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DOES SEX ACCELERATE EVOLUTION?
Vinton ThompsonrConmittee on Evolutionary Biology
University of ChicegoChicago, r11. 60537
Receivetl Ju]-y 10' 19?5
ABSTMCT: Most biologists bel ieve that sex (reconbinat ion) acceleratesad.aptation and evolution by speeding response to clirectional sefeetion. Thisbel-ief d.oes not hold up r:nder close serunity. Several experiments, a numberof computer simulations, and. various works of theory all suggest that sex wil-1acceferate response to selection only when populations are very small or whenthey exhibit substantial negative linkage clisequilibrim. Neither conditionappears to be especially conmon in nature, so the role of sex in evolutionremains enigmatie. Mod.el-s invoking migration and. mixing of populations ortemporally fluctuating envlronments may offer a way out, but the assumptionson which they are based are largely untested.. Sex mey act most often to slowor mod.erate response to selection, directly contrad.icting the notions that nowprevail. SeveraL unsettled. points must be resolvecl before we can ad"equatelyassess the role of sex in nature, arnong them: (f) Ooes evolution proceed.primarily through the reassortment of genes pre-existing at high frequency ordoes it proceed. through the combination ancl spreacl of new or previously raremutations? (2) Rre complex inter-Locus interactions or additive gene effectsthe rul-e in nature? (3) Are asexual populations regularly geneticallyinpoverished? ( l+) Does
Itg"oup selection play an important role in evolution?
Sex, genet ie recombinat ion, is a randonizing process, reshuff l ing genesalnong genomes and tearing apart ord.erly assoeiations of alleles at d.ifferentloci. But biologists regr:larIy assign to sex an apparently opposite roIe, aconstructive role, in nature. fhey ho1d. up sex as the primary source of novelgenotypes and. the single maJor mechanism facilitating progressive evolution.The f i rst assert ion must be true for most macroscopie organisms, the seeond isprobably fa1se. Beeause, contrary to prevalling belief, there is little or noevid.ence that sex speeds genetic adaptation to ehanged or changing environnents.In this paper I srumnarize the history of evolutionary interpretations of sexantl present some evid.ence that sex may most often facilitate evolution byslowing it d.own.
The Historical- Setting
Most populat ions of organisms part ic ipate in sexuaf processes, some eachgeneration, some intermittently. But historically biologists were slow torecognize the ubiquity of sex (Olby, 1966), They did. not recognize plants assexual beings until the end of the seventeenth centuryn and they overlookedthe sexual nature of protozoan eonJugation until the end. of the nineteenthcentury. Recombination processes in bacteria and viruses have been elucidatedonly in the last three decad.es. Nevertheless, omit t ing the special case ofmicroorganisms, the near rxriversality of sexual- processes becarne a wel-1entrenched tenent of biolory by the nid-nineteenth century. The burd.en ofproof fel1 on those who d.or.:.bted its applicability to partieular cases. Para-d.oxica11y, recognition of the ubiquity of sex suppressed. serious inquiry intolts ftnd.anental nature. Sex appeared to be co-extensive with life and many
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Evo1. Theory l-:l-31-156 (February, 19T6)
r32 V. THOMPSON
biologists interpreted. fertil ization as a seni-nystical life-renewing pheno-menon. Even in the late nineteenth centrrry, as the cybological facts offertil ization vere rrrveiled, this attltude lirgered on in the reJuvenescencetheories of Maupas, Bl l tschl i , and Hertwig (Jennlngs,] .929; Wei.smann, 1892).
But mid.-nineteenth century discoveries of several cases of parthenogenesis
and apomixis in higher organisms left open the possibility of interest inbiparental reproduction as a thing in itself. ff sex could be dispensed. withafber all, the reasons underlying its persistenee in most organisms becane ava1id. subJect of inquiry. After Darwln biologlsts could seek evolutionarybases for the retention of sex. fhe task feI1 initially to August Weismann, aGerman cybologist.
Early in his evolutionary stuclies Weismann concluded. that external factorsmust have no influence on the hered.itary tlisposition of organlsms, thatacquired characteristics are not inherited.. He cha.upioned this iclea so force-
fully that his na.me beenme synonyuous with anti-La,narckism in the popular loreof science. Weismannts strong anti-T'a.marekian stand raisecl anew a maJor ques-
tion that Darnrin never adequate\y resolvecl, the souree of hereditary variation.ttgowrttWeismann askecl, ttcan cleep-seated hered.itary charaeters arise at allt if
they are not proclucecl by the external influenees to rhlch the inclivid.ual is
exposed?rt The source of hered.itary variation, he answered:"is to be lookecl for in the fotm of reprocluction by whieh thegreat naJority of existing orgenisms are propogatecl: viz. o insexual reproductlon, or, as HH,ckel calls it a.nphigonic repro-ductlon. in amphigonic reprocluctlon two groups of heretlitarytend.encies are as it were cornbined. I regard this combinationas the cause of herectitary ind.ividual characters, and I believethat the produetlon of such characters is the true signlficanceo1' qrnphlgonic reproduction. The obJect of this proeess is tocreate those individual differences which form the material outof whieh rtatural selection produces new speeiestt (Weismann,
1BPt, p. 279).In other word.s Weismann postulateti that sexual- reproduction generates thegenetic variation that forms the raw material of naturaL selection.
Ttre observation that sexual reprocluetion generates hered.itary tliversity was
not original to Weismann. Plant breeders had been aiware of this fact for quite
a long time and the physieian Erasnus Darnin (grandfather of Charles) had. set
it clovn in the scientific literature in the late eighteenth centuryr complete
with a theory that asexual- propagation is coupleil with an inabiLity to evolve
novel or improvecl fo:ms (Dar:win, ]-.796, w. l+9r, 5aE). Charles Darr'' in hinse].f
at f i rst adhered to his grandfatherts viens on sex (De Beer, 1p50a, p. )+1) '
but 1ater in life he repucliated. the idea that crossing is the maJor source of.
herect i tary var iat ion (Oi.nr inn tB?5, Vof. I pp. 19?, 398, Vol. f I pp. 2\2,252)
and ad.opted a very ctlfferent view of the role of sex in nature. Weismannrs
contribution 1ay in r:nlting the facts of sexual reproduction with a coherent
theory of hereclity and. anchoring both in errolutionary theory. Our contemporary
unclerstand.ing of the evolutionary role of sex begins with Weismann and his works
on the subJect stil l cleserve study.Given Weismannts early leatl, we ur:ight suppose that the evolutionary theory
of sexual reproduction woulcl by non be fairly advanced'. This is not the case.
To the question posed by Weisnann (and. e:rpressed succinctly by Maynard. Snith'
19?1b, is ttlrhat use is sextt) we have yet to elaborate a really satisfactory
arswer. TLre reasons for this faiLure are not hard. to find. fn the first place
sex is not an ordinary evolutlonary attribute. By all appearanees it confers
on ind.ividual carriers an evolutionary tlisaclvantage, sometimes a very severe
one (Maynarcl Snith, 19?1a1 19rub, 19?l+). Consequentl-y marrSr have sought''
DOES SEX ACCMENATE EVOLUTTON? t??
consciously and othe:nrise, to find" the evolutionary atlvantage of sex in benefitsaccruing to whole populations. Fisher (1958, p. 50) even sr.iggested. that sexmay be the only exa^mp1e of a trait that has evolved for the aclvantage of speciesrather than individuals. Other cornnentators insist that the persistence ofsex be interpreted in terms of short term indiviclual adva.ntage (WiUians , 1956,l-gTr; Willia.rns and Mitton, 1973; Ghiselin, 1971+). Virtually all investigatorsfrom Weismann on (r89r, pp. zB8-289;1901+, p. 223) agree that sexual reprod.ue-tion must have once conferred. ind.iviclual selective advantage, sometime in theevoluti"onary past. Wtratever the outcome of this d.ebate, inter-demic or ttgrouptt
selection must be seriously investigated as an agent in the evolution of sex,and the ecological and evolutionary moclels for group seleetion are less wellestablished. than the traditional models for ind.ividuaL selection.
The second reason for our failure to establish a satisfaetory explanationfor sex is perhaps more fund.amental. Weismannrs theory and. its subseguentMend.elien elaborations (for an early exa.mple see East, 1918) prettict thatsexual adnixture of genomes wiJ.l generate herectitary variability and pronotethe formation of noveL hereditary combinations. But every theory of sexual acl-vantage nust hypothesize the nature of the genetic variation on which sexualsystems operate. Weismsnn sinoply assumed. that because natural sel-ection hasworked such tremenclous ehange in the organie worId., the store of stand.inggenetic variation must be very lerge ancl must be available to sexual crossingand. selection. However, the precise nature of the genetic variation on whichsex operates should, as we shall see, profountLly affect the roJ-e of sex in evolu-tion. And regard.ing the nature of selectable variation, population biologistsdo not agree. They divide into two ca,mps. fhe substance of the disagreementbetween these schools appears in especially sharp relief in their contrastingattituttes towarcls the evolutionary advantage of sex (Crow and Kimura, 1970r pp.313-315; Lewontin, 1974, p. f96), Ihey appeal- to very different moclels ofstand.ing genetic variation in natural populations. Consequently, they constructvery different models regard.ing the benefits of biparental reproduction.
fhe Fisher-lrtuller Mutation fheory of Sexual Ad.vantage
Ttre most eoherent eontenporary theory of sexual advantage derives fromearly work by Fisher (r9SO) and Mu1ler (fg32). They argued that in asexualpopulations tvo or more different ad.vantageous mutations can be incorporatedonly if they occur simulteneously in the sa,ne inclivid.ual or sequentially in thesame elone. Since mr:tation rates are Iow, sequential incorporation nust be theru1e, and the incorporation of several mutations must be a slow anit inefficientprocess. In sexual populations favorable nutations occurring d.uring a given timeperiod. in different ind.ivitluals may be brought together in their d.escendants.A1l- other things being equal, sexual populations shor.rld ineorporate combinationsof favorable mutations more rapidly than their asexual cowtterparts.
Several authors have clevbloped and quantified. the Fisher-!fuI1er argument(Mu]-l.er, 1958, 196\; Crow and Kimura, 1965, t959; Bodmer, 19?0t Maynard snith,1971b, f97lr ; Karl in, l r973; Felsenstein, 19?l+; Nyberg, 1975). Ulan (195?) '
Schrand.t and Ula.n (fgru), and Reed, Toombs and Barricelli (tg6l) have alsod.eveloped ideas along sinilar lines. .Llthough in prenises and detailed resultsthese works d.iffer in significant respects, they share: 1) the assumption thatinitial gene frequencies of favored. aIleles are ve?y small, and 2) ttre conclu-sion that sexual reproiluction can substantially accel-erate the rate of evolution.In all these mod.els evolution depends on the spread of rare favorable mutationsof small effect. They aecept inplicitly the classical theory of populationstructure (Dobzhansky, 1955, 19?O; Lewontin, 19?l+), which postulates that thepreponderance of seleetively relevant genetic variation ln a local populationconsists at any given time of a few favorecl alleles on their way toward.s fixation.
13h V. THOMPSON
Even granted the questionable premises of the elassical theory' the Fisher-Muller argr:nent may be more restricted in epplieation than its proponents havegenerally reeognized.. Using a clete:ministic haploid two-Iocus model' Eshel
ancl Fel6man (f9?0) have tlemonstrated that the postulated advantage of sexual
reprod.uction may depenct on rather special fitness relationships between loci.
They consider a population initially eonsisting entirely of 49 genotypes.
A mutates at a fow rate to a and B to !r vith fitness relationships as follows:
Genotype
Fitness
AB Ab sB
1"2"2
ab
"1
Eshel and. Feldman show that if the mutations are lnclivlttually tleleterious but
advantageous in conbination (so < I < s., ), and provictecl that the loci freely
recombine and nutation rates afe suffieiently small, the ttouble mutant ean
never increase in frequency much beyond the ortler of the mutation rate. fn art
asexual (non-recombining) population, by contrast, the double mutant, when it
occurs, vill increase to fixation. Kar1in and McGregor (f9?f) nave extencled
this result to two-locus cliploid systems. ltfuller hinself reeognized this
theoretical pitfall. It clrove hin to argue that the prevalence of sexual
reproduction testifies in iteelf to the leatling role of rfadtlitivert genetic
ef iects in evolut ion ( l tut ter, 1958, 195\).But Eshel antt Felclman analyze another set of relations that cast even
greater doubt on the generality of the Fisher-1,/hr11er theory. Suppose that both
nutations are beneficial antt that ln conbination they are more beneficial than
either alone (s^ t 1, s, ) 1, s, > so). Maynard SEith ( fg58) has shown that
in this case wh6n fitne*ses are-multfplieative (so- = s-' ) sexual and asexual
populations wil1 incorporate the doubLe mutant at'exactly the sane rate. This,
Eshel an6 Feldman pginl out, is a very special case. If fitnesses. are ttsuper-
nultiplicativet' (so' . s., ) the freguency of clouble mutants wiIL actually in-
""."r-u more rapiaff in atexgal populations. Only in the case that fitnesses
are ttsubmultiplicativeu ( "2'
, sr) wil1 sexual populations incorl>orate the
d.ouble mutant nore raPidlYlThe submr:ttiplicative case lncludes one very inportant subcase, the ease of
str ictadct i t iv i lyofef fects.Letso=1*x.Fornul t ip l icat ivef i tnessess- =1* Zx+xa, Foraclc l i t ive f i tn6sses sl =1*2x. Acldi t ive f i tnesses are
rt*ry, subnultiplicative. Note that as theratlvantages assoeiated with singLe
mutations becone very smal-l, nultiplicative fitnesses converge towarcls the addi-
tive ease. Not only are the aclva.ntages of recombination restricted to a narrow
range of fitness relationships between loci, they tencl to tlisappear the more
c1o-ely the loci under selection approach one assu:nption of the classical
hypothesis, relatively snall fitness d'ifferences between alle1es.
Using haploid two-loeus moclels Karlin (rgtg) has extended. Eshel and Ferclmanrs
work to finite populations. Recombination, he fintl.s, tencls to speed the first
appearance of double mutants in populations, bt! tencls to slow clorm their
subsequent rate of incorporation, even in the absence of selection' Karlin
derives a nunber of other intriguing results and. his carefbl nork cleserves
close attention. Like the work notecl above, it casts d.oubt on the general
applicability of the Fisher-lhrller theory'
Reassortment Theories of Sexual Advantage
The Fisher-lrhr1ler theozy emphasizes the potential power of reconibination to
produce one new genotype from marqr. In sharp contrast stancl several rather
more dtisparate t[eories whieh emphasize the power of reconbination to produce
DOES SH( ACCELERATE EVOLUITON? r35
many new genotlDes from a fev. And whereas the Fisher-Muller theory postulatesvery linited standing genetie variation, these reassortment theories of sexualadva.ntage, in com4on with the balance school orJ6i'ffi-eenetics fp"uirr"""xv,:"955, 1970; Lewonti-n, 197h), postulate large anounts of selectively relevantgenetic variation in natural populations.
The reassortment theories date tiireetly back to Weismann (f89f, 1892).(Ttre relationship of the Fisher-Mul1er theory to Weismannrs id.eas is lessdirect than Mr:ller, 1932, PuSgests, though it cloes bear some resemblance toweismannrs later work, 190\, in whieh he aceepts the existenee of mutation-likeevents.) fn Weismannts view selection acts to perpetuate the best of the verylarge numbers of hereditary conbinations produced by sexual crossingrso that Lsenvironments chenge species adapt in concert. convlrsely:
"a11 speeies with purely parthenogenetic reprocluction are sure todie out; not, indeed., because of any failure in meeting the exist-ing eond'itions of Iife, but beeause they are incapable of trans-fo'ning themselves into new species, or, in fact, of adaptingthemselves to any new cond. l t ions"(weisnann, r-99r, p. zrg).
Later Weismann softened his view on the innutability oi tarthenogenetie species,but he stil1 helct that tttheir capability of transfo:mation must be much smallerthan in bisexual speciesrr (Weisnann, 1892, p. 166).
Contemporary reassortment theories stem primarily from early work byDarlington, Mather, and Dobzhansky, and to a lesser extent Wright. Darllngton(t932, 1939, 1958) antl l&ather (rg\i and. taterj enptrasize the rot-e of linkagein the controlled. release of genetic variation, Darlington concentrating on trrereeombinational implieations of various alternative brled.ing systems, Mitheron a very speeial tleory of the rol-e of llnkage, to be aiscussea in d.etailbe1ow. Dobzhansky (fg:f, \955, ]r9|lg, t9?O)
"ire""es the purported. role of
Drosophilg chromosomal inversj.ons as instruments of atlaptive recmbination sup-pression. Wrightfs posi t lon ( f93f and tater) is a bi t subt ler and has hacl lessinf luence. Recombinat ion, he bel ieves, utd.er l ies speeies potent ial for, butnot necessarily species reallzation of, evolutionary advance (wright, ri3r analater). All four authors share Weismannrs basic conclusion, that in the longrun sexual speeies outlast and outevolve asexual competitors because they ar-better able to tap existing hered.itary variation and put it to use.
The reassortment theorists put fo::ward two sorts of evid.ence or argunentto support their hypotheses. On one hand. they invoke experimental evid.eneethat recombination generates a widle array of genotypes. Dobzhanskyf s views inparticular have inspired. a large number of experiments designed. to demonstrate therecombinational generation of genetic variability from sma]-l nr:mbers of wi1d-derived $*p!ifg chromosomes (Dobzhansky, 19)+6; Waltaee et al ,, 1953; Spasskyet al . , 1956; speiss r , 1958, 1959;
-Dobzhansky et al , , rgl lg; Kr imbas, 19dr;-speiss and Al- lenr 196l; . [ t len, 1956; Kosuda and Moriw*i , 19?1; and see arelated experiment by Mitchel1, 1958). These experiments d.o demonstrate thatrecombination can generate large genetic varience for partlcular characteristicsstarting from single pairs of chromosomes. They d.o not, and. this is important,establish the natr:re of the underlying genetic variation (Speiss an4 Allen,L96I; Lewontin, f97\, pp. 6f-68).
On a more abstract 1evel supporters of the reassortment theories often faIIto calculating the very large numbers of possible genotypes that recombinationalnong a moclerate nurnber of polynorphic loci night produce. For ex4ilple, if nvariabl-e loci segregate for x a1le1es each, the number of possible haploidnSepotfneg is x" (Wrieht, l.932) and the nr:mber of possible tlipfoid genotypes is.1X 1 Xrr-r +-adrrres clearly enormous for any appreeiable number of segregating\ 2 I , rL6w
loci . weismann hinsetf (rA9rr pp. 131+-135) very early establ ished this
L36 V. TTTOMPSON
trad.ition of argument by overnhelming calculation. It has since become virtu-
a1ly cie rigueur to include in evolutionarily oriented genetles texts a numerica^I
exa,npfi of ttre power of sexual reproduetion to generate lmmense numbers of
g"nolyp"". Almost a}rays this tahes the fo:m of a sma1l integer raised to an
incomprehensible po\rer. The inplication, sonetimes expIlcit, someti.mes not'
is that with so many genot rpes at lts dlisposal natural seleetion must be all
the more effective in promoting atlaptation to diverse and cha^nging environments.
But even assr:ming that the reassortment theorists are correet in their in-
ference that sexual reproduction can a.ntl cloes procluce an almost bound.less
d.iversity of genotypes, tliversity does not translate autonatically into evolu-
tionary advantage or advance. fn a population that has evolvecl for some time
in a constant environment exactly the opposite nay be true. Well ailapted'
genotypes nay be at high frequency. Thelr erosion through recombination will
io*"r- lhe r.productive success of sexual inclividuals antl the mean fitness of
the population. The generation of diversity will be ill-aclaptive per se. To
ma11e their theories work proponents of the reaseortment theories of sexual
advantage must hypothesize temporally changing environnents or nigration a.ulong
geogr"phically varied environments. Recombination a,mong existing selected
!"ttotypus is a plausible evolutlonary aclvantage only when organisms regularly
encounter environnents d.ifferent from those of their parents or more distant
progenitors. Even when environnents change, d.ifferent patterns of variation
or treterogeniety may inply very itifferent eonsequences for patterns of recom-
bination (urtrr.", 1tb3; Ttroclay, 1953; Levins, I965a, 1958), a topic exe'rnined
in more tletail- below.Flna11y, the consequenees of recombination a,mong a nultitude of existing
genotypes must depena very much on the (prevailing) nature of inter-Iocus
interact ions among al Ieles, Just as the precise nature of these interact ions
is crucial to the Fisher-Mul1er theory' wright (r9gr and' later) tras emphasized
the importance of this problem. Selective values at one locus may depend. on
a11eles present at other loci in the sa,nre Senome. Selection will tencl to drive
large p"nni"ti" popr:lations to the most accessible well-aclapted eombinations'
not necessarily the best. Should recombination subsequently throw up geno-
types better atiapted to prevailing cond.itions they will be swanped by recombina-
tion with eonnon genotypes. Unless the recombinable eomponents are advanta-
geous separately as well as together (genetically adttitive in a loose sense),
ttre test- ad.apted. combinations may never increase in frequeney uncler ind'ivid.ual
selection. The primary evolutionary question becomes I'whether there may not
be, after all, "ote
*u,y in which there may be selection anong the innumerable
favorable possibilities providetl by reeomilnation anong interacting genes"
i;ri;;;; ti6i). Once "gain,
sexual reprocluction may ensure a,:nple genetic
variition, but it d.oes not ensure that it can or will be put to use'
Like wright, the other founders of the reassortment theories recognize and.
at times tal<e pains to emphasize the dual nature of reeombination, the fact
that it tears apart wetl atlaptetl genotJrpes as reatlily as it throws then
together. But in seience, al in politics, lrritten rrord's and social influence
nay not conpletely coincide. Casting aside the nuances, subtleties, artcl
qrrlfi.fi""tions thly may have attached to their ffirotheses, the reassortment
fheorists, aideti Uy tfrlorists of the Fisher-ltuller school, have proJected' a
straightforwartl qna,mbiguous conclusion to biologists at 1arge, tlre conclusion
that sex accelerat"" t-spot se to selection, thereby facilitating evolutionary
change. Thls id.ea appears over a^ncl over, hid.d.en apcl overt, in the general
Iiterature of biology. It crops up as an auxiliary assumption in a trost of
more specialized nrort" on evolution ancl breeding systems. Most biologists
believe that it is true.
DOES SEX ACCELERA1E EVOLUTTON? r37
Recombination ancl Rate of Response to Selection
Despite most biologistsr uncritical acceptance of the notion that sexaccelerates evolution, the iclea has, until very recently, never been put toexperimental test, never, that is, with one maJor exception. fhe exeeptionalexperiment we owe to Carson (fg:a), who built his work to some extent on earlierexperiments by Rasmuson (f95\, 1955). Carson (t955a, ]-955b, I95'l) hypothesized.that structural monomorphism in the chronosomes of marginal Drosophila popula-tions promotes the fo::rnation of genetic novelties and therefore promotes morerapid. response to select ion. To test this idea he selected. for not i l i ty, acomplex behavioral trait, in populations of D. 49!gg!9, a species poltrrnorphicfor an extensive array of inversions involviig ;ost of its lenone. Towardsthe central part of the D. robusta clistribution imilividuals tentl to be highlyheterozygous for inversions. Toward.s the species margi.ns inversion frequenciesand inversion heterozygosity d.rop off sharply, so that most ind.ividuals are homo-zygous for stand.artl chromosome sequenees. Since inversion heterozygositystrongly suppresses recornbination, reeombination should be freer in marglnalpopulations.
Carson selected. for six generations on several separate 1ines, each deriveclfrom a single pair mating. Some parental pairs cane from a central p,opulation,others from a marginal population. By the last two generations the marginallines exceed.ed. the central lines in mean response, leading Carson to thiseautious interpretation :
"The enount and speed of response to selection appears to begreater in lines which are structurall-y homozygous than thoser+hich are structurally heterozygous. The nost likely cause ofthis d.ifference is considered to be the very much smaller a,mountof reconbination which is possible between polygene complexes inthe seet ional ly heterozygous [central ] l ines.t t
Re-analysis of Carsonts published. ilata suggests that the marginal and cen-tral lines d.id. not d.iffer significantLy in mean response. Neither set of linesis eonsistently higher in response and the d.ifference between the mean responsesis significant at the 10% 1evel in only one generation, the fifth. Interesting-1y, the variance in response anong the central (restricteci recombination) linesis consistently greater than the variance in response anong the narginal- l-ines.Measured in terms of score achieved this is true ln every generation.
Carsonts d.ata provid.e little support for hls hypothesis, all the less takinginto accor:nt the conrpletely d.ifferent geographic origins (a^nd. thus potential-l-yvery tlifferent gene pools) of his suppressed and recombining 1ines. Neverthe-1ess, his experiment stood. virbually alone for over a decad.e as the singledirect test of the effect of recombination on speed. of evolution, the singled.ireet test of the reassortment theories. Evidently biologists were deeplypred. isposed to accept Carsonrs conclusions, however tenuous their factual base(for an apparent except i .on see Jain and Suneson,1966). People fel t no compel-ling need to repeat or extend his work.
Recently, a nr:mber of norkers have retested. the hypothesis that recombinationspeed.s response to d. i rect ional select ion. McPhee and. Robertson (t9?0) selectedfor high and. 1ow sternopleural bristle number, putatively a polygenic trait, inDrosophifa melanogaster, using bal-ancer ehromosomes to suppress auto:somal recom-bination in certain selection lines. In one experiment they seleetecl for lowbrist lb m:mber, in a second they selected in both direet ions. In the f i rstcase they found a tend.ency for suppressed recombination to suppress response.In the second ease suppressed recombination seemed to suppress response in highselected l ines but had not icably less effeet on 1ow selected l ines. Overal l ,on a transformed. scale of measurement, the suppressed reeombination lines
138 V. THOMPSON
averaged only about 75/' of the total response of the no:mally recombiningcontrols. The results are not quite as clear-cut as they night first appear.McPhee and Robertson measure total response in terns of score achieved at theencl of selection, when most of their lines have effeetively plateaued.' oreeased to respond.. From their published. graphs it appears that rates of res-ponse in the suppressed ancl normal lines were very simLlar until the suppressed.lines begen to plateau, at lower average levels of resp'onse.
f fol1owed. up McPhee ancl Robertsonfs work with a sinilar experiment usingphototaxis mazes (Hadler, 195\) to select sixteen comonly derived D. melanogasterpopulations for positive photota:cis, another putatively polygenic trait. Insome populations f suppressed. autosomal reconbination using balancer ehrono-somes, in others recombination proceedecl norualIy. The responses of thesuppressed. reconrbination lines anct their normal eor:nterparts were intlistin-guishable, with one possible except ion. As in Carsonts work, the data hint
that lines in which recombination was blockecl exhibited. more variable response.The primary result is clear. Sex had no detectable effeet on mean rate of res-porr"" to selection. This work is reported. in d.etail elsewhere (fhornpson, t9?\,
and subnitted. for publieation).Markow (f9?l+, ].975) has cond.ucted a series of experiments sinilar to my own.
She too selected for phototaxis in several D. melanogaster populationsr suppres-
sing recombination in some, allowlng no::nal reconbination in others. Thot:gh
her work paralIe1s mine in many details, she d.raws the opposite conclusion.
Certain combinations of balancers, she asserts, do suppress response to selec-
t ion for posi t ive or negat ive phototancis, though in the maJori ty of cases,
recombination suppression seems to have no effect. Three factors make Markowts
results d.ifficult or impossible to interpret. Firstn she ran a single popula-
t ion to test each conbinat ion of balancers for select ion in a given direct ion.
Since variation a:nong replicate lines in phototaxis selection experiments is
very large (fhonpson 19?\, and sr:bnitted. for publication), experiments without
replication may give very nisleacling results. Secondly, her experiments
included no controls to aclequately d.istinguish the norphologieal effects of
balancers from the effects of recombination EI gg.r a ciistinction that proved.
to be important in ny work. Finally, she initiatecl her experiments by nixing
together rnany clifferent populations of heterogeneous origin, a practice 1ike1y
to introd.uce artificial linkage disequilibrium, profor:nd.Iy eomplieating the
interpretat ion of results (see below). Str ict ly speaking, Markowrs results are
compatible with ny ovn, since she reports that suppression of autosomal recom-
Uination alone has no effect on response to selection for positive phototaxis.
Taken together, the experiments of Carson, MePhee a^ntl Robertson, and
Markow, as rrell as ny own experiments, do not provide a very satisfactory
ansver to the questitn ttd.oes recombination speed response to selection?tt My
work suggests that the answer is no. The othersr work suggests the opposite
conclusion but their clata are not partieularly eonvincing. This exhausts the
experimental d.ata on manipulated. recombination and. directional selection. But
we can appeal these apparently conflicting results to another quite separate
body of work, computer sinulation studies of directional selection in nulti-
locus systems with various d'egrees of linkage'
Computer Sinulation Stud.ies and the Reassortment Theories
Four sets of computer studies bear directly on our cliscussion. They all
simulate the evolution lmder d.irectional selection of many linked. loci with
allefes at intersed.iate frequencies. In an early stutly Fraser (tg>l) mod.e1ed.
the evolution of two chromosomes, eaeh with three loei p,olynorphic for two
allefes. We car] sunmarize his resufts as follows: t) ffre tighter the linkage'
DOES SEX ACCELERATE EVOLUTION? 139
the slover the rate of response to seleetion. 2) ttre smaller the population,
the greater the effect of linkage. 3) Ihe farther the chromosomes in the
original population from the optimr:m genottrrpe (ttre greater the initial negativelinkage tlisequilibrirm), the greater the effect of linkage. 0n the whole theeffects of linkage were snal1 unless linkage was very tight.
t' lartin and Cockerfran (1950) fottowed up Fraserrs vork with a more extensivestudy on single chromosome systems with five or twenty loci. Most runs they
initiated. with random eombinations of aIleles at clifferent loci (linkage equi-
libriurn), but they initiated. a few rr.ms in complete negative linkage d.isequi-l-ibriqn ("loaded repulsion") so that forrncling ind.ividuals were all of genotype
10101/O1O1O where 1 and O represent the favored antt disfavored alleIes at each
locus. Like Fraser they for.urd that initial negative linkage clisequilibrium may
d.rastically affect response, the tighter the linkage the slower the response.With initial linkage equilibrium, linkage effeets rrere sma1l but signifieantt
the larger the number of loci and tighter the linkage the slower the response.
In general smaller population size slowed response and exaggerated. the effeets
of l inkage.Fraser and Martin and Coekerham sinulated relatively smal1 populations'
ranging in effective size from four to fiity. Using a ten locus mod,eI, You::g(tg66) extenttetl sinulation to larger populations, effective size at least one
hr:ndred, with initial linkage equilibrir:m. Under these eonditions linkage hacl
very little effeet on response. Unfortunately, the tightest linkage Young
exa:nined nas only .05, a rather high nininua rate of recombination.Probably the most extensive sinulation studies of linhage and selection to
date are those of Qureshi, Kenpthorne and Hazel (1958) and Qureshi (1968).
They studied a for:r chromosome h0 loeus model with populations in initial
linkage equilibrirr:r. Restriction of recombination had negligible effect in the
early generat ions of select ion, but tend.ed. to slov d.own, or at least restr ict t
response in the long rrrn. Again, linkage effeets increased with decreasing
population size. Qureshi et al. conclude that the inhibitory effeet of small
population size on rate of response appears to increase in geometrie propor-
lion to the tightness of linkage between loci. With moderately large popula-
t ions (sixty-four incl iv iduals), l inkage effeets seem to be negl igible for
recombinat ion rates of .05 or more.A fev more abstract simuLation studies also merit attention. Latter (tg66)
simulated a two locus model and for:nd that popr:lation size has a much larger
proportionate effect on rate of response than linkage, the sryallqr the popula-
l iot , the smal ler the average response. Hi l l anct Robertson (1955), also
studying a two locus system, for:nd. that over a wide range of paraneters linkage
effects may be adequately deseribetl by the term Nc rhere N is effeetive popula-
tion size a,nd. c is recombination rate. Large population size compensates for
tight linkage. Hill and Robertson also found that linkage has little effect
on response in initial generations, but d.oes slow response and the rate of
,pp"o""h to fixation in later generations. Robertson (fgtO) has extend'ed
their work to systems of many linkecl 1oci, showing that as the mmber of loci
increases, so too wi l l the inhibi taory effects of l inkage on total seleet ion
response (t f r" f i - i ts to select ion), t t rougtr the proeess tends toward a l i rni t at
a few dozen loci. Robertson eonel-udes that the effects of linkage on d.irec-
tional selection for a trait d.eter:m:inecl by a moderate number of loci with
inter"med.iate gene frequencies and initial linkage equilibrirn viIl be sma11'
"much lessrtt he says, tttha.n I had expectecl and less than might be asswecl from
d.iseussions of linkage in the literature'Renarkably, reference to these simulation stuclies is virtually absent from
the f i terature diseussing the evolut ionary role of sex (Felsenstein, 19?\, c loes
discuss Hill and. Robertsonrs work in relation to the Fisher-l"hrller theory),
th0 V. TIIOMPSON
perhaps because they have been clireetecl torards a practical pr€blemr the roLe
Lf reconbination in agricultural breeding prograns. Whatever the reason for
their neglect, the computer stuclies suggest that two naJor factors shoultl
clominate the relationship between recombination anci directlonal selection:
1) population size, ancl e) tfre state of linkage equilibrfu:n. These factors
are afso key to untlerstantling the varioue derivative moclels of the Fisher-
Mu]ler theory (Karl in, l :973; Felsenstein' 19?\).1'he importance of population size for the reassorbment theories is not
d.ifficult to grasp. Given a system involving many variable loel, populations
of small to moclerate size sinply cannot harbor al.l possible genotypes simul-
taneously. Suppose, for exa.mp1e, that in a haploicl ten locue system with
initial gene frequencies all equal to 0.1, seleetlon favors indivicluals of
genotype 1111111i11 (using the notation introtluced above). If.inter-locus
*ffufi" combinations are initially rand.om (tinkage equilibrium), the probabll-
ity. i,hat any givenr,organism will harbor the optinal conblnation is only
O.tt' = g.7Z x 1O-*. In smaIl populations optimal combinations &re unlikely
to exist; the larger the number of loci invoLved. end the smalLer the fre-
quencies of desirable alleles at each locus, the smaller the chance beeomes.
When optimal combinations must be producecl throrrgh reeombination, linkage
imped.es their prod.uction; the sme.ller the population size ancl tighter the
tint<age, the longer the average wait for recombinants and the slover the
initiation of response to selection if response tlepend.s on the ereation of
new genotypes from existing genes.
firrit" population size nay influenee total response (ttre linits of selee-
tion) as nrell as rate of response to selection. fn tightly llnked' systems
chromosomal combinations tend. to behave as nultiple alleles at a single loeus.
Selection operates to sort out existing chromosomes and tlrives the best
towards fixation. Should. the best chromosome happen to carry unclesirable
alleles these wil1 be driven to fixation along with the rest unlesg r-ecombinetion
intervenes. The final response will not be the optimr.m possible response.
In small populations random loss of deslrable al1eIes during the course of
seleet ion wi l l aLso reduce f inal response; the shorter the period. of select lont
the less probable this process becomes, but the more probable the fixatlon
of r:ndesirable alleles thror:gh association with goocl ones. Selection response
becomes, in a sense, a race between recombination and genetie- _$rlfb, a rela-
tionship that r:nd.erii"" the nodels of Hill and Robertson (1956) and' Robertson
(fgfO).- In the context of a rather clifferent selection notlel, Franklin and.
Lewontin (fgfO) note that finite population size itself cletersines the exis-
tenee of an optinr:m reeombination fraction'nid f in i te p6pulat ion size inf luence the experinental results discussedv4$ + r . .3 vv I
above? Yes, almost certainly. carson selectecl on populations of very sma11
sizen four pairs of parents per line per generation. we can ascribe his
positive resrrlts, if they are rea-l at-alt, d.irectly to snall population size.
Mcphee and Robertson selected on populations of effective size about ten.
Their resufts too may be ascribed. to finite population size. In fact '
that
is how they analy"e th"r themselves (ttroqtt they are concerned. with limits to
sefeetion, not rate of response per se). Markow and. f both seleeted on popula-
tions approaehing the size at which Qureshi et al. found. virtually no effect of
reasonably loose 1inkage on response. I for:ncl that recombination has no effect
on mean response. Mariowts data are at feast consistent with this assertion.
Sex, it appears, should speed. response to selection, Just as the reassort-
ment theorists pred.ict, but the effect should be significant only in very sma1l
populations, sma]ler, perhaps, tha,n are like1y to be the rule in nature' If
lfri.s is the maJor firnction of sex, sex must p18y a linited' role in evolution'
But then why cto so many species cling tenaciously to sexual reproduetion? Are
DOES SEX ACCELENATE EVOLUTION? 141
there perhaps other aclvantages to sex associated nith the second naJor factorformd to influence the sinulation results, linkage d.isequilibrir.u?
Linkage Disequilibrium and. Matherrs Polygene Iheory
Linkage disequilibriwto non-rand.om association of aIle1es across 1oci, mayspeed or slow response to selection, clepentling on its direetion. Positive link-age d.isequilibrir:rn, an excess of coupling conbinations (11 and O0 for a two locuscase), so that alleles influencing a trait in the ssJne d.irection tend. to beassociated in the sa,ne chromosomes (or haploid genotypes), speed.s response tosel-ection by exaggerating genotypic variance vithin populations. Negative link-age clisequilibrir.m, an excess of repulsion combinatlons (Ot ana tO), slows res-ponse to selection by depressing genotypic variance. Felsenstein (t965) provesthese relationships rigorously for two haploid models and a more limited ttip-loid nodeI. Antl they are evid.ent in Lewontinfs (f951+a) general fo:ruula forgene frequency change in deterministic two loeus linked systems with d.iseretegenerat ions:
Ax. a1
6;
6x.1
frequency of the ith alleIemean fitness of populatlonrecombination fractionfitness of double heterozygotelinkage d.isequilibrium dete:nrinant
E, t - * . )t- .*- ; .
L1
. RDWJ -]-] ' '
where x* =
R=w. r -
II
D
In the terminolory introdueed above D is x"rxnn - xr^x^" where the xfs representfrequencies of the coupling and repulsion to'nUYnati6ilsY' Note that when D = O(tintage equilibruum), the te:m RDW.,., drops out of the equation and recombinationd.oes not effect response. This sugfiEsts a priorl that only in the presence oflinkage disequilibrium (initiat or othe:sise) witt sex influence selection invery large populations, a point confirmed. by Karlin (]rglS) ana by Felsenstein(fgf\) who notes that recombination can influence the gene pool only by breakingdorrn linkage d.isequilibrium.
Mather (f9\f, I9It2,191+3) has proposed a very influential model for thefunction of sex in natural populations. His argument relies ciecisively oninteraction between recombination and linkage d.isequilibrim; it rests on threemaJor premises: (1) Quantitative traits are determined. by nany loei of sma11,equaI, ancl ad.d.itive effect dispersed. throughout the genome. (2) fhese loeiexhibit inter"mecliate gene frequencies (plaeing Mather squareJy in the reassorb-ment ca^:np). (S) fn the short te:m environments fluetuate erratically a.ntl oftenabruptly, but med.ir:m term selection favors internediate phenotypes for mostmeasurable characteristies. Over time, intetsecliate optimum phenotypes maychange in response to long ter"rr directional environmental changes.
Populations, the argurnent goes, face eonflieting evolutionary requirements.They must preserve their capacity for long terrn change without responcling toostrongly to short terr selective pressures. Mather suggests that Iinka.ge re-sofves this contratliction in the following way. fn polygenic systems manydif,ferent genotypes nay dete:rnine a^rry given phenotype. For internediate optimaselection favors chromosomes with balanced eombinations of alleles ad.d.ing toor subtracting from a particular trait. Combinations like 111000 or 101010 arefavored over combinations like 001000 or 111110. Furthentore, selection wiIlfavor conbinations that nininize the probability of creating unbalanced. chromo-somes through recombination. Chromosome pairs like 101010 and 010101 are better
1\2 V. THOMPSON
balaneed than pairs like 111000 and 000111. In the first case five recombinationevents are required. to procluce the extrene allelic combinations, in the seeondonly one. Populations will strike a balanee between the proliferation of wel-lbalaneed eombinations through selection ancl their erosion through recombination;the tighter the linkage, the greater the pred.ominanee of balanced combinations,and the less the flexibility of the population in response to directional selec-t ion.
Matherrs polygene theory pred.iets the generation of substantial negativelinkage d.isequilibriun in natural populations. Negative linkage tlisequilibriumslows d.ireetional selection. Recombination disrupts linkage d.isequilibriun.Therefore in l{atherrs model sex shoulcl accelerate response to d.ireetionalselection for traits that have been und.er selection for intermediate optina.This is the source of Matherfs very large eontribution to the notion that sexaccel-erates evolut ion (see, for exa.mp1e, Carsonr 1958), but the fact that themodel- depends so crucially on negative linkage d.isequilibrir:m is alnost alweysoverlooked..
Populat ion genet ic ists have raised tvo ser ious obJect ions to Matherfs motlel(Wrieht, I9\5; Levont in, 195\b). First , i t d.oes not provide for the long termmaintenance of polynorphisn at individual loci. Eventually populat j"ons will goto fixation for single well balancecl combinations; evolution will staIl. Inad.d.ition, to maintain balanced conbinations at significant frequencies recom-bination between loci must be very smalI, on the order of magnitud.e of theselect ion coeff ic ients associated. with ind. iv ic lual loci . Since the nodel pre-d.icts many 1oci, selection coefficients at each must be smal1 and the linkagebetveen loci would have to be inprobably tight. Mather (fg:S) answered theseobJections by appealing to selection experiments showing period.s of "acceleratedresponser" ir whieh populations that have failed. to respond for a nurber ofgenerations renew their advance, ofben abruptly a.nd for a linited period..Ttrese responses Mather attributes to rare recombinations among closely llnkedloci in balanced. polygenic systems. The facts d.o not support this interpretation.
Matherrs own early experiments (Matherr lgl+1) may serve as an example. Heselected D. melanogaster populations for high antl low abdominal bristle number.Response lras uneven, alternating between periocls of little or no progress andperiods of rapid. ad.vence. But the selected popi:lations were very sma11, twoparents of eaeh sex per generation. fn tiny popu.lations recombinationaleffects on selection d.o not necessarily imply linkager let a-lone linkage dis-equilibriurn. Even should substantial linkage disequilibriun exist in smallpopulations, it rnay reflect the random processes inherent in populations off in i te size (Sved", 1969, 19?1; Hi l l and Robertson, 1958; Ohta and Kimura, L969).
Virtually all other reports of striking accelerated response fit the sa,mepattern (payne, l )2O; Sisnand. is, a)\2; Mather and Harr ison, lp l+p; Fraser et aI . ,I955i Scowcroft , 7956; Hosgood, MacBean and Parsons, 1p68; MacBean, MeKenzieand Parsons, 19?1; fhoday and Boan, I95I; Thod.ay, Gibson and Spickett, 1951+;Spickett and Ttrod.ay, L965). fn most cases populat ion size is very smaIl , f ivepairs of parents per generation or fewer. In ad.dition, most accelerated. res-ponse experiments have involved base populations in some sense heterogeneous inorigin. I.4ather, for example, selected on flies tlerived. from a cross betweenfaboratory stocks of very d.ifferent origin, introclucing another very realpotential source of linkage d.isequilibrir.rm. The experinents of MacBean et al.and Thod.ay and his co-workers are tel11ng in this respect. They present cred.ibleevj.d.ence that certain observed. acceferated. responses do in fact stem from recon-bination between closely l-inked t'Ioei". But in each case the locl invol-vedeontribute a sizable portion of total selection response. They are loci ofmaJor effect, not polygenes in Matherfs sense. And even then Thoclay et al. areforced to postulate that they built negative linkage tlisequilibrirm into their
DOES SEX ACCELERATE EVOLTJTION? I lr?
base populations. Fina1llr, it is inportant to note that many accelerated. res-ponses may have no relation to reeombination anong linked. Ioci. Fraser and.Hansche (rg6l+) ana Wright (tg6g) present alternative models for sueh effeets,and Fraser et al. Oge>) present evid.ence that aceelerated responses duringseleetion for high scuteller bristle nr.mber (ttre trait employed in many of theexperiments above) may not be clirectly due to artifleial selection at all.
Linkage Disequilibrium in Nature
Despite the absence of convincing evidence srrpporting Matherts hypothesis,interest in selection nodels that generate linkage tlisequilibrir:m has recentlygrown. This reflects Lewontin and. KoJinats (1950) d.enonstration that epistaticinteraetions between loci nay lead to stable linkage clisequilibrir:m and, the sub-sequent d.emonstration by many authors that selection for intermed.iate optinr:mphenotypes in acld.itive nulti-Loeus systems mey leacl to the build up of consiiler-able long term negative linkage clisequilibrirrn (Lewontin, fp6l+b; Fraser, Mil1erand Burnell, 1965; Wi1ls, Crenshaw anti Vitale, 19?O; Franklin and Lewontin,1970). fhese models, l ike Matherfs, require t ight l inkage. Now, with thed.iscovery of very high Ieve1s of eleetrophoretically d.etectable protein varia-tion, close linkage of many poly:norphie loci has become a tenable proposition(d. iscussion in Lewontin, 19?h).
At this writing direct evid.enee for widespread. linkage d.isequilibrium innatural populations j.s sparse and. linited. for the most part to special cir-eumstances. Many investigators have d.etected linkage disequilibrir.m involvingdipteran inversion polymorphisns (Levitan, 1955, 1958, 19?3a, 1973b; Levi tanand Salzano, 1959; Stalker, 1950, 195\; Brncic , t )6l- ; Mather, 196, Sperl ichand Feuerbach-I{ravlag, I)6), L97\; Martin, 1965; Prakash and Lewontin, 1968,19?1; Prakash and Merritt, 1972; Pralrash, f9?\; Nair and Brncic, 1971; KoJimanGillespie and Tobari, 1970; Multain Mettler and Chigusa, 1971; Mukai, Watanabeand Yamaguchi, f9?\; Le.ng1ey, Tobari and KoJima, 19?\). Others have reportedinter-locus d.isequilibrirrm in self-fertil izing plants (A1lara et al ., ] '972),in predominantly parbhenogenetic Daphnia (itebert, 19?4), ed anong very tightlylinked ancl perhaps functionally and. phylogenetically related. loci in Drosophila(Roberts and Baker, 19?3; Baker, f975). fn addit ion, Clarke ( fgt t+) t rasrecently called. attention to older stud.ies on flowering plantsn snails, and.butterflies which ind.icate substantial clisequilibrium betveen closely linketlloci controlling relatetl norphologieal characters,
A few investigators have detected. occasional cases of linkage disequilibriurin regularly outbreed.ing organisms among loci that are fairly widely spaced. andnot obviously firnctionally related (Zouros and Krimbas, 19?3; Zouros, et al.,t97\i Franklin, 1973; Charlesworth and Charlesworth, 19?3; Birley, 19?\). Bychance, the Ctrarlesworths studied fvesf (fgtO) A.mherst D. melanoglg popula-tionn the sa,me population used in ny ovn stud.ies on reco:ntli?i6n ana selectionresponse (Thompson, 1p7\, and. submitted. for publication). Using electrophore-tic teehniques they searched for disequilibrir.m among five third ehromosomel-oei. Among the ten possible two loeus interactions, two proved. to be signifi-cant at the 5% level. In an unrelated. cage population two d.ifferent inter-actions proved to be significant at lhe L% level. Internal consistencies in thed.ata suggest that some of the ctisequilibria, though snallr m&y be real.
The available scant evidenee suggests that, except in a few special cases,linkage clisequilibrium in natural populations is small, smal1 enough certainlyto have no more than a trivial effect on response to seleetion. And. we knowalmost nothing about linkage clisequilibrium alrong loci detertining quantitativetraits. We can only infer its presence or absenee from the resuLts of reeom-bination ancl selection e:rperiments (McPhee and Robertson, 19?0), a risky
1l+\ V. THOMPSON
venture in the absence of inclependent knowledge concerning the number of locisegregating, their linkage relationships, the relative magnitud.es of theireffects, ancl their mod.es of interaetion.
,,' Here then we have a real nystery, a real gap in evolutionary theory. Sexshoultl speed the evolution of smalI populations and. populations in negative
' linkage d.isequilibrir:m, but most populations most of the time must be rathertoo large to benefit from the population stze effect, and the evid.ence out-l-ined above suggests that stancling linkage clisequilibrirm in most populationsis sma11 or absent. In addition biparental reproduetion suffers serious short-cor ingsasar@mecharr ism(Maynard.Sni th,1pJ1a,19?1b).Partheno-genetic females prod,ucing female progeny w111 in general be twice as fit assexuaf femal-es prod.ucing equal numbers of uale end fema-le offspring, and par-thenogenetic populations will reprod.uce twiee as quickly as their sexualcounterparts. Furthernore, biparental reproiluetion requires the union ofga,metes from two individuals, and ofben a temporary union of the intlivid.ualsthemselves. The necessity to Juxtapose ga,metes has led to the evolution ofelaborate morphological and. behavioral characteristics in a wid.e array ofspecies. AniI many seconctary sexual eharacteristics must, as Dar:win (f9Of r p.299) noted long ago, seriously hinder actaptation tottthe general cond.itions oflifefr. Asexual reproduction abolishes the necessity for ga,metic r:nion openingthe way to evofution rrnemcurnberecl by special aclaptatlons for sexuaL search and.attraction. Yet sex persists wid.ely in nature. 
DOES SEX ACCEI,ENATE EVOLI.MION? r45
Mather (rgl+S) eventualLy aband.oned the nixing-of-populations moclel on thegrounds that it representgd !o9 special a case to be of much imlnrtance innature. Crow and Kimura (]?6g) have recently echoecl this sentiment. How com-monly the model applies must vary tremenclously fron species to species, d.epend-ing on population structure and the spatial and temporal heterogeneity ofenvironments. One exanple will i l lustrate the conplexities that may arise.fheoretieal vork by Nei ancl Li (fg?S; Li antt Nei, 19?l+) inaicates that sub-d.ivid.ed. populations in heterogeneous envirorunents with mod.erate anounts ofmigration may exhibit stable linkage disequilibrir:m, even j.n the absenee ofepistatic interactions a,mong the loci involvecl. Because each subd.ivision hasad.apted to a fixecl loeal environment, mi.grantsr genotJrpes are malad.aptive,linkage d.isequilibriurn ls positive, and. sex within subd.ivisions will sl-ow downthe elimination of malaclaptsfl imnigrant alleles by shuffling then into thelocal genotype. But shoulcl local environments be shifting rather than fixed.,so that recombination anong loea1 and migrant genotypes often produces adapt-ively superior eonrbinations, linkage equilibrirlm will be effectively negativeand sex will be advantageous to nany lnpulations.
Soen in this l ight we may reinterpret Carson's ( t955a, I955.b, f958, l9! l9)theory of evolution in marginal populations. He arguecl that in such popula-tions recombination faeilitates the fonnation of novel genotypes adapted tostringent envirorunents; the more reconbination, the faster the adaptation.The arguments above etq)oBe the itiffieulties inherent in this view. 3ut suppose,as Lewontin (f9?l|, p. 15f) areues, that marginal habitats are characterized.by temporal instability, and. that narginal populations are temporally unstableas we1lr fragmenting ancl rea^rnalganating over time. If selective pressures varyfrom sub-population to sub-population, populations may ofben be in negativelinkage d.isequilibrium with regard to environments at hand and sexual repro-duetion may, as Carson proposesr pfry en important role in speed.ing adaptive?acnn hea
This argument may be extended to many or most ttweedytt or ttfugativert specieswhich populate impe:rtanent or erratically shifbing habitats. For exaanple, intemperate climes D. mel-enogaster appears to overnrinter as sma11 populationsconfined to a few restrieted. sites. Each spring ove:nrintering survlvors emergeto build up loca1 populations rhich spread. and intenningle over the course ofthe sunmer reprod.uctive season, a process reflected. in a decline in theal lel isn of lethals in local populat ions as the season progresses (Ives, 1970;Frankl in, 19?3). I f the ningl ing populat ions ref lect select ion in signi f i -ca^ntIy d.ifferent environments, and. if the environments of their d.escend.antsare often significantly ctifferent fron their own, sex may facilitate ad.aptation.Quantitative argunents by llaynarti Snith (rg?ft) suggest that frsignifieanlly
d.ifferent" in this ease means very clifferent ind.eed., with the correlatlonbetween envirorumental attributes relating to different loci changing sign fromgeneration to generation. The extent to which such processes are import,ant innature will d.epend^ very mueh on the interaction of environmental patterns andindividual physiological flexibility within species. If, for exa.rnple, theenvironments of some weedlr species are effectively the same generation aftergenerat ion d.espite constant shi f ts of locat ion, Stebbins ( fg>A) is correct toargue that sex will be d.etrimental to aciaptatlon.
Sex as a Mechanism for Damping Selection Response
Tnplicit in this diseussion so far has been the assumption that geneticchange is good. in itseH, the faster the better. But the mixing-of-populationsnodel- suggests, as Mather (fgl+E) antl fhoday (fg::) pointed out sme tine ago,that geneti.e change vi1l be benefieial only in response to certain patterns of
1\5 V. TITOMPSON
envirorurental change. Levine (f965a, 1958) has cleveloped this theme. Using
a computer to simulate the behavlor of a d.ete::ninistic two-loeus systen with
adctitive interactions in the face of fluctr:otlng envirolments' he d.enonstratesthat optimum recombination levels tlepend on the periotticity or serial auto-
correlation of successive envirorunents. When environment fluctuates rapitLly,with a period short conparetl to generation time, eomplete linkage (no sex)
maximizes population fitness over time. From the point of view of the popula-
tion the environment is r:npredictable (or physiologically averaged.) a.ntt it is
better not to evolve at all. When the perlotl of environmental fluctuationis long compared to generation tine, intertreiliate recombination levels may
naximize fitness over time. Presumably, as the periocl of fluctuation beeomes
very long the populatlon will see the environrnent again as effectively constant
and the optimr:n reeombinati.on rate will again be zero. Sex facilitates evolu-
tion in response to environmental fluctuations of intermediate length. This
result rests on Levinsf use of strictly adclltive fitnesses. Had he used
nultiplicative fitnesses linkage would have had no effect. It would' be
interlsting to repeat this work introdueing finite popuJ-ation size, multiple
Ioci , and other f i tness relat ionships.Note that populations sel-eetetl in different polnts in time, as well as
space, may often trybrictize (plants with variable seecl dormancy, animals with
resting eggsr plants and animals from d.ifferent year elasses), sr:ggesting the
utility of a synthesis corbining the mixing-of-populations and the Levins
models. Levins hlmself (fg5:U) suggests that migratlon serves the evolution-
ary role of d.amping genetlc response to local envirorunental perturbation.
Sei, by scranrbling incoming genes with the loca1 genome, shoulci clelay their
early el iminat ion and faci l i tate this process.i4f art" (Thompsonrlg?\, and submitted. for publication) and Carsonrs clata
(fg:8) suggest, a.nd., it nust be emphasizecl, merely suggest, that suppression of
recombination increases variation in response arnong populations subJected to
direetional selection. By inference, sex shor,rl-d. d.ecrease variation i.n response
arnong replicate populations r:rrd.er selection. ff this phenomenon is real' we
*ry "ttribute
it d3rectly to finite trnpulation size. In infinite populations
wiin no recombination seleetion will (assuming no complex interactions) pick
out the best garnetic combination ancl raise its frequeney to fixation. There
will be no variation in response alrong replicate populations. But in finite
populations the best existing ganete will vary fron replicate to replieater so
lnatrepr icatesotasf f iprr1at ionsvi11varyconsiClerab1y,bothinspeecloft""por"" (vhich will be proportional to the difference in fitness betneen the
besl existing ga,nete and the population nean) anct level of final respon'se.
Best existing gametes do not limit selection response in finite sexual
populations. Seiuaf populations may generate new more highly fit conbinations'
lnoqit these may be torn apart in turn by subsequent bouts of recombination.
In these populations arrays of aIleles' or at l-east arrays of genotypic com-
binations, d.oninate response to sel-ection. Antt aIlelic arrays must be sinilar
from replicate to repllcate, much more similar than;!he near-r:nique genotypic
combinaiions that ctoninate response in finite asexua-l populations. Consequently,
recombination should homogenize response anong replleates at the sane time it
promotes variation within replicates. Sex tends to generate d.iversity within
iopulations, but it should also diminish variation a.mong commonly derived finite
populations uncler d.irectional seleetlon'What role night this phenomenon play in evolution? If inter-demic sefection
is important ancl often favors extreme responses to selection, only those popula-
tions with high or 1on mean response may survive to perpetuate species. Selec-
tion anong speeies woulct favor the erratic collective response of groups _of
asexual populations. This appears rrnlikely. Turning the argument around'
DOES SEX ACCEI,ENATE EVOLUTION? 147
perhaps sex benefits species not by speetling response to selection, but bymod.erating its eourse, so that more populatlons track envlronmenta.l changeefficiently, straying into neither excegsiTe nor insufflclent response. Atthe inter-population 1evel sex d,arpe response to envlror:mental cha.nge. Ineffect this turns Matherfs (fg\S) theory upsicte ilorn. He arguetl that linkage,the negation of sex at the chromosome leveJ., moclerates response to eelectionwithin populations. I suggest that llnkage exa,ggeratee tbe range of responsea.urong populations. This hypothesis depend.e crucially on llnited population si.ze,and. on the assumption that constellations of popuJ-ations evolve in sonethlngapproaehing mutual isolation, conditione that d.o not apply to nany species innature.
But work by several authors (Lewontin antt KoJina, 1950; Felsenstetn, 1955;Bod:ner and. Felsenstein, f967) suggests a roLe of more genera-]- significance forsex in large natural populatlons. Using varlous models they show that direc-tional selection generates llnkage d.isequllibrfun in the presence of epistaticinteractions among loci. fhe d.ireetion of the linkage tllsequillbrium, positiveor negative, d.epend.s directly on the sign of the epistatic interaction, so thatpositive epistasis lead.s to positive linkage tiisequillbrlun, negative epistasisto negative linkage disequilibrirur. As noted above (see the section on Matherfspolygene theory), positive linkage d"isequilibrir:m speecls response to selectionwhile negative linkage d.isequilibriu has the opposlte effect. By d.isruptingli.nkage d.isequilibrfu.rm, reeomblnation tend.s to counter theee effects.
I suggest that ln nature environnental changes ofben confer great selectivead.vantage on certain combinations of allel-es alnong pollmorphlc loci previouslyindepend.ent in their effects on fitness. In other words, fluctuations in en-vironment often lead to positive epistasis. If this phenomenon occurs regularly,directional selection will generate positive linkage disequllibriumrwhich inturn w-il1 hasten evolutionary response. Recombination, countering this trend,will tend. to slow response, lessening reaction to envirorunental change. Thekey point is that positive fitness contributions by loei in cmbination begreater then the assumption of complete ind.ependence between loci would. suggest.How mueh greater? For two loeus haploid. systems with tllscrete generations,recombination will- slow response to selection,when loci show supermultlplicativeeffectscussion
on fitness (nsUet a^nd. Feldman, 19?0; Karli,n, l:9'l3i and see the tlis-the Fisher-Muller theory at the beginning of this paper).
Noting that reeombination will slow selection response in some circumstances,Eshel and Feldnan (f9?0) suggest that sex facilitates evolution in cha^ngingenvironments by ttprolonging the pollmorphic statertt o*, as Eshel (f9tf) re-states their conclusion, by curbing tttoo-rapid. genetic response to irregularand temporal environmental changestt. Ttrey state thls suggestion in the contextof the Fisher-Mul1er moclel (evolution through the spread. antl combination of nerror previously rare mutations) tut I believe it fits the prenises of thereassortment theories Just as welI. Sex, I suggest, generally retard.s ehangein gene a,nd genotype frequencies in the face of short ter-m environnental change.It d.oes not accel-erate evolution, it slows evolution d.own. Should this provetrue, the negation of Matherrs hypothesis proceeds a step further. Linkage'Matherts mod.erating factor, shoulcl exaggerate selection respone'e, because popu-lations und.er seleetion w111 show transient positive linkage d.isequilibrir:m'not the more or less permanent negative linkage d.isequilibrium that Matherhypothesized..
The hypothesis that sex mod.erates selection response by ndtigating a spon-taneous tenclency toward.s positive linkage clisequilibrium helps to resofve certaind.ifficutties that afflict some of the earlier reassortment theories of recom-bination and sex. For exa.mp1e, margr theories asserting that sex acceleratesevolution depend in the last analysis on the hypothesized. presence of negative
1l+8 V. THOMPSON
linkage clisequilibrium in:natural populations, a ffirothesis for which there isvery littte evidenee. I suggest, in contrast, that positive linkage d.isequi-librir:m d.evelops as a largely transitory phenomenon in populations under direc-tional selection, a^ndl that sex frrnctions precisely to ninimize its d.evelopment'a notion conpatible with the tlata fron natr.ral and experinental populations. In
ad.d.ition, the present lrypothesis applies to large populations. ft cloes not, asmany reassortment theories clo, require r:nrealistically smal1 population sizes.
Fina11y, it helps circumvent trro naJor clifficulties eonfronting the nixing-of-populations hypothesis, the neeessity for continual- nigration among or a,nralga-mation between separate local populations, and the conconitant neeessity forcomparatively finely balancect relationships anor€ selective forces in theenvironments involved. Because, according to the hypothesis that sex countersthe effects of positive epistasis, sex plays its main role within loca1 popula-
t ions.lltre notion that sex serves prinariJ.y to slow response to selection is a
venerable but neglected concept. It fo::lred. the basis for Charles Danrinrs later
views on the evoiutionary function of sex (De Beer, 1960b, p. 151+; O1by, 1966).Danrin saw in sex a mechanism for quashing over-strong response to local andshort-tern selection. Crossbreed.ing, he earne to believe, blencls large varia-tions out of existence so that only small recurring variations appearing innany ind.ivid.uals aecumulate in species. For Danrin the main role of sex is not
to generate variability; it is to eneure a grailual, untform'adaptive responseto selection in the face of environmental heterogenelty. [he ideas discussed
above threaten to bring the d.iseussion of sex baek arounct fult circle' to aproposal, however poorly ground.ed. in its original form, that prectates Weismann.
I notetl that we have failecl to car4f Weismannrs vork through to the end..We have failecl to elucid.ate in a fund.a,mental way the role of sex in evolution.perhaps the reasons for this are now more clear. The sinplest impliclt hypo-
thesis of the reassortment theories, that sex speeds response to d.irectionalselection, will hold true only for linlted. clrcumstaneesr cireumstances like1y
to prove uncomnon in nature. It is not diffieult to conJure alternativetheories of sexual actvantage, but it is very clifficult to test the assumptions
on which these theories are based.. Ttre Fisher-Ifuller theory, for exa,mple' has
been ably and. subtly developecl over the years, most recently by Karlin (fgf3)
and Felsenstein (fgfl1). But the assmption on which the theory is based.' the
notion that evolution proceed.s prinariJ;y through the rise and spread of new or
previously rare mutationsr me,v have no basis in faet. .d satisfactory theory of
sexual reproduetion will require more und.erstanding than we now possess concern-
ing the preeise nature of ad.aptive genetic variation, the effective patterns of
environment which organisms encounter, md the role of inter-demic selection in
evolution.frhe last factor deser:rres special coment. As noted beforer Willisns (t966'
;197.-) and others staunchly maintain that the maintenance of sex in populations
should be interpreted without resort to moilels requiring group selection. Ttre
mod.els discusseil in this paper all inply group selection' some more openly thart
others. 1'hey neglect inttividual selection anc! they d.o not in themselves explain
what maintains sex in populations potentially or aetually polyrnorphic for its
presenee or absence. biven the li;ited question t'cloes sex accelerate evolution?",
this issue is not especially lnportant. Given the broader question rrwtqr does
sex survive in speeies?tt , i t may be er l t ical .Another point neglected in most d.iseussions of sex to date merits close
attention. f have implieitly assumed that sexual and asexual populations c('m-
pete in a-11 other respects on equal terms, that they are born fu11 blovn into
lhe world with equal- standing genetic vari-ation. This accurately refleets my
own experimental d.esign (Ttrompson, 19?l+) tut it nay not reprod.uce so faithfully
DOES SEX ACCELERATE EVOLUi'ION? 1l+9
the realities of nature. Asexual populatlons must often be genetically impov-erishecl, particularly when they descend from smaLl nrmbers of intlivid.uals, apoint crucial to the argurnents of Willians ancl Mltton (fgtS) and the erux of arecent polemic concerning an altogether tlifferent model for the role of sex innature (fhoday, 19?\; Roughgarden, 19?l+).
Potential genetic impoverishment may profounally complieate analysis of therole of sex in evolution. ldeynarcl Snith (l-9t>) asserts, foi exa,mpIe, thatasexual populations will orclinarily responcl to seleetlon through the prolifera-tion of single clones representing the fittest available genotype in eaeh popu-lation. This would wipe out genetic variance, not only for characters und.erselection, but for all other characters as well, effectlvely eJ-inrinating thepossibility of further evolutionary ehange ln the absence of new mutation.Willia.rns (f9?5, p. 151) argues along similar lines that asexual populations will-come to harbor one or at most a few genotypes, greatly restricting potential forevolutionary change. If the absence of sex does drastically linlt geneticvariation in species, sex must in the long run aceelerate evolutiont but in atrivial manne!, anil a manner d.i'voreecl from the lnmediate argr.ments of theFisher-}ful1er school and, the reassortnent theorists.
Limited. but compelllng eviclence from asexual species apparently saves theargument from this ignoninious end. Ma.ny asexual I'speciestt do show substantialgenetic variation, both anong lndividua,ls within populations ancl among popula-tions (Suonalainen and Sauran L9?3; Solbrig and Sinpson, 19?h; Lokki et aI.,l :g75) ancl references in i le Wet ancl Stalker, 19?\, anct Wil l ians, 1pf! , p. 150).Evidentlyn the absence of sex cloes not spe1I iloon to the raw material of naturalselection. It Just introcluces another factor, one of manyr that restrictsvariation. Perhaps sex speeds evolution on one hand. by promoting the d.iversi-fication of genotypes and slows it down on the other throrrgh the mechanismssuggested above, the relative strength of each effect d.epend.ing on populationsize and structure.
By approaching sex from the other sicle, by studying patterns of sexualsystems j.n nature, we might hope to infer something about sex itself. This isa hazardous end.eavor. For instance, manlr organisms switch from asexual tosexual reproduction when they face maJor environmental change (Chiselin, 197\;Wil l iarns, 1975). Does sex in these cases faci l i tate faster genet ic adaptat ionto new envlronments? Or cloes it curb too rapid ad.aptation to cond.itions extremeand., from the stanctpoint of later generationo, temporary and passing? Neitherhypothesis particularly excels or suffers at the hand.g of the accumulatecl data
of natural history. The faets d.o not force the issue, and taken alone' Isuspect they never wi1l.
Acknowledgrents
I thank J. l{aynartl Snith, L. Va"n Va1en, J. Felsenstein, G. Williarns, a.ndan anonJ[nous reviewer for nany helpful coments. Renaining errors are mi.net
not theirs. l"ly intellectual clebt to R.C. Lewontin shoultl be evid.ent. NDEA
Title fV and Forcl For:nclation Fellowships supportecl this end^eavor.
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