The effects of subdivision on the genetic divergence of populations and species

Abstract. An island model of migration is used to study the effects of subdivision within populations and species on sample genealogies and on between-population or between-species measures of genetic variation. The model assumes that the number of demes within each population or species is large. When populations (or species), connected either by gene flow or historical association, are themselves subdivided into demes, changes in the migration rate among demes alter both the structure of genealogies and the time scale of the coalescent process. The time scale of the coalescent is related to the effective size of the population, which depends on the migration rate among demes. When the migration rate among demes within populations is low, isolation (or speciation) events seem more recent and migration rates among populations seem higher because the effective size of each population is increased. This affects the probability of reciprocal monophyly of two samples, the chance that a gene tree of a sample matches the species tree, and relative likelihoods of different types of polymorphic sites. It can also have a profound effect on the estimation of divergence times.     

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.     

F(st) in a Hierarchical Island Model

It is shown that in a hierarchical island model, in which demes within a neighborhood exchange migrants at a much higher rate than do demes in different neighborhoods, hierarchical F statistics introduced by S. Wright can indicate the extent of gene flow within and between neighborhoods. At equilibrium, the within-neighborhood inbreeding coefficient, FSN, is approximately 1/(1 + 4Nm1) where N is the deme size and m1 is the migration rate among demes in the same neighborhood. The between-neighborhood inbreeding coefficient, FNT, is approximately 1/(1 + 4Ndm2) where d is the number of demes in a neighborhood and m2 is the migration rate among demes in different neighborhoods.     

Microhabitat Types Promote the Genetic Structure of a Micro-Endemic and Critically Endangered Mole Salamander (Ambystoma leorae) of Central Mexico

The reduced immigration and emigration rates resulting from the lack of landscape connectivity of patches and the hospitality of the intervening matrix could favor the loss of alleles through genetic drift and an increased chance of inbreeding. In order for isolated populations to maintain sufficient levels of genetic diversity and adapt to environmental changes, one important conservation goal must be to preserve or reestablish connectivity among patches in a fragmented landscape. We studied the last known population of Ambystoma leorae, an endemic and critically threatened species. The aims of this study were: (1) to assess the demographic parameters of A. leorae and to distinguish and characterize the microhabitats in the river, (2) to determine the number of existing genetic groups or demes of A. leorae and to describe possible relationships between microhabitats types and demes, (3) to determine gene flow between demes, and (4) to search for geographic locations of genetic discontinuities that limit gene flow between demes. We found three types of microhabitats and three genetically differentiated subpopulations with a significant level of genetic structure. In addition, we found slight genetic barriers. Our results suggest that mole salamander’s species are very sensitive to microhabitat features and relatively narrow obstacles in their path. The estimates of bidirectional gene flow are consistent with the pattern of a stepping stone model between demes, where migration occurs between adjacent demes, but there is low gene flow between distant demes. We can also conclude that there is a positive correlation between microhabitats and genetic structure in this population.     

Consequences of population structure on genes under balancing selection

This paper describes a new approach to modeling population structure for genes under strong balancing selection of the type seen in plant self-incompatibility systems and the major histocompatibility complex (MHC) system of vertebrates. Simple analytic solutions for the number of alleles maintained at equilibrium and the expected proportion of alleles shared between demes at various levels are derived and checked against simulation results. The theory accurately captures the dynamics of allele number in a subdivided population and identifies important values of m (migration rate) at which allele number and distribution change qualitatively. Starting from a panmictic population, as migration among demes decreases a qualitative change in dynamics is seen at approximately m(crit) approximately equal to the square root of(s/4piNT) where NT is the total population size and s is a measure of the strength of selection. At this point, demes can no longer maintain their panmictic allele number, due to increasing isolation from the total population. Another qualitative change occurs at a migration rate on the same order of magnitude as the mutation rate, mu. At this point, the demes are highly differentiated for allele complement, and the total number of alleles in the population is increased. Because in general u < m<(crit) at intermediate migration rates slightly fewer alleles may be maintained in the total population than are maintained at panmixia. Within this range, total allele number may not be the best indicator of whether a population is effectively panmictic, and some caution should be used when interpreting samples from such populations. The theory presented here can help to analyze data from genes under balancing selection in subdivided populations.     

Migration and recovery of the genetic diversity during the increasing density phase in cyclic vole populations

In cyclic populations, high genetic diversity is currently reported despite the periodic low numbers experienced by the populations during the low phases. Here, we report spatio-temporal monitoring at a very fine scale of cyclic populations of the fossorial water vole (Arvicola terrestris) during the increasing density phase. This phase marks the transition from a patchy structure (demes) during low density to a continuous population in high density. We found that the genetic diversity was effectively high but also that it displayed a local increase within demes over the increasing phase. The genetic diversity remained relatively constant when considering all demes together. The increase in vole abundance was also correlated with a decrease of genetic differentiation among demes. Such results suggest that at the end of the low phase, demes are affected by genetic drift as the result of being small and geographically isolated. This leads to a loss of local genetic diversity and a spatial differentiation among demes. This situation is counterbalanced during the increasing phase by the spatial expansion of demes and the increase of the effective migration among differentiated demes. We provide evidences that in cyclic populations of the fossorial water voles, the relative influence of drift operating during low density populations and migration occurring principally while population size increases interacts closely to maintain high genetic diversity.     

Extranuclear differentiation and gene flow in the finite island model

Use of sequence information from extranuclear genomes to examine deme structure in natural populations has been hampered by lack of clear linkage between sequence relatedness and rates of mutation and migration among demes. Here, we approach this problem in two complementary ways. First, we develop a model of extranuclear genomes in a population divided into a finite number of demes. Sex-dependent migration, neutral mutation, unequal genetic contribution of separate sexes and random genetic drift in each deme are incorporated for generality. From this model, we derive the relationship between gene identity probabilities (between and within demes) and migration rate, mutation rate and effective deme size. Second, we show how within- and between-deme identity probabilities may be calculated from restriction maps of mitochondrial (mt) DNA. These results, when coupled with our results on gene flow and genetic differentiation, allow estimation of relative interdeme gene flow when deme sizes are constant and genetic variants are selectively neutral. We illustrate use of our results by reanalyzing published data on mtDNA in mouse populations from around the world and show that their geographic differentiation is consistent with an island model of deme structure.     

Intra-deme molecular diversity in spatially expanding populations

We report here a simulation study examining the effect of a recent spatial expansion on the pattern of molecular diversity within a deme. We first simulate a range expansion in a virtual world consisting in a two-dimensional array of demes exchanging a given proportion of migrants (m) with their neighbors. The recorded demographic and migration histories are then used under a coalescent approach to generate the genetic diversity in a sample of genes. We find that the shape of the gene genealogies and the overall pattern of diversity within demes depend not only on the age of the expansion but also on the level of gene flow between neighboring demes, as measured by the product Nm, where N is the size of a deme. For small Nm values (< approximately 20 migrants sent outwards per generation), a substantial proportion of coalescent events occur early in the genealogy, whereas with larger levels of gene flow, most coalescent events occur around the time of the onset of the spatial expansion. Gene genealogies are star shaped, and mismatch distributions are unimodal after a range expansion for large Nm values. In contrast, gene genealogies present a mixture of both very short and very long branch lengths, and mismatch distributions are multimodal for small Nm values. It follows that statistics used in tests of selective neutrality like Tajima's D statistic or Fu's F(S) statistic will show very significant negative values after a spatial expansion only in demes with high Nm values. In the context of human evolution, this difference could explain very simply the fact that analyses of samples of mitochondrial DNA sequences reveal multimodal mismatch distributions in hunter-gatherers and unimodal distributions in post-Neolithic populations. Indeed, the current simulations show that a recent increase in deme size (resulting in a larger Nm value) is sufficient to prevent recent coalescent events and thus lead to unimodal mismatch distributions, even if deme sizes (and therefore Nm values) were previously much smaller. The fact that molecular diversity within deme is so dependent on recent levels of gene flow suggests that it should be possible to estimate Nm values from samples drawn from a single deme.     

EVOLUTION OF ALTRUISM IN KIN-STRUCTURED AND RANDOM SUBDIVIDED POPULATIONS

A. population structure favorable to the evolution of an altruistic trait is studied by Monte Carlo simulation. The model is based on a small-scale nonindustrial human society but seems generalizable to other highly social mammals. Three hierarchical levels are recognized: 1) the ecologically isolated local group (hamlet) which may be composed of kin and/or unrelated individuals; 2) the deme (settlement) comprising several such groups which interbreed; and 3) the set of demes (metapopulation) among which gene flow occurs. The first two levels of the model are based on D. S. Wilson's structured deme concept; the third allows for gene flow among demes in the metapopulation and for the structured diffusion of alleles across a wider area than might be included within the scope of a single deme. The simulation models genetic drift by a process of hamlet formation which may be random, or variously kin-structured. Hamlets may then become extinct based on a probability function of their gene frequencies. Individual selection within settlements is modeled deterministically, and gene flow among settlements is modeled as two-dimensional steppingstone migration of random or kin-structured groups. Results of the simulations show that, with realistic values for group sizes, moderate extinction rate, and high rates of migration (m > 27%), disadvantageous alleles (s = 10% and 25%) may increase markedly due to differential hamlet extinction over the course of 50 generations. The greater the degree of kin-structuring of founder groups, the higher the variance among hamlets and the faster the rate of increase of the allele for altruism. Nonetheless, even in some randomly founded groups, a clear increase in the altruism gene frequency occurred. It is also notable that kin-structured group selection by hamlet extinction may be effective when the initial frequency of altruism genes is very low (average of one per deme) and among a relatively small number of demes (25). Thus the process of group extinction in a hierarchically structured population allows rapid increase of an allele for altruism under plausible demographic conditions.     

The structured ancestral selection graph and the many-demes limit

We show that the unstructured ancestral selection graph applies to part of the history of a sample from a population structured by restricted migration among subpopulations, or demes. The result holds in the limit as the number of demes tends to infinity with proportionately weak selection, and we have also made the assumptions of island-type migration and that demes are equivalent in size. After an instantaneous sample-size adjustment, this structured ancestral selection graph converges to an unstructured ancestral selection graph with a mutation parameter that depends inversely on the migration rate. In contrast, the selection parameter for the population is independent of the migration rate and is identical to the selection parameter in an unstructured population. We show analytically that estimators of the migration rate, based on pairwise sequence differences, derived under the assumption of neutrality should perform equally well in the presence of weak selection. We also modify an algorithm for simulating genealogies conditional on the frequencies of two selected alleles in a sample. This permits efficient simulation of stronger selection than was previously possible. Using this new algorithm, we simulate gene genealogies under the many-demes ancestral selection graph and identify some situations in which migration has a strong effect on the time to the most recent common ancestor of the sample. We find that a similar effect also increases the sensitivity of the genealogy to selection.     

Population genetics of Japanese monkeys: II. Blood protein polymorphisms and population structure

Genetic variability in individual troops of the Japanese macaque (Macaca fuscata fuscata) was quantified by the proportion of polymorphic loci and the average heterozygosity per individual from the results of starch-gel electrophoreses of blood proteins controlled by 32 independent genetic loci. The former averaged 9.2% and the latter 1.3%, the values being remarkably lower than those estimated for other animal populations. Geographical distribution of the genetic variations was not uniform in the whole species but the variants occurred only in limited areas. Assuming the selective neutrality of segregating alleles and the two-dimensional stepping-stone model of population structure, the genetic migration rate between the local demes per generation could be estimated to average less than inverse of average effective deme size. Here, the local deme is not a troop itself, but it consists of several troops tightly connected with each other by frequent exchanges of reproductive males. Analyses of correlation between geographic and genetic distances between troops revealed that the gene constitutions of two troops apart more than 100 km on an island could be regarded as practically independent of each other. These results suggest that the population structure of the Japanese macaque species has a tendency to split into a number of local subpopulations in which the effect of random genetic drift is prevailing.     

High gene flow across large geographic scales reduces extinction risk for a highly specialised coral feeding butterflyfish

The vulnerability of ecologically specialised species to environmental fluctuations has been well documented. However, population genetic structure can influence vulnerability to environmental change and recent studies have indicated that specialised species may have lower genetic diversity and greater population structuring compared to their generalist counterparts. To examine whether there were differences in population genetic structure between a dietary specialist (Chaetodon trifascialis) and a dietary generalist (Chaetodon lunulatus) we compared the demographic history and levels of gene flow of two related coral-feeding butterflyfishes. Using allele frequencies of ≥11 microsatellite loci and >350 bases of mitochondrial control region sequence our analyses of C. trifascialis and C. lunulatus from five locations across the Pacific Ocean revealed contrasting demographic histories and levels of genetic structure. Heterozygosity excess tests, neutrality tests and mismatch distributions were all highly significant in the dietary specialist C. trifascialis (all P < 0.01), suggesting genetic bottlenecks have occurred in all locations. In contrast, we found little evidence of genetic bottlenecks for the dietary generalist C. lunulatus. High gene flow and low genetic structuring was detected among locations for C. trifascialis (amova: R(ST) = 0.0027, P = 0.371; Φ(ST) = 0.068, P < 0.0001). Contrary to our expectations, a greater level of genetic structuring between locations was detected for C. lunulatus (amova: R(ST) = 0.0277, Φ(ST) = 0.166, both P < 0.0001). These results suggest that dietary specialisation may affect demographic history through reductions in population size following resource declines, without affecting population structure through reductions in gene flow in the same way that habitat specialisation appears to. Although C. trifascialis is highly vulnerable to coral loss, the high gene flow detected here suggests populations will be able to recover from local declines through the migration of individuals.     

PERSPECTIVE: THE THEORIES OF FISHER AND WRIGHT IN THE CONTEXT OF METAPOPULATIONS: WHEN NATURE DOES MANY SMALL EXPERIMENTS

We critically review the two major theories of adaptive evolution developed early in this century, Wright's shifting balance theory and Fisher's large population size theory, in light of novel findings from field observations, laboratory experiments, and theoretical research conducted over the past 15 years. Ecological studies of metapopulations have established that the processes of local extinction and colonization of demes are relatively common in natural populations of many species and theoretical population genetic models have shown that these ecological processes have genetic consequences within and among local demes. Within demes, random genetic drift converts nonadditive genetic variance into additive genetic variance, increasing, rather than limiting, the potential for adaptation to local environments. For this reason, the genetic differences that arise by drift among demes, can be augmented by local selection. The resulting adaptive differences in gene combinations potentially contribute to the genetic origin of new species. These and other recent findings were not discussed by either Wright or Fisher. For example, although Wright emphasized epistatic genetic variance, he did not discuss the conversion process. Similarly, Fisher did not discuss how the average additive effect of a gene varies among demes across a metapopulation whenever there is epistasis. We discuss the implications of such recent findings for the Wright-Fisher controversy and identify some critical open questions that require additional empirical and theoretical study.     

Geographical variation in selection, from phenotypes to molecules

Molecular technologies now allow researchers to isolate quantitative trait loci (QTLs) and measure patterns of gene sequence variation within chromosomal regions containing important polymorphisms. I develop a simulation model to investigate gene sequence evolution within genomic regions that harbor QTLs. The QTLs influence a trait experiencing geographical variation in selection, which is common in nature and produces obvious differentiation at the phenotypic level. Counter to expectations, the simulations suggest that selection can substantially affect quantitative genetic variation without altering the amount and pattern of molecular variation at sites closely linked to the QTLs. Even with large samples of gene sequences, the likelihood of rejecting neutrality is often low. The exception is situations where strong selection is combined with low migration among demes, conditions that may be common in many plant species. The results have implications for gene sequence surveys and, perhaps more generally, for interpreting the apparently weak connection between levels of molecular and quantitative trait variation within species.     

Gene genealogies in a metapopulation

A simple genealogical process is found for samples from a metapopulation, which is a population that is subdivided into a large number of demes, each of which is subject to extinction and recolonization and receives migrants from other demes. As in the migration-only models studied previously, the genealogy of any sample includes two phases: a brief sample-size adjustment followed by a coalescent process that dominates the history. This result will hold for metapopulations that are composed of a large number of demes. It is robust to the details of population structure, as long as the number of possible source demes of migrants and colonists for each deme is large. Analytic predictions about levels of genetic variation are possible, and results for average numbers of pairwise differences within and between demes are given. Further analysis of the expected number of segregating sites in a sample from a single deme illustrates some previously known differences between migration and extinction/recolonization. The ancestral process is also amenable to computer simulation. Simulation results show that migration and extinction/recolonization have very different effects on the site-frequency distribution in a sample from a single deme. Migration can cause a U-shaped site-frequency distribution, which is qualitatively similar to the pattern reported recently for positive selection. Extinction and recolonization, in contrast, can produce a mode in the site-frequency distribution at intermediate frequencies, even in a sample from a single deme.     

The coalescent in an island model of population subdivision with variation among demes

A simple genealogical structure is found for a general finite island model of population subdivision. The model allows for variation in the sizes of demes, in contributions to the migrant pool, and in the fraction of each deme that is replaced by migrants every generation. The ancestry of a sample of non-recombining DNA sequences has a simple structure when the sample size is much smaller than the total number of demes in the population. This allows an expression for the probability distribution of the number of segregating sites in the sample to be derived under the infinite-sites mutation model. It also yields easily computed estimators of the migration parameter for each deme in a multi-deme sample. The genealogical process is such that the lineages ancestral to the sample tend to accumulate in demes with low migration rates and/or which contribute disproportionately to the migrant pool. In addition, common ancestor or coalescent events tend to occur in demes of small size. This provides a framework for understanding the determinants of the effective size of the population, and leads to an expression for the probability that the root of a genealogy occurs in a particular geographic region, or among a particular set of demes.     

Microsatellite Analyses of Blacktip Reef Sharks (Carcharhinus melanopterus) in a Fragmented Environment Show Structured Clusters

The population dynamics of shark species are generally poorly described because highly mobile marine life is challenging to investigate. Here we investigate the genetic population structure of the blacktip reef shark (Carcharhinus melanopterus) in French Polynesia. Five demes were sampled from five islands with different inter-island distances (50–1500 km). Whether dispersal occurs between islands frequently enough to prevent moderate genetic structure is unknown. We used 11 microsatellites loci from 165 individuals and a strong genetic structure was found among demes with both F-statistics and Bayesian approaches. This differentiation is correlated with the geographic distance between islands. It is likely that the genetic structure seen is the result of all or some combination of the following: low gene flow, time since divergence, small effective population sizes, and the standard issues with the extent to which mutation models actually fit reality. We suggest low levels of gene flow as at least a partial explanation of the level of genetic structure seen among the sampled blacktip demes. This explanation is consistent with the ecological traits of blacktip reef sharks, and that the suitable habitat for blacktips in French Polynesia is highly fragmented. Evidence for spatial genetic structure of the blacktip demes we studied highlights that similar species may have populations with as yet undetected or underestimated structure. Shark biology and the market for their fins make them highly vulnerable and many species are in rapid decline. Our results add weight to the case that total bans on shark fishing are a better conservation approach for sharks than marine protected area networks.     

TESTING MODELS OF MIGRATION AND ISOLATION AMONG POPULATIONS OF CHINOOK SALMON (ONCORHYNCHUS TSCHAWYTSCHA)

The chinook salmon (Oncorhynchus tschawytscha) is a behaviorally, morphologically, and ecologically variable species distributed over a large geographic range. Although previous genetic surveys have revealed considerable genetic differences among populations with different life history types and from different major river drainages, it is not clear to what degree these genetically distinct populations are connected by low levels of gene flow. The work described in this paper addresses this question by surveying DNA restriction site variation at six nuclear genes from nine populations encompassing most of the species's North American range, and then attempting to fit the patterns of variation observed at these genes to five different evolutionary models using computer simulations of the coalescent process. Two commonly used constant population size models, one hypothesizing no migration among populations and one hypothesizing equal rates of migration among populations, were found to be statistically inconsistent with the observed patterns of variation. The other three models, which involved either recent divergence among populations coupled with large changes in populations size, unequal migration rates among populations, or selection, were all found to be consistent with the observed patterns of variation. Assuming selective neutrality, these results suggest that either the populations have all descended from a common ancestral population within the last ~50,000 years and have all suffered large declines in effective population size since that time, or that they have a more ancient divergence time but are connected by low levels of gene flow. These conclusions rest on the assumption of selective neutrality. With the methods employed, it was not possible to simultaneously test hypotheses of both selective neutrality and population structure.     

Small-world networks decrease the speed of Muller's ratchet

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of non-recombining genomes, such as the mitochondria, the degeneration of the Y chromosome, and the evolution of sex and recombination. Here we study the speed of Muller's ratchet in a spatially structured population which is subdivided into many small populations (demes) connected by migration, and distributed on a graph. We studied different types of networks: regular networks (similar to the stepping-stone model), small-world networks and completely random graphs. We show that at the onset of the small-world network - which is characterized by high local connectivity among the demes but low average path length - the speed of the ratchet starts to decrease dramatically. This result is independent of the number of demes considered, but is more pronounced the larger the network and the stronger the deleterious effect of mutations. Furthermore, although the ratchet slows down with increasing migration between demes, the observed decrease in speed is smaller in the stepping-stone model than in small-world networks. As migration rate increases, the structured populations approach, but never reach, the result in the corresponding panmictic population with the same number of individuals. Since small-world networks have been shown to describe well the real contact networks among people, we discuss our results in the light of the evolution of microbes and disease epidemics.