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.     

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.     

Outbreeding depression, but no inbreeding depression in haplodiploid Ambrosia beetles with regular sibling mating

In sexual reproduction the genetic similarity or dissimilarity between mates strongly affects offspring fitness. When mating partners are too closely related, increased homozygosity generally causes inbreeding depression, whereas crossing between too distantly related individuals may disrupt local adaptations or coadaptations within the genome and result in outbreeding depression. The optimal degree of inbreeding or outbreeding depends on population structure. A long history of inbreeding is expected to reduce inbreeding depression due to purging of deleterious alleles, and to promote outbreeding depression because of increased genetic variation between lineages. Ambrosia beetles (Xyleborini) are bark beetles with haplodiploid sex determination, strong local mate competition due to regular sibling mating within the natal chamber, and heavily biased sex ratios. We experimentally mated females of Xylosandrus germanus to brothers and unrelated males and measured offspring fitness. Inbred matings did not produce offspring with reduced fitness in any of the examined life-history traits. In contrast, outcrossed offspring suffered from reduced hatching rates. Reduction in inbreeding depression is usually attributed to purging of deleterious alleles, and the absence of inbreeding depression in X. germanus may represent the highest degree of purging of all examined species so far. Outbreeding depression within the same population has previously only been reported from plants. The causes and consequences of our findings are discussed with respect to mating strategies, sex ratios, and speciation in this unusual system.     

Effects of population structures and selection strategies on the purging of inbreeding depression due to deleterious mutations

Stochastic simulations were run to compare the effects of nine breeding schemes, using full-sib mating, on the rate of purging of inbreeding depression due to mutations with equal deleterious effect on viability at unlinked loci in an outbred population. A number of full-sib mating lines were initiated from a large outbred population and maintained for 20 generations (if not extinct). Selection against deleterious mutations was allowed to occur within lines only, between lines or equal within and between lines, and surviving lines were either not crossed or crossed following every one or three generations of full-sib mating. The effectiveness of purging was indicated by the decreased number of lethal equivalents and the increased fitness of the purged population formed from crossing surviving lines after 20 generations under a given breeding scheme. The results show that the effectiveness of purging, the survival of the inbred lines and the inbreeding level attained are generally highest with between-line selection and lowest with within-line selection. Compared with no crossing, line crossing could lower the risk of extinction and the inbreeding coefficient of the purged population substantially with little loss of the effectiveness of purging. Compromising between the effectiveness of purging, and the risk of extinction and inbreeding coefficient, the breeding scheme with equal within- and between-line selection and crossing alternatively with full-sib mating is generally the most desirable scheme for purging deleterious mutations. Unless most deleterious mutations have relatively large effects on fitness in species with reproductive ability high enough to cope with the depressed fitness and thus increased risk of extinction with inbreeding, it is not justified to apply a breeding programme aimed at purging inbreeding depression by inbreeding and selection to a population of conservation concern.     

Incest versus abstinence: reproductive trade‐offs between mate limitation and progeny fitness in a self‐incompatible invasive plant

Plant mating systems represent an evolutionary and ecological trade‐off between reproductive assurance through selfing and maximizing progeny fitness through outbreeding. However, many plants with sporophytic self‐incompatibility systems exhibit dominance interactions at the S‐locus that allow biparental inbreeding, thereby facilitating mating between individuals that share alleles at the S‐locus. We investigated this trade‐off by estimating mate availability and biparental inbreeding depression in wild radish from five different populations across Australia. We found dominance interactions among S‐alleles increased mate availability relative to estimates based on individuals that did not share S‐alleles. Twelve of the sixteen fitness variables were significantly reduced by inbreeding. For all the three life‐history phases evaluated, self‐fertilized offspring suffered a greater than 50% reduction in fitness, while full‐sib and half‐sib offspring suffered a less than 50% reduction in fitness. Theory indicates that fitness costs greater than 50% can result in an evolutionary trajectory toward a stable state of self‐incompatibility (SI). This study suggests that dominance interactions at the S‐locus provide a possible third stable state between SI and SC where biparental inbreeding increases mate availability with relatively minor fitness costs. This strategy allows weeds to establish in new environments while maintaining a functional SI system.     

SEVERE INBREEDING DEPRESSION AND NO EVIDENCE OF PURGING IN AN EXTREMELY INBRED WILD SPECIES—THE CHATHAM ISLAND BLACK ROBIN

Although evidence of inbreeding depression in wild populations is well established, the impact of genetic purging in the wild remains controversial. The contrasting effects of inbreeding depression, fixation of deleterious alleles by genetic drift, and the purging of deleterious alleles via natural selection mean that predicting fitness outcomes in populations subjected to prolonged bottlenecks is not straightforward. We report results from a long‐term pedigree study of arguably the world's most inbred wild species of bird: the Chatham Island black robin Petroica traversi, in which conditions were ideal for purging to occur. Contrary to expectations, black robins showed a strong, negative relationship between inbreeding and juvenile survival, yielding lethal equivalents (2B) of 6.85. We also determined that the negative relationship between inbreeding and survival did not appear to be mediated by levels of ancestral inbreeding and may be attributed in part to unpurged lethal recessives. Although the black robin demographic history provided ideal conditions for genetic purging, our results show no clear evidence of purging in the major life‐history trait of juvenile survival. Our results also show no evidence of fixation of deleterious alleles in juvenile survival, but do confirm that continued high levels of contemporary inbreeding in a historically inbred population could lead to additional severe inbreeding depression.     

Effects of Interference Between Selected Loci on the Mutation Load,Inbreeding Depression,and Heterosis

A classical prediction from single-locus models is that inbreeding increases the efficiency of selection against partially recessive deleterious alleles (purging), thereby decreasing the mutation load and level of inbreeding depression. However, previous multilocus simulation studies found that increasing the rate of self-fertilization of individuals may not lead to purging and argued that selective interference among loci causes this effect. In this article, I derive simple analytical approximations for the mutation load and inbreeding depression, taking into account the effects of interference between pairs of loci. I consider two classical scenarios of nonrandomly mating populations: a single population undergoing partial selfing and a subdivided population with limited dispersal. In the first case, correlations in homozygosity between loci tend to reduce mean fitness and increase inbreeding depression. These effects are stronger when deleterious alleles are more recessive, but only weakly depend on the strength of selection against deleterious alleles and on recombination rates. In subdivided populations, interference increases inbreeding depression within demes, but decreases heterosis between demes. Comparisons with multilocus, individual-based simulations show that these analytical approximations are accurate as long as the effects of interference stay moderate, but fail for high deleterious mutation rates and low dominance coefficients of deleterious alleles.     

THE ROLE OF GENES OF LARGE EFFECT ON INBREEDING DEPRESSION IN MIMULUS GUTTATUS

Severe inbreeding depression is routinely observed in outcrossing species. If inbreeding load is due largely to deleterious alleles of large effect, such as recessive lethals or steriles, then most of it is expected to be purged during brief periods of inbreeding. In contrast, if inbreeding depression is due to the cumulative effects of many deleterious alleles of small effect, then it will be maintained in the face of periodic inbreeding. Whether or not inbreeding depression can be purged with inbreeding in the short term has important implications for the evolution of mating systems and the probability that a small population will go extinct. In this paper I evaluate the extent to which the tremendous inbreeding load in a primarily outcrossing population of the wildflower, Mimulus guttatus, is due to alleles of large effect. To do this, I first constructed a large outbred “ancestral” population by randomly mating plants collected as seeds from a natural population. From this population I formed 1200 lines that were maintained by self-fertilization and single seedling descent: after five generations of selling, 335 lines had survived the inbreeding process. Selection during the line formation is expected to have largely purged alleles of large effect from the collection of highly inbred lines. Because alleles with minor effects on fitness should have been effectively neutral, the inbreeding depression due to this class of genes should have been unchanged. The inbred lines were intercrossed to form a large, outcrossed “purged” population. Finally, I estimated the fitness of outbred and selfed progeny from the ancestral and purged populations to determine the contribution of major deleterious alleles on inbreeding depression. I found that although the average fitness of the outcrossed progeny nearly doubled following purging, the limited decline in inbreeding depression and limited increase in inbred fitness indicates that alleles of large effect are not the principle cause of inbreeding depression in this population. In aggregate, the data suggest that lethals and steriles make a minority contribution to inbreeding depression and that the increased outbred fitness is due primarily to adaptation to greenhouse conditions.     

TRANSMISSION ADVANTAGE FAVORS SELFING ALLELE IN EXPERIMENTAL POPULATIONS OF SELF‐INCOMPATIBLE WITHERINGIA SOLANACEA (SOLANACEAE)

The evolution of self‐fertilization is one of the most commonly traversed transitions in flowering plants, with profound implications for population genetic structure and evolutionary potential. We investigated factors influencing this transition using Witheringia solanacea, a predominantly self‐incompatible (SI) species within which self‐compatible (SC) genotypes have been identified. We showed that self‐compatibility in this species segregates with variation at the S‐locus as inherited by plants in F1 and F2 generations. To examine reproductive assurance and the transmission advantage of selfing, we placed SC and SI genotypes in genetically replicated gardens and monitored male and female reproductive success, as well as selfing rates of SC plants. Self‐compatibility did not lead to increased fruit or seed set, even under conditions of pollinator scarcity, and the realized selfing rate of SC plants was less than 10%. SC plants had higher fruit abortion rates, consistent with previous evidence showing strong inbreeding depression at the embryonic stage. Although the selfing allele did not provide reproductive assurance under observed conditions, it also did not cause pollen discounting, so the transmission advantage of selfing should promote its spread. Given observed numbers of S‐alleles and selfing rates, self‐compatibility should spread even under conditions of exceedingly high initial inbreeding depression.     

Environmental conditions during early life determine the consequences of inbreeding in Agrostemma githago (Caryophyllaceae)

In an inbred population, selection may reduce the frequency of deleterious recessive alleles through a process known as purging. Empirical studies suggest, however, that the efficacy of purging in natural populations is highly variable. This variation may be due, in part, to variation in the expression of inbreeding depression available for selection to act on. This experiment investigates the roles of life stage and early‐life environment in determining the expression of inbreeding depression in Agrostemma githago. Four population‐level crosses (‘self’, ‘within’, ‘near’ and ‘far’) were conducted on 20 maternal plants from a focal population. Siblings were planted into one of three early environmental treatments with varying stress levels. Within the focal population, evidence for purging of deleterious recessive alleles, as well as for variation in the expression of inbreeding depression across the life cycle was examined. In addition, the effect of early environment on the expression of inbreeding depression and the interaction with cross‐type was measured. We find that deleterious recessive alleles have not been effectively purged from our focal population, the expression of inbreeding depression decreases over the course of the life cycle, and a stressful early environment reduces the variance in inbreeding depression expressed later in life, but does not consistently influence the relative fitness of inbred versus outcrossed individuals.     

THE OPPORTUNITY FOR BALANCING SELECTION IN EXPERIMENTAL POPULATIONS OF CAENORHABDITIS ELEGANS

The role of balancing selection in maintaining diversity during the evolution of sexual populations to novel environments is poorly understood. To address this issue, we studied the impact of two mating systems, androdioecy and dioecy, on genotype distributions during the experimental evolution of Caenorhabditis elegans. We analyzed the temporal trajectories of 334 single nucleotide polymorphisms, covering 1/3 of the genome, and found extensive allele frequency changes and little loss of heterozygosities after 100 generations. As modeled with numerical simulations, SNP differentiation was consistent with genetic drift and average fitness effects of 2%, assuming that selection acted independently at each locus. Remarkably, inbreeding by self‐fertilization was of little consequence to SNP differentiation. Modeling selection on deleterious recessive alleles suggests that the initial evolutionary dynamics can be explained by associative overdominance, but not the later stages because much lower heterozygosities would be maintained during experimental evolution. By contrast, models with selection on true overdominant loci can explain the heterozygote excess observed at all periods, particularly when negative epistasis or independent fitness effects were considered. Overall, these findings indicate that selection at single loci, including purging of recessive alleles, underlies most of the genetic differentiation accomplished during the experiment. Nonetheless, they also imply that maintenance of genetic diversity may in large part be due to balancing selection at multiple loci.     

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.     

Perspective: purging the genetic load: a review of the experimental evidence

Inbreeding depression, the reduction in fitness that accompanies inbreeding, is one of the most important topics of research in evolutionary and conservation genetics. In the recent literature, much attention has been paid to the possibility of purging the genetic load. If inbreeding depression is due to deleterious alleles, whose effect on fitness are negative when in a homozygous state, then successive generations of inbreeding may result in a rebound in fitness due to the selective decrease in frequency of deleterious alleles. Here we examine the experimental evidence for purging of the genetic load by collating empirical tests of rebounds in fitness-related traits with inbreeding in animals and plants. We gathered data from 28 studies including five mammal, three insect, one mollusc, and 13 plant species. We tested for purging by examining three measures of fitness-component variation with serial generations of inbreeding: (1) changes in inbreeding depression, (2) changes in fitness components of inbred lines relative to the original outbred line, and (3) purged population (outcrossed inbred lines) trait means as a function of ancestral outbred trait means. Frequent and substantial purging was found using all three measures, but was particularly pronounced when tracking changes in inbreeding depression. Despite this, we found little correspondence between the three measures of purging within individual studies, indicating that the manner in which a researcher chooses to estimate purging will affect interpretation of the results obtained. The discrepancy suggests an alternative hypothesis: rebounds in fitness with inbreeding may have resulted from adaptation to laboratory conditions and not to purging when using outcrossed inbred lines. However, the pronounced reduction in inbreeding depression for a number of studies provides evidence for purging, as the measure is likely less affected by selection for laboratory conditions. Unlike other taxon-specific reviews on this topic, our results provide support for the purging hypothesis, but firm predictions about the situations in which purging is likely or the magnitude of fitness rebound possible when populations are inbred remain difficult. Further research is required to resolve the discrepancy between the results obtained using different experimental approaches.     

Long-term exhaustion of the inbreeding load in Drosophila melanogaster

Inbreeding depression, the decline in fitness of inbred individuals, is a ubiquitous phenomenon of great relevance in evolutionary biology and in the fields of animal and plant breeding and conservation. Inbreeding depression is due to the expression of recessive deleterious alleles that are concealed in heterozygous state in noninbred individuals, the so-called inbreeding load. Genetic purging reduces inbreeding depression by removing these alleles when expressed in homozygosis due to inbreeding. It is generally thought that fast inbreeding (such as that generated by full-sib mating lines) removes only highly deleterious recessive alleles, while slow inbreeding can also remove mildly deleterious ones. However, a question remains regarding which proportion of the inbreeding load can be removed by purging under slow inbreeding in moderately large populations. We report results of two long-term slow inbreeding Drosophila experiments (125–234 generations), each using a large population and a number of derived lines with effective sizes about 1000 and 50, respectively. The inbreeding load was virtually exhausted after more than one hundred generations in large populations and between a few tens and over one hundred generations in the lines. This result is not expected from genetic drift alone, and is in agreement with the theoretical purging predictions. Computer simulations suggest that these results are consistent with a model of relatively few deleterious mutations of large homozygous effects and partially recessive gene action.Subject terms: Quantitative trait, Inbreeding     

Rapid loss of self‐incompatibility in experimental populations of the perennial outcrossing plant Linaria cavanillesii

Transitions from self‐incompatibility to self‐compatibility in angiosperms may be frequently driven by selection for reproductive assurance when mates or pollinators are rare, and are often succeeded by loss of inbreeding depression by purging. Here, we use experimental evolution to investigate the spread of self‐compatibility from one such population of the perennial plant Linaria cavanillesii into self‐incompatible (SI) populations that still have high inbreeding depression. We introduced self‐compatible (SC) individuals at different frequencies into replicate experimental populations of L. cavanillesii that varied in access to pollinators. Our experiment revealed a rapid shift to self‐compatibility in all replicates, driven by both greater seed set and greater outcross siring success of SC individuals. We discuss our results in the light of computer simulations that confirm the tendency of self‐compatibility to spread into SI populations under the observed conditions. Our study illustrates the ease with which self‐compatibility can spread among populations, a requisite for species‐wide transitions from self‐incompatibility to self‐compatibility.     

The divergence history of the perennial plant Linaria cavanillesii confirms a recent loss of self‐incompatibility

Many angiosperms prevent inbreeding through a self‐incompatibility (SI) system, but the loss of SI has been frequent in their evolutionary history. The loss of SI may often lead to an increase in the selfing rate, with the purging of inbreeding depression and the ultimate evolution of a selfing syndrome, where plants have smaller flowers with reduced pollen and nectar production. In this study, we used approximate Bayesian computation (ABC) to estimate the timing of divergence between populations of the plant Linaria cavanillesii that differ in SI status and in which SI is associated with low inbreeding depression but not with a transition to full selfing or a selfing syndrome. Our analysis suggests that the mixed‐mating self‐compatible (SC) population may have begun to diverge from the SI populations around 2810 generation ago, a period perhaps too short for the evolution of a selfing syndrome. We conjecture that the SC population of L. cavanillesii is at an intermediate stage of transition between outcrossing and selfing.     

Costs of selfing prevent the spread of a self‐compatibility mutation that causes reproductive assurance

In flowering plants, shifts from outcrossing to partial or complete self‐fertilization have occurred independently thousands of times, yet the underlying adaptive processes are difficult to discern. Selfing's ability to provide reproductive assurance when pollination is uncertain is an oft‐cited ecological explanation for its evolution, but this benefit may be outweighed by costs diminishing its selective advantage over outcrossing. We directly studied the fitness effects of a self‐compatibility mutation that was backcrossed into a self‐incompatible (SI) population of Leavenworthia alabamica, illuminating the direction and magnitude of selection on the mating‐system modifier. In array experiments conducted in two years, self‐compatible (SC) plants produced 17–26% more seed, but this advantage was counteracted by extensive seed discounting—the replacement of high‐quality outcrossed seeds by selfed seeds. Using a simple model and simulations, we demonstrate that SC mutations with these attributes rarely spread to high frequency in natural populations, unless inbreeding depression falls below a threshold value (0.57 ≤ δ_threshold ≤ 0.70) in SI populations. A combination of heavy seed discounting and inbreeding depression likely explains why outcrossing adaptations such as self‐incompatibility are maintained generally, despite persistent input of selfing mutations, and frequent limits on outcross seed production in nature.     

LIFETIME INBREEDING DEPRESSION,PURGING, AND MATING SYSTEM EVOLUTION IN A SIMULTANEOUS HERMAPHRODITE TAPEWORM

Classical theory on mating system evolution suggests that simultaneous hermaphrodites should either outcross if they have high inbreeding depression (ID) or self‐fertilize if they have low ID. However, a mixture of selfing and outcrossing persists in many species. Previous studies with the tapeworm Schistocephalus solidus have found worms to self‐fertilize some of their eggs despite ID. The probability for selfing to spread depends on the relative fitness of selfers, as well as the genetic basis for ID and whether it can be effectively purged. We bred S. solidus through two consecutive generations of selfing and recorded several fitness correlates over the whole life cycle. After one round of selfing, ID was pronounced, particularly in early‐life traits, and the conservatively estimated lifetime fitness of selfed progeny was only 9% that of the outcrossed controls. After a second generation of selfing, ID remained high but was significantly reduced in several traits, which is consistent with the purging of deleterious recessive alleles (the estimated load of lethal equivalents dropped by 48%). Severe ID, even if it can be rapidly purged, likely prevents transitions toward pure selfing in this parasite, although we also cannot exclude the possibility that low‐level selfing has undetected benefits.     

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.     

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.