EVOLUTIONARY GENETICS Concepts and Case Studies Concepts and Case Studies AG = G(Y-PP) G + 2M M /=i Edited by Charles W Fox Jason B Wolf Copyrighted mate ■ EVOLUTIONARY GENETICS Copyrighted material * EVOLUTIONARY GENETICS Concepts and Case Studies Edited by Charles W Fox Jason B Wolf OXFORD UNIVERSITY PRESS 2006 OXFORD Oxford University Press, I n c publisher works that further Oxford University'* objective of excellence in research, scholarship* and education, Oxford New York Auckland i ape Town Dar es Salaam Hong Konp Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil U i i l r Crrch Republic France Greece Guatemala H u n g r y Italy japan Poland IVirtugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vsrmam C o p y r i g h t © 0 b y O x f o r d U n i v e r s i t y Press, I n c Published by Oxford Unisrrsity Press, l o c 198 Madison Avenue, New York, New* York 10016 www.aupamn Oxford it a repstered trademark of Oxford University Pre» All right* reserved N o part of t h n publication may be reproduced* stotcd in a retrieval system, or transmmrd in any form or by any means* electronic, mechanical, photocopying* recording or otherwise, without thr prior permi**Hin of Oxford Uniteniry Prr** library of Congress Carak^Ln$*in-l\jhlicarion Data Evolutionary genets»; concepts and case srudhcVrdited by Oiaries V Pox, Jason B Wolf p ion Includes bibliographical rrtereiKev M N - I J 978*0-19-516817-4; 978-CM9-5I6818-1 jpbL) tSBNO J9 516817 ; A S I (phk.) L Kvotunonary genetics | I ) N I M : L Genetic*, Population 2- F.volufson 3, Gcitotypt* 4T M o M s Genetic* Variation (Genetics) Q H 4SfF.92S 2005) Fox, Charles W I I Wolf, Jason K QH390.E94 2005 572J'3S—dc22 2005011131 Printed ill the United States of America on acid-free paper Preface E v o l u t i o n a r y genetics is broad field that has T h e signature o f this r e v o l u t i o n is clearly seen 111 seen particularly r a p i d g r o w t h and expansion this v o l u m e , in w h i c h t h e m a j o r i t y o f chapters in recent years T h i s diverse field is unified hy a sec discuss patterns o r processes t h a i occur at t h e o f m i r r o r -image goals: (1) t o understand the impact molecular level o r have been influenced by t h e t h a t e v o l u t i o n a r y processes have o n the patterns o f availability of molecular d a t a genetic v a r i a t i o n w i t h i n and a m o n g p o p u l a t i o n s o r A l t h o u g h w e m a y define evolutionary genetics species and (2) t o understand the consequences o f as a single integrated f i e l d , there is a c o n t i n u u m in these patterns o f genetic variation l o r various evolu* t h e degree t o w h i c h research is e v o l u t i o n a r y versus l i o n a r y processes Research i n evolutionary genetic* genetic stretches across a c o n t i n u u m o f scale, f r o m studies informs molecular geneticists, whose primary interest At one extreme» evolutionary genetics o f D N A sequence e v o l u t i o n (e.g Chapters and 9i may he f i n d i n g and characterizing genes affecting t o studies o f multivariate phenorypic evolution (e.g., traits, of the consequences t h a t p o p u l a t i o n suhdivi* C h a p t e r ) , and across a c o n t i n u u m o f rime, f r o m siou and linkage d i s e q u i l i b r i u m have o n their inter ancient events that lead t o current species diversity pretation o f associations between loci and trait (e.g., Chapter 281 t o r a p i d e v o l u t i o n seen over rela- expression (e.g., Tcmpleton et aL 2005) At t h e other tively short t i m e scales in experimental e v o l u t i o n extreme, evolutionary biologists may use t h e results studies (Chapter ) o f these *gene discovery" studies t o identify genes A major cause o f the recent g r o w t h and e x p a n - that underlie e v o l u t i o n a r y i m p o r t a n t genetic varia­ t i o n o f evolutionary genetics has been the modern l i o n (e.g.* Beldade et a l 0 ) However, differ» r e v o l u t i o n in molecular biology, w h i c h has fueled entitling research into t h e extremes o f these the g r o w t h o f areas o f evolutionary genetic* focused categories is b e c o m i n g increasingly o n the analysis o f sequence d a t a , the g e n o t y p e - e v o l u t i o n a r y approaches permeate genetics just as difficult as phenotype relationship, and genome e v o l u t i o n molecular biology permeates evolutionary biology A l t h o u g h many o f t h e questions at the forefront T h e development o f this b o o k was i n i t i a t e d o f the field have been a r o u n d stnee the early days late in 0 I t was conceived as a c o m p a n i o n t o o f evolutionary genetics (e.g., since the M o d e r n Evolutionary Ecology: Concepts arul CMS*' Studies Synthesis), the availability o f relatively inexpensive (edited by Fox et a l 0 ) , also published by h i g h - t h r o u g h put genetic technology and t h e result- O x f o r d University Press O u r p r i m a r y objective i n i n g large databases o f molecular genetic data has led this b o o k , as in t o the emergence o f m a n y new areas o f study provide a c o l l e c t i o n of readings that w i l l i n t r o d u c e and a sort o f r e v o l u t i o n in e v o l u t i o n a r y genetics, students t o concepts and c o n t e m p o r a r y its c o m p a n i o n v o l u m e , is to research p r o g r a m s in evolutionary genetics O u r hope w h e n some o f the research areas and thus discover t h e conceiving this volume was that it m i g h t be adopted vast literature t h a t w c have been unable t o include ai« a text f o r graduate courses and seminars* as ha* here, been the case for Evolutionary Fxology We thus T h e volume is structured i n t o six parts A l t h o u g h targeted the level o f this book so that it can be used this might suggest that there are six clearly defined by advanced undergraduates, graduate students, sets o f topics, such structuring is somewhat a r t i f i ­ and established researchers in genetics or e v o l u t i o n cial Evolutionary genetics is a highly integrated l o o k i n g for a concise i n t r o d u c t i o n t o evolutionary field w i t h n o clear lines d i v i d i n g research topics genetics Authors were asked t o target this audience T h e structure o f t h e book is simply a convenient w h i l e w r i t i n g , and reviewers and t h e editors focused w a y o f collecting m o r e related topics together We on n u k i n g the volume accessible t o this audience start w i t h a collection o f chapters presenting many w h i l e reviewing each chapter o f the principles o f e v o l u t i o n a r y genetics that serve Chapter authors are all leading researchers in as the f o u n d a t i o n for the rest o f the subject (Part I) their fields and were chosen t o p r o v i d e their partic­ For this part readers need have o n l y a decent back­ ular perspectives on a topic Chapters thus represent g r o u n d in genetics, t h o u g h a b a c k g r o u n d in e v o l u ­ the current stage o f evolutionary genetics better than tionary biology w i l l certainly be helpful Later parts any single-authored t e x t b o o k c o u l d , a n d the diver­ o f the book assume an understanding o f b o t h general sity o f authors introduces readers t o the divcrsiry o f concepts o f genetics and the concepts presented in ideas, approaches, and o p i n i o n s t h a t are the nature earlier p a n s Parts I W V are ordered hierarchically o f science However, a m u l t i - a u t h o r e d textbook starting at the basic level o f biological c o m p l e x i t y , presents special challenges A u t h o r s vary in the level t h e D N A sequence (Part I I ) , b u i l d i n g t h r o u g h devel­ at w h i c h they present material and in the a m o u n t o p m e n t (Part I I I ) t o studies o f complex phenotypes o f b a c k g r o u n d that they expect readers t o have (quantitative genetics; P a n I V ) and on t o the inter­ Authors also vary in their w r i t i n g styles, t h e w a y actions between i n d i v i d u a l s and their environment that they organize their chapters a n d , o f course, each (sexual and social selection; also Part I V ) These has a unique perspective o n the overall field We parts are f o l l o w e d by one on the genetics o f species have attempted t o minimize this v a r i a t i o n t h r o u g h differences and speciation (Part V ) that integrates a u t h o r guidelines and by aggressively e d i t i n g and across the hierarchy o f complexity t o investigate wrhat revising chapters H o w e v e r , some variation a m o n g is often considered the most f u n d a m e n t a l problem chapters is unavoidable and reflects the variation in in evolutionary biology: the o r i g i n o f species, l a s t l y styles and approaches c o m m o n t h r o u g h o u t science w c include a part i l l u s t r a t i n g h o w the theoretical, A s w i t h any b o o k , especially an edited v o l u m e , conceptual, and e m p i r i c a l approaches developed in this book is not comprehensive T o keep the length previous chapters are applied t o specific p r o b l e m s of the book practical, and the price a f f o r d a b l e , w c in b i o l o g y (Part V I ) T h e potential choice o f topics had t o impose restrictions o n chapter length and the here is e n o r m o u s but w e could choose only a couple number o f references T h i s a l l o w e d us t o increase o f representative examples that w e find particularly the diversity o f subjects covered but at the expense exciting, o f depth o f coverage M o s t topics could fill an entire Because w c enforced length restrictions on book ( a n d m a n y are indeed the subject o f entire chapters, many i m p o r t a n t and exciting topics were books) Chapters are intended t o serve as introduc­ necessarily left o u t O t h e r topics were outside the tions t o their t o p i c , focusing o n basic concepts expertise o f t h e authors o r w e r e i m p o r t a n t topics rather than becoming comprehensive reviews (the that did not fit well into the structure o f the chapters reference l i m i t was intended t o minimize t h e latter) W c thus include a large number o f boxes focusing Such a f o r m a t imposed unavoidable l i m i t a t i o n s o n on specific topics presented largely independently authors a n d , as e d i t o r s , w e take responsibility for o f the m a i n body of the text w i t h w h i c h they arc the necessary omission o f missing topics and the associated W i t h the exception o f Box 24.1 { w h i c h lack o f many a d d i t i o n a l references that are perhaps w c use t o introduce Part V, Genetics o f Speciation), equally a p p r o p r i a t e as examples o r case studies all boxes appear w i t h i n the pages o f t h e chapters t o Chapters include a "Suggestions for Further Reading" w h i c h they arc most relevant M a n y w r crc w r i t t e n section t o guide readers o n where t o go next for by the same author as the chapter that they comple­ a d d i t i o n a l coverage o f t h e topic We hope that read­ ment; these largely e x p a n d o n topics m e n t i o n e d in ers w i l l be inspired t o delve m o r e fully i n t o at least the main body o f t h e chapter o r they present a topic that did not fit well in the main body of the chapter Other boxes were written by scientists who did not write full chapters; these boxes read more like mini-chapters Most could indeed have been full chapters but, alas, the realities of publish­ ing prevented us from including every chapter we would want* We also included three boxes on model organisms in biology* (in Pan V!) since so much of what we know about evolutionary genet* ics, and biology in general, comes from studies of model organisms The choice of box topics reflects the views of the editors, the reviewers, and the many chapter authors who suggested topics for boxes Lastly, we have compiled a glossary of terms» Initially wc asked authors to include footnotes or tables defining the terminology of their Held but the large number of submissions made this impractical, so we converted these (at the suggestion of multiple authors) to a glossary at the end of the text* It is by no means a comprehensive glossary of genetics or even evolutionary genetics terms* it is intended to aid the reader by providing definitions for terms that might be considered jargon special to some areas of research, or terms that you know you once learned but may have since forgoncn; that is, the terminology not necessarily standard in a working scientist's vocabulary* The glossary entries are largely written by the chapter authors, heavily supplemented (and editcd> by the editors; we have thus given the appropriate author credit after each entry In a few cases we have included multiple entries for a single term because multiple entries were submitted by authors and the difference between those entries was itself informative Each chapter and box was reviewed by at least one other contributor to the book and, in most cases, one or more external reviewers Wc are truly indebted t o all these reviewers for generously donating their time and providing thorough and constructive reviews Without their help it would nor have been possible t o produce such a volume given the vast diversity of topics covered and the limits of the editors* expertise We thus thank the external reviewers, including Hiroshi Akashi, Cerise Allen, Bill Atchlcy, Score Carrol), James Crow, Mary* Kllen Cze^ak, Tony Frankino, Oscar Ciagginrti, C William Kirkpatrick, Larry Leamy, Susan Lindquist, Curt ivcly, Manyuan )~ong, Bryant McAllister, Tami Mcndclson, Dchra Murray, Joshua Mutic, John Obrycki, Susan Perkins, Massimo Pigliucci, Richard Preziosi, Will Provine, David Queller, Glenn-Peter Sactre» Laura Salter, Douglas Schemske, llamish Spencer, Marc Tatar, Kric (Rick) Taylor, L i n d i Wahi, Cunrcr Wagner, John Wakeley, Bruce Walsh, Joe Williams, and a few others who asked to remain anonymous Wc also thank Lisa Hitchcock, Denise Johnson, and Oriaku N j o k u for help proofreading chapter* and references* Finally, and most importantly, we thank the authors for their willingness 10 invest the subsian* rial amount of time needed t o write excellent chap* ters and boxes* The success of the volume ultimately depends on the quality of the contributions by authors Wc are fortunate to have recruited an out­ standing group o f scientists who dedicated tremen­ dous time and effort to making this project a success Thank you for being such a wonderful group of people with which t o work! Charles W Fox Jason B* Wolf Stochastic Processes in Evolution 67 :00 50 Gererat^r 5.1 The probability Thar a new mutanon will have been lost by a particular generation* FIGURE of extinction within the first few generations is remarkably similar among all three mutations In particular; the probability of loss in the first gener­ ation is close to one third* as we already know* After a few generations, the extinction probabilities of advantageous mutations appears t o asymptote while that for the neutral allele continues on toward I The fixation probability of the mutation with a 10% selective advantage is particularly striking as, even though this would be considered very strong selection, % of the time rhis wonderful mutation is lost As these extinction probabilities are among the most important quantities that we have in evolution* it is imponant to know how they were obtained* The curves in Figure 5.1 come from the theory of branching processes, which is beyond the scope of this chapter Feller (1968) remains one of the clear­ est expositions of these processes ami is highly recommended A derivation of the probability of ulti­ mate extinction, the asymptotic values in Figure 5.1, may be found in Box 5.1 There it is shown that the probability of ultimate survival of a new mutation with a selective advantage of s is approximately 2$toz* where « Thus, the probability that a new mutation will enter the popu­ lation in a particular generation and ultimately fix is 2NYj We could call it a success when a new mutation arises that ultimately fixes in a particular generation and a failure when this doe* noi occur This language shows that the time until the appear­ ance of the first mutation that ultimately fixes has a geometric distribution That is, the probability that ihc origination time is i generations is 2Nrs\t ~ 2NrsY~\ 69 This approach has one conspicuous peculiarity; Why should the selection coefficients of all ongin.it* mg mutations be the same* If a substitution increases the level of adaptation of a species, would not subse­ quent advantageous mutations have smaller selec­ tion coefficients? Kxplicif models of adaptive evolution from KisherS (1958) original geometric model up through O r r s (2002) recent work all have the property that a sequence of substituting alleles has decreasing selection coefficients I See Box 5,2 lor a simulation of one of Orr's models,) In fact they all have the property that evolution stagnates after a few substitutions either because the supply of advantageous mutations has been exhausted or because the selection coefficients become so small that originations fail to appear in an e v o l u t i o n a r y reasonable span of time Under these models, evolution produces a small burst of substitutions and then nothing An intriguing aspect of these models is chat the number of substitutions in a burst is insensitive t o the mutation rate, population size, M\K\ selection coefficients, l o r example, in some of the models the mean depends on the loga­ rithm of the population size; in others ir is inde­ pendent of population sue (Gillespie 2002), box 5.2 shows how t o study some properties of a hurst using computer simulations I'or continuous evolution we need only add one new element: a changing environment If the envi­ ronment changes, a new hurst of substitutions can occur We expect a similar burst of substi rut urns to follow each change in the environment If A is the Copyrighted material Principles of Evolutionary Genet IC5 70 Alan O r r (e.g., O r r 2002) has been w o r k i n g o n some fascinating properties o f a simple model o f adaptive e v o l u t i o n called the m u t a t i o n a l landscape model* Under this m o d e l , w c imagine rhac some allcle w i t h fitness w$ is currently fixed in the p o p u l a t i o n * Suppose that there are n alleles one m u t a t i o n a l step away f r o m the fixed allcle a n d that t h e fitnesses o f these n allclcs arc assigned at r a n d o m and independently f r o m the same p r o b a b i l i t y d i s t r i b u t i o n (A n o r m a l d i s t r i b u t i o n w o r k s fine here*} T h e neighboring allc­ lcs arc labeled such that A} is the most fit allcle, Y is the next most fit* and so f o r t h If selection is sufficiently s t r o n g , then only alleles that are m o r e fit t h a n the f i x e d alle­ les can themselves become fixed* The p r o b a b i l i t y that the « h allcle fixes is -, J = l,2,*.*,m 5,+s2 « + *_ if there happen t o be m allclcs that arc m o r e fit than t h e fixed allcle I n this expression 5, = wt-u\x is just the selection coefficient o f the i t h allcle T h u s , the p r o b a b i l i t y that a particular allcle fixes is p r o p o r t i o n a l t o its selection coefficient* as seems o b v i o u s A s i m u l a t i o n o f this model begins w i t h n + alleles w i t h r a n d o m fitnesses and the fixed allcle being the / t h most fit allcle / should be viewed as a parameter o f the modcL Figure I shows the results o f 10 replicate evolutions o f the model w i t h n = 10,000, / = , and fitnesses d r a w n f r o m a n o r m a l d i s t r i b u t i o n w i t h standard deviation , N o t i c e that even t h o u g h there are 19 alleles that are m o r e fit t h a n the originally f i x e d allclcs, e v o l u t i o n usually (7 o u t o f 10 times) stops after one o r t w o substitutions W h i l e , on average, the biggest j u m p in fitness occurs w i t h the first substitution, the repli­ cates show a great deal o f scatter in the fitnesses o f f i x e d allclcs* 0,05 0.045 i 004 0035 003 0.Q2S Step FIGURE Ten trajectories f r o m the m u t a t i o n a l landscape m o d e l Copyrighted materi Stochastic Processes in Evolution BOX 5.2 71 (cent.) T h e p y t h o n a i d e (or ( h i * s i m u l a t i o n is below Readers- are encouraged t o p i a \ a r o u n d w i t h the model and f i n d its properties P y t h o n code for m u t a r i o n a l landscape s i m u l a t i o n front random import * f r o m math i m p o r t * randont_fitness - l a m b d a : gausstO.0,0.01) del titncss_array(w, n , rngh " R e t u r n s a list o f those allclcs m o r e fit rhan w " hetrcr_alleles = |\vj f o r i in xrangcln): r = mgO if r > w : better_allclcs,appcndfr) bcncr_allelcs.sonO return bettcr_aHcles defchoosc_allc)c( fitnesses): " " R e t u r n s the i n d e x o f the f i x e d allele T h e first allele in fitnesses is the s t a n d a r d / " " * selection_eoe(s = [f - f i t n e s s o | | l o r f in fitnesses] sum_sc ^ sum(sclection_eoefs) probabilities = [s I sum_sc (or s in selection_cotfs| running_sum - 0.0 r - random!) i for p in probabilities: running_sum + = p if r u n n i n g sum > r: return i i • I def e v o l u t i o n a l , «tart, r n g ) : initial_alleles - |rngO for i in x r a n g e ( n + D | initial_alleles.sorr(i allclcs ■ i n i t i a l allclcs|-siart:| n x e d _ a U e l c s M ( , allclcs|0])l while lenialleta) > I : lixed_allele = (chwsc_alIele(allelcsM fixed_alleles,appendMfixed_allele T alldes|li*ed allelc|)} alleles = fiincs*_array(fixtd.alleles[-l][l| % n, rnj** return fixed alleles rate o f change per generation in those aspects of We have arrived at a rate o f substitution that is rhe e n v i r o n m e n t t h a t affect o u r locus, then the rate essentially independent o f the p o p u l a t i o n size, the of substitution per generation is just the rate of m u t a t i o n rare, and the strength o f selection and change o f the e n v i r o n m e n t , K about as different from o u r previous rate, p - 2Nvs^ times the mean number o f f i x a t i o n s f o l l o w i n g a change, as w e c o u l d imagine There is n o consensus in p o p u ­ lation genetics a b o u t w h i c h race is better or, in fact, whether either is w o r c h v of o u r a t t e n t i o n , Copyrighted material 72 Principles of Evolutionary Genetics In this section wc have given a description of the stochastic dynamics of originations of advanta­ geous mutations This is an important stochastic process not only because of its consequences for adaptation, but because of the hitchhiking of genome segments that invariably accompanies the substitu­ tion of a new mutation In the next three sections wc will look at the stochastic forces that impact mutations once they leave the caldron and begin their sojourn in the realm of common alleles Genetic Drift The origins o f much of mathematical population genetics, including the stochastic theory, can be found in Fisher's monumental 1922 paper* In this paper Fisher considers two models that incorpo­ rate randomness The first appears in a treatment of the survival probability of "individual genes*1 as described previously Fisher went on to treat "Factors not acted on by selection." and, in so doing, intro­ duced genetic drift t o population genetics: If p be the proportion of any gene, and q its allelomorph in a dimorphic factor, then in n individuals of any generation we have 2np genes scattered at random Further, if a second generation of n individuals be now formed at random, the standard departure of p from its previous value will be *Jpql2rt for a diploid population The reason for using binomial sampling is not at all obvious or even plausible In this section will we (1) illustrate the problem with binomial sampling, (2) show that Fisher's standard deviation is reasonable without binomial sampling, and (3) discuss some of the prop­ erties of genetic drift The motivation for mathematical models of genetic drift is usually somewhat contrived The hagof-marbles metaphor that is often used in teaching genetic drift is a wonderful device for learning rhc consequences of binomial sampling» but the biolog­ ical underpinnings are not at all clear To see this, imagine a haploid population with two allcles, A\ and A ; , with frequencies p and q = I -p If there are rV individuals in the population, then Np o f these will be A | and Nq will be A2* To form the next gener­ ation, we imagine that the number of offspring for each individual is chosen at random from the same probability distribution ct the number of offspring from the i t h At be X, and from the ith A» be Y r The allele frequency in the next generation will be Number of A{ offspring X Total number of offspring X + Y where X = Xl+X2+ ,+XNf Y = Yl+Y1 o\ ■ He went on t o conclude that the rate of loss o f genetic variation is 1/4« (Later, Sewall Wright corrected this result t o 1/2«.) The loss of genetic variation due to this "Hagcdoorn effect" he thought was insignificant: As few specific groups contain less than 10,000 individuals between whom interbreeding takes place, the period required for the action of the Hagedoorn effect, in the entire absence of muta­ tion, is immense» Curiously, Fisher does not motivate or attempt to justify his assertion that the "standard departure of p' is yfpqfln (Standard departure is an old name for standard deviation.) Today, we typi­ cally model genetic drift with binomial sampling and from this obtain a standard deviation of + „+Vwr The bag-of-marbles metaphor suggests that the distribution of the number of / \ ( allcles in the next generation, J, is the binomial distribution Pro b{x^ = (yW-' But why? in our model, the number of Ax indi­ viduals in the next generation is called X and its distribution can be that of any positive integer-valued random variable For example, X could have a geometric, negative binomial, Poisson, or some other distribution And why should the total number of individuals, X + Y, be N? In fact, a binomial distri­ bution is only appropriate when two conditions arc met: The total number of offspring is set at some fixed number and the distributions of X and Y are Poisson Biologically, we are in trouble because stud­ ies of offspring distributions in natural populations Stochastic P r o c e w s in Evolution seldom* if ever, find Poisson distributions In general, the variance in the number of offspring is larger than the mean The idea of fixing the total number of offspring at N before forming the next generation is strange as well Population sizes of most species fluctuate significantly over relatively small numbers of generations, In our model, that fluctuation is embodied by the distribution of X + Y, which cannot be set at a fixed number N without disrupting the biological appeal of the model* Docs this mean that genetic drift is a flawed concept? Nut at all; it only means thai binomial sampling is not a good mirror of the demography of natural populations Fortunately, much of theo­ retical population genetics does not deal directly with the binomial distribution but uses large N approx­ imations such as diffusion models For these* ihe binomial distribution is only used to obtain the variance ot p\ which can be obtained directly with­ out any reference to a binomial distribution To see this* first rewrite p ' a s X-E{X} E[XL X-E\X}*Y-E{Y) 1+ E{X] ? = E(x}.f:{v| E{X) + £{V1 (5.4) where the notation E\X] refers to the expected value (or mean I of X An application of the delta method of statistics will allow us to obtain useful approximations of p\ Toward this end, define X-EJXJ ind • *y X-E{X} + Y-ti{Y) h{X\+E{Y) (The 8s are small when N is large because of the law of large numbers.) Note that H| 1/2N As consequence, the a m o u n t o f genetic v a r i a t i o n it the neutral locus w i l l also even­ tually decrease w i t h increasing p o p u l a t i o n size 11 Random Environments he last stochastic process TO be discussed is selec­ A n y o n e familiar w i t h genetic d r i f t w i l l recoil f r o m t i o n in a r a n d o m environment O u r goal is not t o the idea t h a t neutral v a r i a t i o n can decrease w i t h give an extensive treatment of this rich area, but increasing p o p u l a t i o n size T h e reason tor tins i* rather t o give a few simple results that can l>e used that the rate o f hitchhiking is increasing w i t h increas­ t o c o m p a r e the role o f this source o f randomness ing p o p u l a t i o n size ( p = 4Nvs) a n d , as a conse­ w i t h those discussed earlier All o u r w o r k w i l l focus quence neutral v a r i a t i o n is reduced* T h e nature of o n a two-nllelc, a d d i t i v e d i p l o i d model in w h i c h the the f u n c t i o n a l relationship between p and N fitnesses of the three genotypes are: in e v o l u t i o n is not at all clear A l t h o u g h w e frequently use p ^ 4Nvs in discussions o f adaptive e v o l u t i o n , AtA} this may w e l l he a p o o r choice as the underlying U U , model is so at variance w i t h o u r usual notions of A , ^ A ^ l+|U, +V,)/2 l + V/ adaptive evolution It is clear that w e cannot under* stand the relationship between neutral variation and Assume that the selection coefficients (.' and V, p o p u l a t i o n size w i t h o u t k n o w i n g m o r e about p change at r a n d o m t h r o u g h t i m e and that their relationship values in a particular generation arc independent o f between p and \ \ o u r results on genetic draft suggest all values in previous generations That is, assume that levels o f genetic v a r i a t i o n w i l l not necessarily t h a t \it and V, are not autocorrelated If p is the show a s t r o n g dependency on p o p u l a t i o n size This frequency o f the \ \ allele, then the change in its is a g o o d t h i n g as one conspicuous c o n u n d r u m in frequency in a single generation is No matter what the functional p o p u l a t i o n genetics has been that o u r drift-based theories predict a strong dependency of level* o f v a r i ­ Ap ation on population size but observations generally show a weak dependency at best This is often called 2l + p ( t/ ( +