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Transcript
Classification of Hypotheses on the Advantage of Amphimixis A. S. Kondrashov A classification of hypotheses on the advantage of amphimixis over apomixis is presented. According to "Immediate Benefit" hypotheses, amphimixis is advantageous regardless of reciprocal gene exchange, because either it directly increases fitness of the progeny, reduces the deleterious mutation rate, or makes selection more efficient. In contrast, "Variation and Selection" hypotheses attribute the advantage of amphimixis to the reciprocal gene exchange that alters genetic variability and response to selection among the progeny. Most such hypotheses assume that amphimixis Increases variability and efficiency of selection, but some claim that amphimixis decreases response to selection. Variation and Selection hypotheses require that some factor, either random drift or epistatic selection, makes distributions of different alleles nonindependent, while another factor, either changes of the genotype witnesses or deleterious mutations, makes overrepresented genotypes nonoptimal. Numerous Variation and Selection hypotheses, dealing with either unstructured or spatially structured populations, are reviewed. Two of them seem most plausible: better responsiveness of the amphimictic population to widely fluctuating selection, and lower mutation load in the amphimictic population under synergistic selection against deleterious mutations. In both cases the large advantage of amphimixis requires rather stringent conditions, which could be falsified by careful experiment. Further progress in understanding the evolution of amphimixis will depend mostly on such experimental work. From the Section of Ecology and Systematics, Corson Hall, Cornell University, Ithaca, NY 14853. This paper was delivered at a symposium titled "The Evolution of Sex" sponsored by the American Genetic Association at Virginia Polytechnic Institute and State University in Blacksburg, Virginia, on July 10 and 11, 1992. I am grateful to James F. Crow for many discussions and constant nterest in this work; to John Maynard Smith for a valuable clarification about environmental deterministic models; to Mikhail 0. Ptitsyn for information about Serebrovsky's book; and to Nick Barton, Deborah Charlesworth, John Willis, and Martha Hamblin for many useful comments on the manuscript. This work was supported by the fellowship from the University of Chicago and by NIH grant GM 36827. Journal of Heredity 1993;84:372-387: 0022-1503/93/$5.00 After more than a century of debate, the major factors of the evolution of reproduction are still obscure. During the past 25 years, hypotheses have become so numerous and diverse that their classification is a necessity. The time is probably ripe for this: no fundamentally new hypothesis has appeared in the last 5 years, and I would be surprised-and delighted-if some important idea remains unpublished. Here I present a classification of hypotheses on what makes amphimixis-that is, a life cycle with alternating syngamy and meiosis-advantageous over apomixis-or production of offspring from single mitotically derived cells. Amphimixis is used instead of the potentially confusing term "sexual reproduction" because sexes are exogamous classes of gametes. In some cases of "sexual reproduction," any pair of gametes can form a zygote (e.g., homothally in fungi), and there are no sexes. Similarly, apomixis is used instead of "asexual reproduction" because the latter also sometimes includes vegetative repro- duction when a progeny appears from many cells. The proposed classification is based on population genetic reasoning, because I believe that genetic processes in populations are the key factor in the evolution of reproduction. Other approaches would lead to very different classifications. In an ecological classification, for example, hypotheses that invoke changing selection caused by negative biotic interactions would be placed together. Here, however, they belong to several different classes because I am not concerned with why a population is under some particular mode of selection, but only with what populational processes this leads to. Many features of my classification are not new. I accept Felsenstein's (1974, 1985, 1988) understanding of the basic dichotomy between "Immediate Benefit" and "Variation and Selection" hypotheses. The distinction between the two factors that can cause nonindependence of distributions of different alleles, genetic drift and epistatic selection, was also emphasized by Felsenstein (1985) who, however, ignored all other differences between various hypotheses. The 2 x 2 classification of the Variation and Selection hypotheses concerned with unstructured populations was proposed independently by Maynard Smith (1988a) and Kondrashov (1988a). However, some other decisions are new, and I hope that this classification will help organize the variety of ideas. Only a few early works will be cited (see Farley 1982; Mooney 1992). Consideration of each hypothesis and of its possible significance will be brief. I ask those who favor hypotheses that will be dismissed in one or two sentences to realize that this reflects the lack of space, not lack of respect for their views. Only the simplest problem of the competition between obligate amphimixis (high rates of recombination and outcrossing are assumed) and obligate apomixis is considered here, although I will sometimes use results on individual selection. The advantage of amphimixis in such a situation is necessary to protect the amphimictic population from apomictic clones that appear from it in one step. Here, group selection arguments are necessary and sufficient (Maynard Smith 1978; see the last sentence in the book): competing against obligate apomicts is always a group selection process. Still the group selection advantage of amphimixis should be relatively short term in the sense that after a transition to apomixis some bad consequences should appear soon, before amphimicts are outcompeted (Maynard Smith 1978, Ch. 1). This advantage must also be large, because it must outweigh the twofold cost of amphimixis with anisogamy and 1:1 sex allocation (see Lively and Lloyd 1990), together with its other costs (Crow 1988, 1992; Daly 1978; Hastings 1992; Lewis 1983). In some taxa the transition from amphimixis to secondary apomixis is very difficult (Maynard Smith 1986; Tortolero and Medina 1992), although it still may be successfully completed in the long run (Suomalainen et al. 1987). Particularly in mammals, both female and male gametes are necessary to start development (see Markert 1988), because of different patterns of DNA methylation. Thus, mammals are probably the only group in which virgin birth is impossible without a miracle. In such cases no short-term evolutionary factor protecting amphimixis is necessary. However, such protection is required in many other groups, certainly including some of the ancestors of mammals, where transition to apomixis can be simple, and in taxa where apomixis and amphimixis coexist (see Hebert et al. 1989). Therefore, ignoring the problem of maintaining amphimixis (Margulis and Sagan 1986) is incorrect. Obviously, the group selection advantage of obligate amphimixis over obligate apomixis does not guarantee that individual selection will cause gradual evolution of amphimixis from apomixis, or that recombination or outcrossing rates in the amphimictic population will not be gradually reduced to zero, essentially destroying amphimixis. These two problems are more complex and will not be systematically considered here, but usually individual selection for amphimixis requires more stringent conditions than group selection. Therefore, a group selection advantage for amphimixis gives necessary, but not sufficient, conditions for its existence. Immediate Benefit Versus Variation and Selection If we bear in mind that in sexual propagation twice as many individuals are required inorder to produce any number of descendants and if we further remember the important morphological differentiations which must take place in order to render sexual propagation possible, we are led to the conviction that sexual propagation must confer immense benefits upon organic life. I believe that such beneficial results will be found in the fact that sexual propagation may be regarded as a source of individual variability, furnishing material for the operation of natural selection (Weismann 1887, p. 609). In modern terms, this remarkable statement attributes the advantage of amphimixis to the changes of variability among the progeny, due to reciprocal gene exchange (segregation and recombination). Obviously, these changes can be beneficial only indirectly, through their influence on the results of selection, because reciprocal processes do not alter the allele frequencies and, thus, cannot "improve" the population directly. This idea gave rise to various hypotheses, which I call Variation and Selection. Different hypotheses offer different reasons for why amphimixis changes variability, and why this is beneficial. Usually, following Weismann, amphimixis is supposed to increase variability and thus enhance the response to selection, although some hypotheses claim that amphimixis actually reduces variability or, at least, decreases response to selection. Alternatively, reciprocal gene exchange, together with the changes of variability it may cause, can be viewed as only a neutral or even detrimental by-product of some other process which confers an immediate benefit and, thus, is the real reason for the existence of amphimixis. The first such non-Weismannian hypothesis claimed that amphimixis is necessary for "rejuvenation." More recently several other hypotheses of this kind were proposed. Such hypotheses are in some sense simpler than the Weismannian hypotheses because their key arguments do not require quantitative analysis at the population level. Thus, I treat them first. Immediate Benefit Hypotheses When talking about a benefit, we must ask "to whom?" and "why?" As far as I know, nobody has attributed any benefit of amphimixis to the parents who are engaged in it, and the supposed beneficiaries are the offspring. Three broad immediate benefits are possible: (1) increased fitness of offspring not caused by changes in their genotypes, (2) better offspring genotypes because of a lower deleterious mutation rate, and (3) better offspring genotypes because of more effective selection (Appendix 1). The possibility that amphimixis evolved for the benefit of parasitic DNA (see Hickey and Rose 1988) may be relevant to its origin, but not to its maintenance, especially in multicellular organisms. Parasites can only decrease the fitness of amphimicts as a group (Hastings 1992), and, in contrast to E. coli, where F- cells may be unable to refuse mating with F ones, an apomictic dandelion will not change its habits only because its amphimictic neighbor is sick. Increased Fitness of Progeny Regardless of Genotypes Amphimixis and apomixis are profoundly different at the cellular and organismal levels and, in principle, any feature that distinguishes amphimixis could be claimed to enhance the fitness of amphimictically produced progeny. Of course, amphimicts must be compared with "real" apomicts, which reproduce quite efficiently, and not with half-evolved secondary forms suffering from "sexual hang-ups" (Maynard Smith 1986). Two options are: 1. A progeny is better off having two parents-father and mother (Lloyd 1980, p. 91). This a very straightforward as- Kondrashov Advantages of Amphinis 373 sumption, because, from the point of view of a diploid progeny, two parents instead of one is a major distinguishing property of amphimixis. 2. Chromosome conjugation during meiosis allows repair of double-strand DNA damage (see Bernstein and Bernstein 1991; Dougherty 1955; Michod 1993), which could provide a mechanism for "rejuvenation" (see Bell 1988; Bernstein and Bernstein 1991, pp. 6-10; Farley 1982, pp. 203-208). Both hypotheses can work even in a monomorphic population and do not require population genetic analysis. However, they have serious problems. The number of parents is irrelevant in species without parental care. Even in monogamous species when the father cares for the progeny, amphimixis is defenseless against females who are behaviorally normal but produce only daughters by apomixis. Repair of double-strand damage may, at best, require chromosome conjugation, but not amphimixis: permanently diploid or polyploid apomicts, which are numerous among lower eukaryotes (Margulis et al. 1990), could also do this. In fact, doublestrand gaps may be efficiently repaired in diploid mitosis without any significant increase of crossing over of outside markers (Nassif and Engels 1993). Moreover, there is no direct evidence that DNA repair is a purpose of meiosis. On the contrary, the data (Cao et al. 1990) show that doublestrand breaks are deliberately introduced during meiosis to initiate reciprocal recombination, while in mutants incapable of recombination these breaks do not appear. This is hardly consistent with the view that recombination is only a by-product of the repair of such breaks. This view also failed to provide a credible explanation for outcrossing (Maynard Smith 1988a, p. 107; Szatmary and K6ver 1991). "Rejuvenation" in some experiments with ciliates may simply reflect the inability of the macronucleus to reproduce itself indefinitely (perhaps because it divides amitotically, see Bell 1988). If so, rejuvenation is not related to the evolutionary advantage of amphimixis any more than aging in higher organisms, where both apomixis and amphimixis can produce equally "young" offspring. Decreased Deleterious Mutation Rate Three hypothetical mechanisms for a decrease in the deleterious mutation rate under amphimixis have been proposed: 1. Most new mutations are deletions, which form gaps during chromosome con- 374 The Joumal of Heredity 1993:85) jugation, and these gaps can be filled by biased conversion (Bengtsson 1985). 2. Most new mutations are insertions, which loop out during conjugation and can be cut out (Ettinger 1986). 3. Most new epimutations are demethylations, which can be reverted during conjugation by maintenance methylases (Holliday 1988). All three hypotheses claim that there is some nonreciprocal genetic process associated with chromosome conjugation, which, in contrast to harmful conventional nonreciprocal processes (Crow 1991), is beneficial, because the cell can distinguish between good and bad. Of course, hypotheses 1 and 2 cannot be simultaneously correct, because each length difference can be viewed as the result of either insertion or deletion. In contrast to the hypothesis that considers DNA damage, these hypotheses can account for syngamy and outcrossing (Holliday 1988, p. 53). Suppose that a nonreciprocal process usually goes in the right direction, but sometimes makes a mistake. This leads to a homozygous mutation (or epimutation) which, however, can be reverted with high probability after mating with an unrelated individual. All three hypotheses require high genomic deleterious mutation (or epimutation) rates, to make their reduction important, and some population genetic analysis is necessary to evaluate its consequences. An important conclusion from this analysis is that even rare cases when a bad allele is mistakenly favored by the nonreciprocal process have disproportionately severe consequences on fitness (Bengtsson 1990). Thus, deleterious mutations or epimutations must almost always have a particular molecular nature, which seems impossible. Furthermore, no extant data show that the proposed mechanisms actually exist. More Efficient Selection In an amphimictic population there is a component of fitness-mating successthat does not exist under apomixis. With polygamy, more stringent selection among males is not involved with any additional cost. The same is true for selection among abundant male gametes or pollen. Therefore, amphimixis can be beneficial due to increased efficiency of selection if there is a positive correlation between the fitnesses of progeny and of the father. This was first noted by Geodakyan (1965, p. 106) who concluded that "the advantages of sexual reproduction with two different sexes are not limited to genetic heterogeneity of the progeny." Sexual selection can actually cause females to choose best mates or best gametes (Trivers 1976; see also Manning 1984; Manning and Jenkins 1980; Seger and Hamilton 1988, p. 190). In case of gamete or pollen selection (see Walsh and Charlesworth 1992) this also requires similar selection in the haploid and diploid phases (Crow 1991; Hastings 1991), which may be the case if selection operates through pollen viability. Here amphimixis is supposed not to create variability "furnishing material for the operation of natural selection" but to improve selection itself. Obviously, females should choose the best males. Recently, Koeslag and Koeslag (1993) claimed that even preferring the standard mates may be beneficial. This can probably be true if variability is caused by severely deleterious mutations with low frequencies, so that most individuals do not carry them, and if "standard" means "best." If, however, we consider slightly deleterious mutations, the population distribution of their number per genome is roughly symmetrical, and average individuals have just average genotypes. The "better selection" hypothesis requires serious population genetic analysis. In particular, selection tends to reduce the heritability of fitness, so that some process must operate to create additive genetic variance. This is also essential for Weismannian hypotheses. Additional work is needed to calculate the advantage of different modes of mate choice in various situations. I regard the better selection hypothesis as the only one of importance within the Immediate Benefit category. However, it can hardly be the leading factor in the evolution of amphimixis (D. Charlesworth and Charlesworth 1992) and certainly has only limited applicability, because exclusion of some gametes from syngamy is costly in isogamous amphimicts (probably including the primitive ones), while exclusion of some individuals is costly in monogamous populations. Classification of Variation and Selection Hypotheses In the early age of population genetics, the advantage of reciprocal gene exchange was widely assumed to be self-evident and large. The main argument was that segregation and recombination lead, in heterozygous parents, to enormous genetic variability among the progeny, which dramatically increases the opportunity for selection (e.g., Castle 1916, 1930; East 1918; Jennings 1913; Morgan 1913; Svedelius 1927). Most of the recent progress in the area was stimulated by the realization that (1) reciprocal gene exchange does not always change variability and that (2) when it does, this is not always advantageous. Of course, the same problems are also relevant to the opposite view (Walton 1915), which attributes the benefit of amphimixis to reduction of variability among the progeny. It is now well understood that when different alleles are not associated (i.e., when they are distributed in the population independently) reciprocal gene exchange has no effect on the genetic structure of the progeny at the level of the whole population (see Felsenstein 1988). If the haploid phase of the amphimictic life cycle is considered, segregation is always useless, while in the diploid phase it has no effect when alleles of the same locus are unassociated (Hardy-Weinberg equilibrium). Recombination is useless if alleles of different loci are unassociated (linkage equilibrium). Therefore, insofar as segregation and recombination rapidly destroy associations, some factor must, to make transition to apomixis disadvantageous, constantly re-create them. However, even if distributions of different alleles are nonindependent-that is, if associations exist-there is no guarantee that their destruction is advantageous. First of all, there must be some nonneutral genetic variability, so that selection must constantly operate in the population despite the fact that it removes maladapted genotypes and usually decreases nonneutral variability. This problem was appreciated very early: "In a mass culture the favorable combinations for that culture will soon be made, ... the race will become a pure strain, and further conjugation could do nothing for it even if it were transferred to a medium insulted to it" (Morgan 1913, p. 11). Thus, some factor must permanently supply nonneutral genetic variability. But even when associations involve nonneutral alleles, their reduction, which means destruction of the genotypes already tested by selection, can be harmful. When a population without spatial structure is considered, each of the questions"What creates associations?" and "What makes their destruction beneficial?"-allows two answers, which leads to the 2 x 2 classification of the relevant Variation and Selection hypotheses (Table 1, com- Table . Clasificaton of Variation and Selection bypotbeases (local population) Cause of nonindependence Genetic drift Epistatic selection Causes of excess of nonoptimal genotypes: Deleterious mutations Changes of environment Environmental stochastic (ES) Environmental deterministic (ED) pare with Maynard Smith 1988a, p. 115, 1989, p. 253; Kondrashov 1988a, p. 436). Hypotheses from these four classes will be considered next (Appendix 2), then populations with spatial structure, where associations within subpopulations are important (Appendix 3), will be examined. Two Causes of Associations Between Alleles Distributions of different alleles can become nonindependent due to either stochastic (genetic drift in finite populations) or deterministic (epistatic selection in populations of any size) factors. Both repulsion (alleles with similar phenotypic effects are distributed more uniformly than randomly, so that the variance is decreased) and coupling (similar alleles tend to be together, which leads to increased variance) associations may be created. The origin of associations due to genetic drift was described in the context of the evolution of amphimixis by Felsenstein (1988, pp. 82-85). The simplest example is that if a genotype has an expected frequency of 10 6 in a population of size 104, then the distributions of alleles that constitute this genotype simply cannot be independent. Roughly speaking, there will be no individuals of such genotype 99 generations out of every 100 and one such individual in the rest. Thus, the actual frequency of the rare genotype is usually slightly less than expected (0) but sometimes is much higher (10 4), and most of the time the alleles that constitute it are in repulsion, but rarely is there a much stronger coupling association. In this case, the repulsion association can have a disproportionately high effect (see below). In contrast, ifthe considered genotype is frequent, a finite population spends approximately equal time with coupling and repulsion associations, and random drift is probably not important for our purposes. Creation of associations by epistatic selection was studied by Felsenstein (1965). Imagine a pair of factors I and 11, such that each individual carries two of them. These two factors can be either alleles of the same locus, if we consider the diploid phase, or equally frequent alleles at two loci, when Mutational stochastic (MS) Mutational deterministic (MD) I means, say, A or B, while II means a or b, if individuals are haploid. When these factors are distributed independently in the population, the frequencies of individuals carrying none, one, and two of factor 11are p, = a2 , p, = 2a(1 - a), and P2 = (I - a)2 , where a is the frequency of factor II. Evidently, under any a, PoP = 0.25pl2 (if we distinguish between different orders of factors and consider four frequencies, Poo = Po, Po = Plo = 0.5p,, and p, = P3, this implies d = ooP], - P0,opo = 0, where d is the coefficient of linkage disequilibrium, see Lewontin 1974, p. 284). It is easy to show that, after selection, independence persists only if w,2 = w, where wi is the relative fitness of individuals carrying i factors II. This means that these factors influence the fitness independently, in the sense that the fitness of a genotype is a product of "fitnesses" of factors which constitute it. Otherwise, if w,2 > w0w2, selection causes excess of individuals with one factor 11, such that after selection PPz < 0.25p,2 , while if w,2 < uw2, such individuals are in deficit and PoP2 > 0. 25p, 2 after selection. Obviously, the first case yields repulsion and the second gives coupling association. Multiplicative selection that does not create associations is always directionalthat is, wl is between w0 and w2 (the case of no selection, w0 = w, = w2 also belongs here), while stabilizing selection [w > max(uw, w2)] causes repulsion and disruptive selection [w < min(ub,w2 )] causes coupling association. Of course, directional selection can also cause association in either direction. If selection acts on the total number of factors II, coupling associations facilitate selection, while repulsion associations slow it down (obviously, with p = 1 selection is impossible, see Felsenstein 1988, p. 77). The situation is analogous if a genome carries many factors and selection acts on the total number of factors of some type in the genome. If factors are distributed independently, the trait x, a continuous approximation to the number of factors, has Gaussian distribution. Selection w(x) does not change the variance of this distribution if w(x) = e, which corresponds Kondrashov ·Advantages of Amphimuxis 375 to multiplicative selection w(x) = (1 + s)' in the discrete case. Selection always decreases the population variance ("narrowing" selection), causing repulsion association, if [uw(x)'/w(x)]' < 0 for all x, and increases the variance ("widening" selection) and causes coupling association if [w(x)'/w(x)]' > 0 for all x(Shnol and Kondrashov, 1993). As in the case of two factors, stabilizing selection (e.g., of Gaussian shape) causes repulsion and disruptive selection coupling associations. Interestingly, the realistic modes of directional selection, where fitness tends to some positive limit when x changes in one direction, and to zero when it changes in the other, also usually cause repulsion associations. f the trait is the number of deleterious mutations and w'(x) < 0, selection is narrowing under synergistic epistatis-that is, when each mutation added causes a larger change (decrease) in relative fitness (Kimura and Maruyama 1966). Conversely, if the trait is the number of beneficial mutations and u(x)' > 0, selection is narrowing under diminishing epistasis-that is, when each additional mutation results in a smaller change (increase) of relative fitness (Crow and Kimura 1965; Eshel and Feldman 1970). Two Causes of the Advantage of Destroying Associations Obviously, destruction of associations is not always beneficial. Consider an apomictic population under constant selection. At equilibrium it can either be completely genetically monomorphic or it can consist of one heterozygous genotype (if individuals are diploid) or of several genotypes, which can happen either if these genotypes have exactly the same fitnesses or, more realistically, if selection is frequency-dependent. In the first case, segregation and recombination are useless; in the second and third, they are deleterious because of segregation and recombination load (Crow 1970), with the sole unlikely exception of the case when frequency-dependence exactly favors the independent distribution of alleles, when the reciprocal gene exchange is neutral. Thus, an apomictic population under constant selection reaches an optimal state and, as long as nothing disturbs the match between selection and the population distribution, segregation and recombination are (contrary to some claims, see Wills 1981, pp. 275-276) deleterious or, at best, neutral (Fisher 1930; see Liberman and Feldman 1986). Selection tends to create 376 The Journal of Heredity 1993:845) an excess of "good" genotypes, and the destruction of associations may be advantageous only if some factor permanently impairs the match between the genotypes and what selection favors, which make overrepresented "good" genotypes maladapted. Of course, this also requires the presence of nonneutral genetic variability. What can cause a population distribution to deviate from the optimum? In principle, several forces can do this, including changes of selection, mutations, random drift, and immigration. So far I have touched on only the first two forces as factors that can make destruction of associations advantageous in unstructured population. Thus we come to the second dimension for the 2 x 2 classification of Variation and Selection hypotheses dealing with such populations (Table 1). Drift can be important within subpopulations of a structured population, but in unstructured populations of reasonable size it is probably too slow. Nobody, to my knowledge, has considered the possible advantage of amphimixis in populations under pressure from immigrants, which are either maladapted themselves or produce maladapted hybrids. This scenario does not seem plausible because amphimixis can cause matings of well-adapted residents with these immigrants. If some factor causes deviation of the population distribution from the optimal, two different situations are possible. First, this deviation can lead to directional selection (e.g., in case of deleterious mutations or of beneficial mutations which can be interpreted as the consequences of irreversibly changing selection) or stabilizing selection with the optimum deviating from the population mean (when, for example, this optimum fluctuates). In both cases repulsion associations are created either by random drift or by directional or stabilizing selection. Their destruction is beneficial only if selection is mostly directional, when the increased variance enhances the ability of a population to respond. Alternatively, selection may fluctuate between narrowing (stabilizing or directional) on the one hand, and widening (disruptive) on the other, thus creating associations in alternating directions at different times. Destruction of such alternating associations can also be beneficial in some situations. In this case, then, amphimixis can both increase and decrease (by destroying coupling associations) the variance, making selection either more or less efficient, which allows for many dif- ferent possibilities. Let us now consider four classes of Variation and Selection hypotheses that can be applied to geographically unstructured populations. Environmental Stochastic (ES) Hypotheses Generating associations by random drift is a very slow process, if the population is not extremely small. Therefore, if all the possible genotypes are present in substantial numbers, selection (and we are interested in highly selectable variability) can easily overcome any effects of random drift. Thus, all stochastic hypotheses depend on rare events. In unstructured populations such events appear most naturally if we assume an irreversibly changing environment in which adaptation depends on the immediate incorporation of new beneficial mutations because the same alleles were always deleterious in the past and, thus, are initially absent in the population. Interactions Between Beneficial Mutations If selection favors previously deleterious alleles at more than one locus simultaneously, finite amphimictic populations can accumulate beneficial mutations faster than apomictic, because mutations that appear in different individuals can later be combined in the same genotype. This is usually called the Fisher-Muller hypothesis (Fisher 1930; Muller 1932; see Crow and Kimura 1965), although Morgan (1913, p. 14) expressed essentially the same idea much earlier saying that with amphimixis "the new character would be brought into relation with all the other variations that are found in the component races and increase thereby its chances of favorable combination." Similarly, in diploid amphimictic populations a beneficial mutation can become homozygous without appearing twice (Kirkpatrick and Jenkins 1989). In infinitely large populations, as long as mutations occur independently, their distributions are initially independent. However, the expected frequencies of genotypes carrying many mutations are extremely low, and randomly generated associations make selection less efficient, because repulsion associations are disproportionally important (called the HillRobertson effect; see Felsenstein 1988, pp. 82-86). Thus, even in very large, but finite, populations new beneficial mutations are mostly in repulsion association (Crow and Kimura 1969; Felsenstein 1988, p. 79; Maynard Smith 1978, p. 15; Quammen and Nyberg 1989), so that the best genotypes are initially absent and amphimixis can accelerate evolution. If the environment changes rapidly-that is, if previously deleterious alleles become beneficial at several loci each generation-amphimixis can greatly increase the ability of populations of any reasonable size to adapt (Griffin 1983). Interactions Between Beneficial and Deleterious Mutations Usually, the name Fisher is mentioned only in connection with interactions between beneficial mutations. Actually, Fisher (1930, p. 122) considered, in the same sentence, two related but different phenomena: If ... the mutation rates, both of beneficial and of deleterious mutations, are high enough to maintain any considerable genetic diversity, it will only be the best adapted genotypes which can become the ancestors of further generations and the beneficial mutations which occur will have only the minutest chance of not appearing in types of organisms so inferior to some of their competitors, that their offspring will certainly be supplanted by those of the latter. Thus, under apomixis a beneficial mutation must, to confer maximal advantage, appear in a genome which not only carries all the beneficial mutations available but also is deleterious mutation-free. Otherwise, either the beneficial mutation is eliminated or its spread leads to fixation of one or more deleterious alleles. Obviously, there is no such restriction in an amphimictic population (Manning and Jenkins 1980; Manning and Thompson 1984). As before, here amphimixis is advantageous because it destroys repulsion associations created by the appearance of rare beneficial mutations. However, the current mechanism does not require that more than one beneficial mutation is on its way to fixation at any time, because deleterious mutations are always present. Therefore, randomly generated associations can interfere even with slow evolution. Interactions Between Beneficial Mutations and Polymorphisms If selection maintains a polymorphism in an apomictic population, the genotype with the highest frequency will accumulate beneficial mutations faster than others. This may destroy the polymorphism (Manning 1983), whereas if selection strongly protects it, a beneficial allele must independently take over each genotype (Manning 1982c) to take over the whole population. This is not the case with amphimixis, which can thus have some advantage. Fluctuating Selection In Finite Populations Seger and Hamilton (1988, p. 190) suggested that biotic interactions can drive some genotypes to very low frequencies even when the environment does not change irreversibly. Then such genotypes can go extinct by chance, and amphimixis can be beneficial by recreating them after they become favorable again. I am not aware of other attempts to attribute importance to the rare events which are necessary for ES hypotheses under fluctuating, instead of irreversible, selection. Possible Importance of ES Hypotheses Stochastic hypotheses apply only to finite populations. However, this can hardly be a serious limitation of ES hypotheses if the population waits for beneficial mutations at several loci or when slightly deleterious mutations are considered, because in both cases the expected frequency of a genotype in which a new beneficial allele can cause maximal advantage can be extremely low. Thus, populations of any possible size still may behave as finite. However, ES hypotheses do not easily lead to a short-term advantage of amphimixis (Wiener et al. 1992). Inability of an apomictic population to incorporate new beneficial mutations becomes important only after a new mutation is incorporated into an amphimictic population. Thus, the characteristic time after which transition to apomixis becomes deleterious is no less than the average interval between successive fixations of beneficial alleles under amphimixis. Actually, this time can be much longer, if the absence of many new beneficial alleles in an apomictic population is alone sufficient to counterbalance its twofold advantage. Thus, ES hypotheses can lead to shortterm advantage of amphimixis, and, therefore, to its protection from apomictic clones, only in populations that undergo fast, irreversible changes. Most data indicate that in nature irreversible changes are, in fact, very slow. Besides, even very low rates of recombination and outcrossing can destroy the randomly generated associations, so that stochastic hypotheses (both environmental and mutational) can hardly explain the evolution within amphimictic populations. Therefore, deterministic hypotheses are generally more promising. However, genetic drift can be important in the long run, limiting the life span of obligately apomictic populations and determining their taxonomic distribution. Probably the slower rate of accumulation of beneficial mutations in the presence of deleterious mutations is the most important among the ES hypotheses. Environmental Deterministic (ED) Hypotheses Irreversibly changing selection can also lead to an advantage of amphimixis when genetic drift can be ignored. Even if initially beneficial mutations are distributed independently, repulsion associations will be created by selection that favors them if they interact with diminishing epistasis. Because epistatic selection can create associations very quickly; the deterministic advantage of amphimixis may be large and short term; and, in contrast to stochastic hypotheses, no rare events are necessary here. Thus, amphimixis may be advantageous when the alleles that are beneficial under a "new" environment were already beneficial in the past and, consequently, always have significant frequencies. This means that selection can be fluctuating instead of irreversible. Therefore, the deterministic advantage of amphimixis can appear due to the reorganization of preexisting variability, without immediate incorporation of rare and new mutations, if the necessary allele combinations are underrepresented. However, maintaining substantial variability under fluctuating selection is not automatic and requires some specific conditions. If selection fluctuates widely, amphimixis can be advantageous by enhancing the population's response. An opposite phenomenon is also possible: amphimixis can decrease the reaction of the population to some regimes of fluctuating selection, and this can also be beneficial. Irreversible Environment Suppose that selection is either directional or stabilizing with a moving optimum. In both cases, the population lags behind the optimum. Such selection naturally leads to repulsion associations between the alleles that influence the trait in the same direction and to reduced variance of their number per genome. Restoration of the variance by amphimixis is beneficial because Kondrashov Advantages of Amphimxis 377 it enhances the population response to selection (Eshel and Feldman 1970; Felsenstein 1965; Fraser 1957; Mather 1943; Maynard Smith 1978, p. 14). Like the corresponding ES hypothesis, this requires that more than one allele be simultaneously on their way to fixation. Asignificant advantage of amphimixis is possible in this situation (B. Charlesworth 1993, in press; Crow 1992), but this requires strong and effectively directional selection, which causes substantial lag load (Maynard Smith 1978, p. 21). Under Gaussian selection, the optimum must move each generation by at least about 3% of the standard deviation of the population distribution of the trait to cause a higher mean fitness of the amphimictic population. If it moves faster, the advantage of amphimixis can be very large (B. Charlesworth 1993, in press). Obviously, in the long run, the population mean must evolve irreversibly at the same rate. Fluctuating Environment: Better Responsiveness Assume that selection-for example, the optimum of stabilizing selection-fluctuates within some range and that the amplitude of fluctuations is large while their typical period is not very short. Then there is a big advantage of, and time for, adaptation, and the best strategy is to follow these fluctuations with as small a lag as possible. Thus, like under irreversible selection, amphimixis can be advantageous by destroying repulsion associations, which are constantly created by selection, but irreversible changes in the population can be avoided. Quantitatively, the effect of amphimixis on fitness depends on the balance between directional selection (when destruction of repulsion associations and increased variance are beneficial) and stabilizing selection (when an increase of variance is disadvantageous) (Bergman and Feldman 1990; B. Charlesworth 1993, in press; Korol and Preigel 1989; Korol et al. 1990; Mather 1943; Maynard Smith 1980, 1988b; Slatkin and Lande 1976; Treisman 1976). Thus, the larger the amplitude of changes in the fitness optimum, the more advantageous is the amphimixis (B. Charlesworth 1993, in press). Under the simplest "all-or-nothing" selection (fitness is 1 if the trait deviates no more than d from the optimum; otherwise fitness is zero) amphimixis is advantageous ifthere is no "middle" genotype with positive (i.e., 1) fitness under any possible selection regime. Otherwise an apomictic 378 The Joural of Heredty 1993:84(5) population consisting of individuals with this genotype will win (Treisman 1976). This condition requires that the amplitude of fluctuations of the optimum is more than 2d.Then, after one "environmental cycle," every clone and thus the whole apomictic population will die. The variance of quantitative traits is probably always smaller than the width of the selection function that acts on them. About 32% of a population with a Gaussian distribution deviates from the mean by more than I SD. Thus, d must be at least about 1 SD of the trait to prevent too high a genetic load, even when the population mean coincides with the fitness optimum. Experimental data (Turelli 1984) suggest that the trait variance usually is about one order of magnitude smaller than the width of the selection curve. Therefore, absence of the "middle" genotypes requires fluctuations of the fitness optimum with the range of at least I SD of a trait, and probably much larger. Consideration of Gaussian selection, where apomixis is selected against if every genotype sometimes has very low fitness, leads to a similar conclusion (B. Charlesworth, 1993, in press). Directional selection with fluctuating direction also acts similarly. The situation probably remains essentially the same if selection acts on many traits simultaneously, because selection still cannot be too stringent in terms of individual traits without causing too high a load. If, for example, the population mean and the fitness optimum coincide, individuals who deviate from the mean by less than I SD in every trait must have high fitnesses. Thus, the projection of the fitness optimum on each axis must fluctuate, to ensure the advantage of amphimixis, in the range of at least I SD of the trait. Still, with many traits, amphimixis can be maintained more easily because fluctuation of the fitness optimum even within some limited volume may lead to effectively irreversible selection (Kondrashov AS, unpublished). Similar phenomena are possible even with one locus if selection acts during the diploid phase (Weinshall 1986). Here, however, there is probably "not enough room" to make better responsiveness advantageous with only two alleles. In this case, if the fitness of the heterozygote is more than the geometric mean of fitnesses of homozygotes (a condition for repulsion association), an apomictic population consisting of heterozygous individuals wins. However, amphimixis can be advantageous with three alleles if allele A, (ei- ther homo- or heterozygous) is necessary to survive during the first generation, allele A2 is necessary during the second, and allele A3 is necessary during the third. In this case the apomictic population is extinct after three generations because no genotype contains all three alleles and thus no clone can survive all three seasons, whereas an amphimictic population persists indefinitely because all genotypes are present in each generation (Eshel and Weinshall 1987; Weinshall 1986; Weinshall and Eshel 1987). Obviously, here the advantage of amphimixis is caused exclusively by segregation. Fluctuating selection itself does not maintain variability, and the population eventually becomes monomorphic, even if it causes a drastic decrease of the mean fitness (Lande 1977; Lewontin 1964; Maynard Smith 1979). Thus, ED hypotheses depend on the protection of variability by some factor, e.g., mutations or frequencydependent selection (as above). So far we have considered here only directional and stabilizing selection, which usually create only repulsion associations. However, amphimixis can also enhance response to selection, which leads to associations in alternating directions. All existing models of this kind were created in terms of individual loci. Suppose that selection acts during haplophase in a population with two loci and two alleles at each locus. Suppose that, for some reason, selection is cyclical and favors, successively, AB, aB, ab, and Ab genotypes. Then, just before selection starts to favor AB again, this genotype can be underrepresented because selection has not favored it for a long time (of course, the corresponding epistasis is required). Now amphimixis is advantageous because it increases the population response to selection (Bell and Maynard Smith 1987). Probably, several other models in which negative biotic interactions are considered lead to the advantage of amphimixis due to such a mechanism (Glesener 1979; Hamilton 1980; Nee 1989). Fluctuating Environment: Nonresponsiveness If selection fluctuates very frequently, the best strategy for the population may be to adopt the genetic composition corresponding to some average selection and to minimize the response to its fluctuations. Remarkably, amphimixis may lead to this, which can give it an advantage (Thompson 1976; Walton 1915). In such situations "without sexual crossing, there would be endless changes ... , & hence there could be no improvement' (Darwin 1838 in Barrett et al. 1987, p. 410). Consider the extreme case of a population with one locus and two alleles A, and A2. Suppose (Hamilton WD, personal communication) that in odd generations heterozygotes are inviable, while in even generations both homozygotes are inviable. Then an apomictic population will go extinct after two generations, while an amphimictic population, which starts every generation in the same Hardy-Weinberg distribution, persists indefinitely with a load of 0.5. An analogous model can, of course, be formulated in terms of a polygenic trait with alternating disruptive and stabilizing selection. In the case of one diallelic locus, amphimixis can be advantageous even if the fitnesses of the three genotypes fluctuate independently, because this also leads to alterations between narrowing and widening selection, although a large advantage requires unrealistically strong selection. This situation was studied by Roughgarden (1991), in an article with the modest title "The Evolution of Sex," who concluded that the advantage of amphimixis is caused by "nonresponsiveness of an amphimictic population to changing conditions." If, however, fluctuations are rare, amphimixis becomes disadvantageous (Roughgarden 1991, figure 4). The first model of this kind was proposed by Sturtevant and Mather (1938) and is also based on alternating stabilizing and disruptive selection. However, instead of one locus and diploid selection it considered two diallelic loci under selection acting in haploid phase which favors genotypes AB and ab in odd generations and genotypes Ab and aB in even ones. If we characterize the genotype by the number of alleles denoted by a capital letter, this is exactly the same alternation of stabilizing and disruptive selection as described above. Here amphimixis cannot maintain the frequency of 25% for all genotypes, because interlocus associations are destroyed only asymptotically. Still, it can reduce the amplitude of their fluctuations, which, as before, is advantageous if selection fluctuates frequently (B. Charlesworth 1976; Sasaki and Iwasa 1987), because every genotype is produced until it becomes favored. In both these models, amphimixis is beneficial under alternation of pure stabilizing and disruptive selection due to segregation (one locus) or recombination (two loci), while allele frequencies remain invariant. But in some other cases of fluctuating selection, which causes alternation in the direction of associations, allele frequencies probably change too widely, and amphimixis was reported to be beneficial due to nonresponsiveness because it "stores temporarily bad alleles" (Hamilton et al. 1990). Remarkably, the models of Bell and Maynard Smith (1987) and of Sturtevant and Mather (1938) consider the same genetic variability, and in both cases the direction of associations alternates. Nevertheless, selection is very different, the period of changes is much longer, and the allele frequencies are variable in the first model. Consequently, in these models amphimixis is advantageous for opposite reasons: better responsiveness in the first case, and nonresponsiveness in the second. Possible Importance of ED Hypotheses The problem with hypotheses assuming irreversible selection, namely the lack or rarity of such changes in nature, is relevant to both ES and ED hypotheses. However, according to the ED mechanism, amphimixis can also enjoy a considerable advantage of similar nature under widely fluctuating selection. Even in this case, the advantage always requires wide changeseither in the mean values of polygenic traits or in allele frequencies at individual loci. The time over which apomixis goes extinct cannot be shorter than the characteristic period of such changes. So far, no data suggest that such changes are actually widespread in nature. A serious problem with many ED models is maintaining variability. If selection with a fluctuating optimum in polygenic traits is assumed, variability can be maintained by conditionally beneficial mutations (see Kondrashov and Turelli 1992). Another option is frequency-dependent selection, which naturally appears under negative biotic interactions in which being common can be disadvantageous (Hamilton 1993; Hutson and Law 1981; Jaenike 1978; Levin 1975). However, conditions for maintaining variability and for the advantage of amphimixis can be contradictory (Moore and Hines 1981). Of course, amphimixis is always disadvantageous when beneficial mutations interact synergistically or when selection favors combinations of individually deleterious mutations. In terms of quantitative genetics, amphimixis reduces the efficiency of selection that can act only on the additive component of the genetic variance, compared with the total variance under apomixis. Amphimixis cannot be advantageous if this effect is large (Crow and Kimura 1965; Eshel and Feldman 1970). Many authors emphasize negative biotic interactions as the possible cause of selection to maintain amphimixis. Some of them consider the effects of drift or of spatial structure, but most such models are clearly of the ED type, because coevolution between predator and prey or host and parasite leads to fluctuating selection. Unfortunately, in many articles of this kind, the mode of selection that acts on a population in which amphimixis is maintained is not reported. It seems, however, that most, if not all, such models lead to associations in alternating directions. More explicit description of selection resulting from ecological processes would be very helpful and can lead to different conclusions (May and Anderson 1983). It would be interesting to see if negative biotic interactions could lead to the advantage of amphimixis if the species interact through polygenic traits, instead of individual loci, and if associations are always of the repulsion type. As far as narrowing (directional or stabilizing) selection is considered, associations are always repulsion, although selection may, at different moments, favor different directions of associations (B. Charlesworth 1993, in press; Maynard Smith 1988b). In this case, the advantage of amphimixis can be caused only by better responsiveness. In contrast, if in some dimension selection is sometimes widening (disruptive), it can actually create associations in alternating directions, instead of just favoring them. The advantage of amphimixis can appear both because of better responsiveness, when optimal genotypes are underrepresented but all the necessary alleles are present (Bell and Maynard Smith 1987), and because of nonresponsiveness, when amphimixis prevents the population from losing either genotypes (B. Charlesworth 1976; Sturtevant and Mather 1938) or alleles (Hamilton et al. 1990) that are temporarily deleterious. It does not seem plausible that amphimixis can always reduce variance among progeny. This could happen only if selection is permanently widening, but in such a case apomixis would be favored. The claim of Walton (1915) was partially based on confusion, because selfing was considered instead of apomixis (see Castle 1916). However, all "nonresponsiveness" hypotheses assume that amphimixis reduces Kondrashov *Advantages of Amphimixis 379 the variance sometimes. Such hypotheses are very diverse and, although frequent alternation of stabilizing and disruptive selection does not seem realistic, may be rather attractive theoretically. Alternating selection at one locus with two alleles allows elimination of apomixis in two generations. Thus, if God wanted to maintain amphimixis, it could have been done very easily. Mutational Stochastic (MS) Hypothesis Muller's Ratchet Muller (1964) noted that in an apomictic population random loss of the mutationfree genotype is irreversible, ignoring backward mutations (Muller's ratchet), whereas amphimixis easily recreates such a genotype. This can give amphimixis a considerable advantage because only complete loss of a normal allele at a locus is irreversible in an amphimictic population. This advantage is even stronger if accumulation of mutations leads to a decrease of the population size, which in turn facilitates their further accumulation (mutational meltdown, see Lynch et al. 1993). Quantitatively, the rate with which Muller's ratchet clicks depends on the expected absolute number of mutation-free (or, more generally, the best available) individuals in a population, N.,,,. With N,, below or about 10, such individuals will be lost very soon; if Nt,, = 25, the ratchet operates slowly; and if N,,, = 100 or more, it practically does not work (Haigh 1978). Therefore, the importance of the ratchet under a given effective population size, N,, depends critically on the expected frequency of best genotypes, NP,. If selection maintains polymorphism in an apomictic population, the genotype with the lower equilibrium frequency will accumulate deleterious mutations more rapidly, which may cause the loss of the polymorphism (Manning 1982a,b) and provide some advantage for amphimixis. Possible Importance of MS Hypothesis Muller's ratchet has been studied mostly with multiplicative selection. Then p,, = e- u/, where U is the genomic deleterious mutation rate and s is a selection coefficient against a mutant allele. This led to the conclusion that with U = I the ratchet is an important factor with s = 0.01 - 0.1 in populations of any reasonable size (paradoxically, very deleterious mutations are of less danger in this case; see Lynch et al. 1993; Pamilo et al. 1987). 380 The Joumal of Heredity 1993:84(5) However, this conclusion is sensitive to the form of selection. With strict truncation selection, where individuals with k or less mutations have a fitness of 1 and all others die, all individuals in an equilibrium apomictic population have exactly k mutations. Therefore, p,, = 1, and the ratchet cannot operate. Truncation selection represents the extreme case of synergistic epistasis, but pA,, grows, while the mutations are accumulated, even under moderate degrees of epistasis, which slows down the ratchet and may even effectively stop it (D. Charlesworth et al. 1993, in press; Kondrashov AS, unpublished). Two other problems with Muller's ratchet are inherent to all stochastic hypotheses that depend on rare events. First, Muller's ratchet cannot provide a short-term advantage. The characteristic time after which apomicts become maladapted because of the ratchet is probably at least on the order of 100 generations, as long as the population size is not extremely small (Lynch et al., 1993). If mutations are significantly deleterious, the expected frequency of the best class is high, so that the ratchet operate slowly; with slightly deleterious mutations, on the other hand, many clicks of the ratchet are necessary before apomixis becomes maladapted. Second, even very low rates of recombination or outcrossing are sufficient to stop the ratchet. Thus, Muller's ratchet is incapable of influencing the processes ir amphimictic populations and explaining the evolution of its features (D. Charlesworth et al. 1992, 1993, in press). However, it probably can be an important factor in long-term evolution of obligate apomicts. Mutational Deterministic (MD) Hypothesis Muller's Hatchet Although synergistic epistasis slows down the ratchet, it can make amphimixis advantageous for a purely deterministic reason. Such epistasis makes selection against deleterious mutations more efficient in the sense that the same U can be counterbalanced with a much smaller mutation load, L (Crow 1970). This is true only if the population has a high variance of the number of mutations per individual. Synergistic epistasis reduces this variance, undermining its own efficiency. Therefore, under apomixis, L = 1 - e u regardless of the form of selection (Kimura and Maruyama 1966). By contrast, amphimixis destroys repulsion associations between deleterious alleles and restores the variance. This allows the efficiency of epistatic selection to persist in equilibrium, leading to much lower load (Crow 1970; Kimura and Maruyama 1966). With Uon the order of 1 or more, the resulting advantage of amphimixis may be enough to compensate for the twofold advantage of apomixis (Kondrashov 1982). This is the mutational deterministic (MD) hypothesis for the evolution of amphimixis. For example, consider again the case of truncation selection. In an equilibrium apomictic population, all the individuals have exactly k mutations, and a progeny survives only if it does not receive new, deleterious mutations. If mutations occur independently, this happens with probability e ' , so that L = I - e ' , which is very close to I under large U. The same selection has very different consequences with amphimixis where, under free recombination, the associations between loci are reduced twofold each generation. Thus, an equilibrium variance of the per-genome number of mutations before selection, a2, is at least M/2, where M k and is the mean number of mutations per genome. When a fraction, L, of the population is removed by selection, the absolute value of the selection differential, D, the difference between the mean numbers of mutations after and before selection, can be arbitrarily large, provided that a is large enough. At equilibrium U = - D and the load is small if a > U, which requires M > 2 ! (see Kondrashov 1988a). Thus, if mutations are only slightly deleterious, so that k is large, synergistic epistasis can allow the population to survive under any U This effect is caused by both recombination and, if selection acts in the diploid phase, segregation, which alone can lead to significant decrease of the load under moderate U (B. Charlesworth 1990; Dickson and Manning 1984; Manning and Dickson 1986). Muller (1950, p. 151) was probably the first to realize that synergistic epistasis can decrease the mutation load, and Kimura and Maruyama (1966) and Crow (1970) showed that this happens only with amphimixis. However, they did not draw any evolutionary implications because at that time U was assumed to be too low for changes of the mutation load to be important (in their Table 1, Kimura and Maruyama considered only two possible values of U,0.10 and 0.14). This view changed during the 1970s (Crow 1979; Crow and Kimura 1979; Mukai et al. 1972) after which the MD hypothesis was proposed (Crow 1983; Crow and Simmons 1983, p. 7; Kondrashov 1982). Actually, the same idea was applied earlier to the evolution of recombination in an amphimictic population (Feldman et al. 1980). However, the MD hypothesis has sometimes been completely ignored, even quite recently (e.g., Felsenstein 1988). Possible Importance of MD Hypothesis Deleterious mutations are ubiquitous, and formally the MD hypothesis is simple and certainly correct (B. Charlesworth 1990). Its applicability depends only on the magnitude of the genomic deleterious mutation rate and the mode of selection against mutations in nature. Amphimixis in Spatially Structured Populations So far we have considered unstructured populations. Spatial structure has a profound impact on population processes, and maintenance of amphimixis is no exception. Still, the two basic requirements for any Variation and Selection hypothesiscreation of associations and the advantage of destroying them-remain valid. In a spatially structured population, each subpopulation may be considered as a sample from the whole population. If subpopulations are finite, then sampling leads to genetic drift and associations are created within each subpopulation. If, however, the size of subpopulations is too large to make drift important, associations can be generated only by epistatic selection. Thus, as before, both stochastic and deterministic hypotheses are possible here. Felsenstein (1985) correctly noted that sampling from a structured population is essentially the same process as that from random drift in an unstructured population, when the whole next generation is a sample of the progeny created in the previous generation. However, in contrast to an unstructured population, here many samples with different associations coexist in each generation. Therefore, following Maynard Smith (1978, p. 123), consider the hypotheses involving spatial structure separately. Actually, the samples assumed here are usually just breeding pairs, and the stochastic hypotheses considered here emphasize, in accord with the views of East (1918) and Svedelius (1927), the variability among relatives. In this case, in contrast with stochastic hypotheses concerned with unstructured populations, amphimixis can have a rather short-term advantage. This is caused by the fact that here the sample size is so small (two parents) that associations are generated instantly, although Felsenstein (1985) attributed this, I believe erroneously, to stronger selection. Obviously, only in a structured population, which consists of many "samples," can such a small sample size be assumed without the immediate loss of genetic variability. Variability of Relatives: Difference Between Parents and Offspring Amphimixis causes differences between genotypes of both parents and each offspring. Rice (1983a,b) suggested that this may preclude the spread of diseases that may be transmitted during reproduction. This is one more hypothesis based on negative interspecific interactions. Variability of Relatives: Chances to Include the Optimal Genotype Variability among competing sibs generated by amphimixis can be beneficial for two reasons (Young 1981). First, it increases the probability that at least one of them has a genotype necessary for survival under some particular conditions (Williams 1975; Williams and Mitton 1973). Obviously, it requires changing selection in a patch where the family lives, because otherwise apomicts who have the same genotypes as parents have the advantage. Substantial advantage of amphimixis requires actually very strong selection (Barton and Post 1986; Bulmer 1980; Taylor 1979). The advantage probably disappears when the number of winners per patch grows. Variability of Relatives: Benefits of Diversity Itself Alternatively, the diversity itself can be beneficial if it reduces the intensity of competition (Bell 1982; Maynard Smith 1978; Price and Waser 1982). This can provide a substantial advantage for amphimixis. The same mechanisms can be applied to other close relatives if they compete with each other. This idea is unique among all Variation and Selection hypotheses. Here drift is responsible not only for creation of associations, but also for deviation of the subpopulation composition from the optimum prescribed by frequency-dependent selection. With any reasonable size of the unstructured population this can hardly happen, so that only environmental and mutational hypotheses were proposed for such populations. The possibility of "stochastic stochastic" mechanism is one more reason why structured populations should be considered separately. Deterministically Generated Associations In principle, amphimixis can be beneficial in a spatially structured population in which the size of each subpopulation is large. This idea was first proposed by Aleksandr Serebrovsky (1973) in a book written in 1939 but only published 25 years after his death. Serebrovsky noted that if different subpopulations accumulate beneficial alleles at different loci, amphimixis with intersubpopulational mating can be beneficial because of "summation of evolutionary achievements" (p. 101). Similarly, Maynard Smith (1978) considered the situation when a patch in which an AB genotype is optimal is colonized by immigrants from two patches with Ab and aB genotypes. Such models were studyed by Slatkin (1975) and D. Charlesworth and Charlesworth (1979). Possible Importance of Hypotheses Based on Spatial Structure Obviously, these hypotheses are of limited applicability because many populations are essentially panmictic. The only exception is the first hypothesis, because the contact between parents and offspring always exists. I do not think, however, that the conditions when this hypothesis works are common. In fact, amphimixis, where reproductively transmitted parasites are not confined to separate lineages and one individual can infect many, facilitates the spread of diseases (Hickey and Rose 1988). AIDS would not spread in an apomictic population, despite the absence of genetic differences between parents and offspring. The advantage of amphimixis due to diversity between sibs or other relatives involved in competition is more plausible. However, the first mechanism requires that sibs are competing in the same place but under conditions different from those under which their parents were selected (Maynard Smith, 1988a, p. 121). This can be the case only if selection in each patch changes frequently, which makes it unrealistic. The second mechanism is more plausible. Here selection can be constant both in time and space, and uniformly favors diversity within each patch. I doubt that this can be a major factor in the evolution of amphimixis, but biologically the situation is quite realistic. Hypotheses that depend on determin- Kondrashov ·Advantages of Amphimbs 381 istically generated associations in structured populations imply that the alleles necessary for adaptation in some particular place must frequently be supplied by immigration. Obviously this requires some degree of uniformity of conditions throughout the whole range of the population, because otherwise adaptations of the subpopulations to unique local features would make immigrants unsuccessful. In this case, however, it is not clear why a large subpopulation cannot acquire the necessary beneficial alleles without immigration. One possibility is independent fluctuations of the environment in different places. Thus the best source of alleles that become beneficial in some place can be the adjacent populations, where they may already be frequent. Quantitative analysis shows, however, that spatial heterogeneity of selection, both invariant and fluctuating, is not effective in maintaining amphimixis when the subpopulations are large (Case and Bender 1981; D. Charlesworth and Charlesworth 1979). The hypotheses involved with spatially structured populations which have so far been proposed consider either selection or drift as the factor that makes destruction of associations beneficial. Of course, one may also attribute this to deleterious mutations if, for example, only mutationfree individuals can survive in the progeny from each mating. Such hypotheses, however, will be subject to the same limitations. Why, After All, Does Amphimixis Exist? Three general conclusions can be made from this review and classification of hypotheses. First, obligate amphimixis can be beneficial over obligate apomixis under a variety of different circumstances. Particularly, hypotheses which assume that associations between alleles are generated by selection, instead of drift, have gained much strength in the last 10 years. Thus, Felsenstein's (1974) conclusionthat only those who consider effects of finite population size find amphimixis advantageous-is no longer valid. Naive beliefs that an advantage for amphimixis can come from its ability to increase variability and, thus, facilitate adaptive changes, to help eliminate deleterious mutations, or to reduce competition between relatives all have turned out to be true under some conditions. All models reviewed above are formally correct and, although more work 382 The Joumrnal of Heredity 1993:84(5) is needed to refine some of them, their basic features are well understood. Second, all plausible hypotheses can provide the substantial short-term advantage for amphimixis only under rather stringent conditions (rapid irreversible evolution, wide fluctuations of fitness optimum, high genomic deleterious mutation rate, etc.), although some Variation and Selection hypotheses (ES and MS) can easily provide the large, long-term advantage. Therefore, it seems that the very existence of amphimixis carries some important information about natural populations. Of course, all Immediate Benefit hypotheses could lead to a short-term advantage of amphimixis because transition to apomixis is punished immediately. However, currently there are no data on any large, immediate benefits of amphimixis. Third, we are astonishingly ignorant of what actually happens in nature. We have enough, even more than enough, possible solutions that require totally different characterization of the basic features of populations, but we do not have facts to decide which solutions are actually relevant. However, I agree with Felsenstein (1988) that the current state of "the paradox of sex" issue does not represent an isolated crisis in evolutionary biology. Instead, it reflects the chronic lack of knowledge about natural populations. This is caused both by an inherent difficulty in measuring populational parameters (Lewontin 1974) and by the view, still popular among experimentalists, that making hypotheses is a mental exercise, not an invitation to do clearly defined experiments. Of course, amphimixis may be beneficial for more than one reason. One can imagine that in rapidly evolving flowering plants amphimixis combines beneficial mutations; in a small population of Latimeria it stops Muller's ratchet; in snails it prevents sibs from competing too hard; in Drosophila melanogasterit reduces mutational load under synergistic epistasis; in mammals there is simply no way back to apomixis; while in other cases amphimixis is maintained by fluctuating selection (caused mostly by parasites). Even in the same population amphimixis can repair doublestrand DNA damages, reverse mutations, improve selection, and prevent populations from responding to selection too fast all at the same time. Such a "pluralistic" view attracts growing support, perhaps because by accepting any single hypothesis you make more enemies than friends. Currently, this cannot be ruled out. However, I find it rather unlikely. Genetically amphimixis is a remarkably uniform phenomenon (although it may have appeared independently several times, Ivanov 1970; Margulis et al. 1990), which may well have only one cause. The hypotheses that can explain the origin, maintenance, and evolution of features of amphimixis from the same point of view are, of course, especially attractive (this, however, does not guarantee that they are correct). Moreover, the pluralistic view impedes designing and making critical experiments aimed at falsifying various hypotheses and, therefore, should be accepted only if more than one hypothesis is directly supported by data. What Can Be Said About Different Hypotheses Now? 1do not believe that there is any inherited immediate benefit of amphimixis important enough to account for its existence, although the improvement of selection may play some role. Of course, direct evidence can change this view. Therefore, only Variation and Selection hypotheses are discussed here. In unstructured populations stochastic hypotheses are less plausible because they cannot provide the short-term advantage. Hypotheses that involve rare beneficial mutations are probably irrelevant under normal conditions of slow evolution, while they, together with Muller's ratchet, may play some role in limiting the time of existence of obligately apomictic populations (Bell 1988; Chao 1990; Chao et al. 1992). The ED hypotheses that attribute the advantage of amphimixis to destruction of associations in alternating directions, either due to better responsiveness (Bell and Maynard Smith 1987; Nee 1989) or to nonresponsiveness (B. Charlesworth 1976; Hamilton et al. 1990; Roughgarden 1991), do not look plausible because they require frequent alternation of stabilizing and disruptive selection, and this has not been observed in nature. Finally, all hypotheses that require spatial structure, except the one that considers parent-offspring transmission of pathogenes, can be relevant only to forms with very limited dispersal. Therefore, two hypotheses seem to be the most plausible: ED (with better responsiveness of an amphimictic population because of destruction of repulsion associations created by either irreversibly changing or widely fluctuating selection) and MD. They have some features in comon: both require, as well as other Variation and Selection hypotheses, substantial nonneutral additive genetic variance; both assume that selection is (at least most of the time) directional; and both claim that amphimixis is beneficial because it enhances the population's response to selection (B. Charlesworth 1989). Quantitative analysis shows that, according to both hypotheses, an amphimictic population protected against invasion by apomictic clones can have low load (lag-load in the first case, and mutational load in the second). Other features of ED and MD hypotheses are, however, profoundly different. Most important, they depend on totally different modes of genetic variability. The ED hypotheses requires conditionally beneficial variability, where alleles and genotypes that are currently maladapted can become beneficial in the future. Thus, selection is assumed to permanently create new adaptations (see Lewontin 1974). In contrast, the MD hypothesis depends on unconditionally deleterious variability, which can never be utilized for adaptation, and on stabilizing selection sensu Schmalhausen (1949). As Williams (1966, p. 54) put this: "I regard it as unfortunate that the theory of natural selection was first developed as an explanation for evolutionary change. It is much more important as an explanation for the maintenance of adaptation." The data on quantitative variability do not allow one to decide which mutationsconditionally beneficial or unconditionally deleterious-are more important (Kondrashov and Turelli 1992). In some sense the MD hypothesis is simpler because the same factor causes the deviation of population mean from the optimum and maintains variability, while with fluctuating selection the maintenance of variability requires mutation, frequency-dependence, or something else. There are no data to prove that widely changing selection, required by ED hypotheses, is uncommon in nature. However, the traits often remain practically invariant during very long time intervals (B. Charlesworth 1993, in press). Recently, Meselson and Welch (unpublished) showed that in two species of bdelloid rotifers different alleles of the same loci are extremely divergent, which seems to confirm the absence of amphimixis in this group during millions of years. If so, this is in conflict with any hypothesis that claims that amphimixis is a means to accelerate irreversible evolution, because bdelloid rotifers became a diverse and successful group without it. There are even fewer data to test the hypothesis that the fitness optimum fluctuates widely, although it is usually assumed to coincide with the population mean (Turelli 1984), which is inconsistent with large and rapid fluctuations. In contrast, the scarce data on deleterious mutation rates show that Uis at least about 1, which is consistent with the MD hypothesis (B. Charlesworth et al. 1990; Houle et al. 1992; Mukai et al. 1972), although more experiments are needed. Evidence of synergistic epistasis is very scanty (Malmberg 1977; Mukai 1969). In addition to the group selection advantage of amphimixis, the MD hypothesis may also account for gradual evolution of the features of amphimictic populations, including recombination rates (B. Charlesworth 1990; Feldman et al. 1980; Kondrashov 1984a), outcrossing (B. Charlesworth et al. 1991; D. Charlesworth et al. 1990, 1992, 1993, in press; Kondrashov 1985; Michod and Gayley 1992; Uyenoyama and Waller 1991a,b), facultative apomixis (Kondrashov 1984b, 1985), mate choice (Kondrashov 1988b; Rice 1988), and the relative length of the haploid and diploid phases (Kondrashov and Crow 1991; Otto and Goldstein 1992; Perrot et al. 1991). Probably, it may also explain the gradual origin of amphimixis (Bengtsson 1992). In contrast, the ED hypotheses were so far applied only to the evolution of recombination (Bergman and Feldman 1990; B. Charlesworth, 1993, in press; Korol and Preigel 1989; Korol et al. 1990). It seems that both hypotheses predict significant selection for free recombination in the amphimictic population under similar conditions, which are usually more restrictive than those required for the group selection advantage of amphimixis. Particularly, the genetic load (either mutational or lag) should be at least about 0.2-0.4. with U >> 1, it can be considered proven. What Data Do We Need? Let us start with the data we no longer need. These include much indirect evidence, usually from correlations of the mode of reproduction with some vaguely defined features of the environment. Higher incidence of apomixis in simple, novel, or disturbed habitats (Bell 1982; Glesener and Tilman 1978) among endosymbionts (Law and Lewis 1983) and overall distribution of modes of reproduction among taxa and ecosystems (Bell 1982; Halvorson and Monroy 1985; Jackson et al. 1985; Shields 1982) are very interesting and have In the last case even measurements of epistasis are unnecessary, because long existence of a population under such U is impossible unless it is present. Remarkably, Uis an organismal, and not a population-level, parameter, so that it can be measured relatively easily. Still, the problem is that slightly deleterious mutations cannot be individually detected without using molecular methods. It is generally accepted, however, that the total per-genome mutation rate in mammals is more than 100 (see Kondrashov 1988a), and the only problem is what proportion of these mutations are deleterious. Molecular methods can be decisive in solving stimulated much thought, but they clearly cannot lead to rejection of any hypothesis. Similarly, the correlation between high incidence of amphimixis with high infestation by parasites (Lively 1992) can be viewed as evidence that amphimixis either protects the population from parasites (and, therefore, is replaced by apomixis if they are absent) or facilitates their spread, or is favored by the same factor that causes high infestation. Instead of such correlations, we need data that explicitly test different hypotheses in various natural populations. For Immediate Benefit hypotheses, this means that a postulated immediate benefit of amphimixis should be demonstrated directly. For Variation and Selection hypotheses, three levels of proof are possible. The first and the best one is to observe postulated changes in the genetic composition of the progeny, together with their effect on the population fitness. The second one is to show the existence of conditions that make these postulated changes beneficial. The third and final one is to compare the fitnesses of amphimictically and apomictically produced progeny. This last approach is the least direct, and its results may simply suggest that amphimixis has some short-term advantage in a particular situation (Harshman and Futuyma 1985; Kelley et al. 1988). However, if the fitness is measured under carefully described conditions, more information can be obtained (Kelley 1989a,b). Clearly, hypotheses leading to predictions that are easier to falsify are especially attractive, and from this point of view my favorite MD hypothesis is the uncontested winner. Its validity depends on a single parameter, the genomic deleterious mutation rate U. If U 1 in some popu- lation, MD hypothesis cannot be applied to it; with Uclose to 1, it is plausible; and Kondrashov Advantages of Arnphimixs 383 this problem (Kondrashov and Crow 1993). The importance of Muller's ratchet also mostly depends on a single parameter: the absolute number of individuals in apomictic populations with a minimal number of mutations. This is more difficult to measure than U. Besides, it is not clear what should be measured in an amphimictic population to determine whether Muller's ratchet protects it from invasion of apomictic clones. This problem is worth investigating. ED hypotheses that postulate destruction of repulsion associations require wide changes of selection. These changes must also be rather (but not too) fast and frequent, to provide a short-term advantage to amphimixis and to prevent the adaptation of apomicts due to new mutations. Unfortunately, selection is very difficult to measure. However, changes of selection must lead to large and relatively rapid changes in mean values of the traits involved, on the order of the standard deviation and probably much more, which will be easiest to detect. Instead of studying the same population over the long term, one can simultaneously investigate different populations. Profound differences, both phenotypic and genetic, among such populations would be strong evidence of fluctuating selection, provided that they cannot be attributed to permanent differences between conditions in different places. Of course, stability or spatial uniformity of some traits, which is what is routinely observed, can simply mean that these particular traits are not related to the advantage of amphimixis. Thus, systematic studies of the changes of natural populations in time and space are needed. ED hypotheses assuming association in alternating directions (either of better responsiveness or of nonresponsiveness type) are even more difficult to reject, because they predict smaller or no fluctuations of allele frequencies, requiring only large and frequent fluctuations of fitnesses. This requires direct measurement of selection and of the factors that cause its changes. Negative biotic interactions have repeatedly been proposed as such factors. It seems, however, that all the models of this type considered so far assume alternation of stabilizing and disruptive selection and "gene-to-gene" relationships between the ability of parasites to attack and of hosts to defend themselves. This might not apply in higher animals that have general-purpose immune systems capable of 384 The Joumal of Heredity 1993:84(5) acting against unpredictable threats (Bremermann 1987, p. 147). ES hypotheses critically depend on how frequently new, beneficial mutations go to fixation. In chemostat populations this can happen remarkably frequently (Paquin and Adams 1983), but there are no data from natural populations. For hypotheses involved with spatial structure, current data do not show a large advantage of more diverse sibships (Bell 1991; Kelley 1989b). In contrast, there is some evidence that the difference between parents and offspring may be advantageous (Kelley 1989a, in preparation), but more data are necessary. Formulation of falsifiable predictions should shift the emphasis to decisive experiments. I believe that further progress in our understanding of the evolution of reproduction will depend on the results of such experiments much more than on theoretical work: "It is only by the further accumulation of facts in various groups of plants and animals that we may at length be in position to determine what if any unifying principle there may be in this wide-spread phenomenon of sexuality" (Blakeslee 1907, p. 372). Appendix 1. Immediate Benefit Hypotheses Amphimixis is supposed to be directly beneficial because: 1. It increases fitness of the progeny: a. Because a diploid progeny has two parents instead of one (Lloyd 1980) b. Because double-strand DNA damages can be repaired during chromosome conjugation in meiosis (Dougherty 1955; see Bernstein and Bernstein 1991) 2. It reduces the deleterious mutation rate: a. Because most deleterious mutations are deletions, which can be recognized as gaps when chromosomes conjugate, and can be filled by biased gene conversion (Bengtsson 1985) b. Because most deleterious mutations are insertions, which can be recognized as loops when chromosomes conjugate, and can be cut (Ettinger 1986) c. Because most deleterious epimutations are demethylations, which can be recognized and reverted when chromosomes conjugate (Holliday 1988) 3. It increases efficiency of selection: Because selection among males or male gametes may be costless (Geodakyan 1965; Trivers 1976) Appendix 2. Variation and Selection Hypotheses (Local Population) Amphimixis is supposed to be beneficial because there is: 1. In ES hypotheses: a. More rapid accumulation of beneficial mutations at many loci simultaneously (Fisher 1930; Morgan 1913; Muller 1932) b. More rapid accumulation of beneficial mutations in the presence of deleterious mutations (Fisher 1930; Manning and Jenkins 1980) c. More rapid accumulation of beneficial mutations when polymorphisms are maintained in other loci (Manning 1982c, 1983) 2. In ED hypotheses: a. An increased rate of evolution under an irreversibly changing environment (Eshel and Feldman 1970, case b; Mather 1943) b. An increased rate with which a population follows the widely fluctuating environment (Mather 1943; Maynard Smith 1980; Treisman 1976) c. A decreased rate with which a population follows frequently fluctuating environment (B. Charlesworth 1976; Sturtevant and Mather 1938) 3. In the MS hypothesis: A reversion of random losses of deleterious mutation-free genotypes (Muller 1964) 4. 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