Estimation of the rate and effects of deleterious genomic mutations in finite populations with linkage disequilibrium

Under several assumptions such as infinite population size with unlinked loci at linkage equilibrium (LD) under mutation-selection (M-S) balance, the rate (U), and the average effects (dominance and selection coefficients h and s) of deleterious genomic mutations (DGM) can be estimated by the Deng-Lynch method in some natural populations. However, all natural populations are finite in size and many of them are not large enough to be considered as approximately infinite. In the absence of an analytical estimation approach to characterize DGM in finite populations, we test the robustness and applicability of the Deng-Lynch method in finite populations with computer simulations. The results indicate that the estimation obtained by the Deng-Lynch method in finite populations with LD is generally robust when population size is greater than 400. With constant mutation effects, in outcrossing populations, the estimates U and ? are unbiased or only slightly upwardly biased, and ? is unbiased for most cases. In highly selfing populations, U and ? are upwardly biased, U is no more than 1.5U and ? is less than 1.1 h, and ? is either unbiased or slightly downwardly biased. With variable mutation effects, U ranges from 0.56 to 0.72U, and s ranges from 1.4 to 1.8s. Generally speaking, with the same finite population size, the estimation in outcrossing populations is better than in highly selfing populations. Given that even the order of the magnitude of the parameters of DMG (U in particular) is controversial, our investigation here may provide a basis for using the Deng-Lynch method to characterize DGM in finite populations of size greater than 400 in the presence of LD.     

Estimation of deleterious genomic mutation parameters in natural populations by accounting for variable mutation effects across loci

The genomes of all organisms are subject to continuous bombardment of deleterious genomic mutations (DGM). Our ability to accurately estimate various parameters of DGM has profound significance in population and evolutionary genetics. The Deng-Lynch method can estimate the parameters of DGM in natural selfing and outcrossing populations. This method assumes constant fitness effects of DGM and hence is biased under variable fitness effects of DGM. Here, we develop a statistical method to estimate DGM parameters by considering variable mutation effects across loci. Under variable mutation effects, the mean fitness and genetic variance for fitness of parental and progeny generations across selfing/outcrossing in outcrossing/selfing populations and the covariance between mean fitness of parents and that of their progeny are functions of DGM parameters: the genomic mutation rate U, average homozygous effect s, average dominance coefficient h, and covariance of selection and dominance coefficients cov(h, s). The DGM parameters can be estimated by the algorithms we developed herein, which may yield improved estimation of DGM parameters over the Deng-Lynch method as demonstrated by our simulation studies. Importantly, this method is the first one to characterize cov(h, s) for DGM.     

Characterization of deleterious mutations in outcrossing populations.

Deng and Lynch recently proposed estimating the rate and effects of deleterious genomic mutations from changes in the mean and genetic variance of fitness upon selfing/outcrossing in outcrossing/highly selfing populations. The utility of our original estimation approach is limited in outcrossing populations, since selfing may not always be feasible. Here we extend the approach to any form of inbreeding in outcrossing populations. By simulations, the statistical properties of the estimation under a common form of inbreeding (sib mating) are investigated under a range of biologically plausible situations. The efficiencies of different degrees of inbreeding and two different experimental designs of estimation are also investigated. We found that estimation using the total genetic variation in the inbred generation is generally more efficient than employing the genetic variation among the mean of inbred families, and that higher degree of inbreeding employed in experiments yields higher power for estimation. The simulation results of the magnitude and direction of estimation bias under variable or epistatic mutation effects may provide a basis for accurate inferences of deleterious mutations. Simulations accounting for environmental variance of fitness suggest that, under full-sib mating, our extension can achieve reasonably well an estimation with sample sizes of only approximately 2000-3000.     

INBREEDING DEPRESSION,GENETIC LOAD,AND THE EVOLUTION OF OUTCROSSING RATES IN A MULTILOCUS SYSTEM WITH NO LINKAGE

We studied deterministic models of multilocus systems subject to mutation–selection balance with all loci unlinked, and with multiplicative interactions of the loci affecting fitness, in partially self-fertilizing populations. The aim was to examine the fitnesses of the zygotes produced by outcrossing and by selling, and the magnitude of inbreeding depression, in populations with different levels of inbreeding. The fates of modifiers of the outcrossing rate were also examined. With biologically plausible parameter values, inbreeding depression can be very large in moderately selfing populations, particularly when the mutant alleles are fairly recessive and selection is weak. A modifier allele reducing the selfing rate can be favored under these circumstances. In more inbred populations, inbreeding depression is lower, and selection favors alleles that increase the selfing rate. When inbreeding depression is caused by mutant alleles with strong selective disadvantage, modifiers causing large increases in selfing can often be favored even when the inbreeding depression exceeds one-half, though in these circumstances modifiers increasing selfing by smaller amounts are usually eliminated. Weaker selection appears to be more favorable to the maintenance of outcrossing.     

Hidden genetic variance contributes to increase the short‐term adaptive potential of selfing populations

Standing genetic variation is considered a major contributor to the adaptive potential of species. The low heritable genetic variation observed in self‐fertilizing populations has led to the hypothesis that species with this mating system would be less likely to adapt. However, a non‐negligible amount of cryptic genetic variation for polygenic traits, accumulated through negative linkage disequilibrium, could prove to be an important source of standing variation in self‐fertilizing species. To test this hypothesis, we simulated populations under stabilizing selection subjected to an environmental change. We demonstrate that, when the mutation rate is high (but realistic), selfing populations are better able to store genetic variance than outcrossing populations through genetic associations, notably due to the reduced effective recombination rate associated with predominant selfing. Following an environmental shift, this diversity can be partially remobilized, which increases the additive variance and adaptive potential of predominantly (but not completely) selfing populations. In such conditions, despite initially lower observed genetic variance, selfing populations adapt as readily as outcrossing ones within a few generations. For low mutation rates, purifying selection impedes the storage of diversity through genetic associations, in which case, as previously predicted, the lower genetic variance of selfing populations results in lower adaptability compared to their outcrossing counterparts. The population size and the mutation rate are the main parameters to consider, as they are the best predictors of the amount of stored diversity in selfing populations. Our results and their impact on our knowledge of adaptation under high selfing rates are discussed.     

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.     

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.     

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.     

Mutation-selection balance in mixed mating populations

An approximation to the average number of deleterious mutations per gamete, Q, is derived from a model allowing selection on both zygotes and male gametes. Progeny are produced by either outcrossing or self-fertilization with fixed probabilities. The genetic model is a standard in evolutionary biology: mutations occur at unlinked loci, have equivalent effects, and combine multiplicatively to determine fitness. The approximation developed here treats individual mutation counts with a generalized Poisson model conditioned on the distribution of selfing histories in the population. The approximation is accurate across the range of parameter sets considered and provides both analytical insights and greatly increased computational speed. Model predictions are discussed in relation to several outstanding problems, including the estimation of the genomic deleterious mutation rates (U), the generality of "selective interference" among loci, and the consequences of gametic selection for the joint distribution of inbreeding depression and mating system across species. Finally, conflicting results from previous analytical treatments of mutation-selection balance are resolved to assumptions about the life-cycle and the initial fate of mutations.     

Limited phenological and pollinator-mediated isolation among selfing and outcrossing Arabidopsis lyrata populations

Transitions from outcrossing to selfing have been a frequent evolutionary shift in plants and clearly play a role in species divergence. However, many questions remain about the initial mechanistic basis of reproductive isolation during the evolution of selfing. For instance, how important are pre-zygotic pre-pollination mechanisms (e.g. changes in phenology and pollinator visitation) in maintaining reproductive isolation between newly arisen selfing populations and their outcrossing ancestors? To test whether changes in phenology and pollinator visitation isolate selfing populations of Arabidopsis lyrata from outcrossing populations, we conducted a common garden experiment with plants from selfing and outcrossing populations as well as their between-population hybrids. Specifically, we asked whether there was isolation between outcrossing and selfing plants and their between-population hybrids through differences in (1) the timing or intensity of flowering; and/or (2) pollinator visitation. We found that phenology largely overlapped between plants from outcrossing and selfing populations. There were also no differences in pollinator preference related to mating system. Additionally, pollinators preferred to visit flowers on the same plant rather than exploring nearby plants, creating a large opportunity for self-fertilization. Overall, this suggests that pre-zygotic pre-pollination mechanisms do not strongly reproductively isolate plants from selfing and outcrossing populations of Arabidopsis lyrata.     

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.     

Selfing and outcrossing in hermaphrodite freshwater gastropods (Basommatophora): where, when and why

Hermaphrodite freshwater snails offer the opportunity to study the evolution of selling and outcrossing. Laboratory studies using genetic markers have shown that selling is possible in all species investigated, although outcrossing seems to be favoured in most. Predominance of outcrossing is promoted by sperm storing for up to several months. Studies using electrophoretic markers also suggest that outcrossing is the main breeding system in natural populations. However, heterozygote deficiencies found in some populations could indicate (partial) selfing. The evolution of self-fertilization and cross-fertilization is driven by numerous forces. Inbreeding depression is thought to select for outcrossing, and has been experimentally investigated in hermaphrodite freshwater snails. Other traits have evolved that prevent selfing. On the other hand, selfing could be selected under low density, or to preserve local adaptation, or when aphallic individuals occur within populations.     

INBREEDING DEPRESSION WITH HETEROZYGOTE ADVANTAGE AND ITS EFFECT ON SELECTION FOR MODIFIERS CHANGING THE OUTCROSSING RATE

The equilibrium level of inbreeding depression in populations with different selfing rates is studied for models with symmetrical or asymmetrical heterozygous advantage at several loci with partial linkage. As for the case of a single locus, the inbreeding depression caused by loci with heterozygous advantage can be higher for partially selfing populations than for complete outcrossing. The spread of modifier alleles at another locus that affects the selfing rate is studied. The stability of outcrossing populations to invasion by alleles that give increased selfing is found to depend on levels of inbreeding depression being greater than one-half, in accordance with earlier models that assumed a fixed level of inbreeding depression. However, in partially selfing populations the spread of such alleles can be checked by smaller levels of inbreeding depression than one-half, so that they do not always spread to fixation. This is interpreted as being due to associations between the genotypes at the modifier locus and the selected loci, together with increasing inbreeding depression as selfing increases, and does not occur if the inbreeding depression is due to mutation-selection balance.     

The evolutionary response of mating system to heterosis

Isolation allows populations to diverge and to fix different alleles. Deleterious alleles that reach locally high frequencies contribute to genetic load, especially in inbred or selfing populations, in which selection is relaxed. In the event of secondary contact, the recessive portion of the genetic load is masked in the hybrid offspring, producing heterosis. This advantage, only attainable through outcrossing, should favour evolution of greater outcrossing even if inbreeding depression has been purged from the contributing populations. Why, then, are selfing‐to‐outcrossing transitions not more common? To evaluate the evolutionary response of mating system to heterosis, we model two monomorphic populations of entirely selfing individuals, introduce a modifier allele that increases the rate of outcrossing and investigate whether the heterosis among populations is sufficient for the modifier to invade and fix. We find that the outcrossing mutation invades for many parameter choices, but it rarely fixes unless populations harbour extremely large unique fixed genetic loads. Reversions to outcrossing become more likely as the load becomes more polygenic, or when the modifier appears on a rare background, such as by dispersal of an outcrossing genotype into a selfing population. More often, the outcrossing mutation instead rises to moderate frequency, which allows recombination in hybrids to produce superior haplotypes that can spread without the mutation's further assistance. The transience of heterosis can therefore explain why secondary contact does not commonly yield selfing‐to‐outcrossing transitions.     

Effect of partial selfing and polygenic selection on establishment in a new habitat

This article analyzes how partial selfing in a large source population influences its ability to colonize a new habitat via the introduction of a few founder individuals. Founders experience inbreeding depression due to partially recessive deleterious alleles as well as maladaptation to the new environment due to selection on a large number of additive loci. I first introduce a simplified version of the inbreeding history model to characterize mutation‐selection balance in a large, partially selfing source population under selection involving multiple nonidentical loci. I then use individual‐based simulations to study the eco‐evolutionary dynamics of founders establishing in the new habitat under a model of hard selection. The study explores how selfing rate shapes establishment probabilities of founders via effects on both inbreeding depression and adaptability to the new environment, and also distinguishes the effects of selfing on the initial fitness of founders from its effects on the long‐term adaptive response of the populations they found. A high rate of (but not complete) selfing is found to aid establishment over a wide range of parameters, even in the absence of mate limitation. The sensitivity of the results to assumptions about the nature of polygenic selection is discussed.     

Allee effect and self-fertilization in hermaphrodites: reproductive assurance in demographically stable populations

The fact that selfing increases seed set (reproductive assurance) has often been put forward as an important selective force for the evolution of selfing. However, the role of reproductive assurance in hermaphroditic populations is far from being clear because of a lack of theoretical work. Here, I propose a theoretical model that analyzes self-fertilization in the presence of reproductive assurance. Because reproductive assurance directly influences the per capita growth rate, I developed an explicit demographic model for partial selfers in the presence of reproductive assurance, specifically when outcrossing is limited by the possibility of pollen transfer (Allee effect). Mating system parameters are derived as a function of the underlying demographical parameters. The functional link between population demography and mating system parameters (reproductive assurance, selfing rate) can be characterized. The demographic model permits the analysis of the evolution of self-fertilization in stable populations when reproductive assurance occurs. The model reveals some counterintuitive results such as the fact that increasing the fraction of selfed ovules can, in certain circumstances, increase the fraction of outcrossed ovules. Moreover, I demonstrate that reproductive assurance per se cannot account for the evolution of stable mixed selfing rates. Also, the model reveals that the extinction of outcrossing populations depends on small changes in population density (ecological perturbations), while the transition from outcrossing to selfing can, in certain cases, lead the population to extinction (evolutionary suicide). More generally, this paper highlights the fact that self-fertilization affects both the dynamics of individuals and the dynamics of selfing genes in hermaphroditic populations.     

Relatively weak inbreeding depression in selfing but also in outcrossing populations of North American Arabidopsis lyrata

Hermaphroditic plants can potentially self‐fertilize, but most possess adaptations that promote outcrossing. However, evolutionary transitions to higher selfing rates are frequent. Selfing comes with a transmission advantage over outcrossing, but self‐progeny may suffer from inbreeding depression, which forms the main barrier to the evolution of higher selfing rates. Here, we assessed inbreeding depression in the North American herb Arabidopsis lyrata, which is normally self‐incompatible, with a low frequency of self‐compatible plants. However, a few populations have become fixed for self‐compatibility and have high selfing rates. Under greenhouse conditions, we estimated mean inbreeding depression per seed (based on cumulative vegetative performance calculated as the product of germination, survival and aboveground biomass) to be 0.34 for six outcrossing populations, and 0.26 for five selfing populations. Exposing plants to drought and inducing defences with jasmonic acid did not magnify these estimates. For outcrossing populations, however, inbreeding depression per seed may underestimate true levels of inbreeding depression, because self‐incompatible plants showed strong reductions in seed set after (enforced) selfing. Inbreeding‐depression estimates incorporating seed set averaged 0.63 for outcrossing populations (compared to 0.30 for selfing populations). However, this is likely an overestimate because exposing plants to 5% CO₂ to circumvent self‐incompatibility to produce selfed seed might leave residual effects of self‐incompatibility that contribute to reduced seed set. Nevertheless, our estimates of inbreeding depression were clearly lower than previous estimates based on the same performance traits in outcrossing European populations of A. lyrata, which may help explain why selfing could evolve in North American A. lyrata.     

Mixed mating in natural populations of the chestnut blight fungus, Cryphonectria parasitica

As in plants, fungi exhibit wide variation in reproductive strategies and mating systems. Although most sexually reproducing fungi are either predominantly outcrossing or predominantly selfing, there are some notable exceptions. The haploid, ascomycete chestnut blight pathogen, Cryphonectria parasitica, has previously been shown to have a mixed mating system in one population in USA. In this report, we show that both selfing and outcrossing occur in 10 additional populations of C. parasitica sampled from Japan, Italy, Switzerland and USA. Progeny arrays from each population were assayed for segregation at vegetative incompatibility (vic) and DNA fingerprinting loci. Outcrossing rates (t(m)) were estimated as the proportion of progeny arrays showing segregation at one or more loci, corrected by the probability of nondetection of outcrossing (alpha). Estimates of t(m) varied from 0.74 to 0.97, with the lowest rates consistently detected in USA populations (0.74-0.78). Five populations (four in USA and one in Italy) had t(m) significantly less than 1, supporting the conclusion that these populations exhibit mixed mating. The underlying causes of variation in outcrossing rates among populations of C. parasitica are not known, but we speculate that--as in plants--outcrossing is a function of ecological, demographic and genetic factors.     

Mating system in Mexican populations of the annual herb Solanum rostratum Dunal (Solanaceae)

Traditionally, annual colonising species are expected to have high rates of self‐fertilisation, although recent theoretical and empirical studies have shown that cross‐fertilisation can be selected for under heterogeneous pollination environments. Solanum rostratum is a self‐compatible annual herb that colonises disturbed habitats. Despite the lack of physiological mechanisms to prevent self‐fertilisation, pollen transfer between individuals is expected to be favoured because of its complex floral morphology. In previous studies of S. rostratum it has been shown that anther dimorphism within flowers results in precise pollen placement on the pollinator's body, and the presence of mirror‐image floral morphs within plants promotes outcrossing in experimental arrays. However, the mating system of natural populations of S. rostratum has never been assessed, and thus whether it is predominantly selfing or outcrossing remains unknown. We hypothesise that floral and inflorescence morphology of S. rostratum should facilitate cross‐fertilisation, making it a predominantly outcrossing despite its lack of a self‐incompatibility system. To test this hypothesis, we estimated outcrossing rates by genotyping 700 individuals at 13 microsatellite loci, sampled from four populations across a 690‐km transect in the species' native range. We found that populations had mean outcrossing rates of 0.70 ± 0.03, with multiple sires contributing to paternity of each progeny array (average effective number of sires = 8.97 ± 0.57). This indicates that natural populations S. rostratum have relatively high levels of outcrossing, probably facilitated by its floral and inflorescence morphology. We speculate that partial selfing in this species may be an unavoidable consequence of displaying multiple flowers at the same time (geitonogamy), as well as the result of self‐pollen transfer by illegitimate visitors.     

Postcopulatory sexual selection reduces genetic diversity in experimental populations of Caenorhabditis elegans

Postcopulatory sexual selection affects the evolution of numerous features ranging from mating behavior to seminal fluid toxicity to the size of gametes. In an earlier study of the effect of sperm competition risk on sperm size evolution, experimental populations of the nematode Caenorhabditis elegans were maintained either by outcrossing (sperm competition present) or by selfing (no sperm competition), and after 60 generations, significantly larger sperm had evolved in the outcrossing populations. To determine the effects of this selection on population genetic variation, we assessed genetic diversity in a large number of loci using random amplification of polymorphic DNA-PCR. Nearly 80% of the alleles present in parental strain populations persisted in the 6 experimental populations after the 60 generations and, despite a 2.2-fold difference in expected heterozygosity, the resulting levels of genetic variation were equivalent between the outcrossing and selfing experimental populations. By inference, we conclude that genetic hitchhiking due to sexual selection in the experimental populations dramatically reduced genetic diversity. We use the levels of variation in the selfing populations as a control for the effects of drift, and estimate the strength of sexual selection to be strong in obligatorily outcrossing populations. Although sequential hermaphrodites like C. elegans probably experience little sexual selection in nature, these data suggest that sexual selection can profoundly affect diversity in outcrossing taxa.