A cornucopia of diversity-Ranunculales as a model lineage.

The Ranunculales are a hyperdiverse lineage in many aspects of their phenotype, including growth habit, floral and leaf morphology, reproductive mode, and specialized metabolism. Many Ranunculales species, such as opium poppy and goldenseal, have a high medicinal value. In addition, the order includes a large number of commercially important ornamental plants, such as columbines and larkspurs. The phylogenetic position of the order with respect to monocots and core eudicots and the diversity within this lineage make the Ranunculales an excellent group for studying evolutionary processes by comparative studies. Lately, the phylogeny of Ranunculales was revised, and genetic and genomic resources were developed for many species, allowing comparative analyses at the molecular scale. Here, we review the literature on the resources for genetic manipulation and genome sequencing, the recent phylogeny reconstruction of this order, and its fossil record. Further, we explain their habitat range and delve into the diversity in their floral morphology, focusing on perianth organ identity, floral symmetry, occurrences of spurs and nectaries, sexual and pollination systems, and fruit and dehiscence types. The Ranunculales order offers a wealth of opportunities for scientific exploration across various disciplines and scales, to gain novel insights into plant biology for researchers and plant enthusiasts alike.

Rethinking pathways to the dioecy-polyploidy association: Genera with many dioecious species have fewer polyploids.

PREMISE: Numerous studies have found a positive association between dioecy and polyploidy; however, this association presents a theoretical conflict: While polyploids are predicted to benefit from self-reproduction for successful establishment, dioecious species cannot self-reproduce. We propose a theoretical framework to resolve this apparent conflict. We hypothesize that the inability of dioecious species to self-reproduce hinders their establishment as polyploids. We therefore expect that genera with many dioecious species have fewer polyploids, leading to a negative association between polyploidy and dioecy across genera. METHODS: We used three publicly available databases to determine ploidy and sexual systems for 131 genera and 546 species. We quantified (1) the relationship between the frequency of polyploid species and the frequency of dioecious species across genera, and (2) the proportion of polyploids with hermaphroditism and dioecy across species, adjusting for phylogenetic history. RESULTS: Across genera, we found a negative relationship between the proportion of polyploids and the proportion of dioecious species, a consistent trend across clades. Across all species, we found that sexual system (dioecious or not) was not associated with polyploidy. CONCLUSIONS: Polyploids are rare in genera in which the majority of species are dioecious, consistent with the theory that self-reproduction favors polyploid establishment. The low frequency of polyploidy among dioecious species indicates the association is not as widespread as previously suggested. Our findings are consistent with previous studies identifying a positive relationship between the two traits, but only if polyploidy promotes a transition to dioecy, and not the reverse.

Characterization of a sperm motility signalling pathway in a gonochoric coral suggests conservation across cnidarian sexual systems.

Most stony corals liberate their gametes into the water column via broadcast spawning, where fertilization hinges upon the activation of directional sperm motility. Sperm from gonochoric and hermaphroditic corals display distinct morphological and molecular phenotypes, yet it is unknown whether the signalling pathways controlling sperm motility are also distinct between these sexual systems. Here, we addressed this knowledge gap using the gonochoric, broadcast spawning coral Astrangia poculata. We found that cytosolic alkalinization of sperm activates the pH-sensing enzyme soluble adenylyl cyclase (sAC), which is required for motility. Additionally, we demonstrate for the first time in any cnidarian that sAC activity leads to protein kinase A (PKA) activation, and that PKA activity contributes to sperm motility activation. Ultrastructures of A. poculata sperm displayed morphological homology with other gonochoric cnidarians, and sAC exhibited broad structural and functional conservation across this phylum. These results indicate a conserved role for pH-dependent sAC-cAMP-PKA signalling in sperm motility across coral sexual systems, and suggest that the role of this pathway in sperm motility may be ancestral in metazoans. Finally, the dynamics of this pH-sensitive pathway may play a critical role in determining the sensitivity of marine invertebrate reproduction to anthropogenic ocean acidification.

The spatial arrangement of sexes is related to reproductive allocation in mosses: a comparative study of reproductive allocation in three different monoicous sexual systems.

BACKGROUND AND AIMS: We examined the relationship between reproductive allocation and vegetative growth in three monoicous sexual systems of bryophytes. The sexual systems show a gradient of increasing distance between the sexes, from gonioautoicous to cladautoicous to rhizautoicous. Here, we investigated the following two hypotheses: (1) reproductive allocation differs between sexes and sexual systems, and male reproductive allocation increases with increasing distance between male and female gametangia; and (2) reproductive allocation is negatively related to vegetative growth. METHODS: We sampled the three sexual systems, represented by three moss species of the genus Fissidens in the Atlantic Forest of Southeastern Brazil. Ramets were washed in the laboratory; the reproductive structures were detached from the vegetative ramets and sorted regarding sex and individual, dried at 70 °C for 72 h, and weighed in an ultramicrobalance. We calculated the mean reproductive and vegetative mass and reproductive allocation and used generalized linear models to test our predictions. KEY RESULTS: Reproductive allocation differed between species and sexes. It was higher in the rhizautoicous than in the cladautoicous and gonioautoicous species. Mean reproductive allocation was greater in males than in females of the rhizautoicous species, greater in females than males of the cladautoicous species, and did not differ between the sexes in the gonioautoicous species. Estimates of reproductive and vegetative mass were positively related in females of the rhizautoicous species. Vegetative mass was not related to reproductive allocation in the gonioautoicous species, but negatively related to reproductive allocation in the male and female branchlets of the cladautoicous species and in the female ramets of the rhizautoicous species. CONCLUSIONS: The reproductive allocation patterns differ between the rhizautoicous species and the 'truly' monoicous species, with shorter intersexual distances, which implies that our hypotheses were supported only in part. We suggest that the hypotheses should be reformulated and tested further by comparing 'truly' monoicous species with dioicous species and by including other genera.

Dioecy Is Associated with High Genetic Diversity and Adaptation Rates in the Plant Genus Silene.

About 15,000 angiosperm species (∼6%) have separate sexes, a phenomenon known as dioecy. Why dioecious taxa are so rare is still an open question. Early work reported lower species richness in dioecious compared with nondioecious sister clades, raising the hypothesis that dioecy may be an evolutionary dead-end. This hypothesis has been recently challenged by macroevolutionary analyses that detected no or even positive effect of dioecy on diversification. However, the possible genetic consequences of dioecy at the population level, which could drive the long-term fate of dioecious lineages, have not been tested so far. Here, we used a population genomics approach in the Silene genus to look for possible effects of dioecy, especially for potential evidence of evolutionary handicaps of dioecy underlying the dead-end hypothesis. We collected individual-based RNA-seq data from several populations in 13 closely related species with different sexual systems: seven dioecious, three hermaphroditic, and three gynodioecious species. We show that dioecy is associated with increased genetic diversity, as well as higher selection efficacy both against deleterious mutations and for beneficial mutations. The results hold after controlling for phylogenetic inertia, differences in species census population sizes and geographic ranges. We conclude that dioecious Silene species neither show signs of increased mutational load nor genetic evidence for extinction risk. We discuss these observations in the light of the possible demographic differences between dioecious and self-compatible hermaphroditic species and how this could be related to alternatives to the dead-end hypothesis to explain the rarity of dioecy.

Sexual selection on male but not female function in monoecious and dioecious populations of broadleaf arrowhead (Sagittaria latifolia).

Direct measures of sexual selection in plants are rare and complicated by immobility and modular growth. For plants, instantaneous measures of fitness typically scale with size, but covariances between size and mating success could obscure the detection of sexual selection. We measured the magnitude of sexual selection in a monoecious and a dioecious population of the clonal plant Sagittaria latifolia using Bateman gradients (ßss). These gradients were calculated using parentage analysis and residual regression to account for the effects of shoot and clone size on mating and reproductive success. In both populations, (i) there was greater promiscuity via male function than via female function and (ii) ßss were positive, with significant associations between mating and reproductive success for male but not female function. Moreover, estimated ßss were similar for the monoecious and dioecious populations, possibly because non-overlapping female and male sex phases in hermaphroditic S. latifolia reduced the scope for interference between sex functions during mating. This study builds on previous studies of selection on plant mating traits, and of sexual selection under experimental conditions, by showing that sexual selection can operate in natural populations of plants, including populations of hermaphrodites.

Contrasting patterns of genetic diversity and differentiation across the continental disjunct range of a sexually polymorphic aquatic plant.

BACKGROUND AND AIMS: Reproductive systems enabling opportunities for self-fertilization influence population genetic structure and play a key role in colonization and genetic differentiation during range expansion. Because of their well-developed powers of dispersal, aquatic plants often have widespread disjunct geographical distributions, providing opportunities to investigate the role of reproductive systems in structuring genetic variation between parts of the range that differ in migration history and ecology. METHODS: We compared reproductive systems and spatial genetic structure of the freshwater aquatic macrophyte Sagittaria latifolia between disjunct western and eastern ranges of North America (NA). Populations of this species are most commonly either monoecious or dioecious. We examined chloroplast DNA haplotype variation to test the hypothesis that the western range of this species represents a secondary colonization from the east, and evaluated the roles of reproductive system differences and geography in structuring contemporary patterns of genetic variation at 11 polymorphic SSR (simple sequence repeat) loci. KEY RESULTS: Chloroplast haplotyping revealed a single haplotype in western NA compared to numerous haplotypes in eastern NA, consistent with a genetic bottleneck during westward migration. Estimates of genetic diversity in eastern NA populations differed significantly between reproductive systems, but this pattern was not evident in the western range. Eastern populations could be reliably assigned to genetic clusters based on their reproductive systems, whereas western populations clustered primarily by geographical location. CONCLUSIONS: The sparser distribution of aquatic habitats in the drier western range of S. latifolia, combined with secondary colonization of this region, probably cause the lower genetic diversity and increased differentiation among populations, possibly overriding the effects of reproductive system evident in the eastern portion of the range. Our findings demonstrate that the complex interplay between migratory history, reproductive systems and habitat availability plays an important role in structuring spatial patterns of genetic variation in disjunct plant populations.

The Mendelian inheritance of gynomonoecy: insights from Anacyclus hybridizing species.

PREMISE: Gynomonoecy is an infrequent sexual system in angiosperms, although widely represented within the Asteraceae family. Currently, the hypothesis of two nuclear loci controling gynomonoecy is the most accepted. However, the genic interactions are still uncertain. Anacyclus clavatus, A. homogamos, and A. valentinus differ in their sexual system and floral traits. Here, we investigate the inheritance of gynomonoecy in this model system to understand its prevalence in the family. METHODS: We selected six natural populations (two per species) for intra- and interspecific experimental crosses, and generated a total of 1123 individuals from the F1 generation, F2 , and backcrosses for sexual system characterization. The frequency of gynomonoecy observed for each cross was tested to fit different possible hypotheses of genic interaction. Additionally, the breeding system and the degree of reproductive isolation between these species were assessed. RESULTS: Complementary epistasis, in which two dominant alleles are required for trait expression, explained the frequencies of gynomonoecy observed across all generations. The heterozygosity inferred in Anacyclus valentinus, as well as its lower and variable seed set, is congruent with its hybrid origin. CONCLUSIONS: In our model system gynomonoecy is controlled by complementary epistasis of two genes. A common origin of this sexual system in Asteraceae, in which genic duplications, mutations, and hybridization between lineages played a key role, is hypothesized whereas independent evolutionary pathways and possibly diverse underlying genetic factors are suggested for gynomonoecy expression in other angiosperm families.

Variability of mitochondrial ORFans hints at possible differences in the system of doubly uniparental inheritance of mitochondria among families of freshwater mussels (Bivalvia: Unionida).

BACKGROUND: Supernumerary ORFan genes (i.e., open reading frames without obvious homology to other genes) are present in the mitochondrial genomes of gonochoric freshwater mussels (Bivalvia: Unionida) showing doubly uniparental inheritance (DUI) of mitochondria. DUI is a system in which distinct female-transmitted and male-transmitted mitotypes coexist in a single species. In families Unionidae and Margaritiferidae, the transition from dioecy to hermaphroditism and the loss of DUI appear to be linked, and this event seems to affect the integrity of the ORFan genes. These observations led to the hypothesis that the ORFans have a role in DUI and/or sex determination. Complete mitochondrial genome sequences are however scarce for most families of freshwater mussels, therefore hindering a clear localization of DUI in the various lineages and a comprehensive understanding of the influence of the ORFans on DUI and sexual systems. Therefore, we sequenced and characterized eleven new mitogenomes from poorly sampled freshwater mussel families to gather information on the evolution and variability of the ORFan genes and their protein products. RESULTS: We obtained ten complete plus one almost complete mitogenome sequence from ten representative species (gonochoric and hermaphroditic) of families Margaritiferidae, Hyriidae, Mulleriidae, and Iridinidae. ORFan genes are present only in DUI species from Margaritiferidae and Hyriidae, while non-DUI species from Hyriidae, Iridinidae, and Mulleriidae lack them completely, independently of their sexual system. Comparisons among the proteins translated from the newly characterized ORFans and already known ones provide evidence of conserved structures, as well as family-specific features. CONCLUSIONS: The ORFan proteins show a comparable organization of secondary structures among different families of freshwater mussels, which supports a conserved physiological role, but also have distinctive family-specific features. Given this latter observation and the fact that the ORFans can be either highly mutated or completely absent in species that secondarily lost DUI depending on their respective family, we hypothesize that some aspects of the connection among ORFans, sexual systems, and DUI may differ in the various lineages of unionids.

Evolution of sexual systems and growth habit in Mussaenda (Rubiaceae): Insights into the evolutionary pathways of dioecy.

Dioecy is a rare sexual system that is thought to represent an "evolutionary dead end". While many studies have addressed the evolution of dioecy and/or its relationship with the evolution of the woody habit, few have explored the relationship between dioecy and climbing habit, and their effects on diversification rates. Here, we study the evolution of sexual systems and growth habit in Mussaenda (Rubiaceae) using a robust phylogeny of the genus based on eight plastid regions and a broad sampling of taxa (92 of the 132 species were sampled). A time-calibrated tree was constructed to estimate diversification rates in different clades and its correlates with focal characters. More specifically, we assess evolutionary correlations between dioecy and climbing habit and their respective influences on diversification rates. Ancestral character state reconstructions revealed that distyly is the most likely ancestral state in Mussaenda. Distyly has subsequently given rise to dioecy, short-styled floral monomorphism, and long-styled floral monomorphism. Dioecy has evolved independently at least four times from distyly, and has reversed to homostylous hermaphroditism at least twice, which does not support the "evolutionary dead end" hypothesis. A significant correlation between the evolution of dioecy and climbing growth form was found in Mussaenda. It is possible that a strong association between high net diversification rates and dioecy may exist in Mussaenda, but no association was found with climbing habit.

On the rarity of dioecy in flowering plants.

Dioecy, the coexistence of separate male and female individuals in a population, is a rare but phylogenetically widespread sexual system in flowering plants. While research has concentrated on why and how dioecy evolves from hermaphroditism, the question of why dioecy is rare, despite repeated transitions to it, has received much less attention. Previous phylogenetic and theoretical studies have suggested that dioecy might be an evolutionary dead end. However, recent research indicates that the phylogenetic support for this hypothesis is attributable to a methodological bias and that there is no evidence for reduced diversification in dioecious angiosperms. The relative rarity of dioecy thus remains a puzzle. Here, we review evidence for the hypothesis that dioecy might be rare not because it is an evolutionary dead end, but rather because it easily reverts to hermaphroditism. We review what is known about transitions between hermaphroditism and dioecy, and conclude that there is an important need to consider more widely the possibility of transitions away from dioecy, both from an empirical and a theoretical point of view, and by combining tools from molecular evolution and insights from ecology.

A Century of Sex Determination in Flowering Plants.

Plants have evolved a diverse array of strategies for sexual reproduction, particularly through the modification of male and female organs at distinct points in development. The immense variation in sexual systems across the land plants provides a unique opportunity to study the genetic, epigenetic, phylogenetic, and ecological underpinnings of sex determination. Here, we reflect on more than a century of research into flowering plant sex determination, placing a particular focus on the foundational genetic and cytogenetic observations, experiments, and hypotheses. Building on the seminal work on the genetics of plant sex, modern comparative genomic analyses now allow us to address longstanding questions about sex determination and the origins of sex chromosomes.

Dioecy does not consistently accelerate or slow lineage diversification across multiple genera of angiosperms.

Dioecy, the sexual system in which male and female organs are found in separate individuals, allows greater specialization for sex-specific functions and can be advantageous under various ecological and environmental conditions. However, dioecy is rare among flowering plants. Previous studies identified contradictory trends regarding the relative diversification rates of dioecious lineages vs their nondioecious counterparts, depending on the methods and data used. We gathered detailed species-level data for dozens of genera that contain both dioecious and nondioecious species. We then applied a probabilistic approach that accounts for differential speciation, extinction, and transition rates between states to examine whether there is an association between dioecy and lineage diversification. We found a bimodal distribution, whereby dioecious lineages exhibited higher diversification in certain genera but lower diversification in others. Additional analyses did not uncover an ecological or life history trait that could explain a context-dependent effect of dioecy on diversification. Furthermore, in-depth simulations of neutral characters demonstrated that such bimodality is also found when simulating neutral characters across the observed trees. Our analyses suggest that - at least for these genera with the currently available data - dioecy neither consistently places a strong brake on diversification nor is a strong driver.

Increased diversification rates follow shifts to bisexuality in liverworts.

Shifts in sexual systems are one of the key drivers of species diversification. In contrast to angiosperms, unisexuality prevails in bryophytes. Here, we test the hypotheses that bisexuality evolved from an ancestral unisexual condition and is a key innovation in liverworts. We investigate whether shifts in sexual systems influence diversification using hidden state speciation and extinction analysis (HiSSE). This new method compares the effects of the variable of interest to the best-fitting latent variable, yielding robust and conservative tests. We find that the transitions in sexual systems are significantly biased toward unisexuality, even though bisexuality is coupled with increased diversification. Sexual systems are strongly conserved deep within the liverwort tree but become much more labile toward the present. Bisexuality appears to be a key innovation in liverworts. Its effects on diversification are presumably mediated by the interplay of high fertilization rates, massive spore production and long-distance dispersal, which may separately or together have facilitated liverwort speciation, suppressed their extinction, or both. Importantly, shifts in liverwort sexual systems have the opposite effect when compared to angiosperms, leading to contrasting diversification patterns between the two groups. The high prevalence of unisexuality among liverworts suggests, however, a strong selection for sexual dimorphism.

Hybridization is associated with changes in sexual system in the bryophyte genus Atrichum.

PREMISE OF THE STUDY: Over 50% of bryophytes have separate sexes, and numerous transitions have occurred between combined and separate sexes. Polyploidy and hybridization is one proximate mechanism hypothesized to cause evolutionary transitions to hermaphroditism in bryophytes because sex is expressed at the haploid stage and in nonpolyploid dioecious species males have a single V chromosome and females a U. Hermaphroditism can arise if gametophytes of allopolyploids have both U and V chromosomes. We examined the association between polyploidy and hermaphroditism in the bryophyte genus Atrichum, which has species where gametophytes can be haploid, diploid, or triploid, and some species have hermaphroditic individuals. METHODS: We generated phylogenies of Atrichum from sequences of three plastid regions (rbcL, rps4, and trnL-trnF) and the second intron for the nuclear gene Leafy/Floricaula to further understand the relationships among haploid, diploid, and triploid species, and those with combined or separate sexes. KEY RESULTS: The existence of multiple sequences of Leafy/Floricaula in diploid and triploid, but not haploid, individuals is consistent with independent allopolyploid origins of the diploid and triploid species. Allopolyploidy was associated with a likely gain in hermaphroditism in triploid Atrichum undulatum and possibly diploid A. altecristatum, but not in the allopolyploid A. crispulum (diploid at the gametophyte level). CONCLUSIONS: These results highlight a role for hybridization and polyploidy in sexual system evolution, but the presence of diploid (allopolyploid) dioecious species suggest that other factors may influence the maintenance of sexual systems after an evolutionary transition.

A field test of a model for the stability of androdioecy in the freshwater shrimp, Eulimnadia texana.

The evolution of hermaphroditism from dioecy is a poorly studied transition. Androdioecy (the coexistence of males and hermaphrodites) has been suggested as an intermediate step in this evolutionary transition or could be a stable reproductive mode. Freshwater crustaceans in the genus Eulimnadia have reproduced via androdioecy for 24+ million years and thus are excellent organisms to test models of the stability of androdioecy. Two related models that allow for the stable maintenance of males and hermaphrodites rely on the counterbalancing of three life history parameters. We tested these models in the field over three field seasons and compared the results to previous laboratory estimates of these three parameters. Male and hermaphroditic ratios within years were not well predicted using either the simpler original model or a version of this model updated to account for differences between hermaphroditic types ('monogenic' and 'amphigenic' hermaphrodites). Using parameter estimates of the previous year to predict the next year's sex ratios revealed a much better fit to the original relative to the updated version of the model. Therefore, counter to expectations, accounting for differences between the two hermaphroditic types did not improve the fit of these models. At the moment, we lack strong evidence that the long-term maintenance of androdioecy in these crustaceans is the result of a balancing of life history parameters; other factors, such as metapopulation dynamics or evolutionary constraints, may better explain the 24+ million year maintenance of androdioecy in clam shrimp.

Variation and evolution of sex ratios at the northern range limit of a sexually polymorphic plant.

Gender strategies involve three fundamental sex phenotypes - female, male and hermaphrodite. Their frequencies in populations typically define plant sexual systems. Patterns of sex-ratio variation in a geographical context can provide insight into transitions among sexual systems, because environmental gradients differentially influence sex phenotype fitness. Here, we investigate sex-ratio variation in 116 populations of Sagittaria latifolia at the northern range limit in eastern N. America and evaluate mechanisms responsible for the patterns observed. We detected continuous variation in sex phenotype frequencies from monoecy through subdioecy to dioecy. There was a decline in the frequency and flower production of females in northerly populations, whereas hermaphrodite frequencies increased at the range limit, and in small populations. Tests of a model of sex-ratio evolution, using empirical estimates of fitness components, indicated that the relative female and male contribution of males and hermaphrodites to fitness is closer to equilibrium expectations than female frequencies. Plasticity in sex expression and clonality likely contribute to deviations from equilibrium expectations.

Size-dependent gender modification in Lilium apertum (Liliaceae): does this species exhibit gender diphasy?

BACKGROUND AND AIMS: Variation in the relative female and male reproductive success of flowering plants is widespread, despite the fundamental hermaphroditic condition of the majority of species. In many hermaphroditic populations, environmental conditions and their influence on development and size can influence the gender expression of individuals through the formation of hermaphroditic and unisexual flowers. This study investigates the hypothesis that the bulbous, animal-pollinated, perennial Lilium apertum (Liliaceae) exhibits a form of size-dependent gender modification known as gender diphasy, in which the sexual expression of individuals depends on their size, with plants often changing sex between seasons. METHODS: Variation in floral traits was examined in relation to their size using marked individuals in natural populations, and also under glasshouse conditions. Measurements were taken of the height, flower number, floral sex expression, flower size, flower biomass and pollen production of individuals over consecutive years between 2009 and 2012 in seven populations in south-west China. KEY RESULTS: Flowers of L. apertum are either perfect (hermaphroditic) or staminate (male) and, in any given season, plants exhibit one of three sex phenotypes: only hermaphrodite flowers, a mixture of hermaphroditic and male flowers, or only male flowers. Transitions between each of these sex phenotypes were observed over consecutive years and were commonly size-dependent, particularly transitions from small plants bearing only male flowers to those that were taller with hermaphroditic flowers. Hermaphroditic flowers were significantly larger, heavier and produced more pollen than male flowers. CONCLUSIONS: The results for L. apertum are consistent with the 'size advantage hypothesis' developed for animal species with sex change. The theory predicts that when individuals are small they should exhibit the sex for which the costs of reproduction are less, and this usually involves the male phase. L. apertum provides an example of gender diphasy, a rare sexual system in flowering plants.

The evolution of plant reproductive systems: how often are transitions irreversible?

Flowering plants are characterized by striking variation in reproductive systems, and the evolutionary lability of their sexual traits is often considered a major driver of lineage diversification. But, evolutionary transitions in reproductive form and function are never entirely unconstrained and many changes exhibit strong directionality. Here, I consider why this occurs by examining transitions in pollination, mating and sexual systems, some of which have been considered irreversible. Among pollination systems, shifts from bee to hummingbird pollination are rarely reversible, whereas transitions from animal to wind pollination are occasionally reversed. Specialized pollination systems can become destabilized through a loss of pollinator service resulting in a return to generalized pollination, or more commonly a reliance on self-pollination. Homomorphic and heteromorphic self-incompatibility systems have multiple origins but breakdown to self-compatibility occurs much more frequently with little evidence for subsequent gains, at least over short time-spans. Similarly, numerous examples of the shift from outcrossing to predominant self-fertilization are known, but cases of reversal are very limited supporting the view that autogamy usually represents an evolutionary dead-end. The evolution of dioecy from hermaphroditism has also been considered irreversible, although recent evidence indicates that the occurrence of sex inconstancy and hybridization can lead to the origin of derived sexual systems from dioecy. The directionality of many transitions clearly refutes the notion of unconstrained reproductive flexibility, but novel adaptive solutions generally do not retrace earlier patterns of trait evolution.

Discrete time model of sexual systems.

Small factors are the biggest contributors to the biggest changes in an ecosystem which may lead to its demise. Simple things such as tweaking the humidity or tampering with the temperature can be the downfall of the habitants and the ecosystem itself. These changes can be observed right now with the consistent temperature increase on Earth along with the slew of issues that come with global warming. A small change in a few degrees in temperature can perish an entire food supply and the habitat of many already endangered beings forcing them to either adapt or die. Within such an ecosystem the main reason it withstands the test of time boils down to one simple thing; reproduction. This creates the natural question of asking oneself: How does an ecosystem replenish itself and is able to resist collapsing? To even begin considering this thought, one must realise that the size of the population is the key to gaining a deeper understanding as two constituents that are important from evolutionary theory are survival and reproduction. The case of asexual reproducers, it is not difficult to see any alterations that can be introduced to increase reproductivity. Meanwhile, for sexual reproducers, the evolution to increase reproductivity can be observed by looking into the generational data of the species. A certain group of time-based dynamic systems that are connected to a sexual system are the point of contention. The suggested model is a dynamic representation of a hermaphrodite population which is described through quadratic stochastic operators. The key findings offer fresh insights into the future of hermaphrodite populations, that is perhaps a probable solution to prevent the decline of endangered or at-risk species. This demonstrates a fresh perspective on reproduction, which is explored through a purely mathematical approach.