TESTING MODELS OF SEX RATIO EVOLUTION IN A GYNODIOECIOUS PLANT: FEMALE FREQUENCY COVARIES WITH THE COST OF MALE FERTILITY RESTORATION

In many gynodioecious species, cytoplasmic male sterility genes (CMS) and nuclear male fertility restorers (Rf) jointly determine whether a plant is female or hermaphrodite. Equilibrium models of cytonuclear gynodioecy, which describe the effect of natural selection within populations on the sex ratio, predict that the frequency of females in a population will primarily depend on the cost of male fertility restoration, a negative pleiotropic effect of Rf alleles on hermaphrodite fitness. Specifically, when the cost of restoration is higher, the frequency of females at equilibrium is predicted to be higher. To test this prediction, we estimated variation in the cost of restoration across 26 populations of Lobelia siphilitica, a species in which Rf alleles can have negative pleiotropic effects on pollen viability. We found that L. siphilitica populations with many females were more likely to contain hermaphrodites with low pollen viability. This is consistent with the prediction that the cost of restoration is a key determinant of variation in female frequency. Our results suggest that equilibrium models can explain variation in sex ratio among natural populations of gynodioecious species.     

Modeling gynodioecy: novel scenarios for maintaining polymorphism

Nuclear-cytoplasmic gynodioecy is a breeding system of plants in which females and hermaphrodites co-occur in populations, and gender is jointly determined by cytoplasmic male sterility (CMS) genes and nuclear restorers of male fertility. Persistent polymorphism at both CMS and nuclear-restorer loci is necessary to maintain this breeding system. Theoretical models have explained how nuclear-cytoplasmic gynodioecy can be stable for certain assumptions. However, recent advances in our understanding of the genetics, population biology, and molecular mechanisms of sex determination in nuclear-cytoplasmic gynodioecious species suggest the utility of new models with different underlying assumptions. In this article, we examine different negative pleiotropic fitness effects of nuclear restorers (costs of restoration) using genetic and population assumptions based on recent literature. Specifically, we model populations with two CMS types and separate nuclear restorer loci for each CMS type. Under these assumptions, both overdominance for fitness and frequency-dependent selection at nuclear-restorer loci can support nuclear-cytoplasmic gynodioecy. Costs of restoration can be either dependent or independent of the cytoplasmic background. Seed fitness costs are more vulnerable to fixation of CMS types than pollen costs. Survivorship costs are effective at maintaining polymorphism even when total reproductive effects are low. Overall, our models display differences in the stability of nuclear-cytoplasmic gynodioecy and predicted population sex ratios that should be informative to researchers studying gynodioecy in the wild.     

Sex‐specific fitness variation in gynodioecious Beta vulgaris ssp. maritima: do empirical observations fit theoretical predictions?

In gynodioecious species, in which hermaphroditic and female plants co-occur, the maintenance of sexual polymorphism relies on the genetic determination of sex and on the relative fitness of the different phenotypes. Flower production, components of male fitness (pollen quantity and pollen quality) and female fitness (fruit and seed set) were measured in gynodioecious Beta vulgaris spp. maritima, in which sex is determined by interactions between cytoplasmic male sterility (CMS) genes and nuclear restorers of male fertility. The results suggested that (i) female had a marginal advantage over hermaphrodites in terms of flower production only, (ii) restored CMS hermaphrodites (carrying both CMS genes and nuclear restorers) suffered a slight decrease in fruit production compared to non-CMS hermaphrodites and (iii) restored CMS hermaphrodites were poor pollen producers compared to non-CMS hermaphrodites, probably as a consequence of complex determination of restoration. These observations potentially have important consequences for the conditions of maintenance of sexual polymorphism in B. vulgaris and are discussed in the light of existing theory on evolutionary dynamics of gynodioecy.     

Disentangling the causes of heterogeneity in male fecundity in gynodioecious Beta vulgaris ssp. maritima

Variation among individuals in reproductive success is advocated as a major process driving evolution of sexual polymorphisms in plants, such as gynodioecy where females and hermaphrodites coexist. In gynodioecious Beta vulgaris ssp. maritima, sex determination involves cytoplasmic male sterility (CMS) genes and nuclear restorers of male fertility. Both restored CMS and non-CMS hermaphrodites co-occur. Genotype-specific differences in male fitness are theoretically expected to explain the maintenance of cytonuclear polymorphism. Using genotypic information on seedlings and flowering plants within two metapopulations, we investigated whether male fecundity was influenced by ecological, phenotypic and genetic factors, while taking into account the shape and scale of pollen dispersal. Along with spatially restricted pollen flow, we showed that male fecundity was affected by flowering synchrony, investment in reproduction, pollen production and cytoplasmic identity of potential fathers. Siring success of non-CMS hermaphrodites was higher than that of restored CMS hermaphrodites. However, the magnitude of the difference in fecundity depended on the likelihood of carrying restorer alleles for non-CMS hermaphrodites. Our results suggest the occurrence of a cost of silent restorers, a condition supported by scarce empirical evidence, but theoretically required to maintain a stable sexual polymorphism in gynodioecious species.     

Consequences of inbreeding for offspring fitness and gender in Silene vulgaris,a gynodioecious plant

Abstract In gynodioecious plants, hermaphrodite and female plants co‐occur in the same population. In these systems gender typically depends on whether a maternally inherited cytoplasmic male sterility factor (CMS) is counteracted by nuclear restorer alleles. These restorer alleles are often genetically dominant. Although plants of the female morph are obligatorily outcrossing, hermaphrodites may self. This selfing increases homozygosity and may thus have two effects: (1) it may decrease fitness (i.e. result in inbreeding depression) and (ii) it may increase homozygosity of the nuclear restorer alleles and therefore increase the production of females. This, in turn, enhances outcrossing in the following generation. In order to test the latter hypothesis, experimental crosses were conducted using individuals derived from four natural populations of Silene vulgaris, a gynodioecious plant. Treatments included self‐fertilization of hermaphrodites, outcrossing of hermaphrodites and females using pollen derived from the same source population as the pollen recipients, and outcrossing hermaphrodites and females using pollen derived from different source populations. Offspring were scored for seed germination, survivorship to flowering and gender. The products of self‐fertilization had reduced survivorship at both life stages when compared with the offspring of outcrossed hermaphrodites or females. In one population the fitness of offspring produced by within‐population outcrossing of females was significantly less than the fitness of offspring produced by crossing females with hermaphrodites from other populations. Self‐fertilization of hermaphrodites produced a smaller proportion of hermaphroditic offspring than did outcrossing hermaphrodites. Outcrossing females within populations produced a smaller proportion of hermaphrodite offspring than did crossing females with hermaphrodites from other populations. These results are consistent with a cytonuclear system of sex determination with dominant nuclear restorers, and are discussed with regard to how the mating system and the genetics of sex determination interact to influence the evolution of inbreeding depression.     

Relative fitness of females and hermaphrodites in a natural gynodioecious population of wild radish,Raphanus sativus L. (Brassicaceae): comparison based on molecular genotyping

In many gynodioecious species, sex determination involves both cytoplasmic male‐sterility (CMS) genes and nuclear genes that restore male function. Differences in fitness among genotypes affect the dynamics of those genes, and thus that of gynodioecy. We used a molecular marker to discriminate between hermaphrodites with and without a CMS gene in gynodioecious Raphanus sativus. We compared fitness through female function among the three genotypes: females, hermaphrodites with the CMS gene and those without it. Although there was no significant difference among the genotypes in seed size, hermaphrodites without the CMS gene produced significantly more seeds, and seeds with a higher germination rate than the other genotypes, suggesting no fitness advantage for females and no benefit to bearing the CMS gene. Despite the lack of fitness advantage for females in the parameter values we estimated, a theoretical model of gynodioecy shows it can be maintained if restorer genes impose a cost paid in pollen production. In addition, we found that females invest more resources into female reproduction than hermaphrodites when they become larger. If environmental conditions enable females to grow larger this would facilitate the dynamics of CMS genes.     

Variation in pollen production and pollen viability in natural populations of gynodioecious Beta vulgaris ssp. maritima: evidence for a cost of restoration of male function?

Gynodioecious species are defined by the co-occurrence of two clearly separated categories of plants: females and hermaphrodites. The hermaphroditic category may, however, not be homogeneous, as male fitness may vary among hermaphrodites as a result of many biological factors. In this study, we analysed estimates of pollen quantity and viability in the gynodioecious Beta vulgaris ssp. maritima, comparing hermaphrodites bearing a male-fertile cytotype and hermaphrodites bearing cytoplasmic male sterility (CMS) genes, which are counteracted by nuclear restoration factors. We show that: (i) pollen quantity continuously varies among restored hermaphrodites, suggesting a complex genetic determination of nuclear restoration; (ii) pollen viability was lower in restored (CMS) hermaphrodites than in non-CMS hermaphrodites, probably because of incomplete restoration in some of these plants; and (iii) pollen quantity and viability also varied among hermaphrodites with male-fertile cytotypes, possibly a result of a silent cost of restoration. Finally, we discuss the consequences of these results for pollen flow and the dynamics of gynodioecy.     

Effects of fine‐scale genetic structure on male mating success in gynodioecious Beta vulgaris ssp. maritima

Plant mating systems are known to influence population genetic structure because pollen and seed dispersal are often spatially restricted. However, the reciprocal outcomes of population structure on the dynamics of polymorphic mating systems have received little attention. In gynodioecious sea beet (Beta vulgaris ssp. maritima), three sexual types co‐occur: females carrying a cytoplasmic male sterility (CMS) gene, hermaphrodites carrying a non‐CMS cytoplasm and restored hermaphrodites that carry CMS genes and nuclear restorer alleles. This study investigated the effects of fine‐scale genetic structure on male reproductive success of the two hermaphroditic forms. Our study population was strongly structured and characterized by contrasting local sex‐ratios. Pollen flow was constrained over short distances and depended on local plant density. Interestingly, restored hermaphrodites sired significantly more seedlings than non‐CMS hermaphrodites, despite the previous observation that the former produce pollen of lower quality than the latter. This result was explained by the higher frequency of females in the local vicinity of restored (CMS) hermaphrodites as compared to non‐CMS hermaphrodites. Population structure thus strongly influences individual fitness and may locally counteract the expected effects of selection, suggesting that understanding fine scale population processes is central to predicting the evolution of gender polymorphism in angiosperms.     

Local population structure and sex ratio: evolution in gynodioecious plants

Although the influence of population structure on evolution has been explored previously in a variety of theoretical studies, there are few examples of specific traits whose fitness is likely to be modified by the local structure. Here we focus on a specific trait, sex expression in gynodioecious plants, and derive a model in which the fitness of females and hermaphrodites is a function of the local sex ratio. By using the concept d genes. As a consequence, when local demes vary in sex ratio, a polymorphism for a cytoplasmic male sterility (CMS) allele can be maintained in the absence of nuclear alleles that restore male function. When of subjective frequencies, it is shown that among-deme variance in the local sex ratio reduces the average fitness of females when pollen availability limits fertility. In contrast, sex ratio variance increases the fitness of hermaphrodites from the perspective of maternally inherited genes and lessens the negative impact of pollen limitation on hermaphrodite fitness when it is measured from the perspective of biparentally inheriterestorer alleles are introduced into the model, polymorphism cannot be maintained simultaneously at both the cytoplasmic and nuclear loci. In that case, the CMS allele spreads to fixation, and the equilibrium frequency of females is an inverse function of the equilibrium frequency of the restorer allele, which increases with increased structure. The results exemplify how population structure can greatly alter the fitness and evolution of a frequency-dependent trait.     

Evidence of restoration cost in the annual gynodioecious Phacelia dubia

A negative pleiotropic effect on fitness of nuclear sex‐determining genes (cost of restoration) could explain nuclear–cytoplasmic gynodioecy but rarely has been demonstrated empirically. In a gynodioecious Phacelia dubia population, maternal lineages produce only hermaphroditic progenies irrespective of the pollen parent (N) or can segregate females (S). Natural progenies of N maternal plants had lower seed viability than that of S. Full‐sib progenies of unrelated hermaphrodites from all possible matings between N and S lineages had similar pollen filling but differed in sporophyte performance, mainly at seed germination stage. A discrete multivariate analysis reveals that the performance of N_♀ × S_♂ progeny at early stages of development was significantly lower than that of the other three types of mating in agreement with the silent‐cost‐of‐restoration hypothesis, affecting the sporophyte. The restoration cost and male sterility appear to be dominant and consequence of nuclear–cytoplasmic incompatibilities that may maintain nuclear–cytoplasmic polymorphism by frequency‐dependent selection.     

Paternal leakage sustains the cytoplasmic polymorphism underlying gynodioecy but remains invasible by nuclear restorers

Cytoplasmic male sterility (CMS) in plants often results in gynodioecious populations, composed of hermaphrodites and male-sterile females. All models of gynodioecy assume maternal inheritance of the cytoplasmic alleles and postulate a variety of negatively frequency-dependent mechanisms to maintain the cytoplasmic polymorphisms observed in many natural populations. However, in some plant species, mitochondria are transmitted at least occasionally by pollen, a process called paternal leakage. We show that even a small amount of paternal leakage is sufficient to sustain a permanent, stable cytoplasmic polymorphism. Because only hermaphrodites provide pollen in gynodioecious species, the effects of paternal leakage are biased and occur more often from the non-CMS male-fertile haplotype to the CMS male-sterile haplotype. We also show that a nuclear restorer disrupts the polymorphic cytoplasmic equilibrium, leading to fixation of both the CMS allele and the restorer. Although a dominant nuclear restorer fixes, it fixes much more slowly than in the standard CMS models. Although a stable cytonuclear polymorphism is possible with "matching alleles" nuclear restoration, oscillations to low frequencies present a risk of loss by drift. Paternal leakage enhances the stability of joint cytonuclear polymorphism by reducing the chance that a CMS allele is lost by drift.     

Effects of CMS types and restorer alleles on plant performance in Plantago lanceolata L.: an indication for cost of restoration

In gynodioecious species, male steriles co-occur with hermaphrodites. Usually, the male sterile trait is maternally inherited, hence it is called Cytoplasmic Male Sterility (CMS). Nuclear loci restore male fertility in combination with their ‘own’ specific cytoplasmic types. In theory, two fitness components are important for the maintenance of this breeding system: a fitness advantage of the male steriles, and costs of restoration. The costs of restoration are alleged negative pleiotropic effects of restorer alleles. In this study the effects of different CMS types on plant performance and the cost of restoration were assessed in two experiments with Plantago lanceolata L. Biomass production differed significantly between the CMS types studied. In order to assess the costs of restoration, hermaphrodites with or without restorer alleles for a CMS type other than its own were compared. The studied restorer alleles caused a reduction in weight per seed, but the number of seeds produced was unaffected. The estimated cost of restoration measured as reduction of seed biomass was 13% for restorer alleles for CMSI. However, in the second experiment no pleiotropic effects of restorer alleles were detected, either because the assumptions for the experimental set-up were not valid or the costs of restoration may not always be expressed.     

HOW SELFING,INBREEDING DEPRESSION,AND POLLEN LIMITATION IMPACT NUCLEAR‐CYTOPLASMIC GYNODIOECY: A MODEL

Gynodioecy, the co‐occurrence of females and hermaphrodites, is often due to conflicting interactions between cytoplasmic male sterility genes and nuclear restorers. Although gynodioecy often occurs in self‐compatible species, the effect of self‐pollination, inbreeding depression, and pollen limitation acting differently on females and hermaphrodites remains poorly known in the case of nuclear‐cytoplasmic gynodioecy (NCG). In this study, we model NCG in an infinite population and we study the effect of selfing rate, inbreeding depression, and pollen limitation on the maintenance of gynodioecy and on sex ratios at equilibrium. We found that selfing and inbreeding depression have a strong impact, which depends on whether restorer cost acts on male or female fitness. When cost affects male fitness, the strength of cost has no effect, whereas selfing and inbreeding depression only impact gynodioecy by modifying the value of the female advantage. When cost affects female fitness, selfing facilitates NCG and reduces the role of strength of the cost, even when no inbreeding depression occurs, whereas inbreeding depression globally restricts the maintenance of the polymorphism. Finally, we found that pollen limitation could additionally strongly modify the dynamic of gynodioecy. We discuss our findings in the light of empirical data available in gynodioecious species.     

Testing why the sex of the maternal parent affects seedling survival in a gynodioecious species

In gynodioecious plants, seed offspring from hermaphrodites often perform less well than those from females. This lower performance sometimes can be attributed to inbreeding by hermaphrodites or to relatively greater provisioning of individual seeds by females. However, these hypotheses are not explanatory when only outcrossing occurs and when individual seeds of the two morphs are equally well provisioned. Three hypotheses may explain the lower fitness of seed offspring from hermaphrodites in such cases. The morphology hypothesis states that the opportunity for gametophytic selection is lower within flowers of hermaphrodites compared to flowers on females, because the perfect flowers of hermaphrodites are relatively short-styled. The cytotype hypothesis states that the performance difference is directly caused by an individual's cytotype, whose frequency in the population may differ for the two sex morphs. The pleiotropy hypothesis states that negative pleiotropic effects of nuclear restorer alleles or alleles hitchhiking with them are expressed more often by offspring from hermaphrodites. We performed two experiments using the gynodioecious plant Silene acaulis to contrast these hypotheses. In our first experiment we contrasted the morphology and pleiotropy hypotheses by performing controlled pollinations and subsequently planting seeds in both the greenhouse and field. Hermaphrodites of S. acaulis can produce both pistillate and perfect flowers, which allowed us to determine whether flower morphology affects offspring survivorship independent of the sex of the maternal parent. We found that neither seed mass nor germination differed between seeds from females and hermaphrodites. Offspring from pistillate flowers on hermaphrodites did not differ significantly in their survival compared to offspring from perfect flowers on hermaphrodites, but had lower survivorship compared to offspring from pistillate flowers on females, refuting the morphology hypothesis. In a second experiment, we compared offspring survival of full-sibling pairs of females and hermaphrodites (who shared the same cytoplasm) to contrast the cytotype and pleiotropy hypotheses. We found that seed offspring from females and hermaphrodites that shared the same cytoplasm differed in their survival, which is counter to the prediction of the cytotype hypothesis. In both experiments, the sex of the maternal parent significantly affected offspring survival, with seed offspring from hermaphrodites surviving less well than those from females. These results support the pleiotropy hypothesis. We conclude by discussing alternative ways of thinking about negative pleiotropic effects of nuclear restorers or "the cost of restoration."     

A field guide to models of sex-ratio evolution in gynodioecious species

Gynodioecious plant species, species in which individuals are females or hermaphrodites, are ideal systems for studying connections between genetics, ecology, and long‐term evolutionary changes because sex determination can be complex, involving cytoplasmic and/or nuclear genes, and sex ratio is often variable across landscapes. Field data are needed to evaluate the many theories concerning this breeding system. In order to facilitate the gathering of relevant data, this paper introduces the four types of gynodiocy (nuclear, nuclear‐cytoplasmic and stochastic gynodioecy plus subdioecy), describes example species and expected patterns, discusses the various forces that drive the evolution of female frequencies, and gives concrete advice on where to start collecting data for different systems. For species in which females are relatively rare, we recommend reciprocal crosses to determine if sex‐determination is nuclear or nuclear‐cytoplasmic along with a search for correlations between female frequencies and ecological factors. For species in which females are common and sex ratios are highly variable, we recommend looking at female offspring sex ratios to determine if females are primarily produced in ephemeral epidemics. In the course of this discussion, we argue that the majority of natural gynodioecious species will have complex sex determination in which multiple cytoplasmic male sterility (CMS) genes interact with multiple nuclear restorers of fertility. Sex‐ratio evolution in such species will be primarily influenced by fitness differences among hermaphrodites (costs of restoration) and less influenced by fitness differences between the sexes (compensation). Metapopulation dynamics alone may explain population sex ratios of species in which females are associated with marginal environments or hybrid zones; however, we feel that in most cases equilibrium forces within populations and metapopulation dynamics among populations each explain portions of the sex‐ratio pattern.     

Inbreeding effects on progeny sex ratio and gender variation in the gynodioecious Silene vulgaris (Caryophyllaceae)

In gynodioecious species, sex expression is generally determined through cytoplasmic male sterility genes interacting with nuclear restorers of the male function. With dominant restorers, there may be an excess of females in the progeny of self-fertilized compared with cross-fertilized hermaphrodites. Moreover, the effect of inbreeding on late stages of the life cycle remains poorly explored. Here, we used hermaphrodites of the gynodioecious Silene vulgaris originating from three populations located in different valleys in the Alps to investigate the effects of two generations of self- and cross-fertilization on sex ratio and gender variation. We detected an increase in females in the progeny of selfed compared with outcrossed hermaphrodites and inbreeding depression for female and male fertility. Male fertility correlated positively with sex ratio differences between outbred and inbred progeny, suggesting that dominant restorers are likely to influence male fertility qualitatively and quantitatively in S. vulgaris. We argue that the excess of females in the progeny of selfed compared with outcrossed hermaphrodites and inbreeding depression for gamete production may contribute to the maintenance of females in gynodioecious populations of S. vulgaris because purging of the genetic load is less likely to occur.     

Sex-ratio evolution in nuclear-cytoplasmic gynodioecy when restoration is a threshold trait

Gynodioecious plant species, which have populations consisting of female and hermaphrodite individuals, usually have complex sex determination involving cytoplasmic male sterility (CMS) alleles interacting with nuclear restorers of fertility. In response to recent evidence, we present a model of sex-ratio evolution in which restoration of male fertility is a threshold trait. We find that females are maintained at low frequencies for all biologically relevant parameter values. Furthermore, this model predicts periodically high female frequencies (>50%) under conditions of lower female seed fecundity advantages (compensation, x = 5%) and pleiotropic fitness effects associated with restorers of fertility (costs of restoration, y = 20%) than in other models. This model explains the maintenance of females in species that have previously experienced invasions of CMS alleles and the evolution of multiple restorers. Sensitivity of the model to small changes in cost and compensation values and to initial conditions may explain why populations of the same species vary widely for sex ratio.     

Fine scale spatial structuring of sex and mitochondria in Silene vulgaris

Fine scale spatial structure (FSSS) of cytoplasmic genes in plants is thought to be generated via founder events and can be amplified when seeds germinate close to their mother. In gynodioecious species these processes are expected to generate FSSS in sex ratio because maternally inherited cytoplasmic male sterility genes partially influence sex expression. Here we document a striking example of FSSS in both mitochondrial genetic markers and sex in roadside populations of Silene vulgaris. We show that in one population FSSS of sexes influences relative fruit production of females compared to hermaphrodites. Furthermore, FSSS in sex ratio is expected to persist into future generations because offspring sex ratios from females are female-biased whereas offspring sex ratios from hermaphrodites are hermaphrodite-biased. Earlier studies indicated that pollen limitation is the most likely mechanism underlying negative frequency dependent fitness of females. Our results support the theoretical predictions that FSSS in sex ratio can reduce female fitness by decreasing the frequency at which females experience hermaphrodites. We argue that the influence of FSSS on female fitness is complementary to the influence of larger scale population structure on female fitness, and that population structure at both scales will act to decrease female frequencies in gynodioecious species. Better comprehension of the spatial structure of genders and genes controlling sex expression at a local scale is required for future progress toward understanding sex ratio evolution in gynodioecious plants.     

POPULATION SEX STRUCTURE AND REPRODUCTIVE FITNESS IN GYNODIOECIOUS SIDALCEA MALVIFLORA MALVIFLORA (MALVACEAE)

The spatial distribution of females and hermaphrodites within gynodioecious populations is expected to exert considerable selective pressure on gender fitness through pollen limitation of seed set. If pollen flow is predominantly local, seed set in individual plants may be sensitive to the proximity of pollen donors; pollen limitation of seed set may occur if hermaphrodites are locally rare. Under such circumstances, female fitness will be negatively frequency dependent and hermaphrodite fitness will be positively frequency dependent. Given local seed dispersal, a nonrandom clumped distribution of the genders is expected in gynodioecious populations due to the heritability of gender in gynodioecious species. If gender fitness is frequency dependent, such structure should favor hermaphrodites and select against females. To test this hypothesis, I quantified the distribution of the genders in terms of nearest neighbors and neighborhood sex ratio in two populations of gynodioecious Sidalcea malviflora malviflora. I then measured the effect of neighborhood sex ratio on open-pollinated seed set and pollen limitation in both manipulated and unmanipulated neighborhoods. Results indicate that the genders have a patchy distribution and that both genders are pollen limited and show an increase in seed set with an increase in neighborhood hermaphrodite frequency. The observed population sex structure favors hermaphrodites and disadvantages females. These results highlight the importance that population-level traits can have in determining individual fitness and the evolution of sex ratios in gynodioecious species.     

Modelling the maintenance of male-fertile cytoplasm in a gynodioecious population

Gynodioecy is the co-occurrence of females and hermaphrodites in populations. It is usually due to the combined action of cytoplasmic male sterility (CMS) genes and nuclear genes that restore male fertility. According to previous theoretical studies, it is very difficult to explain the maintenance of gynodioecy with CMS and male-fertile cytotypes, although it has been observed in some species. However, only very specific situations have been investigated so far. We present a model to investigate the conditions that promote the maintenance of this breeding system in the case of an outcrossed species when CMS and male-fertile (non-CMS) cytotypes are present in an infinite panmictic population. We show that the type of cost of restoration strongly affects the conditions for stable maintenance of gynodioecy. Stable nuclear-cytoplasmic gynodioecy requires a female advantage, which is a classical condition for gynodioecy, but also a cost of CMS for female fitness, which had been rarely investigated. A cost of restoration is also needed, which could affect either pollen or seeds. Finally, we found that gynodioecy was attainable for a large set of parameter values, including low differences in fitness among genotypes and phenotypes. Our theoretical predictions are compared with previous theoretical work and with results of empirical studies on various gynodioecious species.