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S Gavrilets

Publications and source records attributed to S Gavrilets.

At least 19 recordsLinked to original sources
PubMed2005

20 questions on adaptive dynamics.

Adaptive Dynamics is an approach to studying evolutionary change when fitness is density or frequency dependent. Modern papers identifying themselves as using this approach first appeared in the 1990s, and have greatly increased up to the present. However, because of the rather technical nature of many of the papers, the approach is not widely known or understood by evolutionary biologists. In this review we aim to remedy this situation by outlining the methodology and then examining its strengths and weaknesses. We carry this out by posing and answering 20 key questions on Adaptive Dynamics. We conclude that Adaptive Dynamics provides a set of useful approximations for studying various evolutionary questions. However, as with any approximate method, conclusions based on Adaptive Dynamics are valid only under some restrictions that we discuss.

Adaptation, Biological↗
PubMed2001

The evolution of female mate choice by sexual conflict.

Although empirical evidence has shown that many male traits have evolved via sexual selection by female mate choice, our understanding of the adaptive value of female mating preferences is still very incomplete. It has recently been suggested that female mate choice may result from females evolving resistance rather than attraction to males, but this has been disputed. Here, we develop a quantitative genetic model showing that sexual conflict over mating indeed results in the joint evolution of costly female mate choice and exaggerated male traits under a wide range of circumstances. In contrast to tradition explanations of costly female mate choice, which rely on indirect genetic benefits, our model shows that mate choice can be generated as a side-effect of females evolving to reduce the direct costs of mating.

Animals↗
PubMed2000

Waiting time to parapatric speciation.

Using a weak migration and weak mutation approximation, I studied the average waiting time to parapatric speciation. The description of reproductive isolation used is based on the classical Dobzhansky model and its recently proposed multilocus generalizations. The dynamics of parapatric speciation are modelled as a biased random walk performed by the average genetic distance between the residents and immigrants. If a small number of genetic changes is sufficient for complete reproductive isolation, mutation and random genetic drift alone can cause speciation on the time-scale of ten to 1,000 times the inverse of the mutation rate over a set of loci underlying reproductive isolation. Even relatively weak selection for local adaptation can dramatically decrease the waiting time to speciation. The actual duration of the parapatric speciation process (that is the duration of intermediate forms in the actual transition to a state of complete reproductive isolation) is shorter by orders of magnitude than the overall waiting time to speciation. For a wide range of parameter values, the actual duration of parapatric speciation is of the order of one over the mutation rate. In general, parapatric speciation is expected to be triggered by changes in the environment.

Animals↗
PubMed2000

Rapid evolution of reproductive barriers driven by sexual conflict.

A growing amount of experimental data indicates extremely rapid evolution of traits and proteins related to fertilization in many diverging taxa. These data come from studies of sperm or pollen competition between closely related species, and from molecular studies of fertilization proteins. The positive selection for evolutionary novelty that appears to be acting on fertilization systems seems paradoxical because successful reproduction requires the close matching of female and male traits. It has been suggested that perpetual coevolution between the sexes can result from sexual conflict in mating. Sexual conflict occurs when characteristics that enhance the reproductive success of one sex reduce the fitness of the other sex. Numerous examples of sexual conflict resulting from sensory exploitation, polyspermy and the cost of mating have been discussed in detail. The potential for coevolution due to such conflict has been evaluated experimentally. Here I develop a simple mathematical model describing coevolutionary dynamics of male and female traits involved in reproduction. The model shows that continual change in such traits at a constant speed is expected whenever females (or eggs) experience fitness loss from having too many compatible males (or sperms). The plausibility of runaway coevolution increases with increasing population size. Rapid evolution of reproductive barriers driven by sexual conflict may explain increased speciation rates after colonization of new habitats ('adaptive radiation') and high species richness in resource-rich environments.

Animals↗
PubMed2000

Maintenance of genetic variation in phenotypic plasticity: the role of environmental variation.

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.

Alleles↗
PubMed2000

Patterns of parapatric speciation.

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.

Animals↗
PubMed2000

Dynamics of speciation and diversification in a metapopulation.

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.

Algorithms↗
PubMed1999

Global dispersal reduces local diversity.

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.

Animals↗
PubMed1998

Rapid parapatric speciation on holey adaptive landscapes.

A classical view of speciation is that reproductive isolation arises as a by-product of genetic divergence. Here, individual-based simulations are used to evaluate whether the mechanisms implied by this view may result in rapid speciation if the only source of genetic divergence are mutation and random genetic drift. Distinctive features of the simulations are the consideration of the complete process of speciation (from initiation until completion), and of a large number of loci, which was only one order of magnitude smaller than that of bacteria. It is demonstrated that rapid speciation on the time-scale of hundreds of generations is plausible without the need for extreme founder events, complete geographic isolation, the existence of distinct adaptive peaks or selection for local adaptation. The plausibility of speciation is enhanced by population subdivision. Simultaneous emergence of more than two new species from a subdivided population is highly probable. Numerical examples relevant to the theory of centrifugal speciation and to the conjectures about the fate of 'ring species' and 'sexual continuums' are presented.

Biological Evolution↗
PubMed1998

Coevolutionary chase in two-species systems with applications to mimicry.

We study a general dynamical model describing coevolution of two haploid populations with two alleles at a single locus under weak linear symmetric frequency-dependent selection. A novel and more realistic element of our modeling approach is that both species are allowed to evolve. We analyse conditions for "evolutionary chase" between two phenotypically similar species in which one species evolves to decrease its resemblance with the other species while this other species evolves to increase its resemblance with the first species. We apply our results to a series of simple population genetics models describing classical Müllerian and Batesian mimicries as well as intermediate cases. We show that one of the most important factors influencing the plausibility of non-equilibrium dynamics in systems of mimicry is the relationship between the strength of between-species and within-species interactions. This indicates that this relationship should be the focus of both experimental and theoretical work. Our results suggest that systematic studies of frequencies of different mimicry morphs through time may be very useful.

Animals↗
PubMed1998

One-locus two-allele models with maternal (parental) selection.

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.

Alleles↗
PubMed1997

Coevolutionary chase on exploiter-victim systems with polygenic characters.

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.

Animals↗
PubMed1997

Percolation on the fitness hypercube and the evolution of reproductive isolation.

We study the structure and properties of adaptive landscapes arising from the assumption that genotype fitness can only be 0 (inviable genotype) or 1 (viable genotype). An appropriate image of resulting ("holey") fitness landscapes is a (multidimensional) flat surface with many holes. We have demonstrated that in the genotype space there are clusters of viable genotypes whose members can evolve from any member by single substitutions and that there are "species" defined according to the biological species concept. Assuming that the number of genes, n, is very large while the proportion of viable genotypes among all possible genotypes, p, is very small, we have deduced many qualitative and quantitative properties of holey adaptive landscapes which may be related to the patterns of speciation. Relationship between p and n determines two qualitatively different regimes: subcritical and supercritical. The subcritical regime takes place if p is extremely small. In this case, the largest clusters of viable genotypes in the genotype space have size of order n and there are many of such size; typical members of a cluster are connected by a single ("evolutionary") path; the number of different (biological) species in the cluster has order n; the expected number of different species in the cluster within k viable substitutions from any its member is of order k. The supercritical regime takes place if p is small but not extremely small. In this case, there exists a cluster of viable genotypes (a "giant" component) that has size of order 2n/n; the giant component comes "near" every point of the genotype space; typical members of the giant component are connected by many evolutionary paths; the number of different (biological) species on the "giant" component has at least order n2; the expected number of different species on the "giant" component within k viable substitution from any its member is at least of order kn. At the boundary of two regimes all properties of adaptive landscapes undergo dramatic changes, a physical analogy of which is a phase transition. We have considered the most probable (within the present framework) scenario of biological evolution on holey landscapes assuming that it starts on a genotype from the largest connected component and proceeds along it by mutation and genetic drift. In this scenario, there is no need to cross any "adaptive valleys"; reproductive isolation between populations evolves as a side effect of accumulating different mutations. The rate of divergence is very fast: a few substitutions are sufficient to result in a new biological species. We argue that macroevolution and speciation on "rugged" fitness landscapes proceed according to the properties of the corresponding holey landscapes.

Animals↗
PubMed1995

Intermittency and transient chaos from simple frequency-dependent selection.

Frequency-dependent selection is an important determinant of the evolution of gametophytic self-incompatibility systems in plants, aposematic (warning) and cryptic coloration, systems of mimicry, competitive interactions among members of a population, mating preferences, predator-prey and host-parasite interactions, aggression and other behavioural traits. Past theoretical studies of frequency-dependent selection have shown it to be a plausible mechanism for the maintenance of genetic variability in natural populations. Here, through an analysis of a simple deterministic model for frequency-dependent selection, we demonstrate that complex dynamic behaviour is possible under a broad range of parameter values. In particular we show that the model exhibits not only cycles and chaos but also, for a more restricted set of parameters, transient chaos and intermittency: alterations between an apparently deterministic behaviour and apparently chaotic fluctuations. This behaviour, which has not been stressed within the population genetics literature, provides an explanation for erratic dynamics of gene frequencies.

Alleles↗
PubMed1995

Dynamics of polygenic variability under stabilizing selection, recombination, and drift.

We study the transient dynamics of the genotypic variance of an additive trait under stabilizing selection, recombination and random drift. We show how interaction of these factors determines the form and the rates of change of different components of the genotypic variance. Let Vg be the genic variance of the trait and CL be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that 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 afterwards. We show that the number of loci, n, and the population size, N, affect the expected dynamics of Vg mainly through the ratio N/n. We use our analytical and numerical results in interpreting the published results of artificial stabilizing selection experiments. The analysis suggests that it is drift and not selection that most likely led to the reduction of genetic variability in most of these experiments. Even very strong stabilizing selection only slowly removes polygenic variability from populations.

Algorithms↗
PubMed1994

Maintenance of multilocus variability under strong stabilizing selection.

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.

Alleles↗
PubMed1994

Dynamics of genetic variability in two-locus models of stabilizing selection.

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.

Animals↗