RESPONSE TO SELECTION IN PARTIALLY SELF-FERTILIZING POPULATIONS. I. SELECTION ON A SINGLE TRAIT

Self-fertilization is a common form of reproduction in plants and it has important implications for quantitative trait evolution. Here, I present a model of selection on quantitative traits that can accommodate any level of self-fertilization. The “structured linear model” (SLM) predicts the evolution of the mean phenotype as a function of three distinct quantities: the mean additive genetic value, the directional dominance, and the mean inbreeding coefficient. Stochastic simulations of truncation selection demonstrate the accuracy of the SLM in predicting changes in the mean and variance of a quantitative trait over the full range of selfing rates. They also illustrate how complex interactions between selection and mating system determine the population distribution of inbreeding coefficients and also the amount of linkage disequilibrium. Changes in the genetic variance due to linkage disequilibria, which are commonly referred to as the “Bulmer effect,” are greatly magnified by selfing. This complicates the relationship between selfing rate and response to selection. Like the random mating theory, the parameters of the SLM can be estimated from phenotypic data.     

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.     

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.     

No correlation between inbreeding depression and delayed selfing in the freshwater snail Physa acuta

Inbreeding depression, one of the main factors driving mating system evolution, can itself evolve as a function of the mating system (the genetic purging hypothesis). Classical models of coevolution between mating system and inbreeding depression predict negative associations between inbreeding depression and selfing rate, but more recent approaches suggest that negative correlations should usually be too weak or transient to be detected within populations. Empirical results remain unclear and restricted to plants. Here, we evaluate, for the first time, the within-population genetic correlation between inbreeding depression and a trait that controls the amount of self-fertilization (the waiting time) in a self-fertile hermaphroditic animal, the freshwater snail Physa acuta. Using a large quantitative-genetic design (36 grand-families and 348 families), we observe abundant within-population family-level genetic variation for both inbreeding depression (estimated for survival, fecundity, and size) and the degree of behavioral selfing avoidance. However, we detected no correlation between waiting time and inbreeding depression across families. In agreement with recent models, this result shows that mutational variance rather than differential purging accounts for most of the genetic variance in inbreeding depression within a population.     

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.     

Effects of population size and metapopulation dynamics on a mating-system polymorphism

The evolutionary dynamics of neutral alleles under the Wright-Fisher model are well understood. Similarly, the effect of population turnover on neutral genetic diversity in a metapopulation has attracted recent attention in theoretical studies. Here we present the results of computer simulations of a simple model that considers the effects of finite population size and metapopulation dynamics on a mating-system polymorphism involving selfing and outcrossing morphs. The details of the model are based on empirical data from dimorphic populations of the annual plant Eichhornia paniculata, but the results are also of relevance to species with density-dependent selfing rates in general. In our model, the prior selfing rate is determined by two alleles segregating at a single diploid locus. After prior selfing occurs, some remaining ovules are selfed through competing self-fertilisation in finite populations as a result of random mating among gametes. Fitness differences between the mating-system morphs were determined by inbreeding depression and pollen discounting in a context-dependent manner. Simulation results showed evidence of frequency dependence in the action of pollen discounting and inbreeding depression in finite populations. In particular, as a result of selfing in outcrossers through random mating among gametes, selfers experienced a "fixation bias" through drift, even when the mating-system locus was selectively neutral. In a metapopulation, high colony turnover generally favoured the fixation of the outcrossing morph, because inbreeding depression reduced opportunities for colony establishment by selfers through seed dispersal. Our results thus demonstrate that population size and metapopulation processes can lead to evolutionary dynamics involving pollen and seed dispersal that are not predicted for large populations with stable demography.     

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.     

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.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

Pollination ecology and inbreeding depression control individual flowering phenologies and mixed mating

We analyze evolution of individual flowering phenologies by combining an ecological model of pollinator behavior with a genetic model of inbreeding depression for plant viability. The flowering phenology of a plant genotype determines its expected daily floral display which, together with pollinator behavior, governs the population rate of geitonogamous selfing (fertilization among flowers on the same plant). Pollinators select plant phenologies in two ways: they are more likely to visit plants displaying more flowers per day, and they influence geitonogamous selfing and consequent inbreeding depression via their abundance, foraging behavior, and pollen carry‐over among flowers on a plant. Our model predicts two types of equilibria at stable intermediate selfing rates for a wide range of pollinator behaviors and pollen transfer parameters. Edge equilibria occur at maximal or minimal selfing rates and are constrained by pollinators. Internal equilibria occur between edge equilibria and are determined by a trade‐off between pollinator attraction to large floral displays and avoidance of inbreeding depression due to selfing. We conclude that unavoidable geitonogamous selfing generated by pollinator behavior can contribute to the common occurrence of stable mixed mating in plants.     

Effect of recurrent selfing on inbreeding depression and mating system evolution in an autopolyploid plant

Genome duplication resulting in polyploidy can have significant consequences for the evolution of mating systems. Most theory predicts that self‐fertilization will be selectively favored in polyploids; however, many autopolyploids are outcrossing or mixed‐mating. Here, we examine the hypothesis that the evolution of selfing is restricted in autopolyploids because the genetic cost of selfing (i.e., inbreeding depression) increases monotonically with successive generations of inbreeding. Using the herbaceous, autotetraploid plant Chamerion angustifolium, we generated populations with different inbreeding coefficients (F= 0, 0.17 and 0.36) through three consecutive generations of selfing and compared their magnitudes of inbreeding depression in a common environment. Mating system estimates for four natural populations confirmed that tetraploid selfing rates (s_m= 0.25, SE = 0.02) are similar to those of diploids (s_m= 0.12, SE = 0.12; F_1,2= 1.34, P= 0.37) indicating that both cytotypes are predominantly outcrossing. Compared to an outbred control line, mean inbreeding depression for seed production, survival, and height (vegetative and total) in the inbred line differed among generations (inbreeding coefficients). Across all stages, inbreeding depression (relative to control) was positively related to generation (inbreeding coefficient). Although the initial costs of inbreeding in extant and newly synthesized polyploids may be low compared to diploids, the monotonic increase in inbreeding depression with repeated inbreeding may limit the extent to which selfing variants are favored.     

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.     

An association between a floral trait and inbreeding depression

Abstract.— Inbreeding depression is a general phenomenon that is well documented in many plants and animals. Furthermore, it is generally considered to be the driving force behind mating-system evolution. Traditionally, the focus has been on the mean level of inbreeding depression in populations. However, more recently, the variation in inbreeding depression among individuals within populations has been shown to be influential in mating-system evolution. One set of theories predicts that genetic associations will develop between a mating-system locus and loci causing inbreeding depression, whereas another suggests either that no such association will occur or that it will be difficult to detect empirically. Here, we focus on variation in inbreeding depression among individuals and present empirical evidence of a genetic association between genes causing inbreeding depression and a floral trait influencing the mating system (i.e., selfing rate). We found a positive association between inbreeding depression and herkogamy (the degree to which the stigma and anthers are separated) in an annual plant, Gilia achilleifolia . These results are consistent with theory predicting that an individual's history of inbreeding will affect its level of inbreeding depression and highlight the potential importance of genetic associations between selfing-modifier traits and viability in mating-system evolution.     

Inbreeding depression and mixed mating in Leptosiphon jepsonii: a comparison of three populations

BACKGROUND AND AIMS: Inbreeding depression is thought to play a central role in the evolution and maintenance of cross-fertilization. Theory indicates that inbreeding depression can be purged with self-fertilization, resulting in positive feedback for the selection of selfing. Variation among populations of Leptosiphon jepsonii in the timing and rate of self-fertilization provides an opportunity to study the evolution of inbreeding depression and mating systems. In addition, the hypothesis that differences in inbreeding depression for male and female fitness can stabilize mixed mating in L. jepsonii is tested. METHODS: In a growth room experiment, inbreeding depression was measured in three populations with mean outcrossing rates ranging from 0.06 to 0.69. The performance of selfed and outcrossed progeny is compared at five life history stages. To distinguish between self-incompatibility and early inbreeding depression, aborted seeds and unfertilized ovules were counted in selfed and outcrossed fruits. In one population, pollen and ovule production was quantified to estimate inbreeding depression for male and female fitness. KEY RESULTS: Both prezygotic barriers and inbreeding depression limited self seed set in the most outcrossing population. Cumulative inbreeding depression ranged from 0.297 to 0.501, with the lowest value found in the most selfing population. Significant inbreeding depression for early life stages was found only in the more outcrossing populations. Inbreeding depression was not significant for pollen or ovule production. CONCLUSIONS: The results provide modest support for the hypothesized relationship between inbreeding depression and mating systems. The absence of early inbreeding depression in the more selfing populations is consistent with theory on purging. Differences in male and female expression of inbreeding depression do not appear to stabilize mixed mating in L. jepsonii. The current estimates of inbreeding depression for L. jepsonii differ from those of previous studies, underscoring the effects of environmental variation on its expression.     

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.     

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.     

Can varying inbreeding depression select for intermediary selfing rates?

We study the evolution of the self-fertilization of an annual hermaphroditic plant under varying inbreeding depression. While classical population genetic models treat inbreeding depression as a constant parameter, recent empirical research has shown that changing environmental conditions can make inbreeding depression vary. Here, we create a simple phenotypic model, assuming variable inbreeding depression. We investigate how different types of variability (spatial, temporal, and spatiotemporal variability) affect the evolution of selfing rates in three models. Two main results, which differ from the classical predictions, emerge from this study. First, we find that fluctuating environments, which influence the magnitude of inbreeding depression, are able to select for evolutionarily stable intermediary selfing rates. Second, we show that spatiotemporal variation of inbreeding depression can lead to the development and the maintenance of polymorphic selfing rates within a population.     

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.     

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.