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.     

On the Origin of Meiotic Reproduction: A Genetic Modifier Model

We study the conditions under which a rare allele that modifies the relative rates of meiotic reproduction and apomixis increases in a population in which meiotic reproduction entails selfing as well as random outcrossing. A distinct locus, at which mutation maintains alleles that are lethal in homozygous form, determines viability. We find that low viability of carriers of the lethal alleles, high rates of selfing, dominance of the introduced modifier allele, and lower rates of recombination promote the evolution of meiosis. Meiotic reproduction can evolve even in the absence of linkage between the modifier and the viability locus. The adaptive value of meiotic reproduction depends on the relative viabilities of offspring derived by meiosis and by apomixis, and on associations between the modifier and the viability locus. Meiotic reproduction, particularly under selfing, generates more diverse offspring, including those with very high and very low viability. Elimination of offspring with low viability generates positive associations between enhancers of meiotic reproduction and high viability. In addition, partial selfing generates positive associations in heterozygosity (identity disequilibrium) between the modifier and the viability locus, even in the absence of linkage. The two kinds of associations together can compensate for initial reductions in mean offspring viability under meiotic reproduction.     

Coevolution of self-fertilization and inbreeding depression. III. Homozygous lethal mutations at multiple loci.

We study the evolution of the rate of self-fertilization in response to deleterious mutations at multiple loci. Although partial selfing induces associations among loci even in the absence of linkage, associations among mutations at different loci are of a smaller order of magnitude than the mutation rate. Genotypes that carry homozygous lethal mutations in heterozygous form at i loci occur in frequencies of the order (Ti) mu i, in which T denotes the number of viability loci and mu the mutation rate. While associations between mutations at different loci remain small even under inbreeding, each viability locus develops an association with the modifier of the rate of self-fertilization that substantially affects the evolution of the breeding system. Positive associations between enhancers of selfing and haplotypes carrying multiple wild-type alleles and positive associations in heterozygosity between the modifier locus and the viability loci promote evolutionary increases in the rate of self-fertilization.     

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.     

Allee effect and self-fertilization in hermaphrodites: reproductive assurance in a structured metapopulation

Reproductive assurance through selfing during colonization events or when population densities are low has often been put forward as a mechanism selecting for the evolution of self-fertilization. Such arguments emphasize on the role of both local demography and metapopulation processes. We developed a model for the evolution of self-fertilization in a structured metapopulation in which local densities are not steady because of population growth. Reproduction by selfing is density-independent (reproductive assurance) but selfed seeds endure inbreeding depression, whereas reproduction by outcrossing is density-dependent (Allee effect). First, we derived an analytical criterion for metapopulation viability as a function of the selfing rate and metapopulation parameters. We show that outcrossers can develop a viable metapopulation when they produce a high amount of dispersal seeds that counterbalances their incapacity to found new populations from low densities. Second, the model shows there is a positive feedback between demography and outcrossing rates, leading to either complete outcrossing or selfing. Specifically, we illustrate that inbreeding depression can paradoxically favor the evolution of selfing because of its negative effect on density. Also, complete outcrossing can be selected despite pollen limitation, although it does not provide a full seed set. This model underlines the influence of the mating system both on demography and gene dynamics in a metapopulation context.     

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.     

Inbreeding depression in self-incompatible and self-compatible populations of Leavenworthia alabamica

Inbreeding depression is one of the leading factors preventing the evolution of self-fertilization in plants. In populations where self-fertilization evolves, theory suggests that natural selection against partially recessive deleterious alleles will reduce inbreeding depression. The purpose of this study was to evaluate this hypothesis by comparing the magnitude of inbreeding depression in self-incompatible and self-compatible populations of Leavenworthia alabamica. Within-population crosses were conducted to compare the quantity and quality of offspring produced by outcrossing and self-fertilization. These progeny were grown in a common greenhouse and inbreeding depression was measured in germination, survival, biomass, transition rate to flowering, flower number, petal length, pollen grains/anther, pollen viability, and ovule number. In comparison to outcrossing, self-fertilization led to the production of fewer and smaller seeds within self-incompatible populations. Moreover, inbreeding depression was observed in eight of 11 offspring traits within self-incompatible populations of L. alabamica. In contrast, there was significant inbreeding depression only in flower number within self-compatible populations. The results of this study are consistent with the idea that self-fertilization selectively removes partially recessive deleterious alleles causing inbreeding depression in natural plant populations. However, in plant species such as L. alabamica where self-compatibility may evolve in small populations following long-distance dispersal, declines in inbreeding depression may also be facilitated by genetic drift.     

On the evolution of genetic incompatibility systems. V. Origin of sporophytic self-incompatibility in response to overdominance in viability

Conditions for the origin of partial sporophytic self-incompatibility (SSI) are obtained from two quantitative models, which differ with respect to the determination of offspring viability. Offspring viability depends solely on the source (self or nonself) of the fertilizing pollen in the first model, which describes changes only at a primitive S-locus itself. Two loci evolve in the second model: overdominant viability selection maintains an arbitrary number of alleles at one locus, with SSI under the control of a separate locus. In both cases, the origin of SSI requires that the relative change in the numbers of offspring derived by the two reproductive modes compensate for the twofold cost of outcrossing. In the first model studied, the viability of inbred offspring fully determines the relative change in the numbers of inbred and outbred offspring produced. In the second model, the relative change in offspring numbers depends in addition on associations between the S-locus and the viability locus. Because these two-locus associations are comparable in magnitude to the differences between the viabilities of inbred and outbred offspring, SSI can arise under less restrictive conditions than expected from the one-locus model. Greater allelic multiplicity at the viability locus facilitates the origin of SSI by reducing the relative viability of inbred offspring. Tight linkage between the S-locus and the viability locus and high rates of receipt of self-pollen promote the generation and maintenance of associations between the S-locus and the viability locus. In populations in which more than two viability alleles are maintained, the active S-allele can invade even in the absence of linkage with the viability locus. The present study establishes that incompatibility systems can arise in response to identity disequilibrium between a modifier of incompatibility and a locus subject to overdominant viability selection; in particular, compensation for the twofold cost of outcrossing does not require preexisting gametic level disequilibria.     

繁殖保障和延迟自交的研究进展

尽管植物在进化过程中面临不利自花授粉的选择,但许多植物仍维持混合的授粉机制。繁殖保障假说是解释自交进化的最重要因子之一,一直是植物生殖生态学和进化生物学关注的焦点之一。概述了近年来的主要研究热点及其进展,包括自交进化的遗传和生态机制及理论模型探讨、繁殖保障假说的提出、验证自交能否提供繁殖保障的例证、延迟自交的类型及延迟自交能否提供繁殖保障的例证等方面。介绍了我国在繁殖保障和延迟自交方面研究的现状和不足之处,结合国际上研究繁殖保障假说的发展趋势已由单季节、单种群、单因子的研究阶段过渡到多季节、多种群、多因子（自交方式及其所占比例、花粉折损、种子折损、自交率和近交衰退）的综合研究阶段,及由传统的、经典的研究方法过渡到应用现代实验手段（如SSR、SNP等分子标记）和先进仪器设备的研究阶段,提出今后研究中应注意的问题。有必要借用多学科（植物学、生态学和分子生物学）的方法及手段进行不同物种的对比和综合细致的研究。     

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.     

POLLEN DISCOUNTING AND THE SPREAD OF A SELFING VARIANT IN TRISTYLOUS EICHHORNIA PANICULATA: EVIDENCE FROM EXPERIMENTAL POPULATIONS

Floral traits that increase self-fertilization are expected to spread unless countered by the effects of inbreeding depression, pollen discounting (reduced outcross pollen success by individuals with increased rates of self-fertilization), or both. Few studies have attempted to measure pollen discounting because to do so requires estimating the male outcrossing success of plants that differ in selfing rate. In natural populations of tristylous Eichhornia paniculata, selfing variants of the mid-styled morph are usually absent from populations containing all three style morphs but often predominate in nontrimorphic populations. We used experimental garden populations of genetically marked plants to investigate whether the effects of population morph structure on relative gamete transmission by unmodified (M) and selfing variants (M‘) of the mid-styled morph could explain their observed distribution. Transmission through ovules and self and outcross pollen by plants of the M and M’ morphs were compared under trimorphic, dimorphic (S morph absent), and monomorphic (L and S morphs absent) population structures. Neither population structure nor floral morphology affected female reproductive success, but both had strong effects on the relative transmission of male gametes. The frequency of self-fertilization in the M' morph was consistently higher than that of the M morph under all morph structures, and the frequency of self-fertilization by both morphs increased as morph diversity of experimental populations declined. In trimorphic populations, total transmission by the M and M' morphs did not differ. The small, nonsignificant increase in selfing by the M' relative to the M morph was balanced by decreased outcross siring success, particularly on the S morph. In populations lacking the S morph, male gamete transmission by the M' morph was approximately 1.5 times greater than that by the M morph because of both increased selfing and increased success through outcross pollen donation. Therefore, gamete transmission strongly favored the M' morph only in the absence of the S morph, a result consistent with the distribution of the M' morph in nature. This study indicates that floral traits that alter the selfing rate can have large and context-dependent influences on outcross pollen donation.     

Self-fertilization and the evolution of recombination

In this article, we study the effect of self-fertilization on the evolution of a modifier allele that alters the recombination rate between two selected loci. We consider two different life cycles: under gametophytic selfing, a given proportion of fertilizations involves gametes produced by the same haploid individual, while under sporophytic selfing, a proportion of fertilizations involves gametes produced by the same diploid individual. Under both life cycles, we derive approximations for the change in frequency of the recombination modifier when selection is weak relative to recombination, so that the population reaches a state of quasi-linkage equilibrium. We find that gametophytic selfing increases the range of epistasis under which increased recombination is favored; however, this effect is substantial only for high selfing rates. Moreover, gametophytic selfing affects the relative influence of different components of epistasis (additive x additive, additive x dominance, dominance x dominance) on the evolution of the modifier. Sporophytic selfing has much stronger effects: even a small selfing rate greatly increases the parameter range under which recombination is favored, when there is negative dominance x dominance epistasis. This effect is due to the fact that selfing generates a correlation in homozygosity at linked loci, which is reduced by recombination.     

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.     

Ovule discounting in an outcrossing, cryptically dioecious tree

Ovule discounting denotes the reduction in the number of ovules available for cross-fertilization due to the interference of inferior pollen. Traditionally, ovule discounting has been discussed solely from the perspective of compromised outcrossing opportunities as a result of selfing, but the principle is more general. Here, we extend its applicability beyond the simple contrast between selfing and outcrossing by showing that, in the cryptically dioecious tree species Fraxinus ornus, ovule discounting through frequent outcrossing with inferior fathers also constitutes a substantial cost of mating. In F. ornus, hermaphrodites produce pollen capable of siring offspring, but these offspring are less viable than those sired by males and are inferred to produce few, if any, surviving progeny. In this paper, we used microsatellite markers to analyze the mating system and paternity in a wild population of F. ornus. We found that the effective number of sires per mother was low (N(ep) = 2.93 to 4.95), and that paternity was correlated among progeny sampled from the same mother, but not among progeny sampled from neighboring mothers. Despite the existence of a local spatial genetic structure (up to 30 m), we found no evidence of biparental inbreeding. There was negligible selfing by hermaphrodites, but they sired approximately one fourth of the seeds produced by other hermaphrodites. Given that these progeny are not inferred to reach reproductive maturity, this constitutes a substantial cost of ovule discounting in the broad sense. We discuss the possible reasons for why hermaphrodites invest resources into inferior pollen.     

FIXATION PROBABILITIES OF SELFING RATE MODIFIERS IN SIMULATIONS WITH SEVERAL DELETERIOUS ALLELES WITH LINKAGE

The fixation rates of selfing rate modifiers were found by stochastic simulation in an infinite site model, including effects of several deleterious alleles with variable effects, which were randomly distributed in the genome without assuming any pollen discounting. Previous results on the evolution of selfing obtained by more precise methods were in this study further validated, and it was concluded that the effect of genetic associations on the evolution of mating systems is small except in the case of full pollen discounting. Furthermore, attention was given to the uneven distribution of the genetic load in the population, and the accompanying large among-genome variation in fixation rates. This among-genome variation will be of significance for 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.     

Selection caused by self-fertilization

The generally held view that increased self-fertilization should be advantageous in the absence of counteracting selective forces reducing viability or fertility is reexamined. It is pointed out that the models on which this view is based all imply a gain in male (pollen) fertility with increased selfing. Hence, the postulated advantage may equally well be due to increased fertility, a fact which reopens the discussion on the selective significance of differential selfing. A new model for differential self-fertilization is presented which avoids built-in fertility selection by explicitly considering pollen available for self- and for cross-pollination. Plant types are distinguished with respect to their amounts r_i of pollen available for self-pollination, and these types are assumed to be identical with respect to their pollen and ovule fertilities. Moreover, the efficiency of cross-pollination is allowed to depend, for example, on population density, thus giving rise to a parameter b called “crossing potential”, while the efficiency of self-pollination is described by a parameter a called “selfing potential”. These parameters may be conceived of as ecological parameters. Increasing r_i produces a simultaneous increase in each of the four measures of self-fertilization (introduced in Part I of the present series) irrespective of the values of the ecological parameters. It is then shown that increased selfing can be both advantageous and disadvantageous in terms of fitness, dependig on the ecological parameters as well as on the mode of self-fertilization (i.e. where selfing occurs before or after outcrossing). The main result is, roughly, that for both selfing modes high crossing and low selfing potential favour increased cross-fertilization, while the reverse favours increased self-fertilization. However, the regions for a and b in which this holds true differ substantially for the two selfing modes. In the complements of these regions strange conditions for the evolution of increased selfing or outcrossing, respectively, exist. The significance of these results for explaining experimental observations is discussed.     

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.     

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.