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We build a spatial individual-based multilocus model of homoploid hybrid speciation tailored for a tentative case of hybrid origin of Heliconius heurippa from H. melpomene and H. cydno in South America. Our model attempts to account for empirical patterns and data on genetic incompatibility, mating preferences and selection by predation (both based on coloration patterns), habitat preference, and local adaptation for all three Heliconius species. Using this model, we study the likelihood of recombinational speciation and identify the effects of various ecological and genetic parameters on the dynamics, patterns, and consequences of hybrid ecological speciation. Overall, our model supports the possibility of hybrid origin of H. heurippa under certain conditions. The most plausible scenario would include hybridization between H. melpomene and H. cydno in an area geographically isolated from the rest of both parental species with subsequent long-lasting geographic isolation of the new hybrid species, followed by changes in the species ranges, the secondary contact, and disappearance of H. melpomene-type ecomorph in the hybrid species. However, much more work (both empirical and theoretical) is necessary to be able to make more definite conclusions on the importance of homoploid hybrid speciation in animals.

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.

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.

Females of many species are frequently courted by promiscuous males of their own and other closely related species. Such mating interactions may impose strong selection on female mating preferences to favor trait values in conspecific males that allow females to discriminate them from their heterospecific rivals. We explore the consequences of such selection in models of the evolution of female mating preferences when females must interact with heterospecific males from which they are completely postreproductively isolated. Specifically, we allow the values of both the most preferred male trait and the tolerance of females for males that deviate from this most preferred trait to evolve. Also, we consider situations in which females base their mating decisions on multiple male traits and must interact with males of multiple species. Females will rapidly differentiate in preference when they sometimes mistake heterospecific males for suitable mates, and the differentiation of female preference will select for conspecific male traits to differentiate as well. In most circumstances, this differentiation continues indefinitely, but slows substantially once females are differentiated enough to make mistakes rare. Populations of females with broader preference functions (i.e., broader tolerance for males with trait values that deviate from females' most preferred values) will evolve further to differentiate if the shape of the function cannot evolve. Also, the magnitude of separation that evolves is larger and achieved faster when conspecific males have lower relative abundance. The direction of differentiation is also very sensitive to initial conditions if females base their mate choices on multiple male traits. We discuss how these selection pressures on female mate choice may lead to speciation by generating differentiation among populations of a progenitor species that experiences different assemblages of heterospecifics. Opportunities for differentiation increase as the number of traits involved in mate choice increase and as the number of species involved increases. We suggest that this mode of speciation may have been particularly prevalent in response to the cycles of climatic change throughout the Quaternary that forced the assembly and disassembly of entire communities on a continentwide basis.

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.

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.

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.

We study the strength of the genetic barrier to neutral gene flow in a general one-locus, two-allele model that includes viability selection as well as fertility selection and premating isolation. We have separately considered adult migration and pollen migration. Our theoretical results suggest that selection against hybrid formation in the form of fertility selection or assortative mating is more effective in preventing introgression of neutral alleles than is reduction in hybrid viability. We argue that in experimental studies of introgression testing of F 1 hybrids is as important as testing of parental forms. To illustrate the utility of this approach, we estimate the strength of the barrier to neutral gene flow between Piriqueta caroliniana and P. viridis, between Iris hexagona and I. fulva, and between Chorthippus brunneus and C. biguttulus., (© 1998 The Society for the Study of Evolution.)

Dobzhansky's model of epistatic selection assumes that viable genotypes form "clusters" in genotype space so that populations can evolve from one state to a reproductively isolated state following a "ridge" of well-fit genotypes without crossing any deep adaptive valleys. Recently, the importance of Dobzhansky-type models in evolutionary studies has been reemphasized by Gavrilets (1997a) and Gavrilets and Gravner (1997) who argue that the existence of "ridges" of well-fit genotypes connecting reproductively isolated genotypes is actually a general property of multidimensional adaptive landscapes. Using rigorous techniques and numerical simulations, I analyze clines in the frequencies of selected and neutral alleles maintained by a balance of migration and Dobzhansky-type epistatic selection acting on two diallelic loci. I show that Dobzhansky-type epistatic selection can build up a very strong barrier to neutral gene flow. I describe properties of clines that are indicative of Dobzhansky-type selection., (© 1997 The Society for the Study of Evolution.)

A common conclusion in several recent publications devoted to the deterministic analysis of the third phase of Wright's shifting-balance theory is that under reasonable conditions phase three should proceed easily. I argue that the mathematical equations analyzed in these papers do not correspond to the biological situation they were meant to describe. I present a more appropriate study of the third phase of the shifting balance. My results show that the third phase can proceed only under much more restricted conditions than the previous studies suggested. Migration should be neither too strong not too weak relative to selection. The higher peak should be sufficiently dominant over the lower peak. Recombination can greatly reduce the plausibility of this phase or completely preclude peak shifts. A very important determinant of the ultimate outcome of the competition between different peaks is the topological structure of the network of demes. Peak shifts in two-dimensional networks of demes are more difficult than in one-dimensional networks. Phase three can be accomplished easiest if it is initiated in one of the peripheral demes., (© 1996 The Society for the Study of Evolution.)

We propose a simple model for analyzing the effects of microenvironmental variation in quantitative genetics. Our model assumes that the sensitivity of the phenotype to fluctuations in microenvironment has a genetic basis and allows for genetic correlation between trait value and microenvironmental sensitivity. We analyze the effects of short-term stabilizing and directional selection on the genotypic and microenvironmental components of phenotypic variance. Our model predicts that stabilizing selection on a quantitative trait increases developmental canalization. We show that stabilizing selection can result in an increase in the heritability. Our findings may provide an explanation for the results of selection experiments in which artificial stabilizing selection did not change the heritability coefficient or increased it., (© 1994 The Society for the Study of Evolution.)