ALLOCATION TO ATTRACTIVE STRUCTURES IN ANIMAL-POLLINATED FLOWERS

An optimal allocation model was developed for the evolutionarily stable size of attractive structures of flowers (ESA) in animal-pollinated plants. It was assumed that a plant can change the sizes of attractive and sexual structures of a flower and the size and the number of flowers. In the absence of constraints on flower size, the ESA should not depend on the frequency of self-fertilization or the sexuality of plants. However, with constraints on flower size, the ESA decreases with increasing self-fertilization, except in special cases, and it is possible that males have a larger or a smaller ESA than females. Thus, differences in self-fertilization and sexuality alone cannot explain the differences in allocation among nondomesticated plants. In addition, attractive structures can contribute more to male or female function depending on the cost of gamete production, pollination efficiency for pollen and ovules, and pollinator availability.     

How geitonogamous selfing affects sex allocation in hermaphrodite plants

Does the mode of self-pollination affect the evolutionarily stable allocation to male vs. female function? We distinguish the following scenarios. (1) An ‘autogamous’ species, in which selfing occurs within the flower prior to opening. The pollen used in selfing is a constant fraction of all pollen grains produced. (2) A species with ‘abiotic pollination’, in which selfing occurs when pollen dispersed in one flower lands on the stigma of a nearby flower on the same plant (geitonogamy). The selfing rate increases with male allocation but a higher selfing rate does not mean a reduced export of pollen. (3) An ‘animal-pollinated’ species with geitonogamous selfing. Here the selfing rate also increases with male allocation, but pollen export to other plants in the population is a decelerating function of the number of simultaneously open flowers. In all three models selfing selects for increased female allocation. For model 3 this contradicts the general opinion that geitonogamous selfing does not affect evolutionarily stable allocations. In all models, the parent benefits more from a female-biased allocation than any other individual in the population. In addition, in models 2 and 3, greater male allocation results in more local mate competition. In model 3 and in model 2 with low levels of inbreeding depression, hermaphroditism is evolutionarily stable. In model 2 with high inbreeding depression, the population converges to a fitness minimum for the relative allocation to male function. In this case the fitness set is bowed inwards, corresponding with accelerating fitness gain curves. If the selfing rate increases with plant size, this is a sufficient condition for size-dependent sex allocation (more allocation towards seeds in large plants) to evolve. We discuss our results in relation to size-dependent sex allocation in plants and in relation to the evolution of dioecy.     

Evolutionary Assurance vs. Mixed Mating

Reproductive assurance is a widely accepted explanation for the evolution of selfing, although theory suggests that an evolutionarily stable mixed mating strategy does not maximize seed production. We present a correlation analysis involving 28 species representing 23 families showing that selfing can evolve independently of inbreeding depression. We discuss the cost-benefit trade-off of selfing, in particular the incongruence of whether delayed selfing provides reproductive assurance in 22 species representing 14 families, in which pollen and seed discounting are minimized when pollinators or mates are scarce. Reproductive assurance, in response to frequent pollinator failure, can be reconciled with an evolutionarily stable mixed mating system contributed to by delayed selfing, which is still advantageous even if there is strong inbreeding depression.     

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.     

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。     

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.     

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.     

THE EFFECT OF INVESTMENT IN ATTRACTIVE STRUCTURES ON ALLOCATION TO MALE AND FEMALE FUNCTIONS IN PLANTS

Expressions for male and female fitnesses of partially self-fertilizing cosexual plants are derived, assuming that allocation to pollinator attraction at the time of flowering may decrease resources available for male and female primary structures. The total female fertility is assumed to be controlled by factors at two stages, flowering-time and fruiting-time, with resources for fruit maturation being limited so that maximum seed production may be limited by the availability of these resources. The fitness formulas are used to calculate ESS (evolutionarily stable strategy) allocations at flowering time to primary male and female sex functions and to attractive structures. These are compared with some data that are available for dry weights of different flower parts. The fitnesses of unisexual mutant forms are calculated, assuming that they are introduced into a population consisting mostly of the initial cosexual form and that they obey the same gain curves as that form. When compared with the fitness of the ESS cosexual form, this enables one to ask whether unisexual forms will be favored. We show that the spread of females is unlikely, unless there is high inbreeding depression and a rather high selfing rate, and that in some circumstances a linear relation between number of fertilized ovules and number of seeds matured can be less favorable for the invasion of females than is a highly concave relation. With a nearly linear relation between numbers of fertilized ovules and mature seeds, invasion by females is more likely when investment in attraction is low than when it is high. These effects are discussed in relation to the distribution of dioecy. The spread of male mutants is never likely in these models.     

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.     

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.     

Effects of reproductive compensation, gamete discounting and reproductive assurance on mating-system diversity in hermaphrodites

Hermaphroditism allows considerable scope for contributing genes to subsequent generations through various mixtures of selfed and outcrossed offspring. The fitness consequences of different family compositions determine the evolutionarily stable mating strategy and depend on the interplay of genetic features, the nature of mating, and factors that govern offspring development. This theoretical article considers the relative contributions of these influences and their interacting effects on mating-system evolution, given a fixed genetic load within a population. Strong inbreeding depression after offspring gain independence selects for exclusive outcrossing, regardless of the intensity of predispersal inbreeding depression, unless insufficient mating limits offspring production. The extent to which selfing evolves under weak postdispersal inbreeding depression depends on predispersal inbreeding depression and the opportunity for resource limitation of offspring production. Mixed selfing and outcrossing is an evolutionarily stable strategy (ESS) if selfed zygotes survive poorly, but selfed offspring survive well, and maternal individuals produce enough "extra" eggs that deaths of unviable outcrossed embryos do not impact offspring production (reproductive compensation). Mixed mating can also be an ESS, despite weak lifetime inbreeding depression, if self-mating reduces the number of male gametes available for outcrossing (male-gamete discounting). Reproductive compensation and male-gamete discounting act largely independently on mating-system evolution. ESS mating systems always involve either complete fertilization or fertilization of enough eggs to induce resource competition among embryos, so although reproductive assurance is adaptive with insufficient mating, it is never an ESS. Our results illustrate the theoretical importance of different constraints on offspring production (availability of male gametes, egg production, and maternal resources) for both the course and outcome of mating-system evolution, whereas unequal competition between selfed and outcrossed embryos has limited effect. These results also underscore the significance of heterogeneity in the nature and intensity of inbreeding depression during the life cycle for the evolution of hermaphrodite mating systems.     

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.     

The inbreeding depression cost of selfing: Importance of flower size and population size in Collinsia parviflora (Veronicaceae)

Inbreeding depression should evolve with selfing rate when frequent inbreeding results in exposure of and selection against deleterious alleles. The selfing rate may be modified by plant traits such as flower size, or by population characteristics such as census size that can affect the probability of biparental inbreeding. Here we quantify inbreeding depression (δ) among different population sizes of Collinsia parviflora, a wildflower with interpopulation variation in flower size, by comparing fitness components and multiplicative fitness of experimentally produced selfed and outcrossed offspring. Selfed offspring had reduced multiplicative fitness compared to outcrossed offspring, but inbreeding depression was low in all combinations of population size and flower size (δ ≤ 0.05) except in large populations of large-flowered plants (δ = 0.45). The decrement to multiplicative fitness with inbreeding was not affected by population size nested within flower size, but differed between small- and large-flowered plants: small-flowered populations had lower overall inbreeding depression (δ = 0.04) compared to large-flowered populations (δ = 0.25). The difference in load with flower size suggests that either selection has removed deleterious recessive alleles or these alleles have become fixed in small-flowered, potentially more selfing populations, but that purging has not occurred to the same extent in presumably outcrossing large-flowered populations.     

INBREEDING AND THE COST OF MEIOSIS: THE EVOLUTION OF SELFING IN POPULATIONS PRACTICING BIPARENTAL INBREEDING

The effect of biparental inbreeding on the conditions governing the evolution of selfing is examined using recursions in mating-type frequencies. Sibmating in combination with random outcrossing influences two key determinants of the adaptive value of selfing: 1) the meiotic cost of biparental reproduction and 2) the level of inbreeding depression due to deleterious mutations. Biparental inbreeding serves to maintain biparental reproduction by increasing relatedness between parents and their biparentally derived offspring and introduces the possibility of an optimal mating system that incorporates both modes of reproduction. Biparental inbreeding serves to promote uniparental reproduction by reducing the relative inbreeding depression suffered by uniparental offspring. The net effect of these two antagonistic trends depends upon the extent to which mutational load accounts for differences in the numbers of the two types of offspring. A brief summary of the empirical literature suggests that: 1) biparental inbreeding may occur in populations exhibiting mixed mating systems; 2) while inbreeding depression represents an important factor, it does not account entirely for differences in offspring number between the two modes of reproduction.     

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.     

EFFECTS OF CROSS AND SELF-FERTILIZATION ON PROGENY FITNESS IN LOBELIA CARDINALIS AND L. SIPHILITICA

Inbreeding depression, or the decreased fitness of progeny derived from self-fertilization as compared to outcrossing, is thought to be the most general factor affecting the evolution of self-fertilization in plants. Nevertheless, data on inbreeding depression in fitness characters are almost nonexistent for perennials observed in their natural environments. In this study I measured inbreeding depression in both survival and fertility in two sympatric, short-lived, perennial herbs: hummingbird-pollinated Lobelia cardinalis (two populations) and bumblebee-pollinated L. siphilitica (one population). Crosses were performed by hand in the field, and seedlings germinated in the greenhouse. Levels of inbreeding depression were determined for one year in the greenhouse and for two to three years for seedlings transplanted back to the natural environment. Fertility was measured as flower number, which is highly correlated with seed production under natural conditions in these populations. Inbreeding depression was assessed in three ways: 1) survival and fertility within the different age intervals; 2) cumulative survival from the seed stage through each age interval; and 3) net fertility, or the expected fertility of a seed at different ages. Net fertility is a comprehensive measure of fitness combining survival and flower number. In all three populations, selfing had nonsignificant effects on the number and size of seeds. Lobelia siphilitica and one population of L. cardinalis exhibited significant levels of inbreeding depression between seed maturation and germination, excluding the consideration of possible differences in dormancy or longterm viability in the soil. There was no inbreeding depression in subsequent survival in the greenhouse in any population. In the field, significant survival differences between selfed and outcrossed progeny occurred only in two years and in only one population of L. cardinalis. For both survival and fertility there was little evidence for the expected differences among families in inbreeding depression. Compared to survival, inbreeding depression in fertility (flower number) tended to be much higher. By first-year flower production, the combined effects on survival and flower number caused inbreeding depression in net fertility to reach 54%, 34% and 71% for L. siphilitica and the two populations of L. cardinalis. By the end of the second year of flowering in the field, inbreeding depression in net fertility was 53% for L. siphilitica and 54% for one population of L. cardinalis. For the other population of L. cardinalis, these values were 76% through the second year of flowering and 83% through the third year. Such high levels of inbreeding depression should strongly influence selection on those characters affecting self-fertilization rates in these two species.     

RECONSTRUCTING ORIGINS OF LOSS OF SELF‐INCOMPATIBILITY AND SELFING IN NORTH AMERICAN ARABIDOPSIS LYRATA: A POPULATION GENETIC CONTEXT

Theoretical and empirical comparisons of molecular diversity in selfing and outcrossing plants have primarily focused on long‐term consequences of differences in mating system (between species). However, improving our understanding of the causes of mating system evolution requires ecological and genetic studies of the early stages of mating system transition. Here, we examine nuclear and chloroplast DNA sequences and microsatellite variation in a large sample of populations of Arabidopsis lyrata from the Great Lakes region of Eastern North American that show intra‐ and interpopulation variation in the degree of self‐incompatibility and realized outcrossing rates. Populations show strong geographic clustering irrespective of mating system, suggesting that selfing either evolved multiple times or has spread to multiple genetic backgrounds. Diversity is reduced in selfing populations, but not to the extent of the severe loss of variation expected if selfing evolved due to selection for reproductive assurance in connection with strong founder events. The spread of self‐compatibility in this region may have been favored as colonization bottlenecks following glaciation or migration from Europe reduced standing levels of inbreeding depression. However, our results do not suggest a single transition to selfing in this system, as has been suggested for some other species in the Brassicaceae.     

Evolution of the Selfing Rate and Resource Allocation Models

Abstract First, evolutionary theories of selfing of terrestrial plants are reviewed briefly. The evolution of the selfing rate is controlled mainly by (1) the benefit of enhanced genetic relatedness to seeds and (2) the cost of lowered fitness of selfed offspring (inbreeding depression), being modified by (3) fertility assurance under pollen limitation, (4) reduced performance as pollen donor, (5) reduced expenditure to male function, and (6) lowered genetic recombination. Models of the joint evolution of selfing and inbreeding depression predict either strong outcrossing or predominant selfing. Although wind-pollinated plants fit the prediction, some animal-pollinated species have intermediate selfing rates, refuting the theory.
Second, three resource allocation models are analyzed, in which an individual plant optimally allocates limited resources to outcrossed seeds, selfed seeds, and to energy reserves for the next year. The first model explains how the number of outcrossed and selfed offspring change with plant size when they differ in dispersal distance. The second model predicts that, in a disturbed habitat, the plant is likely to be annual and to produce both selfed and outcrossed seeds; in contrast, in a stable habitat, the plant tends to be perennial and to abort selfed seeds selectively. Hand pollination may increase seed production for perennials but not for annuals. The third model explains the observed difference between animal and wind pollinated plants in the out-crossing rate pattern by the difference in the way pollen acquisition increases with investment.     

THE EVOLUTION OF ASSORTATIVE MATING AND SELFING WITH IN- AND OUTBREEDING DEPRESSION

The effect of inbreeding and outbreeding depression on the evolution of assortment are often considered separately. For instance, inbreeding depression is usually thought to shape selfing rates whereas outbreeding depression is commonly thought to affect the evolution of assortative mating. In this article, we consider the evolution of assortment in a context of local adaptation and we show that it is a typical situation in which both effects act simultaneously to shape the degree of selfing or assortative mating. More specifically, we show that selection on a modifier of mating can be partitioned into three distinct effects: a transmission advantage, an association to heterozygosity (proportional to inbreeding depression), and an association to beneficial alleles (proportional to outbreeding depression), so that random mating may evolve even with strong local adaptation. In addition, we show that it is necessary to carefully delimit the conditions for polymorphism at local adaptation locus to study the evolution of assortment. In particular, the range of parameters most favorable to the maintenance of polymorphism corresponds to situations favoring less assortment.