Search

We recently synthesized and reinterpreted published studies to advance an epigenetic model for the development of homosexuality (HS). The model is based on epigenetic marks laid down in response to the XX vs. XY karyotype in embryonic stem cells. These marks boost sensitivity to testosterone in XY fetuses and lower it in XX fetuses, thereby canalizing sexual development. Our model predicts that a subset of these canalizing epigenetic marks stochastically carry over across generations and lead to mosaicism for sexual development in opposite-sex offspring--the homosexual phenotype being one such outcome. Here, we begin by outlining why HS has been under-appreciated as a commonplace phenomenon in nature, and how this trend is currently being reversed in the field of neurobiology. We next briefly describe our epigenetic model of HS, develop a set of predictions, and describe how epigenetic profiles of human stem cells can provide for a strong test of the model., (© 2013 The Authors. Bioessays published by WILEY Periodicals, Inc.)

Formation of partially reproductively isolated ecotypes in the rough periwinkle, Littorina saxatilis, may be a case of incipient nonallopatric ecological speciation. To better understand the dynamics of ecotype formation, its timescale, driving forces and evolutionary consequences, we developed a spatially explicit, individual-based model incorporating relevant ecological, spatial and mate selection data for Swedish L. saxatilis. We explore the impact of bounded hybrid superiority, ecological scenarios and mate selection systems on ecotype formation, gene flow and the evolution of prezygotic isolation. Our model shows that ecotypes are expected to form rapidly in parapatry under conditions applicable to Swedish L. saxatilis and may proceed to speciation. However, evolution of nonrandom mating had complex behaviour. Ecotype evolution was inhibited by pre-existing mating preferences, but facilitated by the evolution of novel preferences. While in many scenarios positive assortative mating reduced gene flow between ecotypes, in others negative assortative mating arose, preferences were lost after ecotype formation, preferences were confined to one ecotype or the ancestral ecotype became extinct through sexual selection. Bounded hybrid superiority (as observed in nature) enhanced ecotype formation but increased gene flow. Our results highlight that ecotype formation and speciation are distinct processes: factors that contribute to ecotype formation can be detrimental to speciation and vice versa. The complex interactions observed between local adaptation and nonrandom mating imply that generalization from data is unreliable without quantitative theory for speciation.

We study victim-exploiter coevolution in a spatially heterogeneous island model. In each species, fitness consequences of between-species interactions are controlled by a single haploid diallelic locus. Our emphasis is on the conditions for the maintenance of genetic variation, the dynamic patterns observed, the extent of local adaptation and genetic differentiation between different demes, and on how different parameters (such as the strength and heterogeneity in selection, migration rates, and the number of sites) affect the dynamic and static behavior of the system. We show that under spatially homogeneous selection the maintenance of genetic variation is possible through asynchronous nonlinear dynamics where the allele frequencies in a majority of demes quickly synchronize but the rest do not. Spatially heterogeneous selection can maintain genetic variation even if migration rates are maximal. This happens in an oscillatory way. Genetic variation is most likely to be maintained at high levels if the heterogeneity in selection is large. If there are some restrictions on migration, genetic variation can be maintained at a stable equilibrium. This behavior is most likely at intermediate migration rates. In this case, the system can exhibit high spatial subdivision as measured by F(ST) values but relatively low local adaptation.

We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large number n of continuously varying traits. In a simple model of random fitness assignment, viable phenotypes are likely to form a giant connected cluster percolating throughout the phenotype space provided the viability probability is larger than 1/2(n). The second model explicitly describes genotype-to-phenotype and phenotype-to-fitness maps, allows for neutrality at both phenotype and fitness levels, and results in a fitness landscape with tunable correlation length. Here, phenotypic neutrality and correlation between fitnesses can reduce the percolation threshold, and correlations at the point of phase transition between local and global are most conducive to the formation of the giant cluster. In the third class of models, particular combinations of alleles or values of phenotypic characters are "incompatible" in the sense that the resulting genotypes or phenotypes have zero fitness. This setting can be viewed as a generalization of the canonical Bateson-Dobzhansky-Muller model of speciation and is related to K-SAT problems, prominent in computer science. We analyze the conditions for the existence of viable genotypes, their number, as well as the structure and the number of connected clusters of viable genotypes. We show that analysis based on expected values can easily lead to wrong conclusions, especially when fitness correlations are strong. We focus on pairwise incompatibilities between diallelic loci, but we also address multiple alleles, complex incompatibilities, and continuous phenotype spaces. In the case of diallelic loci, the number of clusters is stochastically bounded and each cluster contains a very large sub-cube. Finally, we demonstrate that the discrete NK model shares some signature properties of models with high correlations.

Sexual conflict has been suggested as a general cause of genetic diversification in reproductive characters, and as a possible cause of speciation. We use individual-based simulations to study the dynamics of sexual conflict in an isolated diploid population with no spatial structure. To explore the effects of genetic details, we consider two different types of interlocus interaction between female and male traits, and three different types of intra-locus interaction. In the simulations, sexual conflict resulted in at least the following five regimes: (1) continuous coevolutionary chase, (2) evolution toward an equilibrium, (3) cyclic coevolution, (4) extensive genetic differentiation in female traits/genes only, and (5) extensive genetic differentiation in both male and female traits/genes. Genetic differentiation was hardly observed when the traits involved in reproduction were determined additively and interacted in a trait-by-trait way. When the traits interacted in a component-by-component way, genetic differentiation was frequently observed under relatively broad conditions. The likelihood of genetic differentiation largely depended on the number of loci and the type of within-locus dominance. With multiple loci per trait, genetic differentiation was often observed but sympatric speciation was typically hindered by recombination. Sympatric speciation was possible but only under restrictive conditions. Our simulations also highlight the importance of stochastic effects in the dynamics of sexual conflict.

Homosexuality is a common occurrence in humans and other species, yet its genetic and evolutionary basis is poorly understood. Here, we formulate and study a series of simple mathematical models for the purpose of predicting empirical patterns that can be used to determine the form of selection that leads to polymorphism of genes influencing homosexuality. Specifically, we develop theory to make contrasting predictions about the genetic characteristics of genes influencing homosexuality including: (i) chromosomal location, (ii) dominance among segregating alleles and (iii) effect sizes that distinguish between the two major models for their polymorphism: the overdominance and sexual antagonism models. We conclude that the measurement of the genetic characteristics of quantitative trait loci (QTLs) found in genomic screens for genes influencing homosexuality can be highly informative in resolving the form of natural selection maintaining their polymorphism.

We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits that are also subject to direct stabilizing selection toward intermediate optima. Using a weak-selection approximation, we derive analytical results for a symmetric case with equal locus effects and no mutation, and we complement these results by numerical simulations of more general cases. We show that mutualistic and competitive interactions always result in coevolution toward a stable equilibrium with no more than one polymorphic locus per species. Victim-exploiter interactions can lead to different dynamic regimes including evolution toward stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance, whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties. First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci.

The paper entitled "Sympatric speciation," which was published by John Maynard Smith in 1966, initiated the development of mathematical models aiming to identify the conditions for sympatric speciation. A part of that paper was devoted to a specific two-locus, two-allele model of sympatric speciation in a population occupying a two-niche system. Maynard Smith provided some initial numerical results on this model. Later, Dickinson and Antonovics (1973) and Caisse and Antonovics (1978) performed more extensive numerical studies on the model. Here, I report analytical results on the haploid version of the Maynard Smith model. I show how the conditions for sympatric and parapatric speciation and the levels of resulting genetic divergence and reproductive isolation are affected by the strength of disruptive selection and nonrandom mating, recombination rate, and the rates of male and female dispersal between the niches.

Theoretical studies of speciation have been dominated by numerical simulations aiming to demonstrate that speciation in a certain scenario may occur. What is needed now is a shift in focus to identifying more general rules and patterns in the dynamics of speciation. The crucial step in achieving this goal is the development of simple and general dynamical models that can be studied not only numerically but analytically as well. I review some of the existing analytical results on speciation. I first show why the classical theories of speciation by peak shifts across adaptive valleys driven by random genetic drift run into trouble (and into what kind of trouble). Then I describe the Bateson-Dobzhansky-Muller (BDM) model of speciation that does not require overcoming selection. I describe exactly how the probability of speciation, the average waiting time to speciation, and the average duration of speciation depend on the mutation and migration rates, population size, and selection for local adaptation. The BDM model postulates a rather specific genetic architecture of reproductive isolation. I then show exactly why the genetic architecture required by the BDM model should be common in general. Next I consider the multilocus generalizations of the BDM model again concentrating on the qualitative characteristics of speciation such as the average waiting time to speciation and the average duration of speciation. Finally, I consider two models of sympatric speciation in which the conditions for sympatric speciation were found analytically. A number of important conclusions have emerged from analytical studies. Unless the population size is small and the adaptive valley is shallow, the waiting time to a stochastic transition between the adaptive peaks is extremely long. However, if transition does happen, it is very quick. Speciation can occur by mutation and random drift alone with no contribution from selection as different populations accumulate incompatible genes. The importance of mutations and drift in speciation is augmented by the general structure of adaptive landscapes. Speciation can be understood as the divergence along nearly neutral networks and holey adaptive landscapes (driven by mutation, drift, and selection for adaptation to a local biotic and/or abiotic environment) accompanied by the accumulation of reproductive isolation as a by-product. The waiting time to speciation driven by mutation and drift is typically very long. Selection for local adaptation (either acting directly on the loci underlying reproductive isolation via their pleiotropic effects or acting indirectly via establishing a genetic barrier to gene flow) can significantly decrease the waiting time to speciation. In the parapatric case the average actual duration of speciation is much shorter than the average waiting time to speciation. Speciation is expected to be triggered by changes in the environment. Once genetic changes underlying speciation start, they go to completion very rapidly. Sympatric speciation is possible if disruptive selection and/or assortativeness in mating are strong enough. Sympatric speciation is promoted if costs of being choosy are small (or absent) and if linkage between the loci experiencing disruptive selection and those controlling assortative mating is strong.

It is well established that sexual conflict can drive an endless coevolutionary chase between the sexes potentially leading to genetic divergence of isolated populations and allopatric speciation. We present a simple mathematical model that shows that sexual conflict over mating rate can result in two other general regimes. First, rather than "running away" from males, females can diversify genetically into separate groups, effectively "trapping" the males in the middle at a state characterized by reduced mating success. Female diversification brings coevolutionary chase to the end. Second, under certain conditions, males respond to female diversification by diversifying themselves. This response results in the formation of reproductively isolated clusters of genotypes that emerge sympatrically.

We study genetic variation in phenotypic plasticity maintained by a balance between mutation and weak stabilizing selection. We consider linear reaction norms allowing for spatial and/or temporal variation in the environments of development and selection. We show that the overall genetic variation maintained does not depend on whether the trait is plastic or not. The genetic variances in height and slope of a linear reaction norm, and their covariance, are predicted to decrease with the variation in the environment. Non-pleiotropic loci influencing either height or slope are expected to decrease the genetic variance in slope relative to that in height. Decrease in the ratio of genetic variance in slope to genetic variance in height with increasing variation in the environment presents a test for the presence of loci that only influence the slope, and not the height. We use data on Drosophila to test the theory. In seven of eight pair-wise comparisons genetic variation in reaction norm is higher in a less variable environment than in a more variable environment, which is in accord with the model's predictions.

We develop a simple framework for modeling speciation and diversification as a continuous process of accumulation of genetic (or morphological) differences accompanied by species and subpopulation extinction and/or range expansion. This framework can be used to approach a number of questions such as species-area distribution, species-range size distribution, the rate of ecological turnover, asymmetries of range division between sister species, waiting time until speciation and extinction, the relationship between the geographic range size and the probability of speciation, the relationships between subpopulation-level parameters and metapopulation-level parameters, and the effects of taxonomic level on these rates, distributions, and parameters. We illustrate some of these applications using numerical simulations. We develop approximations describing the dependence of the number of different taxonomic units, their average range size, and the rate of their turnover on the system size, the rate of fixation of genetic (or morphological) changes in local demes, and the rate of local extinction and colonization.

Geographic variation may ultimately lead to the splitting of a subdivided population into reproductively isolated units in spite of migration. Here, we consider how the waiting time until the first split and its location depend on different evolutionary factors including mutation, migration, random genetic drift, genetic architecture, and the geometric structure of the habitat. We perform large-scale, individual-based simulations using a simple model of reproductive isolation based on a classical view that reproductive isolation evolves as a by-product of genetic divergence. We show that rapid parapatric speciation on the time scale of a few hundred to a few thousand generations is plausible even when neighboring subpopulations exchange several individuals each generation. Divergent selection for local adaptation is not required for rapid speciation. Our results substantiates the claims that species with smaller range sizes (which are characterized by smaller local densities and reduced dispersal ability) should have higher speciation rates. If mutation rate is small, local abundances are low, or substantial genetic changes are required for reproductive isolation, then central populations should be the place where most splits take place. With high mutation rates, high local densities, or with moderate genetic changes sufficient for reproductive isolation, speciation events are expected to involve mainly peripheral populations.

Metapopulation models and stepping-stone models in genetics are based on very different underlying dispersal structures, yet it can be difficult to distinguish the behaviour of the two kinds of models. We demonstrate a striking qualitative difference in the equilibrium behaviour possible with these two kinds of dispersal. If, in a local patch, there are multiple stable equilibria (and consequently an unstable equilibrium), we demonstrate that, for the spatial system with a metapopulation structure, at equilibrium every patch has to be near one of the stable equilibria. This contrasts with the clinal structure possible with a stepping-stone or continuous space model; thus the result can be used to deduce qualitative information about the form of dispersal from observations of allele frequencies.

I formulate and study a series of simple one-locus two-allele models for maternal (parental) selection. I show that maternal (parental) selection can result in simultaneous stability of equilibria of different types. Thus, in the presence of maternal (parental) selection the outcome of population evolution can significantly depend on initial conditions. With maternal selection, genetic variability can be maintained in the population even if none of the offspring of heterozygous mothers survive. I demonstrate that interactions of maternal and paternal selection can result in stable oscillations of genotype frequencies. A necessary condition for cycling is strong selection.

I study the dynamics of a simple quantitative genetic model describing coevolution of two antagonistic species of the victim-exploiter type. In this model, individuals are different with respect to an additive polygenic character that is under direct stabilizing selection and which also determines the strength of within and between species interactions. The model assumes that between species interactions are most intense when the victim's and exploiter's phenotypes match. I show that a cyclic coevolutionary chase is possible under a broad range of conditions. In most cases, the system cycles if the "victim" has a stronger incentive to win and/or a larger genetic variance, and is under stronger stabilizing selection than the "exploiter". The results presented here provide counter-examples to recent studies that (1) question the applicability of "Red Queen" and "arms race" metaphors for continuously varying traits; (2) argue for the existence of crucial differences between major and minor loci dynamics; and (3) attribute a stabilizing role to coevolution.

We study a two locus model, with additive contributions to the phenotype, to explore the dynamics of different phenotypic characteristics under stabilizing selection and recombination. We demonstrate that the interaction of selection and recombination results in constraints on the mode of phenotypic evolution. Let Vg be the genic variance of the trait and CL be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that, independent of the initial conditions, the dynamics of the system on the plane (Vg, CL) are typically characterized by a quick approach to a straight line with slow evolution along this line afterward. We analyze how the mode and the rate of phenotypic evolution depend on the strength of selection relative to recombination, on the form of fitness function, and the difference in allelic effect. We argue that if selection is not extremely weak relative to recombination, linkage disequilibrium generated by stabilizing selection influences the dynamics significantly. We demonstrate that under these conditions, which are plausible in nature and certainly the case in artificial stabilizing selection experiments, the model can have a polymorphic equilibrium with positive linkage disequilibrium that is stable simultaneously with monomorphic equilibria.

We present exact conditions for stability of monomorphic equilibria in a general multilocus multiallele system and of specific polymorphic equilibria in general one- and two-locus multiallele systems. We show how these exact results on one- and two-locus systems can be used in approximate analysis of polymorphic equilibria in multilocus systems under selection strong relative to recombination. We determine conditions for existence and stability of polymorphic equilibria in specific models of quadratic stabilizing selection on additive polygenic traits.

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent "stabilizing selection" independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let Vm be the genetic variance supplied by mutation (or migration) each generation, Vg be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order Vm/Vg. In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.

We study a two locus model with additive contributions to the phenotype to explore the relationship between stabilizing selection and recombination. We show that if the double heterozygote has the optimum phenotype and the contributions of the loci to the trait are different, then any symmetric stabilizing selection fitness function can maintain genetic variability provided selection is sufficiently strong relative to linkage. We present results of a detailed analysis of the quadratic fitness function which show that selection need not be extremely strong relative to recombination for the polymorphic equilibria to be stable. At these polymorphic equilibria the mean value of the trait, in general, is not equal to the optimum phenotype, there exists a large level of negative linkage disequilibrium which "hides" additive genetic variance, and different equilibria can be stable simultaneously. We analyze dependence of different characteristics of these equilibria on the location of optimum phenotype, on the difference in allelic effect, and on the strength of selection relative to recombination. Our overall result that stabilizing selection does not necessarily eliminate genetic variability is compatible with some experimental results where the lines subject to strong stabilizing selection did not have significant reductions in genetic variability.

We study multilocus polymorphism under selection, using a class of fitness functions that account for additive, dominant, and pairwise additive-by-additive epistatic interactions. The dynamic equations are derived in terms of allele frequencies and disequilibria, using the notions of marginal systems and marginal fitnesses, without any approximations. Stationary values of allele frequencies and pairwise disequilibria under weak selection are calculated by regular perturbation techniques. We derive conditions for existence and stability of the multilocus polymorphic states. Using these results, we then analyze a number of models describing stabilizing selection on additive characters, with some other factors, and determine the conditions under which genetic quantitative variability is maintained.

An approach to the investigation of the evolution of quantitative traits on the basis of analysis of two-locus marginal systems dynamics has been developed. It has been shown that under stabilizing selection the "quasi-stationary" state is quickly reached and maintained continuously. The "quasi-stationary" state is characterized by small changes in allele frequencies and by linkage disequilibrium that significantly decreases genotypic variance. Equations defining the role of linkage disequilibrium in the stationary state of mutation-selection balance are derived.