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.     

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.     

The cost of fluctuating inbreeding depression

We present a phenotypic model for the evolution of self-fertilization in an infinite population of annual hermaphrodites for the case in which fitness and inbreeding depression vary among generations (e.g., due to fluctuations in the environment from year to year). Conditions for the evolution of selfing, mixed mating, and outcrossing are derived and are compared with results from numerical calculations that assume a normal distribution of inbreeding depression. In contrast to the situation in which inbreeding depression does not vary, when inbreeding depression fluctuates in a stochastic manner among generations with a mean less than 0.5, selfing is not necessarily selected. Thus, fluctuating inbreeding depression can be viewed as an additional cost of selfing that may stabilize mixed mating systems. These results emphasize the need to take into account fluctuating inbreeding depression in empirical studies aimed at understanding mating system evolution in annuals.     

Allee effect and self-fertilization in hermaphrodites: reproductive assurance in demographically stable populations

The fact that selfing increases seed set (reproductive assurance) has often been put forward as an important selective force for the evolution of selfing. However, the role of reproductive assurance in hermaphroditic populations is far from being clear because of a lack of theoretical work. Here, I propose a theoretical model that analyzes self-fertilization in the presence of reproductive assurance. Because reproductive assurance directly influences the per capita growth rate, I developed an explicit demographic model for partial selfers in the presence of reproductive assurance, specifically when outcrossing is limited by the possibility of pollen transfer (Allee effect). Mating system parameters are derived as a function of the underlying demographical parameters. The functional link between population demography and mating system parameters (reproductive assurance, selfing rate) can be characterized. The demographic model permits the analysis of the evolution of self-fertilization in stable populations when reproductive assurance occurs. The model reveals some counterintuitive results such as the fact that increasing the fraction of selfed ovules can, in certain circumstances, increase the fraction of outcrossed ovules. Moreover, I demonstrate that reproductive assurance per se cannot account for the evolution of stable mixed selfing rates. Also, the model reveals that the extinction of outcrossing populations depends on small changes in population density (ecological perturbations), while the transition from outcrossing to selfing can, in certain cases, lead the population to extinction (evolutionary suicide). More generally, this paper highlights the fact that self-fertilization affects both the dynamics of individuals and the dynamics of selfing genes in hermaphroditic populations.     

INBREEDING DEPRESSION UNDER JOINT SELFING,OUTCROSSING, AND ASEXUALITY

Partial asexual reproduction was introduced into a model of inbreeding depression due to nearly recessive lethal mutations in a partially selfing population. The frequencies of asexuality, selfing, and outcrossing were either constant or occurred in cycles of a single sexual generation followed by one or more asexual generations. We found that increasing the degree of asexuality generally increases the inbreeding depression maintained in an equilibrium population with a given selfing rate. This is due to the increase in the number of mutations relative to sexual generations during which selfing-induced purging of mutations may take place. For very high genomic mutation rates, sufficient to produce a threshold rate of self-fertilization for purging recessive lethal mutations, asexuality can have the opposite effect, decreasing equilibrium inbreeding depression, because of an increase in the efficiency of selection against mutations in heterozygotes with asexuality.     

Inbreeding depression due to overdominance in partially self-fertilizing plant populations

The effect of the rate of partial self-fertilization and viability selection on the magnitude of inbreeding depression was investigated for the overdominance genetic model. The influence of these factors was determined for populations with equilibrium genotypic frequencies. Inbreeding depression was measured as the normalized disadvantage in mean viability of selfed progeny as compared to outcrossed progeny. When caused by symmetric homozygous disadvantage at a single locus it is shown always to be less than one-third. Moreover, for fixed rates of self-fertilization, its maximum value is found at intermediate levels of homozygous disadvantage. As the rate of self-fertilization increases, inbreeding depression increases and the homozygote viability that results in maximum depression tends toward one-half the heterozygote viability. Symmetric selection against homozygotes at multiple loci can lead to substantially higher values than selection at a single-locus. As the number of independent loci involved increases, inbreeding depression can reach high levels even though the selfing rate is low. Viability distributions for progenies produced from both random mating and self-fertilization were derived for the case of symmetric selection at independently assorting multiple loci. Distributions of viabilities in progenies resulting from mixtures of selfing and outcrossing were shown to be bimodal when inbreeding depression is high.     

The evolution of self-fertilization in density-regulated populations

The evolution of selfing in hermaphrodites has been studied to reveal the demographic conditions that lead to intermediate selfing rates. Using a demographic model based on Ricker-type density regulation, we assume first that, independent of population density, inbred individuals survive less well than outbred individuals and second, that inbred and outbred individuals differ in their competitive abilities in density-regulated populations. The evolution of selfing, driven by inbreeding depression and the cost of outcrossing, is then analysed for three fundamentally different demographic scenarios: stable population densities, deterministically varying population densities (resulting from cyclical or chaotic population dynamics) and stochastic fluctuations of carrying capacities (resulting from environmental noise). We show that even under stable demographic conditions evolutionary outcomes are not confined to either complete selfing or full outcrossing. Instead, intermediate selfing rates arise under a wide range of conditions, depending on the nature of competitive interactions between inbred and outbred individuals. We also explore the evolution of selfing under deterministic and stochastic density fluctuations to demonstrate that such environmental conditions can evolutionarily stabilize intermediate selfing rates. This is the first study, to our knowledge, to consider in detail the effect of density regulation on the evolution of selfing rates.     

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.     

How does pollination mutualism affect the evolution of prior self‐fertilization? A model

The mode of pollination is often neglected regarding the evolution of selfing. Yet the distribution of mating systems seems to depend on the mode of pollination, and pollinators are likely to interfere with selfing evolution, since they can cause strong selective pressures on floral traits. Most selfing species reduce their investment in reproduction, and display smaller flowers, with less nectar and scents (referred to as selfing syndrome). We model the evolution of prior selfing when it affects both the demography of plants and pollinators and the investment of plants in pollination. Including the selfing syndrome in the model allows to predict several outcomes: plants can evolve either toward complete outcrossing, complete selfing, or to a stable mixed‐mating system, even when inbreeding depression is high. We predict that the evolution to high prior selfing could lead to evolutionary suicides, highlighting the importance of merging demography and evolution in models. The consequence of the selfing syndrome on plant–pollinator interactions could be a widespread mechanism driving the evolution of selfing in animal‐pollinated taxa.     

THE EVOLUTION OF SELF-FERTILIZATION AND INBREEDING DEPRESSION IN PLANTS. II. EMPIRICAL OBSERVATIONS

A bimodal distribution of outcrossing rates was observed for natural plant populations, with more primarily selfing and primarily outcrossing species, and fewer species with intermediate outcrossing rate than expected by chance. We suggest that this distribution results from selection for the maintenance of outcrossing in historically large, outcrossing populations with substantial inbreeding depression, and from selection for selfing when increased inbreeding, due to pollinator failure or population bottlenecks, reduces the level of inbreeding depression. Few species or populations are fixed at complete selfing or complete outcrossing. A low level of selfing in primarily outcrossing species is unlikely to be selectively advantageous, but will not reduce inbreeding depression to the level where selfing is selectively favored, particularly if accompanied by reproductive compensation. Similarly, occasional outcrossing in primarily selfing species is unlikely to regularly provide sufficient heterosis to maintain selection for outcrossing through individual selection. Genetic, morphological and ecological constraints may limit the potential for outcrossing rates in selfers to be reduced below some minimum level.     

Mating system variation along a successional gradient in the allogamous and colonizing plant Crepis sancta (Asteraceae)

We analysed mating system in an annual and colonizing plant, Crepis sancta, that occupies different successional stages in the French Mediterranean region. Based on a previous experiment, we hypothesized that low inbreeding depression measured in young successional stages should select for selfing whereas higher inbreeding depression in old stages should select for outcrossing. Nine populations of C. sancta (Asteraceae) from contrasting successional stages were used to analyse (1) Seed set after autonomous and enforced selfing in controlled conditions and (2) outcrossing rates in natural conditions using allozymes (progeny array analysis). We found that C. sancta possesses a pseudo‐self‐incompatibility system and that mating system varies among populations. Allozymes revealed that the population multilocus outcrossing rates vary from 0.77 to 0.99. The lowest outcrossing rates occur in the youngest successional stages and complete outcrossing is found in old stages. The data partially agree with the predictions we made and the results are more generally discussed in the light of factors changing during succession. We did not find any evidence of reproductive assurance in the nine populations, contrary to what is often assumed as a major factor governing mating system evolution in colonizing species. We propose that mating system variation can be interpreted as the result of the balance between the cost of outcrossing and inbreeding depression in a metapopulation context.     

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.     

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.     

Adaptive significance of self-fertilization in a hermaphroditic perennial, Trillium camschatcense (Melanthiaceae)

The evolution of self-fertilization from primarily outcrossing ancestors is one of the most common evolutionary transitions in plants; however, the ecological mechanisms that maintain self-fertilization have remained controversial. Theoretical studies suggest that selfing is advantageous over outcrossing in terms of genetic transmission and assurance of seed production under pollen-limited circumstances. Trillium camschatcense is a herbaceous perennial distributed in Hokkaido and northern Honshu, Japan. Geographical variation in the breeding system (self-compatible, SC; or self-incompatible, SI) has been reported in populations in Hokkaido. Here, we used several SC and SI populations of T. camschatcense to investigate the adaptive significance and the evolutionary basis of self-fertilization. Pollination experiments and genetic analyses demonstrated that the potential availability of outcross pollen in SC populations was sufficient and that the number of pollen donors was equal to that of SI populations. However, despite the high availability of outcross pollen, the SC populations produced seeds predominantly by selfing and so underwent severe inbreeding depression. Although none of the suggested advantages for self-fertilization were supported by our analyses, we propose two possible scenarios for the evolution of self-fertilization in T. camschatcense.     

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.     

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.     

EVOLUTION OF GYNODIOECY AND MAINTENANCE OF FEMALES: THE ROLE OF INBREEDING DEPRESSION,OUTCROSSING RATES,AND RESOURCE ALLOCATION IN SCHIEDEA ADAMANTIS (CARYOPHYLLACEAE)

Levels of inbreeding depression, outcrossing rates, and phenotypic patterns of resource allocation were studied to examine their relative importance in the maintenance of high numbers of females in gynodioecious Schiedea adamantis (Caryophyllaceae), an endemic Hawaiian shrub found in a single population on Diamond Head Crater, Oahu. In studies of inbreeding depression in two greenhouse environments, families of hermaphrodites exhibited significant inbreeding depression (δ = 0.60), based on a multiplicative fitness function using seeds per capsule, germination, survival, and the inflorescence biomass of progeny. Differences between inbred and outcrossed progeny were smallest at the early stage of seeds per capsule and more pronounced at the later stages of survival and inflorescence production. These results are consistent with inbreeding depression caused by many mutations of small effect. Using allozyme analyses, the inbreeding coefficient of adult plants in the field was not significantly different from zero, implying that δ in nature may be equal to one. The single locus estimate of the outcrossing rate for hermaphrodites was 0.50 based on progeny that survived to flowering; corrected for the disproportionate loss before flowering of progeny from selfing, the adjusted outcrossing rate at the zygote stage was 0.32, suggesting that considerable selfing occurs in hermaphrodites. Females were totally outcrossed. When females and hermaphrodites were compared for reproductive output in the field, females produced over twice as many seeds per plant as hermaphrodites, primarily because females had far more capsules per inflorescence than hermaphrodites. Females had greater mass per seed than hermaphrodites in the field, either because of greater provisioning or reduced inbreeding depression. There was no significant differential mortality with respect to sex over a seven year period. The higher number of seeds per plant of females, combined with substantial inbreeding depression and relatively high selfing rates for hermaphrodites, are probably responsible for the maintenance of females in this population. The predicted frequency of females based on data for seed production, the adjusted selfing rate, and inbreeding depression is 42%, remarkably close to the observed frequency of 39%. High levels of inbreeding depression suggest that considerable quantitative genetic variation is present for traits affecting fitness in this population, despite low allozyme variability and a presumed founder effect.     

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.     

Outcrossing rate and inbreeding depression in the perennial yellow bush lupine, Lupinus arboreus (Fabaceae)

Little is known about the breeding systems of perennial Lupinus species. We provide information about the breeding system of the perennial yellow bush lupine, Lupinus arboreus, specifically determining self-compatibility, outcrossing rate, and level of inbreeding depression. Flowers are self-compatible, but autonomous self-fertilization rarely occurs; thus selfed seed are a product of facilitated selfing. Based on four isozyme loci from 34 maternal progeny arrays of seeds we estimated an outcrossing rate of 0.78. However, when we accounted for differential maturation of selfed seeds, the outcrossing rate at fertilization was lower, ～0.64. Fitness and inbreeding depression of 11 selfed and outcrossed families were measured at four stages: seed maturation, seedling emergence, seedling survivorship, and growth at 12 wk. Cumulative inbreeding depression across all four life stages averaged 0.59, although variation existed between families for the magnitude of inbreeding depression. Inbreeding depression was not manifest uniformly across all four life stages. Outcrossed flowers produced twice as many seeds as selfed flowers, but the mean performance of selfed and outcrossed progeny was not different for emergence, seedling survivorship, and size at 12 wk. Counter to assumptions about this species, L. arboreus is both self-compatible and outcrosses ～78% of the time.