THE ROLE OF ANDRODIOECY AND GYNODIOECY IN MEDIATING EVOLUTIONARY TRANSITIONS BETWEEN DIOECY AND HERMAPHRODITISM IN THE ANIMALIA

Dioecy (gonochorism) is dominant within the Animalia, although a recent review suggests hermaphroditism is also common. Evolutionary transitions from dioecy to hermaphroditism (or vice versa) have occurred frequently in animals, but few studies suggest the advantage of such transitions. In particular, few studies assess how hermaphroditism evolves from dioecy or whether androdioecy or gynodioecy should be an “intermediate” stage, as noted in plants. Herein, these transitions are assessed by documenting the numbers of androdioecious and gynodioecious animals and inferring their ancestral reproductive mode. Both systems are rare, but androdioecy was an order of magnitude more common than gynodioecy. Transitions from dioecious ancestors were commonly to androdioecy rather than gynodioecy. Hermaphrodites evolving from sexually dimorphic dioecious ancestors appear to be constrained to those with female‐biased sex allocation; such hermaphrodites replace females to coexist with males. Hermaphrodites evolving from sexually monomorphic dioecious ancestors were not similarly constrained. Species transitioning from hermaphroditic ancestors were more commonly androdioecious than gynodioecious, contrasting with similar transitions in plants. In animals, such transitions were associated with size specialization between the sexes, whereas in plants these transitions were to avoid inbreeding depression. Further research should frame these reproductive transitions in a theoretical context, similar to botanical studies.     

Gynodioecy to dioecy: are we there yet?

Background

The ‘gynodioecy–dioecy pathway’ is considered to be one of the most important evolutionary routes from hermaphroditism to separate sexes (dioecy). Despite a large accumulation of evidence for female seed fertility advantages in gynodioecious species (females and hermaphrodites coexist) in support of the first step in the gynodioecy–dioecy pathway, we still have very little evidence for the second step, i.e. the transition from gynodioecy to dioecy.

Scope

We review the literature to evaluate whether basic predictions by theory are supported. To establish whether females'' seed fertility advantage and frequencies are sufficient to favour the invasion of males, we review these for species along the gynodioecy–dioecy pathway published in the last 5 years. We then review the empirical evidence for predictions deriving from the second step, i.e. hermaphrodites'' male fertility increases with female frequency, selection favours greater male fertility in hermaphrodites in gynodioecious species, and, where males and hermaphrodites coexist with females (subdioecy), males have greater male fertility than hermaphrodites. We review how genetic control and certain ecological features (pollen limitation, selfing, plasticity in sex expression and antagonists) influence the trajectory of a population along the gynodioecy–dioecy pathway.

Conclusions

Females tend to have greater seed fertility advantages over hermaphrodites where the two coexist, and this advantage is positively correlated with female frequency across species, as predicted by theory. A limited number of studies in subdioecious species have demonstrated that males have an advantage over hermaphrodites, as also predicted by theory. However, less evidence exists for phenotypic selection to increase male traits of hermaphrodites or for increasing male function of hermaphrodites in populations with high female frequency. A few key case studies underline the importance of examining multiple components of male fertility and the roles of pollen limitation, selfing and plasticity, when evaluating advantages. We conclude that we do not yet have a full understanding of the transition from gynodioecy to dioecy.     

Sexual specialization and inbreeding avoidance in the evolution of dioecy

Dioecy has evolved independently, many times, among unrelated taxa. It also appears to have evolved along two contrasting pathways: (1) from hermaphroditism via monoecy to dioecy and (2) from hermaphroditism via gynodioecy to dioecy. Most dioecious plants have close cosexual relatives with some means of promoting outcrossing (e.g., herkogamy, dichogamy, self-incompatibility, or monoecy). To the extent that these devices prevent inbreeding, the evolution of dioecy in these species cannot logically be attributed to selection for outcrossing. In these cases, the evolution of dioecy is, we believe, due to selection for sexual specialization. However, in other species, that lack outbreeding close relatives, dioecy may have evolved from gynodioecy (males and hermaphrodites) as an outbreeding device. Subsequent disruptive selection and selection for sexual specialization may have also shaped the evolution of dioecy from gynodioecy in these species, resulting in two genetically determined, constant sex morphs. Both pathways for the evolution of dioecy require the operation of disruptive selection, though the gynodioecy route involves more restrictive disruptive selection and a genetic designation of gender. In contrast, the monoecy route is not dependent on the genetic designation of two sex morphs, but, rather, allows the possibility of sexual intermediates and sexual lability. Both pathways produce one morph in which maleness is suppressed and another in which the female function is negligible or nonexistent—the reproductive mode recognized as dioecy. Evidence is presented here to support the thesis that instances of sexual lability, the presence of an array of sexual intermediates, sex-switching, and sexual niche segregation can be explained in terms of the pathway that was taken in the evolution of a particular dioecious species. In addition, the degree of sexual dimorphism seen in dioecious species is correlated with mode of pollination (insector wind-pollinated) and other ecological factors.     

Sexual dimorphism in gender plasticity and its consequences for breeding system evolution

Flowering plants are able to develop gametes throughout their lives. As a consequence, environmental conditions can impact this development and alter a plant's functional gender or the degree to which it achieves fitness through male or female function. Two dimorphic breeding systems are widespread among angiosperm families: gynodioecy (hermaphrodites and females) and dioecy (males and females). Gynodioecy can evolve into dioecy, via loss of female function on the hermaphrodites, or it can remain stable. Here I discuss how developmental plasticity of gender can impact the sex ratio of populations and thereby influence the transition of one breeding system into another. I review studies showing that greater plasticity of fruit production by hermaphrodites as compared with females causes sex ratios among populations to vary in response to environmental conditions, with higher female frequency expected in harsh or low-quality sites. I also review how dioecy may evolve in dry sites to avoid inbreeding and any consequent inbreeding depression. Taken together, these studies show the importance of understanding how ecological development affects functional gender and consequently the evolutionary stability or malleability of dimorphic breeding systems.     

When males and hermaphrodites coexist: a review of androdioecy in animals

Androdioecy (populations consisting of males and hermaphrodites)is a rare mating system in plants and animals: up to 50 plantsand only 36 animals have been described as being androdioecious,with most of the latter being crustaceans. To date, a thoroughcomparative analysis of androdioecy in animals has not beenundertaken. Herein we present such an analysis. Androdioecyhas only been extensively surveyed in 2 animal taxa: the nematodeCaenorhabditis and the clam shrimp Eulimnadia. The other majortaxon having androdioecious species is the Cirripedia (barnacles),but there are only limited studies on androdioecy in this group.In animals, androdioecy is found either in species that havemorphologically and ecologically distinct sexes (that is, hermaphroditesand small, "complemental" males) that are derived from hermaphroditicancestors (that is, the barnacles) or in species that have similarly-sizedmales and hermaphrodites that have been derived from dioeciousancestors (the remaining androdioecious species). We suggestthat the barnacles have evolved a sexual specialization in theform of these complemental males that can more efficiently usethe constrained habitats that these barnacles often experience.For the remaining species, we suggest that androdioecy has evolvedas a response to reproductive assurance in species that experienceepisodic low densities. Additionally, we hypothesize that thedevelopment of mechanisms allowing reproductive assurance inspecies with a number of sexually differentiated traits is mostlikely to result in androdioecy rather than gynodioecy (mixturesof females and hermaphrodites), and that these species may bedevelopmentally constrained to stay androdioecious rather thanbeing capable of evolving into populations solely consistingof efficient, self-compatible hermaphrodites. We conclude bysuggesting several areas in need of further study to understandmore completely the evolution and distribution of this interestingmating system in animals.     

The evolution of gender specialization from dimorphic hermaphroditism: paths from heterodichogamy to gynodioecy and androdioecy

Several different pathways for the evolution of dioecy from hermaphroditism have been invoked and analyzed. These have largely considered either the spread of male- or female-sterility mutations in a monomorphic hermaphroditic population (i.e., the evolution of gynodioecy or androdioecy, respectively) or the gradual divergence in sex allocation of two classes of individuals, one that becomes increasingly male and the other that becomes increasingly female in functional gender (the paradioecy pathway). Here we assess the conditions under which male- or female-sterility mutations may invade and spread in a heterodichogamous population, that is, a dimorphic population composed of protandrous and protogynous individuals. Our model is formally applied to heterodichogamous populations, but the ideas we explore may also apply to the evolution of separate sexes in distylous species, where plants are either long- or short-styled. The model predicts that, under many circumstances, conditions for the evolution of gynodioecy and androdioecy in a heterodichogamous population are the same as those for their evolution from monomorphic populations. However, if one or the other of the two morphs are already somewhat specialized in their functional gender, as might occur if the quality or quantity of seed set is time dependent, the conditions for the invasion of males or females are relaxed. In particular, androdioecy can evolve more easily under such circumstances in heterodichogamous populations than in monomorphic hermaphroditic populations.     

Pollen limitation and the evolution of androdioecy from dioecy

Androdioecy is an unusual breeding system in which populations consist of separate male and hermaphrodite individuals. The evolution of androdioecy is still poorly understood; however, there is evidence from several androdioecious species that the breeding system may have evolved from dioecy (males and females). This article presents a simple deterministic model showing that androdioecy can evolve from dioecy under a broad range of realistic conditions. For the evolution of androdioecy from dioecy, hermaphrodites must be able to invade the dioecious population. Then, males must be maintained, while females are eliminated. Hermaphrodite invasion is favored when females are pollen limited and hermaphrodites have high overall fertility and are self-fertile. Male maintenance is favored when hermaphrodites resemble females, having high seed production and low pollen fitness, and when the selfing rate is not too high. These conditions were satisfied over a broad and realistic range of parameter values, suggesting that the evolution of androdioecy from dioecy is highly plausible.     

Selfish male‐determining element favors the transition from hermaphroditism to androdioecy

According to the current, widely accepted paradigm, the evolutionary transition from hermaphroditism toward separate sexes occurs in two successive steps: an initial, intermediate step in which unisexual individuals, male or female, sterility mutants coexist with hermaphrodites and a final step that definitively establishes dioecy. Two nonexclusive processes can drive this transition: inbreeding avoidance and reallocation of resources from one sexual function to the other. Here, we report results of controlled crosses between males and hermaphrodites in Phillyrea angustifolia, an androdioecious species with two mutually intercompatible, but intraincompatible groups of hermaphrodites. We observed different segregation patterns that can be explained by: (1) epistatic interactions between two unlinked diallelic loci, determining sex and mating compatibility, and (2) a mutation with pleiotropic effects: female sterility, full compatibility of males with both hermaphrodite incompatibility groups, and complete male‐biased sex‐ratio distortion in one of the two groups. Modeling shows that these mechanisms can explain the high frequency of males in populations of P. angustifolia and can promote the maintenance of androdioecy without requiring inbreeding depression or resource reallocation. We thus argue that segregation distortion establishes the right conditions for the evolution of cryptic dioecy and potentially initiates the evolution toward separate sexes.     

Analysis of sexual polymorphism of the plant from subclass Rosidae in Siberia

Sexual systems and association with several ecological and life history attributes were examined for 977 native angiosperms of subclass Rosidae in Siberia. The majority of angiosperms in Siberia are hermaphrodites (87.7%, N = 867). The most widespread forms of sexual differentiations are andromonoecy, gynodioecy, and dioecy. The rarest forms of sexual differentiations are monoecy, trioecy, and androdioecy. Seven of 34 families are the richest in species with sexual differentiation: Aceraceae, Elaeagnaceae, Haloragaceae, Rhamnaceae, Dipsacaceae, Apiaceae, and Geraniaceae.     

Differences in female reproductive success between female and hermaphrodite individuals in the subdioecious shrub Eurya japonica (Theaceae)

Subdioecy is thought to occupy a transitional position in the gynodioecy–dioecy pathway, explaining one of the evolutionary routes from hermaphroditism to dioecy. Quantifying any female reproductive advantage of females versus hermaphrodites is fundamental to examining the spectrum between subdioecy and dioecy; however, this is challenging, as multiple interacting factors, such as pollen limitation and resource availability, affect plant reproduction. We compared the female reproductive success of females and hermaphrodites via a field experiment in which we hand‐pollinated individuals of the subdioecious shrub Eurya japonica of similar size growing under similar light conditions. Effects of pollen limitation and seed quality were also evaluated through comparing the results of hand‐ and natural‐pollination treatments and performing additional laboratory and greenhouse experiments. Overall, females had higher fruit set and produced heavier fruit and more seeds than hermaphrodites, and these results were more pronounced for hand‐pollinated than for natural‐pollinated plants of both sexes. We also found that seeds naturally produced by females had a higher mean germination rate. These results indicate that females had a pronounced advantage in female reproductive success under conditions of no pollen limitation. The sexual difference in the degree of pollen limitation suggests a pollinator‐mediated interaction, whereas the higher female reproductive success of females even under natural conditions implies that E. japonica is a good model species for elucidating the later stages of the gynodioecy–dioecy pathway.     

Androdioecy and the evolution of dioecy

The likelihood that dioecy could evolve via androdioecy is examined. It is concluded that female-sterility mutations are unlikely to be able to invade populations of self-compatible hermaphrodite species, even if the resources that an hermaphrodite devotes to seed production can be diverted to yield increased survival and also to increase male fertility. These findings are in agreement with the great rarity of androdioecy. Claimed cases of androdioecy are reviewed. All of the species in question appear to be functionally dioecious, with females retaining substantial anther vestiges. It is argued that this morphological androdioecy is in no way indicative of a previous functionally androdioecious state. The details of the reproductive biology of many of these species seem rather to be consistent with their having evolved dioecy via gynodioecy.
The rarity of androdioecy, as a route to the evolution of dioecy, suggests that re-allocation of reproductive resources is unlikely to be the sole factor of importance, and supports an important role for inbreeding avoidance. The fact that females in some dioecious species retain anthers of substantial size, containing considerable quantities of pollen, gives further support to the view that male-sterility mutations can sometimes be favoured even when little or no resources are re-allocated to male functions. This is impossible without substantial selfing and inbreeding. It is therefore concluded that inbreeding avoidance is generally important in the evolution of dioecy, though reallocation of reproductive resources is also necessary.     

Intersexual conflict in androdioecious clam shrimp: Do androdioecious hermaphrodites evolve to avoid mating with males?

A recent sexual conflict model posits that a form of intersexual conflict may explain the persistence of males in androdioecious (males + hermaphrodites) populations of animals that are being selected to transition from dioecious (gonochoristic) mating to self‐compatible hermaphroditism. During the evolutionary spread of a self‐compatible hermaphrodite to replace females, the selective pressures on males to outcross are in conflict with the selective pressures on hermaphrodites to self. According to this model, the unresolved conflict interferes with the evolutionary trajectory from dioecy to hermaphroditism, slowing or halting that transition and strengthening the otherwise “transitory” breeding system of androdioecy into a potentially stable breeding strategy. Herein, we assess this model using two dioecious and two androdioecious clam shrimp (freshwater crustaceans) to ask two questions: (1) Have hermaphrodites evolved so that males cannot effectively recognize them?; and (2) Do androdioecious hermaphrodites avoid males? Androdioecious males made more mistakes than dioecious males when guarding potential mates suggesting that androdioecious males were less effective at finding hermaphrodites than dioecious males were at finding females. Similarly, in a three‐chambered experiment, focal hermaphrodites chose to aggregate with their same sex, whereas focal dioecious males chose to aggregate with the alternate sex. Together, these two experiments support the sexual conflict model of the maintenance of androdioecy and suggest that hermaphrodites are indeed evolving to avoid and evade males.     

Can females benefit from selfing avoidance? Genetic associations and the evolution of plant gender

Evolutionary stability of dioecy and nuclear gynodioecy in higher plants requires that females produce over twice as many successful seeds as hermaphrodites. This fitness differential is widely thought to derive primarily from the advantages of outcrossing caused by high selfing rates and inbreeding depression in the hermaphrodite. This study hypothesized that (i) extraordinarily high deleterious mutation rates are necessary to double female seed success due to outcrossing, and (ii) the large difference in outcrossing rates between sex morphs causes differential purging of these mutations, resulting in additional genetic selection on male sterility. Using genetically explicit models, I showed that the phenotypic outcrossing advantage requires at least one new highly recessive deleterious mutation per genome per generation, regardless of selection coefficient. However, under this mutational regime, differential purging created strong genetic selection against recessive male sterility that overwhelmed the phenotypic selection in favour of outcrossing. In very small populations and for dominant male sterility, this genetic selection was weaker or absent. This first genetically explicit study of the outcrossing advantage of unisexual females may shed new light on both the genetic and selective conditions for the evolution of gynodioecy and dioecy.     

The differentiation and development of pistils of hermaphrodites and pistillodes of males in androdioecious Osmanthus fragrans L. and implications for the evolution to androdioecy

The evolutionary pathway between hermaphroditism and dioecy draws widespread interests, and androdioecy is rarely achieved as an intermediate state between the two breeding systems. Flower bud differentiations in the pistils of hermaphrodites and the pistillodes of males in androdioecious Osmanthus fragrans L. were investigated by paraffin sectioning to elucidate the evolution to androdioecy. Results showed that the regularity and rhythm in flower bud differentiation between males and hermaphrodites were almost consistent and included six main stages. However, the hermaphrodites always lagged behind the males at each stage. The apical floret in the same inflorescence developed earlier than did the lateral ones in both hermaphrodites and males. The most significant difference between males and hermaphrodites was observed at the carpel differentiation stage. Two carpel primordia appeared inside the stamens of both males and hermaphrodites at the initial stage. These two carpels gradually fused with each other in hermaphrodites and eventually developed into a normal pistil with a stigma, a style, and an ovary. However, a cavity grew conspicuously over time between two carpels as developed in males. The two carpels eventually developed into a pistillode with two independent bracteal tissues. However, from the whole development process, the male retained the developmental residue of the hermaphrodite. Thus, the pistillodes of males could be traced to the pistils of hermaphrodites. This finding shows that males may be derived from hermaphrodites in O. fragrans. On the basis of this finding and previous studies on Oleaceae, androdioecy could be regarded as a transition from hermaphroditism to dioecy in this family.     

Do tiny males grow up? Sperm competition and optimal resource allocation schedule of dwarf males of barnacles

Barnacles, marine crustaceans, have three sexual patterns: simultaneous hermaphroditism, dioecy and androdioecy. In dioecy and androdioecy, large individuals (females and hermaphrodites, respectively) are attached by dwarf males. Depending on species, some dwarf males grow up, others do not in their life time. To investigate which environmental conditions affect growth patterns of dwarf males of barnacles, we investigate the evolutionarily stable life history strategy of dwarf males using Pontryagin's maximum principle. Sperm competition among dwarf males and that among dwarf males and large hermaphrodites is taken into account. Dwarf males grow up in food-rich environments, while they do not grow at all in food-poor environments. ESS of the resource allocation schedule between reproduction and growth follows an "intermediate growth strategy" (simultaneous growth and reproduction) for dioecious species, in which sperm competition is not severe. On the other hand, it approaches "bang-bang control" (switching from allocating all resources toward growth then to reproduction), as sperm competition against surrounding large hermaphrodites becomes severe in androdioecious species.     

Determinants of sex allocation in a gynodioecious wild strawberry: implications for the evolution of dioecy and sexual dimorphism

One evolutionary pathway from plants with combined male and female functions (hermaphroditism) to those with separate sexes (dioecy) involves females coexisting with hermaphrodites (gynodioecy). The research presented here explores sex allocation in Fragaria virginiana (a gynodioecious wild strawberry), within the context of theory on the gynodioecy–dioecy transition. By growing clonally replicated plants in the greenhouse and surveying six populations in situ, I evaluated the effects of plant size, genotype, sexual identity, population of origin and female frequency on sex allocation. I found significant positive effects of plant size on most sex allocation traits studied. In addition to strong sex-specific allocation patterns, I found significant broad-sense heritabilities for all traits, suggesting that plants could respond to selection. Moreover, there was a negative genetic correlation between pollen production and fruit set per flower within hermaphrodites, lending support to a basic assumption of sex allocation theory. On the other hand, several sex allocation traits, namely pollen and ovules per flower in hermaphrodites, were positively genetically correlated, suggesting that they may act to constrain the evolution of sexual dimorphism. Populations differed in the frequency of females, and females were more prevalent on sites with lower soil moisture and where hermaphrodites were least likely to produce fruit, suggesting that females’ seed fitness relative to that of hermaphrodites may be strongly environment-dependent in this species.     

Sex determination and the evolution of dioecy from monoecy in Sagittaria latifolia (Alismataceae)

The role of mutations of small versus large effect in adaptive evolution is of considerable interest to evolutionary biologists. The major evolutionary pathways for the origin of dioecy in plants (the gynodioecy and monoecy-paradioecy pathways) are often distinguished by the number of mutations involved and the magnitude of their effects. Here, we investigate the genetic and environmental determinants of sex in Sagittaria latifolia, a species with both monoecious and dioecious populations, and evaluate evidence for the evolution of dioecy via gynodioecy or monoecy-paradioecy. We crossed plants of the two sexual systems to generate F1, F2 and backcross progeny, and grew clones from dioecious populations in low-and high-fertilizer conditions to examine sex inconstancy in females and males. Several lines of evidence implicate two-locus control of the sex phenotypes. In dioecious populations sex is determined by Mendelian segregation of alleles, with males heterozygous at both the male- and female-sterility loci. In monoecious populations, plants are homozygous for alleles dominant to male sterility in females and recessive to female sterility in males. Experimental manipulation of resources revealed sex inconstancy in males but not females. These results are consistent with predictions for the evolution of dioecy via gynodioecy, rather than the expected monoecy-paradioecy pathway, given the ancestral monoecious condition.     

An angiosperm-wide analysis of the gynodioecy–dioecy pathway

Background and Aims

About 6 % of an estimated total of 240 000 species of angiosperms are dioecious. The main precursors of this sexual system are thought to be monoecy and gynodioecy. A previous angiosperm-wide study revealed that many dioecious species have evolved through the monoecy pathway; some case studies and a large body of theoretical research also provide evidence in support of the gynodioecy pathway. If plants have evolved through the gynodioecy pathway, gynodioecious and dioecious species should co-occur in the same genera. However, to date, no large-scale analysis has been conducted to determine the prevalence of the gynodioecy pathway in angiosperms. In this study, this gap in knowledge was addressed by performing an angiosperm-wide survey in order to test for co-occurrence as evidence of the gynodioecy pathway.

Methods

Data from different sources were compiled to obtain (to our knowledge) the largest dataset on gynodioecy available, with 275 genera that include at least one gynodioecious species. This dataset was combined with a dioecy dataset from the literature, and a study was made of how often dioecious and gynodioecious species could be found in the same genera using a contingency table framework.

Key Results

It was found that, overall, angiosperm genera with both gynodioecious and dioecious species occur more frequently than expected, in agreement with the gynodioecy pathway. Importantly, this trend holds when studying different classes separately (or sub-classes, orders and families), suggesting that the gynodioecy pathway is not restricted to a few taxa but may instead be widespread in angiosperms.

Conclusions

This work complements that previously carried out on the monoecy pathway and suggests that gynodioecy is also a common pathway in angiosperms. The results also identify angiosperm families where some (or all) dioecious species may have evolved from gynodioecious precursors. These families could be the targets of future small-scale studies on transitions to dioecy taking phylogeny explicitly into account.     

Evolutionary transitions among dioecy,androdioecy and hermaphroditism in limnadiid clam shrimp (Branchiopoda: Spinicaudata)

Examinations of breeding system transitions have primarily concentrated on the transition from hermaphroditism to dioecy, likely because of the preponderance of this transition within flowering plants. Fewer studies have considered the reverse transition: dioecy to hermaphroditism. A fruitful approach to studying this latter transition can be sought by studying clades in which transitions between dioecy and hermaphroditism have occurred multiple times. Freshwater crustaceans in the family Limnadiidae comprise dioecious, hermaphroditic and androdioecious (males + hermaphrodites) species, and thus this family represents an excellent model system for the assessment of the evolutionary transitions between these related breeding systems. Herein we report a phylogenetic assessment of breeding system transitions within the family using a total evidence comparative approach. We find that dioecy is the ancestral breeding system for the Limnadiidae and that a minimum of two independent transitions from dioecy to hermaphroditism occurred within this family, leading to (1) a Holarctic, all‐hermaphrodite species, Limnadia lenticularis and (2) mixtures of hermaphrodites and males in the genus Eulimnadia. Both hermaphroditic derivatives are essentially females with only a small amount of energy allocated to male function. Within Eulimnadia, we find several all‐hermaphrodite populations/species that have been independently derived at least twice from androdioecious progenitors within this genus. We discuss two adaptive (based on the notion of ‘reproductive assurance’) and one nonadaptive explanations for the derivation of all‐hermaphroditism from androdioecy. We propose that L. lenticularis likely represents an all‐hermaphrodite species that was derived from an androdioecious ancestor, much like the all‐hermaphrodite populations derived from androdioecy currently observed within the Eulimnadia. Finally, we note that the proposed hypotheses for the dioecy to hermaphroditism transition are unable to explain the derivation of a fully functional, outcrossing hermaphroditic species from a dioecious progenitor.     

Nuclear androdioecy and gynodioecy

We formulate two single-locus Mendelian models, one for androdioecy and the other one for gynodioecy, each with 3 parameters: t the male (female) fertility rate of males (females) to hermaphrodites, s the fraction of the progeny derived from selfing; and g the fitness of inbreeders. Each model is expressed as a transformation of a 3 dimensional zygotic algebra, which we interpret as a rational map of the projective plane. We then study the dynamics for the evolution of each reproductive system; and compare our results with similar published models. In this process, we introduce a general concept of fitness and list some of its properties, obtaining a relative measure of population growth, computable as an eigenvalue of a mixed mating transformation for a population in equilibrium. Our results concur with previous models of the evolution of androdioecy and gynodioecy regarding the threshold values above which the sexual polymophism is stable, although the previous models assume constant the fraction of ovules from hermaphrodites that are self pollinated, while we assume constant the fraction of the progeny derived from selfing. A stable androdioecy requires more stringent conditions than a stable gynodioecy if the amount of pollen used for selfing is negligible in comparison with the total amount of pollen produced by hermaphrodites. Otherwise, both models are identical. We show explicitly that the genotype fitnesses depend linearly on their frequencies. Simulations show that any population not at equilibrium always converges to the equilibrium point of higher fitness. However, at intermediate steps, the fitness function occasionally decreases.