Maintenance of gynodioecy in Wurmbea biglandulosa (Colchicaceae): gender differences in seed production and progeny success

 In gynodioecious species, females contribute genes to future generations only through ovules, and to persist in populations they must have a compensatory advantage compared with hermaphrodites that reproduce via ovules and pollen. This compensation can result from greater fecundity and/or superior success of progeny from females. We examined differences in seed production and progeny success between females and hermaphrodites in the geophyte Wurmbea biglandulosa to explain the maintenance of females. Females produced more ovuliferous flowers and had more ovules per flower than did hermaphrodites but this did not necessarily result in greater fecundity, in part because seed production of females was pollen-limited. Over four years in one population, open-pollinated females produced 1.32 more seeds than open-pollinated hermaphrodites (range 1.09–1.63). In two other populations examined for one year only females produced 1.07 and 0.79 as many seeds as hermaphrodites. Seed production of open-pollinated females and hermaphrodites was only 55% and 73% that of cross-pollinated plants, respectively, indicating that both genders were pollen-limited but females more so than hermaphrodites. Open-pollinated seeds from females were 1.18–1.27 times more likely to germinate than seeds from hermaphrodites. No gender differences existed in seedling growth or survival. Hermaphrodites were self-compatible, but selfed seed set was only 80% that of crossed seed set. Crossed seed set of females and hermaphrodites did not differ. Assuming nuclear control of male sterility, relative female fitness is insufficient to maintain females at their current frequencies of 17%, and substantial female fitness advantages at later life-cycle stages are required. Received May 4, 2001 Accepted February 25, 2002     

Evidence of gynodioecy and sex ratio variation in Wurmbea biglandulosa (Colchicaceae)

 A valuable approach to understanding the evolution of gender dimorphism involves studies of single species that exhibit intraspecific variation in sexual systems. Here we survey sex ratios in 35 populations of Wurmbea biglandulosa, previously described as hermaphroditic. We found pronounced intraspecific variation in sexual systems; populations in the northeastern part of the species' range were hermaphroditic, whereas other populations were gynodioecious and contained 2–44% females. Populations with lower annual rainfall were more likely to be gynodioecious, supporting the view that gender dimorphism evolves more frequently in harsher environments. In gynodioecious populations, however, female frequency was not related to either annual rainfall or habitat, indicating that other factors are important in determining sex ratio variation. Females had smaller flowers and shorter stems than did hermaphrodites, potentially providing a basis for resource compensation. A female fecundity advantage may contribute to the maintenance of females in populations because females produced more ovuliferous flowers and had more ovules per flower than did hermaphrodites. Received March 2, 2001 Accepted February 25, 2002     

Inbreeding and outbreeding depression in Caenorhabditis nematodes

The nematode Caenorhabditis elegans reproduces primarily by self-fertilization of hermaphrodites, yet males are present at low frequencies in natural populations (androdioecy). The ancestral state of C. elegans was probably gonochorism (separate males and females), as in its relative C. remanei. Males may be maintained in C. elegans because outcrossed individuals escape inbreeding depression. The level of inbreeding depression is, however, expected to be low in such a highly selfing species, compared with an outcrosser like C. remanei. To investigate these issues, we measured life-history traits in the progeny of inbred versus outcrossed C. elegans and C. remanei individuals derived from recently isolated natural populations. In addition, we maintained inbred lines of C. remanei through 13 generations of full-sibling mating. Highly inbred C. remanei showed dramatic reductions in brood size and relative fitness compared to outcrossed individuals, with evidence of both direct genetic and maternal-effect inbreeding depression. This decline in fitness accumulated over time, causing extinction of nearly 90% of inbred lines, with no evidence of purging of deleterious mutations from the remaining lines. In contrast, pure strains of C. elegans performed better than crosses between strains, indicating outbreeding depression. The results are discussed in relation to the evolution of androdioecy and the effect of mating system on the level of inbreeding depression.     

Mating system instability in Schiedea menziesii (Caryophyllaceae)

We investigated inbreeding depression and selfing in hermaphroditic Schiedea menziesii to assess the stability of the breeding system. A combination of high selfing rates and strong inbreeding depression suggests that the mating system is unstable. The population-level selfing rate measured in three years ranged considerably from 0.425 (SE = 0.138) to 0.704 (0.048); family measures of selfing rate varied from zero to one in all three years. Inbreeding coefficients did not differ from zero, suggesting that inbred plants do not survive to reproduction in the field. Average inbreeding depression measured in two greenhouse experiments was 0.608-0.870, with values for individual plants ranging from -0.170 to 0.940. The magnitude of inbreeding depression expressed at different life-history stages depended on experimental conditions. When plants were grown during the winter, inbreeding depression was expressed at early and late life-history stages. When plants were grown during the summer, inbreeding depression was detected for germination but not for later life-history stages. Inbreeding depression for vegetative and inflorescence biomass was also measured using field-collected seeds where cross status was assigned using genotypes determined electrophoretically. We did not detect a relation between inbreeding depression and the selfing rate at the level of the individual plant. We saw no evidence for intrafloral selfing, suggesting that the evolution of increased selfing through autogamy is unlikely, despite high selfing rates. A more likely outcome of breeding system instability is the evolution of gynodioecy, which occurs in species of Schiedea closely related to S. menziesii. Females have been detected in progeny of S. menziesii that have been raised in the greenhouse. In the absence of biotic pollen vectors, the failure of these females to establish in the natural population may result from the absence of adaptations for wind pollination.     

Inbreeding and outbreeding effects on pollen fitness and zygote survival in Silene nutans (Caryophyllaceae)

In plants, selfing and outcrossing may be affected by maternal mate choice and competition among pollen and zygotes. To evaluate this in Silene nutans, we pollinated plants with mixtures of (1) self‐ and outcross pollen and (2) pollen from within a population and from another population. Pollen fitness and zygote survival was estimated from the zygote survival and paternity of seeds. Self pollen had a lower fitness than outcross pollen, and selfed zygotes were less likely, or as likely, to develop into seeds. Hybrid zygotes survived as frequently or more than local zygotes, and pollen from one of the populations fertilized most ovules in both populations. Our results thus indicate strong maternal discrimination against selfing, whereas the success of outbreeding seems mostly affected by divergent pollen performance. The implications for the evolution of maternal mate choice are discussed.     

Inbreeding depression and selfing rates in a self-compatible,hermaphroditic species,Schiedea membranacea (Caryophyllaceae)

Inbreeding depression and selfing rates were investigated in Schiedea membranacea (Caryophyllaceae), a hermaphroditic species endemic to the Hawaiian Islands. Most theoretical models predict high inbreeding depression in outcrossing hermaphroditic species and low inbreeding depression in inbreeding species. Although high outcrossing rates and high levels of inbreeding depression are characteristic of many species of Schiedea, self- fertilization is common among relatives of hermaphroditic S. membranacea, and high selfing rates and low levels of inbreeding depression were predicted in this species. Sixteen individuals grown in the greenhouse were used to produce selfed and outcrossed progeny. Inbreeding depression, which was evident throughout the stages measured (percentage viable seeds per capsule, mean seed mass, percentage seed germination, percentage seedling survival, and biomass after 8 mo), averaged 0.70. Inbreeding depression among maternal families varied significantly for all measured traits and ranged from −0.12 to 0.97. Using isozyme analysis, the multilocus selfing rate varied from 0.13 to 0.38 over 4 yr. Contrary to the initial prediction of high selfing and low inbreeding depression based on phylogenetic relationships within Schiedea, low selfing rates and high levels of inbreeding depression were found in S. membranacea. These results indicate that outcrossing is stable in this species and maintained by high levels of inbreeding depression.     

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.     

Sex among the flowers: the distribution of plant mating systems

Previous reviews of plant outcrossing rate survey data have agreed that predominant selfing and predominant outcrossing are alternative stable states of mating system evolution. We reanalyzed the most recent data and plot outcrossing rates as a continuous variable rather than as a class variable. Wind-pollinated species are indeed bimodal. However, the shape of the distributions for animal-pollinated species reveals that intermediate rates of outcrossing are common (49% of species fall between 20% and 80% outcrossing). Consequently, we suggest that mating system is best considered a continuous rather than a discrete character of plant populations.     

Severe outbreeding and inbreeding depression maintain mating system differentiation in Epipactis (Orchidaceae)

In hermaphroditic plants, theory for mating system evolution predicts that populations will evolve to either complete autonomous selfing (AS) or complete outcrossing, depending on the balance between automatic selection favouring self‐fertilization and costs resulting from inbreeding depression (ID). Theory also predicts that selection for selfing can occur rapidly and is driven by purging of genetic load and the loss of ID. Therefore, selfing species are predicted to have low levels of ID or even to suffer from outbreeding depression (OD), whereas predominantly outcrossing species are expected to have high levels of ID. To test these predictions, we related the capacity of AS to the magnitude of early‐acting inbreeding or OD in both allogamous and autogamous species of the orchid genus Epipactis. For each species, the level of AS was assessed under controlled greenhouse conditions, whereas hand‐pollinations were performed to quantify early costs of inbreeding or OD acting at the level of fruit and seed production. In the autogamous species, the capacity of AS was high (> 0.72), whereas in the allogamous species AS was virtually absent (< 0.10). Consistent with our hypothesis, allogamous Epipactis species had significantly higher total ID (average: 0.46) than autogamous species, which showed severe costs of OD (average: ?0.45). Overall, our findings indicate that strong early‐acting ID represents an important mechanism that contributes to allogamy in Epipactis, whereas OD may maintain selfing in species that have evolved to complete selfing.     

Gender variation and the evolution of dioecy in Wurmbea dioica (Liliaceae)

A major obstacle for empirical tests of hypotheses concerning the evolution of dioecy in flowering plants is the limited number of species that possess both cosexual and dioecious populations. Wurmbea dioica (Liliaceae) is a diminutive, fly-pollinated geophyte native to temperate Australia. Marked geographical variation of floral traits is evident, particularly with respect to sex expression. A survey of phenotypic gender in 45 populations from Western Australia (WA), South Australia (SA), Victoria (Vic) and the Australian Capital Territory (ACT) revealed two contrasting patterns. Populations in SA, Vic, and ACT were uniformly dimorphic for gender, containing female and male plants, whereas populations in WA were either monomorphic or dimorphic. In most dimorphic populations varying numbers of male plants produced hermaphrodite flowers (male inconstancy). There was a significant negative relationship between female frequency and the proportion of inconstant male plants. Depending on region and population, male plants produced more flowers of larger size than females. In WA monomorphic populations often occurred on rich, moist soils at high density, whereas dimorphic populations were more commonly found at lower density on shallow soils in drier areas. In an area of sympatry, plants with contrasting sexual systems flowered at different times and were ecologically differentiated. The patterns of gender variation in W. dioica indicate that dioecy has evolved via the gynodioecious pathway. The spread of females in monomorphic populations may be favoured where ecological conditions result in increased selfing and inbreeding depression in hermaphrodites.     

Pollen transfer dynamics and the evolution of gametophytic self-incompatibility

Recent studies of mating system evolution have attempted to include aspects of pollination biology in analysis of both theoretical models and experimental systems. In light of this growing trend, we propose a simple population genetic model for the evolution of gametophytic self-incompatibility, incorporating parameters for pollen discounting and pollen export/capture. In this model, we consider several cases that span the spectrum for dominance of the mutant self-incompatibility allele and for the degree of incompatibility conferred by the allele. We confirm earlier results that inbreeding depression is required for successful invasion of the self-incompatibility allele and we demonstrate that, unless pollen discounting is very low, the level of inbreeding depression must be very high for an allele conferring self-incompatibility to become established. Finally, we show that the dominance of the mutant allele has a greater impact on the fate of a newly arisen self-incompatibility allele than the strength of the incompatibility conferred by the allele. In particular, the more recessive the self-incompatibility expression in heterozygote stigmas and the weaker the response induced, the easier it is for a self-incompatibility allele to invade.     

Analysis of inbreeding depression in mixed-mating plants provides evidence for selective interference and stable mixed mating

Hermaphroditic individuals can produce both selfed and outcrossed progeny, termed mixed mating. General theory predicts that mixed-mating populations should evolve quickly toward high rates of selfing, driven by rapid purging of genetic load and loss of inbreeding depression (ID), but the substantial number of mixed-mating species observed in nature calls this prediction into question. Lower average ID reported for selfing than for outcrossing populations is consistent with purging and suggests that mixed-mating taxa in evolutionary transition will have intermediate ID. We compared the magnitude of ID from published estimates for highly selfing (r > 0.8), mixed-mating (0.2 ≤ r ≥ 0.8), and highly outcrossing (r < 0.2) plant populations across 58 species. We found that mixed-mating and outcrossing taxa have equally high average lifetime ID (δ= 0.58 and 0.54, respectively) and similar ID at each of four life-cycle stages. These results are not consistent with evolution toward selfing in most mixed-mating taxa. We suggest that prevention of purging by selective interference could explain stable mixed mating in many natural populations. We identify critical gaps in the empirical data on ID and outline key approaches to filling them.     

Inbreeding depression in two species of Mimulus (Scrophulariaceae) with contrasting mating systems

We examined the effect of self- and cross-pollination on germination success, flowering probability, pollen and ovule production, survivorship, and adult aboveground biomass in two species of Mimulus with contrasting mating systems: the highly seifing M. micranthus and an outcrossing population of M. guttatus. Cross-pollinations were performed both within and between populations in order to examine the scale at which the genetic load is distributed. We found significant inbreeding depression in M. guttatus in four of the six traits, with the highest inbreeding depression observed in biomass (68% and 69% based on within- and between-population crosses, respectively) and lowest in ovule production (21% based on between-population crosses only). M. micranthus displayed significant inbreeding depression in only two of the six traits examined. Again, we observed the highest inbreeding depression in biomass (47–60% based on within- and between-population crosses, respectively), but both traits showing significant differences between self and outcross progeny expressed lower inbreeding depression than in M. guttatus. We detected no significant inbreeding depression for either pollen or ovule production in M. micranthus. An estimate of total inbreeding depression based on the multiplicative effects of all traits was also lower in M. micanthus than∗∗∗ in M. guttatus. Our results are consistent with the expected purging of genetic load in populations with high selfing rates. The absence of inbreeding depression in M. micranthus pollen and ovule production, two traits with strong links to fitness in a selfing annual, further suggests the important role of directional selection in determining the population's genetic load. Comparison of cross-pollinations made within and between populations revealed little evidence of divergence of genetic load among the M. micranthus and M. guttatus populations examined.     

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.     

Exploring the genetic basis and proximate causes of female fertility advantage in gynodioecious Thymus vulgaris

In many gynodioecous species, females produce more viable seeds than hermaphrodites. Knowledge of the relative contribution of inbreeding depression in hermaphrodites and maternal sex effects to the female fertility advantage and the genetic basis of variation in female fertility advantage is central to our understanding of the evolution of gender specialization. In this study we examine the relative contribution of inbreeding and maternal sex to the female fertility advantage in gynodioecious Thymus vulgaris and quantify whether there is genetically based variation in female fertility advantage for plants from four populations. Following controlled self and outcross (sib, within-population, and between-population) pollination, females had a more than twofold fertility advantage (based on the number of germinating seeds per fruit), regardless of the population of origin and the type of pollination. Inbreeding depression on viable seed production by hermaphrodites occurred in two populations, where inbreeding had been previously detected. Biparental inbreeding depression on viable seed production occurred in three of four populations for females, but in only one population for hermaphrodites. Whereas the maternal sex effect may consistently enhance female fertility advantage, inbreeding effects may be limited to particular population contexts where inbreeding may occur. A significant family x maternal sex interaction effect on viable seed production was observed, illustrating that the extent of female fertility advantage varies significantly among families. This result is due to greater variation in hermaphrodite (relative to female) seed fertility between families. Despite this genetic variation in female fertility advantage and the highly female biased sex ratios in populations of T. vulgaris, gynodioecy is a stable polymorphism, suggesting that strong genetic and/or ecological constraints influence the stability of this polymorphism.     

Anther-stigma separation is associated with inbreeding depression in Datura stramonium,a predominantly self-fertilizing annual

Abstract.— Genetically based variation in outcrossing rate generates lineages within populations that differ in their history of inbreeding. According to some models, mating-system modifiers in such populations will demonstrate both linkage and identity disequilibrium with fitness loci, resulting in lineage-specific inbreeding depression. Other models assert that differences among families in levels of inbreeding depression are mainly attributable to random accumulation of genetic load, unrelated to variation at mating-system loci. We measured female reproductive success of selfed and outcrossed progeny from naturally occurring lineages of Datura stramonium , a predominantly self-fertilizing annual weed that has heritable variation in stigma-anther separation, a trait that influences selfing rates. Progeny from inbred lineages (as identified by high degree of anther-stigma overlap) showed equal levels of seed production, regardless of cross type. Progeny from mixed lineages (as identified by relatively high separation between anthers and stigma) showed moderate levels of inbreeding depression. We found a significant correlation between anther-stigma separation and relative fitness of selfed and outcrossed progeny, suggesting that family-level inbreeding depression may be related to differences among lineages in inbreeding history in this population. Negative inbreeding depression in putatively inbred lineages may be due in part to additive effects or to epistatic interactions among loci.     

Inbreeding avoidance and female mate choice shape reproductive skew in capuchin monkeys (Cebus capucinus imitator)

Reproductive skew in multimale groups may be determined by the need for alpha males to offer reproductive opportunities as staying incentives to subordinate males (concessions), by the relative fighting ability of the alpha male (tug‐of‐war) or by how easily females can be monopolized (priority‐of‐access). These models have rarely been investigated in species with exceptionally long male tenures, such as white‐faced capuchins, where female mate choice for novel unrelated males may be important in shaping reproductive skew. We investigated reproductive skew in white‐faced capuchins at Sector Santa Rosa, Costa Rica, using 20 years of demographic, behavioural and genetic data. Infant survival and alpha male reproductive success were highest in small multimale groups, which suggests that the presence of subordinate males can be beneficial to the alpha male, in line with the concession model's assumptions. None of the skew models predicted the observed degree of reproductive sharing, and the probability of an alpha male producing offspring was not affected by his relatedness to subordinate males, whether he resided with older subordinate males, whether he was prime aged, the number of males or females in the group or the number of infants conceived within the same month. Instead, the alpha male's probability of producing offspring decreased when he was the sire of the mother, was weak and lacked a well‐established position and had a longer tenure. Because our data best supported the inbreeding avoidance hypothesis and female choice for strong novel mates, these hypotheses should be taken into account in future skew models.     

Evolution of Inbreeding and Outcrossing in Ferns and Fern-Allies

Abstract Mating systems of 18 species of homosporous ferns follow a bimodal distribution, similar to that observed for seed plants (Schemske and Lande, 1985). Most species are highly outcrossing, a few are inbreeding, and two species examined to date have mixed mating systems. Equisetum arvense and several species of lycopods are also highly outcrossing. Several mechanisms, including inbreeding depression, antheridiogen, and ontogenetic sequences that result in effectively unisexual gametophytes, promote outcrossing in homosporous ferns and perhaps other homosporous pteridophytes as well. In some species of homosporous ferns, selection has favored the evolution of inbreeding as an adaptation for colonization. High levels of intra- and interpopulational gene flow via spore dispersal, coupled with high levels of intergametophytic crossing, generally lead to genetically homogeneous populations and species of homosporous ferns. However, rock-dwelling ferns and ferns from xeric habitats may exhibit significant population genetic structure due to physically patchy habitats. Reticulate evolution in homosporous ferns may be enhanced by high levels of intergametophytic crossing.     

Environmental stress and the evolution of dioecy: Wurmbea dioica (Colchicaceae) in Western Australia

Stressful ecological conditions have been implicated in the evolution of separate sexes in plants. Gender dimorphic species are often found in drier habitats than their sexually monomorphic relatives, and gynodioecious populations appear closer to a dioecious state as resources, particularly water, become limiting. This pattern could result if dry conditions decrease the relative seed fitness of cosexual plants, allowing female plants to become established in monomorphic populations. We studied geographical variation in gender expression and biomass allocation among 12 monomorphic and dimorphic populations of Wurmbea dioica along a latitudinal precipitation gradient in southwestern Australia to provide insight into mechanisms by which aridity might favor transitions between sexual systems. Plants in monomorphic and dimorphic populations exhibited contrasting gender expression and patterns of biomass allocation in areas with different levels of precipitation. Among dimorphic populations, lower precipitation was associated with a higher frequency of female plants, and reduced allocation to female function by hermaphrodites during flowering. In contrast, stress conditions had no effect on female allocation at flowering in monomorphic populations. Across latitudes, unisexuals and cosexuals exhibited consistent differences in above ground traits, with cosexuals having larger leaves, taller stems and larger flowers. Although all plants were smaller under drier conditions, cosexuals decreased above ground allocation to vegetative and reproductive structures with decreasing latitude. In contrast, unisexuals increased allocation to reproduction in drier areas at the expense of below ground size. Aridity was associated with reduced flower size among all gender classes, but not with changes in flower number. These data do not support the hypothesis that resource limitation of female allocation in cosexual populations favors the establishment of gender dimorphism in W. dioica. Alternative hypotheses, involving higher selfing rates and enhanced survival of unisexuals relative to cosexuals under resource-limited conditions, are discussed as possible explanations for the origin of dioecy in W. dioica. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effects of biparental inbreeding on the evolution of gynodioecy: A model and a case study inChionographis japonica var.kurohimensis

To examine the evolution of gynodioecy under biparental inbreeding, we developed a new theoretical model and tested it by estimating paramaeters incorporated in the model in a gynodioecious population ofChionographis japonica var.kurohimensis. The model and the results showed biparental inbreeding affects the evolution of gynodioecy, but the effect is very small.