v i r i l i t y 28 The f e r t i l i t y count 28 Sperm displacement 32 Sexual s e l e c t i o n 35 The tendency of females to remate 36 A n a l y s i s 39 A model on v i r i l i t y e s t i m a t i o n 39 Fur ther t e s t s of v i r i l i t y s e l e c t i o n 45 E s t i m a t i o n of SR v i r i l i t y 49 D i s c u s s i o n 51 PART II - ON AUTOSOMAL MODIFIERS 71 A b s t r a c t 72 I n t r o d u c t i o n 73 "The model 77 v i Genera l d e s c r i p t i o n 77 The model 78 R e s u l t s 86 D i s c u s s i o n 89 PART I I I - INTROGRESSION EXPERIMENTS 97 A b s t r a c t 98 I n t r o d u c t i o n 99 M a t e r i a l s and methods . . . 1 0 4 R e s u l t s 109 Experiment I 109 Experiment II 112 D i s c u s s i o n 118 On the sr t r a i t 118 On h y b r i d s t e r i l i t y 127 EPILOGUE 146 References 150 Appendix 160 v i i LIST OF TABLES Table 1-1. F e r t i l i t y counts 61 Table 1-2. T e s t i n g the t h r e s h o l d model 62 Table 1-3. Sperm displacement 63 Table 1-4. Mate cho ice s by females 64 Table 1-5. Remating tendency of females 65 Table 1-6. P r o p o r t i o n of daughters 66 Table 11 — 1 . Sex-dependent transmisson of autosomal m o d i f i e r s 94 Table 111 — 1. F e r t i l i t y and sr expres s ion of recombinant males 135 Table I I I - 2 . F e r t i l i t y and sr expres s ion of recombinant males 136 Table I I I - 3 . F e r t i l i t y and sr expres s ion of recombinant males 137 Table I I I - 4 . F e r t i l i t y and sr expres s ion of recombinant males 138 v i i i LIST OF FIGURES F i g u r e 1-1. Male r eproduc t ive stages 30 F i g u r e 1-2. The frequency-dependent v i r i l i t y f u n c t i o n 67 F igure 1-3. The d i s t r i b u t i o n of sex-composi t ions 68 F i g u r e 1-4. L i k e l i h o o d r a t i o s for X 69 F igure 1-5. Observed v s . expected p r o p o r t i o n s of daughters 70 F igure 11 — 1 . The fate of autosomal m o d i f i e r s 95 F igure I I - 2 . The advantage of m o d i f i e r s over t h e i r a l l e l e s 96 F i g u r e 111 — 1 . Graphic r e p r e s e n t a t i o n of i n v e r s i o n s on XR . .139 F i g u r e I I I - 2 . I n t r o g r e s s i o n p r o t o c o l for Experiment I 140 F i g u r e 111-3 . I n t r o g r e s s i o n p r o t o c o l for Experiment II . . . . 1 4 1 F i g u r e I I I -4a . A model on the evo lu t ion of the SR i n v e r s i o n 1 42 F igure I I I -4b . A model on the evo lu t ion of the SR i n v e r s i o n , 143 F igure I I I -4c . A model on the e v o l u t i o n of the SR i n v e r s i o n F igure I I I - 5 . E v o l u t i o n of asymmetric s t e r i l i t y i n t e r a c t ions 145 i x ACKNOWLEDGEMENTS I am g r a t e f u l to D r . C. F . Wehrhahn, my s u p e r v i s o r , not only for h i s s u p e r v i s i o n of t h i s t h e s i s but a l s o fo r h i s pa t ience i n l e a d i n g me i n t o the f a s c i n a t i n g f i e l d of P o p u l a t i o n G e n e t i c s . I a l s o wish to express my many thanks to D r . A . T. Beckenbach who in t roduced me to exper imenta l p o p u l a t i o n genetics- in genera l and the Sex-Rat io problem i n s p e c i f i c . Without h i s i n s p i r a t i o n , encouragement, and generos i ty i n l end ing me h i s l a b o r a t o r y resources and, more i m p o r t a n t l y , h i s knowledge of t h i s i n t e r e s t i n g problem, t h i s work would not have been p o s s i b l e . I am indebted to D r s . D. G. Holm, J . Myers and R. Ward for c r i t i c a l l y reading the manuscript and for s e r v i n g on my research committee. Thanks a l s o go t o the Department of B i o l o g i c a l Sc iences of Simon Fraser U n i v e r s i t y , i t s f a c u l t y and s t a f f for o f f e r i n g me the conveniences and atmosphere normal ly reserved for t h e i r own graduate s tudent s . The U n i v e r s i t y of B r i t i s h Columbia supported me w i t h three years of U n i v e r s i t y Graduate F e l l o w s h i p which I g r e a t l y a p p r e c i a t e . Throughout the whole course of t h i s s tudy, my wife gave me every sor t of support one cou ld ever ask f o r . Her a t t e n t i v e n e s s as an audience and p a r t i c i p a t i o n i n v a r i o u s stages are i n t e g r a l pa r t s of t h i s work. In the r e a l sense, she i s as much an author of t h i s t h e s i s as I am. F i n a l l y , I ded ica te t h i s t h e s i s to my parents whose conf idence i n me and respect for i n t e l l e c t u a l a c t i v i t i e s l e d me onto an academic c a r e e r . 1 PROLOGUE 2 In 1922, A . H. S tur tevant d i s covered in D r o s o p h i l a a f f i n i s some p e c u l i a r crosses which y i e l d e d predominantly daughters (Morgan, B r i d g e s , and S t u r t e v a n t , 1925). S i x t y years have passed, but our understanding of t h i s phenomenon has lagged f a r behind what one would have expected of an i n t e r e s t i n g and important q u e s t i o n . T h i s phenomenon was subsequently found i n many spec ies of D r o s o p h i l a : D. obscura (Gershenson, 1928), D. pseudoobscura and D. p e r s i m i l i s (S tur tevant and Dobzhansky, 1936), D. paramelanica ( S t a l k e r , 1961), D. subobscura (Jungen, 1967) and many other s p e c i e s . Thi s phenomenon has s ince been r e f e r r e d to as " s e x - r a t i o " e x p r e s s i o n . A c a r e f u l genet ic a n a l y s i s by Gershenson (1928) showed that the gene (or genes) for " s e x - r a t i o " expres s ion i s on the X chromosome. Subsequent s t u d i e s (S tur tevant and Dobzhansky, 1936; S t a l k e r , 1961) showed that these " s e x - r a t i o " genes are always a s s o c i a t e d w i t h i n v e r s i o n s on X chromosomes, denoted by prev ious authors as Xr or SR. Male c a r r i e r s of SR chromosomes t r ansmi t predominantly X at the expense of Y chromosomes and hence produce almost e x c l u s i v e l y daughters . In D. pseudoobscura, for example, daughters account for 95-99 % of the progeny of " s e x - r a t i o " males. (Females heterozygous for SR are apparent ly normal i n segregat ion (Gershenson, 1928) ) . Sandler and N o v i t s k i (1957) r e f e r r e d to a d i s t o r t i o n i n the frequency of a l l e l e s among gametes of a heterozygous parent as m e i o t i c d r i v e . " S e x - r a t i o " i n D r o s o p h i l a i s a case of sex-l i n k e d m e i o t i c d r i v e . S i m i l a r cases have been found i n the b u t t e r f l y , Acraen encedon (Chant ler and Owen, 1972) and i n the 3 mosquito, Aedes aegypt i (Hickey and C r a i g , 1966). The reason " s e x - r a t i o " i s not only an i n t e r e s t i n g but a l s o an important phenomenon i s that answers to many ques t ions concerning t h i s p e c u l i a r t r a i t have ex tens ive i m p l i c a t i o n s for many problems of genera l i n t e r e s t i n e v o l u t i o n a r y g e n e t i c s . Questions about the " s e x - r a t i o " t r a i t f a l l i n t o three c a t e g o r i e s : I . S ince SR i s t r a n s m i t t e d by males at twice the ra te of the standard X (denoted as ST) , what prevents SR from being f i x e d and, as a consequence of t h a t , p o p u l a t i o n e x t i n c t i o n ? PART I of t h i s t h e s i s dea l s s p e c i f i c a l l y w i t h the r o l e of n a t u r a l s e l e c t i o n i n m a i n t a i n i n g the SR polymorphism. I I . Suppressor m o d i f i e r s of the " s e x - r a t i o " expres s ion which render SR males capable of producing normal male and female progeny have been found i n some, but not a l l s p e c i e s . PART II i s a study on the fa te of autosomal m o d i f i e r s under d i f f e r e n t regimes of n a t u r a l s e l e c t i o n . Both s t u d i e s dea l w i t h d i f f e r e n t aspects of n a t u r a l s e l e c t i o n i n the " s e x - r a t i o " system and, hence, are r e l a t e d to each other i n an i n t i m a t e way. Both s tud ie s t r e a t the SR t r a i t as determined by a s i n g l e Mendel ian gene. But , i n f a c t , the SR t r a i t i n v o l v e s a gene complex bound t i g h t l y by chromosomal i n v e r s i o n s (sometimes r e f e r r e d to as supergenes) . There fo re : I I I . What i s the nature, of genes w i t h i n SR i n v e r s i o n s ? What are the number and l o c a t i o n s of 4 gene l o c i a s s o c i a t e d w i t h the " s e x - r a t i o " express ion? How does t h i s "supergene" evolve? To my knowledge, PART I I I of t h i s t h e s i s i s the f i r s t s u c c e s s f u l attempt to prov ide some answers to these q u e s t i o n s . An attempt to answer the ques t ions of category I i s a l s o par t of the grand program i n populaton genet ic s to demonstrate n a t u r a l s e l e c t i o n at work. N a t u r a l s e l e c t i o n i n v a r i o u s forms -s t a b i l i z i n g s e l e c t i o n , b a l a n c i n g s e l e c t i o n and d i r e c t i o n a l s e l e c t i o n - i s undoubtedly the crux of the Neo-Darwinian theory of e v o l u t i o n (Dobzhansky, 1970). Two major types of genet ic v a r i a n t s i n n a t u r a l popu la t ions have been s t u d i e d by g e n e t i c i s t s for t h i s purpose. The f i r s t c l a s s i s p r o t e i n and a l l o z y m i c v a r i a n t s which have l a v i s h l y fue led the decade-long " S e l e c t i o n i s m - N e u t r a l i s m c o n t r o v e r s y " . In g e n e r a l , mutat ion pressure and genet ic d r i f t seem to have played a very important r o l e i n shaping the genet ic s t r u c t u r e of p o p u l a t i o n s . I t i s p o s s i b l e , without i n v o k i n g b a l a n c i n g s e l e c t i o n or d i r e c t i o n a l s e l e c t i o n , to account fo r the data on the genet ic s t r u c t u r e from many major taxa at the molecular l e v e l . On the other hand, the Neo-Darwinian view encounters many d i f f i c u l t i e s i n e x p l a i n i n g v a r i a t i o n at the molecular l e v e l . D i r e c t i o n a l s e l e c t i o n cannot e x p l a i n the r e l a t i v e l y constant r a t e of amino a c i d s u b s t i t u t i o n i n many d i f f e r e n t l i n e a g e s . Ba l anc ing s e l e c t i o n w i t h overdominance works w e l l only i n t w o - a l l e l e cases (Lewontin et a l , 1978; Maruyama and N e i , 1981). O p e r a t i o n a l l y , an experimenter cannot 5 know for sure i f s e l e c t i o n i s a c t i n g on the a l lozyme locus i n ques t ion or on the genet ic background. For the purpose of demonstrat ing n a t u r a l s e l e c t i o n at work, a l l o z y m i c v a r i a n t s are not the best c a n d i d a t e s . Two books, one by Lewontin (1974) and the other by Nei (1975), have e x c e l l e n t summaries of t h i s cont rover sy (a l so see Kimura, 1979; Chakraborty et a l , 1980). The second c l a s s of v a r i a n t s c o n s i s t s of the chromosomal i n v e r s i o n s or so c a l l e d "supergenes" . S ince these i n v e r s i o n s normal ly i n c l u d e a s i g n i f i c a n t p o r t i o n of the genome, there i s l i t t l e doubt that i n v e r s i o n s are of s e l e c t i v e importance. The s t u d i e s of f i t n e s s components p ioneered by Prout (1965, 1969, 1971a, b) ushered in a sys temat ic method of s tudying the s e l e c t i v e d i f f e r e n c e s of genes. One s a l i e n t f i n d i n g of t h i s approach i s that var i ances i n the es t imates of s e l e c t i o n components are g e n e r a l l y so l a rge that the sample s i z e s have to be much grea ter than one might have p r o j e c t e d based on a s impler des ign or on sheer " i n t u i t i o n " . T h i s i s why chromosomal i n v e r s i o n s are important i n exper imenta l p o p u l a t i o n g e n e t i c s : There are great s e l e c t i v e d i f f e r e n c e s among n a t u r a l l y o c c u r r i n g chromosomal v a r i a n t s . Dobzhansky (1970) documented long term s t u d i e s on the coadapted genes a s s o c i a t e d w i t h d i f f e r e n t i n v e r s i o n s on the t h i r d chromosome of D. pseudoobscura and i t s r e l a t i v e s . Inver s ions of the t h i r d chromosome are i n t e r e s t i n g because of the h igh l e v e l of polymorphism. However, the l ack of c l e a r - c u t f i t n e s s - r e l a t e d phenotypes a s s o c i a t e d w i t h them i s a d i sadvantage . In t h i s c o n t e x t , the " Sex-Rat io " i n v e r s i o n i s an e x c e l l e n t model system for the s tud ie s of n a t u r a l s e l e c t i o n 6 which has to be f a i r l y intense i n order to o f f s e t the e f f e c t of m e i o t i c d r i v e . Questions s i m i l a r to those i n the second category posed above have been d e a l t w i t h i n the Segregat ion D i s t o r t e r (SD) system of D. melanogaster (Prout et a l . , 1973; Thompson and Feldman, 1974, 1976). The dynamics of suppressor m o d i f i e r s i n the SR system i s very d i f f e r e n t from that of SD. The i n t e r p l a y of the " s e x - r a t i o " genes and the m o d i f i e r s of t h e i r expres s ion a c t u a l l y re s t on the general sex r a t i o theory proposed by F i s h e r (1930, 1958, p159) i n response to Darwin ' s (1871, p399) o l d p u z z l e : " I former ly thought that when a tendency to produce the two sexes i n equal numbers was advantageous to the s p e c i e s , i t would f o l l o w from n a t u r a l s e l e c t i o n , but I now see that the whole problem i s so i n t r i c a t e that i t i s sa fer to leave i t s s o l u t i o n for the f u t u r e . " F i s h e r ' s s o l u t i o n to t h i s problem i s t h i s : S ince the " t o t a l r eproduc t ive output " of each sex i n the p o p u l a t i o n i s e x a c t l y the same, genes a s soc i a t ed w i t h the rare sex have a grea ter s e l e c t i v e advantage over t h e i r a l l e l e s u n t i l the female/male r a t i o IN THE POPULATION becomes one. Therefore for any p o p u l a t i o n w i t h sex chromosomes segregat ing i n a Mendelian f a s h i o n , no gene capable of d i s t o r t i n g sex r a t i o can increase i n frequency. We w i l l r e f e r to t h i s gene as an " s r m o d i f i e r " . F i s h e r ' s theory has i t s e x c e p t i o n s . A p o p u l a t i o n w i t h the SR chromosome does not produce two sexes i n equal numbers. As Hamilton (1967) po in ted out , s e x - l i n k e d sr m o d i f i e r s would escape the s o r t of s t a b i l i z i n g s e l e c t i o n i n F i s h e r ' s genera l theory ( there are c e r t a i n l y other ways to produce e x t r a o r d i n a r y 7 sex r a t i o s ) . What i s i n t e r e s t i n g i s that autosomal sr m o d i f i e r s , s e l e c t e d aga ins t i n most p o p u l a t i o n s , c o u l d be favored i n popu la t ions which c o n t a i n SR chromosomes and thus have a deviant female/male r a t i o . PART I I presents an e x p l i c i t treatment of t h i s i n t e r p l a y . The treatment prov ides a d i f f e r e n t view on the i n t e r a c t i o n of m e i o t i c d r i v e genes and t h e i r m o d i f i e r s when the former are sex-l i n k e d . The r e s u l t s obta ined i n PART I I l end s t rong support to the study of v i r i l i t y s e l e c t i o n i n PART I . The t h i r d category of ques t ions i s an important key to a more profound understanding of the coadapta t ion hypothes i s advocated by Dobzhansky (1970). The concept of coadapta t ion i n c l u d e s "both s e l e c t i o n of a l l e l e s at d i f f e r e n t l o c i w i t h i n gene arrangements to produce a h a p l o i d genome that i s p h y s i o l o g i c a l l y ba lanced , and s e l e c t i o n of a l l e l e s of the same l o c i between i n v e r s i o n s to produce h e t e r o s i s i n he terokaryotypes " (Prakash and Lewont in , 1968). Coadaptat ion i n the l a t t e r sense has been s tud ied by Dobzhansky and Pavlovsky (1958). They showed that "heterokaryotes are h e t e r o t i c when the arrangements come from the same p o p u l a t i o n but not when they come from d i f f e r e n t p o p u l a t i o n s " . D i r e c t evidence of coadapta t ion i n the former sense i s d i f f i c u l t to o b t a i n because a coadapted gene complex, being a c l u s t e r of genes bound together by the i n v e r s i o n , d e f i e s recombinat ion s t u d i e s which have to be performed to separate the genes w i t h i n the i n v e r s i o n s . S tud ies on the l i n k a g e a s s o c i a t i o n of a l lozymes w i t h i n each 8 i n v e r s i o n (Prakash and Lewont in , 1968, 1971) are not c o n c l u s i v e as far as the proof of the coadapta t ion hypothes i s i s concerned (Nei and L i , 1975, 1980). The cont rover sy over the i n t e r p r e t a t i o n of these data i s an ex tens ion of the " S e l e c t i o n i s m - N e u t r a l i t y " debate . In PART I I I , t h e . l i n k a g e a s s o c i a t i o n of genes which are d i r e c t l y i n v o l v e d i n " s e x - r a t i o " expres s ion were s t u d i e d . These genes a r e , beyond any doubt, s e l e c t i v e l y very d i f f e r e n t . I b e l i e v e the r e s u l t s are d i r e c t evidence for the coadapta t ion h y p o t h e s i s . Moreover, there i s some ba s i s for s p e c u l a t i o n on the e v o l u t i o n of the " s e x - r a t i o " genet ic systems i n the two s i b l i n g s p e c i e s : D. pseudoobscura and D. p e r s i m i l i s . F i n a l l y , the study of PART I I I p rov ides u s e f u l i n f o r m a t i o n on the s t e r i l i t y i n t e r a c t i o n between the two s i b l i n g s p e c i e s . Prev ious s t u d i e s ( eg . , Dobzhansky, 1936; Pontecorvo, 1943; Tan, 1946; Zouros, 1981) suggested a dominant r o l e of the X chromosome i n the s t e r i l i t y i n t e r a c t i o n between genes of d i f f e r e n t D r o s o p h i l a s p e c i e s . T h i s study prov ides data on the r o l e s of v a r i o u s segments of the X chromosome i n the s t e r i l i t y i n t e r a c t i o n . Each part of t h i s t h e s i s , except the b i b l i o g r a p h y , i s presented as an independent e n t i t y a l though there are many c ros s re ferences among them. The b i b l i o g r a p h y , as a whole , i s l i s t e d at the end of the t h e s i s . 9 PART I VIRILITY DEFICIENCY AND THE SEX-RATIO TRAIT IN DROSOPHILA PSEUDOOBSCURA 10 ABSTRACT Prev ious s t u d i e s on f i t n e s s components of D r o s o p h i l a have shown the overwhelming importance of v i r i l i t y s e l e c t i o n . In t h i s s tudy , the v i r i l i t y component of s e l e c t i o n i s f u r t h e r p a r t i t i o n e d i n t o two subcomponents- one w i t h respect to v i r g i n females and the other w i t h respect to n o n - v i r g i n females . I t i s shown how an underest imate of v i r i l i t y s e l e c t i o n would r e s u l t i f the d i f f e r e n c e between the two subcomponents i s not heeded. The p a r t i t i o n i n g of v i r i l i t y s e l e c t i o n i s a p p l i e d to the Sex-Rat io system of D. pseudoobscura. The Sex-Rat io males are found to s u f f e r s u b s t a n t i a l v i r i l i t y r e d u c t i o n which would not have been detected o t h e r w i s e . The s i g n i f i c a n c e of t h i s f i n d i n g i s d i scus sed i n l i g h t of two s p e c i f i c observa t ions u s u a l l y a s s o c i a t e d w i t h the Sex-Rat io polymorphism i n t h i s s p e c i e s . One i s the absence of suppressor m o d i f i e r s of " s e x - r a t i o " expres s ion and the other i s the temperature-dependent d i s t r i b u t i o n of the Sex-Rat io t r a i t . 11 INTRODUCTION The concept of p a r t i t i o n i n g the a c t i o n of n a t u r a l s e l e c t i o n i n t o s e v e r a l f i t n e s s components has been e l u c i d a t e d by Prout (1971a, b ) , Bundgaard and C h r i s t i a n s e n (1972), C h r i s t i a n s e n and Frydenberg (1973) and many other workers . Contrary to the t r a d i t i o n a l concept ion of n a t u r a l s e l e c t i o n , i t has been repeated ly repor ted that the a d u l t male component ( v i r i l i t y s e l e c t i o n ) , in s t ead of v i a b i l i t i e s of zygotes , i s the dominant one that governs the genet ic compos i t ion of D r o s o p h i l a p o p u l a t i o n s ( P r o u t , 1971a, b ; Bundgaard and C h r i s t i a n s e n , 1972; Anderson et a l , 1979; B r i t t n a c h e r , 1981). R e c e n t l y , many aspects of the reproduc t ive b i o l o g y of D r o s o p h i l a have been de sc r ibed i n d e t a i l . I t i s the o b j e c t i v e of t h i s work to look i n t o t h r e e • a s p e c t s of r e p r o d u c t i v e b i o l o g y r a r e l y s p e c i f i e d i n the a n a l y s i s of male v i r i l i t y . The study i s then a p p l i e d to the polymorphism of i n v e r s i o n s on the X chromosome of D r o s o p h i l a pseudoobscura - Sex-Rat io (SR) and Standard(ST) . The f i r s t aspect of i n t e r e s t i s m u l t i p l e mating of female D r o s o p h i l a . Cobbs' (1977) c o n s e r v a t i v e es t imate of the p r o p o r t i o n of m u l t i p l y inseminated females i n a n a t u r a l p o p u l a t i o n of D. pseudoobscura i s 0 .55 . Levine et a l (1981) es t imated the frequency of double in semina t ion in nature to be 0 .92 . Reports on m u l t i p l e mating of female D r o s o p h i l a under l a b o r a t o r y c o n d i t i o n s are numerous (Dobzhansky and P a v l o v s k y , 1967; Milkman and Z e i t l e r , 1974; Beckenbach, 1981). Secondly , the p a t t e r n of sperm u t i l i z a t i o n i n D r o s o p h i l a as a consequence of m u l t i p l e inseminaton has been the subject of many .papers 12 (Kaufman and Demerec 1942; Lefevre and Jonsson, 1962; Prout and Bundgaard, 1977; Beckenbach, 1981; for a review see F o w l e r , 1973). I t i s g e n e r a l l y t rue that the sperm e j a c u l a t e from the second male w i l l d i s p l a c e e i t h e r p a r t i a l l y or complete ly sperm of the f i r s t male s to red i n the female r eproduc t ive t r a c t , a process r e f e r r e d to as sperm d i sp lacement . T h i r d l y , sexual s e l e c t i o n on males ( i e . , mate choice by females) i s b e l i e v e d to be much more intense than i t i s on females ( for evidence on D r o s o p h i l a , see Bateman, 1948; B r i t t n a c h e r , 1981). Thi s observa t ion i s the ba s i s of many models on sexual s e l e c t i o n (O'Donald , 1980). Sexual s e l e c t i o n on males i s indeed a great d r i v i n g force of the dynamics of many genet i c systems.(Buundgaard and C h r i s t i a n s e n , 1972; Anderson et a l . , 1979). However, b e h a v i o r a l s tud ie s suggest that i n t e n s i t i e s of sexual s e l e c t i o n v a r y . One great source of v a r i a t i o n i s the h i s t o r y of c o u r t s h i p a female rece ived (Ehrman and Sp ie s s , 1969; Speiss and Kruckeberg , 1981). I t i s a l o g i c a l ex tens ion to suggest that i n t e n s i t i e s of mate s e l e c t i o n by females vary w i t h t h e i r mating h i s t o r y . To take these three aspects of r eproduc t ive b i o l o g y i n t o account , i t i s most convenient to p a r t i t i o n v i r i l i t y s e l e c t i o n i n t o two subcomponents; one w i t h respect to v i r g i n females , the other w i t h respect to n o n - v i r g i n females . Th i s approach w i l l f a c i l i t a t e a more accurate est imate of male v i r i l i t y . There are reasons to dea l w i t h the two subcomponents s e p a r a t e l y . The progeny count of a male inseminat ing a v i r g i n 13 female i s undoubtedly d i f f e r e n t from that of a male mated to a n o n - v i r g i n . A l s o the i n t e n s i t y of sexual s e l e c t i o n by a v i r g i n female might not be as s t rong as that of a n o n - v i r g i n female. Laboratory observa t ions i n v a r i a b l y suggest tha t n o n - v i r g i n females are l e s s r e c e p t i v e than v i r g i n females and hence, may be more d i s c r i m i n a t o r y among mates. In t h e o r y , i t has been suggested that female f i t n e s s can be g r e a t l y enhanced by s t a r t i n g reproduc t ion e a r l y (Lewont in , 1965). A v i r g i n D r o s o p h i l a may lower her t h r e s h h o l d of r e c e p t i v i t y for t h i s reason w h i l e a n o n - v i r g i n can a f f o r d to r e j e c t many c o u r t i n g males before accep t ing a s u i t a b l e one without s a c r i f i c i n g her l i f e t i m e p r o d u c t i o n . I t i s g e n e r a l l y accepted that a s i n g l e e j a c u l a t e secures s u f f i c i e n t sperm supply for the D r o s o p h i l a females and remating normal ly does not come as a consequence of shortage i n sperm supply (Lefevre and Jonsson, 1962; Prout and Bundgaard, 1977; Beckenbach, 1981). In g e n e r a l , the v i r g i n component of v i r i l i t y s e l e c t i o n i n c l u d e s both mate s e l e c t i o n by v i r g i n females and the f e r t i l i t y count i n a s i n g l e v i r g i n mat ing . Th i s component has o f ten been equated to the o v e r a l l male v i r i l i t y . The n o n - v i r g i n component c o n s i s t s of mate s e l e c t i o n by n o n - v i r g i n females as w e l l as sperm displacement by the males mated to them. The r e l a t i v e c o n t r i b u t i o n of the two components to the o v e r a l l male v i r i l i t y hinges on the remating tendency of females . Throughout the t e x t , I w i l l r e f e r to male f e r t i l i t y s p e c i f i c a l l y as the number of eggs of a VIRGIN female which a male can f e r t i l i z e i n a s i n g l e mat ing . Male v i r i l i t y r e f e r s to 1 4 the male a d u l t component of f i t n e s s encompassing male f e r t i l i t y , sexual s e l e c t i o n and sperm d i sp lacement . To examine the new v i r i l i t y model w i t h both a v i r g i n and a n o n - v i r g i n component, i t i s d e s i r a b l e to apply t h i s v i r i l i t y concept to a n a t u r a l genet ic system i n which the r o l e of v i r i l i t y s e l e c t i o n has been debated and i s s t i l l u n r e s o l v e d . One i d e a l system for measuring the v i r i l i t y d i f f e r e n c e s i s the SR polymorphism i n the obscura group of D r o s o p h i l a , e s p e c i a l l y i n D. pseudoobscura. The Sex-Rat io (SR) t r a i t i s s e x - l i n k e d and i s a s s o c i a t e d w i t h three i n v e r s i o n s on the r i g h t arm of the X chromosome. In t h i s paper, SR denotes the Sex-Rat io t r a i t as w e l l as the Sex-Rat io chromosome and ST denotes t h e i r Standard c o u n t e r p a r t . Males c a r r y i n g SR produce predominantly (95-99%) X - b e a r i n g sperm w h i l e females c a r r y i n g i t apparent ly are normal i n terms of s e g r e g a t i o n . Since an SR male produces TWICE as many X-bear ing sperm as ST males , the ques t ion i s why would SR not have spread r a p i d l y i n the popu la t ion? Hamilton (1965) gave a numer ica l example i n which the p o p u l a t i o n went e x t i n c t i n about f o r t y generat ions because of the decrease i n the number of males due to an increase i n the SR frequency. Indeed, Wal lace (1968) thought that SR would e v e n t u a l l y run to f i x a t i o n and must represent a s p e c i a l case of group s e l e c t i o n i n which l o c a l popu la t ions would c o l l a p s e from a l ack of males . W a l l a c e ' s reasoning i n invok ing group s e l e c t i o n i s that he f e l t the c o n d i t i o n s r e q u i r e d for n a t u r a l s e l e c t i o n to account for the 1 5 SR polymorphism are too s t r i n g e n t . However, C u r t s i n g e r and Feldman's (1980) r e s u l t s suggest that a wide range of s e l e c t i o n c o e f f i c i e n t s c o u l d s a t i s f y the c o n d i t i o n s of a s t a b l e polymorphism. In p a r a l l e l to the Segregat ion D i s t o r t e r system i n D. melanogaster , there have been attempts to look for m o d i f i e r s of the m e i o t i c d r i v e . The r e s u l t s are not encouraging i n D. pseudoobscura ( P o l i c a n s k y and Dempsey 1978; Beckenbach et a l . , 1982). The t h e o r e t i c a l c o n d i t i o n s under which suppressor m o d i f i e r s of SR expres s ion w i l l and w i l l not increase i n the p o p u l a t i o n have been worked out ( PART II of t h i s t h e s i s ) . In s h o r t , suppressor m o d i f i e r s of SR expres s ion i s not an a l t e r n a t i v e to n a t u r a l s e l e c t i o n as a ba l anc ing force of the SR polymorphism. I t i s , t h e r e f o r e , necessary to f i n d out how n a t u r a l s e l e c t i o n o f f s e t s the e f f e c t of m e i o t i c d r i v e and mainta ins the polymorphism. P o l i c a n s k y and E l l i s o n (1970) found that h a l f the spermatids of the SR males , presumably those bear ing Y-chromosomes, degenerate i n the course of spermiogenes i s . Based on t h i s f i n d i n g , P o l i c a n s k y (1974, 1979) suggested that SR males c o n t r i b u t e only h a l f as many sperm to the gametic pool as the ST males do e i t h e r because of a r e d u c t i o n i n the volume of sperm e j a c u l a t e s or because of a reduced mating success . Beckenbach (1978), however, found that an SR male i s as f e r t i l e as an ST male except when males are younger than 36 hours o l d or when males have j u s t engaged i n m u l t i p l e matings s e r i a l l y . As p o i n t e d out by C u r t s i n g e r and Feldman (1980), the male adu l t 16 component of s e l e c t i o n alone i s not capable of m a i n t a i n i n g the SR polymorphism. N e i t h e r the reduced f e r t i l i t y nor the lowered mating success proposed by P o l i c a n s k y (1974, 1979) c o u l d be s o l e l y r e s p o n s i b l e for the maintenance of t h i s polymorphism. The t h e o r e t i c a l c o n d i t i o n s for a s t a b l e SR polymorphism were f i r s t worked out by Edwards (1961). Wal lace (1948) and C u r t s i n g e r and Feldman (1980) employing d i f f e r e n t exper imenta l techniques have each generated a set of s e l e c t i o n c o e f f i c i e n t s for the f i v e p o s s i b l e genotypes ( i e . two male genotypes and three female genotypes ) . The r e s u l t s of both s t u d i e s p r e d i c t a s t a b l e SR polymorphism and n e i t h e r study supports the idea of s t rong v i r i l i t y s e l e c t i o n aga ins t SR males . Al though v i r i l i t y s e l e c t i o n i s no longer b e l i e v e d to be the on ly s e l e c t i o n component o p e r a t i n g i n the SR system, i t s r o l e i n the maintenance of the SR polymorphism i n D. pseudoobscura deserves more d e t a i l e d i n v e s t i g a t i o n s for the f o l l o w i n g reasons . F i r s t , as emphasized p r e v i o u s l y , t h i s component of s e l e c t i o n i s very important in other genet i c systems of D r o s o p h i l a and yet has a subcomponent e x e r c i s e d by n o n - v i r g i n females which u s u a l l y escapes a t t e n t i o n . Second, the absence of suppressor m o d i f i e r s of SR expres s ion i n n a t u r a l popu la t ions of D. pseudoobscura suggests an o v e r a l l low f i t n e s s of SR males (no grea ter than 0.3 r e l a t i v e to Standard males , see PART II of t h i s t h e s i s ) . S ince prev ious es t imates of l a r v a l v i a b i l i t y of SR males r e l a t i v e to ST males were always much higher than 0 . 3 , the male adu l t component of s e l e c t i o n may account for the d i f f e r e n c e . T h i r d , n e i t h e r i n n a t u r a l nor i n l a b o r a t o r y p o p u l a t i o n s i s SR 17 polymorphism the r u l e . Th i s means that the f i t n e s s e s of the genotypes w i t h SR suggested p r e v i o u s l y fo r polymorphic popu la t ions are overest imates for the monomorphic p o p u l a t i o n s . There c o u l d be an undetected s e l e c t i o n component which ac t s aga ins t SR. The absence or low f requencies of the SR chromosome i s u s u a l l y a s s o c i a t e d w i t h low temperature and there are p h y s i o l o g i c a l reasons that v i r i l i t y may be temperature-dependent (see RESULTS). E p l i n g et a l (1957), Baldwin (1979) and Bryant et a l (1982) reported a seasonal f l u c t u a t i o n of SR f requencies i n d i f f e r e n t p o p u l a t i o n s . Dobzhansky (1944) repor ted that the frequency of the SR t r a i t i s h ighes t (around 30%) i n Northern Mexico and Southern A r i z o n a , decreases w i t h i n c r e a s i n g l a t i t u d e , and vanishes nor th of the C a l i f o r n i a - O r e g o n border . There i s a l s o a negat ive c o r r e l a t i o n between the SR frequency and a l t i t u d e (Baldwin 1979). The d i s t r i b u t i o n of the SR t r a i t seems to be temperature dependent. In the next s e c t i o n , a hypothes i s about the p o s s i b l e e f f e c t s of low temperature on the v i r i l i t y of SR males i s proposed. Th i s hypothes i s i s based on the c y t o l o g i c a l evidence prov ided by P o l i c a n s k y and E l l i s o n (1970) and on the r e p r o d u c t i v e b i o l o g y of D r o s o p h i l a repor ted by Lefevre and Jonsson (1962). With an exper imenta l des ign to look i n t o d e t a i l s of v i r i l i t y s e l e c t i o n in which m u l t i p l e mating by females i s a l l o w e d , Beckenbach (1982) r e c e n t l y es t imated the v i r i l i t y of the SR males to be much l e s s than 50% of that of the ST males . Th i s ob se rva t ion supports the view that i n t e n s i t i e s of v i r i l i t y 18 s e l e c t i o n would be underest imated i f a s imple exper imenta l des ign i s used. In RESULTS, v i r i l i t y d i f f e r e n c e s between SR and ST males i n terms of f e r t i l i t y count (wi th respect to v i r g i n females) as w e l l as sperm displacement are shown. N o n - v i r g i n females are a l s o found to d i s c r i m i n a t e aga ins t SR males w h i l e mate d i s c r i m i n a t i o n by v i r g i n females i s much l e s s pronounced. Remating tendency of females i s examined w i t h the a i d of a very polymorphic l o c u s , e s t e ra se -5 . The o v e r a l l male v i r i l i t y i s a j o i n t e f f e c t of a l l these f a c t o r s . In ANALYSIS, a s imple mathematical model i s developed to take i n t o account a l l of these f a c t o r s . Thi s model a l s o has one i n t e r e s t i n g p r o p e r t y . I t suggests frequency-dependence of male v i r i l i t y a l though none of the parameters governing v i r i l i t y i s frequency-dependent. I t i s important to make a sharp d i s t i n c t i o n between the apparent frequency-dependence as a consequence of the i n t e r p l a y of parameters and the t rue frequency-dependence w i t h a p h y s i o l o g i c a l or b e h a v i o r a l b a s i s . P o p u l a t i o n g e n e t i c i s t s have developed s e v e r a l models to d i s t i n g u i s h the two fundamentally d i f f e r e n t phenomena (Prout , 1965; O'Donald , 1977; Kence, 1980; Ta j ima , u n p u b l i s h e d ) . Th i s s imple model adds a new item to the category of apparent frequency-dependence. F i n a l l y , a t e s t of the j o i n t e f f e c t of a l l the f a c t o r s i s c a r r i e d out and the v i r i l i t y of SR males r e l a t i v e to ST males i s e s t i m a t e d . 19 MATERIALS AND METHODS S t r a i n s : The SR and ST s t r a i n s were d e r i v e d from two sources . The ones from San Diego , CA. were e x t r a c t e d by D. Haymer. A. T. Beckenbach made a v a i l a b l e the SR and ST s t r a i n s from the R i v e r s i d e , CA. p o p u l a t i o n s . The SR stock was made homozygous and was mainta ined by o u t c r o s s i n g a p r o p o r t i o n of homozygous females to ST to o b t a i n SR males . The SR stock t h e r e f o r e has the same genet ic background as ST. Two s e x - l i n k e d marker genes were used i n t h i s exper iment : v e r m i l i o n and e s t e ra se -5 . The v e r m i l i o n stock was prov ided by N a t i o n a l D r o s o p h i l a Species Resources Center at The U n i v e r s i t y of Texas, A u s t i n . To prevent the inbreed ing e f f e c t on t h i s s t r a i n , i t was outcrossed to the ST stock and made homozygous a g a i n . F i v e l i n e s were mainta ined i n the subsequent p e r i o d . We w i l l denote v / v and v / y as v e r m i l i o n females and males . The s tandard ized stock for de te rmina t ion of e s terase-5 a l l e l e s was sent to our l a b o r a t o r y by S. B r y a n t . The remating experiment descr ibed l a t e r used females from a newly e x t r a c t e d l i n e f i x e d for the 1.00 a l l e l e . Males used i n that experiment c a r r y i n g other known E s t - 5 a l l e l e s were d e r i v e d by mating v i r g i n females from the s t andard ized Es t -5 stock to ST males . Th i s p r a c t i c e minimized the e f f e c t of inbreed ing i n the s t andard ized s t o c k . Genera l procedures : A l l s tocks were kept i n incubator s w i t h a 12/12 h r . day /n ight c y c l e which ensured a peak of mating 20 a c t i v i t i e s at "dawn". A l l mating experiments took advantage of t h i s d i u r n a l c y c l e . Food medium i s s tandard Oak Ridge medium of corn meal , agar , sucrose , g lucose , yeast and s a l t . P r o p i o n i c a c i d / p h o s p h o r i c a c i d mixture was used to i n h i b i t mold growth. Because an exces s ive q u a n t i t y of t h i s mold i n h i b i t o r was found to r e t a r d the development of l a r v a e , a p i l o t experiment was done to determine the lowest l e v e l for e f f e c t i v e mold i n h i b i t i o n which was adopted i n l a t e r exper iments . Exper imenta l f l i e s were anes thes i zed w i t h carbon d i o x i d e only when necessary . Ether was used only on f l i e s tha t were to be d i s c a r d e d . The f l i e s were kept i n 8 dram s h e l l v i a l s or b o t t l e s . The p o p u l a t i o n cages used are made of p l e x i g l a s s , 30cm x20cm x20cm w i t h two f i n e screened windows and a s leeved opening. Determinat ion of Es t -5 a l l e l e s was performed on h o r i z o n t a l s t a r c h g e l e l e c t r o p h o r e s i s w i t h cont inuous buf fer system. Although prev ious workers encountered some d i f f i c u l t y w i t h s t a r c h g e l i n determining Es t -5 a l l e l e s , the technique used here gave good r e s o l u t i o n when s t andard ized s tocks were t e s t e d . The f e r t i l i t y count : Females used were homozygous ST and were 4-5 days o l d v i r g i n s . The males, SR and ST, were a l l 4 days o l d at the time of mat ing . Males were t r e a t e d i n the f o l l o w i n g ways: i ) one mat ing/day : In the three days p r i o r to mating w i t h the exper imenta l female, each male was separated and conf ined w i t h v i r g i n females to " d r a i n " h i s sperm supp ly . A f re sh v i r g i n 21 female rep laced the o l d one each day. A number of these females were a l lowed to depos i t eggs a f terwards and most of them had indeed been inseminated . i i ) Three mat ings /day : Each male was o f f e r e d three to four v i r g i n females per day i n the two days p r i o r to mating w i t h the exper imenta l females . A g a i n , a h igh percentage of these females were inseminated . i ) and i i ) were both performed at 22 C. i i i ) Temperature t reatment : Males were s tored at 14 C immediately a f t e r e c l o s i o n for four days p r i o r to mat ings . The c o n t r o l experiment used four days o l d v i r g i n males reared at 22 C. A f t e r each male was t r e a t e d i n one of the above ways, i t was conf ined w i t h an exper imenta l v i r g i n female at room temperature (20 -24 C) i n a v i a l . N o r m a l l y , mating was observed and the p a i r was separated immediate ly ; o therwi se , they were separated eight , hours l a t e r . The female was then t r a n s f e r r e d every day for nine days to a new v i a l c o n t a i n i n g f r e s h food. The o f f s p r i n g were counted and sexed a f t e r they emerged. Sperm d i sp lacement : Males i n . th i s experiment were t r e a t e d in e x a c t l y the same way as i n the prev ious experiment . Exper imenta l females used were homozygous for v e r m i l i o n . Three-day o l d v e r m i l i o n females were a l lowed to mate w i t h three day o l d v e r m i l i o n males i n a one day p e r i o d . Each i n d i v i d u a l female was then kept i n a v i a l f o r egg d e p o s i t i o n . Three days l a t e r , two of these exper imenta l females were con f ined w i t h two 22 exper imenta l males for one and a h a l f days . Each p u t a t i v e doubly inseminated female was then separated i n t o a new v i a l and was t r a n s f e r r e d every two to three days for 12 days . The procedure ensured a reasonable chance of female remat ing . In a d d i t i o n , s ince the absence of v e r m i l i o n females i n the progeny a f t e r the second mating may mean e i t h e r complete sperm displacement by the second males or the f a i l u r e of females to mate w i t h v e r m i l i o n males at the f i r s t mating t r i a l , eggs l a i d between the f i r s t and second mating helped the observer to d i s t i n g u i s h the two a l t e r n a t i v e s . I f o n l y v e r m i l i o n f l i e s were recovered i n the progeny, the mother was c l a s s i f i e d as having f a i l e d to engage i n the second mat ing . U n l i k e the prev ious experiment i n which the t o t a l number of o f f s p r i n g was the concern , t h i s experiment prov ided data on the r e l a t i v e gametic c o n t r i b u t i o n of the two males w i t h which the exper imenta l female mated. The progeny c o n s i s t e d of three genotypes: v / v , v / y (both have a v e r m i l i o n phenotype) and v/+. Let t h e i r numbers be x , y , and x ' r e s p e c t i v e l y . I f the second male was ST, the observed p a t t e r n i s roughly x+x'=y, and the p r o p o r t i o n of o f f s p r i n g fa thered by the second male i s w = x ' / ( x + x ' ) . Any v / y male c o u l d have been fa thered by e i t h e r the f i r s t or the second male. I f the second male was SR, we observed roughly x=y and the p r o p o r t i o n , w, was approximate ly x ' / ( x + y + x ' ) . To c a l c u l a t e the mean and the v a r i a n c e of the p r o p o r t i o n of o f f s p r i n g f a thered by the second males and to perform the s t a t i s t i c a l t e s t s , the standard angular t r ans fo rmat ion for 23 p r o p o r t i o n s , sin~l.|w~, was used. A l l s t a t i s t i c a l t e s t s were done on t h i s new q u a n t i t y . The mean of the i n t e n s i t y of sperm displacement for ST or SR (p or q i n Table 2 and 3) was obta ined by the reverse t r ans format ion of the mean of t h i s new q u a n t i t y . Sexual s e l e c t i o n : To determine the genotype of the mate, SR or ST, of a female, the sex compos i t ion of her progeny was examined. One of the advantages of t h i s exper imenta l des ign over the method of d i r e c t observa t ions i s that sexual s e l e c t i o n c o u l d be measured i n a p o p u l a t i o n which remained undi s turbed throughout the exper imenta l p e r i o d . Two p o p u l a t i o n s were c o n s t r u c t e d : one c o n s i s t e d of v i r g i n females, the other of n o n - v i r g i n females . A l l females were homozygous fo r v e r m i l i o n . In the f i r s t p o p u l a t i o n , 120 v i r g i n females, aged between 4-6 days , were put i n t o a p o p u l a t i o n cage for 12 hours w i t h 72 ST males and 72 SR males, aged between 3-5 days . Ninety four of these females were c o l l e c t e d from the cage and each one of them was separated i n t o a v i a l f o r egg d e p o s i t i o n for 2-4 days. There i s no ambiguity from sex compos i t ion i n the progeny about the p a t e r n a l genotypes. For the second p o p u l a t i o n , 200 three day o l d v i r g i n females were a l lowed to mate w i t h v e r m i l i o n males for one day, and four days l a t e r , were put i n t o the cage w i t h 72 ST males and 72 SR males for one day. In t o t a l 164 of the females were r e t r i e v e d from the cage. S i x t y - t w o of them produced only v e r m i l i o n F t and apparent ly f a i l e d to remate. For the remaining 102 f a m i l i e s , three types of o f f s p r i n g were recovered : v / v , v / y and v/+ w i t h 24 the numbers of each genotype being x , y , and x ' r e s p e c t i v e l y . F l i e s of the v/+ genotype were d e f i n i t e l y f a thered by the second male. We have to d i s t i n g u i s h between two hypotheses . Hypothes i s I : The second mate was ST and we should expect x+x'=y Hypothes i s I I : The second mate was SR and we should expect x=y. Simple b i n o m i a l t e s t s would have the r e s o l v i n g power to d i s t i n g u i s h them prov ided that x ' i s s u f f i c i e n t l y l a r g e , i e . sperm displacement i s s u f f i c i e n t l y s t rong ( for example, > 50%). In most cases , the t e s t accepts one hypothes i s and r e j e c t s the other at the 5% s i g n i f i c a n c e l e v e l . In other words, the genotype of the second mate of most females can be u n e q u i v o c a l l y determined. Data on the genotypic compos i t ion of the progeny of 14 females r e j e c t both hypotheses at the 5% l e v e l . In that event , the hypothes i s that y i e l d s a sma l le r Z va lue (the s t andard ized normal random v a r i a b l e ) i s accepted . In the remaining f i v e f a m i l i e s , there i s a preponderance of progeny from the f i r s t male and n e i t h e r hypothes i s can be r e j e c t e d . The c r i t e r i o n of comparing z values favors the second hypothes i s (SR as the second mate) i n a l l f i v e ca ses . Independent observa t ions support t h i s v i ew: O c c a s i o n a l l y , SR males f a i l to d i s p l a c e more than 20% of the s t o r e d sperm w h i l e such cases are q u i t e rare i n matings w i t h ST males . These c a l c u l a t i o n s add up to the second row of Table 4. Haldane (1959) developed an unbiased e s t imator to c a l c u l a t e 25 r e l a t i v e v i a b i l i t i e s . The same procedure was adopted to c a l c u l a t e r e l a t i v e mating success , v , and v 2 , i n Table 4. I f the number of females mated to ST i s a and to SR i s b , the unbiased e s t imator of v , i s b/( l+a) and the va r i ance i s approximate ly v , (1+v , ) / (a+b) . The remating experiment : The procedure of t h i s experiment i s to g ive a female of a known genotype many chances i n a sequence to mate w i t h males of d i f f e r e n t genotypes. By examining the genotypes of the o f f s p r i n g throughout the mother ' s l i f e t i m e r e p r o d u c t i o n , we c o u l d determine how of ten mating r e c u r s . The marker gene i n t h i s experiment i s the s e x - l i n k e d es terase-5 locus w i t h s i x i d e n t i f i a b l e a l l e l e s : 0 .85 , 0 .97 , 1.00, 1.03, 1.09 and 1.12. A l l females used were homozygous for the 1.00 a l l e l e . The f i r s t mating of a l l 20 females were w i t h males c a r r y i n g the same 1.00 a l l e l e and the mating was observed. Succes s fu l c o p u l a t i o n i n t h i s spec ie s l a s t s about 4-5 min . A t y p i c a l sequence of mating t r i a l s of these females i s the f o l l o w i n g : A f t e r the f i r s t mating w i t h a 1.00 male was observed, the female was conf ined w i t h two 1.12 males i n a v i a l w i t h f re sh food . Two days l a t e r , the female was t r a n s f e r r e d to a new v i a l c o n t a i n i n g two 0.97 males . The same procedure was fo l l owed w i t h 1.03 males , .85 males and 1.09 males i n that o r d e r . In the end, the female was a l lowed to l ay eggs by i t s e l f i n another new v i a l . S ince Es t -5 i s s e x - l i n k e d , the F , females emerging from the s i x v i a l s conta ined i n f o r m a t i o n on p a t e r n i t y i n that s p e c i f i c p e r i o d when eggs were l a i d . I t i s t h e r e f o r e p o s s i b l e 26 to detec t the gametic c o n t r i b u t i o n of most of the males before t h e i r sperm are d i s p l a c e d by the next male. The arrangement of the m a t i n g - t r i a l sequence i s always i n such a way that the genotype of the c o p u l a t i n g male i s s u f f i c i e n t l y d i f f e r e n t from that of the prev ious male for easy i d e n t i f i c a t i o n . For example, the sequence shown above i s 1 .12- .97-1.03 - . 8 5 - 1 . 0 9 . The maternal a l l e l e , 1.00, serves as a very good reference p o i n t . Three to s i x F, females from each of the s i x v i a l s were assayed for t h e i r Es t -5 a l l e l e s . A male was cons idered to have f a i l e d to mate i f h i s a l l e l e was not detected i n the progeny c o l l e c t e d from subsequent egg samples. Fur ther t e s t s of v i r i l i t y s e l e c t i o n : S ix l a b o r a t o r y popu la t ions were c o n t r i v e d . F i v e of them s t a r t e d w i t h 30 v i r g i n ST/ST females , 10 ST males and 10 SR males . One p o p u l a t i o n c o n s i s t e d of 45 v i r g i n females , 15 ST males and 15 SR males . On day 0, a l l f l i e s were 3 days o l d . The experiment was done at 14 C and few eggs were l a i d i n the f i r s t three days. Eggs were c o l l e c t e d from the p o p u l a t i o n s i n the f o l l o w i n g p e r i o d s : day 4-6, day 8.-9, day 11-12 and day 14. Fresh food medium was s u p p l i e d between each egg sampl ing . F, from these egg samples were counted and sexed. Egg samples c o l l e c t e d on day 14 were d i f f e r e n t from o t h e r s : Females and males i n each p o p u l a t i o n were separated on day 14 and each female c o l l e c t e d was put i n t o a v i a l and a l lowed to l ay eggs for 2-3 days . Sex compos i t ion from each f ami ly was recorded and the d i s t r i b u t i o n of i t i s presented i n F i g . 3. The 27 sum of data from a l l the f a m i l i e s c o n s t i t u t e s the sex compos i t ion of the samples of day 14. Due to the d i f f i c u l t y i n r e t r i e v i n g the f l i e s from the cages, on ly 115 out of the o r i g i n a l 195 females c o n t r i b u t e d to the c o l l e c t i o n of day 14. Data from a l l s i x cages were pooled together i n Table 6. 28 RESULTS The t h r e s h o l d hypothes i s on male v i r i l i t y The f e r t i l i t y count The very f i r s t element of male v i r i l i t y i s the f e r t i l i t y count , d e f i n e d as the number of progeny a male can produce by in semina t ing a VIRGIN female. P o l i c a n s k y (1974) repor ted a d r a s t i c r e d u c t i o n of f e r t i l i t y of SR males under c i rcumstances which very l i k e l y demand the maximal ra te of sperm rep len i shment . In other s i t u a t i o n s where t h i s ra te i s c r u c i a l to the f e r t i l i t y count (eg. when very young males or s e r i a l l y mated males are used) , Beckenbach (1978) d i d f i n d some d i f f e r e n c e i n f e r t i l i t y between SR and ST males . For four day o l d v i r g i n males , however, he found no d i f f e r e n c e i n f e r t i l i t y . Under s i m i l a r c o n d i t i o n s , C u r t s i n g e r and Feldman (1980) c o u l d not demonstrate any f e r t i l i t y d e f i c i e n c y . These f i n d i n g s suggest that the f e r t i l i t y d e f i c i e n c y of SR males i s c o n d i t i o n a l on the demand for sperm rep len i shment . I t i s a l o g i c a l ex tens ion from P o l i c a n s k y and E l l i s o n ' s (1970) f i n d i n g to say that SR males can r e p l e n i s h sperm at about h a l f the r a t e of that of ST males . In order to see the e f f e c t of t h i s d e f i c i e n c y i n the ra te of spermatogenesis on f e r t i l i t y we have to examine d i f f e r e n t stages of male r eproduc t ion i l l u s t r a t e d below. 29 Spermatogenesis sperm storage i n sperm f e r t i -( replenishment) seminal v e s i c l e e j a c u l a t i o n l i z a t i o n I I I I I I IV F i g . 1 Male Reproduct ive Stages For the purpose of the present work, other aspects of male r eproduc t ion ( e g . , the p roduc t ion of seminal f l u i d ) were not cons idered when determining the r e l a t i v e f e r t i l i t y of SR males (see Fowler , 1973). A d i f f e r e n c e at Stage I between SR and ST males w i l l not be detec ted at Stage IV unless t h i s d i f f e r e n c e p e r s i s t s through the second and the t h i r d s tage . Unders tandably , i f the sperm d e p l e t i o n ra te at seminal v e s i c l e s (Stage I I ) i s too low to exer t a strenuous demand on spermatogenesis , the r e d u c t i o n of sperm replenishment ra te i s not c r i t i c a l to male f e r t i l i t y . In t h e i r n a t u r a l environment, male D r o s o p h i l a may not have to meet a sperm demand w i t h t h e i r f u l l c a p a c i t y . I t i s i n t e r e s t i n g to know the l e v e l of sperm demand at which SR males begin to s u f f e r a f e r t i l i t y r e d u c t i o n . Table 1a shows the numbers of o f f s p r i n g produced by males at d i f f e r e n t l e v e l s of sperm demand. For SR males, n e i t h e r v i r g i n s nor those which mated once everyday show any l o s s of LEAF 30 OMITTED IN PAGE NUMBERING. 31 f e r t i l i t y . T h i s r e s u l t i s i n accordance w i t h Beckenbach's (1978) r e p o r t . SR males that mated as o f ten as three times a day do su f f e r a 35% r e d u c t i o n i n f e r t i l i t y i n t h e i r l a s t mating compared to ST males s i m i l a r l y t r e a t e d . Roughly, a 50% r e d u c t i o n i s r e q u i r e d to o f f s e t the advantage i n m e i o t i c d r i v e . Note that t h i s count i s done on the l a s t mating of the t rea tment . The cumulat ive count would be h igher than t h i s f i g u r e s ince we know SR males are as f e r t i l e as ST males in the f i r s t few mat ings . The c o n c l u s i o n i s that the SR males are no l e s s f e r t i l e than ST males . Even i f the mating frequency of males i s as h igh as three times a day, the f e r t i l i t y l o s s i s s t i l l l i m i t e d (much l e s s than 35%). The dilemma i s : i f males mate so o f t e n , most matings i n nature would i n v o l v e n o n - v i r g i n females ( a f t e r a l l , on average females mate as f r e q u e n t l y as males ) . The f e r t i l i t y count , i n the f i r s t p l a c e , would l o se i t s v a l i d i t y i n e x p l a i n i n g the dynamics of the SR system. As a l r eady d i s c u s s e d , the geographica l and temporal d i s t r i b u t i o n of SR i n nature suggests to us the temperature-dependence of the SR polymorphism. W i t h i n the normal range of temperature i t i s p o s s i b l e that the sperm replenishment rate decreases w i t h temperature. I t i s hypothes ized that f e r t i l i t y s e l e c t i o n favors ST males over SR males at low temperature . Let us cons ider the scheme i n which i t takes ST males 1 u n i t of time to r e p l e n i s h the l o s s of sperm through e j a c u l a t i o n w h i l e 2 u n i t s of time i s r e q u i r e d for SR males . I f lowered temperature 32 reduces the replenishment rate by h a l f for both genotypes, i t would cost the ST males one e x t r a u n i t of time whi l e the t o l l would be doubled for t h e i r SR c o u n t e r p a r t s . Data of Table 1b r e j e c t t h i s h y p o t h e s i s . F e r t i l i t y d i f f e r e n c e s between SR and ST are i n s i g n i f i c a n t both at 22 C and at 14 C. The f a i l u r e to detect a s i g n i f i c a n t f e r t i l i t y r e d u c t i o n i n SR males i s not a s u r p r i s e . Demerec and Kaufman (1942) counted the number of sperm i n e j a c u l a t e s of s e r i a l l y -mated male D. melanogaster and found i n the female t r a c t only 60% as many sperm at males' second mating as at t h e i r f i r s t mating (Stage I I I ) . However, no d i f f e r e n c e i n the progeny count was detected (Stage I V ) . Th i s f i n d i n g suggests that a 50% d i f f e r e n c e i n the sperm replenishment ra te i s i n s u f f i c i e n t to b r i n g about any change i n f e r t i l i t y count s . The f e r t i l i t y count at Stage IV i s s imply i n s e n s i t i v e to d i f f e r e n c e s at the prev ious three s tages . Sperm displacement Sperm displacement i s the measure of male v i r i l i t y w i t h respect to n o n - v i r g i n females . T h i s aspect of v i r i l i t y probably p l a y s a more important r o l e than the f e r t i l i t y count because n o n - v i r g i n mating i s more preva lent than was once thought (Cobbs 1975; Levine e_t a_l, 1981). In a d d i t i o n , the knowledge on D r o s o p h i l a r eproduc t ive b i o l o g y suggests that sperm displacement i s a more acute measure of d i f f e r e n c e s in sperm e j a c u l a t i o n than the f e r t i l i t y count i s . 33 Lefevre and Jonsson (1962) found that female D. melanogaster can s to re on ly about 20% of the sperm e j a c u l a t e d by a f u l l y fecund male. Once the sperm are s t o r e d , the e f f i c i e n c y of u t i l i z a t i o n by the female i s c l o s e to 1. T h i s e x p l a i n s Kaufman and Demerec's (1942) f i n d i n g of no d i f f e r e n c e i n f e r t i l i t y count de sp i t e a r e d u c t i o n in the number of sperm e j a c u l a t e d . Then, why are so many sperm e j acu la ted? Lefevre and Jonsson proposed a d i l u t i o n model for sperm displacement which suggest t h a t , on a female ' s remat ing , the sperm e j a c u l a t e from the c o p u l a t i n g male d i l u t e s that s tored from prev ious matings and i s favored i n f e r t i l i z a t i o n . One i s there fo re tempted to hypothes ize that the adapt ive s i g n i f i c a n c e of the q u a n t i t y of sperm e j a c u l a t e d bears on the a b i l i t y of the c o p u l a t i n g male to d i s p l a c e sperm from prev ious . mat ings , r a ther than on the number of progeny i t can fa ther by mating a v i r g i n female. In terms of f e r t i l i t y count s , t h i s hypothes i s s t a te s that the female ' s c a p a c i t y for sperm storage i s the t h r e s h o l d for sperm e j a c u l a t e s . Once the volume of the sperm e j a c u l a t e exceeds the t h r e s h o l d l e v e l of the female storage c a p a c i t y , the f e r t i l i t y count reaches a p l a t e a u . On the other hand, the hypothes i s p r e d i c t s a greater degree of sperm displacement by a male e j a c u l a t i n g a l a r g e r q u a n t i t y of sperm than that e j a c u l a t i n g a smal ler one even though both exceed the t h r e s h o l d l e v e l i n volume. Consequent ly , males would more of ten e x h i b i t v i r i l i t y d i f f e r e n c e s i n the i n t e n s i t i e s of sperm d i sp lacement , but not i n f e r t i l i t y c o u n t s . I w i l l r e f e r to t h i s hypothes i s as the " t h r e s h o l d mode l " . Table 2 a and b support 34 t h i s hypothes i s q u i t e w e l l . Whi le mating treatment apparent ly had no e f f e c t on the f e r t i l i t y of ST males, the s e r i a l l y mated males su f fe red a 35% reduc t ion i n sperm displacement c a p a b i l i t y . Presumably, the volume of sperm e j a c u l a t e of the s e r i a l l y - m a t e d males , whi l e being reduced so much as to r e s u l t i n a 35% l o s s i n sperm d i sp lacement , was s t i l l above the t h r e s h o l d and there fo re y i e l d s the same f e r t i l i t y count . Low temperature treatment has s i m i l a r e f f e c t s on both measurements as the mating t rea tment . The t h r e s h o l d model i l l u s t r a t e s the r e l a t i o n s h i p between Stage I I I (sperm e j a c u l a t i o n ) and stage IV ( f e r t i l i z a t i o n ) of male r e p r o d u c t i o n . I t can then be i n f e r r e d t h a t , i f the 50% r e d u c t i o n i n sperm replenishment of SR males indeed r e s u l t s i n a smal ler sperm e j a c u l a t e , the d i f f e r e n c e c o u l d be detected i n sperm d i sp lacement . Table 3 a and b show that SR males are s i g n i f i c a n t l y weaker i n sperm displacement than ST males i n a l l t rea tments . (Note that Table 1 a and b show t h a t , i n terms of f e r t i l i t y count , only one of the treatments de tec t s d i f f e r e n c e between SR and ST males ) . Two way ANOVA a l s o shows: 1) SR males are u n c o n d i t i o n a l l y weaker in sperm displacement than ST males (the column e f f e c t ) . 2) Mat ing and temperature treatments on males r e s u l t i n a s i g n i f i c a n t l o s s i n sperm displacement c a p a b i l i t y (the row e f f e c t ) . 3) The i n t e r a c t i o n component i n Table 3b i s h i g h l y s i g n i f i c a n t 35 suggest ing that low temperature has a greater e f f e c t i n reducing the sperm displacement c a p a b i l i t y of SR males than that of ST males. S i m i l a r l y , mating treatments i n Table 3a a l s o show t h a t , as matings of males become more f requent , the SR males become 15%, 20% and 50% weaker i n sperm displacement than ST males. Note that none of the e f f e c t s d i s cus sed above would be as pronounced i f data on the f e r t i l i t y count , in s tead of sperm displacement were i n t e r p r e t e d . To summarize the r e s u l t s : i ) Sperm d i sp lacement , the component of v i r i l i t y s e l e c t i o n w i t h respect to n o n - v i r g i n females, i s a more acute measure of v i r i l i t y d i f f e r e n c e s than f e r t i l i t y count which i n v o l v e s only v i r g i n females . i i ) SR males, s u f f e r i n g a 50% r e d u c t i o n i n sperm replenishment r a t e , are as f e r t i l e as ST males i n the f e r t i l i t y count but are much weaker i n sperm di sp lacement . Sexual s e l e c t ion The o b j e c t i v e of t h i s s e c t i o n i s to f i n d out i f n o n - v i r g i n females are more d i s c r i m i n a t o r y to SR males than v i r g i n females a r e . Table 4 shows the r e s u l t of the sexual s e l e c t i o n experiment . The p r o p o r t i o n of n o n - v i r g i n females mated to an SR male i s s i g n i f i c a n t l y lower than that of v i r g i n females.mated to an SR male (z=1.85, p<.05). S i m i l a r l y , the mating success of an SR male r e l a t i v e to that of an ST male w i t h respect to v i r g i n females (v , ) i s s i g n i f i c a n t l y h igher than that w i t h respect to n o n - v i r g i n females , v 2 (z=1.72, p<.05). N o n - v i r g i n females are indeed more d i s c r i m i n a t o r y to SR males than v i r g i n females . 36 The es t imated value of v , i s not s i g n i f i c a n t l y d i f f e r e n t from 1. On the other hand, the es t imated value of v 2 i s s i g n i f i c a n t l y sma l le r than 1. Both the expected va lue (.52) and the upper l i m i t (.73) of v 2 are used i n l a t e r s e c t i o n s . (For the unbiased e s t imator of v , and v 2 used here , see Haldane (1959)) . The fa r r i g h t column shows the numbers of females which d i d not engage i n any mating d u r i n g the p e r i o d of the experiment . I t i s assumed that a l l 93 v i r g i n females that mated i n the 12 h r . p e r i o d have not remated and that the 102 non-v i r g i n females have remated only once i n the 18 h r . p e r i o d . Although the es t imated v , and v 2 are a s s o c i a t e d w i t h l arge s tandard e r r o r s , they are s t a t i s t i c a l l y d i f f e r e n t from each o t h e r . I t i s t h i s d i f f e r e n c e that should be heeded i n the study of v i r i l i t y s e l e c t i o n . The tendency of females to remate To est imate v i r i l i t y , we have to be able to assess the r e l a t i v e importance of the two components of v i r i l i t y s e l e c t i o n , which , i n t u r n , depends on how often the females remate. By t h a t , we are a c t u a l l y a sk ing two q u e s t i o n s . i ) What i s the mean and d i s t r i b u t i o n of " w a i t i n g t ime" ( i n the mathematical sense) between two consecut ive matings? i i ) Does the mean and d i s t r i b u t i o n of " w a i t i n g t ime" change as the mating s t a tus changes? .( 'Mating s t a tu s i s d e f i n e d as the number of matings i n which a female engages.) Informat ion on the f i r s t ques t ion i s a v a i l a b l e i n the 37 l i t e r a t u r e . The o b j e c t i v e of t h i s s e c t i o n i s to p rov ide an answer to the second q u e s t i o n . The a l t e r n a t i v e hypothes i s for t h i s ques t ion i s that a female becomes l e s s r e c e p t i v e as her mating s t a tus changes, hence, the mean " w a i t i n g t ime" i n c r e a s e s . To begin w i t h , we w i l l ask i f females are w i l l i n g to mate more than two or three t imes w i t h i n a ten day p e r i o d . The technique us ing Es t -5 a l l e l e s enables us to f o l l o w the mating sequence of each female up to the s i x t h mat ing . Fourteen of the 15 females which were o f fe red s i x genotypes of males c o n s e c u t i v e l y i n a 10 day p e r i o d mated four or f i v e t i m e s . The other one mated at l e a s t three t imes . Four other females which were o f f e r e d f i v e genotypes of males a l l mated three or four t imes . The he terogene i ty among females seems n e g l i g i b l e . Matings w i t h the same male, w i t h males of the same genotype or w i t h males weak i n sperm displacement c o u l d c e r t a i n l y go undetected. In na ture , the female remating frequency may not be as h i g h as t h i s r e s u l t suggests but there i s l i t t l e doubt that D r o s o p h i l a females have the tendency to engage i n many matings i n t h e i r l i f e t i m e . This i s a l s o one of the c o n c l u s i o n s reached by Prout and Bundgaard (1977). Table 5 g ives the r e s u l t of remating tendency of females accord ing to t h e i r mating s t a t u s . The l a s t row suggests that the p r o b a b i l i t y of a female to remate i n a two day p e r i o d does not vary w i t h her mating s t a t u s . I t i s a s u r p r i s e tha t i n t h i s experiment the t r i p l y and quadruply mated females are somewhat more r e c e p t i v e to mates than the s i n g l y mated females . The 38 answer to the second ques t ion posed above, t h e r e f o r e , i s : No, a female does not become l e s s r e c e p t i v e s o l e l y because of her mating s t a t u s . Table 5 a l s o shows that the female ' s tendency to remate depends very much on the c o u r t i n g males . Males from d i f f e r e n t i sofemale l i n e s (wi th d i f f e r e n t Es t -5 a l l e l e s ) vary enormously i n t h e i r mating success . In h i s study of remat ing , Beckenbach (1981) concluded that remating p r o b a b i l i t i e s , a f t e r a short postmating r e f r a c t o r y p e r i o d , are p r o p o r t i o n a l to the l eng th of t i m e . H i s r e s u l t of an e x p o n e n t i a l d i s t r i b u t i o n of " w a i t i n g t ime" together w i t h data presented i n t h i s s e c t i o n suggest a s imple approximation to the remating proces s : a Poisson proces s . In s h o r t , i n a Poisson proces s , at time t , the d i s t r i b u t i o n of mating s t a tus of females f o l l o w s a Poi s son d i s t r i b u t i o n w i t h parameter X t , where X, the remating r a t e , i s to be e s t imated . T h i s approximat ion of the mating process g r e a t l y s i m p l i f i e s the task of e v a l u a t i n g v i r i l i t y s e l e c t i o n when both the v i r g i n and n o n - v i r g i n component of i t have to be cons idered (see ANALYSIS ) . The r e s u l t s obta ined i n t h i s s e c t i o n only a s ser t that the event of remating of female D r o s o p h i l a can be t r e a t e d as a Poi s son proces s . The h igh ra te of remating i n Table 5 should not be used w i t h conf idence i n v i r i l i t y e s t i m a t i o n . The ra te of female remat ing , X, w i l l c e r t a i n l y vary w i t h d i f f e r e n t exper imenta l de s i gns . In the f o l l o w i n g s e c t i o n , X i s es t imated from data of the exper imenta l p o p u l a t i o n . 39 ANALYSIS The o b j e c t i v e of t h i s s e c t i o n i s t h r e e f o l d : f i r s t , to develop a s imple mathematical model to est imate the male a d u l t component of f i t n e s s ; second, to subject t h i s model , which i n c o r p o r a t e s a l l the v i r i l i t y elements presented i n RESULTS, to f u r t h e r t e s t s ; t h i r d , to g ive es t imates on the v i r i l i t y of SR males . In a d d i t i o n , some i n t e r e s t i n g p r o p e r t i e s of t h i s mathematical model w i l l be d i s c u s s e d . A model on v i r i l i t y e s t i m a t i o n DEFINITIONS: Let the r e l a t i v e f e r t i l i t y of two genotypes of males , A and B, be 1 and c r e s p e c t i v e l y ( c<1 ) . To be s p e c i f i c , A can be r e f e r r e d to as ST and B as SR. I n t e n s i t y of sperm displacement p or q i s d e f i n e d as the p r o p o r t i o n of sperm i n the female storage organ which i s d i s p l a c e d i f the l a s t male she mated w i t h i s of genotype A or B r e s p e c t i v e l y ; ( l e t p > q ) . 1-p or 1-q i s there fo re the p r o p o r t i o n of sperm remaining i n the female t r a c t from prev ious mat ings . The same " d i l u t i o n " assumption i s made i f the female has engaged i n more than two mat ings . Therefore ( 1 - p ) z i s the p r o p o r t i o n of sperm from e a r l i e r matings remaining undi sp laced when the female has mated s e r i a l l y to two A males . Let y be the frequency of genotype B among males . Let u , ( y ) and u 2 ( y ) be the p r o b a b i l i t i e s of a v i r g i n female and a n o n - v i r g i n female mating w i t h a B male r e s p e c t i v e l y . Let v , and v 2 be the mating success of a B male r e l a t i v e to that of 40 an A male w i t h respect to v i r g i n females and n o n - v i r g i n females r e s p e c t i v e l y . Then, v i y v 2 y u , (y) = and u 2 (y) = (1 ) {(l-y)+v,y} { d - y ) + v 2 y } I t has been reported by many au thor s , c h i e f l y Ehrman and Spiess (eg. Ehrman, 1967, 1970; S p i e s s , 1968, 1970) that v , i s frequency-dependent. (For c a u t i o n s about p o s s i b l e exper imenta l e r r o r s , see Kence, 1981; Ta j ima , unpub l i shed ) . N e v e r t h e l e s s , the two parameters , v , and v 2 , are assumed to be cons tants p a r t l y because n e i t h e r v , nor v 2 has been demonstrated to be frequency-dependent i n the SR system. More i m p o r t a n t l y , I in tend to show that the assumption, v , * v 2 , a lone i s s u f f i c i e n t to b r i n g about frequency-dependent v i r i l i t y s e l e c t i o n without e i t h e r of these parameters being frequency-dependent. To c a l c u l a t e v , ; (1) i s rearranged to be v i = ( u , ( y ) / y } / { ( 1 - u , ( y ) ) / ( 1 - y ) } . The same procedure i s used to c a l c u l a t e v 2 . I t i s the i n t e n t i o n of t h i s work to exp lore the male v i r i l i t y d i f f e r e n c e which the male f e r t i l i t y count and v i r g i n female ' s cho ice of mates f a i l to r e v e a l , there fo re i t i s assumed that c=1 and v,=1. In the remainder of the s e c t i o n , time t i s de f ined to be the age of an i n d i v i d u a l female w i t h t=0 being the time of her f i r s t mat ing , ra ther than the time of emergence. 41 THE MODEL: The random v a r i a b l e F-, i s de f ined to be the p r o p o r t i o n of f e r t i l i z e d eggs of a randomly chosen female l a i d between her i - t h and i+1 t h mating which are f a thered by B males . The d i s t r i b u t i o n s and va r i ance s of F-, 's are r e q u i r e d for the t e s t of the model and are g iven i n APPENDIX. The e x p e c t a t i o n of F l + 1 c o n d i t i o n a l on F , i s E(F w l |F. ) = u 2 (y){q+(1-q) F,} + {1-u 2 (y) } { (1-p) F,} = u 2 ( y ) q + { l - b ( y ) } F i where b(y) = p - u 2 ( y ) ( p - q ) , i= 1, 2, 3, The u n d e r l y i n g assumption i s that females would remate before they s t a r t to su f f e r from a shortage of sperm i n t h e i r s torage organs . The e x p e c t a t i o n of F W l i s there fore E ( F ; + 1 ) = u 2 ( y ) q + {1-b(y) }E(F . ) u 2 ( y ) - { E ( F 1 ) b ( y ) - u 2 ( y ) q ) = + { l _ b ( y ) } ' b(y) b(y) u , ( y ) c where E ( F , ) = (2) u , (y)c + {1-u,(y)} In order to a c t u a l l y t e s t the v i r i l i t y d i f f e r e n c e between two genotypes (eg. SR and ST) , the F ' s have to be de f ined as a f u n c t i o n of t i m e . Let F ( t ) be the p r o p o r t i o n of eggs f e r t i l i z e d by sperm of B males when females are aged ( t , t + d t ) . Let I(t-) be the number of matings a female has engaged i n p r i o r to time t . I t was suggested p r e v i o u s l y that I ( t ) c o n s t i t u t e s a pois son proces s . 42 i e . , Prob{ I ( t ) = i } = e x p(-xt) (X.t)'~V(i-1)! = g M ( i ) and E{I ( t ) } = X. t +1 where 1/ X. i s the mean " w a i t i n g t ime" ( i n the s t o c h a s t i c sense) between two consecut ive mat ings . The p r o b a b i l i t y d i s t r i b u t i o n of F ( t ) i s Prob{F(t)=z} = E Pj:ob{F(t)=z, l ( t ) = i } i-= I P r o b { l ( t ) = i} Prob{F( t ) 11 (t.)} i = Z q K i ( i ) Prob{F-, = z} , . t h e r e f o r e , E{F(t ) } = E z Prob{F(t)=z} z = E z E g ^ ( i ) Prob{F, =z} = E E (F • ) g ( i ) u 2 ( y ) q E ( F , ) b ( y ) - u 2 ( y ) q . , = E g ( i ) + E {1-b(y)} g v + ( i ) b(y) '• ' b(y) * u 2 ( y ) q = {1- exp(-b(y)X.t)} + e x p ( - M y ) X t ) E ( F , ) (3) b(y) We are i n t e r e s t e d only i n the c o n t r i b u t i o n of a B male to the gametic pool r e l a t i v e to that of an A male. The r e l a t i v e v i r i l i t y i s thus de f ined as E (F ( t ) ) / y S ( t ) = — ( 4) { 1- E ( F ( t ) ) } / (1-y) and, u 2 ( y ) q ( l - y ) b ( y ) Lim s ( t ) = t-*"0 b (y)y b ( y ) - u 2 ( y ) = (q/p) v 2 (5) Eq . 5 shows t h a t , a f t e r repeated matings , the frequency of p a t e r n a l genes i n the z y g o t i c poo l reaches an e q u i l i b r i u m determined by the r e l a t i v e displacement a b i l i t y of the two genotypes and by mate cho ice by n o n - v i r g i n females. Note that c and v , d i sappear i n (5 ) . However,, at a female ' s v i r g i n mat ing , the r e l a t i v e v i r i l i t y i s governed only by c and v , : E ( F , ) / y s(0) = = c v , . (6) (1-E(F , ) } / (1-y) As mentioned, we are i n t e r e s t e d i n the case c=v,=1. The v i r i l i t y f u n c t i o n , s ( t ) , m o n o t o n i c a l l y decreases from cv , to ( q / p ) v 2 . Thi s v i r i l i t y f u n c t i o n at t = 0 and at t=t*>is a s imple f u n c t i o n of a smal l set of w e l l - d e f i n e d parameters . The a c t u a l v i r i l i t y of males, however, depends on how r a p i d l y s ( t ) approaches ( q / p ) v 2 from c v , . Male v i r i l i t y i s c o n v e n t i o n a l l y equated to s(0) (=cv,) wi thout reference to q/p or v 2 . In c o n t r a s t , t h i s new v i r i l i t y f u n c t i o n p r e d i c t s that r e l a t i v e gametic c o n t r i b u t i o n s of males e i t h e r increase or decrease as females grow o l d e r . Thi s p r e d i c t i o n i s t e s t ed i n the next s e c t i o n . ON FREQUENCY-DEPENDENT VIRILITY SELECTION: The v i r i l i t y f u n c t i o n (eq. 4) i s a compl ica ted e x p r e s s i o n . We w i l l dea l w i t h a s p e c i a l case i n which the v i r i l i t y of males d i f f e r s on ly i n t h e i r mating success w i t h respect to n o n - v i r g i n females . Let 44 c=v,=1 and p=q, we then o b t a i n from ( 2 ) , ( 3 ) , and (4) v 2 + ( 1 - y ) ( 1 - v 2 ) e x p ( - p X t ) s ( t ) = 1- y ( 1 - v 2 ) e x p ( - p X t ) I t f o l l o w s that 3 s - ( 1 - v 2 ) e x p ( - p X t ) { ( 1 - V 2) ( l - e x p ( - p x t ) ) } (7) <0. 3 y ( l - y ( 1 - v 2 ) e x p ( - p x t ) } Eq (7) suggests t h a t , as the frequency of B males i n c r e a s e s , t h e i r v i r i l i t y decreases . F i g . 2 g ives an example of the e f f e c t of the genotypic f requencies on the r e l a t i v e v i r i l i t y . From the es t imates of the v i r i l i t y of SR males at v a r i o u s f requenc ies (see the l a s t paragragrph of ANALYSIS, ) . One can e a s i l y recognize that the e f f e c t of frequency-dependence i s not overwhelmingly s t r o n g . N e v e r t h e l e s s , t h i s e f f e c t should he lp to balance the SR polymorphism. In the numer ica l example w i t h p , q and v 2 (=.52) adopted from the RESULTS s e c t i o n , v i r i l i t y s e l e c t i o n can even mainta in the SR polymorphism by i t s e l f . The balance of t h i s polymorphism i n nature i s c o n c e i v a b l y much more compl ica ted than the so lo a c t i o n of v i r i l i t y s e l e c t i o n , but there should be l i t t l e doubt that v i r i l i t y s e l e c t i o n does p lay a r o l e . I f the mate preference of n o n - v i r g i n females i s i n the oppos i te d i r e c t i o n to that of v i r g i n females ( i e . , v t > 1 >v 2 ) , the e f f e c t of frequency-dependence would be s t ronger than what i s repor ted here . 45 Further t e s t s of v i r i l i t y s e l e c t ion In RESULTS, i t was shown that SR males are l e s s v i r i l than ST males when the females they mate w i t h are n o n - v i r g i n s ; o t h e r w i s e , the v i r i l i t y d i f f e r e n c e i s i n s i g n i f i c a n t . . In the l a s t s e c t i o n , the v i r i l i t y f u n c t i o n , s ( t ) , was developed to i n c o r p o r a t e these f i n d i n g s . We can then p r e d i c t t h a t , as a cohort of v i r g i n females mate and remate c o n t i n u a l l y , the gametic c o n t r i b u t i o n of SR males to the progeny decreases and approaches an e q u i l i b r i u m . The e a s i e s t way to determine the gametic c o n t r i b u t i o n of SR males r e l a t i v e to ST males i s to score for the sex composi t ion i n the progeny. For i n s t a n c e , i f the frequency of SR males equals that of ST males and the v i r i l i t y of SR males decreases from s ( t 0 )=1 to s ( t 1 ) = 0 . 5 , the expected change i n the p r o p o r t i o n of daughters i s roughly from 0.75 to 0 .67 . As the example shows, a 50% reduc t ion i n the v i r i l i t y of SR males changes the sex compos i t ion i n the progeny by only a sma l l f r a c t i o n . A l a rge sample s i z e i s there fo re necessary . The s t a t i s t i c a l s t r u c t u r e has been worked out and i s presented i n APPENDIX. The data are presented i n Table 6. There i s c l e a r l y a t rend of decrease i n the p r o p o r t i o n of females which i s a s ign of weakened v i r i l i t y of SR males . I t i s important to note that • t h i s experiment was done at 14 C. To t e s t i f the magnitude of weakening of the SR v i r i l i t y i s i n accordance w i t h data of the RESULTS s e c t i o n , the ra te of female remat ing , X., has to be e s t imated . In the remainder of t h i s s e c t i o n , I w i l l present the procedure for e s t i m a t i n g X. The v i r i l i t y model d i s cus sed 46 p r e v i o u s l y w i l l then be t e s t e d on the ba s i s of t h i s es t imated X as w e l l as the v i r i l i t y parameters presented b e f o r e . E s t i m a t i o n of X. from p o p u l a t i o n d a t a : I t would be most d e s i r a b l e to e x t r a c t i n f o r m a t i o n on X. from the same exper imenta l des ign that y i e l d e d the data of Table 6. The reason i s obv ious : The a c t u a l remating rate i n the p o p u l a t i o n cage from which the data of Table 6 were c o l l e c t e d may not be the same as the remating ra te i n other exper iments . The h igh remating rate reported i n Table 5 i s almost c e r t a i n l y an overest imate for t h i s exper iment . The sex composi t ion data of Table 6 were the t o t a l of 196 f a m i l i e s . Each f ami ly was d e r i v e d from an i n d i v i d u a l female i n the p a r e n t a l p o p u l a t i o n . I f we have the data of sex compos i t ion i n each f a m i l y , i t would be p o s s i b l e to est imate X.. Suppose that X i s very smal l and most females remain s i n g l y mated throughout the experiment, the d i s t r i b u t i o n of sex compos i t ion would be bimodal w i t h one peak at .5 (ST-mated) and the other around .99 (99% females, i e . , SR -mated) . A l t e r n a t i v e l y , i f females remate reasonably o f ten and sperm displacement i s not always complete , the d i s t r i b u t i o n of sex composi t ion should s h i f t from b i m o d a l i t y as females remate. The ra te of the s h i f t i s i n f o r m a t i v e about the value of X. F o r t u n a t e l y , sperm displacement of SR males at 14 C i s f a i r l y weak (Table 3) and there would be s u b s t a n t i a l "sperm m i x i n g " . The r e s u l t of t h i s sperm mix ing on the d i s t r i b u t i o n of sex compos i t ion of 115 f a m i l i e s i s presented i n F i g . 3. These f ami ly data add up to the day-14 c o l l e c t i o n of Table 6. 47 In APPENDIX, a method, a numer ica l Maximum L i k e l i h o o d Es t imator ( MLE ) , i s p rov ided to es t imate X. from the data of F i g . 3. Th i s method computes the l i k e l i h o o d , L ( X ) , of o b t a i n i n g the observed d i s t r i b u t i o n g iven X. F i g . 4 g ives the r a t i o s of L ( x ) / L ( X 0 ) where L ( X 0 ) i s the maximum l i k e l i h o o d o b t a i n e d . I t suggests the MLE of 1/X ( i e . , average " w a i t i n g t ime" between matings) to be somewhere between 4-4.5 days . I w i l l assume 1/X to be 4 i n the subsequent t e s t s . Note that the l i k e l i h o o d of X=0 (L(0) ) i s i n f i n i t e s i m a l r e l a t i v e to L ( l / 4 ) . T h i s means that i t i s f a i r l y u n l i k e l y to ob ta in data w i t h a p r o f i l e l i k e that of F i g . 3 when females do not engage i n m u l t i p l e matings ( i e . , X=0). Tests of the v i r i l i t y model: The p r e d i c t e d and observed decrease i n the v i r i l i t y of SR males at 14 C i s presented i n F i g . 5 . The expected va lues are based on data presented i n Table lb ( f e r t i l i t y ) , Table 3b (sperm d i s p l a c e m e n t ) , Table 4 ( sexual s e l e c t i o n ) and F i g . 4 ( X ) . Eqs. (10) and (11) i n APPENDIX were used to c a l c u l a t e the means and var i ance s of p r o p o r t i o n s of females i n the progeny. Observed va lues are from Table 6. The h o r i z o n t a l l i n e i s what one would expect i f females d i d not remate. A g a i n , i t can be seen that an overes t imate of the v i r i l i t y of SR males would r e s u l t i f on ly v i r g i n females are c o n s i d e r e d . The expected r e l a t i v e v i r i l i t y based on the es t imated v 2 (=.52) does not f i t the observed p a t t e r n as c l o s e l y as the expec ta t ion based on the upper l i m i t of v 2 (=.73) does. 48 I t i s l i k e l y that sexual s e l e c t i o n aga ins t SR males by non-v i r g i n females (v 2 ) i s not as s t rong as Table 4 suggests . P o s s i b l e reasons w i l l be d i s c u s s e d . The e r r o r around the es t imated v 2 i s indeed the grea te s t source of v a r i a t i o n i n the p r e d i c t i o n of t h i s v i r i l i t y model . N e v e r t h e l e s s , g iven the v a r i a t i o n i n these es t imates of v 2 (see Table 4 ) , the observa t ion s t i l l agrees reasonably w e l l w i t h the p r e d i c t i o n . Another source of concern about t h i s t e s t i s that the "observed" value of day 0 was p r o j e c t e d from the r e s u l t of a c o n t r o l experiment (which was designed to es t imate the r e l a t i v e v i a b i l i t i e s of the two sexes ) . Th i s p r a c t i c e i s necessary because egg samples obta ined in the f i r s t three days are u s u a l l y very smal l at 14 C. In APPENDIX , another t e s t which u t i l i z e s only the observed p r o p o r t i o n s of females a c t u a l l y obta ined from the exper imenta l p o p u l a t i o n i s c a r r i e d out ( i e . , on ly samples c o l l e c t e d on and a f t e r day 5 are c o n s i d e r e d ) . The power of t h i s t e s t i s weak bu t , nonethe le s s , i s s t i l l s t rong enough to r e j e c t v i r i l i t y e s t imates based s o l e l y on mating of v i r g i n females . On the other hand, i t cannot r e j e c t the v i r i l i t y model presented above. 49 E s t i m a t i o n of SR v i r i l i t y The v i r i l i t y f u n c t i o n , s ( t ) , in t roduced p r e v i o u s l y i s not r e a d i l y a p p l i c a b l e to the c o n v e n t i o n a l d i s c r e t e genera t ion model of p o p u l a t i o n g e n e t i c s . To approximate the v i r i l i t y of SR males, S, i n the sense of a d i s c r e t e generat ion model, two age-dependent t r a i t s of females have to be cons idered— the age-s p e c i f i c f e c u n d i t y and the m o r t a l i t y of fecund females . Let z ( t ) be the p r o p o r t i o n of eggs a female l a y s at age ( t , t + d t ) . G e n e r a l l y , z ( t ) increases i n the f i r s t s e v e r a l days and s tays at a p l a t e a u for one to two weeks and then decreases g r a d u a l l y . Let m(T) be the p r o b a b i l i t y of a female s u r v i v i n g to and dy ing on day T a f t e r i t s f i r s t mat ing . For any female which d i e s at age T, the gametic c o n t r i b u t i o n by SR males to her l i f e t i m e z y g o t i c output i s The r e l a t i v e male v i r i l i t y , S, w i t h respect to a cohort of females i n a p o p u l a t i o n w i t h a s t a b l e age s t r u c t u r e i s there fore H(T) = E ( F ( t ) ) z ( t ) dt whi l e her t o t a l output i s Z(T) = T z ( t ) dt . o (H/Z) /y S (8) ( 1 - H / Z ) / ( 1 - Y ) where H H(T)m(T) dT o z r z ( T ) m ( T ) dT . Eq . 8 i s used to compute the r e l a t i v e v i r i l i t y of SR 50 males . The age s p e c i f i c f e c u n d i t y , z ( t ) " , at 22 C obta ined i n t h i s study i s very s i m i l a r to that repor ted by Beckenbach (1978). At 14 C, egg l a y i n g i s delayed by about two days . Note that i t i s the r e l a t i v e q u a n t i t y of eggs l a i d each day that i s p e r t i n e n t to v i r i l i t y e s t i m a t i o n . The m o r t a l i t y of fecund females i s u s u a l l y q u i t e smal l w i t h i n two weeks i n the l a b o r a t o r y p o p u l a t i o n s . In na ture , however, Dobzhansky and Wright (1942) es t imated the d a i l y m o r t a l i t y of D. pseudoobscura a d u l t s to be about 8%. I w i l l use Dobzhansky and W r i g h t ' s es t imate of m(T) i n v i r i l i t y e s t i m a t i o n . Because F i g . 5 suggests that the upper l i m i t of the es t imated v 2 (=.73) r e s u l t s in a b e t t e r f i t than the es t imated one (v 2 =0.52) , both va lues are used. At 14 C, w i t h a l l v i r i l i t y elements i n c o r p o r a t e d , SR males are expected to be only about 30-37% v i r i l compared to ST males. (S=.30 i f v 2 = .52 ; S=.37 i f v 2 = . 7 3 ) . T h i s low l e v e l of v i r i l i t y i s more than s u f f i c i e n t to o f f s e t the advantage of the m e i o t i c a l l y d r i v e n SR chromosome. At 22 C, the es t imated r e l a t i v e v i r i l i t y i s as f o l l o w i n g : F r e q . of SR males v 2 =.52 v 2 =.73 . 1 .52 .65 .5 .50 .64 .9 .48 .63 A g a i n , v i r i l i t y r e d u c t i o n i n SR males i s q u i t e s u b s t a n t i a l . The i m p l i c a t i o n of the low v i r i l i t y of SR males w i l l be d i s c u s s e d . 51 DISCUSSION The s tud ie s of f i t n e s s components of s imple genet ic systems pioneered by Prout (1965, 1969, 1971a, b) have opened a new door to the understanding of a fundamental ques t ion of e v o l u t i o n a r y b i o l o g y : How does n a t u r a l s e l e c t i o n govern the changes of gene frequency i n n a t u r a l popu la t ions? Prev ious s tud ie s of f i t n e s s components of D r o s o p h i l a p o p u l a t i o n s brought our a t t e n t i o n to the male adu l t component of s e l e c t i o n ( v i r i l i t y s e l e c t i o n ) d e s p i t e the c o n v e n t i o n a l wisdom concerning the " s t r u g g l e for-s u r v i v a l " ( v i a b i l i t y s e l e c t i o n ) . In a d d i t i o n , v i r i l i t y s e l e c t i o n i s undoubtedly the most i n t r i g u i n g f i t n e s s component i n terms of i t s consequences on genet ic changes of p o p u l a t i o n s . Numerous t h e o r e t i c a l s tud ie s have been devoted to i t (see O 'Dona ld , 1980 fo r r e v i e w ) . In t h i s s tudy , the male a d u l t component of f i t n e s s i s f u r t h e r p a r t i t i o n e d i n t o two subcomponents, each of which has i t s own v i r i l i t y e lements . These elements (the f e r t i l i t y count , sperm d i sp lacement , sexual s e l e c t i o n and the female remating tendency) were examined s epara te ly i n RESULTS and were j o i n t l y sub ject to another t e s t i n ANALYSIS . To conc lude , an accurate es t imate of the male adu l t component of s e l e c t i o n r e q u i r e s the p a r t i t i o n i n g of i t i n t o a subcomponent w i t h respect to v i r g i n females and another w i t h respect to n o n - v i r g i n females . I t was a l s o shown repeatedly how underest imates of v i r i l i t y s e l e c t i o n would have r e s u l t e d i f an o v e r s i m p l i f i e d exper imenta l des ign was used. Th i s theme i s supported by a recent study of Beckenbach (1982). 52 By a p p l y i n g t h i s v i r i l i t y concept to the SR polymorphism i n D. pseudoobscura, i t was found that SR males were indeed l e s s v i r i l than ST males , in c o n t r a s t to the r e s u l t s of Beckenbach (1978) and C u r t s i n g e r and Feldman (1980). V i r i l i t y s e l e c t i o n by i t s e'ir i s not l i k e l y to be s o l e l y r e s p o n s i b l e for the SR polymorphism as Edward's (1961) and C u r t s i n g e r and Feldman's (1980) t h e o r e t i c a l s tud ie s c l e a r l y showed. Thi s s tudy , however, throws some l i g h t on two p u z z l i n g ques t ions concerning the SR t r a i t of D. pseudoobscura. F i r s t l y , as mentioned, the search for m o d i f i e r s i n D. pseudoobscura has been f r u i t l e s s . The absence of suppressor m o d i f i e r s of s e x - r a t i o expres s ion suggests , i n t h e o r y , an o v e r a l l low f i t n e s s of SR males r e l a t i v e to ST males (Part II of t h i s t h e s i s ) . Prev ious es t imates (Wal lace , 1948; C u r t s i n g e r and Feldman, 1980) of t h i s r e l a t i v e f i t n e s s are much too h igh to prevent the spread of autosomal m o d i f i e r s i n n a t u r a l p o p u l a t i o n s . The d i screpancy between the theory and exper imenta l r e s u l t s can be e x p l a i n e d i f prev ious e s t imates of v i a b i l i t i e s are c o r r e c t but v i r i l i t y s e l e c t i o n was underes t imated , l e ad ing to an overes t imate of o v e r a l l f i t n e s s of SR males . T h i s exper imenta l study on v i r i l i t y s e l e c t i o n lends s t rong support to the e x p l a n a t i o n . Combining prev ious es t imates of male v i a b i l i t i e s and the es t imates of v i r i l i t y i n t h i s s tudy, the absence of suppressor m o d i f i e r s i n D. pseudoobscura p o p u l a t i o n s and many years of e f f o r t s by SR workers to measure f i t n e s s e s can both now be f i t i n t o a more genera l p i c t u r e of the SR polymorphism. We may now be on a sa fer ground to equate "the f a i l u r e " to f i n d suppressor m o d i f i e r s to "the absence" of them. 53 Secondly , the frequency of SR i s i n genera l i n v e r s e l y r e l a t e d w i t h temperature i n na ture . Th i s negat ive c o r r e l a t i o n , r e f l e c t e d i n the g e o g r a p h i c a l , temporal and a l t i t u d i n a l d i s t r i b u t i o n of SR (Dobzhansky, 1944; E p l i n g et a l , 1957; B a l d w i n , 1979; Bryant et a l , 1980) suggests an i n c r e a s i n g i n t e n s i t y of n a t u r a l s e l e c t i o n aga ins t SR c a r r i e r s as temperature decreases . The c o r r e l a t i o n between temperature and the frequency of SR i n n a t u r a l p o p u l a t i o n s i s c e r t a i n l y not a p e r f e c t one as one would have expected, but i s nonetheless reasonably w e l l e s t a b l i s h e d w i t h i n a medium temperature range by these independent f i e l d i n v e s t i g a t i o n s . In the l a s t s e c t i o n of ANALYSIS, i t was shown that SR males are 35-50% l e s s v i r i l than ST males at 22 C but are 65% l e s s v i r i l at 14 C. V i r i l i t y s e l e c t i o n at 14 C can more than o f f s e t , the advantage SR acqu i re s through m e i o t i c d r i v e . Informat ion about other s e l e c t i o n components at t h i s temperature i s scanty but i t i s not hard to see why no SR chromosome has been d i s covered i n the nor thern part of the d i s t r i b u t i o n of D. pseudoobscura. The v i r i l i t y d i f f e r e n c e at 14 C i s mainly due to a d r a s t i c r e d u c t i o n i n the sperm d i s p l a c i n g a b i l i t y of SR males (Table 3b) de sp i t e t h e i r normal f e r t i l i t y count (Table 1b). The v i r i l i t y concept proposed i n t h i s study does b r i n g i n t o l i g h t v i r i l i t y d i f f e r e n c e s which otherwise would have escaped d e t e c t i o n . In the remainder of t h i s s e c t i o n , I w i l l d i s c u s s v a r i o u s aspects of each v i r i l i t y element as w e l l as t h e i r j o i n t e f f e c t . 54 1) Sperm d i sp lacement : To secure i t s r eproduct ive success , a male D r o s o p h i l a may have evolved v a r i o u s " s t r a t e g i e s " to c ircumvent the m u l t i p l e - m a t i n g behavior of females . I t can t r y to d i s p l a c e sperm of other males, or a l t e r n a t i v e l y , to r e s i s t other males from d i s p l a c i n g i t s own sperm s tored i n the female r e p r o d u c t i v e t r a c t as many other i n s e c t s do (Parker , 1970; Prout and Bundgaard, 1977). Sperm displacement i s t r e a t e d i n t h i s study more or l e s s as a t r a i t of the c o p u l a t i n g males regard le s s of the prev ious mates of the females . Indeed, i f the t h r e s h o l d hypothes i s on sperm displacement proposed above i s c o r r e c t , the best a D r o s o p h i l a male can do aga ins t sperm displacement i s to e j a c u l a t e a l a r g e r volume than the storage c a p a c i t y of females, a r e l a t i v e l y easy task for most males (Lefevre and Jonsson, 1962). The strenuous work for D r o s o p h i l a males i s to d i s p l a c e o t h e r s ' sperm. In the experiments of sperm displacement presented in Table 3, both SR and ST males were examined for t h e i r a b i l i t y to d i s p l a c e the sperm of v e r m i l i o n males . The r e s u l t s of Table 3 thus t e l l us at l e a s t the r e l a t i v e d i s p l a c i n g c a p a c i t y of ST and SR males . One c o r o l l a r y of the t h r e s h o l d model i s that the i n t e n s i t y of sperm displacement does not depend on the v i r i l i t y of males whose sperm are to be d i s p l a c e d , as long as t h e i r sperm e j a c u l a t e s exceed the t h r e s h o l d l e v e l . Because v e r m i l i o n males used i n t h i s experiment are no l e s s f e r t i l e than the w i l d type , t h i s may be the case . In other words, the data do not merely r e f l e c t the r e l a t i v e i n t e n s i t y of sperm displacement between SR and ST males; they may a l s o represent the absolute displacement 55 a b i l i t y i n the absence of c o m p l i c a t i o n s by v i s i b l e mutants . For many f i t n e s s r e l a t e d t r a i t s , the r e l a t i v e va lues are s u f f i c i e n t to de sc r ibe the dynamics of gene frequency changes. V i a b i l i t y and mating success are examples. For sperm displacement (p and q of eqs. (4) and (5) ) , the r e l a t i v e v a l u e , q /p , determines the asymptote of the v i r i l i t y f u n c t i o n , s ( t ) (eq. ( 5 ) ) , but the ra te of approaching that asymptote i s a l s o governed by the values of p and q . Hence the r a t i o q/p a lone i s i n s u f f i c i e n t for v i r i l i t y e s t i m a t i o n . 2) Sexual s e l e c t i o n : Th i s p a r t i c u l a r v i r i l i t y element i s the grea tes t source of v a r i a t i o n i n v i r i l i t y e s t i m a t i o n . What i s demonstrated c l e a r l y i n Table 4 i s that n o n - v i r g i n females d i s c r i m i n a t e aga ins t SR males much more s t r o n g l y than v i r g i n females do. There are s evera l advantages of the exper imenta l des ign used here . Exper imenta l males of e i t h e r genotype are not marked i n any way. T h e i r r e l a t i v e mating success was determined by examining the progeny of each i n d i v i d u a l female. (This p r a c t i c e i s somewhat compl ica ted when de termin ing mating success w i t h respect to n o n - v i r g i n females, see the MATERIALS AND METHODS s e c t i o n . ) As a consequence of t h a t , the r e l a t i v e mating successes (v , and v 2 ) c o u l d both be d i r e c t l y measured ir\ the  p o p u l a t i o n . Di s turbances of the mating behavior of f l i e s were m i n i m i z e d . Mat ing a c t i v i t i e s of D r o s o p h i l a f o l l o w a d i u r n a l c y c l e w i t h a sharp peak at the n i g h t / d a y i n t e r f a c e (Hardeland, 1972). I t i s not p o s s i b l e to avo id d i s t u r b i n g the d i u r n a l c y c l e of f l i e s w i t h d i r e c t observa t ions i n mating chambers. In 56 a d d i t i o n , the number and d e n s i t y of f l i e s may a l s o a f f e c t r e l a t i v e mating success . Because v , and v 2 obta ined i n t h i s experiment were to be subject to f u r t h e r t e s t s in other l a b o r a t o r y p o p u l a t i o n s , the c o n d i t i o n s under which v , and v 2 were measured were s i m i l a r to those i n l a t e r t e s t s . For t e c h n i c a l reasons, v e r m i l i o n females homozygous for ST were used. Al though for the purpose of demonstrat ing v , r v 2 , i t i s on ly necessary to use females ( v i r g i n s and n o n - v i r g i n s ) of the same genotype, the a c t u a l v a l u e s . o f v , and v 2 may be somewhat d i f f e r e n t from those o b t a i n e d . To compensate for t h i s e f f e c t , both the es t imated value of v 2 and the upper l i m i t of i t were used. F o r t u n a t e l y , the c o n c l u s i o n i s not s i g n i f i c a n t l y a f f e c t e d by t h i s v a r i a t i o n (see the l a s t two paragraphs of ANALYSIS ) . 3) The tendency of females to remate: In RESULTS, assumptions r e q u i r e d to t r e a t the event of females ' mating as a Po i s son process were e x p e r i m e n t a l l y examined. In ANALYSIS, the average w a i t i n g time (1 /X.) between two consecut ive matings was est imated to be about 4 days , w i t h the assumptions of a Poi s son process and the a i d of a Maximum L i k e l i h o o d E s t i m a t o r . Why i s such a compl ica ted treatment needed? For v i r i l i t y e s t i m a t i o n , a q u a n t i t a t i v e assessment of the r e l a t i v e importance of the two components of v i r i l i t y s e l e c t i o n i s necessary . Th i s assessment r e q u i r e s i n f o r m a t i o n on how the event of remating recurs w i t h time and the s imples t form of recurrence w i t h time i s the Poisson process which has only one 57 parameter, X . . Severa l s tud ie s on remating tendencies of female D r o s o p h i l a i n n a t u r a l popu la t ions provide very u s e f u l i n f o r m a t i o n about the extent of remating i n nature (Milkman and Z e i t l e r , 1974; Cobbs, 1977; Lev ine et a l , 1979). These s tud ie s i n f e r r e d m u l t i p l e p a t e r n i t y from the genotypes of the mother and her o f f s p r i n g w h i c h , however, are i n s u f f i c i e n t fo r the e s t i m a t i o n of X . . F i r s t , the frequency d i s t r i b u t i o n of a l l e l e s used to i d e n t i f y p a t e r n a l genotypes i s u s u a l l y h i g h l y skewed. Thi s means that the p r o b a b i l i t y of a female mated to males of the same genotype i s q u i t e h i g h . Remating of t h i s k i n d would not be d e t e c t e d . Second, in format ion on m u l t i p l e mating i s best preserved i f on ly one h a l f of sperm from prev ious matings are d i s p l a c e d . Males c a r r y i n g ST u s u a l l y d i s p l a c e more than 90% of sperm i n the females ' s torage organs (Table 3 ) . With these l i m i t a t i o n s , Cobbs (1977) s t i l l caught some a u t h e n t i c t r i p l y -mated females . T h i r d , without knowledge of the age of females, i t i s not p o s s i b l e to est imate the remating ra te - even i f t h e i r mating h i s t o r y can be u n e q u i v o c a l l y determined. I t i s p r e c i s e l y these d i f f i c u l t i e s that mot ivated the experiments l e a d i n g to the r e s u l t s of Table 5 and F i g . 4. The s i m u l a t i o n of the mating event by a Poi s son process assumes that the p r o b a b i l i t y of a female to remate remains r e l a t i v e l y constant throughout the exper imenta l p e r i o d . The p r o p o r t i o n of females which have not mated i s expected to decrease e x p o n e n t i a l l y (and smoothly) w i t h t i m e . However, i t has been shown that D r o s o p h i l a spec ies e x h i b i t s t rong d i u r n a l 58 v a r i a t i o n i n c o u r t i n g a c t i v i t y , (Hardeland, 1972) and that l i g h t i s the p r i n c i p a l causa l f a c t o r of the d i u r n a l p e r i o d i c i t y of the f l i e s (Dobzhansky and E p l i n g , 1944). There fore , i n r e a l i t y , t h i s p r o p o r t i o n may a c t u a l l y decrease i n a stepwise f a s h i o n . The e x p o n e n t i a l curve only serves as an approximat ion to t h i s s tep f u n c t i o n . For the same reason, the obse rva t ion of a short r e f r a c t o r y p e r i o d a f t e r each mating does not i n v a l i d a t e the Poi s son process as an a p p r o x i m a t i o n . Bundgaard and C h r i s t i a n s e n (1972) repor ted a two hour r e f r a c t o r y p e r i o d a f t e r each mating w i t h i n which a D. melanogaster female would not remate at a l l . Th i s p e r i o d i s repor ted to be 12 hours i n D. pseudoobscura (Beckenbach, 1981). The r e f r a c t o r y p e r i o d i s g e n e r a l l y s h o r t e r than the p e r i o d i c i t y of the d i u r n a l c y c l e ; hence, those newly-mated females would have resumed the normal l e v e l of r e c e p t i v i t y before the next a c t i v i t y peak. 4) The t e s t of the o v e r a l l e f f e c t of v i r i l i t y s e l e c t i o n : The v i r i l i t y f u n c t i o n , s ( t ) , p r e d i c t s that v i r i l i t y of SR males becomes g r a d u a l l y weakened as females remate. R e l a t i v e v i r i l i t y of SR and ST males was est imated from the p r o p o r t i o n of daughters i n t h e i r progeny ( i e . , A ( t ) i n APPENDIX ) . I t i s p o s s i b l e to determine the p a t e r n a l genotype of each i n d i v i d u a l female by chromosomal squash or g e l e l e c t r o p h o r e s i s . However, the l a rge sample s i z e , thousands i n each sample, r e q u i r e d to determine r e l a t i v e v i r i l i t y makes these methods u n f e a s i b l e (eq. (1) of APPENDIX ) . Bes ides , the two techniques would not 59 prov ide much more in format ion on v i r i l i t y d i f f e r e n c e s than what i s conta ined i n the s t a t i s t i c , A ( t ) . There are two sources of concern about the s t a t i s t i c A ( t ) . F i r s t , SR males produce a t i n y p r o p o r t i o n of sons (1-3% in the s t r a i n s used) . Thi s p r o p o r t i o n becomes s i g n i f i c a n t i f the p a r e n t a l genera t ion c o n s i s t s mostly of SR males. In that event , males i n the progeny cannot be determined w i t h conf idence i f they are fa thered by ST males . The experiment t h e r e f o r e s t a r t e d w i t h equal frequency of SR and ST males . Consequently , a 50% r e d u c t i o n i n the v i r i l i t y of SR males would only r e s u l t i n a l e s s than 10% change i n p r o p o r t i o n s of daughters . T h i s i s one very important reason for l a r g e samples. Second, l i k e any attempt to measure v i r i l i t y d i f f e r e n c e s , t h i s experiment had to use v i a b i l i t y es t imates from supplementary experiments . The v i a b i l i t y of ST males r e l a t i v e to ST/ST females was es t imated to be .81 i n a c o n t r o l p o p u l a t i o n . The p r o p o r t i o n of daughters i n the sample of day 0 of Table 6 was c a l c u l a t e d based on 1) equal f e r t i l i t y and mating success of SR and ST males w i t h respect to to v i r g i n females and, 2) the es t imated r e l a t i v e v i a b i l t i y of the two sexes ( . 8 1 ) . To prevent the v i r i l i t y t e s t from being confounded by v i a b i l i t y e s t i m a t i o n , the s t a t i s t i c A ( t 1 ) - A ( t 2 ) i s used i n APPENDIX . T h i s s t a t i s t i c represents the d i f f e r e n c e i n sex compos i t ions of samples c o l l e c t e d at time t , and t 2 r e s p e c t i v e l y . A v i r i l i t y model w i t h a s imple component expects the d i f f e r e n c e always to be 0 r egard le s s of any v i a b i l i t y d i f f e r e n c e among genotypes. S i m i l a r l y , t h i s q u a n t i t y i s only 60 m a r g i n a l l y a f f e c t e d by v a r i a t i o n i n v i a b i l i t y es t imates when both v i r i l i t y components are c o n s i d e r e d . The c o n c l u s i o n thus d e r i v e d a l s o supports the v i r i l i t y concept proposed i n t h i s s tudy . F i n a l l y , i t i s worthwhi le to comment b r i e f l y on frequency-dependent v i r i l i t y s e l e c t i o n . The frequency-dependent proper ty d e r i v e d i n ANALYSIS i s not a p p l i c a b l e to Ehrman's (1967,1970) and Sp ie s s 1 (1968,1970) obse rva t ion on the mating advantage of rare males . I t i s ra ther an attempt to show that frequency-dependent v i r i l i t y s e l e c t i o n can a r i s e w i t h v , and v 2 be ing c o n s t a n t s , i e . , without "females c a r r y i n g out the d i f f i c u l t task of d i s c r i m i n a t i n g between rare and common males" (O'Donald , 1977). Whi le D r o s o p h i l a workers cont inue t h e i r search for the b e h a v i o r a l ba s i s of frequency- dependence (Ehrman, 1972; Spiess and Kruckeberg , 1980), t h e o r e t i c a l s tud ie s on "apparent frequency-dependent s e l e c t i o n " r e s u l t i n g from constant mating preferences w i l l a l s o prove to be b e n e f i c i a l to our unders tanding of t h i s phenomenon (O'Donald , 1977; Kence, 1980; Ta j ima , u n p u b l i s h e d ) . TABLE 1.a F e r t i l i t y Count At D i f f e r e n t Mating Frequencies Mat ing F r e q . SR ST (10) (10) v i r g i n males 4 3 1 . 8 ± 4 7 . 2 3 9 7 . 1 ± 6 8 . 0 P>.1 (8) (8) 1 mating/day 4 2 4 . 8 ± 9 1 . 2 4 0 0 . 3 ± 4 2 . 5 P>. 1 (10) (10) 3 mating/day 2 5 7 . 6 ± 1 0 9 . 9 405 .1±66 .1 P<.01 TABLE 1 .b F e r t i l i t y Count At D i f f e r e n t Temperature Temperature SR ST (10) (10) 22 C 4 3 1 . 8 ± 4 7 . 2 3 9 7 . 1 ± 6 8 . 0 P>.1 (12) (12) 14 C 3 4 2 . 3 ± 9 4 . 2 3 9 1 . 5 ± 6 2 . 2 P>.05 Note- Numbers i n the bracket s are sample s i z e s . 62 TABLE 2.a E f f e c t Of Mating Frequency On ST Male V i r i l i t y V i r g i n Males Males Mated 3 Times/day f e r t i l i t y count (10) 3 9 7 . 1 ± 6 8 . 0 (10) 4 0 5 . 1 ± 6 6 . 1 P>. 1 sperm displacement (21 ) p = .979 (22) p = .619 P<.01 TABLE 2.b E f f e c t Of Temperature On ST Male V i r i l i t y 22 C 14 C f e r t i l i t y count • (10) 3 9 7 . 1 ± 6 8 . 0 (12) 3 9 1 . 5 ± 6 2 . 2 P>. 1 sperm d i splacement (21 ) p = .979 (24) p = .94 P<.02 Note- Numbers i n the bracket s are sample s i z e s . A l l males used i n t h i s experiment are ST males. p i s the p r o p o r t i o n of sperm d i s p l a c e d by a c o p u l a t i n g ST male. 63 TABLE 3.a Sperm Displacement At D i f f e r e n t Mating Frequencies Mating F r e q . SR ST (22) (21) v i r g i n males q = .828 p = .979 . P<.01 (8) (10) 1 mating/day q = .793 p = .995 P<.01 (24) (22) 3 mating/day q = .322 p = .619 P<.01 TABLE 3.b Sperm Displacement At D i f f e r e n t Temperature Temperature SR ST (22) (21) 22 C q = .828 p = .979 P<.01 (36) (24) 14 C q = .355 p = .940 P<.01 Note- Numbers i n the bracket s are sample s i z e s . The row e f f e c t and column e f f e c t i n Table 3.a are h i g h l y s i g n i f i c a n t i n a Two Way ANOVA. A l l e f f e c t s are h i g h l y s i g n i f i c a n t i n Table 3 .b . p and q are the p r o p o r t i o n s of sperm d i s p l a c e d by ST males and by SR males r e s p e c t i v e l y . TABLE 4 Mate Choice By V i r g i n and N o n - v i r g i n Females Male Genotypes ST SR V i r g i n Females 49 44 Non-vi r g i n Females 67 35 93 v , = .88 ( .52 , 1.34) 1 02 v 2 = .52 62 ( .30 , .73) Note - The numbers i n the bracket s are the 95% conf idence i n t e r v a l for v , and v 2 r e s p e c t i v e l y . Both v , and v 2 are the mating success of an SR r e l a t i v e to that of an ST male. X - Numbers of females which f a i l e d to mate (or remate) . 6 5 TABLE 5 Remating Tendency of Females genotype of males mating s t a tu s of females 1 2 3 4 T o t a l .85 1/1 7/7 6/8 2/3 16/19 .97 4/8 8/10 0/1 - 12/19 1.03 0/1 1/9 0/7 0/2 1/19 1.09 5/5 1/1 6/6 3/3 15/15 1.12 8/12 2/2 3/5 - 13/19 Z 18/26 18/20 15/20 5/6 =.692 =.90 =.75 =.833 Note- The e n t r y , x / y , means that x out of y females at the i n d i c a t e d mating s t a tus remated w i t h i n a two day p e r i o d . Mating s t a tus of a female i s the number of times she has mated. Males are c l a s s i f i e d by the es t-5 a l l e l e they c a r r y . E - T r i a l s w i t h 1.03 males are exc luded . 66 TABLE 6 A Test of The Male V i r i l i t y Model at 14 C The n - t h Day C o l l e c t i o n of Eggs 0 5 8 11 14 No. females ' - 2,554 2,184 2,302 5,908 No. males - 1,025 954 1,075 3,101 % Female (79.0) (71.4) (69.6) (68.2) (65.6) Note- Sex compos i t ion in F, samples c o l l e c t e d at 14 C. The p a r e n t a l genera t ion c o n s i s t s of 195 females , 75 ST males and 75 SR males . Expected p r o p o r t i o n of daughters on day 0 i s based on equal f e r t i l i t y of SR and ST males and on the es t imated r e l a t i v e v i a b i l i t y of the two sexes ( . 8 1 ) . 67 F i g u r e 1-2. The frequency-dependent v i r i l i t y f u n c t i o n , s ( t ) . Th i s f u n c t i o n i s shown to decrease w i t h the age of females . Thi s func t ion i s the r e l a t i v e v i r i l i t y of males of d i f f e r e n t genotypes. As females remate c o n t i n u a l l y , the average gametic c o n t r i b u t i o n of the weaker males decrease a l though they are a l l e q u a l l y v i r i l e at the females ' v i r g i n mat ing . The higher the frequency of weaker males, the more r a p i d l y the r e l a t i v e v i r i l i t y decreases . 67a 68 Figure 1-3. The d i s t r i b u t i o n of sex-composi t ions from 115 f a m i l i e s . A Maximum L i k e l i h o o d Es t imator i s developed to es t imate X based on these data (see t e x t ) . FREQUENCY C D i — CO O CO CO 4^ cn c o OO J X o o r o ^ ro no cn o 4^  H 4-8^9 69 F igure 1-4. L i k e l i h o o d r a t i o s for X . . L ( X . ) i s the l i k e l i h o o d of o b t a i n i n g the data of F i g . 3 g iven the remating r a t e , X. . The maximum l i k e l i h o o d i s obta ined at X . 0 = l / 4 and 1 /X i s the average time elapsed between mat ings . 70 F i g u r e 1-5. Observed v s . expected p r o p o r t i o n s of daughters . A decreased p r o p o r t i o n of daughters i s an i n d i c a t i o n of weakened v i r i l i t y of SR males . The dots represent observed values i n Table 6. The l i n e s are expected values based on eq. (10) of APPENDIX. V e r t i c a l bars are standard e r r o r s c a l c u l a t e d w i t h eq . (11) of APPENDIX. Parameter va lues used in these equat ions , i f not s p e c i f i e d , are adopted from the RESULTS s e c t i o n . 70a PART II FATE OF AUTOSOMAL MODIFIERS OF THE SEX-RATIO TRAIT DROSOPHILA AND OTHER SEX-LINKED MEIOTIC DRIVE SYSTEMS 72 ABSTRACT A model i s proposed to de scr ibe the behavior of autosomal suppressor m o d i f i e r s of " S e x - R a t i o " m e i o t i c d r i v e i n D r o s o p h i l a . These m o d i f i e r s ., i f n e u t r a l i n f i t n e s s , are expected to increase because they tend to be a s s o c i a t e d w i t h the rare sex (males ) . However, s e l e c t i o n opera t ing on the s e x - l i n k e d d r i v e locus w i l l sometimes act aga ins t autosomal m o d i f i e r s as w e l l because the two l o c i are always i n gametic phase d i s e q u i l i b r i u m . C o n d i t i o n s under which m o d i f i e r s w i l l not increase are presented i n terms of the f i t n e s s e s at the s e x - l i n k e d d r i v e l o c u s . To prevent the increase of m o d i f i e r s , the f i t n e s s of Sex-Rat io males r e l a t i v e to Standard males has to be no grea ter than 0.3 and there has to be overdominance in females . T h i s model i n t e g r a t e s f i n d i n g s from the search for m o d i f i e r s and r e s u l t s from the measurement of f i t n e s s e s . 73 INTRODUCTION Many p l a n t s and animals possess gene l o c i where the two segregat ing a l l e l e s of a heterozygous parent are not recovered at the expected 1:1 r a t i o . M e i o t i c d r i v e i s used to denote d i s t o r t i o n i n frequency of a l l e l e s among gametes of the heterozygous parent (Sandler and N o v i t s k i , 1957). Th i s d e f i n i t i o n of m e i o t i c d r i v e r u l e s out gametic s e l e c t i o n and z y g o t i c s e l e c t i o n but does not n e c e s s a r i l y imply non-Mendelian segregat ion as "a consequence of the mechanics of the m e i o t i c d i v i s i o n s " ( H a r t l , 1977). Peacock and M i k l o s (1973) reviewed s e v e r a l d i f f e r e n t me io t i c d r i v e systems i n D r o s o p h i l a . M e i o t i c d r i v e i n v o l v i n g sex chromosomes i s of s p e c i a l i n t e r e s t , both for i t s s i g n i f i c a n c e i n e v o l u t i o n a r y theory and for i t s p o t e n t i a l a p p l i c a t i o n to pest c o n t r o l . S e x - l i n k e d m e i o t i c d r i v e has been found in the b u t t e r f l y , Acraen encedon (Chanter and Owen, 1972), i n the mosquito , Aedes aegypt i (Hickey and C r a i g , 1966), and i n many species of D r o s o p h i l a (S tur tevant and Dobzhansky, 1936; S t a l k e r , 1960; N o v i t s k i , 1947). T h i s paper i s concerned w i t h s e x - l i n k e d m e i o t i c d r i v e i n D r o s o p h i l a which i s u s u a l l y r e f e r r e d to as the Sex-Rat io c o n d i t i o n . Species w i t h the Sex-Rat io c o n d i t i o n have two types of X chromosome, X and X r . Male c a r r i e r s of Xr (often r e f e r r e d to as Sex-Rat io or SR chromosome) t ransmi t only X-bear ing sperm and produce predominantly daughters . In the absence of c o u n t e r a c t i n g s e l e c t i o n and m e i o t i c d r i v e suppressor genes, Xr w i l l be t r a n s m i t t e d at twice the ra te of Standard X (ST chromosome) by males . Eventua l f i x a t i o n of Xr would cause the \ 74 e x t i n c t i o n of the p o p u l a t i o n . I n v e s t i g a t o r s of t h i s problem have t h e r e f o r e fo l lowed two d i r e c t i o n s : i ) to measure the r e l a t i v e f i t n e s s of the genotypes i n ques t ion and i i ) to search for m o d i f i e r genes which suppress segregat ion d i s t o r t i o n i n XrY males . In t h i s paper, a t h e o r e t i c a l model i s developed to i n t e g r a t e f i n d i n g s of the two l i n e s of exper imenta l work. Edwards (1961) put forward the t h e o r e t i c a l c o n d i t i o n s under which a set of f i t n e s s va lues w i l l l ead to a s t a b l e polymorphism for the Sex-Rat io t r a i t . Wal lace (1948) and C u r t s i n g e r and Feldman (1980) est imated f i t n e s s e s of the f i v e genotypes of D. pseudoobscura . For v a r i o u s reasons, the a d u l t male component of s e l e c t i o n ( v i r i l i t y s e l e c t i o n ) has a t t r a c t e d a great dea l of a t t e n t i o n ( P o l i c a n s k y , 1974, 1979; Beckenbach, 1978; Thompson and Feldman, 1975; C u r t s i n g e r and Feldman, 1980). Al though most of the r e s u l t s do not support the view of s trong v i r i l i t y s e l e c t i o n i n m a i n t a i n i n g the Sex-Rat io polymorphism i n D. pseudoobscura , i t i s p o s s i b l e that the measurements of v i r i l i t y s e l e c t i o n were incomplete (Beckenbach, 1981; PART I of t h i s t h e s i s ) . The search for suppressor m o d i f i e r s has been more succes s fu l , i n D. paramelanica and i n D. a f f i n i s than i n D. pseudoobscura . S t a l k e r (1961) d i scovered a type of suppressor Y-chromosome as w e l l as f a i r l y ex tens ive autosomal suppressor m o d i f i c a t i o n i n D. paramelanica . N o v i t s k i (1947) repor ted r e c e s s i v e autosomal m o d i f i e r s which reversed the segregat ion r a t i o d i s t o r t i o n i n D. a f f i n i s . V o e l k e r (1972), however, suggested exp lana t ions other than autosomal m o d i f i e r s 75 to e x p l a i n N o v i t s k i ' s r e s u l t s . Autosomal genes capable of d i s t o r t i n g the t r ansmi s s ion r a t i o of sex chromosomes have been found i n D. s imulans (Faulhaber , 1967). I t i s a l s o p o s s i b l e that genes i n t r o g r e s s e d from D. pseudoobscura may suppress the Sex-Rat io expres s ion i n D. p e r s i m i l i s ( PART I I I , t h i s t h e s i s ) . However, attempts to search for m o d i f i e r s i n D. pseudoobscura capable of suppress ing i t s own SR expres s ion have f a i l e d ( P o l i c a n s k y and Dempsey 1978; Beckenbach et a_l . , 1982). I t seems d e s i r a b l e to have an hypothes i s capable of account ing for both the presence and absence of m o d i f i e r s i n these spec ies other than the somewhat ad hoc e x p l a n a t i o n that m o d i f i e r s d i d i n some s p e c i e s , and d i d not i n o t h e r s , emerge i n the long h i s t o r y of e v o l u t i o n . Theor ies on the fa te of n e u t r a l m o d i f i e r s of m e i o t i c d r i v e have been developed for autosomal m e i o t i c d r i v e ( c f . Prout e_t a l . , 1973; Thompson and Feldman, 1976). T h e i r r e s u l t s u n f o r t u n a t e l y are not a p p l i c a b l e to m o d i f i e r s of the SR t r a i t for two reasons . F i r s t , i t i s most reasonable to assume.that any s e x - l i n k e d m o d i f i e r of the SR t r a i t can e x i s t on ly i n the hemizygous s t a t e i n males. There fore , whi l e l i n k a g e between an autosomal m e i o t i c d r i v e locus and a m o d i f i e r locus has the tendency to mainta in polymorphism at both l o c i , t h i s i s not so w i t h the SR system. The X - l i n k e d n e u t r a l suppressor m o d i f i e r s w i l l always be l o s t (Thompson and Feldman, 1975) and Y - l i n k e d . n e u t r a l m o d i f i e r s w i l l be f i x e d . Second, a p o p u l a t i o n w i t h s e x - l i n k e d m e i o t i c d r i v e w i l l escape s t a b i l i z i n g s e l e c t i o n which keeps the pr imary female/male r a t i o at 1:1 (Hamilton 1967). A 76 deviant female/male r a t i o adds a new dimension to the SR system. M a f f i and Jayakar (1981) developed a model for the X-Y " l o c u s " and m o d i f i e r s l i n k e d w i t h them. They assumed that a l l genotypes have equal f i t n e s s . The i r model has p o t e n t i a l a p p l i c a t i o n s to s e x - l i n k e d m e i o t i c d r i v e i n A . a e g y p t i . To dea l w i t h the fa te of SR m o d i f i e r s , a d i f f e r e n t model w i t h s e l e c t i o n opera t ing on a X - X r - Y d r i v e locus i s r e q u i r e d . T h i s study was there fo re c a r r i e d out to answer the f o l l o w i n g q u e s t i o n : Under what c o n d i t i o n s can autosomal m o d i f i e r genes which suppress m e i o t i c d r i v e i n XrY males increase? 77 THE MODEL General d e s c r i p t i o n Two opposing s e l e c t i v e forces operate on the u n l i n k e d (autosomal) m o d i f i e r s of the SR t r a i t . We r e f e r to m o d i f i e r a l l e l e s as m and the w i l d type a l l e l e s as M. The i n t u i t i v e reason that m would tend to increase i s t h i s : As long as the o v e r a l l f i t n e s s of XrY males i s greater than 0, the primary female/male r a t i o of the p o p u l a t i o n i s g rea ter than 1. Hence any gene which p r e f e r e n t i a l l y segregates i n t o the rare sex ( i n t h i s case , male) r e l a t i v e to i t s a l l e l e w i l l i n c r e a s e . T h i s i s e x a c t l y what the m o d i f i e r m would do. By suppress ing the segregat ion d i s t o r t i o n i n XrY males, the m o d i f i e r m w i l l be d i s t r i b u t e d more evenly between the two sexes than M which tends to be a s s o c i a t e d w i t h females. The gametic phase d i s e q u i l i b r i u m between a s e x - l i n k e d locus and an autosomal one, c rea ted by m e i o t i c d r i v e and m o d i f i c a t i o n of m e i o t i c d r i v e , i n turn would impose a new s e l e c t i o n regime on the m o d i f i e r locus which i n other respects i s n e u t r a l . The way s e l e c t i o n operates on the m o d i f i e r locus t h e r e f o r e depends on s e l e c t i o n at the Sex-Rat io l o c u s . I t i s the o b j e c t i v e of t h i s study to f i n d c o n d i t i o n s under which s e l e c t i o n at the Sex-Rat io locus w i l l (or w i l l not) o f f s e t the s e l e c t i v e advantage confe r red upon m by a deviant pr imary female/male r a t i o . 78 The model The f i t n e s s matr ices for the nine female genotypes and s i x male genotypes a r e : MM Mm mm MM Mm mm XX U i u 2 u 3 XY v , v 2 v 3 XX r Uft u 5 u 6 XrY v « v 5 v G XrXr u 7 u 8 u 9 . We assume m o d i f i e r s have no e f f e c t on the f i t n e s s of t h e i r bea re r s . A l s o , s ince we are on ly i n t e r e s t e d in the genera l dynamics of the system rather than the e q u i l i b r i u m frequency of each genotype, g e n e r a l i t y would not be l o s t by assuming u,=v,= 1 and by d e a l i n g w i t h genotypic f requencies a f t e r s e l e c t i o n i s completed i n each g e n e r a t i o n , i e u , = u 2 = u 3 = 1 v , = v 2 = v 3 = 1 u« = u 5 = u 6 = a v„ = v 5 = v 6 = c u 7 = u 8 = u g = b . Let p_ -( and g . be the f requencies of the i - t h female genotype and the i - t h male genotype r e s p e c t i v e l y a f t e r s e l e c t i o n i n each genera t ion i s completed; E p- + E q^ = 1. The f requencies are there fore genotypic f requenc ies of e f f e c t i v e mating a d u l t s . We de f ine k• as the d r i v e i n t e n s i t y parameter such that the p r o p o r t i o n of X-bear ing sperm from each male genotype i s 79 MM Mm mm XY 1/2 1/2 1/2 XrY (1 +k 0 ) /2 (1+k,)/2 (1+k 2 )/2 where -1 < k: < 1. When k ; 1, the d r i v e i s complete ; 0, segregat ion i s normal ; k . 1, the d r i v e i s reversed (male s e x - r a t i o ) . S i n c e , at l e a s t i n D. pseudoobscura , the d r i v e i s very near ly complete , i t i s assumed that k 0 =1. Males are o c c a s i o n a l l y recovered from F, of XrY males but are u s u a l l y s t e r i l e . They are apparent ly of XO genotype- a r e s u l t of n o n - d i s j u n c t i o n (S tur tvant and Dobzhansky, 1936; Haymer, 1979). The recurrence equat ions r e l a t i n g genotypic f requencies at genera t ion n+1 to those at generat ion n a r e : T p , ' = u 1 { l / 2 p , q 1 + l / 4 p , q 2 + l / 4 p 2 q ! + l / 8 p 2 q 2 + l / 8 p a q , + l / 4 p a q 2 + l / 8 p 5 q 1 + 1 / I 6 p 5 q 2 ] T p 2 ' = u 2 { l / 4 p 1 q 2 + l / 2 p , q 3 +1/4p 2 q, + l / 4 p 2 q 2 + l / 4 p 2 q 3 + l / 2 p 3 q , + l / 4 p 3 q 2 + l / 8 p 4 q 2 + l / 4 p „ q 3 + l / 8 p 5 q , + l / 8 p 5 q 2 + l / 8 p 5 q 3 + l / 4 p 6 q 1 + l / 8 p 6 q 2 } T p 3 ' = u 3 { l / 8 p 2 q 2 + l / 4 p 2 q 3 + l / 4 p 3 q 2 + l / 2 p 3 q 3 + 1 / I 6 p 5 q 2 + l / 8 p 5 q 3 + l / 8 p 6 q 2 + l / 4 p 6 q 3 } T p a ' = u,{p,qj , + l / 2 p 2 q a + l / 4 p „ q 1 + l / 8 p « q 2 + l / 2 p u q f l 80 +1/8p 5 qi +1/ I6p 5 q 2 + l / 4 p 5 q 4 + l / 2 p 7 q , + l / 4 p 7 q 2 +1/4p 8 q, + l / 8 p 8 q 2 + ( 1 + k , ) [ l / 4 p , q 5 + l / 8 p 2 q 5 + l / 8 p « q 5 +1/I6p 5 q 5 ] } T p 5 ' = u 5 { l / 2 p 2 q 4 +p 3 q 4 + l / 8 p « q 2 + l / 4 p „ q 3 + l / 8 p 5 q 1 + l / 8 p 5 q 2 + l / 8 p 5 q 3 + l / 4 p 5 q u + l / 4 p 6 q , + l / 8 p 6 q 2 + l / 2 p 6 q « + l / 4 p 7 q 2 + l / 2 p 7 q 3 + l / 4 p 8 q , + l / 4 p 8 q 2 + l / 4 p 8 q 3 + l / 2 p 9 q , + l / 4 p 9 q 2 + ( ) [ l / 4 p , q 5 + l / 4 p 2 q 5 + l / 4 p 3 q 5 + l / 8 p , q 5 +1/8p 5 q 5 + l / 8 p 6 q 5 ] + ( 1 + k 2 ) [ l / 2 p 1 q 6 + l / 4 p 2 q 6 + l / 4 p u q 6 + l / 8 p 5 q 6 ] } T p 6 * = u 6 { l / l 6 p 5 q 2 + l / 8 p 5 q 3 - + l / 8 p 6 q 2 + l / 4 p 6 q 3 + l / 8 p 8 q 2 + l / 4 p 8 q 3 + l / 4 p 9 q 2 + l / 2 p 9 q 3 +(1+k, ) [1 /8p 2 q 5 +1 / I6p 5 q 5 + l / 8 p 6 q 5 + l / 4 p 3 q 5 ] + ( 1 + k 2 ) [ l / 4 p 2 q 6 + l / 2 p 3 q 6 + l / 8 p 5 q 6 + l / 4 p 6 q 6 ] } T p 7 ' = u 7 { l / 2 p l t q „ + l / 4 p 5 q « +p 7 q a + l / 2 p 8 q a + ( 1 + k , ) [ l / 8 p „ q 5 + l / 1 6 p 5 q 5 + l / 4 p 7 q 5 +1/8p 8 q s ] } T p 8 ' = u B { l / 4 p 5 q « + l / 2 p 6 q , + l / 2 p 8 q „ + p 9 q « +(1+k, ) [1/8p,q 5 + l / 8 p 5 q 5 + l / 8 p 6 q 5 + l / 4 p 7 q 5 + l / 4 p B q 5 + l / 4 p 9 q 5 ] + ( 1 + k 2 ) [ l / 4 p , q 6 + l / 8 p 5 q 6 + l / 2 p 7 q 6 + l / 4 p 8 q 6 ] } T p 9 ' = u 9 { ( 1 + k , ) [ l / 1 6 p 5 q 5 + l / 8 p 6 q 5 + 1 / 8 p 8 q 5 + l / 4 p 9 q 5 ] + ( 1 + k 2 ) [ l / 8 p 5 q 6 + l / 4 p 6 q 6 + l / 4 p 8 q 6 + l / 2 p 9 q 6 ] } 81 T q , 1 = v 1 { l / 2 p 1 q , + l / 4 p , q 2 + l / 4 p 2 q 1 + l / 8 p 2 q 2 + l / 4 p , q , + l / 8 p „ q 2 + l / 8 p 5 q 1 + l / 1 6 p 5 q 2 + ( 1 - k , ) [ l / 4 p , q 5 + l / 8 p 2 q 5 + l / 8 p « q 5 +1/I6p 5 q 5 ] } T q 2 ' = v 2 { l / 4 p , q 2 + l / 2 p , q 3 + l / 4 p 2 q , + l / 4 p 2 q 2 + l / 4 p 2 q 3 + l / 2 p 3 q , + l / 4 p 3 q 2 + l / 8 p „ q 2 + l / 4 p « q 3 +1/8p 5 qi + l / 8 p 5 q 2 + l / 8 p 5 q 3 + l / 4 p 6 q 1 + l / 8 p 6 q 2 + ( 1 - k , ) [ l / 4 p , q 5 + l / 4 p 2 q 5 + l / 4 p 3 q 5 + l / 8 p „ q 5 + l / 8 p 5 q 5 + l / 8 p 6 q 5 ] + ( l - k 2 ) [ l / 2 p 1 q 6 + l / 4 p 2 q 6 + l / 4 p « q 6 + l / 8 p s q 6 ] } T q 3 ' = v 3 { l / 8 p 2 q 2 + l / 4 p 2 q 3 + l / 4 p 3 q 2 + l / 2 p 3 q 3 +1 / I6p 5 q 2 + l / 8 p 5 q 3 + l / 8 p 6 q 2 + l / 4 p 6 q 3 + ( l - k , ) [ l / 8 p 2 q 5 + l / 4 p 3 q 5 +1 / I6p 5 q 5 + l / 8 p s q 5 ] + ( 1 - k 2 ) [ 1 / 4 p 2 q 6 + l / 2 p 3 q 6 +1/8p 5 q 6 +1/4p 6 q 6 ] Tq« ' = v , { l / 4 p , q , + l / 8 p « q 2 + l / 8 p 5 q 1 +1 / I6p 5 q 2 + l / 2 p 7 q , + l / 4 p 7 q 2 + l / 4 p 8 q , + l / 8 p 8 q 2 + ( 1 - k , ) [ l / 8 p « q 5 + l / 1 6 p 5 q 5 + l / 4 p 7 q 5 + l / 8p 8 q 5 ] } T q 5 ' = v 5 { l / 8 p » q 2 +1/4p u q 3 +1/8p 5 q l + l / 8 p 5 q 2 + l / 8 p 5 q 3 + l / 4 p 6 q 1 + l / 8 p 6 q 2 + l / 4 p 7 q 2 + l / 2 p 7 q 3 + l / 4 p 8 q , + l / 4 p 8 q 2 + l / 4 p B q 3 + l / 2 p 9 q 1 + l / 4 p 9 q 2 ' . + ( 1 - k , ) [ 1 / 8 p , q 5 + l / 8 p 5 q 5 + l / 8 p 6 q 5 + l / 4 p 7 q 5 + l / 4 p 8 q 5 + l / 4 p 9 q 5 ] 82 +(l-k 2 ) [ l /4p»q s +l / 8 p 5 q 6 +l / 2p 7 q 6 +l /4p 8 q 6 ] } T q 6 ' = v 6 { l / l 6 p 5 q 2 +l / 8 p 5 q 3 +l / 8 p 6 q 2 +1/4p 6 q 3 +l / 8 p 8 q 2 +1/4p 8 q 3 + l / 4 p 9 q 2 + l / 2 p 9 q 3 +(l-k 1 ) [ l / l 6p 5 q 5 + l / 8 p 6 q 5 + l / 8 p 8 q 5 +l / 4 p 9 q 5 ] + ( 1 - k 2 ) [ l / 8 p 5 q 6 +l / 4 p 6 q 6 +l / 4p 8 q 6 +l /2p 9 q 6 ] } , (1) where T i s the sum of the r i g h t - h a n d s ides of (1) such that E P j ' + E q . / = 1. To determine the fate of m a f t e r i t i s i n i t i a l l y in t roduced i n t o the p o p u l a t i o n , we can p a r t i t i o n (1) i n t o two separate systems. The f i r s t set of equat ions i s i n terms of h igh frequency v a r i a b l e s p , , p „ , p 7 , q , , and q„ ( i e . , those w i t h the MM genotype) ; other v a r i a b l e s are dropped out from (1 ) . I t can be w r i t t e n as T P 1 * = l / 2q , (p ,+l / 2p 4 ) Tp« ' = a [ l / 2q 1 (p 7 +l / 2p , )+q , (p 1 +l / 2p , ) ] T p 7 ' = b [q , (p 7 +l / 2p f l ) ] T q / = l /2q , (p ,+l /2p«) T q „ ' = l / 2 c q , ( p 7 +l / 2 p » ) . (2) Thi s set of equat ions d e s c r i b e s the change of genotypic f requencies at the d r i v e locus i n the absence of m o d i f i e r s and has been s t u d i e d by a number of a u t h o r s . F o l l o w i n g Edwards (1961), the e q u i l i b r i u m genotypic f requencies are 83 T ' p , = 1/2 T ' q , = 1/2 T ' P f l = a(1/2r+cr) T ' q , = c r / 2 T ' p 7 = b c r 2 (3) where r = [a(1+2c)-2] / [a(1+2c)-4bc] and T' i s the sum of r i g h t hand s ide of (3 ) . The e q u i l i b r i u m i n (3) i s l o c a l l y s t a b l e i f and o n l y i f both denominator and numerator of r_ are p o s i t i v e , i e . , a(1+2c)-2>0 and a(1+2c)-4bc>0. (3 ' ) The second set of l i n e a r equat ions i s used to determine the low frequency v a r i a b l e s p 2 , P s , p 8 , q 2 , and q s ( i e . , those w i t h the Mm genotype) i n terms of themselves as w e l l as h igh frequency v a r i a b l e s . To d e r i v e i t , we drop from (1) those terms which c o n t a i n very- low-frequency v a r i a b l e s ( i e . , those w i t h the mm genotype) and those which c o n t a i n the product of two low frequency v a r i a b l e s . Throughout the t e x t , a s t a b l e Sex-Rat io polymorphism r e f e r s to the c o n d i t i o n s of (3 ' ) w i t h the premise that the frequency of m i s 0. Boundary s t a b i l i t y , i n t u r n , means the boundary on which the frequency of m equals to 0 i s s t a b l e , i e . , m w i l l never i n c r e a s e . I t i s assumed that when m i s i n i t i a l l y in t roduced i n t o the p o p u l a t i o n , the h igh frequency v a r i a b l e s are i n the s t a b l e e q u i l i b r i u m de f ined i n (3 ) . These v a r i a b l e s can then be t r e a t e d as constants in the second l i n e a r system which can be w r i t t e n as : T + p 2 ' = l /4q . ,p 2 + l / 8 q , p 5 + 1 / 8 X l q 2 T + p 5 ' = a { l / 2 q , p 2 +l / 8 ( q , + 2 q „ )p 5 + l / 4 q , p 8 +l / 8 x 2 q 2+l / 8 ( 1 + k , ) x , q 5 } 84 T + p 8 ' = b { l / 4 q « p 5 + i / 2 q « p 8 +1/8(1+k,)x 2 q 5 } T + q 2 ' = 1/4q,p 2 . +1/8q,p 5 +1/8x,q 2 + 1 / 8 ( 1-k , ) « , q 5 T + q 5 ' = c { l / 8 q , p 5 _ + l / 4 q , p 8 + l / 8 x 2 p 2 +1/8(1-k , )x 2 q 5 } (4) where X 1 = 2 p 1 + p „ , x 2 = p „ + 2 p 7 and T + i s T of (2) when a l l f requencies i n v o l v e d are those of e q u i l i b r i u m f requencies i n (3 ) . In summary the two l i n e a r systems we are d e a l i n g w i t h are (2) w i t h h igh frequency v a r i a b l e s i n s t a b l e e q u i l i b r i u m and (4 ) . We may w r i t e out (4) i n terms of vec tor s p = ( p 2 , p 5 , p 8 , q 2 , q 5 ) and P 1 = ( P 2 * f P s ' f P s ' » Q : ' . Qs') such that p ' = Ap. (4 ' ) The c o n d i t i o n for boundary s t a b i l i t y i s that the dominant e igenvalue (X., ) of the t r a n s i t i o n matr ix A of (4 ' ) i s ' s m a l l e r than 1. The c h a r a c t e r i s t i c po lynomia l of A, f ( X ) , w i t h the l e a d i n g term of X. having p o s i t i v e s ign i s i n the form of f ( X , k , ) = X [ ( 1 - k , ) F ( x ) + G U ) ] (5) where F(X.), G(X.) are independent of k , . I t i s immediately c l e a r that one of the c h a r a c t e r i s t i c roots i s 0 . The dominant e igenvalue of A i s r e a l and p o s i t i v e and has m u l t i p l i c i t y equal to 1 (see K a r l i n and T a y l o r , 1975, p545) . I t w i l l be shown i n the f o l l o w i n g s e c t i o n that none of the r e a l r o o t s , except p o s s i b l y the grea tes t one, X , , i s g rea ter 85 than or equal to 1. There fore , the s u f f i c i e n t and necessary c o n d i t i o n for X,<1 i s s imply f ( 1 , k 1 ) > 0 . To show that no root other than the greates t one can be greater than 1, we f i r s t note that G(1)=0 and the c h a r a c t e r i s t i c po lynomia l w i t h X,= 1 i s f ( 1 , k , ) = O - k j F O ) . (6) I t i s apparent that X.= 1 i s a c h a r a c t e r i s t i c root when k, = 1 . Since k,=1 i m p l i e s that M and m are e q u i v a l e n t i n f i t n e s s and i n m e i o t i c d r i v e when m i s r a r e , the magnitude of the v e c t o r , p = (P2/ P 5/ p 8 f q 2 f q s ) i of (4 ' ) should have no tendency to increase or decrease . I t suggests t h a t , i f k,=1, the dominant e igenvalue of A should be 1. For any other r e a l root X. ; at k 1 = 1 , X , < 1 i f i * l (7) s ince X., has m u l t i p l i c i t y equal to 1 . Equat ion (6) can be w r i t t e n out as A-f (1 , k ,) = TI [ l - x •, (k , ) ] i -1 (8) where X. , ' s are func t ions of k , . Comparing (6) and (8 ) , we know that none of the terms 1-X.; ( k , ) changes s i gn or becomes zero for a l l k,<1. I t f o l l o w s from ( 7 ) , for any r e a l e igenvalue of A other than the dominant one, X j ( k 1 ) < 1 for k,<1. As p r e v i o u s l y a s s e r t e d , the c o n d i t i o n for X . ,(k,)<1 i s f ( l , k , ) > 0 . When k,# 1, f ( 1 , k , ) has the same s ign as F ( 1 ) . 86 The c o n d i t i o n for boundary s t a b i l i t y i s the f o l l o w i n g : F(1)= - z 3 c x 2 + zMacq,£, +c(2+a+2b)q,x2 + 2 c ( a + 2 b ) q „ x 2 ] - z [4bc (2+a )q ,q a x 2 + 2c (a+2b)q,* x 2 +8abcq„ J k2 + 2acq,' t x , + a c q , £ , 2 +2c (b-1 )q , x , 5c 2 -acq,a 2 a ] - 4 c q , q u [ a x , i +2bx,x 2 +abx 2 1 ] >0 (9) where z=8T + , x 1=2p,+pi l and £ 2 = p 4 + 2 p 7 as shown i n ( 3 ) . Equat ion (6) a s s e r t s t h a t , as long as the d r i v e i n t e n s i t y parameter ( k , ) of the heterozygote M/m i s l e s s than that of the homozygote ( k 0 - 1 ) , the a c t u a l va lue of k, does not a f f e c t the s t a b i l i t y or i n s t a b i l i t y of the boundary of M. Indeed, the c o n d i t i o n of s t a b i l i t y s t a t ed i n (9) does not depend on the va lue of k , . D i r e c t numer ica l e v a l u a t i o n of e igenvalues of the matr ix A of (4 ' ) by a s tandard computer r o u t i n e g ives the same r e s u l t s as (9) . R e s u l t s The s t a b i l i t y c o n d i t i o n (9) i s a p p l i e d to p a r t i t i o n the f i t n e s s parameter space i n t o d i f f e r e n t r e g i o n s . F i g . 1 g ives the r e s u l t s for d i f f e r e n t va lues of c . The whole shaded area shows the f i t n e s s parameter sets which s a t i s f y the c o n d i t i o n s set f o r t h i n (3 ' ) for a s t a b l e Sex-Rat io polymorphism. The b lack area i n d i c a t e s the parameter sets which s a t i s f y c o n d i t i o n 87 (9 ) . Any p o p u l a t i o n w i t h a f i t n e s s set w i t h i n t h i s area i s immune from spread of suppressor m o d i f i e r s . The c r i t e r i o n of p a r t i t i o n i n g the dark and l i g h t gray areas i s t h a t , i n the absence of any suppressor m o d i f i e r , the e q u i l i b r i u m r a t i o of SR/ST i n males ( s ) i s l e s s than (dark gray) or greater than ( l i g h t gray) 0 . 2 . The gene r a t i o , s , i s determined by s = c r (see ( 3 ) ) . To s a t i s f y the s t a b i l i t y c o n d i t i o n ( 9 ) , the f i t n e s s of SR males r e l a t i v e to ST males ( c ) cannot be much greater than 0.3 and, as a r e s u l t , overdominance i n females i s r e q u i r e d to ma in ta in the Sex-Rat io polymorphism on the boundary. A glance at F i g . 1 may g ive the impress ion that the s t a b i l i t y c o n d i t i o n (9) i s s evere ly r e s t r i c t i v e , i f we only c o n t r a s t the b lack area w i t h the gray one. Indeed, C u r t s i n g e r and Feldman (1980) suggested that c o n d i t i o n s for the Sex-Rat io polymorphism (the whole shaded area in F i g . 1) i s no more s t r i n g e n t than those for polymorphisms of X - l i n k e d genes without segregat ion d i s t o r t i o n . However, the r e s t r i c t i v e n e s s of c o n d i t i o n (9) as a subset of c o n d i t i o n s (3 ' ) does not appear to be so severe i f a very r e a l i s t i c c o n s t r a i n t i s imposed on both (3 1 ) and (9 ) . The e q u i l i b r i u m gene r a t i o ( s ) i n males d e f i n e d by the b lack area never exceeds 0 . 1 . The va lues of s have not been found to be grea ter than 0.2 i n many l a b o r a t o r y experiments (qu i te o f t en s =0) and very r a r e l y exceed 0.2 i n nature (S tur tevant and Dobzhansky, 1936; Ba ldwin , 1979 ; Bryant et a l , 1981). Note that t h e o r e t i c a l gene f requencies d e a l t w i t h i n t h i s paper are 88 the f requencies i n each genera t ion a f t e r s e l e c t i o n i s completed. The va lue 0.2 as a c e i l i n g for observed s may very w e l l be an overest imate i f v i r i l i t y s e l e c t i o n i s taken i n t o account (wi th the assumption that SR males are no more v i r i l than ST males ) . We can now examine the parameter space of f i t n e s s e s which mainta in the Sex-Rat io polymorphism w i t h s <0.2. F a i r l y accurate es t imates of f i t n e s s va lues are r e q u i r e d to determine i f the f i t n e s s set f a l l s i n the b lack area or the dark gray one of F i g . 1. I f i t i s i n the l a t t e r , we c e r t a i n l y w i l l f e e l more encouraged to search for autosomal m o d i f i e r s of the Sex-Rat io t r a i t . On the other hand, d e f i n i t i v e knowledge about the presence or absence of autosomal m o d i f i e r s makes the two areas q u a l i t a t i v e l y d i s t i n c t r a ther than q u a n t i t a t i v e l y c o n t i n u o u s . 89 DISCUSSION Measuring f i t n e s s e s of genotypes, even i n the best c o n t r o l l e d environment w i t h the s imples t genet ic system, i s formidable and the r e s u l t s are u s u a l l y a s s o c i a t e d w i t h huge var i ances as e l u c i d a t e d i n a s e r i e s of papers by P r o u t ( l 9 6 5 , 1969, 1971a, b ) . There have been many attempts to est imate the r e l a t i v e f i t n e s s of a l l genotypes of the Sex-Rat io l o c u s . P a r t l y because of the compl ica ted nature of f i t n e s s e s t i m a t i o n and p a r t l y becausse of the p o t e n t i a l b i a s of any s p e c i f i c exper imenta l c o n d i t i o n ( e . g . , the d e n s i t y of a p o p u l a t i o n , the genet ic background of exper imenta l s tocks and o t h e r s ) , i t i s d e s i r a b l e to approach the problem of Sex-Rat io polymorphism from another p e r s p e c t i v e - the absence or presence of autosomal modi f i e r s . On the other hand, the search for suppressor m o d i f i e r s i s not without i t s d i f f i c u l t y . The technique c o n v e n t i o n a l l y employed i n searching for m o d i f i e r s does not lend i t s e l f to the search for r ece s s ive (or even very weakly dominant) autosomal m o d i f i e r s . I t i s s t i l l i n c o n c l u s i v e i f n a t u r a l popu la t ions of D. pseudoobscura are indeed devoid of Sex-Rat io m o d i f i e r s . C o n d i t i o n (9) hence makes the two exper imenta l approaches complementary to each o t h e r . I t i s s c i e n t i f i c a l l y unsound to a t t r i b u t e the absence of m o d i f i e r s i n D. pseudoobscura , i f they are indeed absent , to the f a i l u r e of m o d i f i e r s to emerge i n the long h i s t o r y of e v o l u t i o n and at the same time e x p l a i n the wide-spread of m o d i f i e r s i n D. paramelanica and other spec ies w i t h another 90 h y p o t h e s i s , probably s i m i l a r to the one proposed here . I n t u i t i o n seems to d i c t a t e that the Y-chromosome i s the most l i k e l y source of suppress ion more or l e s s on the grounds that Y i s the d i r e c t v i c t i m of segregat ion d i s t o r t i o n . The advantage of m over M i s i n t u i t i v e l y l e s s obv ious . We can now make a f i r s t order approximat ion of the advantage confe r red upon the two types of suppressor m o d i f i e r s . Let |_ be the frequency of Xr i n males . Y' (Y w i t h suppressor m o d i f i e r s ) would be t r a n s m i t t e d h a l f the time by i t s c a r r i e r s whi l e normal Y would account for only ( l - f ) / 2 of the gametes of i t s c a r r i e r s . The advantage of Y' over Y i s 1/(1-f ) . On the other hand, the advantage, d i s r e g a r d i n g gametic phase d i s e q u i l i b r i u m , of m over M when m i s i n i t i a l l y in t roduced i n t o the p o p u l a t i o n and k,=0 i s l / ( 1 - f * ) (see Table I ) . The r e s u l t i s i l l u s t r a t e d i n F i g . 2 . Note that the a c t u a l advantage of m over M may be greater or smal ler than l / ( 1 - f a ) depending on the r e l a t i v e f i t n e s s of female genotypes. Y - l i n k e d m o d i f i e r s u s u a l l y have a greater tendency to increase a l though autosomal ones may sometimes enjoy ju s t as much advantage. There i s indeed no reason to view autosomal m o d i f i e r s as of secondary importance to Y - l i n k e d genes, e s p e c i a l l y when i t i s known that Y chromosomes g e n e r a l l y have l i m i t e d amount of genet i c m a t e r i a l . In a d d i t i o n , the c o n d i t i o n for autosomal m o d i f i e r s to increase i s not s t r i n g e n t s ince the d r i v e parameter k, can be anything between -1 to 1 (but not 1) . The complete ly r e c e s s i v e case , k0=k,=1 and k 2 <1, i s somewhat d i f f e r e n t . The c o n d i t i o n s of boundary s t a b i l i t y in t h i s case-91 are not u n l i k e the c o n d i t i o n s for p r o t e c t e d polymorphisms w i t h abso lute dominance proposed by Prout (1968) . Let x be the frequency of m. When k, = 1, d ^ x / d x j x =0. What we need for boundary s t a b i l i t y i s d 1 ^x/dx | _Q <0. Thi s l a t t e r c o n d i t i o n i n v o l v e s k 2 and may r e q u i r e d i f f e r e n t f i t n e s s sets than p r e v i o u l y d i s c u s s e d . I t i s somewhat ea s i e r to dea l w i t h Y - l i n k e d m o d i f i e r s for two reasons . F i r s t , e x p e r i m e n t a l l y they are easy to detect by the c o n v e n t i o n a l t echnique . Second, Y chromosomes, l i k e h a p l o i d genes, have l i t t l e tendency to remain polymorphic when f i t n e s s va lues are cons t an t . T h e o r e t i c a l l y , one j u s t has to look at a s i n g l e Y chromosome from each l o c a l i t y unles s the p o p u l a t i o n i s i n a t r a n s i e n t s t a t e . Th i s may he lp e x p l a i n S t a l k e r ' s (1962) f i n d i n g that the two types of Y chromosomes have a geographica l boundary and r a r e l y remain polymorphic at one l o c a l i t y . The Mm locus can indeed remain polymorphic under some c o n d i t i o n s . Th i s s u b j e c t , together w i t h the complete ly r e c e s s i v e case , ( k , = l ) , w i l l be t r e a t e d in subsequent s t u d i e s . Accord ing to F i g . 1, o v e r a l l f i t n e s s of SR males has to be no grea ter than 0.3 i f the p o p u l a t i o n i s to be immune from spread of autosomal m o d i f i e r s . The reason for t h i s i s that the frequency of e f f e c t i v e mating males of SR genotype determines the pr imary female/male r a t i o of the next genera t ion and hence the advantage of m over M. However, without c o n s i d e r i n g bounday s t a b i l i t y , c can be much h igher than 0.5 and s t i l l 92 account for the observed Sex-Rat io f requencies i n the populat i o n s . The f i t n e s s of SR males can be broken down i n t o the j u v e n i l e component and the a d u l t component of s e l e c t i o n ( v i r i l i t y s e l e c t i o n ) . The j u v e n i l e component of f i t n e s s i s r e l a t i v e l y s t r a i g h t - f o r w a r d c o n c e p t u a l l y whereas the v i r i l i t y component of s e l e c t i o n has at l e a s t two subcomponents- one w i t h respect to v i r g i n females and the other w i t h respect to non-v i r g i n females (PART I , t h i s t h e s i s ) . V i r i l i t y s e l e c t i o n has been shown to be the dominant form of s e l e c t i o n i n many D r o s o p h i l a p o p u l a t i o n s (Bundgaard and C h r i s t i a n s e n , 1972; Anderson, et a l . , 1979) whi l e evidence suggests that i t p l ays only a minor r o l e i n m a i n t a i n i n g the Sex-R a t i o polymorphism in D. pseudoobscura (Cur t s inger and Feldman, 1980). I t may be t h a t , by f a i l i n g to d i f f e r e n t i a t e the mechanisms of v i r i l i t y s e l e c t i o n when females i n v o l v e d are e i t h e r v i r g i n s or n o n - v i r g i n s , we underest imated the i n t e n s i t y of o v e r a l l v i r i l i t y s e l e c t i o n . There i s some evidence to support t h i s hypothes i s when f i t n e s s i s measured at 14 °C (PART I , t h i s t h e s i s ) and at low p o p u l a t i o n d e n s i t y (Beckenbach, 1982). I f there i s indeed no autosomal m o d i f i e r i n the D. pseudoobscura p o p u l a t i o n s , the low value of c p r e d i c t e d by t h i s paper would be i n agreement w i t h the view of intense v i r i l i t y s e l e c t i o n . F i n a l l y , the p r e d i c t e d low frequency of SR i n males ( s <0.1) when s e l e c t i o n i s complete compared to the h igher f requencies at t imes Observed before v i r i l i t y s e l e c t i o n may a l s o suggest v i r i l i t y s e l e c t i o n i n a c t i o n and aga ins t SR males. 94 Table I Sex-dependent t r a n s m i s s i o n of autosomal a l l e l e s female male frequency of each sex (l + f ) / 2 ( l - f ) / 2 r e l a t i v e t r a n s m i s s i o n ra te of autosomal genes 1/(l+f) l / ( 1 - f ) a s s o c i a t e d w i t h each sex p r o p o r t i o n of m i n each sex a 1/2 1/2 p r o p o r t i o n of M i n each sex b l /2(1+f) 1/2(1~f) . average t r a n s m i s s i o n ra te of m l / 2 [ l / d + f ) + l / ( 1 - f ) ] = 1 / d - f 2 ) average t r a n s m i s s i o n rate of M l / 2 [ ( 1 + f ) / ( l + f ) + d - f ) / ( 1 - f ) ] = 1 a b assuming k, = 0 assuming frequency of MM >> frequency of Mm 95 F igure 11 — 1 . The fa te of autosomal m o d i f i e r s . Cross s e c t i o n s of the f i t n e s s parameter space are shown at d i f f e r e n t c v a l u e s . The value of c i s the f i t n e s s of XrY males r e l a t i v e to XY males . Areas of shade, from darkes t to l i g h t e s t , i n d i c a t e f i t n e s s set s which i ) s a t i s f y (3 ' ) and (9) , i i ) s a t i s f y ( 3 ' ) , but not (9 ) , w i t h s <0.2 or i i i ) s a t i s f y (3 ' ) w i t h s >0.2. (see the RESULTS s e c t i o n ) . FITNESS OF X r X r FEMALES (b) 96 Figure I I - 2 . The advantage of m o d i f i e r s over t h e i r a l l e l e s . A f i r s t order approximation of the advantage of Y chromosomes w i t h m o d i f i e r s (Y ' ) over w i l d t y p e Y and the advantage of autosomal m o d i f i e r s (m) over t h e i r non-m o d i f i e r a l l e l e s (M) as func t ions of f . 0.2 0.4 0.6 0.8 FREQ OF X rY GENOTYPE IN MALES (f) PART I I I EVIDENCE FOR EXTENSIVE GENETIC DIFFERENTIATION BETWEEN THE SEX-RATION AND THE STANDARD ARRANGEMENT OF DROSOPHILA PSEUDOOBSCURA AND D. PERSIMILIS AND IDENTIFICATION OF HYBRID STERILITY FACTORS 98 ABSTRACT T h i s study dea l s w i t h " s e x - r a t i o " genes t i g h t l y l i n k e d w i t h i n the Sex-Rat io i n v e r s i o n s . By t a k i n g advantage of the f ac t that the Sex-Rat io chromosome of D. p e r s i m i l i s (SR(B)) i s homosequential to the Standard chromosome of D. pseudoobscura (ST(A)) , two r e c i p r o c a l i n t r o g r e s s i o n experiments were c a r r i e d ou t . I n d i v i d u a l segments of SR(B) or ST(A) were i n t r o g r e s s e d i n t o the genome of D. pseudoobscura or D. p e r s i m i l i s r e s p e c t i v e l y . Males possess ing a h y b r i d SR(B)-ST(A) X chromosome and a genet ic background d e r i v e d from e i t h e r of the two species were t e s t ed for f e r t i l i t y and s e x - r a t i o e x p r e s s i o n . I t was found t h a t , i n terms of the m e i o t i c d r i v e genes, the Sex-Rat io chromosome d i f f e r s e x t e n s i v e l y from the Standard chromosome. Thi s f i n d i n g lends s t rong support to the hypothes i s of gene coadapta t ion which means that genes w i t h i n an i n v e r s i o n j o i n t l y produce a h i g h l y adapted h a p l o i d genome. A d a p t a t i o n , i n t h i s c o n t e x t , i s the advantage of being t r a n s m i t t e d p r e f e r e n t i a l l y . In l i g h t of t h i s f i n d i n g , e v o l u t i o n of the s e x - r a t i o system i n these two s i b l i n g species i s d i s c u s s e d . I n t r o g r e s s i o n experiments a l s o y i e l d e d i n f o r m a t i o n about h y b r i d s t e r i l i t y . Four types of s t e r i l i t y i n t e r a c t i o n s were i d e n t i f i e d , one of them i n v o l v e d at l e a s t three genet ic e lements . With r e c i p r o c a l i n t r o g r e s s i o n , s t e r i l i t y i n t e r a c t i o n s were found to be "a symmetr ic " . The asymmetry i s f u l l y expected from the v iewpoint of e v o l u t i o n of postmating r eproduc t ive i s o l a t i o n . 99 INTRODUCTION To e x p l a i n the ex tens ive polymorphisms of chromosomal i n v e r s i o n s i n D r o s o p h i l a pseudoobscura , Dobzhansky (1970 and re ferences c i t e d t h e r e i n ) invoked the concept of a complex of coadapted genes, or supergene, which behaves l i k e a s i n g l e w e l l -adapted Mendel ian gene. The concept of coadaptat ion inc ludes "both s e l e c t i o n of a l l e l e s at d i f f e r e n t l o c i w i t h i n gene arrangements to produce a h a p l o i d genome that i s p h y s i o l o g i c a l l y ba lanced , and s e l e c t i o n of a l l e l e s of the same l o c i between i n v e r s i o n s to produce h e t e r o s i s i n he terokaryotypes " (Prakash and Lewont in , 1968). I t i s , however, a formidable task to demonstrate the nature of genes w i t h i n an i n v e r s i o n ; i n p a r t i c u l a r , to i d e n t i f y the number and l o c a t i o n s of these genes and the mechanisms by which they together confer h igh f i t n e s s on t h e i r c a r r i e r s . The d i f f i c u l t y i s best i l l u s t r a t e d by the disagreement over the i n t e r p r e t a t i o n of non-random a s s o c i a t i o n s between arrangements of the t h i r d chromosome i n D. pseudoobscura and the e l e c t r o p h o r e t i c a l l e l e s they c a r r y . Prakash and Lewontin (1968) suggested that non-random a s s o c i a t i o n s are evidence that the s t r u c t u r a l genes coding for the p r o t e i n s they examined are par t of the coadapted gene complex. Nei and L i (1975,1980) s t re s sed that the observed p a t t e r n s c o u l d be e x p l a i n e d without re ference to any adapt ive d i f f e r e n c e between e l e c t r o p h o r e t i c a l l e l e s . To support the "supergene" h y p o t h e s i s , i t i s s u f f i c i e n t , as w e l l as necessary , to break the t i g h t l y l i n k e d gene complex and then score for f i t n e s s d i f f e r e n c e s . One approach i s to b r i n g 100 together the same chromosomal arrangement from d i f f e r e n t l o c a l i t i e s (Dobzhansky and P a v l o v s k y , 1958). I f each arrangement represents a d i f f e r e n t adapt ive gene complex, recombinat ion c o u l d d i s r u p t the i n t e g r i t y of these supergenes. To f u r t h e r e l u c i d a t e the nature of coadapted genes i n any i n v e r s i o n , i t i s , however, necessary to have chromosomal arrangements which are a s s o c i a t e d w i t h d i f f e r e n t f i t n e s s - r e l a t e d phenotypes. One such system i s the " S e x - R a t i o " i n v e r s i o n polymorphisms present i n each of the s i b l i n g s p e c i e s , D. pseudoobscura and D. p e r s i m i 1 i s . The r i g h t arm of the X chromosome ( XR ) of each spec ies has two types of arrangements, r e f e r r e d to as Standard (ST) and Sex-Rat io (SR) arrangement r e s p e c t i v e l y . Male c a r r i e r s of the SR chromosome t ransmi t only X-bear ing sperm and produce predominantly daughters . The SR chromosomes, t h e r e f o r e , enjoy a great advantage through m e i o t i c d r i v e . Prev ious s t u d i e s showed that the i n v e r s i o n s between the SR and ST arrangements i n D. pseudoobscura almost complete ly suppress recombinat ion on XR (S tur tevant and Dobzhansky, 1936). S ince genes which j o i n t l y produce the m e i o t i c d r i v e e f f e c t double t h e i r chance of being t r a n s m i t t e d by p a t e r n a l c a r r i e r s , i t i s conce ivab le that any i n v e r s i o n which complete ly or p a r t i a l l y b inds such genes together w i l l increase i n the p o p u l a t i o n . Th i s i s not u n l i k e the l i n k a g e m o d i f i c a t i o n i n the Segregat ion D i s t o r t e r system i n D. melanogaster (Thompson and Feldman, 1974). The genes w i t h i n such a new i n v e r s i o n would be coadapted i n the sense of m e i o t i c d r i v e , not of v i a b i l i t y or 101 f e r t i l i t y . To v e r i f y t h i s coadapta t ion h y p o t h e s i s , i t i s necessary to show t h a t , w i t h i n the SR i n v e r s i o n , there are two or more genes which are i n d i s p e n s i b l e f o r the complete expres s ion of the s e x - r a t i o t r a i t . Tests of t h i s hypothes i s are p o s s i b l e due mainly to s e v e r a l phenomena: F i r s t l y , the F , h y b r i d females of D. pseudoobscura and D. p e r s i m i l i s are both v i a b l e and f e r t i l e a l though the F, h y b r i d males are complete ly s t e r i l e ( L a n c e f i e l d , 1929; and many l a t e r s t u d i e s ) . Secondly, s tud ie s of recombinat ion f requencies between the SR chromosome of D. p e r s i m i l i s (SR(B)) and the ST chromosome of D. pseudoobscura (ST(A)) together w i t h s tud ie s of the banding p a t t e r n of these two chromosomes suggest that ST(A) and SR(B) are homosequential (S tur tevant and Dobzhansky, 1936; Dobzhansky, 1944; and t h i s s t u d y ) . There a re , t h e r e f o r e , three XR arrangements among the two s i b l i n g s p e c i e s . (For an e x p l a n a t i o n of n o t a t i o n , p lease r e f e r to the M a t e r i a l s and Methods s e c t i o n under " N o t a t i o n " ; a l s o , see F i g . 1 for graphic r e p r e s e n t a t i o n . ) T h i r d l y , b iochemica l and v i s i b l e markers are a v a i l a b l e on these chromosomes. The f ac t that ST(A) i s homosequential to SR(B) i s evidence aga ins t the hypothes i s that the i n v e r s i o n per se ( for example, t r a n s p o s i t i o n of promotors ) i s the cause of m e i o t i c d r i v e . Ra ther , i t supports the hypothes i s that the SR i n v e r s i o n s only serve to b ind the "sex-r a t i o " (herea f ter r e f e r r e d to as sr to d i s t i n g u i s h them from the chromosomal arrangements) genes t i g h t l y together by suppress ing any recombinat ion between the SR and ST arrangement. By i n t r o g r e s s i n g SR(B) i n t o D. pseudoobscura by repeated 1 02 backcros s ing o r , r e c i p r o c a l l y , by i n t r o g r e s s i n g ST(A) i n t o D. p e r s i m i l i s , the gene complex w i t h i n the i n v e r s i o n s can be broken up. The chromosomal segments of SR(B) can then be s t u d i e d e i t h e r i n d i v i d u a l l y or i n v a r i o u s combinations for the expre s s ion of the s e x - r a t i o t r a i t . In a d d i t i o n to i n f o r m a t i o n on the genet ic s of the s e x - r a t i o t r a i t , the i n t r o g r e s s i o n of segments of f o r e i g n X-chromosome w i l l a l s o y i e l d in format ion about genet ic i n t e r a c t i o n s u n d e r l y i n g s t e r i l i t y i n h y b r i d males . Most s tud ie s on the r e l a t i v e e f f e c t s of whole chromosomes of D r o s o p h i l a on v a r i o u s p r o p e r t i e s of i n t e r s p e c i f i c h y b r i d s suggest the overwhelming importance of the X chromosome ( e . g . Dobzhansky (1936) on s t e r i l i t y ; Pontecorvo (1943) on v i a b i l i t y ; and Tan (1946) and Zouros (1981) on e t h o l o g i c a l i s o l a t i o n ) . S tud ies on the d ivergence of genet ic m a t e r i a l w i t h i n the X chromosome r e s u l t i n g i n h y b r i d s t e r i l i t y w i l l undoubtedly throw some l i g h t on the e v o l u t i o n of r eproduc t ive i s o l a t i o n between the two s i b l i n g spec i e s . The bas ic i n t r o g r e s s i o n procedure i n v o l v e d r e p l a c i n g the l e f t arm of the X chromosome and a l l autosomes of the h y b r i d females w i t h those of one of the p a r e n t a l species by repeated b a c k c r o s s i n g . The i n v e r s i o n s served to mainta in the i n t e g r i t y of each gene complex dur ing backcros ses . The l a s t s tep was then to ob ta in males w i t h a " h y b r i d XR" and a pure genet ic background from e i t h e r one of the two s p e c i e s . These males were subsequently t e s t ed for f e r t i l i t y and for sr e x p r e s s i o n . The l a s t step of i n t r o g r e s s i o n i s e s s e n t i a l because no f e r t i l e 103 males can be o b t a i n e d before there i s recombinat ion between SR(B) and ST(A) as independently shown by Beckenbach and C u r t s i n g e r (Beckenbach et a l , 1982). I n t r o g r e s s i o n of e i t h e r of the two homosequential chromosome arms, SR(B) or ST(A) , i n t o the other spec ies was c a r r i e d out . R e c i p r o c a l i n t r o g r e s s i o n i s complementary r a ther than redundant for the f o l l o w i n g reasons . I t was hypothes ized (and conf i rmed i n t h i s study) that s e v e r a l h y b r i d s t e r i l i t y f a c t o r s are d i s t r i b u t e d on the X chromosome. I f the sr t r a i t i s c o n t r o l l e d by a l arge number of genes d i sper sed on SR(B) , a s u b s t a n t i a l p o r t i o n of i t has to be i n t r o g r e s s e d to D. pseudoobscura before sr genes can be mapped. T h i s w i l l tend to g ive r i s e to s t e r i l e r a ther than sr males. I t would be more f r u i t f u l in t h i s case to i n t r o g r e s s a smal l segment (or smal l segments) of ST(A) i n t o D. p e r s i m i l i s . On the other hand, i n t r o g r e s s i o n of SR(B) i n t o D. pseudoobscura would be q u i t e f e a s i b l e for mapping sr genes i f sr expres s ion i s c o n t r o l l e d by only one or two l o c i . Th i s procedure , i n complement w i t h r e c i p r o c a l i n t r o g r e s s i o n , a l s o prov ides in format ion on m o d i f i c a t i o n of sr expres s ion by genes of the s i b l i n g s p e c i e s . 1 04 MATERIALS AND METHODS N o t a t i o n : The most commonly used n o t a t i o n , SR for " S e x - R a t i o " chromosome and ST for Standard, presents a s e r i o u s d i f f i c u l t y when a t tempt ing to l o c a l i z e s e x - r a t i o genes w i t h i n the i n v e r s i o n s and when comparing D. pseudoobscura and D. p e r s i m i l i s . In t h i s paper, SR and ST r e f e r s p e c i f i c a l l y to the chromosomal arrangements c a r r y i n g s e x - r a t i o and standard genes r e s p e c t i v e l y , r egard le s s of the banding p a t t e r n s . The lower case terms, sr and s t , r e f e r to the phenotypes and the genes r e s p o n s i b l e for the phenotypes. We now have four arrangements (two of them homosequent ia l ) : SR(A) for the SR arrangement i n D. pseudoobscura ST(A) = SR(B) for the ST arrangement i n D. pseudoobscura and SR arrangement i n D. p e r s i m i l i s r e s p e c t i v e l y , and ST(B) for the ST arrangement i n D. p e r s i m i l i s . W i t h i n each spec ies ( that i s , before gene i n t r o g r e s s i o n ) , SR and ST are a s s o c i a t e d w i t h sr and st phenotypes, r e s p e c t i v e l y . The l e t t e r A i s for D. pseudoobscura and the l e t t e r B for D. p e r s i m i 1 i s . Both f o l l o w the pre-1944 " r a c e " de s i gna t ions for these two s p e c i e s . S t r a i n s : Both ST(B) and SR(B) were r e c e n t l y c o l l e c t e d and i s o l a t e d from Vancouver I s l a n d popu la t ions by A . T. Beckenbach. The SR(A) s t r a i n was c o l l e c t e d i n San Diego, CA. and was made 1 05 a v a i l a b l e by D. Haymer. The ST(A) s t r a i n s were from the N a t i o n a l D r o s o p h i l a Stock Center at the U n i v e r s i t y of Texas, A u s t i n . These two s t r a i n s c a r r y y_ sn v co se sh and se 11 sp t t , r e s p e c t i v e l y . ( F i g . 1; for d e s c r i p t i o n s , see Anderson and Norman, 1977). The mutant 11^ was d i s r e g a r d e d . I n v e r s i o n s between SR(A) and ST(A) , ST(A) and SR(B),and SR(B) and ST(B) mentioned p r e v i o u s l y were i d e n t i f i e d c y t o l o g i c a l l y i n the s t r a i n s used i n t h i s s tudy . Of most i n t e r e s t i s the i d e n t i c a l banding p a t t e r n of ST(A) and SR(B) . Th i s was i n f e r r e d from data on recombinat ion f requencies and from c y t o l o g i c a l comparisons of banding p a t t e r n s . In t h i s s tudy , i t was found that ST(A) and SR(B) chromatids i n the s a l i v a r y g land c e l l s of h y b r i d females are apparent ly capable of complete synaps i s , a l though the a f f i n i t y between ST(A) and SR(B) seems to be weaker than that between c o n s p e c i f i c chromat ids . F i g . 1 shows the arrangements of these chromosomal arms r e l a t i v e to one another . In D. pseudoobscura , recombinat ion between the co-sh reg ion of ST(A) and the corresponding reg ion of SR(A) i s so rare that we cons ider sr genes i n D. pseudoobscura to be complete ly l i n k e d i n t h i s reg ion (S tur tevant and Dobzhansky, 1936). Every XR used i n t h i s study c a r r i e s a d i s t i n c t Es t -5 a l l e l e and, hence, i s e l e c t r o p h o r e t i c a l l y d i s t i n g u i s h a b l e from every other one. I n t r o g r e s s i o n by repeated b a c k c r o s s i n g : Experiment I : In t h i s experiment , SR(B) was i n t r o g r e s s e d i n t o 1 06 the genome of D. pseudoobscura. F i g . 2 i l l u s t r a t e s the procedure . Note that the i n t e g r i t y of SR(B) was mainta ined i n Stage I s ince recombinat ion between SR(A) and SR(B) was complete ly suppressed. Only i n Stage I I was recombinat ion on XR a l l o w e d . Recombinant males w i t h par t of XR from SR(B) and the re s t of the genome from standard males of D. pseudoobscura were then obta ined and t e s t e d for f e r t i l i t y and sr e x p r e s s i o n . Examination of the phenotypes of these recombinant males provided i n f o r m a t i o n on the l o c a t i o n s of i n t r o g r e s s e d SR(B) segments. Experiment I I : Th i s experiment i n v o l v e d i n t r o g r e s s i o n of ST(A) of D. pseudoobscura i n t o the genome of D. p e r s i m i l i s . F i g . 3 i l l u s t r a t e s the i n t r o g r e s s i o n p r o t o c o l . Note t h a t , u n l i k e SR(A) / SR(B) i n Experiment I , recombinat ion between ST(A) /ST(B) i s not complete ly suppressed. There was a r a ther sma l l percentage of c r o s s i n g over between se and sh but double c r o s s i n g over i s q u i t e u n l i k e l y . Among B j - , and B 3 - , ( F i g . 3) females , only those whose sons possess a l l three markers on ST(A) were used i n s u r i n g that the whole ST(A) arm was i n t r o g r e s s e d . Stage II of t h i s experiment a l l o w i n g recombinat ion between SR(B) and ST(A) i s c r u c i a l . As Beckenbach and C u r t s i n g e r (1982) independently showed, a l l males from Stage I c a r r y i n g ST(A) were s t e r i l e a l though some of them were expected to have the re s t of the genome complete ly from D. p e r s i m i l i s . 1 07 The recombinant males thus obta ined c a r r i e d segments of ST(A) , i d e n t i f i a b l e by v i s i b l e genet ic markers , i n a genome d e r i v e d mostly from SR(B) males . These males were t e s t e d for f e r t i l i t y and for t h e i r sr e x p r e s s i o n . V i r g i n females were used to t e s t for f e r t i l i t y and for sr expres s ion of recombinant males . Most of females used i n the experiments were F / s from ST/ST x SR/Y crosses (no male emerged from t h i s c ros s ) and were aged for 4-6 days before mat ing . The v i a l s c o n t a i n i n g v i r g i n females were subsequently examined for any unexpected i n s e m i n a t i o n . None was de tec ted i n s u r i n g that only v i r g i n females were used. For each recombinant male t e s t e d , 3-4 v i r g i n females were used to minimize f a i l u r e of in semina t ion caused by b e h a v i o r a l c o m p l i c a t i o n s . To minimize v i a b i l i t y d i f f e r e n c e s in the F, caused by crowding , f e r t i l e parents were d i s ca rded or t r a n s f e r r e d when a s u f f i c i e n t number of eggs were l a i d . In most f e r t i l e mat ings , more than 30 F, f l i e s were recovered from each male parent . Among these matings , on ly a few male pa ren t s , a l l w i t h the same genotype, c o u l d not be unambiguously c l a s s f i e d as e i t h e r sr or s t . These males , producing 10-20% of sons i n t h e i r progeny, were c l a s s i f i e d as " p a r t i a l s r " . Among those males producing fewer than 30 o f f s p r i n g , only one c o u l d not be c l a s s i f i e d as e i t h e r sr or s t . I t was c l a s s i f i e d as " p a r t i a l s r " . In order to double check the genotypes of recombinant males , some of them, obta ined i n Experiment I where ST(A) c a r r i e d the mutant marker y_ sn v co se sh , were mated to v i r g i n 108 females homozygous for a l l r e c e s s i v e mutants i n q u e s t i o n . Examinations of F , females, and sometimes of F 2 males , obta ined from these matings suggest that the penetrance of the marker genes, y_ sn v co se and sh , are n e a r l y complete i n males . 109 RESULTS Experiment I_ The r e s u l t s are presented i n Tables 1 and 2. The w i l d type genes were i n t r o g r e s s e d from the SR(B) chromosome of D. p e r s i m i l i s . The re s t of the genome i s that of D. pseudoobscura. Mapping s e x - r a t i o genes: I t i s apparent from Table 1 and Table 2 that any chromosomal segment from SR(B) c o n t a i n i n g only one of the three marker genes i s not capable of expres s ing the sr t r a i t by i t s e l f i n the genet ic m i l i e u of D. pseudoobscura. N e i t h e r c o u l d any combinat ion of these segments do so. There c o u l d be two p o s s i b i l i t i e s : F i r s t , some genes ( e i t h e r autosomal or Y - l i n k e d ) from D. pseudoobscura are capable of suppress ing sr expres s ion of SR(B) . Second, an e s s e n t i a l element for sr expre s s ion i s very c l o s e l y l i n k e d to h y b r i d s t e r i l i t y f a c t o r s ; t h e r e f o r e , no f e r t i l e males in Tables 1 and 2 c a r r i e d t h i s e s s e n t i a l element and none of them expressed the sr c h a r a c t e r . Th i s e x p l a n a t i o n i s very l i k e l y i f t h i s sr gene i s l o c a t e d w i t h i n a segment of XR roughly 20 map u n i t s (m.u. ) long between +(se) and +(sh) (see the H y b r i d S t e r i l i t y S e c t i o n ) . The 44 s t e r i l e males of the l a s t two rows of Table 1 might have conta ined t h i s segment. F a i l u r e of a p a r t i c u l a r chromosomal segment to express the sr t r a i t does not mean that i t i s unnecessary for . sr e x p r e s s i o n : i t s imply means that i t i s i n s u f f i c i e n t by i t s e l f . 1 10 To determine which of the two exp lana t ions i s more l i k e l y , r e c i p r o c a l i n t r o g r e s s i o n , d e t a i l e d i n Experiment I I , was c a r r i e d o u t . In that experiment , both the genet ic background and the sr genes were from D. p e r s i m i l i s , t h e r e f o r e , no suppressor m o d i f i c a t i o n of the sr t r a i t has to be c o n s i d e r e d . A l s o , males c a r r y i n g the h y p o t h e t i c a l " e s s e n t i a l sr gene" c l o s e l y l i n k e d to h y b r i d s t e r i l i t y f a c t o r s would be f e r t i l e because h y b r i d s t e r i l i t y f a c t o r s , by d e f i n i t i o n , are not s t e r i l i t y f a c t o r s i n the genet ic m i l i e u of t h e i r own spec ies ( D. p e r s i m i l i s ) . R e s u l t s from Experiment II favor the second a l t e r n a t i v e . H y b r i d s t e r i l i t y f a c t o r s : The male s t e r i l i t y observed i n t h i s study i s not b e l i e v e d to be the consequence of any b e h a v i o r a l a b e r r a t i o n . Some males have been observed to complete c o u r t s h i p and c o p u l a t i o n , yet no v i a b l e F, was observed. I t i s presumably caused by spermatogenic f a i l u r e . From the second row of Table 1, i t i s reasonable to suggest that the reg ion of SR(B) between the +(co) and the +(se) locus does not i n t e r a c t w i t h genes from D. pseudoobscura i n the background to produce s t e r i l e males . Data of Table 1 were t h e r e f o r e arranged without regard to the genotypes at the cjo l o c u s . To g e n e t i c a l l y map the h y b r i d s t e r i l i t y f a c t o r s , we f i r s t note that only 38.1% and 29.8% of males w i t h i n t r o g r e s s e d +(sh) and +(se) a l l e l e , r e s p e c t i v e l y , are f e r t i l e . The genes se and sh are 66.2 m.u. a p a r t . I t can there fo re be i n f e r r e d that 111 there i s a h y b r i d s t e r i l i t y f a c t o r approximate ly 66.2 x .381 = 25.2 m.u. to the r i g h t of +(se) and another about 19.7 m.u. to the l e f t of +(sh). We cannot t e l l from Table 1 i f there are more h y b r i d s t e r i l i t y genes between the two mapped f a c t o r s which are 21 m.u. a p a r t . (The d i s t a n c e s w i l l not be n o t i c e a b l y changed i f m u l t i p l e c r o s s i n g - o v e r i s cons idered us ing Haldane ' s (1919) mapping f u n c t i o n ) . Based on the mapping of the two s t e r i l i t y f a c t o r s , we expect about 5% of males c a r r y i n g se-sh to be s t e r i l e due to double c r o s s i n g o v e r . The observa t ions i n the top two rows of Table 1 do not c o n t r a d i c t t h i s p r o j e c t i o n . S ince the +(co)-+(se) reg ion of SR(B) does not c o n t a i n h y b r i d s t e r i l i t y f a c t o r s , the r e s u l t s presented i n Table 2 us ing se sp t t marked males are i n f o r m a t i v e . The fac t that some of the se++ males are f e r t i l e suggest that the +(sp)-+(tt) reg ion may not c o n t a i n these f a c t o r s . Based on the p r o p o r t i o n of f e r t i l e males among e i t h e r se + + or + s p t t males , two h y b r i d s t e r i l i t y f a c t o r s can be mapped w i t h approximate ly 23 m.u. between them. This d i s t a n c e i s i n agreement w i t h the est imate based on data of Table 1 . The exact l o c a t i o n s of these s t e r i l i t y f a c t o r s mapped w i t h data of Table 1 and 2 are somewhat d i f f e r e n t , a l though not s i g n i f i c a n t l y so . By and l a r g e , i t i s safe to i n f e r the ex i s t ence of two h y b r i d s t e r i l i t y f a c t o r s i n the +(se)-+(sp) reg ion of SR(B) . 1 1 2 Experiment 11 The r e s u l t s of t h i s experiment were presented i n Tables 3 and 4. The mutant genes were i n t r o g r e s s e d from ST(A) w h i l e the re s t of the genome was that of an sr male from D. p e r s i m i l i s . Mapping s e x - r a t i o genes: I t i s important to note that the ABSENCE of the sr t r a i t suggests the presence of an sr gene because, without the i n t r o g r e s s e d gene from D. pseudoobscura, the male i s an sr male. In both Tables 3 and 4, a m a j o r i t y of males r e t a i n i n g the w i l d type a l l e l e from SR(B) at every marker locus (des ignated +++) are sr males . Th i s i n d i c a t e s that the i n t r o g r e s s i o n procedure does not i n t e r f e r e w i t h the expres s ion of sr genes. Those +++ males which have l o s t sr expres s ion can be r e a d i l y . e x p l a i n e d by hidden recombinat ion . The st +++ males i n Table 3 must be the r e s u l t of double c r o s s i n g over s ince co-se-sh covers n e a r l y the whole SR l i n k a g e complex. The p r o p o r t i o n of double c r o s s i n g over i n the se-sh reg ion among those having no c r o s s i n g over or having double c r o s s i n g over i n that reg ion i s 26/143 = 0 .182. (From Table 4, 19 males are of the genotype + sp_ + and 7 are se + tt_ , among 143 males w i t h the genotypes +(se)~ +(tt ) or se ^ t t .) We observed i n Table 3 that 12 out of 71 (ca . 17%) +++ males l o s t the sr e x p r e s s i o n . S i n c e , as we w i l l see l a t e r , every chromosomal segment c o n t a i n i n g any mutant gene locus used i n t h i s study i s i n d i s p e n s i b l e for sr e x p r e s s i o n , the agreement between t h e ' r a t e of double c r o s s i n g over and l o s s of sr expres s ion i s good. S i m i l a r l y , those st 1 1 3 +++ males i n Table 4 can be exp la ined by s i n g l e c r o s s i n g over between co and se. (Data of Table 4 were obta ined us ing an ST(A) s t r a i n w i t h markers only to the r i g h t of s e ) . The most s t r i k i n g observa t ion in Tables 3 and 4 i s that replacement of any segment of SR(B) , except the ones very c l o s e to the t i p of the chromosome ( i n the s h - t t r e g i o n ) , always r e s u l t s i n the l o s s of the sr t r a i t . T h i s suggests that there are sr genes very c l o s e l y l i n k e d to +(co), +(se), +(sp) and +(sh) which are about 30 to 40 m.u. away from t h e i r ne ighbor ing markers . Based on the number of males found to have l o s t the sr e x p r e s s i o n , the upper l i m i t of the d i s t a n c e between each sr f a c t o r and the nearest marker (except +(sh) ) i s es t imated to be roughly 2 m.u. (Since mapping of these sr genes i n v o l v e s double c r o s s i n g over , the a c t u a l d i s t a n c e s c o u l d c o n c e i v a b l y be l a r g e r i f i n t e r f e r e n c e among c r o s s i n g over i s severe . N e v e r t h e l e s s , the c o n c l u s i o n that there are three sr genes, each c l o s e l y l i n k e d w i t h one of the markers c o , se or sp_, should s t i l l be v a l i d because these markers are 30 to 40 m.u. apart from t h e i r ne ighbor ing markers . ) E i g h t out of 83 ++sh males (Table 3) t e s t ed r e t a i n e d the sr t r a i t and three of them showed complete m e i o t i c d r i v e suggest ing the presence of two minor sr genes l o c a t e d 2.4 m.u. (3/83 x 66.2m.u. ) and 6.4 m.u. (8/83 x 66.2 m.u. ) to the l e f t of +(sh). The l o s s of both genes r e s u l t s i n the complete l o s s of m e i o t i c d r i v e whi l e the presence of the l a t t e r alone causes p a r t i a l sr e x p r e s s i o n . The observa t ion that 5 sr genes are t i g h t l y l i n k e d w i t h i n 114 the SR i n v e r s i o n prov ides d i r e c t evidence for the gene coadapta t ion h y p o t h e s i s . These sr genes are coadapted because, when ALL of them are c a r r i e d by a male, t h e i r chance of being t r a n s m i t t e d i s doubled . In the absence of ANY of these genes, the advantage to the res t of them d i s appear s . The way these genes are d i sper sed on SR(B) i s s u f f i c i e n t to e x p l a i n why no sr male was recovered i n Experiment I . There has been some i n t e r e s t i n suppressor m o d i f i e r s of the sr t r a i t (see Part I I of t h i s t h e s i s ) . The i n t r o g r e s s i o n experiments done here , u n f o r t u n a t e l y , do not have the r e s o l v i n g power to show i f any gene from D. pseudoobscura i s capable of suppress ing the expres s ion of SR(B) . Al though there i s a tendency for the p r o p o r t i o n of sr males w i t h genotype ++sh to be higher i n B 3 - 2 than i n B 2 - 2 , i t i s premature to draw any c o n c l u s i o n . H y b r i d S t e r i l i t y F a c t o r s : In Table 4, the p r o p o r t i o n s of f e r t i l e males from B 3 - 2 are always greater than those from B 2 - 2 . S ince the d i f f e r e n c e i s i n the " i m p u r i t y " of the genet ic background (on average, 1/8 of the background of B 2 - 2 males and 1/16 of B 3 - 2 males remain i n the h y b r i d s t a t e ) , the observa t ion suggests some form of s t e r i l i t y i n t e r a c t i o n between the remnant genet ic m a t e r i a l from D. pseudoobscura and the genes on SR(B) . The a n a l y s i s w i l l be based on data from Table 3 because co-se-sh covers most of XR. Two types of s t e r i l i t y i n t e r a c t i o n can be i d e n t i f i e d : 1 15 Type I : The remnant genet ic m a t e r i a l from D. pseudoobscura i n t e r a c t s w i t h genes on SR(B) , as d e s c r i b e d . These remnant genes from D. pseudoobscura are e i t h e r complete ly or p a r t i a l l y dominant over t h e i r a l l e l e s from D. p e r s i m i l i s . Type I I : The genet ic background composed mainly of genes from D. p e r s i m i l i s i n t e r a c t s w i t h the i n t r o g r e s s e d genes from ST(A) . I t i s c l e a r from Table 3 that the f i r s t two genotypes, +++ and ++sh, show l i t t l e f e r t i l i t y d i f f e r e n c e . The data were there fore pooled together under genotype ++-. Thi s obse rva t ion that ++sh males were normal i n f e r t i l i t y suggests that male s t e r i l i t y c o u l d not be of type II i n v o l v i n g the se-sh r e g i o n . N e i t h e r c o u l d hidden recombinat ion i n the +(co)-+(se) reg ion be r e s p o n s i b l e for the observed s t e r i l i t y s i n c e , even without i n t e r f e r e n c e , double c r o s s i n g over can only account for 3% of the s t e r i l e males . S t e r i l i t y i n t e r a c t i o n s of Type I have a l ready been suggested to e x p l a i n the f e r t i l i t y d i f f e r e n c e s between B 2 - 2 and B 3 - 2 males of Table 4. The d i f f e r e n c e between B 2 - 2 and B 3 - 2 of Table 3 i n the p r o p o r t i o n s of f e r t i l e males of genotype ++- i s h i g h l y s i g n i f i c a n t (P<.014) and i s good evidence for Type I s t e r i l i t y . I t i s a l so p o s s i b l e to c a l c u l a t e the number of remnant genes from D. pseudoobscura which are i n v o l v e d in Type I s t e r i l i t y i n t e r a c t i o n s . Suppose there are n independently segregat ing l o c i from D. pseudoobscura each of which i s capable of t o t a l l y d i s r u p t i n g f e r t i l i t y , then the p r o p o r t i o n of f e r t i l e 1 1 6 males i s expected to be ( 1 - 1 / 8 ) * among B 2 - 2 males and (1-1/16)"" among B 3 - 2 males. For n=2, the expected p r o p o r t i o n s are .766 for B 2 - 2 and .879 for B 3 - 2 . We observed 76.3% and 72.2% for the former and 86.7% and 88.6% for the l a t t e r . The agreement i s very good. We may, t h e r e f o r e , conclude that a s i n g l e gene from any of two s p e c i f i c l o c i i n the genome (not i n c l u d i n g XR and Y) of D. pseudoobscura i n t e r a c t s w i t h the +(co)-+(se) reg ion of SR(B) and d i s r u p t s normal spermatogenesis . The word " l o c i " i s used, i n t h i s c o n t e x t , in terchangeably w i t h "chromosomal segments". To e x p l a i n the res t of Table 3 ( i e . , the lower h a l f ) , we note that i ) p r o p o r t i o n s of f e r t i l e males among ++- males are much higher than among the remaining genotypes, i i ) the a c t u a l percentage of f e r t i l e males was s t r o n g l y a f f e c t e d by the genet i c compos i t ion of XR (compare the l a s t s i x genotypes of Table 3 ) , and u n l i k e p r e v i o u s cases , i i i ) the p u r i t y of the genet ic background does not have any e f f e c t on f e r t i l i t y (compare d i f f e r e n t columns i n the lower h a l f of Tab le^3 ) . The data suggest that Type I I i n t e r a c t i o n i s r e s p o n s i b l e for the h y b r i d s t e r i l i t y observed in the lower h a l f of Table 3. As p r e v i o u s l y , data were arranged without regard to sh locus genotypes, s ince that reg ion apparent ly i s not i n v o l v e d i n Type II i n t e r a c t i o n s . I t i s now p o s s i b l e to map the s t e r i l i t y f a c t o r to the co-se r e g i o n . Because 53.4% of + se ^ (~ i s t o r e i t h e r +(sh) or sh) males are f e r t i l e , we i n f e r the s t e r i l i t y f a c t o r to be roughly 16.0 m.u. (.534 x 30 m.u. ) to the l e f t of se . S i m i l a r l y , another f a c t o r i s 10.0 m.u. (.333 x 30 m.u. ) 1 17 to the r i g h t of co . The two s t e r i l i t y f a c t o r s , separated by only 4 m.u. , are s t a t i s t i c a l l y i n d i s t i n g u i s h a b l e (P>.05). I t i s very l i k e l y that the two s t e r i l i t y f a c t o r s are indeed one. Among co se - males, one percent was found to be f e r t i l e . Thi s i s roughly the expected ra te of double c r o s s i n g over , one on each s ide of the s t e r i l i t y f a c t o r j u s t mapped. To conc lude , there i s a s t e r i l i t y i n t e r a c t i o n between a s i n g l e element from the co-se reg ion of ST(A) and the genome (not i n c l u d i n g XR) of D. p e r s i m i 1 i s . Genes that f r e e l y recombine w i t h the sr t r a i t : Recombination i n the y- sn-v reg ion i s not suppressed by the SR i n v e r s i o n (S tur tevant and Dobzhansky, 1936). Because the genes, y_ sn v , are on the X chromosome of D. melanogaster which i s homologous to XL of D. pseudoobscura and D. p e r s i m i l i s , i t i s l i k e l y that these l o c i are on XL of these two s p e c i e s . Some of the recombinant males obta ined from Experiment II possessed genes i n t r o g r e s s e d from the y- sn-v reg ion of ST(A) w i t h the re s t of the genome ( i n c l u d i n g XR) d e r i v e d from D. p e r s i m i l i s . Those males c a r r y i n g only the v gene from ST(A) were i n v a r i a b l y f e r t i l e and were as v i r i l e as normal 'D . p e r s i m i l i s males . On the other hand, among 12 h y b r i d males w i t h a l l three mutant genes, y_ sn v , i n t r o g r e s s e d from ST(A) , none was found to be f e r t i l e . These observa t ions he lp us to map another h y b r i d s t e r i l i t y f a c t o r to the y- sn reg ion of ST(A) , presumably on X L . S t e r i l i t y i n t e r a c t i o n s reported i n t h i s paper are summarized and d i scus sed i n the f o l l o w i n g s e c t i o n . 1 18 DISCUSSION On the sr t r a i t The textbook case of i n d u s t r i a l melanism i n the peppered moth, B i s t o n b e t u l a r i a , has f a s c i n a t e d b i o l o g i s t s not s imply because p igmentat ion i s a very i n t e r e s t i n g phenomenon ( i t indeed i s , see N i jhout ,1981 ) but because the change i n c o l o r a t i o n enables us to have a peek at the grandeur of e v o l u t i o n at work. In t h i s sense, the s tud ie s of the sr t r a i t should be more than a s imple i n q u i r y about the p e c u l i a r u n i s e x u a l progeny of some male D r o s o p h i l a . By s tudy ing the genet ic ba s i s of t h i s t r a i t i n c l o s e l y r e l a t e d spec ie s , we have a very good o p p o r t u n i t y to l e a r n about the e v o l u t i o n of a compl ica ted genet ic system. In p a r t i c u l a r , we have obta ined some i n f o r m a t i o n on the l inkage a s s o c i a t i o n of genes, the fa te of suppressor m o d i f i e r s and the way n a t u r a l s e l e c t i o n operates to m a i n t a i n the s e x - r a t i o polymorphism. S ince there i s always a one-to-one correspondence between the arrangement of the r i g h t arm of the X chromosome and the phenotype i t e x h i b i t s i n both spec ies s t u d i e d , the f i r s t q u e s t i o n concerning the e v o l u t i o n of the sr t r a i t i s n a t u r a l l y about t h i s correspondence. ( I t has been emphasized p r e v i o u s l y that i n v e r s i o n s per se are not r e s p o n s i b l e for sr e x p r e s s i o n . ) The most p l a u s i b l e e x p l a n a t i o n i s that i n v e r s i o n s reduce or complete ly suppress recombinat ion between " s e x - r a t i o " genes w i t h i n the i n v e r s i o n s . The idea i s i l l u s t r a t e d i n F i g . 4a where there are only two 119 l o c i for the sr t r a i t , each w i t h two a l l e l e s , sr and +. The sr a l l e l e s may be s l i g h t l y d e l e t e r i o u s . The sr t r a i t i s manifes ted only when the male has both sr a l l e l e s , s r , and s r 2 . The a n c e s t r a l c o n d i t i o n i s a monomorphism w i t h +, and +2 and the sr genes evolved l a t e r . There i s yet no p o p u l a t i o n genet ic theory s p e c i f i c a l l y developed to study the fa te of such sr genes. As a f i r s t approx imat ion , Crow and Kimura ' s (1965) and N e i ' s (1976) s t u d i e s on coadapted genes are a p p l i c a b l e . In s h o r t , these s t u d i e s suggest that the l i k e l i h o o d fo r the s r genes to increase i n i t i a l l y depends on the frequency of sex-r a t i o males (males c a r r y i n g a l l sr a l l e l e s ) i n the p o p u l a t i o n (stage 2 o f F i g . 4a ) . N a t u r a l s e l e c t i o n would then favor any i n v e r s i o n reducing recombinat ion between s r , and s r 2 i n a way s i m i l a r to those proposed for m o d i f i c a t i o n of l i n k a g e i n t e n s i t y ( N e i , 1967; Thompson and Feldman, 1974). The genes, s r , and s r 2 , are there fore coadapted i n the unusual sense of j o i n t l y d o u b l i n g t h e i r chance of being t r a n s m i t t e d by the p a t e r n a l c a r r i e r s . T h i s coadapta t ion hypothes i s r e q u i r e s that each ST arrangement d i f f e r s from the SR arrangement by a l l e l e s at two or more l o c i . The f i n d i n g in t h i s study of f i v e gene l o c i i n v o l v e d in the d i f f e r e n t i a t i o n between SR(B) and ST(A) d i d not merely f u l f i l l the p r e d i c t i o n of the coadapta t ion h y p o t h e s i s ; i t posed a very p u z z l i n g q u e s t i o n : How does t h i s ex tens ive d i f f e r e n t i a t i o n between the SR and the ST gene complex evolve? Because t h i s study only determined the minimum genet ic d i f f e r e n c e w i t h respect to the sr t r a i t between the ST and SR 120 i n v e r s i o n s , i t i s very l i k e l y that many more l o c i would have been found i f more marker mutants were used. (A reminder : To manifest sr e x p r e s s i o n , sr a l l e l e s at ALL l o c i are needed). F i g . 4a i s no longer a s a t i s f a c t o r y e x p l a n a t i o n of the correspondence of the sr phenotype and the SR i n v e r s i o n when f i v e or more l o c i are i n v o l v e d in sr expres s ion w i t h an i n i t i a l monomorphism of + , + 2 + 3 and + 5 . The data of Table 3 and 4 suggest that only one out of the 64 (=2*) gametic combinat ions manifest sr e x p r e s s i o n , i e . , the one w i t h s r , s r 2 s r 3 s r „ and s r 5 . As a consequence of t h i s , the frequency of s e x - r a t i o males w i l l always be too low for these sr genes to evo lve i n the f i r s t p l a c e . There are two a l t e r n a t i v e s , not n e c e s s a r i l y mutua l ly • e x c l u s i v e , to e x p l a i n the dilemma of too many coadapted genes w i t h i n the SR i n v e r s i o n . The f i r s t one, i l l u s t r a t e d i n F i g . 4b, invokes the i n t e r p l a y of sr genes and t h e i r m o d i f i e r s . In the f o l l o w i n g d i s c u s s i o n , m r e f e r s to any gene capable of suppress ing sr expres s ion and M i s the non-modi f ier a l l e l e . The SR gene complex g r a d u a l l y d iverges from ST because, a f t e r each suppressor m o d i f i e r i s f i x e d i n the p o p u l a t i o n , n a t u r a l s e l e c t i o n tends to s e l e c t for a l l e l e s at other l o c i on SR which re s to re sr e x p r e s s i o n . Th i s model incorpora te s the i n t e r p l a y of two genet ic events : suppress ion and r e s t o r a t i o n of sr e x p r e s s i o n . Suppressor m o d i f i e r s , e i t h e r Y - l i n k e d or autosomal , are q u i t e common i n D. paramelanica ( S t a l k e r , 1961) but have not been found i n D. pseudoobscura ( P o l i c a n s k y and Dempsey, 1978; Beckenbach et a l . , 1982). T h e o r e t i c a l l y , a Y-121 l i n k e d m o d i f i e r w i l l increase i n frequency and become f i x e d as long as suppressor m o d i f i c a t i o n i s s u f f i c i e n t l y s t r o n g . The c o n d i t i o n s for autosomal m o d i f i e r s to increase when rare have been formulated i n PART II of t h i s t h e s i s . One n i c e feature of t h i s model i s that i t expects genes from one p o p u l a t i o n to suppress the expres s ion of sr genes from another p o p u l a t i o n i f the two p o p u l a t i o n s are at d i f f e r e n t stages of F i g . 4b. Evidence i s a v a i l a b l e i n D. paramelanica ( S t a l k e r , 1961) but i s yet to be found i n the two s i b l i n g spec ies s t u d i e d . There a r e , however, d i f f i c u l t i e s w i t h t h i s model. F i r s t l y , a l though suppressor m o d i f i c a t i o n of sr expres s ion has been found to be ex tens ive i n some species and m o d i f i c a t i o n of autosomal m e i o t i c d r i v e (Segregat ion D i s t o r t e r ) i n D. melanogaster has been a t t r i b u t e d to genes on every chromosome, evidence that genes of the SR complex re s to re sr expres s ion a f t e r success ive suppress ion i s l a c k i n g . Nor i s our knowledge of s r expres s ion s u f f i c i e n t to a l l o w us to propose mechanisms of t h i s genet ic event . Secondly , the c o n d i t i o n s for the SR polymorphism (Edwards, 1961) always have to be s a t i s f i e d w i t h a l l the changes i n f i t n e s s e s and i n the i n t e n s i t i e s of m e i o t i c d r i v e . The greater the extent of d i f f e r e n t i a t i o n between the two gene complexes, the more s e r ious the d i f f i c u l t i e s become. The k ind of i n t e r p l a y envisaged i n the model of F i g . 4b i s l i k e l y to have p layed a r o l e i n the e v o l u t i o n of the sr t r a i t . For example, the f i r s t step i n F i g . 4a (the c o e v o l u t i o n of s r . 1 22 and s r 2 ) would be ea s i e r to accompl i sh i f there e x i s t s an in termedia te s ta te of suppressor m o d i f i c a t i o n l i k e the second stage of F i g . 4b. What the model f a i l s to c o n v i n c i n g l y e x p l a i n i s the extent of d i f f e r e n t i a t i o n between the SR and ST gene complexes. S ince the two complexes d i f f e r i n genes of sr expres s ion at the v i c i n i t y of every marker gene used, the t rue extent of d i f f e r e n t i a t i o n i s undoubtedly much greater than was repor ted i n RESULTS and there fo re c o u l d not p o s s i b l y be e x p l a i n e d by the model of F i g . 4b. A l t e r n a t i v e l y , one might cons ider the p o s s i b i l i t y that some or most of the sr genes on SR(B) repor ted i n Table 1-4 were the a n c e s t r a l genes whi l e t h e i r w i l d type a l l e l e s on ST(A) were d e r i v e d l a t e r . F o l l o w i n g the d e f i n i t i o n of suppressor m o d i f i e r s , these new w i l d type genes are equ iva l en t to m o d i f i e r s (m) and the o r i g i n a l sr genes are equ iva l en t to t h e i r non-m o d i f i e r a l l e l e s (M). (The symbols, sr and +, only denote the genes which determine the phenotypes of t h e i r male c a r r i e r s and i n no way connote t h e i r e v o l u t i o n a r y o r i g i n . From an e v o l u t i o n a r y po in t of v iew, an sr gene may mean e i t h e r a gene favored by n a t u r a l s e l e c t i o n for i t s a b i l i t y to d i s t o r t t r a n s m i s s i o n r a t i o i n favor of i t s e l f or the non-modi f ier r e l i c a l l e l e of a suppressor gene which becomes common i n the p o p u l a t i o n . ) The major d i f f i c u l t y w i t h such an i n t e r p r e t a t i o n was p o i n t e d out i n Part II of t h i s t h e s i s : an X - l i n k e d m o d i f i e r i s e v o l u t i o n a r i l y s u i c i d a l and would never have had a chance to increase i n f requency. A s a t i s f a c t o r y e x p l a n a t i o n there fore has to take i n t o account both the i n t r o d u c t i o n of new a l l e l e s 123 ( e i t h e r sr or +) and l i n k a g e m o d i f i c a t i o n ( i e . , chromosomal i n v e r s i o n s ) . The model of F i g . 4c cons ider s a p o p u l a t i o n i n i t i a l l y c o n s i s t i n g of gametotypes + , +2 s r 3 s r „ s r 5 , s r , s r 2 s r 3 s r „ s r 5 and t h e i r recombinants . Thi s i n i t i a l c o n d i t i o n i s e q u i v a l e n t to the second stage of F i g 4a or the t h i r d stage of F i g . 4b. I t can be achieved v i a e i t h e r pathway. An i n v e r s i o n then takes p lace on one of the chromosomes c a r r y i n g s r , and s r 2 (the second stage of F i g . 4 c ) . Let us c a l l t h i s new i n v e r s i o n SR and the o r i g i n a l arrangement ST . At t h i s s tage, a mutat ion from s r , to +« w i t h i n the ST arrangement would not be so much a " s u i c i d a l " event prov ided that l inkage between +,, +2 and +„ was s u f f i c i e n t l y t i g h t (Stage 3 ) . In other words, t h i s new + „ a l l e l e would not have had a chance to be incorpora ted i n t o the SR arrangement and d i d not have the chance of suppress ing m e i o t i c d r i v e which , as mentioned, was s u i c i d a l . The a l l e l e +^  would then increase in the p o p u l a t i o n i f i t i s only s l i g h t l y s u p e r i o r to s r „ in v i a b i l i t y . Muta t ion from s r „ to +4 would a l s o recur i n the SR arrangement but +„ i n that gene arrangement i s s u i c i d a l . The same scheme can be used to e x p l a i n the polymorphisms at the remaining l o c i . I t i s there fo re p o s s i b l e to account for the apparent divergence at so many l o c i between the SR and the ST gene complex. To summarize the model of F i g . 4c : A new gene w i t h i n SR w i l l increase i n frequency only when i t does not d i s r u p t the sr e x p r e s s i o n . Gene s u b s t i t u t i o n w i t h i n SR c o u l d t h e r e f o r e be very c o n s e r v a t i v e . The c o n s t r a i n t i s not a p p l i c a b l e to any 1 24 segment of ST w i t h i n which there i s l i t t l e recombinat ion w i t h SR. The r e l a x a t i o n of t h i s c o n s t r a i n t enabled ST to have evolved much f a s t e r than SR and u l t i m a t e l y accounts for the ex tens ive d ivergence between them. The suggest ion that the a n c e s t r a l popula t ions ' c a r r i e d some s e x - r a t i o genes w h i l e t h e i r w i l d type a l l e l e s ( i e . , m e i o t i c d r i v e m o d i f i e r s ) were d e r i v e d l a t e r i s not e n t i r e l y imaginary . As mentioned i n the MATERIALS AND METHODS s e c t i o n under Experiment I I , there was some recombinat ion between ST(A) and ST(B) i n the se-sh r e g i o n , suggest ing that c r o s s i n g over between the SR(B) (= ST(A) ) and the ST(B) arrangement of D. p e r s i m i l i s i s not uncommon i n that r e g i o n . S ince ST(B) / SR(B) i s c h a r a c t e r i z e d by a b i g i n v e r s i o n i n the middle of XR, the c r o s s i n g over c o u l d be somewhere between sp and sh (see F i g . 1 ) . From Table 3 and 4, we a l ready know SR(B) c a r r i e s two sr genes very c l o s e to sh . The ques t ion i s : Does ST(B) a l s o c a r r y the sr a l l e l e s at these two l o c i ? I f i t does, c r o s s i n g over between SR(B) and ST(B) i n the reg ion c l o s e to sh would not d i s r u p t the i n t e g r i t y of the SR gene complex in D. p e r s i m i l i s . On the other hand, i f i t does not , one would expect some of the D. p e r s i m i l i s males , whi l e possess ing an SR(B) arrangement, to produce progeny w i t h a normal sex c o m p o s i t i o n . Males of a normal phenotype but an SR karyotype have not been reported i n t h i s species (S tur tevant and Dobzhansky, 1936; Dobzhansky, 1944). In other words, recombinat ion has not been found to d i s r u p t the " s e x - r a t i o " gene complex i n t h i s s p e c i e s . The SR gene complex i n D. pseudoobscura has been complete ly 1 25 bound i n t o a supergene by n a t u r a l s e l e c t i o n . Given the p o t e n t i a l h igh rate of chromosomal i n v e r s i o n s (Yamaguchi and M u k a i , 1974), i t i s reasonable to expect an e q u a l l y t i g h t SR gene complex i n i t s s i b l i n g s p e c i e s . In a d d i t i o n , the l i n k a g e a s s o c i a t i o n of e l e c t r o p h o r e t i c a l l e l e s i n SR and ST of D. p e r s i m i l i s observed by P o l i c a n s k y and Zouros (1977) does not seem to support the idea of a " l o o s e " SR gene complex. I t can t h e r e f o r e be i n f e r r e d t h a t , i n the v i c i n i t y of the sh l o c u s , SR(A) , SR(B) and ST(B) a l l c a r r y sr genes whi l e ST(A) c a r r i e s t h e i r w i l d type a l l e l e s . The c o r o l l a r y : The a n c e s t r a l a l l e l e i s the sr a l l e l e (or the non-modi f ie r M) . E v o l u t i o n at t h i s p a r t i c u l a r locus i s more l i k e l y to have proceeded i n the fa shion ' of F i g . 4c than that of F i g . 4b. Another phenomenon of i n t e r e s t i s the apparent ly i d e n t i c a l banding p a t t e r n between ST(A) and SR(B) . T h i s study took advantage of t h i s fac t but has not yet o f f e red any e x p l a n a t i o n for i t . The ST(A) (= SR(B) ) arrangement i s presumably a n c e s t r a l to other i n v e r s i o n s because one other spec ies i n the obscura group of North America , D. miranda , a l s o has an XR very s i m i l a r to ST(A) (Dobzhansky and Tan, 1936). In l i g h t of the models d i s c u s s e d , the fac t that the same arrangement manifes t s d i f f e r e n t phenotypes ( ST(A) = SR(B) ) w h i l e the same phenotype i s a s s o c i a t e d w i t h d i f f e r e n t i n v e r s i o n s ( SR(A) * SR(B) , ST(A) * ST(B) ) i s not by any means unexpected. Because the only e f f e c t of i n v e r s i o n s i s to prevent recombinat ion between SR and ST, i t makes l i t t l e d i f f e r e n c e which chromosome i s i n v e r t e d . To r e c o n s t r u c t the e v o l u t i o n of 1 26 chromosomal i n v e r s i o n s i n t h i s system: A f t e r the s p l i t of D. pseudoobscura and D. p e r s i m i l i s , a s e r i e s of i n v e r s i o n s g r a d u a l l y bound the sr genes i n t o a complex (the present SR(A) ) i n the D. pseudoobscura l i n e a g e . On the other hand, i n the D. p e r s i m i l i s l ineage a chromosome c a r r y i n g some w i l d type genes were rearranged to form the present day ST(B) . Th i s new ST(B) i n v e r s i o n increased i t s frequency i n D. p e r s i m i l i s popu la t ions for v i a b i l i t y or f e r t i l i t y reasons w h i l e SR(A) i n D. pseudoobscura was " m e i o t i c a l l y d r i v e n " to a h igh frequency. The polymorphisms of the two gene complexes, SR and ST , are mainta ined by a balance between n a t u r a l s e l e c t i o n and m e i o t i c d r i v e (see Par t I and Par t I I of t h i s t h e s i s ) . The new i n v e r s i o n s , SR(A) and ST(B) , were pushed to the balanced e q u i l i b r i u m by m e i o t i c d r i v e and n a t u r a l s e l e c t i o n r e s p e c t i v e l y . There are many i n t r i c a t e d e t a i l s l e f t to be worked ou t . An example i s the c o n d i t i o n s under which the apparent a n c e s t r a l arrangement, ST(A) and SR(B) , would become f i x e d for w i l d type a l l e l e s at a l l l o c i on ST(A) and for a l l sr a l l e l e s on SR(B) , a f t e r each spec ies became polymorphic for d i f f e r e n t chromosomal i n v e r s i o n s . Rigorous t h e o r e t i c a l s tud ie s are necessary to answer these q u e s t i o n s . 127 On h y b r i d s t e r i l i t y Caut ion has to be taken when d e a l i n g w i t h i n t e r s t r a i n (and p o s s i b l y i n t e r s p e c i f i c ) c r o s s e s . When two s t r a i n s of D. melanogaster are crossed ( u s u a l l y females from a l a b o r a t o r y s t r a i n and males from a w i l d s t r a i n ) , the F, h y b r i d s q u i t e o f ten show a number of dysgenic t r a i t s , such as s t e r i l i t y , male recombina t ion , e l eva ted mutat ion r a t e , segregat ion d i s t o r t i o n and o t h e r s . The phenomenon was co ined the term h y b r i d dysgenesis by K i d w e l l e t a l (1977) and was the sub ject pf reviews by Sved (1979), B r e g l i a n o et a l (1980), and Green(198 l ) . I t i s now b e l i e v e d that h y b r i d dysgenesis r e s u l t s from i n t e r a c t i o n s between the t ransposab le-e lement-1 ike f a c t o r s on the p a t e r n a l chromosomes (Green, 1981) and the maternal cy top la smic f a c t o r s ( i e . , cy to types ) which are u l t i m a t e l y c o n t r o l l e d by the chromosomes ( B r e g l i a n o et a l , 1980; K i d w e l l , 1981). I t i s important to know to what extent genet ic i n t e r a c t i o n s of t h i s k i n d would a f f e c t the a n a l y s i s of male s t e r i l i t y i n the backcross exper iments . In g e n e r a l , h y b r i d dysgenesis should not be a major source of concern i n the a n a l y s i s of s t e r i l i t y of i n t e r s p e c i f i c h y b r i d s . F i r s t , the nature of s t e r i l i t y of i n t e r s p e c i f i c h y b r i d s may be very d i f f e r e n t from that of h y b r i d dysgenesis (Sved, 1979). The most n o t i c e a b l e d i f f e r e n c e i s that Haldanes ' s r u l e (Haldane, 1922) on s t e r i l i t y of i n t e r s p e c i f i c hybr id s does not apply to h y b r i d dysgenes i s . The r u l e says that " i f one sex i n the F, of i n t e r r a c i a l or i n t e r s p e c i f i c c ros s ses i s absent , rare or s t e r i l e , that sex i s the 128 heterogametic sex " . In h y b r i d dysgenes i s , there i s , i n g e n e r a l , a much more severe e f f e c t on the f e r t i l i t y of h y b r i d females than on that of males. For example, i n the s o - c a l l e d " I -R system", the h y b r i d males are normal i n t h e i r f e r t i l i t y , but not females (Breg l i ano et a l . , 1980). In a d d i t i o n , h y b r i d dysgenesis i s always manifested only in h y b r i d s from one of the r e c i p r o c a l c r o s s e s . T h i s r u l e does not apply to D. pseudoobscura and D. p e r s i m i l i s . H y b r i d F, males from both r e c i p r o c a l crosses between the two spec ies are s t e r i l e whi l e F, females from both crosses are f e r t i l e . Second, even i f h y b r i d dysgenesis i s s t i l l a p o s s i b l e source of e r r o r i n the a n a l y s i s , repeated backcros s ing employed i n t h i s study should have reduced the dysgenic e f f e c t to the l e v e l of i n t r a s t r a i n mating ( B r e g l i a n o , 1980; K i d w e l l , 1981). The mothers of the t e s t ed males ( i e . , B 5 - , and B 3 - . , c rosses i n F i g . 1 and 2) there fore had matching genotypes and cyto types and would not be expected to produce s t rong dysgenic e f f e c t s . The mapping of s t e r i l i t y f a c t o r s r e l i e s on the recombinat ion frequency i n females . Al though one study ( K i d w e l l , 1977) repor ted a n e a r l y two f o l d increase i n the recombinat ion frequency i n F, dysgenic females , the dysgenic e f f e c t on recombinat ion i n t h i s study should not have been more s i g n i f i c a n t than i t was on male s t e r i l i t y . Besides t h a t , the study l a t e r c a r r i e d out by S i n c l a i r and Green (1979) suggested that h y b r i d dysgenesis should not have any s i g n i f i c a n t e f f e c t on the recombinat ion f requencies i n females . For reasons mentioned above, i n the d i s c u s s i o n of h y b r i d 129 male s t e r i l i t y , I cons idered only i n t e r a c t i o n s of chromosomal genes. Most i m p o r t a n t l y , Dobzhansky's (1936) comprehensive study on s t e r i l i t y of h y b r i d males between D. pseudoobscura and D. p e r s i m i l i s underscored the overwhelming e f f e c t of chromosomal i n t e r a c t i o n s . Backcross males i n h i s study w i t h a l l chromosomes from e i t h e r of the two species were f e r t i l e i r r e s p e c t i v e of the source of t h e i r cy top la sm. In summary, four d i f f e r e n t s t e r i l i t y i n t e r a c t i o n s were d i s c o v e r e d . One of them i n v o l v e s the y- sn region on ST(A) and some u n i d e n t i f i e d genes of D. p e r s i m i l i s . Thi s reg ion i s not l i n k e d w i t h the sr genes and i s presumably on XL. The f o l l o w i n g i n t e r a c t i o n s i n v o l v i n g XR w i l l be d i scus sed i n d e t a i l . i ) E i t h e r one of the two genes on SR(B) in the +(se)-+(sp) reg ion i n t e r a c t w i t h u n i d e n t i f i e d genes from the D. pseudoobscura background (Experiment I ) . i i ) A s i n g l e gene on ST(A) i n the co-se reg ion i n t e r a c t s w i t h u n i d e n t i f i e d genes from the D. p e r s i m i l i s background (Type I I of Experiment I I ) . i i i ) E i t h e r one of two dominant autosomal genes from D. pseudoobscura i n t e r a c t s w i t h the +(co)-+(se) reg ion on SR(B) (Type I of Experiment I I ) . Comparing i ) and i i ) , i t i s immediately c l e a r that s t e r i l i t y i n t e r a c t i o n s are "asymmetr ic" . Asymmetry means that i f M(A)-M(B) and N(A)-N(B) are corresponding a l l e l e s i n species A and B at the M and N locus and i f the M(A)-N(B) i n t e r a c t i o n r e s u l t s i n h y b r i d i n v i a b i l i t y or s t e r i l i t y , the r e c i p r o c a l 130 combinat ion M(B)-N(A) i s normal i n v i a b i l i t y and f e r t i l i t y . A g a i n , l e t A and B represent D. pseudoobscura and D. p e r s i m i l i s r e s p e c t i v e l y . In i ) , the N locus i s e i t h e r one of the two genes i n the se-sp reg ion w h i l e the M locus i s not i d e n t i f i e d . In i i ) , the M locus i s the s t e r i l i t y f a c t o r mapped to the co-se r e g i o n . Only the two c a t e g o r i e s , i ) and i i ) , p rov ided i n f o r m a t i o n on s t e r i l i t y t e s t s for the r e c i p r o c a l i n t e r a c t i o n s ( i e . , both M(A) - N(B) and M ( B ) - N(A) were t e s t e d ) . A l l three s t e r i l i t y i n t e r a c t i o n s observed i n i ) and i i ) are asymmetric . T h i s phenomenon i s very important to understanding the e v o l u t i o n of postmating r eproduc t ive i s o l a t i o n . I f s t e r i l i t y i n t e r a c t i o n i s symmetric and the a n c e s t r a l c o n d i t i o n i s , say, M(A) and N ( A ) , n e i t h e r M(B) nor N(B) would have any chance to increa se i t s frequency i n the p o p u l a t i o n s . A new M(B) a l l e l e c o u l d only be a s s o c i a t e d w i t h N(A) and g ive r i s e to s t e r i l e i n d i v i d u a l s . I t i s a l s o t rue for N ( B ) . The f ac t that i n t e r s p e c i f i c s t e r i l i t y per se has no advantage was emphasized by Darwin i n h i s debate w i t h Wallace on the r o l e of n a t u r a l s e l e c t i o n i n "the i n f e r t i l i t y of c r o s s e s " (see W a l l a c e , 1889, P173-179; Mayr, 1959). One p o s s i b l e scheme for the e v o l u t i o n of asymmetric s t e r i l i t y i n t e r a c t i o n s i s shown i n F i g . 5. Let M(B)-N(A) be the a n c e s t r a l c o n d i t i o n and assume that the M(A)-N(B) combinat ion i s r e s p o n s i b l e for h y b r i d s t e r i l i t y . In one spec ies (or p o p u l a t i o n ) , the gene M(A) emerges and i s e v e n t u a l l y f i x e d . The genet i c c o n s t i t u t i o n becomes M(A)-N(A) w h i l e , i n the o t h e r , the c o n s t i t u t i o n becomes M(B)-N(B) . The new 131 a l l e l e s , M(A) and N(B) , in each r e s p e c t i v e species are e n t i r e l y capable of forming f e r t i l e i n d i v i d u a l s . I f we examine the h y b r i d s t e r i l i t y at t h i s s tage, i t i s c l e a r that the s t e r i l i t y i n t e r a c t i o n has to be asymmetric because one of the two r e c i p r o c a l combinat ions , M(B)-N(A) , i s the a n c e s t r a l one. A f t e r the two species are p a r t i a l l y i s o l a t e d , N(A) in F i g . 5 may move up to the a l l e l i c s t a t e 1 whi l e M(B) moves down to the s ta te - 1 . Symmetric s t e r i l i t y i n t e r a c t i o n s would r e s u l t . C o n c e i v a b l y , asymmetric s t e r i l i t y i n t e r a c t i o n s should be found at an intermedia te stage i n the e v o l u t i o n of complete ly c ros s s t e r i l e s p e c i e s . Such an in termedia te s t a te i s expected to be common between c l o s e l y r e l a t e d spec ies such as s i b l i n g s p e c i e s . Data on the way N(B) or M(A) spread i n each r e s p e c t i v e spec ies are l a c k i n g . Wal lace (1889, p177) , Dobzhansky (1937) and M u l l e r (1940, 1942) proposed p l e i o t r o p i s m as an e x p l a n a t i o n whi le Nei (1976), based on Oka's (1974) s tudy, suggested genet ic d r i f t i n smal l p o p u l a t i o n s to be a major f a c t o r . We can now i n f e r from i ) and i i ) that two genes i n the +(se)-+(sp) reg ion on XR of D. p e r s i m i l i s and one gene i n the co-se reg ion of D. pseudoobscura have mutated and become widespread s ince the s p l i t of these two s p e c i e s . These mutat ions have a d i r e c t bear ing on the es tabl i shment of reproduc t ive b a r r i e r s between the two s p e c i e s . The asymmetry of s t e r i l i t y i n t e r a c t i o n s not only t e l l s us the genet ic d i f f e r e n c e s between the two modern spec ies but a l s o y i e l d s in format ion about how the d i f f e r e n c e s have come about . 1 32 I n t e r a c t i o n s of i ) and i i ) do not provide i n f o r m a t i o n on the autosomal genes i n v o l v e d . Some (but perhaps not a l l ) of these "background" genes must be dominant over the a l l e l e from the other spec ies s ince F, h y b r i d males are i n v a r i a b l y s t e r i l e . The evidence of dominance of autosomal h y b r i d s t e r i l i t y genes i s a l s o prov ided i n RESULTS. Comparisons of i ) and i i i ) g ive i n d i c a t i o n s that s t e r i l i t y i n t e r a c t i o n may sometimes i n v o l v e more than two genes. In • i i i ) , a s t e r i l i t y i n t e r a c t i o n of t h i s k i n d was suggested: +/D — +(co), where D i s a dominant autosomal gene from D. pseudoobscura and the re s t i s from D. p e r s i m i l i s . In i ) , however, males w i t h ' D / D and +(co) were not found to be s t e r i l e at a l l (Table 1, second row) . Here , the res t of the genome i s from D. pseudoobscura. In other words, the D — +(co) i n t e r a c t i o n i s suppressed i n the genet ic m i l i e u of D. pseudoobscura but g ives r i s e to male s t e r i l i t y i n that of D. p e r s i m i l i s . The s t e r i l i t y i n t e r a c t i o n noted i n i i i ) c o u l d be more a c c u r a t e l y presented as +/D — +(co) — C, where C i s e i t h e r the Y chromosome of D. p e r s i m i l i s or an undetermined number of autosomal genes from D. p e r s i m i l i s i n the homozygous s t a t e . In the prev ious a n a l y s i s , every p o s s i b l e source of s t e r i l i t y i n t e r a c t i o n s was cons idered except that between the i n t r o g r e s s e d elements on XR from one species and the res t of XR from the o t h e r . I f the w i t h i n - X R i n t e r a c t i o n of t h i s k i n d i s of any importance, we would not expect a steady decrease i n the p r o p o r t i o n of f e r t i l e males when the s i z e of i n t r o g r e s s e d 1 33 chromosomal segment g r a d u a l l y i n c r e a s e s . In s tead , i n t r o g r e s s i o n of par t of XR i s expected to e x h i b i t the maximal l e v e l of s t e r i l i t y i n t e r a c t i o n . R e s u l t s of Table 1 and Table 3 showed a gradual decrease i n the p r o p o r t i o n of f e r t i l e males when more f o r e i g n marker genes were i n t r o g r e s s e d . The complete replacement of XR r e s u l t e d in complete male s t e r i l i t y . The w i t h i n - X R s t e r i l i t y i n t e r a c t i o n was there fo re not c o n s i d e r e d . In the d i s c u s s i o n of e v o l u t i o n of the sr t r a i t and the SR arrangement, i t was p o i n t e d out how genes on d i f f e r e n t chromosomal arrangements i n the same species would have d i v e r g e d . Data obta ined i n t h i s study only p e r t a i n s to the d ivergence of ST(A) and SR(B) . Whether SR(A) shares the same s t e r i l i t y genes w i t h ST(A) and whether ST(B) shares them w i t h SR(B) a r e , indeed, very i n t e r e s t i n g q u e s t i o n s . The answers w i l l p l ay an important r o l e in our understanding of genet ic events u n d e r l y i n g the o r i g i n of D. pseudoobscura and D. p e r s i m i l i s from a common ancestor and subsequent r eproduc t ive i s o l a t i o n . The p e c u l i a r i n v e r s i o n polymorphisms and the a s s o c i a t e d sr t r a i t i n D. pseudoobscura and D. p e r s i m i l i s o f f e r an e x c e l l e n t o p p o r t u n i t y to study the genet ic s of r eproduc t ive i s o l a t i o n . Prev ious s tud ie s on genet ic divergence of D r o s o p h i l a spec ies re s ted t h e i r a n a l y s i s on the e f f e c t s of the whole chromosomes (eg. Dobzhansky, 1936; Ehrman, 1961; Zouros, 1981). With the SR system, i t i s p o s s i b l e to study the e f f e c t s of i n d i v i d u a l segments of X-chromosomes. S ince most s tud ie s c o n f i r m the overwhelming importance of the X-chromosome i n h y b r i d v i a b i l i t y 134 and f e r t i l i t y , the s e x - r a t i o system promises to be a rewarding target for f u r t h e r d e t a i l e d i n v e s t i g a t i o n s . 1 35 TABLE 1 Tests of f e r t i l i t y and sr expre s s ion of recombinant males obta ined i n Experiment I ( s t = co se sh ) Genotypes p r o p o r t i o n of p r o p o r t i o n f e r t i l e males of sr among f e r t i l e males co se sh 10/10 + se sh 15/16 co se + 6/16 + se + 2/5 co + sh 4/16 + + sh 10/31 co + + 0/17 + + + 0/27 25/26 • 0. (96.2) 8/21 (38. 1 ) 1 4/47 (29.8) 0/44 (0.0) W i l d type genes were i n t r o g r e s s e d from SR(B) and mutants were from ST(A) . The re s t of the genome i s from D. pseudoobscura w i t h , on average, about 1% of i t s t i l l remaining i n h y b r i d . Numbers i n bracket s are percentages . 1 36 TABLE 2 Tests of f e r t i l i t y and sr expre s s ion of recombinant males obta ined i n Experiment I (st = se sp t t ) Genotypes p r o p o r t i o n of p r o p o r t i o n f e r t i l e males of sr among f e r t i l e males se sp t t 8/9 se sp + 6/7 se + + 2/11 se + t t 1/3 + sp t t 9/34 + sp + 0/1 + + + 0/22 + + t t 0/18 14/16 (81.3) 3/1 4 (21.4) 9/35 0. (25.7) 0/40 (0.0) W i l d type genes were i n t r o g r e s s e d from SR(B) and mutants were from ST(A) . The re s t of the genome i s from D. pseudoobscura w i t h , on average, about 1% of i t s t i l l remaining i n h y b r i d . Numbers i n bracket s are percentages . 1 37 TABLE 3 Tests of f e r t i l i t y and sr expres s ion of the recombinant males obta ined i n Experiment I I (st = co se sh ) Source of recombinant males Genotypes B 2 - 2 B 3 - 2 T o t a l sr 36 20 pa r t i a1 sr 1 2 + + + st 8 4 f e r t i l e males 45/59 26/30 71/89 (76.3) (86.7) sr 0 3 3 pa r t i a 1 sr 4 1 5 + + sh st 48 27 75 f e r t i l e males 52/72 31/35 83/107 (72.2) (88.6) T o t a l f e r t i l e males 97/131 57/65 ( + + -) (74.0) (87.7) (P=.014) 20/60 (33.3) (No sr males among the f o l l o w i n g genotypes) + se + f e r t i l e males ' 14/22 3/7 31/58 (53.4) + se sh " 12/18 2/11 co + + " 2/10 12/34 co + sh " 5/7 1/9 co se + " 1/41 0/25 co se sh " 1/25 0/35 Mutant genes were i n t r o g r e s s e d from ST(A) , and w i l d type genes were those of SR(B) . The re s t of the genome comes from D. p e r s i m i l i s w i t h , on average, one-e ighth ( B 2 - 2 ) or one-s i x t e e n t h ( B 3 - 2 ) remaining i n the h y b r i d s t a t e . ++- represents e i t h e r +++ or ++sh. Numbers i n bracket s are percentages . 2/1 26 (1.4) 138 TABLE 4 Tests of f e r t i l i t y and sr expres s ion of recombinant males obta ined i n Experiment I I (st = se sp t t ) Source of recombinant males Genotypes B 2 ~ 2 B 3 - 2 sr 6 9 p a r t i a l sr 3 + + + st 2 9 f e r t i l e males 8/21 (38.1) 21/32 (65.6) sr -p a r t i a l s r 1 + + t t st 5 f e r t i l e males 6/1 1 0/1 (No sr males among the f o l l o w i n g genotypes) + sp + f e r t i l e males 1/4 (25.0) 13/15 (86.7) + sp t t " 10/26 (38.5) 10/12 (83.3) se + + " 1/21 (4.8) 5/19 (26.3) se + t t " 1/7 se sp + " 0 / 3 ( 0 . ) 2/9 (22.2) se sp t t " 2/50 (4.0) 2/14 (14.3) Mutant genes were i n t r o g r e s s e d from ST(A) , and w i l d type genes were those of SR(B) . The re s t of the genome comes from D. p e r s i m i l i s w i t h , on average, one-e ighth ( B 2 - 2 ) or one-s i xteenTh~TB7- 2 ) remaining in the h y b r i d s t a t e . Numbers i n bracke t s -a re percentages . O f H • ) — i J S R ( A ) 1 D. pseudoobscura 105.7 135.7 201.9 y s n v co se s h - J — L J O • S - — I — • 1 " - i — S T (A) es t -5 sp tt 111.8 176.7 204 2 O S R ( B ) 1 D. persimilis J - O i ) S T ( B ) ] F i g . 1. Graphic representation of inversions of XR of the s i b l i n g p a i r . The segment within brackets are inversions r e l a t i v e to the ST(A) (= SR(B) ) arrangement. The mutant genes shown are not drawn in correspondence to either the break points of inversions or the centromeres. Stage I . B B-B, SR(A)/SR(A) x SR(B)/Y SR(A)/SR(A) , (d i scarded) SR(A)/SR(A) SR(A)/SR(B) (recombinat ion suppressed) x SR(A)/Y SR(A)/SR(B) , x SR(A)/Y ^ ' ! (repeated backcrosses) SR(A)isR(B) ( fo r Stage I I ) Stage 11. B 5 - 1 B 5 - 2 B , - : SR(A)/SR(B) x ST(A)/Y (from B 5 ) (wi th markers) ST(A)/SR(A) SR(A)/Y . ; (d i scarded) SR(B)/Y ST(A)/SR(B) x ST(A)/Y ( te s ted) ( recombinat ion expected) recombinant males ( tes ted) recombinant males ( tes ted) recombinant females x ST(A)/Y recombinant females F i g . -2. I n t r o g r e s s i o n p r o t o c o l for Experiment I . SR(B) was i n t r o g r e s s e d i n t o the genome of pseudoobscura by repeated b a c k c r o s s i n g i n Stage I . Recombinant males w i t h " h y b r i d XR" were obta ined i n Stage I I . These males were t e s t e d for t h e i r f e r t i l i t y and sr e x p r e s s i o n . , Females were a l lowed to l ay eggs and then were assayed for E s t - 5 a l l e l e s . Homozygotes were d i s c a r d e d . 141 Stage I . ST(A)/ST(A) x ST(B)/Y ( w i t h markers) B, males B-B-ST(A)/ST(B) x ST(B)/Y ( recombinat ion g r e a t l y reduced) males and ST(B)/ST(B) , (d i scarded) males and ST(B)/ST(B) ST(A)/ST(B) x ST(B)/Y ST(A)/ST(B) ( f o r Stage I I ) Stage I I . Bn o (n= 2 or 3 ) ST(A)/ST(B) x SR(B)/Y (from B ) B n 1 ST(B)/SR(B) 2 ST(A)/SR(B) ? x ST(B)/Y (d i scarded) ( recombinat ion expected) B, recombinant males ( t e s ted ) recombinant females F i g . 3. I n t r o g r e s s i o n p r o t o c o l for Experiment I I . ST(A) was i n t r o g r e s s e d i n t o the genome of L\ p e r s i m i1 i s by repeated b a c k c r o s s i n g i n Stage I . Recombinant males w i t h " h y b r i d XR" were obta ined i n Stage I I . These males were t e s t e d for t h e i r f e r t i l i t y and s r e x p r e s s i o n . , Females were a l l o w e d to l a y eggs and then were assayed for Es t -5 a l l e l e s . Homozygotes were d i s c a r d e d . 2 Females were d i s c a r d e d , i f none of t h e i r sons c a r r i e d proper mutants . 142. + 1 + 2 + 1 + 2 + 1 + 2 + i s r 2 S T , + 2 s r , s r 2 + i s r 2 s r , +2 ( s r 2 s r , ) + 1 + 2 ( s r 2 s r , ) F i g . 4 a . A two- locus model on e v o l u t i o n of the a s s o c i a t i o n of SR i n v e r s i o n and the sr phenotype. Males w i t h s t , and s r 2 are s r , but are o therwise S t . ( ) stands for , i n v e r s i o n . 143 +3 s r , +„ +2 +5 +3 s r , +„ +2 + 5 M, —"**• m, s r suppressed sr + 3 s r , + « s r 2 +5 +3 s r , ( s r 2 -f,) +5 m, * m, s r sr +3 s r , ( s r 2 + « ) +5 s r 3 s r , ( s r 2 + *) +5 m 1m 2 * m,m2 suppressed sr sr; ( s r , s r 3 ) ( s r 2 s r « ) ( s r 5 ) m, m 2 m 3 m fl sr F i g . 4b. A model on the e v o l u t i o n of SR of p_;_ pseudoobscura . ST i s assumed to be + 3 + i + a + 2 + s and has remained unchanged. The phenotypes of males posses s ing the i l l u s t r a t e d gene t i c c o n s t i t u t i o n are u n d e r l i n e d , m 's are e i t h e r autosomal or Y -l i n k e d suppressor m o d i f i e r s . M 's are t h e i r non-modi f i e r a l l e l e s . Note the a l t e r n a t i n g s u b s t i t u t i o n of m and sr a l l e l e s for M and + r e s p e c t i v e l y . ( ) stands for i n v e r s i o n . 144 s r 3 +, s r „ +2 s r 5 s r 3 s r , s r , s r 2 s r 5 s r 3 +, + „ +2 s r 5 s r 3 s r , ( s r 2 s r „ ) s r 5 s r 3 +, s r , +2 s r 5 s r 3 s r , ( s r 2 s r „ ) s r 5 s r 3 +, +„ +2 +5 s r 3 s r , ( s r 2 s r 4 ) ( s r 5 ) + 3 + 1 + „ +2 ( s r , s r 3 ) ( s r 2 s r „ ) ( s r 5 ) F i g . 4c . A model fo r the ex tens ive d i f f e r e n t i a t i o n between the SR and ST chromosomes of pseudoobscura . Males w i t h s r , s r 2 s r 3 s r , and s r 5 are sr but are o therwise s t . Note the s u b s t i t u t i o n of +3 + „ and +5 for s r 3 s r , and s r 5 r e s p e c t i v e l y . ( ) stands for i n v e r s i o n . ALLELIC STATE LOCUS M N F i g . 5. A h y p o t h e t i c a l scheme of e v o l u t i o n of asymmetric s t e r i l i t y i n t e r a c t i o n s between spec ies A and B. S t e r i l i t y i n t e r a c t i o n s occur between the a l l e l e at M locus and the a l l e l e at N locus i f they are not i n the same s t a t e or i n ne ighbor ing s t a t e s . M(A) N (A) , M(B) N(B) represent the present day c o n s t i t u t i o n of the two s p e c i e s . M(B)wamam N(A) may represent the a n c e s t r a l c o n d i t i o n . M(A) N(B) i s the observed s t e r i l i t y i n t e r a c t i o n . 1 46 EPILOGUE 147 Ever s ince Gershenson (1928) d i d the f i r s t genet i c a n a l y s i s on the Sex-Rat io problem, p o p u l a t i o n g e n e t i c i s t s have been a sk ing the same q u e s t i o n : " I f SR i s indeed t r a n s m i t t e d by males at twice the ra te of ST, how does n a t u r a l s e l e c t i o n prevent SR from being f i x e d and, as a consequence of t h a t , p o p u l a t i o n e x t i n c t i o n ? " The d i s c o v e r y of the c y t o l o g i c a l ba s i s of the " s e x - r a t i o " expre s s ion i n D. pseudoobscura by P o l i c a n s k y and E l l i s o n (1970) made the ques t ion even more i n t e r e s t i n g . They found that h a l f of the spermat ids , presumably Y-bear ing ones, of SR males f a i l to mature. T h i s f i n d i n g immediately suggested the p o s s i b i l i t y of s t rong f e c u n d i t y s e l e c t i o n aga ins t SR males . T h i s hypothes i s seemed reasonable , e s p e c i a l l y i n l i g h t of s tud ie s on other D r o s o p h i l a genet ic systems which i n v a r i a b l y found very intense v i r i l i t y s e l e c t i o n ( i n c l u d i n g f e c u n d i t y and sexual s e l e c t i o n ) . Subsequent s tud ie s (Beckenbach, 1978; C u r t s i n g e r and Feldman, 1980), however, d i d not f i n d v i r i l i t y s e l e c t i o n aga ins t SR males to be important . The dilemma i s that n a t u r a l s e l e c t i o n must operate aga ins t c a r r i e r s of SR, but male c a r r i e r s , w i t h an apparent d e f i c i e n c y i n spermatogenesis , are not subject to v i r i l i t y s e l e c t i o n . My study r e s o l v e s t h i s dilemma: SR males are indeed much l e s s v i r i l e than ST males when females are n o n - v i r g i n s a l though they are no l e s s v i r i l e when mated w i t h v i r g i n females. The concept of p a r t i t i o n i n g v i r i l i t y s e l e c t i o n i n t o a v i r g i n and a n o n - v i r g i n component 148 should be of genera l v a l i d i t y for other D r o s o p h i l a (or even other i n s e c t ) genet ic systems as w e l l . The ques t ion concerning the maintenance of the SR polymorphism i s by no means the only i n t e r e s t i n g ques t ion about the Sex-Rat io t r a i t . ( C o n c e p t u a l l y , i t may be the l e a s t i n t r i g u i n g one) . One may a l s o ask "What i s the consequence of i n t e r a c t i o n s between the SR chromosome and other autosomal genes?" Genes capable-of suppress ing the " s e x - r a t i o " express ion have been found i n other species of D r o s o p h i l a ( S t a l k e r , 1961) but not i n D. pseudoobscura, the spec ies most i n t e n s i v e l y s tud ied ( P o l i c a n s k y and Dempsey, 1978; Beckenbach et a l . , 1982). My t h e o r e t i c a l study ( PART II ) suggests that s t rong s e l e c t i o n aga ins t SR males would have prevented suppressor m o d i f i e r s from i n c r e a s i n g i n the p o p u l a t i o n . Thi s may he lp e x p l a i n the absence of m o d i f i e r genes i n D. pseudoobscura. (My study of v i r i l i t y s e l e c t i o n by p a r t i t i o n i n g i t i n t o two components indeed suggests that there i s s t rong v i r i l i t y s e l e c t i o n aga ins t D. pseudoobscura SR males ) . There fore , from a seemingly u n r e l a t e d study of m o d i f i e r genes, we have found some f r e s h answers to the h a l f - c e n t u r y o l d ques t ion about how n a t u r a l s e l e c t i o n operates i n the SR system. One of the most e x c i t i n g ques t ions I t r i e d to answer i n t h i s t h e s i s i s : "How does the " s e x - r a t i o " phenotype become a s s o c i a t e d w i t h s p e c i f i c chromosomal i n v e r s i o n s which per se have l i t t l e to do w i t h the " s e x - r a t i o " expre s s ion? " Or 1 49 s imply "How does the system e v o l v e ? " By i n t r o g r e s s i n g the r i g h t arm of the X chromosome from D. pseudoobscura to i t s s i b l i n g s p e c i e s , D. p e r s i m i l i s , and a l s o by c a r r y i n g out the r e c i p r o c a l i n t r o g r e s s i o n , the genes t i g h t l y l i n k e d by i n v e r s i o n s i n t o a "supergene" can be s t u d i e d i n d i v i d u a l l y . The r e s u l t s show that SR d i f f e r s from ST by at  l e a s t 5 gene l o c i and the replacement of any gene on SR by i t s a l l e l e on ST r e s u l t s i n a complete l o s s of the " s e x - r a t i o " e x p r e s s i o n . These f i n d i n g s t r o n g l y support the hypothes i s that genes w i t h i n a chromosomal i n v e r s i o n are "coadapted" . Those genes w i t h i n SR are coadapted i n the unusual sense of m e i o t i c d r i v e . The unexpected f i n d i n g that many genes are i n v o l v e d i n s e x - r a t i o expres s ion has g iven us much i n s i g h t i n t o the e v o l u t i o n of t h i s genet ic system as was d i scus sed i n PART I I I . The s t u d i e s j u s t de sc r ibed a c t u a l l y prov ide many more i n t e r e s t i n g ques t ions for future i n v e s t i g a t i o n s than the ones I have answers f o r . I t i s my hope, tha t these ques t ions w i l l i n the future a t t r a c t more t a l e n t s to work on t h i s f a s c i n a t i n g phenomenon. 150 REFERENCES Anderson, W. W. , L . L e v i n e , 0 . O l i v e r s , J . R. P o w e l l , M. E. DeLa Rosa, V . M. Sa lcoda , M. I . Gaso, and J . Guzman. 1979. 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P o p u l a t i o n genet i c s of m o d i f i e r s of m e i o t i c d r i v e . I . The s o l u t i o n of a s p e c i a l case and some genera l i m p l i c a t i o n s . Theor. Pop. B i o l . 4 :446-465. Sand le r , L . , and E . N o v i t s k i . 1957. M e i o t i c d r i v e as an e v o l u t i o n a r y f o r c e . Amer. N a t u r . 91:105-110. E v o l u t i o n 8:252-290. S i n c l a i r , D. A . R . , and M. M. Green. 1979. Genet ic i n s t a b i l i t y i n D r o s o p h i l a melanoqaster : the e f f e c t of male recomninat ion (MR) chromosomes i n females . Molec . Gen. Genet. 170:219-224 158 S p i e s s , E . B. 1968. Low frequency adbantage i n mating of D r o s o p h i l a pseudoobscura karyotypes . Amer. N a t u r . 102:363-379. Sp ie s s , E . B. 1970. Mat ing propens i ty and i t s genet ic ba s i s i n D r o s o p h i l a . I n : Essays i n E v o l u t i o n and Genet ic s i n honor of Th. Dobzhansky, e d . , m. K. Hecht , pp 315-380. A p p l e t o n - C e n t u r y - C r o f t s . S p i e s s , E . B . , and J . F . Kruckeberg . 1980. M i n o r i t y advantage of c e r t a i n ete c o l o r mutants of D r o s o p h i l a  melanogaster . I I . A b e h a v i o r a l b a s i s . Amer. N a t u r . 115(3):307-327. S t a l k e r , H . D. 1961. The genet ic systems modi fy ing m e i o t i c d r i v e i n D r o s o p h i l a paramelanica . Genet i c s 46:177-202. S t u r t e v a n t , A . H . , .and Th. Dobzhansky. 1936. Geographica l d i s t r i b u t i o n and c y t o l o g y of s e x - r a t i o i n D r o s o p h i l a  pseudoobscura and r e l a t e d s p e c i e s . Genet ic s 21:473-490. Sved, J . A . 1979. The " h y b r i d dysgenes i s " syndrome i n D r o s o p h i l a  melanogaster . B i o s c i e n c e 29:659-664. Ta j ima , F . Is the m i n o r i t y advantage i n male-mating a b i l i t y a s t a t i s t i c a l a r t i f a c t ? (unpub l i shed ) . Tan, C. C. 1946. Genet ic s of sexual i s o l a t i o n between D r o s o p h i l a  pseudoobscura and D r o s o p h i l a p e r s i m i l i s . Genet ic s 31:558-573. Genet ic s 94:1011-1038. Thompson, G . , and M. W. Feldman. 1974. P o p u l a t i o n genet i c s of m o d i f i e r s of m e i o t i c d r i v e . I I . Linkage m o d i f i c a t i o n i n the segregat ion d i s t o r t i o n system. Theor. Pop. B i o l . 5:155-162. Thompson, G . , and M. W. Feldman. 1975. P o p u l a t i o n genet i c s of m o d i f i e r s of m e i o t i c d r i v e . I V . On the e v o l u t i o n of s e x - r a t i o d i s t o r t i o n . Theor. Pop. B i o l . 8 :202-211. Thompson, G . , and M. W. Feldman. 1976. P o p u l a t i o n genet i c s of m o d i f i e r s of m e i o t i c d r i v e . I I I . E q u i l i b r i u m a n a l y s i s of a genera l model for the genet ic c o n t r o l of segregat ion d i s t o r t i o n . Theor. Pop. B i o l . 1 0 ( 0 : 1 0 - 2 5 . Tracey , M. L . 1972. Sex chromosome t r a n s l o c a t i o n s i n the e v o l u t i o n of r eproduc t ive i s o l a t i o n . Genet ic s 72:317-333. 159 V o e l k e r , R. A . 1972. P r e l i m i n a r y c h a r a c t e r i z a t i o n of s e x - r a t i o and r e i n t e r p r e t a t i o n of male sex r a t i o i n D r o s o p h i l a  a f f i n i s . Genet ic s 71:597-606. W a l l a c e , A . R. 1889. Darwinism. M a c m i l l a n , London. W a l l a c e , B. 1948. S tudies on s e x - r a t i o i n D r o s o p h i l a  pseudoobscura. I , s e l e c t i o n and s e x - r a t i o . E v o l u t i o n 2:189-217. W a l l a c e , B. 1950. An experiment on sexual i s o l a t i o n . Dros . I n f o r . Serv . 24:94-96. Yamaguchi, 0 . , and T. Muka i . 1974. V a r i a t i o n of spontaneous r a te s of chromosomal a b e r r a t i o n s i n the second chromosomes of D r o s o p h i l a melanogaster . Genet ic s 78:1209-1221 . Zimmering, S . , and G. L . F o w l e r . 1968. Progeny:sperm r a t i o and n o n f u n c t i o n a l sperm in D r o s o p h i l a melanogaster . Genet . Res. 12:359-363. Zouros, E . 1981. The chromosomal ba s i s of sexual i s o l a t i o n i n two s i b l i n g spec i s of D r o s o p h i l a : D r o s o p h i l a  mojavensis and D. a r i z o n e n s i s . Genet ic s 97:703-718. • •'160 A P P E N D I X The D i s t r i b u t i o n o f f ( t ) L e t b e t h e p r o p o r t i o n o f s p e r m f r o m SP. m a l e s i n t h e f e m a l e s t o r a g e o r g a n b e t w e e n h e r i - t h a n d ( i + l ) - t h m a t i n g s . L e t b e t h e • p r o p o r t i o n o f x 0 p o r X ^ - b e a r i n g s p e r m i n t h e f e m a l e s t o r a g e o r g a n a n d l e t D b e t h e p r o p o r t i o n o f s o n s f a t h e r e d b y t h e SR m a l e s . T h e r e f o r e , f . = h ( 1 - F . ) + ( 1 - D ) F . 1 1 l T h e d i s t r i b u t i o n o f 's a r e e a s i l y o b t a i n a b l e k n o w i n g P/ 3/ U i , U 2 ( a s d e f i n e d p r e v i o u s l y ) . F o r e x a m p l e , l e t SR-ST-SR. b e t h e m a t i n g s e q u e n c e o f a t r i p l y m a t e d f e m a l e . P r o b { S R - S T - S R } = u i ( l - u 2 ) u 2 = P r o b { F 3 = q + ( l - q ) ( 1 - p ) } a n d P r o b { S T - S R - S T } = ( 1 - u i ) u 2 ( l - u 2 ) = P r o b { F 3 = ( 1 - p ) ( q + ( 1 - q ) F l } = P r o b { F 3 = ( 1 - p ) q _} T h e r e f o r e , t h e m e a n , t h e v a r i a n c e a n d t h e d i s t r i b u t i o n o f f . ' s l a r e a l s o a v a i l a b l e . I ( t ) , a s d e f i n e d , i s t h e m a t i n g s t a t u s o f a f e m a l e a t t i m e t . We a r e i n t e r e s t e d i n t h e d i s t r i b u t i o n o f f ( t ) . P r o b { f ( t ) = z } = I P r o b { f . = z } P r o b { I ( t ) = i } = E P r o b { f , = z } g . . ( i ) ( 1 ) 1 At 1 w h e r e g i s t h e P o i s s o n p r o b a b i l i t y w i t h p a r a m e t e r A t . F o r c o n v e n i e n c e , z i s d e s i g n a t e d t o b e e i t h e r .5 o r t h e m i d -v a l u e s o f t h e i n t e r v a l s ( .5 +l.o5, .5 + .05(1 + 1)), 1= 0 , 1 , • • , 9 . :>* 161 A l s o , E ( f " ( t ) ) = E E ( f . n ) g ( i ) j_ 1 At t h e r e f o r e E ( f ( t ) ) a n d V a r ( f ( t ) ) c a n be c a l c u l a t e d . A ( t i ) - A ( t 2 ) : M e a n s a n d V a r i a n c e s I n a c o h o r t w i t h m f e m a l e s and. a m i x t u r e o f m a l e s w i t h e i t h e r SR o r ST g e n o t y p e , we w a n t t o k n o w t h e d i s t r i b u t i o n o f t h e p r o p o r t i o n o f e g g s l a i d a t t i m e t w h i c h w i l l d e v e l o p i n t o f e m a l e s . L e t n_. be t h e n u m b e r o f f e r t i l i z e d e g g s t h e j - t h f e m a l e l a y s i n t h e i n t e r v a l ( t - A t , t + A t ) a n d x_. be t h e n u m b e r o f d a u g h t e r s i n t h a t b a t c h . L e t m be t h e n u m b e r o f m o t h e r s a n d N = E n . . , j 3 A ( t ) = E x. /N ( 2 ) j 3 i s a u s e f u l s t a t i s t i c . To t e s t t h e v i r i l i t y m o d e l w i t h d a t a p r e s e n t e d i n T a b l e 6 , t h e f o l l o w i n g q u a n t i t i e s a r e u s e f u l . E ( A ( t 1 ) - A ( t 2 ) ) = E ( A ( t i ) ) - E ( A ( t 2 ) ) ( 3 ) V a r ( . A C t 1 ) - A C t 2 ) ) = V a r ( A ( t j ) ) + V a r ( A ( t 2 ) ) - 2 C o v ( A ( t x ) , A ( t 2 ) ) ( 4 ) X . ' s a r e i n d e p e n d e n t i d e n t i c a l v a r i a b l e s a n d a r e b i n o m i a l l y d i s t r i b u t e d g i v e n n a n d f ( t ) w h i l e n a n d f ( t ) a r e u n c o r r e l a t e d E (X) = E E E ( X | f ( t ) = z , n = n ) P r o b ( f ( t ) = z , n = n ) z n = E E z n P r o b ( f ( t ) = z ) P r o b ( n = n ) = E ( f ( t ) ) E ( n ) (5) . 162 E X 2 E X E ( X 2 | f ( t ) = z , n = n ) P r o b ( f ( t ) =z ) P r o b (n= n ) z n £ I { ( z n ) 2 + n z ( l - z ) } P r o b ( f ( t ) = z ) P r o b ( n = n ) z n E ( n 2 ) E ( f 2 ( t ) ) + E ( n ) E ( f ( t ) ) - E ( n ) E ( f 2 ( t ) ) V a r X + E X 2 - ( E X ) 2 V a r ( n ) E ( f 2 ( t ) ) + (E (n ) ) 2 V a r ( f ( t ) ) E (n) ( E f ( t ) - E f 2 ( t ) ) (7) I f t h e r e i s h o d i f f e r e n t i a l m o r t a l i t y among g e n o t y p e s , we c a n a s s u m e E ( n ) = N/m a n d d e r i v e t h e f o r m u l a e f o r E ( A ( t ) ) a n d V a r ( A ( t ) ) . H o w e v e r , f r o m e x p e r i m e n t e r s ' p o i n t o f v i e w , i t i s sometimes d e s i r a b l e t o i n c o r p o r a t e d i f f e r e n t i a l m o r t a l i t y i n t o t h e m o d e l a n d f i n d a t e s t s t a t i s t i c w h i c h i s r e a s o n a b l l y r o b u s t t o t h e c h a n g e i n m o r t a l i t y . H e n c e , A ( t j ) - A , ( t 2 ) i s a u s e f u l s t a t i s t i c • I n a d d i t i o n , t h e p r e s e n t v i r i l i t y m o d e l c o n t r a s t s t h e c o n v e n t i o n a l o n e i n t h a t , a s f e m a l e s g e t o l d e r , a d e c r e a s e i n c o n t r i b u t i o n b y o n e o f t h e t w o m a l e g e n o t y p e s i s p r e d i c t e d . . To t e s t t h e m o d e l , i t i s n e c e s s a r y a n d s u f f i c i e n t t o p r e s e n t e v i d e n c e f o r t h e d e c r e a s e ( i e , A ( t ! ) - A ( t 2 ) > 0 ). L e t w be t h e l a r v a l v i a b i l i t y o f m a l e s r e l a t i v e t o t h a t o f f e m a l e s ( u s u a l l y w«1 ) . L e t n . ' a n d x . ' b e t h e 3 D a c t u a l n u m b e r o f p r o g e n y a n d t h e a c t u a l n u m b e r o f d a u g h t e r s r e s p e c t i v e l y o f t h e j - t h f e m a l e w h i c h e m e r g e d a n d w e r e c o u n t e d . l e t N' = £n_. ' . n ^ , s t r i c t l y s p e a k i n g , i s t h e c o r r e c t e d n u m b e r o f p r o g e n y s u r v i v i n g t o e m e r g e n c e i f t h e r e l a t i v e l a r v a l v i a b i l i t y o f m a l e s i s 1. A ( t ) s h o u l d b e m o r e p r o p e r l y r e d e f i n e d • a s m m v : 1 6 3 /m = E ( n ' ) S i n c e n ' a n d , E E ( n ' | f ( t ) = z , n = n ) P r o b ( f ( t ) = z ) P r o b ( n = n ) n = ( n - x ) w + x , w h e r e x i s t h e n u m b e r o f d a u g h t e r , P r o b ( n'=n'| f ( t ) = z , n=n) = P r o b ( x = ( n ' - n w ) / ( 1 - w ) | f ( t ) = z , n=n) I B ( x ; z , n ) i f x i s n o n - n e g a t i v e i n t e g e r = E i n •' B (x ; z , n ) n = E ( ( n ~ x ) w + x ) B ( x ; z , r i ) x ( l - w ) z n + nw T h e r e f o r e , E ( n ' ) = E ( n ) ( ( 1 - w ) E f ( t ) +w) E ( n ) = N ,/m • ( 1 / w ) ( 9 ) w h e r e w = (1-w) E ( f ( t ) ) + w. P u t t i n g ( 2 ) ( 5 ) a n d ( 9 ) t o g e t h e r E ( A ( t ) ) = m E ( X ) / N ' = E ( f ( t ) ) / w ( 1 0 ) S i m i l a r l y , c o m b i n i n g ( 2 ) ( 7 ) a n d ( 9 ) w i t h t h e a s s u m p t i o n t h a t E ( n ) = V a r ( n ) ( f o r i n s t a n c e , t h e z y g o t i c c o n t r i b u t i o n o f a n i n d i v i d u a l f e m a l e f o l l o w s t h e P o i s s o n d i s t r i b u t i o n ) , we o b t a i n V a r ( A ( t ) ) = 1/(N'w) -E ( f 2 ) + 1 / ( m w 2 ) - V a r ( f ( t ) ) + 1/(N'w) • (E ( f ( t ) - E ( f 2 ( t ) ) = l / ( m w 2 ) - V a r ( f ( t ) ) .+ 1 / ( N ' w) • E ( f ( t ) ) ( 1 1 ) T h e o n l y t e r m i n (3) a n d (4) n o t y e t s o l v e d i s C o v ( A ( t i ) , A ( t 2 ) ) w h i c h i s C o v { E x /N ' , E x„ ./N_ ' } m m _ -= E E 1 / ( N 1 ' N 2 ' ) C o v ( x 1 1 # x ) i = l j = l •• m • 3 m = 1 / ( N 1 ' N 2 ' ) E C o v ( x l j f x 2 j ) ( 1 2 ) w h e r e x , a n d x„ . a r e - t h e n u m b e r o f d a u g h t e r s o f t h e i - t h H • 2 j f e m a l e a t t i m e t a n d o f t h e j - t h f e m a l e a t t i m e t ^ r e s p e c t i v e l y . N o t e t h a t x, . a n d x„ . a r e u n c o r r e l a t e d i f i ^ j . L e t C o v ( X ^ , X 2 ) d e n o t e s t h e common c o v a r i a n c e o f X. . a n d X„ . . ID 23 G o v ( A ( t ) , A ( t 2 ) ) = m/(N 'N ') C o v ( X , X ) = m/(N 'N ' ) (EX X - E X ] [ E X 2 ) ( 1 3 ) E ( X 1 X 2 ) = E E E E E { X X I f ( t 1 ) = z 1 , f ( t 2 ) = z 2 , n 1 = n,n = n 2 } z ! z 2 n i n 2 1 2 1 v 1 ^ ^ £-• P r o b { f ( t x ) = z x , f ( t 2 ) - z 2 / n 1 = r i i , n 2 = r i 2 ) ( 1 4 ) E {^ 1X 2| f ( t 1 ) = z 1 , f ( t 2 ) = Z 2 , n 1 = n i , n 2 = n 2 } = E E x j X g P r o b { X p x j , X 2 = x 2 | f ( t j ) = z j , f ( t 2 ) = z 2 , n x = n i , n 2 = n 2 } x 1 x 2 E E x 1 x 2 B ( x 1 ; z 1 , n i ) B ( x 2 ; z 2 , n 2 ) X l X 2 1 ^ ± i i ^ ^ ^ = z 1 z 2 n m 2 S i n c e n^ and n^ a r e i n d e p e n d e n t f r o m f ( t ) and a r e m u t u a l l y : i n d e p e n d e n t f r o m (14), we o b t a i n E ( x i V = E E E E ' z 1 n 1 z 9 ri 9 P r o b ( f ( t i ) =z i , f ( t o ) = z j ) z1 z 2 n1 n 2 • P r o b ( n i = m ) P r o b ( n 2 = n 2 ) = E ( n j ) E ( n 2 ) E (f ( t j ) - f ( t 2 ) ) (15) From (13) and (15), we have Cov (A (t ) , A (t ) ) = m/(N N ) E ( n 1 ) E ( n 2 ) C o v ( f ( t x ) , f ( 1 2 ) ) = 1/m 1/ (wjw 2) Cov (f ( t j ) , f ( t 2 ) ) (16) where w. = (1-w) E ( f ( t , ) ) + w i = 1 o r 2. I t i s n u m e r i c a l l y f e a s i b l e t o c a l c u l a t e C o v ( f ( t ) , f ( t )) . T h e r e f o r e , E ( A ( t )-A ( t 2 ) ) and V a r ( A ( t ) - A ( t 2 ) ) i n (3) and (4) can be c a l c u l a t e d f r o m (10) (11) and ( 1 6 ) . In p r a c t i c e , i t s u f f i c e s t o use (17) i f t h e n u l l h y p o t h e s i s can be r e j e c t e d o r t o use (18) i f t h e n u l l h y p o t h e s i s c a n be a c c e p t e d . Max ( t l f t 2 ) = Max {Var ( A ( 1 1 ) - A ( 1 2 ) ) > = V a r ( A ( t x ) i + V a r ( A ( t 2 ) (17) Min ( t l f t 2 ) = Min {Var (A ( t i ) - A ( 1 2 ) ) } = M a x ( t l f t 2 ) - l/(mw 1w 2) / V a r ( f ( t ! ) -Var (f ( t 2 ) ) (18) (17) can be j u s t i f i e d s i n c e , as t ^ - t 2 becomes s u f f i c i e n t l y l a r g e , A ( t j ) and A ( t 2 ) behave i n d e p e n d e n t l y . The A p p l i c a t i o n of A ( t , ) - A ( t 2 ) to Data of Table 6 N u l l - H y p o t h e s i s - Females have not remated in the exper imenta l p e r i o d or females have remated but i n t e n s i t i e s of v i r i l i t y s e l e c t i o n remain unchanged as females remate. In both cases , the expected va lues of A ( t , ) - A ( t 2 ) are always 0 w h i l e the standard e r r o r range from 2.05% to 2.4%. The observed va lues of A(8)-A(14) =4.02% and A(5)-A(14) =5.78% are both s i g n i f i c a n t l y d i f f e r e n t from e x p e c t a t i o n . In a d d i t i o n , the N u l l - h y p o t h e s i s expects A ( t ) to be a l i n e a r f u n c t i o n of t w i t h s lope b=0. With the observed. A ( t ) va lues of Table 6 and v a r i a n c e s c a l c u l a t e d from (11) , r e g r e s s i o n y i e l d s a z va lue of -2 .10 (P<0.02) i f b indeed i s 0 . The N u l l -hypothes i s i s r e j e c t e d . A ( t , ) - A ( t 2 ) i s a r a t h e r weak t e s t , n e v e r t h e l e s s , i s s t i l l s t rong enough to r e j e c t the N u l l - h y p o t h e s i s . On the other hand, changes between observed A ( t ) va lues fo r t = 5, 8, 11 arid 14 are not s i g n i f i c a n t l y d i f f e r e n t from the expected changes based on the two expected curves (v 2 =.52 and v 2 =.73) of F i g . 5 . T h e C o m p u t a t i o n o f L ( A i ) / L ( A 2) G i v e n t h e d a t a o f m f e m a l e D r o s o p h i l a , t h e j - t h o n e p r o d u c i n g n_. o f f s p r i n g , among t h e m x_. a r e d a u g h t e r s , i t i s p o s s i b l e t o c a l c u l a t e t h e l i k e l i h o o d o f o b t a i n i n g t h e g i v e n d a t a . T h e l i k e l i h o o d i s a f u n c t i o n o f r e m a t i n g r a t e A. m L ( A ) = n P r o b (x . I n . , A) j - 1 ' 3 3 F o r a g i v e n n_. a n d A a t t i m e t ( = 14 i n F i g u r e ^ ) , P r o b ( X = X j ) E P r o b ( X = x . , f ( t ) = z ) z 3 E P r o b ( f ( t ) = z ) P r o b ( X=x.| f ( t ) = z ) z ^ E P r o b ( f ( t ) =z ) B ( x . ; n . , z ) z ^ ^ T h e f i r s t t e r m i s p r o v i d e d b y ( 1 ) a n d t h e s e c o n d t e r m i s t h e B i n o m i a l p r o b a b i l i t y . L ( A 1 ) / L (A 2) c a n t h e r e f o r e be c a l c u l a t e d . 

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