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.     

Effects of metapopulation processes on measures of genetic diversity

Many species persist as a metapopulation under a balance between the local extinction of subpopulations or demes and their recolonization through dispersal from occupied patches. Here we review the growing body of literature dealing with the genetic consequences of such population turnover. We focus our attention principally on theoretical studies of a classical metapopulation with a 'finite-island' model of population structure, rather than on 'continent-island' models or 'source-sink' models. In particular, we concern ourselves with the subset of geographically subdivided population models in which it is assumed that all demes are liable to extinction from time to time and that all demes receive immigrants. Early studies of the genetic effects of population turnover focused on population differentiation, such as measured by F(ST). A key advantage of F(ST) over absolute measures of diversity is its relative independence of the mutation process, so that different genes in the same species may be compared. Another advantage is that F(ST) will usually equilibrate more quickly following perturbations than will absolute levels of diversity. However, because F(ST) is a ratio of between-population differentiation to total diversity, the genetic effects of metapopulation processes may be difficult to interpret in terms of F(ST) on its own, so that the analysis of absolute measures of diversity in addition is likely to be informative. While population turnover may either increase or decrease F(ST), depending on the mode of colonization, recurrent extinction and recolonization is expected always to reduce levels of both within-population and species-wide diversity (piS and piT, respectively). One corollary of this is that piS cannot be used as an unbiased estimate of the scaled mutation rate, theta, as it can, with some assumptions about the migration process, in species whose demes do not fluctuate in size. The reduction of piT in response to population turnover reflects shortened mean coalescent times, although the distribution of coalescence times under extinction colonization equilibrium is not yet known. Finally, we review current understanding of the effect of metapopulation dynamics on the effective population size.     

Genetic load,inbreeding depression and heterosis in an age‐structured metapopulation

In a metapopulation, the process of recurrent local extinction and recolonization gives rise to an age structure among demes. Recently established demes will tend to differ from older demes in terms of the levels of genetic diversity found within them and the way this diversity is distributed among demes in the same and different ages. The effects of population turnover on average levels of genetic diversity among demes in a metapopulation have been the focus of much attention, both for neutral and nonneutral loci, but much less is known about the distribution of nonneutral genetic diversity among demes of different ages. In this paper, we used computer simulations to study the distribution of genetic load, inbreeding depression and heterosis in an age‐structured metapopulation. We found that, for mildly deleterious mutations, within‐deme inbreeding depression increased, whereas heterosis and genetic load decreased with deme age following severe colonization bottlenecks. In contrast, recessive lethal alleles tended to be purged during colonization, with older populations showing higher genetic load and higher within‐deme inbreeding depression. Heterosis caused by recessive lethal alleles and resulting from gene flow among different demes tended to be greatest for young demes, because the mutations responsible tended to be purged in the first few generations after colonization, but its effects increased again as populations grow older as a result of immigration. Our results point to a need for estimates of genetic diversity, genetic load, within‐deme inbreeding depression and heterosis in demes of different age classes separately.     

NEUTRAL GENETIC DIVERSITY IN A METAPOPULATION WITH RECURRENT LOCAL EXTINCTION AND RECOLONIZATION

Many species exist as metapopulations in balance between local population extinction and recolonization, processes that may strongly affect the distribution of neutral genetic diversity within demes and in the metapopulation as a whole. In this paper we use both the infinite-alleles and the infinite-sites models to reframe Slatkin's propagulepool and migrant-pool models in terms of mean within-deme and among-deme genetic diversity; the infinite-sites model is particularly relevant to DNA sequence data. Population turnover causes a major reduction in neutral genetic diversity within demes, π_S, and in the metapopulation as a whole, π_t. This effect is particularly strong for propagulepool colonization, in which colonists are drawn from a single extant deme. Because metapopulation dynamics affect both within-deme and total metapopulation diversity similarly, comparisons between species with different ecologies on the basis of ratios such as F_ST are difficult to interpret and absolute measures of divergence between populations should be used as well. Although the value of F_ST in a metapopulation with local extinction depends strongly on the mode of colonization, this has almost no effect on the numerator of the F_ST ratio, π_t – π_S, so that F_ST is influenced mainly by the effect of the colonization mode on the denominator (π_t). Our results also indicate that it is inappropriate to use measures of average within-deme diversity in species with population turnover to estimate the scaled mutation rate, θ, because extinction can greatly reduce π_S. Finally, we discuss the effect of population turnover on the effective size of a metapopulation.     

Tests of two methods for identifying founder effects in metapopulations reveal substantial type II error

Genetic analysis has been promoted as a way to reconstruct recent historical dynamics (“historical demography”) by screening for signatures of events, such as bottlenecks, that disrupt equilibrium patterns of variation. Such analyses might also identify “metapopulation” processes like extinction and recolonization or source-sink dynamics, but this potential remains largely unrealized. Here we use simulations to test the ability of two currently used strategies to distinguish between a set of interconnected subpopulations (demes) that have undergone bottlenecks or extinction and recolonization events (metapopulation dynamics) from a set of static demes. The first strategy, decomposed pairwise regression, provides a holistic test for heterogeneity among demes in their patterns of isolation-by-distance. This method suffered from a type II error rate of 59–100 %, depending on parameter conditions. The second strategy tests for deviations from mutation-drift equilibrium on a deme-by-deme basis to identify sites likely to have experienced recent bottlenecks or founder effects. Although bottleneck tests have good statistical power for single populations with recent population declines, their validity in structured populations has been called into question, and they have not been tested in a metapopulation context with immigration (or colonization) and population recovery. Our simulations of hypothetical metapopulations show that population recovery can rapidly eliminate the statistical signature of a bottleneck, and that moderate levels of gene flow can generate a false signal of recent population growth for demes in equilibrium. Although we did not cover all possible metapopulation scenarios, the performance of the tests was disappointing. Our results indicate that these methods might often fail to identify population bottlenecks and founder effects if population recovery and/or gene flow are influential demographic features of the study system.     

The genetic effective size of a metapopulation

The structure of a population over time, space and categories of social and sexual role governs its ability to retain genetic variation in the face of drift. A metapopulation is an extreme form of spatial structure in which loosely coupled local populations 'turnover', that is, suffer extinction followed by recolonization from elsewhere within the metapopulation. These local populations turn over with a characteristic half-life. Based on a simulation model that incorporates both realistic features of population ecology and population genetics, the ability of such a metapopulation to retain genetic variation, which may be defined as proportional to its so-called effective population size, denoted N_e(^meta), can be one to two orders of magnitude lower than the maximum total number of individuals in the system. N_e(meta) depends on the persistence time associated with longevity of local populations (the turnover half-life), the average number of local populations extant in the metapopulation and the gene flow between local populations. Habitat fragmentation, which can create a metapopulation from a formerly continuously distributed species, may have unappreciated large genetic consequences for species impacted by human development.     

Metapopulation models for historical inference

The genealogical process for a sample from a metapopulation, in which local populations are connected by migration and can undergo extinction and subsequent recolonization, is shown to have a relatively simple structure in the limit as the number of populations in the metapopulation approaches infinity. The result, which is an approximation to the ancestral behaviour of samples from a metapopulation with a large number of populations, is the same as that previously described for other metapopulation models, namely that the genealogical process is closely related to Kingman's unstructured coalescent. The present work considers a more general class of models that includes two kinds of extinction and recolonization, and the possibility that gamete production precedes extinction. In addition, following other recent work, this result for a metapopulation divided into many populations is shown to hold both for finite population sizes and in the usual diffusion limit, which assumes that population sizes are large. Examples illustrate when the usual diffusion limit is appropriate and when it is not. Some shortcomings and extensions of the model are considered, and the relevance of such models to understanding human history is discussed.     

Determinants of Genetic Structure in a Nonequilibrium Metapopulation of the Plant Silene latifolia

Population genetic differentiation will be influenced by the demographic history of populations, opportunities for migration among neighboring demes and founder effects associated with repeated extinction and recolonization. In natural populations, these factors are expected to interact with each other and their magnitudes will vary depending on the spatial distribution and age structure of local demes. Although each of these effects has been individually identified as important in structuring genetic variance, their relative magnitude is seldom estimated in nature. We conducted a population genetic analysis in a metapopulation of the angiosperm, Silene latifolia, from which we had more than 20 years of data on the spatial distribution, demographic history, and extinction and colonization of demes. We used hierarchical Bayesian methods to disentangle which features of the populations contributed to among population variation in allele frequencies, including the magnitude and direction of their effects. We show that population age, long-term size and degree of connectivity all combine to affect the distribution of genetic variance; small, recently-founded, isolated populations contributed most to increase F _ST in the metapopulation. However, the effects of population size and population age are best understood as being modulated through the effects of connectivity to other extant populations, i.e. F _ST diminishes as populations age, but at a rate that depends how isolated the population is. These spatial and temporal correlates of population structure give insight into how migration, founder effect and within-deme genetic drift have combined to enhance and restrict genetic divergence in a natural metapopulation.     

The Effects of Background and Interference Selection on Patterns of Genetic Variation in Subdivided Populations

It is well known that most new mutations that affect fitness exert deleterious effects and that natural populations are often composed of subpopulations (demes) connected by gene flow. To gain a better understanding of the joint effects of purifying selection and population structure, we focus on a scenario where an ancestral population splits into multiple demes and study neutral diversity patterns in regions linked to selected sites. In the background selection regime of strong selection, we first derive analytic equations for pairwise coalescent times and F_ST as a function of time after the ancestral population splits into two demes and then construct a flexible coalescent simulator that can generate samples under complex models such as those involving multiple demes or nonconservative migration. We have carried out extensive forward simulations to show that the new methods can accurately predict diversity patterns both in the nonequilibrium phase following the split of the ancestral population and in the equilibrium between mutation, migration, drift, and selection. In the interference selection regime of many tightly linked selected sites, forward simulations provide evidence that neutral diversity patterns obtained from both the nonequilibrium and equilibrium phases may be virtually indistinguishable for models that have identical variance in fitness, but are nonetheless different with respect to the number of selected sites and the strength of purifying selection. This equivalence in neutral diversity patterns suggests that data collected from subdivided populations may have limited power for differentiating among the selective pressures to which closely linked selected sites are subject.     

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.     

Retrospective coalescent methods and the reconstruction of metapopulation histories in the sea

Phylogeographic analyses are a key interface between ecological and evolutionary ways of knowing because such analyses integrate the cumulative effects of demographic (ecological) processes over geological (evolutionary) time scales. Newly developed coalescent methods allow evolutionary ecologists to overcome some limitations associated with inferring population history from classic methods such as Wright’s F _ST. Here we briefly contrast classic and coalescent methods for looking backward in time through a population genetic lens, focusing on the key advantages of the isolation-with-migration (IM) class of coalescent methods for distinguishing ancient connectedness from actual recurrent contemporary gene flow as causes of genetic similarity or differentiation among populations. Making this critical distinction can lead to the discovery of otherwise obscured histories underlying conventional patterns of spatial variation. We illustrate the importance of these insights using analyses of Pacific fishes, snails, and sea stars in which population sizes and divergence times are more important than rates of contemporary gene flow as determinants of population genetic differentiation. We then extend the IM method to genetic data from two model metapopulation species (California abalone, Australian damselfish). The analyses show the potential use of non-equilibrium IM methods for differentiating among metapopulation models that make different predictions about population parameters and have different implications for the design of marine protected areas and other conservation goals. At face value, the results largely rule out classic metapopulation dynamics (dominated by extinction and colonization rather than connectivity via ongoing recurrent gene flow) but, at the same time, do not strongly support a modern marine metapopulation dynamic (ecologically significant connectivity between demes). However, the results also highlight the need for much more data (i.e., loci) sampled on different spatial scales in order to determine whether metapopulation dynamics might exist on smaller scales than are typically sampled by most phylogeographers and landscape geneticists.     

Low genetic diversity and strong but shallow population differentiation suggests genetic homogenization by metapopulation dynamics in a social spider

Mating systems and population dynamics influence genetic diversity and structure. Species that experience inbreeding and limited gene flow are expected to evolve isolated, divergent genetic lineages. Metapopulation dynamics with frequent extinctions and colonizations may, on the other hand, deplete and homogenize genetic variation, if extinction rate is sufficiently high compared to the effect of drift in local demes. We investigated these theoretical predictions empirically in social spiders that are highly inbred. Social spiders show intranest mating, female‐biased sex ratio, and frequent extinction and colonization events, factors that deplete genetic diversity within nests and populations and limit gene flow. We characterized population genetic structure in Stegodyphus sarasinorum, a social spider distributed across the Indian subcontinent. Species‐wide genetic diversity was estimated over approximately 2800 km from Sri Lanka to Himalayas, by sequencing 16 protein‐coding nuclear loci. We found 13 SNPs in 6592 bp (π = 0.00045) indicating low species‐wide nucleotide diversity. Three genetic lineages were strongly differentiated; however, only one fixed difference among them suggests recent divergence. This is consistent with a scenario of metapopulation dynamics that homogenizes genetic diversity across the species' range. Ultimately, low standing genetic variation may hamper a species' ability to track environmental change and render social inbreeding spiders ‘evolutionary dead‐ends’.     

Neutral additive genetic variance in a metapopulation

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's FST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2Ne sigma m2 (1 + FST), where FST is Wright's among-population fixation index, Ne is the eigenvalue effective size of the metapopulation, and sigma m2 is the mutational variance. The expected additive genetic variance within populations is given by 2Ne sigma e2(1-FST), and the variance among demes is given by 4FSTNe sigma m2. These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, QST, is shown to be generally equal to FST for the neutral additive model. Thus, for all population structures, a value of QST greater than FST for neutral loci is evidence for spatially divergent evolution by natural selection.     

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.     

Two waves of diversification in mammals and reptiles of Baja California revealed by hierarchical Bayesian analysis

Many species inhabiting the Peninsular Desert of Baja California demonstrate a phylogeographic break at the mid-peninsula, and previous researchers have attributed this shared pattern to a single vicariant event, a mid-peninsular seaway. However, previous studies have not explicitly considered the inherent stochasticity associated with the gene-tree coalescence for species preceding the time of the putative mid-peninsular divergence. We use a Bayesian analysis of a hierarchical model to test for simultaneous vicariance across co-distributed sister lineages sharing a genealogical break at the mid-peninsula. This Bayesian method is advantageous over traditional phylogenetic interpretations of biogeography because it considers the genetic variance associated with the coalescent and mutational processes, as well as the among-lineage demographic differences that affect gene-tree coalescent patterns. Mitochondrial DNA data from six small mammals and six squamate reptiles do not support the perception of a shared vicariant history among lineages exhibiting a north-south divergence at the mid-peninsula, and instead support two events differentially structuring genetic diversity in this region.     

Comparative phylogeography of tenebrionid beetles in the Aegean archipelago: the effect of dispersal ability and habitat preference

Comparative phylogeographical studies in island archipelagos can reveal lineage-specific differential responses to the geological and climatic history. We analysed patterns of genetic diversity in six codistributed lineages of darkling beetles (Tenebrionidae) in the central Aegean archipelago which differ in wing development and habitat preferences. A total of 600 specimens from 30 islands and eight adjacent mainland regions were sequenced for mitochondrial cytochrome oxidase I and nuclear Muscular protein 20. Individual gene genealogies were assessed for the presence of groups that obey an independent coalescent process using a mixed Yule coalescent model. The six focal taxa differed greatly in the number of coalescent groups and depth of lineage subdivision, which was closely mirrored by the degree of geographical structuring. The most severe subdivision at both mitochondrial DNA and nuclear DNA level was found in flightless lineages associated with presumed stable compact-soil habitats (phrygana, maquis), in contrast to sand-obligate lineages inhabiting ephemeral coastal areas that displayed greater homogeneity across the archipelago. A winged lineage, although associated with stable habitats, showed no significant phylogenetic or geographical structuring. Patterns of nucleotide diversity and local genetic differentiation, as measured using Φ_ST and hierarchical amova , were consistent with high levels of ongoing gene flow in the winged taxon; frequent local extinction and island recolonisation for flightless sand-obligate taxa; and very low gene flow and geographical structure largely defined by the palaeogeographical history of the region in flightless compact-soil taxa. These results show that differences in dispersal rate, mediated by habitat persistence, greatly influence the levels of phylogeographical subdivision in lineages that are otherwise subjected to the same geological events and palaeoclimatic changes.     

A multilocus perspective on the speciation history of a North American aridland toad (Anaxyrus punctatus)

Interpretations of phylogeographic patterns can change when analyses shift from single gene-tree to multilocus coalescent analyses. Using multilocus coalescent approaches, a species tree and divergence times can be estimated from a set of gene trees while accounting for gene-tree stochasticity. We utilized the conceptual strengths of a multilocus coalescent approach coupled with complete range-wide sampling to examine the speciation history of a broadly distributed, North American warm-desert toad, Anaxyrus punctatus. Phylogenetic analyses provided strong support for three major lineages within A. punctatus. Each lineage broadly corresponded to one of three desert regions. Early speciation in A. punctatus appeared linked to late Miocene-Pliocene development of the Baja California peninsula. This event was likely followed by a Pleistocene divergence associated with the separation of the Chihuahuan and Sonoran Deserts. Our multilocus coalescent-based reconstruction provides an informative contrast to previous single gene-tree estimates of the evolutionary history of A. punctatus.     

Local extinction and recolonization, species effective population size, and modern human origins

A primary objection from a population genetics perspective to a multiregional model of modern human origins is that the model posits a large census size, whereas genetic data suggest a small effective population size. The relationship between census size and effective size is complex, but arguments based on an island model of migration show that if the effective population size reflects the number of breeding individuals and the effects of population subdivision, then an effective population size of 10,000 is inconsistent with the census size of 500,000 to 1,000,000 that has been suggested by archeological evidence. However, these models have ignored the effects of population extinction and recolonization, which increase the expected variance among demes and reduce the inbreeding effective population size. Using models developed for population extinction and recolonization, we show that a large census size consistent with the multiregional model can be reconciled with an effective population size of 10,000, but genetic variation among demes must be high, reflecting low interdeme migration rates and a colonization process that involves a small number of colonists or kin-structured colonization. Ethnographic and archeological evidence is insufficient to determine whether such demographic conditions existed among Pleistocene human populations, and further work needs to be done. More realistic models that incorporate isolation by distance and heterogeneity in extinction rates and effective deme sizes also need to be developed. However, if true, a process of population extinction and recolonization has interesting implications for human demographic history.     

The Genealogy of Samples in Models with Selection

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman''s well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman''s coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models, DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case.