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.     

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.     

The evolution of self-fertilization and inbreeding depression under pollen discounting and pollen limitation

We model the evolution of plant mating systems under the joint effects of pollen discounting and pollen limitation, using a dynamic model of inbreeding depression, allowing for partial purging of recessive lethal mutations by selfing. Stable mixed mating systems occur for a wide range of parameter values with pollen discounting alone. However, when typical levels of pollen limitation are combined with pollen discounting, stable selfing rates are always high but less than 1 (0.9相似文献   

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.     

Mitosis, stature and evolution of plant mating systems: low-Phi and high-Phi plants

There is a long-recognized association in plants between small stature and selfing, and large stature and outcrossing. Inbreeding depression is central to several hypotheses for this association, but differences in the evolutionary dynamics of inbreeding depression associated with differences in stature are rarely considered. Here, we propose and test the Phi model of plant mating system evolution, which assumes that the per-generation mutation rate of a plant is a function of the number of mitoses (Phi) that occur from zygote to gamete, and predicts fundamental differences between low-Phi (small-statured) and high-Phi (large-statured) plants in the outcomes of the joint evolution of outcrossing rate and inbreeding depression. Using a large dataset of published population genetic studies of angiosperms and conifers, we compute fitted values of inbreeding depression and deleterious mutation rates for small- and large-statured plants. Consistent with our Phi model, we find that populations of small-statured plants exhibit a range of mating systems, significantly lower mutation rates, and intermediate inbreeding depression, while large-statured plants exhibit very high mutation rates and the maximum inbreeding depression of unity. These results indicate that (i) inbred progeny typically observed in large-statured plant populations are completely lost prior to maturity in nearly all populations; (ii) evolutionary shifts from outcrossing to selfing are generally not possible in large-statured species, rather, large-statured species are more likely to evolve mating systems that avoid selfing such as self-incompatibility and dioecy; (iii) destabilization of the mating system-high selfing rate with high-inbreeding depression-might be a common occurrence in large-statured species; and (iv) large-statured species in fragmented populations might be at higher risk of extinction than previously thought. Our results help to unify and simplify a large and diverse field of research, and serve to emphasize the importance that developmental and genetic constraints play in the evolution of plant mating systems.     

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.     

Functional pleiotropy and mating system evolution in plants: frequency-independent mating

Mutations that alter the morphology of floral displays (e.g., flower size) or plant development can change multiple functions simultaneously, such as pollen export and selfing rate. Given the effect of these various traits on fitness, pleiotropy may alter the evolution of both mating systems and floral displays, two characters with high diversity among angiosperms. The influence of viability selection on mating system evolution has not been studied theoretically. We model plant mating system evolution when a single locus simultaneously affects the selfing rate, pollen export, and viability. We assume frequency-independent mating, so our model characterizes prior selfing. Pleiotropy between increased viability and selfing rate reduces opportunities for the evolution of pure outcrossing, can favor complete selfing despite high inbreeding depression, and notably, can cause the evolution of mixed mating despite very high inbreeding depression. These results highlight the importance of pleiotropy for mating system evolution and suggest that selection by nonpollinating agents may help explain mixed mating, particularly in species with very high inbreeding depression.     

Consequences of life history for inbreeding depression and mating system evolution in plants

Many plants are perennial, but most studies of inbreeding depression and mating system evolution focus on annuals. This paper extends a population genetic model of inbreeding depression due to recessive deleterious mutations to perennials. The model incorporates life history and mating system variation, and multiplicative selection across many genetic loci. In the absence of substantial mitotic mutation, perennials have higher mean fitness and lower, or even negative, inbreeding depression than annuals with the same mating system. As in annuals, self fertilization exposes deleterious recessive mutations to selection, increasing mean fitness and decreasing inbreeding depression. Including mitotic mutation decreases mean fitness while increasing inbreeding depression. Perenniality introduces a kind of selective sieve, such that strongly recessive mutations contribute disproportionately to mean fitness and inbreeding depression. In the presence of high mitotic mutation, this selective sieve may provide a mechanistic basis for high inbreeding depression observed in some long lived perennials. Without substantial mitotic mutation, it is difficult to reconcile genetically based models of inbreeding depression with the empirical generalization that perennials outcross while related annuals self fertilize.     

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

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

Mating 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.     

Pollen transfer dynamics and the evolution of gametophytic self-incompatibility

Recent studies of mating system evolution have attempted to include aspects of pollination biology in analysis of both theoretical models and experimental systems. In light of this growing trend, we propose a simple population genetic model for the evolution of gametophytic self-incompatibility, incorporating parameters for pollen discounting and pollen export/capture. In this model, we consider several cases that span the spectrum for dominance of the mutant self-incompatibility allele and for the degree of incompatibility conferred by the allele. We confirm earlier results that inbreeding depression is required for successful invasion of the self-incompatibility allele and we demonstrate that, unless pollen discounting is very low, the level of inbreeding depression must be very high for an allele conferring self-incompatibility to become established. Finally, we show that the dominance of the mutant allele has a greater impact on the fate of a newly arisen self-incompatibility allele than the strength of the incompatibility conferred by the allele. In particular, the more recessive the self-incompatibility expression in heterozygote stigmas and the weaker the response induced, the easier it is for a self-incompatibility allele to invade.     

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.     

Effects of outcrossing in fragmented populations of the primarily selfing forest herb <Emphasis Type="Italic">Geum urbanum</Emphasis>

In fragmented landscapes, small populations may be subjected to inbreeding or genetic drift. Gene flow is expected to alleviate the burden of deleterious mutations in such populations. The beneficial effects of outcrossing may, however, depend on life history characteristics such as the species’ breeding system. Frequent selfing is expected to purge (sub)lethal alleles and mitigate inbreeding depression, at least if the load of mildly deleterious mutations has not accumulated through genetic drift in populations with a small effective size. Gene-inflow from distant source populations can cause outbreeding depression due to genomic incompatibilities. We tested these predictions using highly fragmented populations of the self-compatible forest herb Geum urbanum. Assessment of mating system parameters using microsatellite markers inferred high selfing rates (92.5%), confirming the predominantly self-fertilizing character of the study species. We conducted experimental pollinations with self and outcross pollen collected from populations at different distances from the target populations. There were no significant signs of inbreeding depression, even in very small target populations. Except for a minor negative effect on the germination rate for the long-distance crosses, we found no effects of outbreeding on fitness estimates.     

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.     

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

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

Loss of gametophytic self-incompatibility with evolution of inbreeding depression

Gametophytic self-incompatibility (SI) in plants is a widespread mechanism preventing self-fertilization and the ensuing inbreeding depression, but it often evolves to self-compatibility. We analyze genetic mechanisms for the breakdown of gametophytic SI, incorporating a dynamic model for the evolution of inbreeding depression allowing for partial purging of nearly recessive lethal mutations by selfing, and accounting for pollen limitation and sheltered load linked to the S-locus. We consider two mechanisms for the breakdown of gametophytic SI: a nonfunctional S-allele and an unlinked modifier locus that inactivates the S-locus. We show that, under a wide range of conditions, self-compatible alleles can invade a self-incompatible population. Conditions for invasion are always less stringent for a nonfunctional S-allele than for a modifier locus. The spread of self-compatible genotypes is favored by extremely high or low selfing rates, a small number of S-alleles, and pollen limitation. Observed parameter values suggest that the maintenance of gametophytic SI is caused by a combination of high inbreeding depression in self-incompatible populations coupled with intermediate selfing rates of the self-compatible genotypes and sheltered load linked to the S-locus.     

Can females benefit from selfing avoidance? Genetic associations and the evolution of plant gender

Evolutionary stability of dioecy and nuclear gynodioecy in higher plants requires that females produce over twice as many successful seeds as hermaphrodites. This fitness differential is widely thought to derive primarily from the advantages of outcrossing caused by high selfing rates and inbreeding depression in the hermaphrodite. This study hypothesized that (i) extraordinarily high deleterious mutation rates are necessary to double female seed success due to outcrossing, and (ii) the large difference in outcrossing rates between sex morphs causes differential purging of these mutations, resulting in additional genetic selection on male sterility. Using genetically explicit models, I showed that the phenotypic outcrossing advantage requires at least one new highly recessive deleterious mutation per genome per generation, regardless of selection coefficient. However, under this mutational regime, differential purging created strong genetic selection against recessive male sterility that overwhelmed the phenotypic selection in favour of outcrossing. In very small populations and for dominant male sterility, this genetic selection was weaker or absent. This first genetically explicit study of the outcrossing advantage of unisexual females may shed new light on both the genetic and selective conditions for the evolution of gynodioecy and dioecy.     

GENETIC ARCHITECTURE OF INBREEDING DEPRESSION AND THE MAINTENANCE OF GAMETOPHYTIC SELF‐INCOMPATIBILITY

Gametophytic self‐incompatibility (GSI) is a widespread genetic system, which enables hermaphroditic plants to avoid self‐fertilization and mating with close relatives. Inbreeding depression is thought to be the major force maintaining SI; however, inbreeding depression is a dynamical variable that depends in particular on the mating system. In this article we use multilocus, individual‐based simulations to examine the coevolution of SI and inbreeding depression within finite populations. We focus on the conditions for the maintenance of SI when self‐compatible (SC) mutants are introduced in the population by recurrent mutation, and compare simulation results with predictions from an analytical model treating inbreeding depression as a fixed parameter (thereby neglecting effects of purging within the SC subpopulation). In agreement with previous models, we observe that the maintenance of SI is associated with high inbreeding depression and is facilitated by high rates of self‐pollination. Purging of deleterious mutations by SC mutants has little effect on the spread of those mutants as long as most deleterious alleles have weak fitness effects: in this case, the genetic architecture of inbreeding depression has little effect on the maintenance of SI. By contrast, purging may greatly enhance the spread of SC mutants when deleterious alleles have strong fitness effects.     

On the evolution of genetic incompatibility systems. IV. Modification of response to an existing antigen polymorphism under partial selfing

A 2-locus model of the evolution of self-incompatibility in a population practicing partial selfing is presented. An allele is introduced at a modifier locus which influences the strength of the rejection reaction expressed by the style in response to antigens recognized in pollen. Two causes of inbreeding depression are investigated. First, offspring viability depends solely on the source (self or non-self) of the fertilizing pollen. Second, offspring viability declines with the expression of recessive deleterious alleles, segregating at a third (disease) locus, which exhibit an imperfect association with antigen alleles. Evolutionary changes occurring at the disease locus are not considered in this study. The condition under which a modifier allele that intensifies the incompatibility reaction increases when rare depends upon the number of antigens, the frequency of recessive deleterious alleles at the disease locus, and the level of association between the antigen locus and the disease locus. It is the improvement of viability among offspring derived by outcrossing, rather than the prevention of self-fertilization, that may represent the primary evolutionary function of genetic incompatibility systems.