On the Evolution of Genetic Incompatibility Systems. VI. a Three-Locus Modifier Model for the Origin of Gametophytic Self-Incompatibility

Recent genetic analyses have demonstrated that self-incompatibility in flowering plants derives from the coordinated expression of a system of loci. To address the selective mechanisms through which a genetic system of this kind evolves, I present a three-locus model for the origin of gametophytic self-incompatibility. Conventional models assume that a single locus encodes all physiological effects associated with self-incompatibility and that the viability of offspring depends only on whether they were derived by selfing or outcrossing. My model explicitly represents the genetic determination of offspring viability by a locus subject to symmetrically overdominant selection. Initially, the level of expression of the proto-S locus is insufficient to induce self-incompatibility. Weak gametophytic self-incompatibility arises upon the introduction of a rare allele at an unlinked modifier locus which enhances the expression of the proto-S locus. While conventional models predict that the origin of self-incompatibility requires at least two- to threefold levels of inbreeding depression, I find that the comparatively low levels of inbreeding depression generated by a single overdominant locus can ensure the invasion of an enhancer of self-incompatibility under sufficiently high rates of receipt of self-pollen. Associations among components of the incompatibility system promote the origin of self-incompatibility. Enhancement of heterozygosity at the initially neutral proto-S locus improves offspring viability through associative overdominance. Further, the modifier that enhances the expression of self-incompatibility develops a direct association with heterozygosity at the overdominant viability locus. These results suggest that the evolutionary processes by which incompatibility systems originate may differ significantly from those associated with their breakdown. The genetic mechanism explored here may apply to the evolution of other systems that restrict reproduction, including maternal-fetal incompatibility in mammals.     

Coevolution of self-fertilization and inbreeding depression. II. Symmetric overdominance in viability

We describe the evolutionary dynamics of a modifier of selfing coevolving with a locus subject to symmetric overdominance in viability under general levels of reduction in pollination success as a consequence of self-fertilization (pollen discounting). Simple models of the evolution of breeding systems that represent inbreeding depression as a constant parameter do not admit the possibility of stable mixed mating systems involving both inbreeding and random mating. Contrary to this expectation, we find that coevolution between a modifier of selfing and a single overdominant locus situated anywhere in the genome can generate evolutionarily attracting mixed mating systems. Two forms of association between the modifier locus and the viability locus promote the evolution of outcrossing. The favored heterozygous genotype at the viability locus develops positive associations with modifier alleles that enhance outcrossing and with the heterozygous genotype at the modifier locus. Associations between outcrossing and high viability evolve immediately upon the introduction of a rare modifier allele, even in the absence of linkage.     

On the evolution of genetic incompatibility systems. IV. Modification of response to an existing antigen polymorphism under partial selfing

A 2-locus model of the evolution of self-incompatibility in a population practicing partial selfing is presented. An allele is introduced at a modifier locus which influences the strength of the rejection reaction expressed by the style in response to antigens recognized in pollen. Two causes of inbreeding depression are investigated. First, offspring viability depends solely on the source (self or non-self) of the fertilizing pollen. Second, offspring viability declines with the expression of recessive deleterious alleles, segregating at a third (disease) locus, which exhibit an imperfect association with antigen alleles. Evolutionary changes occurring at the disease locus are not considered in this study. The condition under which a modifier allele that intensifies the incompatibility reaction increases when rare depends upon the number of antigens, the frequency of recessive deleterious alleles at the disease locus, and the level of association between the antigen locus and the disease locus. It is the improvement of viability among offspring derived by outcrossing, rather than the prevention of self-fertilization, that may represent the primary evolutionary function of genetic incompatibility systems.     

On the Origin of Meiotic Reproduction: A Genetic Modifier Model

We study the conditions under which a rare allele that modifies the relative rates of meiotic reproduction and apomixis increases in a population in which meiotic reproduction entails selfing as well as random outcrossing. A distinct locus, at which mutation maintains alleles that are lethal in homozygous form, determines viability. We find that low viability of carriers of the lethal alleles, high rates of selfing, dominance of the introduced modifier allele, and lower rates of recombination promote the evolution of meiosis. Meiotic reproduction can evolve even in the absence of linkage between the modifier and the viability locus. The adaptive value of meiotic reproduction depends on the relative viabilities of offspring derived by meiosis and by apomixis, and on associations between the modifier and the viability locus. Meiotic reproduction, particularly under selfing, generates more diverse offspring, including those with very high and very low viability. Elimination of offspring with low viability generates positive associations between enhancers of meiotic reproduction and high viability. In addition, partial selfing generates positive associations in heterozygosity (identity disequilibrium) between the modifier and the viability locus, even in the absence of linkage. The two kinds of associations together can compensate for initial reductions in mean offspring viability under meiotic reproduction.     

Coevolution of self-fertilization and inbreeding depression. I. Mutation-selection balance at one and two loci

Simple theories for the evolution of breeding systems suggest that the fate of an allele that modifies the rate of self-fertilization hinges only on the degree to which selfing reduces opportunities for outcrossing ("pollen discounting") and the extent of inbreeding depression. These theories predict that outcrossing evolves whenever deleterious mutations have a more severe effect in combination than expected from their individual effects. We study the evolutionary dynamics of a modifier of the rate of self-fertilization in populations subject to complete pollen discounting and recurrent mutations which impair viability at a single locus in diploids and at two loci in haploids. Our analysis indicates that genetic associations arising immediately upon the introduction of a rare modifier allele generate substantial quantitative and qualitative departures from expectation. Higher rates of segregation under selfing in our one-locus diploid model generate positive associations between enhancers of selfing and wild-type viability alleles, which in turn favor the evolution of selfing under a wider range of conditions than expected. Greater opportunities for recombination under outcrossing in our two-locus haploid model generate positive associations between enhancers of outcrossing and wild-type viability alleles. These associations favor the evolution of outcrossing under a wider range of conditions, and introduce the possibility of stable mixed mating systems involving both selfing and outcrossing. Our explicit analysis of genetic associations between loci affecting viability and the rate of self-fertilization indicates that modifiers that enhance the production of offspring with very high (and very low) viability by promoting segregation or recombination develop positive associations with high viability. This advantage of producing extremes can compensate for an initial disadvantage in offspring number.     

Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.     

Selection in complex genetic systems IV. Multiple alleles and interactions between two loci

Summary A symmetric viability model for two loci with two alleles at one locus and m alleles at the other is suggested and analyzed. The analysis of the equilibria is complete if the two loci are absolutely linked, while if recombination is allowed the analysis is incomplete. The dynamics of the mode! resemble those of the two locus two allele model, namely that for loose linkage there will be no correlation between the loci and for tight linkage there may be strong correlation. The major caveats to this are: 1. The equilibria stable for tight linkage may belong to an array of different structures dependent on the selection and the number of alleles. 2. If both loci are overdominant in viability, the stable equilibria always contain all alleles segregating in the population; otherwise, the stable equilibria may only be two locus two allele high complementarity equilibria for tight linkage. 3. For intermediate linkage values and special selection values the boundary two locus two allele high complementarity equilibria may be stable simultaneously with the totally polymorphic central point at which there is no association between the loci.Dedicated to the memory of Ove Frydenberg.Research supported in part by a grant from the Danish Natural Science Research Council, a grant from National Science Foundation, U.S.A., and by USPHS grant NIH 10452-09-11.     

Evolution of the segregation ratio: modification of gene conversion and meiotic drive

We compare the evolutionary pressures that direct the modification of gene conversion and meiotic drive at loci subject to purifying and overdominant viability selection. Gene conversion differs from meiotic drive in that modifers do not affect their own segregation ratios, even when linked to the viability locus. Segregation distortion generates gametic level disequilibria between alleles at the viability locus and modifiers of gene conversion and meiotic drive: enhancers of segregation distortion become positively associated with driven alleles. Suppression of gene conversion evolves if the driven allele is marginally disadvantageous (overdominant viability selection), and higher rates evolve if the driven alleles are relatively advantageous (purifying viability selection). Gametic disequilibria permit enhancers of meiotic drive that are linked to the driven locus to promote their own segregation. We attribute the failure of genetic modifiers of gene conversion and meiotic drive to maximinize mean fitness to the generation of such associations.     

Learning from rejection: the evolutionary biology of single-locus incompatibility

The self-incompatibility (S-) locus of flowering plants is among the most polymorphic known. PCR methods can now be used to estimate both the number of alleles in natural populations and their sequence diversity. The number of alleles provides an estimate of recent effective population size, thus the S-locus provides a tool for examining how species characteristics affect population size. Sequence relationships among alleles provide another estimate of population size extending millions of years into the past. Relationships between S-alleles and related genes provide a means of dating the age of origin of incompatibility systems and determining which, if any, angiosperm families share incompatibility by homology.     

The genetic basis and experimental evolution of inbreeding depression in Caenorhabditis elegans

Determining the genetic basis of inbreeding depression is important for understanding the role of selection in the evolution of mixed breeding systems. Here, we investigate how androdioecy (a breeding system characterized by partial selfing and outcrossing) and dioecy (characterized by obligatory outcrossing) influence the experimental evolution of inbreeding depression in Caenorhabditis elegans. We derived inbred lines from ancestral and evolved populations and found that the dioecious lineages underwent more extinction than androdioecious lineages. For both breeding systems, however, there was selection during inbreeding because the diversity patterns of 337 single-nucleotide polymorphisms (SNPs) among surviving inbred lines deviated from neutral expectations. In parallel, we also followed the evolution of embryo to adult viability, which revealed similar starting levels of inbreeding depression in both breeding systems, but also outbreeding depression. Under androdioecy, diversity at a neutral subset of 134 SNPs correlated well with the viability trajectories, showing that the population genetic structure imposed by partial selfing affected the opportunity for different forms of selection. Our findings suggest that the interplay between the disruptions of coevolved sets of loci by outcrossing, the efficient purging of deleterious recessive alleles with selfing and overdominant selection with outcrossing can help explain mixed breeding systems.     

Selection of sporophytic and gametophytic self‐incompatibility in the absence of a superlocus

Self‐incompatibility (SI) is a complex trait that enforces outcrossing in plant populations. SI generally involves tight linkage of genes coding for the proteins that underlie self‐pollen detection and pollen identity specification. Here, we develop two‐locus genetic models to address the question of whether sporophytic SI (SSI) and gametophytic SI (GSI) can invade populations of self‐compatible plants when there is no linkage or weak linkage of the underlying pollen detection and identity genes (i.e., no S‐locus supergene). The models assume that SI evolves as a result of exaptation of genes formerly involved in functions other than SI. Model analysis reveals that SSI and GSI can invade populations even when the underlying genes are loosely linked, provided that inbreeding depression and selfing rate are sufficiently high. Reducing recombination between these genes makes conditions for invasion more lenient. These results can help account for multiple, independent evolution of SI systems as seems to have occurred in the angiosperms.     

Tracking human migrations by the analysis of the distribution of HLA alleles, lineages and haplotypes in closed and open populations

The human leucocyte antigen (HLA) system shows extensive variation in the number and function of loci and the number of alleles present at any one locus. Allele distribution has been analysed in many populations through the course of several decades, and the implementation of molecular typing has significantly increased the level of diversity revealing that many serotypes have multiple functional variants. While the degree of diversity in many populations is equivalent and may result from functional polymorphism(s) in peptide presentation, homogeneous and heterogeneous populations present contrasting numbers of alleles and lineages at the loci with high-density expression products. In spite of these differences, the homozygosity levels are comparable in almost all of them. The balanced distribution of HLA alleles is consistent with overdominant selection. The genetic distances between outbred populations correlate with their geographical locations; the formal genetic distance measurements are larger than expected between inbred populations in the same region. The latter present many unique alleles grouped in a few lineages consistent with limited founder polymorphism in which any novel allele may have been positively selected to enlarge the communal peptide-binding repertoire of a given population. On the other hand, it has been observed that some alleles are found in multiple populations with distinctive haplotypic associations suggesting that convergent evolution events may have taken place as well. It appears that the HLA system has been under strong selection, probably owing to its fundamental role in varying immune responses. Therefore, allelic diversity in HLA should be analysed in conjunction with other genetic markers to accurately track the migrations of modern humans.     

Estimating the number,frequency, and dominance of S-alleles in a natural population of Arabidopsis lyrata(Brassicaceae) with sporophytic control of self-incompatibility

In homomorphic plant self-incompatibility (SI) systems, large numbers of alleles may be maintained at a single Mendelian locus. Most estimators of the number of alleles present in natural populations are designed for gametophytic self-incompatibility systems (GSI) in which the recognition phenotype of the pollen is determined by its own haploid genotype. In sporophytic systems (SSI), the recognition phenotype of the pollen is determined by the diploid genotype of its parent, and dominance differs among alleles. We describe research aimed at estimates of S-allele numbers in a natural population of Arabidopsis lyrata (Brassicaceae), whose SSI system has recently been described. Using a combination of pollination studies and PCR-based identification of alleles at a locus equivalent to the Brassica SRK gene, we identified and sequenced 11 putative alleles in a sample of 20 individuals from different maternal seed sets. The pollination results indicate that we have not amplified all alleles that must be present. Extensive partial incompatibility, nonreciprocal compatibility differences, and evidence of weakened expression of SI in some genotypes, prevent us from determining the exact number of missing alleles based only on cross-pollination data. Although we show that none of the theoretical models currently proposed is completely appropriate for estimating the number of alleles in this system, we estimate that there are between 13 and 16 different S-alleles in our sample, probably between 16 and 25 alleles in the population, and discuss the relative frequency of alleles in relation to dominance.     

On the evolution of genetic incompatibility systems. III. Introduction of weak gametophytic self-incompatibility under partial inbreeding

I explore the proposition that genetic incompatibility systems serve as a means for parents to evaluate and discriminate among their own offspring. Conditions for the initial increase of gametophytic self-incompatibility in a self-compatible population undergoing selfing, sibmating, and random outcrossing are reported. The adaptive value of reducing the concordance between offspring and maternal genotypes depends upon the relative changes in the numbers of offspring derived by the three modes, parent-offspring relatedness, and the magnitude of distortion of transmission ratios through pollen. Recessivity of stylar expression and low rates of receipt of pollen from related individuals facilitate the evolution of self-incompatibility. Viewed as a means of preferential maternal investment in offspring of high quality, self-incompatibility may be regarded as serving a function in common with diverse phenomena, including sexual selection, brood reduction, and other forms of prezygotic and postzygotic incompatibility. Associations between incompatibility loci and loci expressing inbreeding depression are expected to improve the reliability of the level of concordance at incompatibility loci as a measure of genomic homozygosity and offspring quality.     

The evolution of self-fertilization in density-regulated populations

The evolution of selfing in hermaphrodites has been studied to reveal the demographic conditions that lead to intermediate selfing rates. Using a demographic model based on Ricker-type density regulation, we assume first that, independent of population density, inbred individuals survive less well than outbred individuals and second, that inbred and outbred individuals differ in their competitive abilities in density-regulated populations. The evolution of selfing, driven by inbreeding depression and the cost of outcrossing, is then analysed for three fundamentally different demographic scenarios: stable population densities, deterministically varying population densities (resulting from cyclical or chaotic population dynamics) and stochastic fluctuations of carrying capacities (resulting from environmental noise). We show that even under stable demographic conditions evolutionary outcomes are not confined to either complete selfing or full outcrossing. Instead, intermediate selfing rates arise under a wide range of conditions, depending on the nature of competitive interactions between inbred and outbred individuals. We also explore the evolution of selfing under deterministic and stochastic density fluctuations to demonstrate that such environmental conditions can evolutionarily stabilize intermediate selfing rates. This is the first study, to our knowledge, to consider in detail the effect of density regulation on the evolution of selfing rates.     

Balancing selection and low recombination affect diversity near the self-incompatibility loci of the plant Arabidopsis lyrata

The self-incompatibility (S-) locus region of plants in the Brassica family is a small genome region. In Arabidopsis lyrata, the S-genes, SRK and SCR, encode the functional female and pollen recognition proteins, which must be coadapted to maintain correct associations between the two component genes, and thus self-incompatibility (SI). Recombinants would be self-compatible and thus probably disadvantageous in self-incompatible species. Therefore, tight linkage between the two genes in incompatibility systems is predicted to evolve to avoid producing such recombinant haplotypes. The evolution of low recombination in S-locus regions has not been rigorously tested. To test whether these regions' per-nucleotide recombination rates differ from those elsewhere in the genome, and to investigate whether the A. lyrata S-loci have the predicted effect on diversity in their immediate genome region, we studied diversity in genes that are linked to the S-loci but are not involved in incompatibility and are not under balancing selection. Compared with other A. lyrata loci, genes linked to the S-loci have extraordinarily high polymorphism. Our estimated recombination in this region, from fitting a model of the effects of S-allele polymorphism on linked neutral sites, supports the hypothesis of locally suppressed recombination around the S-locus.     

FITNESS CONSEQUENCES OF OUTCROSSING IN A SOCIAL SPIDER WITH AN INBREEDING MATING SYSTEM

Inbreeding mating systems are uncommon because of inbreeding depression. Mating among close relatives can evolve, however, when outcrossing is constrained. Social spiders show obligatory mating among siblings. In combination with a female‐biased sex ratio, sib‐mating results in small effective populations. In such a system, high genetic homozygosity is expected, and drift may cause population divergence. We tested the effect of outcrossing in the social spider Stegodyphus dumicola. Females were mated to sib‐males, to a non‐nestmate within the population, or to a male from a distant population, and fitness traits of F1s were compared. We found reduced hatching success of broods from between‐population crosses, suggesting the presence of population divergence at a large geographical scale that may result in population incompatibility. However, a lack of a difference in offspring performance between inbred and outbred crosses indicates little genetic variation between populations, and could suggest recent colonization by a common ancestor. This is consistent with population dynamics of frequent colonizations by single sib‐mated females of common origin, and extinctions of populations after few generations. Although drift or single mutations can lead to population divergence at a relatively short time scale, it is possible that dynamic population processes homogenize these effects at longer time scales.     

Coevolution of self-fertilization and inbreeding depression. III. Homozygous lethal mutations at multiple loci.

We study the evolution of the rate of self-fertilization in response to deleterious mutations at multiple loci. Although partial selfing induces associations among loci even in the absence of linkage, associations among mutations at different loci are of a smaller order of magnitude than the mutation rate. Genotypes that carry homozygous lethal mutations in heterozygous form at i loci occur in frequencies of the order (Ti) mu i, in which T denotes the number of viability loci and mu the mutation rate. While associations between mutations at different loci remain small even under inbreeding, each viability locus develops an association with the modifier of the rate of self-fertilization that substantially affects the evolution of the breeding system. Positive associations between enhancers of selfing and haplotypes carrying multiple wild-type alleles and positive associations in heterozygosity between the modifier locus and the viability loci promote evolutionary increases in the rate of self-fertilization.