Hitchhiking of Deleterious Alleles and the Cost of Adaptation in Partially Selfing Species

Self-fertilization is generally seen to be disadvantageous in the long term. It increases genetic drift, which subsequently reduces polymorphism and the efficiency of selection, which also challenges adaptation. However, high selfing rates can increase the fixation probability of recessive beneficial mutations, but existing theory has generally not accounted for the effect of linked sites. Here, we analyze a model for the fixation probability of deleterious mutants that hitchhike with selective sweeps in diploid, partially selfing populations. Approximate analytical solutions show that, conditional on the sweep not being lost by drift, higher inbreeding rates increase the fixation probability of the deleterious allele, due to the resulting reduction in polymorphism and effective recombination. When extending the analysis to consider a distribution of deleterious alleles, as well as the average fitness increase after a sweep, we find that beneficial alleles generally need to be more recessive than the previously assumed dominance threshold (h < 1/2) for selfing to be beneficial from one-locus theory. Our results highlight that recombination aiding the efficiency of selection on multiple loci amplifies the fitness benefits of outcrossing over selfing, compared to results obtained from one-locus theory. This effect additionally increases the parameter range under which obligate outcrossing is beneficial over partial selfing.     

Inbreeding load, average dominance and the mutation rate for mildly deleterious alleles in Mimulus guttatus

The goal of this study is to provide information on the genetics of inbreeding depression in a primarily outcrossing population of Mimulus guttatus. Previous studies of this population indicate that there is tremendous inbreeding depression for nearly every fitness component and that almost all of this inbreeding depression is due to mildly deleterious alleles rather than recessive lethals or steriles. In this article I assayed the homozygous and heterozygous fitnesses of 184 highly inbred lines extracted from a natural population. Natural selection during the five generations of selfing involved in line formation essentially eliminated major deleterious alleles but was ineffective in purging alleles with minor fitness effects and did not appreciably diminish overall levels of inbreeding depression. Estimates of the average degree of dominance of these mildly deleterious alleles, obtained from the regression of heterozygous fitness on the sum of parental homozygous fitness, indicate that the detrimental alleles are partially recessive for most fitness traits, with h approximately 0.15 for cumulative measures of fitness. The inbreeding load, B, for total fitness is approximately 1.0 in this experiment. These results are consistent with the hypothesis that spontaneous mildly deleterious mutations occur at a rate >0.1 mutation per genome per generation.     

THE EVOLUTION OF SELF-FERTILIZATION AND INBREEDING DEPRESSION IN PLANTS. I. GENETIC MODELS

The amounts of inbreeding depression upon selfing and of heterosis upon outcrossing determine the strength of selection on the selfing rate in a population when this evolves polygenically by small steps. Genetic models are constructed which allow inbreeding depression to change with the mean selfing rate in a population by incorporating both mutation to recessive and partially dominant lethal and sublethal alleles at many loci and mutation in quantitative characters under stabilizing selection. The models help to explain observations of high inbreeding depression (> 50%) upon selfing in primarily outcrossing populations, as well as considerable heterosis upon outcrossing in primarily selfing populations. Predominant selfing and predominant outcrossing are found to be alternative stable states of the mating system in most plant populations. Which of these stable states a species approaches depends on the history of its population structure and the magnitude of effect of genes influencing the selfing rate.     

Mating systems and the evolutionary transition between haploidy and diploidy

According to the 'masking hypothesis', diploids gain an immediate fitness advantage over haploids because diploids, with two copies of every gene, are better able to survive the effects of deleterious recessive mutations. Masking in diploids is, however, a double-edged sword: it allows mutations to persist over tine. In contrast, deleterious mutations are revealed in haploid individuals and are more rapidly eliminated by selection, creating genetic associations that are favourable to haploidy. We model various mating schemes and show that assortative mating, selfing, and apomixis maintain the genetic associations that favour haploidy. These results suggest that a correlation should exist between mating system and ploidy level, with outcrossing favouring diploid life cycles and inbreeding or asexual reproduction favouring haploid life cycles. This prediction can be tested in groups, such as the Chlorophyta, with extensive variation both in life cycle and in reproductive system. Confirming or rejecting this prediction in natural populations would constitute the first empirical test of the masking hypothesis as a force shaping the evolution of life cycles.     

Individual Variation in Inbreeding Depression: The Roles of Inbreeding History and Mutation

We use mutation-selection recursion models to evaluate the relative contributions of mutation and inbreeding history to variation among individuals in inbreeding depression and the ability of experiments to detect associations between individual inbreeding depression and mating system genotypes within populations. Poisson mutation to deleterious additive or recessive alleles generally produces far more variation among individuals in inbreeding depression than variation in history of inbreeding, regardless of selfing rate. Moreover, variation in inbreeding depression can be higher in a completely outcrossing or selfing population than in a mixed-mating population. In an initially random mating population, the spread of a dominant selfing modifier with no pleiotropic effects on male outcross success causes a measurable increase in inbreeding depression variation if its selfing rate is large and inbreeding depression is caused by recessive lethals. This increase is observable during a short period as the modifier spreads rapidly to fixation. If the modifier alters selfing rate only slightly, it fails to spread or causes no measurable increase in inbreeding depression variance. These results suggest that genetic associations between mating loci and inbreeding depression loci could be difficult to demonstrate within populations and observable only transiently during rapid evolution to a substantially new selfing rate.     

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.     

An explicit model for the inbreeding load in the evolutionary analysis of selfing

I present analytical predictions for the equilibrium inbreeding load expected in a population under mutation, selection, and a regular mating system for any population size and for any magnitude and recessivity of the deleterious effects. Using this prediction, I deduce the relative fitness of mutant alleles with small effect on selfing to explore the situations where selfing or outcrossing are expected to evolve. The results obtained are in agreement with previous literature, showing that natural selection is expected to lead to stable equilibria where populations show either complete outcrossing or complete selfing, and that selfing is promoted by large deleterious mutation rates. I find that the evolution of selfing is favored by a large recessivity of deleterious effects, while the magnitude of homozygous deleterious effects only becomes relevant in relatively small populations. This result contradicts the standard assumption that purging in large populations will only promote selfing when homozygous deleterious effects are large, and implies that previously published results obtained assuming lethal mutations in large populations can be extrapolated to nonlethal alleles of similar recessivity. This conclusion and the general approach used in this analysis can be useful in the study of the evolution of mating 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.     

EVOLUTION OF THE MAGNITUDE AND TIMING OF INBREEDING DEPRESSION IN PLANTS

Estimates of inbreeding depression obtained from the literature were used to evaluate the association between inbreeding depression and the degree of self-fertilization in natural plant populations. Theoretical models predict that the magnitude of inbreeding depression will decrease with inbreeding as deleterious recessive alleles are expressed and purged through selection. If selection acts differentially among life history stages and deleterious effects are uncorrelated among stages, then the timing of inbreeding depression may also evolve with inbreeding. Estimates of cumulative inbreeding depression and stage-specific inbreeding depression (four stages: seed production of parent, germination, juvenile survival, and growth/reproduction) were compiled for 79 populations (using means of replicates, N = 62) comprising 54 species from 23 families of vascular plants. Where available, data on the mating system also were collected and used as a measure of inbreeding history. A significant negative correlation was found between cumulative inbreeding depression and the primary selfing rate for the combined sample of angiosperms (N = 35) and gymnosperms (N = 9); the correlation was significant for angiosperms but not gymnosperms examined separately. The average inbreeding depression in predominantly selfing species (δ = 0.23) was significantly less (43%) than that in predominantly outcrossing species (δ = 0.53). These results support the theoretical prediction that selfing reduces the magnitude of inbreeding depression. Most self-fertilizing species expressed the majority of their inbreeding depression late in the life cycle, at the stage of growth/reproduction (14 of 18 species), whereas outcrossing species expressed much of their inbreeding depression either early, at seed production (17 of 40 species), or late (19 species). For species with four life stages examined, selfing and outcrossing species differed in the magnitude of inbreeding depression at the stage of seed production (selfing δ = 0.05, N = 11; outcrossing δ = 0.32, N = 31), germination (selfing δ = 0.02, outcrossing δ = 0.12), and survival to reproduction (selfing δ = 0.04, outcrossing δ = 0.15), but not at growth and reproduction (selfing δ = 0.21, outcrossing δ = 0.27); inbreeding depression in selfers relative to outcrossers increased from early to late life stages. These results support the hypothesis that most early acting inbreeding depression is due to recessive lethals and can be purged through inbreeding, whereas much of the late-acting inbreeding depression is due to weakly deleterious mutations and is very difficult to purge, even under extreme inbreeding.     

Rates of deleterious mutation and the evolution of sex in Caenorhabditis

A variety of models propose that the accumulation of deleterious mutations plays an important role in the evolution of breeding systems. These models make predictions regarding the relative rates of protein evolution and deleterious mutation in taxa with contrasting modes of reproduction. Here we compare available coding sequences from one obligately outcrossing and two primarily selfing species of Caenorhabditis to explore the potential for mutational models to explain the evolution of breeding system in this clade. If deleterious mutations interact synergistically, the mutational deterministic hypothesis predicts that a high genomic deleterious mutation rate (U) will offset the reproductive disadvantage of outcrossing relative to asexual or selfing reproduction. Therefore, C. elegans and C. briggsae (both largely selfing) should both exhibit lower rates of deleterious mutation than the obligately outcrossing relative C. remanei. Using a comparative approach, we estimate U to be equivalent (and < 1) among all three related species. Stochastic mutational models, Muller's ratchet and Hill-Robertson interference, are expected to cause reductions in the effective population size in species that rarely outcross, thereby allowing deleterious mutations to accumulate at an elevated rate. We find only limited support for more rapid molecular evolution in selfing lineages. Overall, our analyses indicate that the evolution of breeding system in this group is unlikely to be explained solely by available mutational models.     

The effect of linkage and population size on inbreeding depression due to mutational load.

Using a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.     

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.     

Digest: Exposing the role of rare alleles in inbreeding depression in monkeyflower*

Outcrossing is maintained in many hermaphroditic species despite theoretical work suggesting that alleles increasing selfing should invade outcrossing populations. Brown and Kelly (2019) identify reasons why this may not have occurred in an outcrossing population of monkeyflower, namely that inbreeding depression causes strong reductions in fitness, resulting in selection for the maintenance of outcrossing. They find that genetic load imposed by rare alleles is inversely correlated with fitness-associated traits, providing evidence that recessive, deleterious alleles contribute to inbreeding depression.     

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.     

MUTATIONAL MELTDOWN IN SELFING ARABIDOPSIS LYRATA

The majority of plant species and many animals are hermaphrodites, with individuals expressing both female and male function. Although hermaphrodites can potentially reproduce by self‐fertilization, they have a high prevalence of outcrossing. The genetic advantages of outcrossing are described by two hypotheses: avoidance of inbreeding depression because selfing leads to immediate expression of recessive deleterious mutations, and release from drift load because self‐fertilization leads to long‐term accumulation of deleterious mutations due to genetic drift and, eventually, to extinction. I tested both hypotheses by experimentally crossing Arabidopsis lyrata plants (self‐pollinated, cross‐pollinated within the population, or cross‐pollinated between populations) and measuring offspring performance over 3 years. There were 18 source populations, each of which was either predominantly outcrossing, mixed mating, or predominantly selfing. Contrary to predictions, outcrossing populations had low inbreeding depression, which equaled that of selfing populations, challenging the central role of inbreeding depression in mating system shifts. However, plants from selfing populations showed the greatest increase in fitness when crossed with plants from other populations, reflecting higher drift load. The results support the hypothesis that extinction by mutational meltdown is why selfing hermaphroditic taxa are rare, despite their frequent appearance over evolutionary time.     

Mutation accumulation in a selfing population: consequences of different mutation rates between selfers and outcrossers

Currently existing theories predict that because deleterious mutations accumulate at a higher rate, selfing populations suffer from more intense genetic degradation relative to outcrossing populations. This prediction may not always be true when we consider a potential difference in deleterious mutation rate between selfers and outcrossers. By analyzing the evolutionary stability of selfing and outcrossing in an infinite population, we found that the genome-wide deleterious mutation rate would be lower in selfing than in outcrossing organisms. When this difference in mutation rate was included in simulations, we found that in a small population, mutations accumulated more slowly under selfing rather than outcrossing. This result suggests that under frequent and intense bottlenecks, a selfing population may have a lower risk of genetic extinction than an outcrossing population.     

HIGH INBREEDING DEPRESSION,SELECTIVE INTERFERENCE AMONG LOCI,AND THE THRESHOLD SELFING RATE FOR PURGING RECESSIVE LETHAL MUTATIONS

The evolutionary dynamics of recessive or slightly dominant lethal mutations in partially self-fertilizing plants are analyzed using two models. In the identity-equilibrium model, lethals occur at a finite number of unlinked loci among which genotype frequencies are independent in mature plants. In the Kondrashov model, lethals occur at an infinite number of unlinked loci with identity disequilibrium produced by partial selfing. If the genomic mutation rate to (nearly) recessive lethal alleles is sufficiently high, such that the mean number of lethals (or lethal equivalents) per mature plant maintained at equilibrium under complete outcrossing exceeds 10, selective interference among loci creates a sharp discontinuity in the mean number of lethals maintained as a function of the selfing rate. Virtually no purging of the lethals occurs unless the selfing rate closely approaches or exceeds a threshold selfing rate, at which there is a precipitous drop in the mean number of lethals maintained. Identity disequilibrium lowers the threshold selfing rate by increasing the ratio of variance to mean number of lethals per plant, increasing the opportunity for selection. This theory helps to explain observations on plant species that display very high inbreeding depression despite intermediate selfing rates.     

The Effect of Deleterious Mutations on Neutral Molecular Variation

Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.     

The Evolution of Selfing Is Accompanied by Reduced Efficacy of Selection and Purging of Deleterious Mutations

The transition from outcrossing to selfing is predicted to reduce the genome-wide efficacy of selection because of the lower effective population size (N_e) that accompanies this change in mating system. However, strongly recessive deleterious mutations exposed in the homozygous backgrounds of selfers should be under strong purifying selection. Here, we examine estimates of the distribution of fitness effects (DFE) and changes in the magnitude of effective selection coefficients (N_es) acting on mutations during the transition from outcrossing to selfing. Using forward simulations, we investigated the ability of a DFE inference approach to detect the joint influence of mating system and the dominance of deleterious mutations on selection efficacy. We investigated predictions from our simulations in the annual plant Eichhornia paniculata, in which selfing has evolved from outcrossing on multiple occasions. We used range-wide sampling to generate population genomic datasets and identified nonsynonymous and synonymous polymorphisms segregating in outcrossing and selfing populations. We found that the transition to selfing was accompanied by a change in the DFE, with a larger fraction of effectively neutral sites (N_es < 1), a result consistent with the effects of reduced N_e in selfers. Moreover, an increased proportion of sites in selfers were under strong purifying selection (N_es > 100), and simulations suggest that this is due to the exposure of recessive deleterious mutations. We conclude that the transition to selfing has been accompanied by the genome-wide influences of reduced N_e and strong purifying selection against deleterious recessive mutations, an example of purging at the molecular level.     

Epistasis,inbreeding depression,and the evolution of self-fertilization

Inbreeding depression resulting from partially recessive deleterious alleles is thought to be the main genetic factor preventing self-fertilizing mutants from spreading in outcrossing hermaphroditic populations. However, deleterious alleles may also generate an advantage to selfers in terms of more efficient purging, while the effects of epistasis among those alleles on inbreeding depression and mating system evolution remain little explored. In this article, we use a general model of selection to disentangle the effects of different forms of epistasis (additive-by-additive, additive-by-dominance, and dominance-by-dominance) on inbreeding depression and on the strength of selection for selfing. Models with fixed epistasis across loci, and models of stabilizing selection acting on quantitative traits (generating distributions of epistasis) are considered as special cases. Besides its effects on inbreeding depression, epistasis may increase the purging advantage associated with selfing (when it is negative on average), while the variance in epistasis favors selfing through the generation of linkage disequilibria that increase mean fitness. Approximations for the strengths of these effects are derived, and compared with individual-based simulation results.