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.     

CORRELATED EVOLUTION OF MATING STRATEGY AND INBREEDING DEPRESSION WITHIN AND AMONG POPULATIONS OF THE HERMAPHRODITIC SNAIL PHYSA ACUTA

Inbreeding depression is one of the main forces opposing the evolution of self-fertilization. Of central importance is the hypothesis that inbreeding depression and selfing coevolve antagonistically, generating either low selfing rate and high inbreeding depression or vice versa. However, there is limited evidence for this coevolution within species. We investigated this topic in the hermaphroditic snail Physa acuta . In this species, isolated individuals delay the onset of egg laying compared to individuals having access to mates. Longer delays ("waiting times") indicate more intense selfing avoidance. We measured inbreeding depression and waiting time in a large quantitative-genetic experiment (281 outbred families derived from 26 natural populations). We observed large genetic variance for both traits and a strong positive genetic covariance between them, most of which resided within rather than among populations. It means that, within populations, individuals with higher mutation load avoided selfing more strongly on average. This genetic covariance may result from pleiotropy and/or linkage disequilibrium. Whatever its genetic architecture, the fact it emerges specifically when individuals are deprived of mates suggests it is not fortuitous and rather reflects the action of natural selection. We conclude that a diversity of mating strategies can arise within populations subjected to variation in inbreeding depression.     

EVALUATING A SIMPLE APPROXIMATION TO MODELING THE JOINT EVOLUTION OF SELF‐FERTILIZATION AND INBREEDING DEPRESSION

A comprehensive understanding of plant mating system evolution requires detailed genetic models for both the mating system and inbreeding depression, which are often intractable. A simple approximation assuming that the mating system evolves by small infrequent mutational steps has been proposed. We examine its accuracy by comparing the evolutionarily stable selfing rates it predicts to those obtained from an explicit genetic model of the selfing rate, when inbreeding depression is caused by partly recessive deleterious mutations at many loci. Both models also include pollen limitation and pollen discounting. The approximation produces reasonably accurate predictions with a low or moderate genomic mutation rate to deleterious alleles, on the order of U = 0.02–0.2. However, for high mutation rates, the predictions of the full genetic model differ substantially from those of the approximation, especially with nearly recessive lethal alleles. This occurs because when a modifier allele affecting the selfing rate is rare, homozygous modifiers are produced mainly by selfing, which enhances the opportunity for purging nearly recessive lethals and increases the marginal fitness of the allele modifying the selfing rate. Our results confirm that explicit genetic models of selfing rate and inbreeding depression are required to understand mating system evolution.     

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.     

Partial male sterility and the evolution of nuclear gynodioecy in plants

Gynodioecy, a genetic dimorphism of females and hermaphrodites, is pertinent to an understanding of the evolution of plant gender, mating and genetic variability. Classical models of nuclear gynodioecy attribute the maintenance of the dimorphism to frequency-dependent selection in which the female phenotype has a fitness advantage at low frequency owing to a doubled ovule fertility. Here, I analyse explicit genetic models of nuclear gynodioecy that expand on previous work by allowing partial male sterility in combination with either fixed or dynamically evolving mutational inbreeding depression. These models demonstrate that partial male sterility causes fitness underdominance at the mating locus, which can prevent the spread of females. However, if partial male sterility is compensated by a change in selfing rate, overdominance at the mating locus can cause the spread of females. Overdominance at introduction of the male sterility allele can be caused by high inbreeding depression and a lower selfing rate in the heterozygote, by purging of mutations by a higher selfing rate in the heterozygote, and by low inbreeding depression and a higher selfing rate in the heterozygote. These processes might be of general importance in the maintenance of mating polymorphisms in plants.     

Inbreeding depression is high in a self‐incompatible perennial herb population but absent in a self‐compatible population showing mixed mating

High inbreeding depression is thought to be one of the major factors preventing evolutionary transitions in hermaphroditic plants from self‐incompatibility (SI) and outcrossing toward self‐compatibility (SC) and selfing. However, when selfing does evolve, inbreeding depression can be quickly purged, allowing the evolution of complete self‐fertilization. In contrast, populations that show intermediate selfing rates (a mixed‐mating system) typically show levels of inbreeding depression similar to those in outcrossing species, suggesting that selection against inbreeding might be responsible for preventing the transition toward complete self‐fertilization. By implication, crosses among populations should reveal patterns of heterosis for mixed‐mating populations that are similar to those expected for outcrossing populations. Using hand‐pollination crosses, we compared levels of inbreeding depression and heterosis between populations of Linaria cavanillesii (Plantaginaceae), a perennial herb showing contrasting mating systems. The SI population showed high inbreeding depression, whereas the SC population displaying mixed mating showed no inbreeding depression. In contrast, we found that heterosis based on between‐population crosses was similar for SI and SC populations. Our results are consistent with the rapid purging of inbreeding depression in the derived SC population, despite the persistence of mixed mating. However, the maintenance of outcrossing after a transition to SC is inconsistent with the prediction that populations that have purged their inbreeding depression should evolve toward complete selfing, suggesting that the transition to SC in L. cavanillesii has been recent. SC in L. cavanillesii thus exemplifies a situation in which the mating system is likely not at an equilibrium with inbreeding depression.     

Little to no inbreeding depression in a tapeworm with mixed mating

Meta‐studies on hermaphrodites have found a negative relationship between primary selfing rates and levels of inbreeding depression (ID) and, thus, generally support purging in inbred systems. However, in plants, high among‐taxa variance in ID results in no difference in the mean ID between outcrossing and mixed‐mating taxa. Selective interference likely explains high ID among mixed‐mating taxa, whereas low levels of ID among mixed‐mating taxa are not as stressed. Among animal hermaphrodites, primarily molluscs, there are little data on mixed‐mating systems. To fill a taxonomic and mating system gap, we tested for ID in a mixed‐mating tapeworm, Oochoristica javaensis. We provide a direct estimate of ID across infection of an intermediate host by comparing selfing rates at two life history stages. We found little to no evidence for ID, and the level of ID falls in line with what is reported for highly selfing species even though O. javaensis has mixed mating. We discuss this result within the context of kin mating in O. javaensis. Our results emphasize that primary selfing rates alone may be insufficient to classify the inbreeding history in all species when testing for a relationship to ID. Mixed‐mating taxa, and possibly some outcrossing taxa, may exhibit low levels of ID if biparental inbreeding is also driving purging. We advocate that ID studies report estimates of inbreeding history (e.g. F_IS or identity disequilibrium) from nature‐derived adult samples to provide context rather than relying on primary selfing rates alone.     

A genetic interpretation of the variation in inbreeding depression

Inbreeding depression is expected to play an important but complicated role in evolution. If we are to understand the evolution of inbreeding depression (i.e., purging), we need quantitative genetic interpretations of its variation. We introduce an experimental design in which sires are mated to multiple dams, some of which are unrelated to the sire but others are genetically related owing to an arbitrary number of prior generations of selfing or sib-mating. In this way we introduce the concept of "inbreeding depression effect variance," a parameter more relevant to selection and the purging of inbreeding depression than previous measures. We develop an approach for interpreting the genetic basis of the variation in inbreeding depression by: (1) predicting the variation in inbreeding depression given arbitrary initial genetic variance and (2) estimating genetic variance components given half-sib covariances estimated by our experimental design. As quantitative predictions of selection depend upon understanding genetic variation, our approach reveals the important difference between how inbreeding depression is measured experimentally and how it is viewed by selection.     

The genetic consequences of fluctuating inbreeding depression and the evolution of plant selfing rates

The magnitude of inbreeding depression, a central parameter in the evolution of plant mating systems, can vary depending on environmental conditions. However, the underlying genetic mechanisms causing environmental fluctuations in inbreeding depression, and the consequences of this variation for the evolution of self‐fertilization, have been little studied. Here, we consider temporal fluctuations of the selection coefficient in an explicit genetic model of inbreeding depression. We show that substantial variance in inbreeding depression can be generated at equilibrium by fluctuating selection, although the simulated variance tends to be lower than has been measured in experimental studies. Our simulations also reveal that purging of deleterious mutations does not depend on the variance in their selection coefficient. Finally, an evolutionary analysis shows that, in contrast to previous theoretical approaches, intermediate selfing rates are never evolutionarily stable when the variation in inbreeding depression is due to fluctuations in the selection coefficient on deleterious mutations.     

Purging of inbreeding depression within a population of Oxalis alpina (Oxalidaceae)

? Premise of the study: Variation among individuals in levels of inbreeding depression associated with selfing levels could influence mating system evolution by purging deleterious alleles, but empirical evidence for this association is limited. ? Methods: We investigated the association of family-level inbreeding depression and presumed inbreeding history in a tristylous population of Oxalis alpina (Oxalidaceae). ? Key results: Mid-styled individuals possessed the greatest degree of self-compatibility (SC) and produced more autogamous capsules than short- or long-styled individuals. Offspring of highly self-compatible mid-styled individuals showed reduced inbreeding depression. Mid-styled plants that produced capsules autogamously exhibited reduced stigma-anther separation compared to mid-styled plants that produced no capsules autogamously. Reduced inbreeding depression was not correlated with stigma-anther separation, suggesting that self-compatibility and autogamy evolve before morphological changes in stigma-anther separation. ? Conclusions: Purging of inbreeding depression occurred in SC mid-styled maternal families. Low inbreeding depression in SC mid-styled plants may lead to retention of the mid-styled morph in populations, despite the occurrence of higher selfing rates in mid-styled relative to short- or long-styled morphs. Variation among individuals in levels of self-fertilization within populations may lead to associations between inbreeding lineages and lower levels of inbreeding depression, influencing the evolution of mating systems.     

EFFECTS OF DIFFERENT LEVELS OF INBREEDING ON PROGENY FITNESS IN PLANTAGO CORONOPUS

Inbreeding depression (δ) is a major selective force favoring outcrossing in flowering plants. Many phenotypic and genetic models of the evolution of selfing conclude that complete outcrossing should evolve whenever inbreeding depression is greater than one-half, otherwise selfing should evolve. Recent theoretical work, however, has challenged this view and emphasized (1) the importance of variation in inbreeding depression among individuals within a population; and (2) the nature of gene action between deleterious mutations at different loci (epistasis) as important determinants for the evolution of plant mating systems. The focus of this study was to examine the maintenance of inbreeding depression and the relationship between inbreeding level and inbreeding depression at both the population and the individual level in one population of the partially self-fertilizing plant Plantago coronopus (L.). Maternal plants, randomly selected from an area of about 50 m² in a natural population, were used to establish lines with expected inbreeding coefficients (f) of 0, 0.25, 0.50, 0.75, and 0.875. Inbreeding depression was estimated both in the greenhouse and at the site of origin of the maternal plants by comparing growth, survival, flowering, and seed production of the progeny with different inbreeding coefficients. No significant inbreeding depression for these fitness traits was detected in the greenhouse after 16 weeks. This was in strong contrast to the field, where the traits all displayed significant inbreeding depression and declined with increased inbreeding. The results were consistent with the view that mutation to mildly deleterious alleles is the primary cause of inbreeding depression. At the family level, significantly different maternal line responses (maternal parent × inbreeding level interaction) provide a mechanism for the invasion of a selfing variant into the population through any maternal line exhibiting purging of its genetic load. At the population level, evidence for synergistic epistasis was detected for the probability of flowering, but not for total seed production. At the family level, however, a significant interaction between inbreeding level and maternal families for both traits was observed, indicating that epistasis could play a role in the expression of inbreeding depression among maternal lines.     

Reproductive compensation in the evolution of plant mating systems

Reproductive compensation, the replacement of dead embryos by potentially viable ones, is known to play a major role in the maintenance of deleterious mutations in mammalian populations. However, it has received little attention in plant evolution. Here we model the joint evolution of mating system and inbreeding depression with reproductive compensation. We used a dynamic model of inbreeding depression, allowing for partial purging of recessive lethal mutations by selfing. We showed that reproductive compensation tended to increase the mean number of lethals in a population, but favored self-fertilization by effectively decreasing early inbreeding depression. When compensation depended on the selfing rate, stable mixed mating systems can occur, with low to intermediate selfing rates. Experimental evidence of reproductive compensation is required to confirm its potential importance in the evolution of plant mating systems. We suggest experimental methods to detect reproductive compensation.     

Patterns of mating-system evolution in hermaphroditic animals: correlations among selfing rate, inbreeding depression, and the timing of reproduction

In hermaphrodites, traits that influence the selfing rate can coevolve with inbreeding depression, leading to the emergence of evolutionary syndromes. Theory predicts a negative correlation between inbreeding depression and selfing rate across species. This prediction has only been examined and validated in vascular plants. Furthermore, selfing rates are often influenced by environmental conditions (e.g., lack of mates or pollinators), and species are predicted to evolve mechanisms to buffer this variation. We extend previous studies of mating-system syndromes in two ways. First, we assembled a new dataset on Basommatophoran snails (17 species, including new data on 12 species). Second, we measured how species responded to variation in mate availability. Specifically, we quantified the waiting time before selfing (i.e., how long the onset of reproduction is delayed in the absence of mates). Selfing rates were negatively correlated with both inbreeding depression and the waiting time. Species with stronger inbreeding depression exhibited longer waiting times. These patterns obtained on Basommatophorans still hold when including eight other hermaphroditic animals. Our results support the hypothesis that selection drives the evolution of mating-system syndromes in animals. The reaction norm of selfing rates to mate availability is a key target of natural selection in this context.     

Evolutionary Assurance vs. Mixed Mating

Reproductive assurance is a widely accepted explanation for the evolution of selfing, although theory suggests that an evolutionarily stable mixed mating strategy does not maximize seed production. We present a correlation analysis involving 28 species representing 23 families showing that selfing can evolve independently of inbreeding depression. We discuss the cost-benefit trade-off of selfing, in particular the incongruence of whether delayed selfing provides reproductive assurance in 22 species representing 14 families, in which pollen and seed discounting are minimized when pollinators or mates are scarce. Reproductive assurance, in response to frequent pollinator failure, can be reconciled with an evolutionarily stable mixed mating system contributed to by delayed selfing, which is still advantageous even if there is strong inbreeding depression.     

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.     

THE RELATIONSHIP BETWEEN MATING-SYSTEM CHARACTERS AND INBREEDING DEPRESSION IN MIMULUS GUTTATUS

Several recent theoretical considerations of mating-system evolution predict within-population covariation between levels of inbreeding depression and genetically controlled mating-system characters. If inbreeding depression is caused by deleterious recessive alleles, families with characters that promote self-pollination should show lower levels of inbreeding depression than families with characters that promote outcrossing. The converse is expected if inbreeding depression is due to overdominant allelic interactions. Whether these associations between mating-system and viability loci evolve will have important consequences for mating-system evolution. The evolution of selfing within the genus Mimulus is associated with a reduction in stigma-anther separation (i.e., a loss of herkogamy) and high autogamous seed set. In this study we compared families from two M. guttatus populations that differed genetically in their degree of stigma-anther separation. In one of these populations we also compared families that differed genetically in the degree to which they autogamously set seed in a pollinator-free greenhouse. Dams often differed significantly in levels of inbreeding depression for aboveground biomass and flower production, but variation in inbreeding depression was never explained by herkogamy class or autogamy class. Several factors might account for why families with traits associated with selfing did not show lower inbreeding depression, and these are discussed. Our study also demonstrated significant variation among self progeny from a given female likely due to differences in pollination date and position of fruit maturation. The detection of significant dam × sire interactions suggests biparental inbreeding or differences in combining ability for specific pairs of parents.     

Levels of inbreeding depression over seven generations of selfing in the androdioecious clam shrimp, Eulimnadia texana

Androdioecy (mixtures of males and hermaphrodites) is a rare mating system in both plants and animals. Theory suggests that high levels of inbreeding depression can maintain males in androdioecious populations if hermaphrodites commonly self-fertilize. However, if inbreeding depression (delta) can be 'purged' from selfing populations, maintaining males is more difficult. In the androdioecious clam shrimp, Eulimnadia texana, delta is estimated to be as high as 0.7. Previous work suggests that this high level is maintained in the face of high levels of inbreeding due to an associative overdominance of fitness-related loci with the sex-determining locus. Such associative overdominance would make purging of inbreeding depression difficult to impossible. The current experiment was designed to determine if delta can be purged in these shrimp by tracking fitness across seven generations in selfing and outcrossing treatments. Evidence of purging was found in one of four populations, but the remaining populations demonstrated a consistent pattern of delta across generations. Although the experimental design allowed ample opportunity for purging, the majority of populations were unable to purge their genetic load. Therefore, delta in this species is likely due to associative overdominance caused by deleterious recessive alleles linked to the sex determining locus.     

Variability of individual genetic load: consequences for the detection of inbreeding depression

Inbreeding depression is a key factor affecting the persistence of natural populations, particularly when they are fragmented. In species with mixed mating systems, inbreeding depression can be estimated at the population level by regressing the average progeny fitness by the selfing rate of their mothers. We applied this method using simulated populations to investigate how population genetic parameters can affect the detection power of inbreeding depression. We simulated individual selfing rates and genetic loads from which we computed fitness values. The regression method yielded high statistical power, inbreeding depression being detected as significant (5?% level) in 92?% of the simulations. High individual variation in selfing rate and high mean genetic load led to better detection of inbreeding depression while high among-individual variation in genetic load made it more difficult to detect inbreeding depression. For a constant sampling effort, increasing the number of progenies while decreasing the number of individuals per progeny enhanced the detection power of inbreeding depression. We discuss the implication of among-mother variability of genetic load and selfing rate on inbreeding depression studies.     

Inbreeding depression maintained by recessive lethal mutations interacting with stabilizing selection on quantitative characters in a partially self‐fertilizing population

The bimodal distribution of fitness effects of new mutations and standing genetic variation, due to early‐acting strongly deleterious recessive mutations and late‐acting mildly deleterious mutations, is analyzed using the Kondrashov model for lethals (K), with either the infinitesimal model for selfing (IMS) or the Gaussian allele model (GAM) for quantitative genetic variance under stabilizing selection. In the combined models (KIMS and KGAM) high genomic mutation rates to lethals and weak stabilizing selection on many characters create strong interactions between early and late inbreeding depression, by changing the distribution of lineages selfed consecutively for different numbers of generations. Alternative stable equilibria can exist at intermediate selfing rates for a given set of parameters. Evolution of quantitative genetic variance under multivariate stabilizing selection can strongly influence the purging of nearly recessive lethals, and sometimes vice versa. If the selfing rate at the purging threshold for quantitative genetic variance in IMS or GAM alone exceeds that for nearly recessive lethals in K alone, then in KIMS and KGAM stabilizing selection causes selective interference with purging of lethals, increasing the mean number of lethals compared to K; otherwise, stabilizing selection causes selective facilitation in purging of lethals, decreasing the mean number of lethals.     

Mating system and ploidy influence levels of inbreeding depression in Clarkia (Onagraceae)

Inbreeding depression is the reduction in offspring fitness associated with inbreeding and is thought to be one of the primary forces selecting against the evolution of self-fertilization. Studies suggest that most inbreeding depression is caused by the expression of recessive deleterious alleles in homozygotes whose frequency increases as a result of self-fertilization or mating among relatives. This process leads to the selective elimination of deleterious alleles such that highly selfing species may show remarkably little inbreeding depression. Genome duplication (polyploidy) has also been hypothesized to influence levels of inbreeding depression, with polyploids expected to exhibit less inbreeding depression than diploids. We studied levels of inbreeding depression in allotetraploid and diploid species of Clarkia (Onagraceae) that vary in mating system (each cytotype was represented by an outcrossing and a selfing species). The outcrossing species exhibited more inbreeding depression than the selfing species for most fitness components and for two different measures of cumulative fitness. In contrast, though inbreeding depression was generally lower for the polyploid species than for the diploid species, the difference was statistically significant only for flower number and one of the two measures of cumulative fitness. Further, we detected no significant interaction between mating system and ploidy in determining inbreeding depression. In sum, our results suggest that a taxon's current mating system is more important than ploidy in influencing levels of inbreeding depression in natural populations of these annual plants.