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.     

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.     

Inbreeding depression in small populations of self-incompatible plants.

Self-incompatibility (SI) is a widespread mechanism that prevents inbreeding in flowering plants. In many species, SI is controlled by a single locus (the S locus) where numerous alleles are maintained by negative frequency-dependent selection. Inbreeding depression, the decline in fitness of selfed individuals compared to outcrossed ones, is an essential factor in the evolution of SI systems. Conversely, breeding systems influence levels of inbreeding depression. Little is known about the joint effect of SI and drift on inbreeding depression. Here we studied, using a two-locus model, the effect of SI (frequency-dependent selection) on a locus subject to recurrent deleterious mutations causing inbreeding depression. Simulations were performed to assess the effect of population size and linkage between the two loci on the level of inbreeding depression and genetic load. We show that the sheltering of deleterious alleles linked to the S locus strengthens inbreeding depression in small populations. We discuss the implications of our results for the evolution of SI systems.     

Effect of selection against deleterious mutations on the decline in heterozygosity at neutral loci in closely inbreeding populations.

Transition matrices for selfing and full-sib mating were derived to investigate the effect of selection against deleterious mutations on the process of inbreeding at a linked neutral locus. Selection was allowed to act within lines only (selection type I) or equally within and between lines (type II). For selfing lines under selection type I, inbreeding is always retarded, the retardation being determined by the recombination fraction between the neutral and selected loci and the inbreeding depression from the selected locus, irrespective of the selection coefficient (s) and dominance coefficient (h) of the mutant allele. For selfing under selection type II or full-sib mating under both selection types, inbreeding is delayed by weak selection (small s and sh), due to the associative overdominance created at the neutral locus, and accelerated by strong selection, due to the elevated differential contributions between alternative alleles at the neutral locus within individuals and between lines (for selection type II). For multiple fitness loci under selection, stochastic simulations were run for populations with selfing, full-sib mating, and random mating, using empirical estimates of mutation parameters and inbreeding load in Drosophila. The simulations results are in general compatible with empirical observations.     

The inbreeding depression cost of selfing: Importance of flower size and population size in Collinsia parviflora (Veronicaceae)

Inbreeding depression should evolve with selfing rate when frequent inbreeding results in exposure of and selection against deleterious alleles. The selfing rate may be modified by plant traits such as flower size, or by population characteristics such as census size that can affect the probability of biparental inbreeding. Here we quantify inbreeding depression (δ) among different population sizes of Collinsia parviflora, a wildflower with interpopulation variation in flower size, by comparing fitness components and multiplicative fitness of experimentally produced selfed and outcrossed offspring. Selfed offspring had reduced multiplicative fitness compared to outcrossed offspring, but inbreeding depression was low in all combinations of population size and flower size (δ ≤ 0.05) except in large populations of large-flowered plants (δ = 0.45). The decrement to multiplicative fitness with inbreeding was not affected by population size nested within flower size, but differed between small- and large-flowered plants: small-flowered populations had lower overall inbreeding depression (δ = 0.04) compared to large-flowered populations (δ = 0.25). The difference in load with flower size suggests that either selection has removed deleterious recessive alleles or these alleles have become fixed in small-flowered, potentially more selfing populations, but that purging has not occurred to the same extent in presumably outcrossing large-flowered populations.     

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

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

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

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

The advantages of segregation and the evolution of sex

In diploids, sexual reproduction promotes both the segregation of alleles at the same locus and the recombination of alleles at different loci. This article is the first to investigate the possibility that sex might have evolved and been maintained to promote segregation, using a model that incorporates both a general selection regime and modifier alleles that alter an individual's allocation to sexual vs. asexual reproduction. The fate of different modifier alleles was found to depend strongly on the strength of selection at fitness loci and on the presence of inbreeding among individuals undergoing sexual reproduction. When selection is weak and mating occurs randomly among sexually produced gametes, reductions in the occurrence of sex are favored, but the genome-wide strength of selection is extremely small. In contrast, when selection is weak and some inbreeding occurs among gametes, increased allocation to sexual reproduction is expected as long as deleterious mutations are partially recessive and/or beneficial mutations are partially dominant. Under strong selection, the conditions under which increased allocation to sex evolves are reversed. Because deleterious mutations are typically considered to be partially recessive and weakly selected and because most populations exhibit some degree of inbreeding, this model predicts that higher frequencies of sex would evolve and be maintained as a consequence of the effects of segregation. Even with low levels of inbreeding, selection is stronger on a modifier that promotes segregation than on a modifier that promotes recombination, suggesting that the benefits of segregation are more likely than the benefits of recombination to have driven the evolution of sexual reproduction in diploids.     

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

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

Simulation of the effect of population size on the evolution of the recombination fraction

A study, by means of computer simulation, has been performed on the evolution of recombination rate modifier genes in a system with three diallelic loci (A, B and C). The locus C, selectively neutral, is responsible for the modification of the recombination fraction between the major loci (A and B) which are subjected to selection. Two models have been analysed, the modifier allele being recessive in one of them, and codominant in the other, with infinite and finite populations. Distinct initial genic frequencies of the major loci and different selection coefficients have been utilised. We have found that the frequency of the allele which favours recombination increases in finite populations, and decreases slightly in infinite populations. These results are consistent with previous theory; presumably, selection favours alleles reducing recombination between epistatically interacting loci in a infinite population, since this reduces the breakup of advantageous combinations of alleles. However, in finite populations, selection favours the breakup of the random linkage disequilibria which are produced by random drift.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

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.     

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.     

Segregation and the evolution of sex under overdominant selection

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

INBREEDING DEPRESSION IN A SELF-COMPATIBLE,ANDRODIOECIOUS CRUSTACEAN,EULIMNADIA TEXANA

The observation that offspring produced by the mating of close relatives are often less fit than those produced by matings between unrelated individuals (i.e., inbreeding depression) has commonly been explained in terms of the increased probability of expressing deleterious recessive alleles among inbred offspring (the partial dominance model). This model predicts that inbreeding depression should be limited in regularly inbreeding populations because the deleterious alleles that cause inbreeding depression (i.e., the genetic load) should be purged by regularly exposing these alleles to natural selection. We indirectly test the partial dominance model using four highly inbred populations of an androdioecious crustacean, the clam shrimp Eulimnadia texana. These shrimp are comprised of males and hermaphrodites, the latter capable of either self-fertilizing or mating with a male (i.e., outcrossing between hermaphrodites is impossible). Hermaphrodites are further subdivided into monogenics (produced via self-fertilization) and amphigenics (produced via self-fertilization or outcrossing). Electrophoretic evidence suggests significant differences in heterozygosity among populations, but that selfing rates were not statistically different (average s = 0.67). Additional electrophoretic analyses reveal that three previously described sex-linked loci (Fum, Idh-1, and Idh-2) are all tightly linked to each other, with crossing over on the order of 1% per generation. Although selfing rates are clearly high, we present evidence that early inbreeding depression (hatching rates, juvenile survival, and age at sexual maturity) exists in all four populations. For all of these factors, inbreeding depression was inferred by the positive correlation of multilocus heterozygosity and fitness. Cumulative inbreeding depression (8) is between 0.41 and 0.47 across all populations, which appears to be too low to limit the effects of purging via identity disequilibrium. Instead, we suggest that the maintenance of inbreeding depression in these populations is due to the observed linkage group, which we suggest contains a large number of genes including many related to fitness. Segregation of such a large linkage group would explain our observations of the predominance of amphigenic hermaphrodites in our field samples and of survival differences between monogenics and amphigenics within selfed clutches. We propose that a modified form of the overdominance model for inbreeding depression operating at the level of linkage groups maintains the observed levels of inbreeding depression in these populations even in the face of high rates of selfing.     

Anther-stigma separation is associated with inbreeding depression in Datura stramonium,a predominantly self-fertilizing annual

Abstract.— Genetically based variation in outcrossing rate generates lineages within populations that differ in their history of inbreeding. According to some models, mating-system modifiers in such populations will demonstrate both linkage and identity disequilibrium with fitness loci, resulting in lineage-specific inbreeding depression. Other models assert that differences among families in levels of inbreeding depression are mainly attributable to random accumulation of genetic load, unrelated to variation at mating-system loci. We measured female reproductive success of selfed and outcrossed progeny from naturally occurring lineages of Datura stramonium , a predominantly self-fertilizing annual weed that has heritable variation in stigma-anther separation, a trait that influences selfing rates. Progeny from inbred lineages (as identified by high degree of anther-stigma overlap) showed equal levels of seed production, regardless of cross type. Progeny from mixed lineages (as identified by relatively high separation between anthers and stigma) showed moderate levels of inbreeding depression. We found a significant correlation between anther-stigma separation and relative fitness of selfed and outcrossed progeny, suggesting that family-level inbreeding depression may be related to differences among lineages in inbreeding history in this population. Negative inbreeding depression in putatively inbred lineages may be due in part to additive effects or to epistatic interactions among loci.     

The evolution of intratetrad mating rates

Intratetrad mating, the fusion of gametes formed in a single meiosis, has unusual consequences for genetic diversity, especially in genome regions linked to mating type loci. Here we investigate the fate of modifier alleles that alter the rate of intratetrad mating, under models of heterozygote advantage and of genetic load resulting from recurrent mutation. In both cases, intratetrad mating is favored if the recombination rate between the selected locus and mating type is less than the frequency of lethal recessive alleles at that locus in the population. Positive feedback often accelerates the invasion of modifiers to the intratetrad mating rate. Recombination rate and intratetrad mating rate exert indirect selection on one another, resulting in a cascading decline in outcrossing, even in the absence of any cost of sex. However, under recurrent mutation, alleles for obligate intratetrad mating invade only very slowly, perhaps explaining why outcrossing can persist at low frequencies in a largely intratetrad mating population.     

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

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

Heterosis and inbreeding depression in bottlenecked populations: a test in the hermaphroditic freshwater snail Lymnaea stagnalis

Small population size is expected to induce heterosis, due to the random fixation and accumulation of mildly deleterious mutations, whereas within‐population inbreeding depression should decrease due to increased homozygosity. Population bottlenecks, although less effective, may have similar consequences. We tested this hypothesis in the self‐fertile freshwater snail Lymnaea stagnalis, by subjecting experimental populations to a single bottleneck of varied magnitude. Although patterns were not strong, heterosis was significant in the most severely bottlenecked populations, under stressful conditions. This was mainly due to hatching rate, suggesting that early acting and highly deleterious alleles were involved. Although L. stagnalis is a preferential outcrosser, inbreeding depression was very low and showed no clear relationship with bottleneck size. In the less reduced populations, inbreeding depression for hatching success increased under high inbreeding. This may be consistent with the occurence of synergistic epistasis between fitness loci, which may contribute to favour outcrossing in L. stagnalis.