The rate of facultative sex governs the number of expected mating types in isogamous species

The role of promiscuous molecular recognition in the evolution of RNase-based self-incompatibility in plants

How do biological networks evolve and expand? We study these questions in the context of the plant collaborative-non-self recognition self-incompatibility system. Self-incompatibility evolved to avoid self-fertilization among hermaphroditic plants. It relies on specific molecular recognition between highly diverse proteins of two families: female and male determinants, such that the combination of genes an individual possesses determines its mating partners. Though highly polymorphic, previous models struggled to pinpoint the evolutionary trajectories by which new specificities evolved. Here, we construct a novel theoretical framework, that crucially affords interaction promiscuity and multiple distinct partners per protein, as is seen in empirical findings disregarded by previous models. We demonstrate spontaneous self-organization of the population into distinct "classes" with full between-class compatibility and a dynamic long-term balance between class emergence and decay. Our work highlights the importance of molecular recognition promiscuity to network evolvability. Promiscuity was found in additional systems suggesting that our framework could be more broadly applicable.

Hermaphroditic origins of anisogamy

Anisogamy-the size dimorphism of gametes-is the defining difference between the male and female sexual strategies. Game-theoretic thinking led to the first convincing explanation for the evolutionary origins of anisogamy in the 1970s. Since then, formal game-theoretic models have continued to refine our understanding of when and why anisogamy should evolve. Such models typically presume that the earliest anisogamous organisms had separate sexes. However, in most taxa, there is no empirical evidence to support this assumption. Here, we present a model of the coevolution of gamete size and sex allocation, which allows for anisogamy to emerge alongside either hermaphroditism or separate sexes. We show that hermaphroditic anisogamy can evolve directly from isogamous ancestors when the average size of spawning groups is small and fertilization is relatively efficient. Sex allocation under hermaphroditism becomes increasingly female-biased as group size decreases and the degree of anisogamy increases. When spawning groups are very small, our model also predicts the existence of complex isogamous organisms in which individuals allocate resources equally to two large gamete types. We discuss common, but potentially unwarranted, assumptions in the literature that could be relaxed in future models. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Parthenogenesis and the Evolution of Anisogamy

Recently, it was pointed out that classic models for the evolution of anisogamy do not take into account the possibility of parthenogenetic reproduction, even though sex is facultative in many relevant taxa (e.g., algae) that harbour both anisogamous and isogamous species. Here, we complement this recent analysis with an approach where we assume that the relationship between progeny size and its survival may differ between parthenogenetically and sexually produced progeny, favouring either the former or the latter. We show that previous findings that parthenogenesis can stabilise isogamy relative to the obligate sex case, extend to our scenarios. We additionally investigate two different ways for one mating type to take over the entire population. First, parthenogenesis can lead to biased sex ratios that are sufficiently extreme that one type can displace the other, leading to de facto asexuality for the remaining type that now lacks partners to fuse with. This process involves positive feedback: microgametes, being numerous, lack opportunities for syngamy, and should they proliferate parthenogenetically, the next generation makes this asexual route even more prominent for microgametes. Second, we consider mutations to strict asexuality in producers of micro- or macrogametes, and show that the prospects of asexual invasion depend strongly on the mating type in which the mutation arises. Perhaps most interestingly, we also find scenarios in which parthenogens have an intrinsic survival advantage yet facultatively sexual isogamous populations are robust to the invasion of asexuals, despite us assuming no genetic benefits of recombination. Here, equal contribution from both mating types to zygotes that are sufficiently well provisioned can outweigh the additional costs associated with syngamy.

Switching environments, synchronous sex, and the evolution of mating types

While facultative sex is common in sexually reproducing species, for reasons of tractability most mathematical models assume that such sex is asynchronous in the population. In this paper, we develop a model of switching environments to instead capture the effect of an entire population transitioning synchronously between sexual and asexual modes of reproduction. We use this model to investigate the evolution of the number of self-incompatible mating types in finite populations, which empirically can range from two to thousands. When environmental switching is fast, we recover the results of earlier studies that implicitly assumed populations were engaged in asynchronous sexual reproduction. However when the environment switches slowly, we see deviations from previous asynchronous theory, including a lower number of mating types at equilibrium and bimodality in the stationary distribution of mating types. We provide analytic approximations for both the fast and slow switching regimes, as well as a numerical scheme based on the Kolmogorov equations for the system to quickly evaluate the model dynamics at intermediate parameters. Our approach exploits properties of integer partitions in number theory. We also demonstrate how additional biological processes such as selective sweeps can be accounted for in this switching environment framework, showing that beneficial mutations can further erode mating type diversity in synchronous facultatively sexual populations.

Drivers of Mating Type Composition in Tetrahymena thermophila

Sex offers advantages even in primarily asexual species. Some ciliates appear to utilize such reproductive strategy with many mating types. However, the factors determining the composition of mating types in the unicellular ciliate Tetrahymena thermophila are poorly understood, and this is further complicated by non-Mendelian determination of mating type in the offspring. We therefore developed a novel population genetics model to predict how various factors influence the dynamics of mating type composition, including natural selection. The model predicted either the coexistence of all seven mating types or fixation of a single mating type in a population, depending on parameter combinations, irrespective of natural selection. To understand what factor(s) may be more influential and to test the validity of theoretical prediction, five replicate populations were maintained in laboratory such that several factors could be controlled or measured. Whole-genome sequencing was used to identify newly arising mutations and determine mating type composition. Strikingly, all populations were found to be driven by strong selection on newly arising beneficial mutations to fixation of their carrying mating types, and the trajectories of speed to fixation agreed well with our theoretical predictions. This study illustrates the evolutionary strategies that T. thermophila can utilize to optimize population fitness.

Oxygen, life forms, and the evolution of sexes in multicellular eukaryotes

The evolutionary advantage of different sexual systems in multicellular eukaryotes is still not well understood, because the differentiation into male and female individuals halves offspring production compared with asexuality. Here we propose that various physiological adaptations to oxidative stress could have forged sessility versus motility, and consequently the evolution of sexual systems in multicellular animals, plants, and fungi. Photosynthesis causes substantial amounts of oxidative stress in photoautotrophic plants and, likewise, oxidative chemistry of polymer breakdown, cellulose and lignin, for saprotrophic fungi. In both cases, its extent precludes motility, an additional source of oxidative stress. Sessile life form and the lack of neuronal systems, however, limit options for mate recognition and adult sexual selection, resulting in inefficient mate-searching systems. Hence, sessility requires that all individuals can produce offspring, which is achieved by hermaphroditism in plants and/or by multiple mating types in fungi. In animals, motility requires neuronal systems, and muscle activity, both of which are highly sensitive to oxidative damage. As a consequence, motility has evolved in animals as heterotrophic organisms that (1) are not photosynthetically active, and (2) are not primary decomposers. Adaptations to motility provide prerequisites for an active mating behavior and efficient mate-searching systems. These benefits compensate for the "cost of males", and may explain the early evolution of sex chromosomes in metazoans. We conclude that different sexual systems evolved under the indirect physiological constraints of lifestyles.

Fitness differences suppress the number of mating types in evolving isogamous species

Sexual reproduction is not always synonymous with the existence of two morphologically different sexes; isogamous species produce sex cells of equal size, typically falling into multiple distinct self-incompatible classes, termed mating types. A long-standing open question in evolutionary biology is: what governs the number of these mating types across species? Simple theoretical arguments imply an advantage to rare types, suggesting the number of types should grow consistently; however, empirical observations are very different. While some isogamous species exhibit thousands of mating types, such species are exceedingly rare, and most have fewer than 10. In this paper, we present a mathematical analysis to quantify the role of fitness variation-characterized by different mortality rates-in determining the number of mating types emerging in simple evolutionary models. We predict that the number of mating types decreases as the variance of mortality increases.

When Synchrony Makes the Best of Both Worlds Even Better: How Well Do We Really Understand Facultative Sex?

Biological diversity abounds in potential study topics. Studies of model systems have their advantages, but reliance on a few well-understood cases may create false impressions of what biological phenomena are the norm. Here I focus on facultative sex, which is often hailed as offering the best of both worlds, in that rare sex offers benefits almost equal to obligate sex and avoids paying most of the demographic costs. How well do we understand when and why this form of sexual reproduction is expected to prevail? I show several gaps in the theoretical literature and, by contrasting asynchronous with synchronous sex, highlight the need to link sex theories to the theoretical underpinnings of bet hedging, on the one hand, and to mate limitation considerations, on the other. Condition-dependent sex and links between sex with dispersal or dormancy appear understudied. While simplifications are justifiable as a simple assumption structure enhances analytical tractability, much remains to be done to incorporate key features of real sex to the main theoretical edifice.

Invasion and Extinction Dynamics of Mating Types Under Facultative Sexual Reproduction

In sexually reproducing isogamous species, syngamy between gametes is generally not indiscriminate, but rather restricted to occurring between complementary self-incompatible mating types. A longstanding question regards the evolutionary pressures that control the number of mating types observed in natural populations, which ranges from two to many thousands. Here, we describe a population genetic null model of this reproductive system, and derive expressions for the stationary probability distribution of the number of mating types, the establishment probability of a newly arising mating type, and the mean time to extinction of a resident type. Our results yield that the average rate of sexual reproduction in a population correlates positively with the expected number of mating types observed. We further show that the low number of mating types predicted in the rare-sex regime is primarily driven by low invasion probabilities of new mating type alleles, with established resident alleles being very stable over long evolutionary periods. Moreover, our model naturally exhibits varying selection strength dependent on the number of resident mating types. This results in higher extinction and lower invasion rates for an increasing number of residents.

Evolution of mating types in finite populations: The precarious advantage of being rare

Sexually reproducing populations with self-incompatibility bear the cost of limiting potential mates to individuals of a different type. Rare mating types escape this cost since they are unlikely to encounter incompatible partners, leading to the deterministic prediction of continuous invasion by new mutants and an ever-increasing number of types. However, rare types are also at an increased risk of being lost by random drift. Calculating the number of mating types that a population can maintain requires consideration of both the deterministic advantages and the stochastic risks. By comparing the relative importance of selection and drift, we show that a population of size N can maintain a maximum of approximately N^1/3 mating types for intermediate population sizes, whereas for large N, we derive a formal estimate. Although the number of mating types in a population is quite stable, the rare-type advantage promotes turnover of types. We derive explicit formulas for both the invasion and turnover probabilities in finite populations.

Convergent evolution of linked mating-type loci in basidiomycete fungi

Sexual development is a key evolutionary innovation of eukaryotes. In many species, mating involves interaction between compatible mating partners that can undergo cell and nuclear fusion and subsequent steps of development including meiosis. Mating compatibility in fungi is governed by the mating type (MAT) loci. In basidiomycetes, the ancestral state is hypothesized to be tetrapolar, with two genetically unlinked MAT loci containing homeodomain transcription factor genes (HD locus) and pheromone and pheromone receptor genes (P/R locus), respectively. Alleles at both loci must differ between mating partners for completion of sexual development. However, there are also basidiomycetes with bipolar mating systems, which can arise through genomic linkage of the HD and P/R loci. In the order Tremellales, bipolarity is found only in the pathogenic Cryptococcus species. Here, we describe the analysis of MAT loci from 24 species of the Trichosporonales, a sister order to the Tremellales. In all of the species analyzed, the MAT loci are fused and a single HD gene is present in each mating type, similar to the organization in the pathogenic Cryptococci. However, the HD and P/R allele combinations in the Trichosporonales are different from those in the pathogenic Cryptococci. This and the existence of tetrapolar species in the Tremellales suggest that fusion of the HD and P/R loci occurred independently in the Trichosporonales and pathogenic Cryptococci, supporting the hypothesis of convergent evolution towards fused MAT regions, similar to previous findings in other fungal groups. Unlike the fused MAT loci in several other basidiomycete lineages though, the gene content and gene order within the fused MAT loci are highly conserved in the Trichosporonales, and there is no apparent suppression of recombination extending from the MAT loci to adjacent chromosomal regions, suggesting different mechanisms for the evolution of physically linked MAT loci in these groups.

Evolution of asymmetric gamete signaling and suppressed recombination at the mating type locus

The two partners required for sexual reproduction are rarely the same. This pattern extends to species which lack sexual dimorphism yet possess self-incompatible gametes determined at mating-type regions of suppressed recombination, likely precursors of sex chromosomes. Here we investigate the role of cellular signaling in the evolution of mating-types. We develop a model of ligand-receptor dynamics, and identify factors that determine the capacity of cells to send and receive signals. The model specifies conditions favoring the evolution of gametes producing ligand and receptor asymmetrically and shows how these are affected by recombination. When the recombination rate evolves, the conditions favoring asymmetric signaling also favor tight linkage of ligand and receptor loci in distinct linkage groups. These results suggest that selection for asymmetric gamete signaling could be the first step in the evolution of non-recombinant mating-type loci, paving the road for the evolution of anisogamy and sexes.

Sexual reproduction, from birds to bees, relies on distinct classes of sex cells, known as gametes, fusing together. Most single cell organisms, rather than producing eggs and sperm, have similar sized gametes that fall into distinct ‘mating types’. However, only sex cells belonging to different mating types can fuse together and sexually reproduce.

At first glance, it seems illogical that cells from the same mating type cannot reproduce with each other, as this restricts eligible partners within a population and makes finding a mate more difficult. Yet the typical pattern amongst single cell organisms is still two distinct classes of sex cells, just as in birds and bees. How did the obsession with mating between two different types become favored during evolution?

One possibility is that cells with different mating types can recognize and communicate with each other more easily. Cells communicate by releasing proteins known as ligands, which bind to specific receptors found on the cell’s surface. Using mathematical modelling, Hadjivasiliou and Pomiankowski showed that natural selection typically favors ‘asymmetric’ signaling, whereby cells evolve to either produce receptor A with ligand B, or have the reverse pattern and produce receptor B with ligand A. These asymmetric mutants are favored because they avoid producing ligands that clog or activate the receptors on their own surface. As a result, different types of cells are better at recognizing each other and mating more quickly.

When cells sexually reproduce they exchange genetic material with each other to produce offspring with a combination of genes that differ to their own. However, if the genes coding for ligand and receptor pairs were constantly being ‘swapped’, this could lead to new combinations, and a loss of asymmetric signaling. Hadjivasiliou and Pomiankowski showed that for asymmetric signaling to evolve, natural selection favors the genes encoding these non-compatible ligand and receptor pairs to be closely linked within the genome. This ensures that the mis-matching ligand and receptor are inherited together, preventing cells from producing pairs which can bind to themselves.

This study provides an original way to address an evolutionary question which has long puzzled biologists. These findings raise further questions about how gametes evolved to become the sperm and egg, and how factors such as signaling between cells can determine the sex of more complex organisms, such as ourselves.

Motion, fixation probability and the choice of an evolutionary process

Seemingly minor details of mathematical and computational models of evolution are known to change the effect of population structure on the outcome of evolutionary processes. For example, birth-death dynamics often result in amplification of selection, while death-birth processes have been associated with suppression. In many biological populations the interaction structure is not static. Instead, members of the population are in motion and can interact with different individuals at different times. In this work we study populations embedded in a flowing medium; the interaction network is then time dependent. We use computer simulations to investigate how this dynamic structure affects the success of invading mutants, and compare these effects for different coupled birth and death processes. Specifically, we show how the speed of the motion impacts the fixation probability of an invading mutant. Flows of different speeds interpolate between evolutionary dynamics on fixed heterogeneous graphs and well-stirred populations; this allows us to systematically compare against known results for static structured populations. We find that motion has an active role in amplifying or suppressing selection by fragmenting and reconnecting the interaction graph. While increasing flow speeds suppress selection for most evolutionary models, we identify characteristic responses to flow for the different update rules we test. In particular we find that selection can be maximally enhanced or suppressed at intermediate flow speeds.

Whether a mutation spreads in a population or not is one of the most important questions in biology. The evolution of cancer and antibiotic resistance, for example, are mediated by invading mutants. Recent work has shown that population structure can have important consequences for the outcome of evolution. For instance, a mutant can have a higher or a lower chance of invasion than in unstructured populations. These effects can depend on seemingly minor details of the evolutionary model, such as the order of birth and death events. Many biological populations are in motion, for example due to external stirring. Experimentally this is known to be important; the performance of mutants in E. coli populations, for example, depends on the rate of mixing. Here, we focus on simulations of populations in a flowing medium, and compare the success of a mutant for different flow speeds. We contrast different evolutionary models, and identify what features of the evolutionary model affect mutant success for different speeds of the flow. We find that the chance of mutant invasion can be at its highest (or lowest) at intermediate flow speeds, depending on the order in which birth and death events occur in the evolutionary process.

Estimating the number of sexual events per generation in a facultatively sexual haploid population

In populations of facultatively sexual organisms, the proportion of sexually produced offspring contributed to each generation is a critical determinant of their evolutionary potential. However, estimating this parameter in natural populations has proved difficult. Here we develop a population genetic model for estimating the number of sexual events occurring per generation for facultatively sexual haploids possessing a biallelic mating-type locus (e.g., Chlamydomonas, ascomycete fungi). Our model treats the population as two subpopulations possessing opposite mating-type alleles, which exchange genes only when a sexual event takes place. Where mating types are equally abundant, we show that, for a neutral genetic marker, genetic differentiation between mating-type subpopulations is a simple function of the effective population size, the frequency of sexual reproduction, and the recombination fraction between the genetic marker and the mating-type locus. We employ simulations to examine the effects of linkage of markers to the mating-type locus, inequality of mating-type frequencies, mutation rate, and selection on this relationship. Finally, we apply our model to estimate the number of sexual reproduction events per generation in populations of four species of facultatively sexual ascomycete fungi, which have been jointly scored for mating type and a range of polymorphic molecular markers. Relative estimates are in line with expectations based on the known reproductive biology of these species.