Resource Allocation and the Evolution of Self-Fertilization in Plants

This article develops a simple evolutionarily stable strategy (ESS) model of resource allocation in partially selfing plants, which incorporates reproductive and sex allocation into a single framework. The analysis shows that, if female fitness gain increases linearly with resource investment, total reproductive allocation is not affected by sex allocation, defined as the fraction of reproductive resources allocated to male function. All else being equal, the ESS total reproductive allocation increases with increasing selfing rate if the fitness of selfed progeny is more than half that of outcrossed progeny, while the ESS sex allocation is always a decreasing function of the selfing rate. Self-fertilization is much more common in annual than in perennial plants, and this association has been commonly interpreted in terms of an effect of life history on mating system. The model in this article shows that self-fertilization can itself cause the evolution of the annual habit. Incorporating the effects of pollen discounting may not have any influence on total reproductive allocation if female fitness gain is a linear function of resource investment, although the evolutionarily stable sex allocation is altered. Evolution of the selfing rate is found to be independent of reproductive and sex allocation under the mass-action assumption that self- and outcross pollen are deposited simultaneously on receptive stigmas and compete for access to ovules.     

EVOLUTIONARILY STABLE SELFING RATES OF HERMAPHRODITIC PLANTS IN COMPETING AND DELAYED SELFING MODES WITH ALLOCATION TO ATTRACTIVE STRUCTURES

I present a resource-allocation model to analyze how patterns of allocation to reproductive structures influence the evolution of selfing rates in hermaphrodites subject to competing and delayed forms of self-fertilization. The evolutionarily stable state does not depend on the mode of pollination. In contrast to previous models in which the number and the size of flowers were not considered, intermediate selfing is not evolutionarily stable with linear constraints on flower number and size. In contrast, intermediate selfing can be evolutionarily stable with nonlinear constraints on flower number and size. Optimal allocations to attractive structures increase and selfing rates decrease in the presence of inbreeding depression. In particular, stable intermediate levels of selfing may be favored when flower number is strongly constrained. Thus, nonlinear constraints on flower number and size could favor the evolution of intermediate selfing in either the delayed or the competing modes of selfing. Outcrossing is not favored in the absence of inbreeding depression, a result inconsistent with Holsinger's results in which allocation to attractive structures was not considered.     

Selection caused by self-fertilization I. Four measures of self-fertilization and their effects on fitness

The standard models of selfing in seed plants consider only the ovules, which are assumed to have a constant selfing rate. It has recently become clear, however, that hermaphrodite or monoecious populations frequently show sexual asymmetry (nonconstant pollen:ovule fertilities among individuals). Such asymmetry usually results in pollen selfing rates which differ from those for the ovules and are frequency-dependent even for constant ovule selfing rates. A recent study of selfing rates for all gametes of an individual is extended here to include four selfing rates (for ovules, pollen, all gametes, and zygotes), and simple mathematical relationships linking the four rates are obtained. Unlike earlier models of selfing, it is not assumed that the ovule selfing rate is constant, but instead that this rate, like all the others, is determined by the mobility of the pollen, which in turn is determined by the floral biology and ecology. It is found that all four selfing rates are usually frequency-dependent. The selfing rate for all gametes (the combined selfing rate) is usually intermediate between those for the ovules and pollen, and the zygotic rate is usually the smallest of the four. The exceptions to the above statements occur for relatively extreme situations, such as complete selfing for pollen or ovules, no selfing, or sexual symmetry. Three modes of selfing are considered: prior (PS), competing (CS), and delayed (DS) self-fertilization. It is shown that if there are at least two types with different selfing rates in the population, then the ranking of their selfing rates may depend upon the frequencies of the types (for the combined and the zygotic rates), may be frequency-independent (ovule rate), or may be dependent or independent, according to the mode of selfing (pollen rate). The effects of the various influences on the amount of selfing are by no means negligible. Thus a numerical study shows pollen selfing rates for one type which vary from 0.09 to 0.96, according to its frequency. Another numerical result shows a change in combined selfing rate from 0.13 to 0.86, depending solely on the mode of selfing. Results for Scots Pine show that an ovule selfing rate of 0.5 was accompanied by a combined rate of 0.143.The population selfing rate is not the same as the mean of individual selfing rates, and can only be obtained if female fitnesses as well as ovule selfing rates are known for each type.Previous models of selfing have failed to distinguish between the effects of increased selfing and increased pollen fertility, with the result that increased selfing always resulted in greater fitness. In the present models the two effects are distinguishable, and it is found that increased selfing may result in increased or decreased fitness, depending also on population density and on a form of pollen density. Thus the old dogma that in the absence of viability and fertility selection increased selfing always results in increased fitness is finally refuted, and the importance of the influence of ecological parameters on selfing and fitness is emphasized, since population density and pollen density influence the selfing rates.     

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.     

Selection in plant populations of effectively infinite size II. Protectedness of a biallelic polymorphism

The biologically important problem of protectedness of genetic polymorphisms in monoecious plant populations exhibiting genotypically determined variation in rates of self-fertilization and sexually asymmetrical fertilities has hitherto escaped exact, analytical treatment for the reason that appropriate mathematical techniques relying on allelic frequencies do not seem to exist. For the particular case of one locus and two alleles it was possible to develop such a technique which provides conditions of high precision for protectedness of an allele. A comparison of the results with those already known from models that appear to be specializations of the present model showed that some of the earlier conclusions can be generalized, while others have to be handled with great care or should even be rejected. Above all, this concerns the role of self-fertilization, which is frequently considered to counteract the establishment of genetic polymorphisms. However, it turned out that increasing the heterozygote selfing rate also increases protectedness for both alleles in all situations. Moreover, even if the amount of self-fertilization is the same for all genotypes, asymmetry in the production of ovules and pollen, which is more the rule than an exception, may imply protectedness only for comparatively large selfing rates. The probably most outstanding finding is that, depending on the ovule and pollen fertilities, protectedness may be realized only within small ranges of selfing rates, and these ranges may vary from arbitrarily low to arbitrarily high rates. On the other hand, if the ovule fertilities show strong overdominance for the heterozygote—more precisely, if the heterozygote produces more than twice as many ovules as either of the homozygotes—both alleles are protected irrespective of the pollen fertilities and rates of self-fertilization; this generalizes earlier results obtained for more specific models.     

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.     

Evolution of seed dormancy due to sib competition: effect of dispersal and inbreeding

The effect of dispersal and inbreeding on the evolution of seed dormancy to avoid sib competition is theoretically investigated, using a model which assumes a plant population with patchy spatial structure in a constant environment. Applying the inclusive fitness method, the evolutionarily stable dormancy rates are analytically derived for three cases: (a) an asexual haploid population, (b) a diploid-hermaphrodite population in which the dormancy rate is controlled by seeds, and (c) a diploid-hermaphrodite population in which the dormancy rate is controlled by mother plants. The evolutionarily stable dormancy rates decrease in the order of case (c), case (a), and case (b). In all the cases, the evolutionarily stable dormancy rates increase with decreasing the dispersal rate. Although inbreeding generally increases the evolutionarily stable dormancy rates, inbreeding due to selfing reduces the rate exceptionally in case (c).     

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.     

ECOLOGICAL GENETICS OF GYNODIOECY IN SILENE VULGARIS: RELATIVE FITNESS OF FEMALES AND HERMAPHRODITES DURING THE COLONIZATION PROCESS

Recent theoretical models have addressed the influence of metapopulation dynamics on the fitness of females and hermaphrodites in gynodioecious plants. In particular, selection is thought to favor hermaphrodites during population establishment because that sex should be less prone to pollen limitation, especially if self-fertilization is possible. However, inbreeding depression could limit this advantage. In this experimental study of Silene vulgaris, a weedy gynodioecious plant, the fitness of females and hermaphrodites was estimated from seed production in both mixed-sex populations and for individuals isolated from these populations by 20, 40, 80, or 160 m. In mixed populations females display statistically significant greater per capita seed production owing to higher capsule production and higher rates of seed germination. The fitness of both sexes declines with increasing isolation, but at different rates, such that in the 160-m treatment hermaphrodites are by far the more fit sex. Allozyme studies suggest that this differential decline is because the selfing rate in hermaphrodites increases as a function of isolation, at least partially compensating for a decline in the availability of outcross pollen. Overall, the negative effects of pollen limitation on females far outweighs the negative effects of inbreeding depression following selfing in hermaphrodites. Thus, extinction/recolonization dynamics would appear to favor hermaphrodites as long as seed dispersal events exceed some critical distance.     

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 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.     

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。     

FEMALE FREQUENCIES IN GYNODIOECIOUS POPULATIONS CORRELATED WITH SELFING RATES IN HERMAPHRODITES

Gynodioecious populations consist of separate hermaphroditic and female individuals. Females are at a selective disadvantage because they contribute genes to the next generation only through ovules, while hermaphrodites contribute genes through ovules and pollen. For females to be maintained in populations they must have some compensating selective advantage. The outcrossing hypothesis postulates that females are maintained because their progeny result from obligate outcrossing, whereas some of the progeny of hermaphrodites result from self-fertilization and are less fit because of inbreeding depression. If correct, the frequency of females should be positively correlated with selfing rates of hermaphrodites in populations. We found a strong positive correlation between female frequency and selfing rates of hermaphrodites (r = 0.91, P < 0.01) in eight gynodioecious populations of Hawaiian species of Bidens. Our results confirm that the obligate outcrossing of females is a major factor maintaining females in gynodioecious populations. However, the observed selfing rates are insufficient by themselves to account for the frequency of females in these populations.     

Parentage versus two-generation analyses for estimating pollen-mediated gene flow in plant populations

Assessment of contemporary pollen-mediated gene flow in plants is important for various aspects of plant population biology, genetic conservation and breeding. Here, through simulations we compare the two alternative approaches for measuring pollen-mediated gene flow: (i) the NEIGHBORHOOD model--a representative of parentage analyses, and (ii) the recently developed TWOGENER analysis of pollen pool structure. We investigate their properties in estimating the effective number of pollen parents (N(ep)) and the mean pollen dispersal distance (delta). We demonstrate that both methods provide very congruent estimates of N(ep) and delta, when the methods' assumptions considering the shape of pollen dispersal curve and the mating system follow those used in data simulations, although the NEIGHBORHOOD model exhibits generally lower variances of the estimates. The violations of the assumptions, especially increased selfing or long-distance pollen dispersal, affect the two methods to a different degree; however, they are still capable to provide comparable estimates of N(ep). The NEIGHBORHOOD model inherently allows to estimate both self-fertilization and outcrossing due to the long-distance pollen dispersal; however, the TWOGENER method is particularly sensitive to inflated selfing levels, which in turn may confound and suppress the effects of distant pollen movement. As a solution we demonstrate that in case of TWOGENER it is possible to extract the fraction of intraclass correlation that results from outcrossing only, which seems to be very relevant for measuring pollen-mediated gene flow. The two approaches differ in estimation precision and experimental efforts but they seem to be complementary depending on the main research focus and type of a population studied.     

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.     

Selection in plant populations of effectively infinite size VI. Overlapping generations

A selection model for iteroparous, monoecious, or hermaphroditic plant populations is considered which encompasses viabilities, pollen fertilities, ovule fertilities, and rates of self-fertilization which may arbitrarily depend on both age and genotype. The general conditions for establishment (which are also those for protectedness) of an allele are derived. The classical conjecture that the conditions of protectedness are the same for separated and overlapping generations if the intrinsic rates of increase are applied is discussed. For this purpose it is necessary to introduce two new intrinsic values: the intrinsic rate of self-fertilization and the intrinsic pollen-to-ovule ratio. The significance of the intrinsic values is demonstrated for complete self-fertilization, selection restricted to differential, partial self-fertilization, and sexual asymmetry (absence of proportionality between pollen and ovule production), including selection restricted to one sex. With the exception of asymmetric selection in both sexes, it turns out that the intrinsic values suffice to state the conditions for protectedness, but more information about the life histories is required to determine the exact speed of establishment. For asymmetric selection in both sexes, the concept of intrinsic value is inadequate for investigating the problem of establishment and thus the evolution of life histories. Since sexual asymmetry is rather the rule than the exception and selfing is common in plants, the consequences for finding optimal life histories are outlined.     

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.     

Evolution of habitat-dependent sex allocation in plants: superficially similar to, but intrinsically different from animals

Because pollen disperses and ovules do not, a basic difference in dispersal abilities of male and female gametes exists in plants. With an analytical model, we show that the combination of such sex-biased dispersal of gametes and variation of habitat quality results in two opposite selective forces acting on the evolution of sex allocation in plants: (i) a plant should overproduce pollen in good patches and overproduce ovules in poor patches in order to equilibrate secondary sex ratios of gametes after pollen dispersal; (ii) a plant should overproduce ovules in good patches and overproduce pollen in poor patches in order to increase the likelihood that its progeny establishes in good patches. Our theoretical results indicate that the evolution of habitat-dependent sex allocation should be favoured in plants, in a direction that depends on the relative dispersal ability of pollen and seeds. We also show that superficially similar predictions obtained for habitat-dependent evolutionarily stable sex allocation in animals actually result from a completely different balance between the two underlying evolutionary forces.