The advantages of segregation and the evolution of sex

In diploids, sexual reproduction promotes both the segregation of alleles at the same locus and the recombination of alleles at different loci. This article is the first to investigate the possibility that sex might have evolved and been maintained to promote segregation, using a model that incorporates both a general selection regime and modifier alleles that alter an individual's allocation to sexual vs. asexual reproduction. The fate of different modifier alleles was found to depend strongly on the strength of selection at fitness loci and on the presence of inbreeding among individuals undergoing sexual reproduction. When selection is weak and mating occurs randomly among sexually produced gametes, reductions in the occurrence of sex are favored, but the genome-wide strength of selection is extremely small. In contrast, when selection is weak and some inbreeding occurs among gametes, increased allocation to sexual reproduction is expected as long as deleterious mutations are partially recessive and/or beneficial mutations are partially dominant. Under strong selection, the conditions under which increased allocation to sex evolves are reversed. Because deleterious mutations are typically considered to be partially recessive and weakly selected and because most populations exhibit some degree of inbreeding, this model predicts that higher frequencies of sex would evolve and be maintained as a consequence of the effects of segregation. Even with low levels of inbreeding, selection is stronger on a modifier that promotes segregation than on a modifier that promotes recombination, suggesting that the benefits of segregation are more likely than the benefits of recombination to have driven the evolution of sexual reproduction in diploids.     

Genetic load in sexual and asexual diploids: segregation, dominance and genetic drift

In diploid organisms, sexual reproduction rearranges allelic combinations between loci (recombination) as well as within loci (segregation). Several studies have analyzed the effect of segregation on the genetic load due to recurrent deleterious mutations, but considered infinite populations, thus neglecting the effects of genetic drift. Here, we use single-locus models to explore the combined effects of segregation, selection, and drift. We find that, for partly recessive deleterious alleles, segregation affects both the deterministic component of the change in allele frequencies and the stochastic component due to drift. As a result, we find that the mutation load may be far greater in asexuals than in sexuals in finite and/or subdivided populations. In finite populations, this effect arises primarily because, in the absence of segregation, heterozygotes may reach high frequencies due to drift, while homozygotes are still efficiently selected against; this is not possible with segregation, as matings between heterozygotes constantly produce new homozygotes. If deleterious alleles are partly, but not fully recessive, this causes an excess load in asexuals at intermediate population sizes. In subdivided populations without extinction, drift mostly occurs locally, which reduces the efficiency of selection in both sexuals and asexuals, but does not lead to global fixation. Yet, local drift is stronger in asexuals than in sexuals, leading to a higher mutation load in asexuals. In metapopulations with turnover, global drift becomes again important, leading to similar results as in finite, unstructured populations. Overall, the mutation load that arises through the absence of segregation in asexuals may greatly exceed previous predictions that ignored genetic drift.     

INBREEDING DEPRESSION UNDER JOINT SELFING,OUTCROSSING, AND ASEXUALITY

Partial asexual reproduction was introduced into a model of inbreeding depression due to nearly recessive lethal mutations in a partially selfing population. The frequencies of asexuality, selfing, and outcrossing were either constant or occurred in cycles of a single sexual generation followed by one or more asexual generations. We found that increasing the degree of asexuality generally increases the inbreeding depression maintained in an equilibrium population with a given selfing rate. This is due to the increase in the number of mutations relative to sexual generations during which selfing-induced purging of mutations may take place. For very high genomic mutation rates, sufficient to produce a threshold rate of self-fertilization for purging recessive lethal mutations, asexuality can have the opposite effect, decreasing equilibrium inbreeding depression, because of an increase in the efficiency of selection against mutations in heterozygotes with asexuality.     

A general model to explore complex dominance patterns in plant sporophytic self-incompatibility systems

We developed a general model of sporophytic self-incompatibility under negative frequency-dependent selection allowing complex patterns of dominance among alleles. We used this model deterministically to investigate the effects on equilibrium allelic frequencies of the number of dominance classes, the number of alleles per dominance class, the asymmetry in dominance expression between pollen and pistil, and whether selection acts on male fitness only or both on male and on female fitnesses. We show that the so-called "recessive effect" occurs under a wide variety of situations. We found emerging properties of finite population models with several alleles per dominance class such as that higher numbers of alleles are maintained in more dominant classes and that the number of dominance classes can evolve. We also investigated the occurrence of homozygous genotypes and found that substantial proportions of those can occur for the most recessive alleles. We used the model for two species with complex dominance patterns to test whether allelic frequencies in natural populations are in agreement with the distribution predicted by our model. We suggest that the model can be used to test explicitly for additional, allele-specific, selective forces.     

Epistatic selection opposed by immigration in multiple locus genetic systems

A model of “complete” epistatis is considered in which all “plus” alleles must be present in an individual before the adaptive phenotype is expressed. The conditions under which the plus alleles and hence the adaptive phenotype can increase and reach a stable equilibrium in the presence of immigration of gametes carrying minus alleles are found. In haploids and diploids in which the plus alleles are recessive, frequencies of the plus alleles are the same at all loci, regardless of the linkage relationships. Tight linkage favors the existence of a locally stable polymorphic equilibrium, but the equilibrium with only minus alleles is locally stable unless there is very tight linkage or very strong selection. Thus, this kind of epistasis, which provides a simple model for a character that requires several components to be present at the same time, is very sensitive to even a small amount of immigration. Hence, the evolution of such characters is likely only in completely rather than partially isolated populations.     

Natural and Sexual Selection on Many Loci

A method is developed that describes the effects on an arbitrary number of autosomal loci of selection on haploid and diploid stages, of nonrandom mating between haploid individuals, and of recombination. We provide exact recursions for the dynamics of allele frequencies and linkage disequilibria (nonrandom associations of alleles across loci). When selection is weak relative to recombination, our recursions provide simple approximations for the linkage disequilibria among arbitrary combinations of loci. We show how previous models of sex-independent natural selection on diploids, assortative mating between haploids, and sexual selection on haploids can be analyzed in this framework. Using our weak-selection approximations, we derive new results concerning the coevolution of male traits and female preferences under natural and sexual selection. In particular, we provide general expressions for the intensity of linkage-disequilibrium induced selection experienced by loci that contribute to female preferences for specific male traits. Our general results support the previous observation that these indirect selection forces are so weak that they are unlikely to dominate the evolution of preference-producing loci.     

Genetics of decayed sexual traits in a parasitoid wasp with endosymbiont-induced asexuality

Trait decay may occur when selective pressures shift, owing to changes in environment or life style, rendering formerly adaptive traits non-functional or even maladaptive. It remains largely unknown if such decay would stem from multiple mutations with small effects or rather involve few loci with major phenotypic effects. Here, we investigate the decay of female sexual traits, and the genetic causes thereof, in a transition from haplodiploid sexual reproduction to endosymbiont-induced asexual reproduction in the parasitoid wasp Asobara japonica. We take advantage of the fact that asexual females cured of their endosymbionts produce sons instead of daughters, and that these sons can be crossed with sexual females. By combining behavioral experiments with crosses designed to introgress alleles from the asexual into the sexual genome, we found that sexual attractiveness, mating, egg fertilization and plastic adjustment of offspring sex ratio (in response to variation in local mate competition) are decayed in asexual A. japonica females. Furthermore, introgression experiments revealed that the propensity for cured asexual females to produce only sons (because of decayed sexual attractiveness, mating behavior and/or egg fertilization) is likely caused by recessive genetic effects at a single locus. Recessive effects were also found to cause decay of plastic sex-ratio adjustment under variable levels of local mate competition. Our results suggest that few recessive mutations drive decay of female sexual traits, at least in asexual species deriving from haplodiploid sexual ancestors.     

A deterministic genetic model for sympatric speciation by sexual selection

A deterministic haploid genetic model confirms and explores in more detail the results of our previous individual-based simulation model for sympatric speciation by sexual selection. With the deterministic model, we are able to elucidate parameter dependence by phase plane analysis. We clarify how and why sympatric speciation by sexual selection can happen in a number of ways: (1) Female preferences for or against particular types of males have different effects. Whereas the former affects how readily speciation is invoked, the latter changes the stability of speciation equilibrium. (2) When there is no cost on male ornamentations, speciation is triggered regardless of initial haplotype frequencies if sufficient female preference is provided. (3) There exists a threshold for female initial frequencies for speciation to be invoked, but male initial frequencies have little effect. (4) A small cost on female mate choice does not cancel speciation, but when large, it greatly reduces the possibility of speciation.     

Sex and recombination purge the genome of deleterious alleles: An Individual Based Modeling Approach

The prevalence of sexual reproduction in most animal species despite its considerable costs such as useless males, energy spent on mating, the cost of meiosis and genome dilution remains a puzzle in evolutionary theory. One prominent single factor attempt to solve this persistent puzzle is the claim that sexual reproduction is instrumental in eliminating deleterious alleles from the species genome by the mechanism of recombination. There are three major versions of the deleterious allele hypothesis: First, the mutational deterministic hypothesis (MDH), which rests on the assumption of negative epistasis, predicts that recombination will help to purge the species genome of deleterious alleles by breaking apart linkages between these alleles. The assumption is that the joint negative effects of linked deleterious alleles is sometimes greater than the effects of the alleles considered separately. Second, there is the hypothesis that sexual reproduction speeds up purifying (negative) selection, which purges the genome of deleterious alleles. Alleles that are less deleterious than the wild type are naturally selected. These alleles, attained via recombination, are sometimes ‘leaky’ mutations giving rise to reduced functionality of attendant proteins. This hypothesis does not necessarily rest on the assumption of negative epistasis, which some argue is relatively rare in nature (Kouyos, Silander and Bonhoeffer (2012)) and which arguably could be seen as a virtue of the purifying selection hypothesis vs. the MDH. Third, Muller's ratchet hypothesis predicts that recombination will help to prevent the buildup of deleterious mutations by the mechanism of recombination. In this study, we focus primarily on testing the purifying selection hypothesis. We performed an individual-based model computer simulation using the program EcoSim to test this hypothesis. The experimental runs for sexual reproduction, asexual reproduction and facultative reproduction involved introducing a deleterious allele into the genome, which exacts an intermediate-level energy penalty on individuals. It was found that whereas on average, deleteriousness consistently declined over 18,000 time-steps due to recombination in sexual reproduction, deleteriousness did not decline for asexual and facultative runs. These results corroborate the hypothesis that recombination due to sexual reproduction helps to eliminate deleterious alleles from the genome through the selection of reduced function mutations.     

FURTHER SIMULATION STUDIES ON EVOLUTION BY GENE DUPLICATION

In order to understand the origin of multigene families, Monte Carlo simulations were performed to see how a genetic system evolves under unequal crossing-over, mutation, random genetic drift and natural selection, starting from a single gene copy. Both haploid and diploid models were examined. Beneficial, neutral, and detrimental mutations were incorporated, and “positive” selection favors those chromosomes (haploid) or individuals (diploid) with more beneficial mutations than others. The same model for haploids was previously investigated with special reference to the evolution of gene organization, and the ratio of the numbers of beneficial genes to pseudogenes was found to be a rough indicator of the relative strengths of positive and negative (against deleterious alleles) natural selection (Ohta, 1987b). In the present paper, the evolution of gene organization and of sequence divergence among genes in the multigene family is examined. It is shown that positive selection accelerates the accumulation of arrays containing different beneficial mutations, but that total divergence including both neutral and beneficial mutations is not very sensitive to positive selection, under this model. The proportion of beneficial mutations in the total mutations accumulated is a better indicator of positive selection than is the total divergence. It is pointed out that various observed examples in which amino-acid substitutions are accelerated, as compared with synonymous substitutions in duplicated genes (Li, 1985), may reflect the effect of selection similar to the present scheme. The diploid model is shown to be more efficient for accumulating beneficial mutations in duplicated genes than the haploid one, and the relevance of this finding to the advantage of sexual reproduction is discussed.     

Selection, mutation and sexual reproduction in an infinite haploid population with a genome of finite length

We present a model which describes mutation, selection and sexual reproduction in an infinite haploid population with a finite genome. Each generation is described using an approximation which assures a certain persistent form of the distribution of the number of deleterious elements. The steady state exists and is determined. In addition, we conclude that the introduction of sexual reproduction increases the mean fitness in the equilibrium.     

Mitotic recombination accelerates adaptation in the fungus Aspergillus nidulans

Understanding the prevalence of sexual reproduction in eukaryotes is a hard problem. At least two aspects still defy a fully satisfactory explanation, the functional significance of genetic recombination and the great variation among taxa in the relative lengths of the haploid and diploid phases in the sexual cycle. We have performed an experimental study to explore the specific advantages of haploidy or diploidy in the fungus Aspergillus nidulans. Comparing the rate of adaptation to a novel environment between haploid and isogenic diploid strains over 3,000 mitotic generations, we demonstrate that diploid strains, which during the experiment have reverted to haploidy following parasexual recombination, reach the highest fitness. This is due to the accumulation of recessive deleterious mutations in diploid nuclei, some of which show their combined beneficial effect in haploid recombinants. Our findings show the adaptive significance of mitotic recombination combined with flexibility in the timing of ploidy level transition if sign epistasis is an important determinant of fitness.     

A bit of sex stabilizes host-parasite dynamics

To date, only a few studies have focused on the effects of sex on population dynamics. Previous models have typically found that sexual reproduction dampens population fluctuations. Although asexual and sexual reproduction are just the two endpoints along a continuum of varying rates of sex, previous work has ignored the effects of intermediate degrees of sex on population dynamics. Here we study the effects of partial sexual reproduction (i.e. sex occurs only every few generations or with small probability in each generation) on the coupled population dynamics of a Nicholson-Bailey host-parasite model. We show that complex dynamics are simplified for high host population growth rates if the frequency of sex is sufficiently high in both host and parasite: sex decreases fluctuations in population density, and leads to non-chaotic dynamics for population growth rates that would result in chaotic dynamics in the absence of sexual reproduction. However, the simplification does not increase gradually with an increasing frequency of sex but appears abruptly at low-to-intermediate frequencies of sex. For some parameter settings, intermediate frequencies of sexual reproduction can simplify the dynamics more than lower or higher frequencies. Thus, in agreement with earlier results, sexual reproduction typically stabilizes complex population dynamics in our models. Additionally, our results suggest that low-to-intermediate frequencies of sex may often be as (or even more) stabilizing as high frequencies.     

Genetic improvement of production while maintaining fitness

Selection for production tends to decrease fitness, in particular, major components such as reproductive performance. Under an infinitesimal genetic model restricted index selection can maintain reproductive performance while improving production. However, reproductive traits are thought to be controlled by a finite number of recessive alleles at low frequency. Culling for low reproduction may weed out the negative homozygous genotypes for reproduction in any generation, thus controlling the frequencies of alleles negative for reproduction. Restricted index selection, culling for low reproduction and a new method called empirical restricted index selection were compared for their efficiency in improving production while maintaining reproduction. Empirical restricted index selection selects animals that have on average the highest estimated breeding values for production and on average the same estimated breeding values for reproduction as the base population. An infinitesimal genetic model and models with a finite number of loci for reproduction with rare deleterious recessive alleles, which have additive, dominant or no pleiotropic effects on production, were considered. When reproduction was controlled by a finite number of loci with rare recessive alleles, restricted index selection could not maintain reproduction. The culling of 20% of the animals on reproduction maintained reproduction with all genetic models, except for the model where loci for reproduction had additive effects on production. Empirical restricted selection maintained reproduction with all models and yielded higher production responses than culling on reproduction, except when there were dominant pleiotropic effects on production.     

Evolutionary Dynamics of ‘the’ Bdelloid and Monogonont Rotifer Life-history Patterns

Substantial differences in both life-table characteristics and reproductive patterns distinguish bdelloid from monogonont rotifers. Bdelloids reproduce only asexually, whereas most monogononts are cyclical parthenogens. We explore some of the adaptive consequences of these life-history differences using a computer model to simulate the evolutionary acquisition of new beneficial mutations. A one-locus mutation-selection regime based on the life-history characteristics of bdelloids indicates that asexuals can maintain higher levels of both allelic and genotypic diversity over a longer time period than obligate sexuals. These results are produced by differences in the magnitude of random genetic drift (RGD) associated with the different types of reproduction. Cyclical parthenogens have significantly higher evolutionary rates than sexual forms in a single-locus model, but incorporate beneficial mutations more slowly than sexuals in a two-locus simulation. Our results are therefore strongly influenced by the number of loci being evaluated as well as the pattern of reproduction. The asexual life history was found to maintain higher levels of allelic diversity than any pattern including sexual reproduction. This intriguing finding is amplified as the number of loci undergoing selection is increased. We end by considering the adaptive consequences of the remarkably divergent life histories found in typical bdelloid and monogonont rotifers.     

Influence of dominance, leptokurtosis and pleiotropy of deleterious mutations on quantitative genetic variation at mutation-selection balance

In models of maintenance of genetic variance (V (G)) it has often been assumed that mutant alleles act additively. However, experimental data show that the dominance coefficient varies among mutant alleles and those of large effect tend to be recessive. On the basis of empirical knowledge of mutations, a joint-effect model of pleiotropic and real stabilizing selection that includes dominance is constructed and analyzed. It is shown that dominance can dramatically alter the prediction of equilibrium V (G). Analysis indicates that for the situations where mutations are more recessive for fitness than for a quantitative trait, as supported by the available data, the joint-effect model predicts a significantly higher V (G) than does an additive model. Importantly, for what seem to be realistic distributions of mutational effects (i.e., many mutants may not affect the quantitative trait substantially but are likely to affect fitness), the observed high levels of genetic variation in the quantitative trait under strong apparent stabilizing selection can be generated. This investigation supports the hypothesis that most V (G) comes from the alleles nearly neutral for fitness in heterozygotes while apparent stabilizing selection is contributed mainly by the alleles of large effect on the quantitative trait. Thus considerations of dominance coefficients of mutations lend further support to our previous conclusion that mutation-selection balance is a plausible mechanism of the maintenance of the genetic variance in natural populations.     

Recombination and loss of complementation: a more than two-fold cost for parthenogenesis

Certain types of asexual reproduction lead to loss of complementation, that is unmasking of recessive deleterious alleles. A theoretical measure of this loss is calculated for apomixis, automixis and endomitosis in the cases of diploidy and polyploidy. The effect of the consequent unmasking of deleterious recessive mutations on fitness is also calculated. Results show that, depending on the number of lethal equivalents and on the frequency of recombination, the cost produced by loss of complementation after few generations of asexual reproduction may be greater than the two-fold cost of meiosis. Maintaining complementation may, therefore, provide a general short-term advantage for sexual reproduction. Apomixis can replace sexual reproduction under a wide range of parameters only if it is associated with triploidy or tetraploidy, which is consistent with our knowledge of the distribution of apomixis.     

THE EFFECTS OF SELECTION IN THE GAMETOPHYTE STAGE ON MUTATIONAL LOAD

We have studied a multilocus selection model of a plant population in which mutations to deleterious alleles occur that may affect not only the diploid sporophyte stage, but also the haploid pollen stage before zygote formation. We investigated the reduction in inbreeding depression (as measured in the sporophyte) caused by the lowering of mutant allele frequencies due to selection in the pollen. This is important for a full understanding of the role of inbreeding depression in the maintenance of outcrossing in seed plants. We also studied the theoretically expected relationship between the pollen fitnesses of different pollen donor genotypes and the fitnesses of the diploid progeny that they sire. This relationship can be compared with the results of experiments in which pollen was subjected to selection, and improved progeny quality was observed. We found that on the mutational load model there is, as expected intuitively, a positive covariance between the pollen and zygote fitnesses, but that it is likely to be small. Subjecting pollen to an episode of strong selection is usually expected to increase sporophyte fitness only slightly.     

Soft selection reduces loss of heterozygosity in asexual reproduction

The adaptive value of sexual reproduction is still debated in evolutionary theory. It has been proposed that the advantage of sexual reproduction over asexual reproduction is to promote genetic diversity, to prevent the accumulation of harmful mutations or to preserve heterozygosity. Since these hypothetical advantages depend on the type of asexual reproduction, understanding how selection affects the taxonomic distribution of each type could help us discriminate between existing hypotheses. Here, I argue that soft selection, competition among embryos or offspring in selection arenas prior to the hard selection of the adult phase, reduces loss of heterozygosity in certain types of asexual reproduction. Since loss of heterozygosity leads to the unmasking of recessive deleterious mutations in the progeny of asexual individuals, soft selection facilitates the evolution of these types of asexual reproduction. Using a population genetics model, I calculate how loss of heterozygosity affects fitness for different types of apomixis and automixis, and I show that soft selection significantly reduces loss of heterozygosity, hence increases fitness, in apomixis with suppression of the first meiotic division and in automixis with central fusion, the most common types of asexual reproduction. Therefore, if sexual reproduction evolved to preserve heterozygosity, soft selection should be associated with these types of asexual reproduction. I discuss the evidence for this prediction and how this and other observations on the distribution of different types of asexual reproduction in nature is consistent with the heterozygosity hypothesis.     

'Haldane's Sieve' in a metapopulation: sifting through plant reproductive polymorphisms

An important result of population genetics is that advantageous mutations will be fixed by selection in a population with a greater probability if they are dominant rather than recessive. This selective filter on new variants entering a population, termed 'Haldane's Sieve', has hitherto been invoked to account for the greater role of dominant than completely recessive mutations in adaptive evolution. Here, we suggest that a process similar to Haldane's Sieve will act on migrants into subpopulations of a metapopulation, and that the repeated action of Haldane's Sieve on alleles maintained by frequency-dependent selection, such as those responsible for many plant reproductive polymorphisms, is expected to bias their frequency distribution in favour of dominant alleles. The genetic and phenotypic signatures left by these processes might provide additional indirect support for the contentious idea that metapopulation dynamics have had an important role in shaping the ecology and evolution of some plant species.