Copyright 0 1989 by the Genetics Society of America On the Origin of Meiotic Reproduction: A Genetic Modifier Model Marcy K. Uyenoyama* and Bengt 0. Bengtssont *Department of Zoology, Duke University, Durham, North Carolina 27706, and tDepartment of Genetics, Lund University, S-223 62 Lund, Sweden Manuscript received May 3 1, 1989 Accepted for publication September 2, 1989 ABSTRACT We study the conditions under which a rare allele that modifies the relative rates of meiotic reproduction and apomixis increases in a population in which meiotic reproduction entails selfing as well as random outcrossing. A distinct locus, at which mutation maintains alleles that are lethal in homozygous form, determines viability. We find that low viability of carriers of the lethal alleles, high rates of selfing, dominance of the introduced modifier allele, and lower rates of recombination promote the evolution of meiosis. Meiotic reproduction can evolve even in the absence of linkage between the modifier and the viability locus. The adaptive value of meiotic reproduction depends on the relative viabilities of offspring derived by meiosis and by apomixis, and on associations between the modifier and the viability locus. Meiotic reproduction, particularly under selfing, generates more diverse offspring, including those with very high and very low viability. Elimination of offspring with low viability generates positive associations between enhancers of meiotic reproduction and high viability. In addition, partial selfing generates positive associations in heterozygosity(identity disequi- librium) between the modifier and the viability locus, even in the absence of linkage. The two kinds of associationstogether can compensate for initial reductions in mean offspring viability under meiotic reproduction. EX comprises a syndromeof diverse processes, not anism to repair DNA [see BERNSTEINet al. (1984, S all of which have necessarily evolved in response 1985) and references therein],combine favorablemu- tothe same selection pressures. Diploidy, meiosis, tations (FISHER 1958,Chapter VI; MULLER 1932; recombination, and outcrossing all promote genetic CROWand KIMURA1965; MAYNARD SMITH 1968; diversity among offspring, but thiscommon effect ESHELand FELDMAN 1970), preventthe accumulation does not by itself imply a common evolutionary func- of deleterious mutations(MULLER 1964; FELSENSTEIN tion. Evolutionaryprocesses maintaining anyone com- 1974), reduce genetic load(CROW 1988), or improve ponent in highly refined sexual systems operate in a average offspringviability by increasing genetic diver- fundamentally different context from those that fa- sity (WILLIAMS1975, Chapter 1). The repair hypoth- vored its origin in primitive sexual systems. MAYNARD esis, which holds that sexuality evolved to reduce the SMITH(1978a, Chapter 1) has drawn a strong distinc- rate atwhich new mutations appear among offspring, tion between theories for the origin and the mainte- lies beyond our study. Neither do the hypothesis of nance of sex (see also CROW 1988).Our deterministic FISHERand MULLERapply to ourmodel, because they two-locus study supports the view that the evolution- require linkage. disequilibrium among multiple loci ary function of meiosis in response to recurrentdele- which affect viability (FELSENSTEIN1974; 1985). We teriousmutation is topromote the production of use our analysis to test and refine the two remaining offspring of very high quality, even at theexpense of heuristic interpretations of the adaptive significance reducing average offspringviability. Because the con- of sexual reproduction. In particular,we examine the ditions most conducive to the origin of meiosis (low generation and consequencesof disequilibrium be- rates of recombination and high rates of selfing) are generally associated with asexuality, our findings sug- tween a locus controlling viability and a modifier of gest that the original adaptive significance of compo- the rate of meiotic reproduction. nents of the sexual syndrome may reverse during the Distinction between isogamy and reduction in out- course of refinement. crossing: MAYNARDSMITH (1 978a, Chapter4; 1978b) Significance of deleterious mutations to the evo- argued that isogamy eliminates the twofold cost of lution of sex: Viewed as aresponse to mutation, meiosis. This conclusion is based on the observation sexual reproduction has been characterizedas a mech- that sexual and asexual species transmitthe same number of genes, provided that individuals can gen- The publication costs of this article were partly defrayed by the payment of page charges. This articlemust therefore be hereby marked“advedsemenf” erate one asexual zygote only at the expense of two in accordance with 18 U.S.C. $1734 solely to indicate this fact. sexual gametes [see Figure 6.2 in MAYNARDSMITH Genetics 123: 873-885 (December, 1989) 874 M. K. Uyenoyama and B. 0. Bengtsson (1978b)l. HOLSINGER, FELDMAN,and CHRISTIANSEN mostclosely to his under negligible investment in (1 984) used the term “pollen discounting” to describe sperm relative to eggs (4 approaching unity). In agree- the reduction in cross-fertilization as a consequence ment with our findings, meiosis doesnot incur a of increased selfing. Although the two processes have twofold cost in this case (HARPER 1982). often been treated as equivalent (CHARLESWORTH Origin of meiosis: Cohen and ZOHARI (1986) de- 1980; UYENOYAMA 1984),isogamy in fact represents rived the evolutionarily stable mixture of clonal and but one energetic constraint which ensures reduced sexual reproduction that maximizes the number of genetic contributions by less sexual forms. clones at equilibrium. Primarily asexual clones allocate In reflection of this identification of isogamy witha resources either to maintaining their own genotypes reduction in the ability to fertilize outcrossed eggs, or to generating novel genotypes through sexual re- most theoretical studies of the evolution of meiotic production. A balance between the generation of new reproduction from apomixis have assumed that either clones and theextinction of existing clones determines (1) two apomictic eggs are replaced by one meiotic the equilibrium number. Higher ratesof sexuality are egg and one sperm, or (2) two apomictic eggs are favored in unsaturated habitats which harbor many replaced by two meiotic eggs with no change in out- unoccupied niches. The force favoring sexuality in crossing success. KONDRASHOV’S(1 985) generalization COHENand ZOHARI’S (1986) model can be regarded of this approach assumes that the relative investment as a formof environmental unpredictability: offspring in apomictic seeds, amphimictic seeds, and pollen are that are unlike the parent survive if they happen to (1 + y)z/2, (1 - z)/2, and (1 - yz)/2, respectively. In be able to exploit a different niche. Other theories the studies of CHARLESWORTH(1980) and MARSHALL incorporating low or negative correlations between and BROWN (1981), the parameter y is set to zero, the selective regimes imposed on parental and off- signifying that apomixis has no effect on pollen pro- spring generations have been discussed by MAYNARD duction. This assumption may hold under well-devel- SMITH(1978a, Chapter 6). oped facultative apomixis (see MAYNARDSMITH We study evolutionary changes of a modifier of 1978a, Chapter 4; MARSHALLand BROWN1981). meiotic reproduction in response to deleterious mu- Because our primary interest lies in the origin of tations at a distinct locus which determines viability. meiosis rather thanits maintenance, we envision prim- Sexual reproduction involves both selfing and random itive organisms thatreproduce either asexually or outcrossing. Because meiosis does not suffer twofolda sexually by mating with another cell capable of con- disadvantage in our formulation, relatively small dif- jugation; in either case, the structural components of ferences in offspring viability can promote its origin. each cell are invested in one daughter cell. In our Further, even if segregation reduces the average via- model, a fractiona of a given genotype reproducesby bility of meiotically-derived offspring, associations be- apomixis, and the remaining fraction (1 - u) under- tween the modifier of reproduction and the viability goes meiosis. We assume that genotypes that repro- locus may permit the evolution of meiotic reproduc- duce by apomixis at a higher rate contribute less to tion. Selfing generates such associations through two effects. First, selfing generates a higher variance in the gamete pool from which offspring are derived by viability among offspring than apomixis. Elimination outcrossing. Because we assume both pollen discount- of the lessviable offspringinduces an association ing (positive y in KONDRASHOV’S(1 985) terminology) between high viability and enhancers of meiotic re- and a constant total number of meiotic and ameiotic production. Second, partial selfing generates identity eggs, our model departs from conventional formula- disequilibrium, even in the absence of linkage (BEN- tions (CHARLESWORTH 1980; MARSHALLAND BROWN NETT and BINET1956; WEIRand COCKERHAM 1973). 1981 ; KONDRASHOV1985), which we regard as more Identity disequilibrium implies a correlation in het- appropriate to the question of the maintenance of erozygosity between loci (HALDANE1949; COCKER- meiotic reproduction than to its origin. HAM and WEIR 1968), with individuals that are het- Unlike these studies, we find that meiosis does not erozygous at the modifier locus likely to be heterozy- incur a twofold