Fixation probability and time in subdivided populations

Demographic histories of ERV-K in humans, chimpanzees and rhesus monkeys

We detected 19 complete endogenous retroviruses of the K family in the genome of rhesus monkey (Macaca mulatta; RhERV-K) and 12 full length elements in the genome of the common chimpanzee (Pan troglodytes; CERV-K). These sequences were compared with 55 human HERV-K and 20 CERV-K reported previously, producing a total data set of 106 full-length ERV-K genomes. Overall, 61% of the human elements compared to 21% of the chimpanzee and 47% of rhesus elements had estimated integration times less than 4.5 million years before present (MYBP), with an average integration times of 7.8 MYBP, 13.4 MYBP and 10.3 MYBP for HERV-K, CERV-K and RhERV-K, respectively. By excluding those ERV-K sequences generated by chromosomal duplication, we used 63 of the 106 elements to compare the population dynamics of ERV-K among species. This analysis indicated that both HERV-K and RhERV-K had similar demographic histories, including markedly smaller effective population sizes, compared to CERV-K. We propose that these differing ERV-K dynamics reflect underlying differences in the evolutionary ecology of the host species, such that host ecology and demography represent important determinants of ERV-K dynamics.

Plant speciation

Like the formation of animal species, plant speciation is characterized by the evolution of barriers to genetic exchange between previously interbreeding populations. Prezygotic barriers, which impede mating or fertilization between species, typically contribute more to total reproductive isolation in plants than do postzygotic barriers, in which hybrid offspring are selected against. Adaptive divergence in response to ecological factors such as pollinators and habitat commonly drives the evolution of prezygotic barriers, but the evolutionary forces responsible for the development of intrinsic postzygotic barriers are virtually unknown and frequently result in polymorphism of incompatibility factors within species. Polyploid speciation, in which the entire genome is duplicated, is particularly frequent in plants, perhaps because polyploid plants often exhibit ecological differentiation, local dispersal, high fecundity, perennial life history, and self-fertilization or asexual reproduction. Finally, species richness in plants is correlated with many biological and geohistorical factors, most of which increase ecological opportunities.

Estimating a geographically explicit model of population divergence

Patterns of genetic variation can provide valuable insights for deciphering the relative roles of different evolutionary processes in species differentiation. However, population-genetic models for studying divergence in geographically structured species are generally lacking. Since these are the biogeographic settings where genetic drift is expected to predominate, not only are population-genetic tests of hypotheses in geographically structured species constrained, but generalizations about the evolutionary processes that promote species divergence may also be potentially biased. Here we estimate a population-divergence model in montane grasshoppers from the sky islands of the Rocky Mountains. Because this region was directly impacted by Pleistocene glaciation, both the displacement into glacial refugia and recolonization of montane habitats may contribute to differentiation. Building on the tradition of using information from the genealogical relationships of alleles to infer the geography of divergence, here the additional consideration of the process of gene-lineage sorting is used to obtain a quantitative estimate of population relationships and historical associations (i.e., a population tree) from the gene trees of five anonymous nuclear loci and one mitochondrial locus in the broadly distributed species Melanoplus oregonensis. Three different approaches are used to estimate a model of population divergence; this comparison allows us to evaluate specific methodological assumptions that influence the estimated history of divergence. A model of population divergence was identified that significantly fits the data better compared to the other approaches, based on per-site likelihood scores of the multiple loci, and that provides clues about how divergence proceeded in M. oregonensis during the dynamic Pleistocene. Unlike the approaches that either considered only the most recent coalescence (i.e., information from a single individual per population) or did not consider the pattern of coalescence in the gene genealogies, the population-divergence model that best fits the data was estimated by considering the pattern of gene lineage coalescence across multiple individuals, as well as loci. These results indicate that sampling of multiple individuals per population is critical to obtaining an accurate estimate of the history of divergence so that the signal of common ancestry can be separated from the confounding influence of gene flow-even though estimates suggest that gene flow is not a predominant factor structuring patterns of genetic variation across these sky island populations. They also suggest that the gene genealogies contain information about population relationships, despite the lack of complete sorting of gene lineages. What emerges from the analyses is a model of population divergence that incorporates both contemporary distributions and historical associations, and shows a latitudinal and regional structuring of populations reminiscent of population displacements into multiple glacial refugia. Because the population-divergence model itself is built upon the specific events shaping the history of M. oregonensis, it provides a framework for estimating additional population-genetic parameters relevant to understanding the processes governing differentiation in geographically structured species and avoids the problems of relying on overly simplified and inaccurate divergence models. The utility of these approaches, as well as the caveats and future improvements, for estimating population relationships and historical associations relevant to genetic analyses of geographically structured species are discussed.

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae(formally exact in the limit of extremely weak migration) for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases-except this last where fixation in a finite time is seen--the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.

Surviving with low genetic diversity: the case of albatrosses

Low genetic diversity is predicted to negatively impact species viability and has been a central concern for conservation. In contrast, the possibility that some species may thrive in spite of a relatively poor diversity has received little attention. The wandering and Amsterdam albatrosses (Diomedea exulans and Diomedea amsterdamensis) are long-lived seabirds standing at an extreme along the gradient of life strategies, having traits that may favour inbreeding and low genetic diversity. Divergence time of the two species is estimated at 0.84 Myr ago from cytochrome b data. We tested the hypothesis that both albatrosses inherited poor genetic diversity from their common ancestor. Within the wandering albatross, per cent polymorphic loci and expected heterozygosity at amplified fragment length polymorphisms were approximately one-third of the minimal values reported in other vertebrates. Genetic diversity in the Amsterdam albatross, which is recovering from a severe bottleneck, was about twice as low as in the wandering albatross. Simulations supported the hypothesis that genetic diversity in albatrosses was already depleted prior to their divergence. Given the generally high breeding success of these species, it is likely that they are not suffering much from their impoverished diversity. Whether albatrosses are unique in this regard is unknown, but they appear to challenge the classical view about the negative consequences of genetic depletion on species survival.

Fixation probability for a beneficial allele and a mutant strategy in a linear game under weak selection in a finite island model

The effect of population structure on the probability of fixation of a newly introduced mutant under weak selection is studied using a coalescent approach. Wright's island model in a framework of a finite number of demes is assumed and two selection regimes are considered: a beneficial allele model and a linear game among offspring. A first-order approximation of the fixation probability for a single mutant with respect to the intensity of selection is deduced. The approximation requires the calculation of expected coalescence times, under neutrality, for lineages starting from two or three sampled individuals. The results are obtained in a general setting without assumptions on the number of demes, the deme size or the migration rate, which allows for simultaneous coalescence or migration events in the genealogy of the sampled individuals. Comparisons are made with limit cases as the deme size or the number of demes goes to infinity or the migration rate goes to zero for which a diffusion approximation approach is possible. Conditions for selection to favor a mutant strategy replacing a resident strategy in the context of a linear game in a finite island population are addressed.

Evolution of coadaptation in a subdivided population

The interplay between population subdivision and epistasis is investigated by studying the fixation probability of a coadapted haplotype in a subdivided population. Analytical and simulation models are developed to study the evolutionary fate of two conditionally neutral mutations that interact epistatically to enhance fitness. We find that the fixation probability of a coadapted haplotype shows a marked increase when the population is genetically subdivided and subpopulations are loosely connected by migration. Moderate migration and isolation allow the propagation of the mutant alleles across subpopulations, while at the same time preserving the favorable allelic combination established within each subpopulation. Together they create the condition most favorable for the ultimate fixation of the coadapted haplotype. On the basis of the analytical and simulation results, we discuss the fundamental role of population subdivision and restricted gene flow in promoting the evolution of functionally integrated systems, with some implications for the shifting-balance theory of evolution.

Direct reciprocity on graphs

Direct reciprocity is a mechanism for the evolution of cooperation based on the idea of repeated encounters between the same two individuals. Here we examine direct reciprocity in structured populations, where individuals occupy the vertices of a graph. The edges denote who interacts with whom. The graph represents spatial structure or a social network. For birth-death or pairwise comparison updating, we find that evolutionary stability of direct reciprocity is more restrictive on a graph than in a well-mixed population, but the condition for reciprocators to be advantageous is less restrictive on a graph. For death-birth and imitation updating, in contrast, both conditions are easier to fulfill on a graph. Moreover, for all four update mechanisms, reciprocators can dominate defectors on a graph, which is never possible in a well-mixed population. We also study the effect of an error rate, which increases with the number of links per individual; interacting with more people simultaneously enhances the probability of making mistakes. We provide analytic derivations for all results.

Natural selection on fecundity variance in subdivided populations: kin selection meets bet hedging

In a series of seminal articles in 1974, 1975, and 1977, J. H. Gillespie challenged the notion that the "fittest" individuals are those that produce on average the highest number of offspring. He showed that in small populations, the variance in fecundity can determine fitness as much as mean fecundity. One likely reason why Gillespie's concept of within-generation bet hedging has been largely ignored is the general consensus that natural populations are of large size. As a consequence, essentially no work has investigated the role of the fecundity variance on the evolutionary stable state of life-history strategies. While typically large, natural populations also tend to be subdivided in local demes connected by migration. Here, we integrate Gillespie's measure of selection for within-generation bet hedging into the inclusive fitness and game theoretic measure of selection for structured populations. The resulting framework demonstrates that selection against high variance in offspring number is a potent force in large, but structured populations. More generally, the results highlight that variance in offspring number will directly affect various life-history strategies, especially those involving kin interaction. The selective pressures on three key traits are directly investigated here, namely within-generation bet hedging, helping behaviors, and the evolutionary stable dispersal rate. The evolutionary dynamics of all three traits are markedly affected by variance in offspring number, although to a different extent and under different demographic conditions.

Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully connected networks and on spatial lattices. The time t* for a favorable mutation to dominate scales with the population size N as N(D+1)/D in D-dimensional hypercubic lattices and as NlnN in fully-connected graphs. It is shown that the surface of the interface between mutants and nonmutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction.

The distribution of beneficial mutant effects under strong selection

For a general theory of adaptation, it is essential to know the distribution of fitness effects of beneficial mutations. Recent theoretical and empirical studies have made considerable progress in determining the characteristics of this distribution. To date, the experiments have largely verified the theoretical predictions. Despite the fact that the theoretical work has assumed small selection coefficients, strong selection has been observed in some experiments, especially those involving novel environments. Here, we derive the distribution of fitness effects among fixed beneficial mutants without the restriction of low selection coefficients. The fate of strongly favored alleles is less affected by stochastic drift while rare, causing the distribution of fitness effects among fixed beneficial mutations to reflect more closely the distribution among all newly arising beneficial mutations. We also find that when many alleles compete for fixation within an asexual population (clonal interference), the beneficial effects of a newly fixed mutant cannot be well estimated because of the high number of subsequent mutations that arise within the genome, regardless of whether selection is strong or weak.

The nature of plant species

Many botanists doubt the existence of plant species, viewing them as arbitrary constructs of the human mind, as opposed to discrete, objective entities that represent reproductively independent lineages or 'units of evolution'. However, the discreteness of plant species and their correspondence with reproductive communities have not been tested quantitatively, allowing zoologists to argue that botanists have been overly influenced by a few 'botanical horror stories', such as dandelions, blackberries and oaks. Here we analyse phenetic and/or crossing relationships in over 400 genera of plants and animals. We show that although discrete phenotypic clusters exist in most genera (> 80%), the correspondence of taxonomic species to these clusters is poor (< 60%) and no different between plants and animals. Lack of congruence is caused by polyploidy, asexual reproduction and over-differentiation by taxonomists, but not by contemporary hybridization. Nonetheless, crossability data indicate that 70% of taxonomic species and 75% of phenotypic clusters in plants correspond to reproductively independent lineages (as measured by postmating isolation), and thus represent biologically real entities. Contrary to conventional wisdom, plant species are more likely than animal species to represent reproductively independent lineages.

Genetic load in subdivided populations: interactions between the migration rate, the size and the number of subpopulations

We assess the relative importance of migration rate, size and number of subpopulations on the genetic load of subdivided populations. Using diffusion approximations, we show that in most cases subdivision has detrimental effects on fitness. Moreover, our results suggest that fitness increases with subpopulation size, so that for the same total population size, genetic load is relatively lower when there are a small number of large subpopulations. Using elasticity analysis, we show that the size of the subpopulations appears to be the parameter that most strongly determines genetic load. interconnecting subpopulations via migration would also be of importance for population fitness when subpopulations are small and gene flow is low. Interestingly, the number of subpopulations has minor influence on genetic load except for the case of both very slightly deleterious mutations and small subpopulations. Elasticities decrease as the magnitude of deleterious effects increases. In other words, population structure does not matter for very deleterious alleles, but strongly affects fitness for slightly deleterious alleles.

Effect of population structure on the amount of polymorphism and the fixation probability under overdominant selection

Under overdominant selection, mutants substantially contribute to increase the amount of polymorphism. It is also known that under neutrality as the migration rates among demes decrease in a subdivided population, the amount of polymorphism increases along with the increase of the effective population size, N(e). In this study, under overdominant selection the effect of population subdivision on the amount of polymorphism was investigated using the diffusion approximation and the low migration approximation. It was shown that if selection is medium or strong (e.g., N(T)s > 1, where N(T) is the population size and s is the selective advantage of heterozygotes), the nucleotide diversity, pi, decreases along with the decrease of Nm against the increase of N(e), where N is the size of demes and m is the migration rate per deme. In addition, the ratio of the nucleotide diversity to the evolutionary rate also decreases along with the decrease of Nm. In some cases the ratio becomes smaller than that expected under neutrality as Nm decreases.

Inbreeding Depression and the Evolution of Dispersal Rates: A Multilocus Model

Inbreeding depression is one of the possible reasons organisms disperse. In this article, we present a two-locus model for the evolution of dispersal in the presence of inbreeding depression. The first locus codes for a modifier of the migration rate, while the second locus is a selected locus generating inbreeding depression. We express the change in frequency of the migration modifier as a function of allele frequencies and genetic associations and then use a quasi-equilibrium assumption to express genetic associations as functions of allele frequencies. Our model disentangles two effects of inbreeding depression: it gives an advantage to migrant individuals because their offspring are on average less homozygous, but it also decreases the degree of population structure, thus decreasing the strength of kin selection for dispersal. We then extend our model to include an infinite number of selected loci. When the cost of dispersal is not too high, the model predictions are confirmed by multilocus simulation results and show that inbreeding depression can have a substantial effect on the dispersal rate. For high costs of dispersal, we observe discrepancies between the model and the simulations, probably caused by associations among selected loci, which are neglected in the analysis.

The origins of eukaryotic gene structure

Most of the phenotypic diversity that we perceive in the natural world is directly attributable to the peculiar structure of the eukaryotic gene, which harbors numerous embellishments relative to the situation in prokaryotes. The most profound changes include introns that must be spliced out of precursor mRNAs, transcribed but untranslated leader and trailer sequences (untranslated regions), modular regulatory elements that drive patterns of gene expression, and expansive intergenic regions that harbor additional diffuse control mechanisms. Explaining the origins of these features is difficult because they each impose an intrinsic disadvantage by increasing the genic mutation rate to defective alleles. To address these issues, a general hypothesis for the emergence of eukaryotic gene structure is provided here. Extensive information on absolute population sizes, recombination rates, and mutation rates strongly supports the view that eukaryotes have reduced genetic effective population sizes relative to prokaryotes, with especially extreme reductions being the rule in multicellular lineages. The resultant increase in the power of random genetic drift appears to be sufficient to overwhelm the weak mutational disadvantages associated with most novel aspects of the eukaryotic gene, supporting the idea that most such changes are simple outcomes of semi-neutral processes rather than direct products of natural selection. However, by establishing an essentially permanent change in the population-genetic environment permissive to the genome-wide repatterning of gene structure, the eukaryotic condition also promoted a reliable resource from which natural selection could secondarily build novel forms of organismal complexity. Under this hypothesis, arguments based on molecular, cellular, and/or physiological constraints are insufficient to explain the disparities in gene, genomic, and phenotypic complexity between prokaryotes and eukaryotes.

Historical events and allelic polymorphism at the gametophytic self-incompatibility locus in Solanaceae

The historical migration rate of a species is often difficult to estimate with neutral markers, because the relationship between the turnover time of the markers and the age of the species commonly remains unknown. Compared with neutral markers, the plant self-incompatibility locus (S) provides a much better source of data for migration-rate estimation due to its high allelic polymorphism and antiquity. Here, the results from extensive surveys of S alleles in two wild solanaceous species, Solanum carolinense and Physalis longifolia, indicate that historical migration rates have differed significantly between the species; the higher migration rate found in S. carolinense appears to have interacted with the balancing selection at the S locus to result in fewer S alleles being maintained in the species. Historical population growth rates estimated via a modified coalescent approach also suggest a faster growing population for S. carolinense than for P. longifolia, which would have further widened their interspecific difference in S-allelle polymorphism. These historical factors may have reduced the probability of new S alleles to prevailing in S. carolinense, leaving old ones segregating at the S locus with little signature of positive selection being currently detectable.

Probability of fixation in a heterogeneous environment

We investigate the probability of fixation of a new mutation arising in a metapopulation that ranges over a heterogeneous selective environment. Using simulations, we test the performance of several approximations of this probability, including a new analytical approximation based on separation of the timescales of selection and migration. We extend all approximations to multideme metapopulations with arbitrary population structure. Our simulations show that no single approximation produces accurate predictions of fixation probabilities for all cases of potential interest. At the limits of low and high migration, previously published approximations are found to be highly accurate. The new separation-of-timescales approach provides the best approximations for intermediate rates of migration among habitats, provided selection is not too intense. For nonzero migration and relatively strong selection, all approximations perform poorly. However, the probability of fixation is bounded above and below by the approximations based on low and high migration limits. Surprisingly, in our simulations with symmetric migration, heterogeneous selection in a metapopulation never decreased-and sometimes substantially increased-the probability of fixation of a new allele compared to metapopulations experiencing homogeneous selection with the same mean selection intensity.

Hamilton and Zuk meet heterozygosity? Song repertoire size indicates inbreeding and immunity in song sparrows (Melospiza melodia)

Hamilton and Zuk's influential hypothesis of parasite-mediated sexual selection proposes that exaggerated secondary sexual ornaments indicate a male's addictive genetic immunity to parasites. However, genetic correlated of ornaments and immunity have rarely been explicitly identified. Evidence supporting Hamilton and Zuk's hypothesis has instead been gathered by looking for positive phenotypic correlations between ornamentation and immunity; such correlations are assumed to reflect causal, addictive relationships between these traits. We show that in a song sparrows, Melospiza melodia, male's song repertoire size, a secondary sexual trait, increased with his cell-mediated immune response (CMI) to an experimental challenge. However, this phenotypic correlation could be explained because both repertoire size and CMI declined with a male's inbreeding level. Repertoire size therefore primarily indicated a male's relative heterozygosity, a non-addictive genetic predictor of immunity. Caution may therefore be required when interpreting phenotypic correlations as support for Hamilton and Zuk's addictive model of sexual selection. However, our results suggest that female song sparrows choosing with large repertoires would on average acquire more outbred and therefore more heterozygous mates. Such genetic dominance effects on ornamentation are likely to influence evolutionary trajectories of female choice, and should be explicitly incorporated into genetic models of sexual selection.

Joint effects of self-fertilization and population structure on mutation load, inbreeding depression and heterosis

Both the spatial distribution of organisms and their mode of reproduction have important effects on the change in allele frequencies within populations. In this article, we study the combined effect of population structure and the rate of partial selfing of organisms on the efficiency of selection against recurrent deleterious mutations. Assuming an island model of population structure and weak selection, we express the mutation load, the within- and between-deme inbreeding depression, and heterosis as functions of the frequency of deleterious mutants in the metapopulation; we then use a diffusion model to calculate an expression for the equilibrium probability distribution of this frequency of deleterious mutants. This allows us to derive approximations for the average mutant frequency, mutation load, inbreeding depression, and heterosis, the simplest ones being Equations 35-39 in the text. We find that population structure can help to purge recessive deleterious mutations and reduce the load for some parameter values (in particular when the dominance coefficient of these mutations is <0.2-0.3), but that this effect is reversed when the selfing rate is above a given value. Conversely, within-deme inbreeding depression always decreases, while heterosis always increases, with the degree of population subdivision, for all selfing rates.

Population genetics of polymorphism and divergence for diploid selection models with arbitrary dominance

We develop a Poisson random-field model of polymorphism and divergence that allows arbitrary dominance relations in a diploid context. This model provides a maximum-likelihood framework for estimating both selection and dominance parameters of new mutations using information on the frequency spectrum of sequence polymorphisms. This is the first DNA sequence-based estimator of the dominance parameter. Our model also leads to a likelihood-ratio test for distinguishing nongenic from genic selection; simulations indicate that this test is quite powerful when a large number of segregating sites are available. We also use simulations to explore the bias in selection parameter estimates caused by unacknowledged dominance relations. When inference is based on the frequency spectrum of polymorphisms, genic selection estimates of the selection parameter can be very strongly biased even for minor deviations from the genic selection model. Surprisingly, however, when inference is based on polymorphism and divergence (McDonald-Kreitman) data, genic selection estimates of the selection parameter are nearly unbiased, even for completely dominant or recessive mutations. Further, we find that weak overdominant selection can increase, rather than decrease, the substitution rate relative to levels of polymorphism. This nonintuitive result has major implications for the interpretation of several popular tests of neutrality.

Evolutionary dynamics on graphs

Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process, is the special case of a fully connected graph with evenly weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbours. We also explore evolution on random and scale-free networks. We determine the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequency-dependent selection and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph. Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics.

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.

The many-demes limit for selection and drift in a subdivided population

A diffusion approximation is obtained for the frequency of a selected allele in a population comprised of many subpopulations or demes. The form of the diffusion is equivalent to that for an unstructured population, except that it occurs on a longer time scale when migration among demes is restricted. This many-demes diffusion limit relies on the collection of demes always being in statistical equilibrium with respect to migration and drift for a given allele frequency in the total population. Selection is assumed to be weak, in inverse proportion to the number of demes, and the results hold for any deme sizes and migration rates greater than zero. The distribution of allele frequencies among demes is also described.

How species evolve collectively: implications of gene flow and selection for the spread of advantageous alleles

The traditional view that species are held together through gene flow has been challenged by observations that migration is too restricted among populations of many species to prevent local divergence. However, only very low levels of gene flow are necessary to permit the spread of highly advantageous alleles, providing an alternative means by which low-migration species might be held together. We re-evaluate these arguments given the recent and wide availability of indirect estimates of gene flow. Our literature review of F(ST) values for a broad range of taxa suggests that gene flow in many taxa is considerably greater than suspected from earlier studies and often is sufficiently high to homogenize even neutral alleles. However, there are numerous species from essentially all organismal groups that lack sufficient gene flow to prevent divergence. Crude estimates on the strength of selection on phenotypic traits and effect sizes of quantitative trait loci (QTL) suggest that selection coefficients for leading QTL underlying phenotypic traits may be high enough to permit their rapid spread across populations. Thus, species may evolve collectively at major loci through the spread of favourable alleles, while simultaneously differentiating at other loci due to drift and local selection.

Recombination and base composition: the case of the highly self-fertilizing plant Arabidopsis thaliana

The effects of recombination and self-fertilization on base composition were investigated both theoretically and experimentally in the Arabidopsis genome. Levels of inbreeding modulate the effect of recombination on base composition.

Background

Rates of recombination can vary among genomic regions in eukaryotes, and this is believed to have major effects on their genome organization in terms of base composition, DNA repeat density, intron size, evolutionary rates and gene order. In highly self-fertilizing species such as Arabidopsis thaliana, however, heterozygosity is expected to be strongly reduced and recombination will be much less effective, so that its influence on genome organization should be greatly reduced.

Results

Here we investigated theoretically the joint effects of recombination and self-fertilization on base composition, and tested the predictions with genomic data from the complete A. thaliana genome. We show that, in this species, both codon-usage bias and GC content do not correlate with the local rates of crossing over, in agreement with our theoretical results.

Conclusions

We conclude that levels of inbreeding modulate the effect of recombination on base composition, and possibly other genomic features (for example, transposable element dynamics). We argue that inbreeding should be considered when interpreting patterns of molecular evolution.

Selection, Subdivision and Extinction and Recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity Nese, which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.

Integration of populations and differentiation of species

The framework for modern studies of speciation was established as part of the Neo-Darwinian synthesis of the early twentieth century. Here we evaluate this framework in the light of recent empirical and theoretical studies. Evidence from experimental studies of selection, quantitative genetic studies of species' differences, and the molecular evolution of 'isolation' genes, all agree that directional selection is the primary cause of speciation, as initially proposed by Darwin. Likewise, as suggested by Dobzhansky and Mayr, gene flow does hold species together, but probably more by facilitating the spread of beneficial mutants and associated hitchhiking events than by homogenizing neutral loci. Reproductive barriers are important as well in that they preserve adaptations, but as has been stressed by botanists for close to a century, they rarely protect the entire genome from gene flow in recently diverged species. Contrary to early views, it is now clear that speciation can occur in the presence of gene flow. However, recent theory does support the long-held view that population structure and small population size may increase speciation rates, but only under special conditions and not because of the increased efficacy of drift as suggested by earlier authors. Rather, low levels of migration among small populations facilitates the rapid accumulation of beneficial mutations that indirectly cause hybrid incompatibilities.

Selection and Drift in Subdivided Populations: A Straightforward Method for Deriving Diffusion Approximations and Applications Involving Dominance, Selfing and Local Extinctions

Population structure affects the relative influence of selection and drift on the change in allele frequencies. Several models have been proposed recently, using diffusion approximations to calculate fixation probabilities, fixation times, and equilibrium properties of subdivided populations. We propose here a simple method to construct diffusion approximations in structured populations; it relies on general expressions for the expectation and variance in allele frequency change over one generation, in terms of partial derivatives of a “fitness function” and probabilities of genetic identity evaluated in a neutral model. In the limit of a very large number of demes, these probabilities can be expressed as functions of average allele frequencies in the metapopulation, provided that coalescence occurs on two different timescales, which is the case in the island model. We then use the method to derive expressions for the probability of fixation of new mutations, as a function of their dominance coefficient, the rate of partial selfing, and the rate of deme extinction. We obtain more precise approximations than those derived by recent work, in particular (but not only) when deme sizes are small. Comparisons with simulations show that the method gives good results as long as migration is stronger than selection.

Distinguishing the Hitchhiking and Background Selection Models

A simple method to distinguish hitchhiking and background selection is proposed. It is based on the observation that these models make different predictions about the average level of nucleotide diversity in regions of low recombination. The method is applied to data from Drosophila melanogaster and two highly selfing tomato species.