Cross-cultural analysis of migration rates: effects of geographic distance and population size.

A model is developed that treats migration rates among populations as a function of the geographic distance between them and the size of both sources and recipient population. Specifically, mij/mjj = a(Ni/Nj)pe-bd, where mij/mjj is the relative migration rate into population j from population i, Ni is the size of the source population, Nj is the size of the recipient population, d is the geographic distance between populations i and j, p is a measure of differential density-dependence, b is a measure of distance decay, and a is an adjustment parameter with little demographic meaning. Methods of parameter estimation and hypothesis testing using maximum likelihood are outlined. These methods are applied to migration matrix data from 13 samples obtained from the literature representing a wide range of ecological settings. All samples show a significant effect of geographic distance on migration, and all but one show a significant effect of differential population size. All but one sample show an overall tendency for migration to be negative density-dependent; that is, the relative migration rate is greater from larger populations to smaller populations than the reverse.     

Using molecular markers with high mutation rates to obtain estimates of relative population size and to distinguish the effects of gene flow and mutation: a demonstration using data from endemic Mauritian skinks

We propose a method of analysing genetic data to obtain separate estimates of the size (N(p)) and migration rate (m(p)) for the sampled populations, without precise prior knowledge of mutation rates at each locus ( micro(L)). The effects of migration and mutation can be distinguished because high migration has the effect of reducing genetic differentiation across all loci, whereas a high mutation rate will only affect the locus in question. The method also takes account of any differences between the spectra of immigrant alleles and of new mutant alleles. If the genetic data come from a range of population sizes, and the loci have a range of mutation rates, it is possible to estimate the relative sizes of the different N(p) values, and likewise the m(p) and the micro(L). Microsatellite loci may also be particularly appropriate because loci with a high mutation rate can reach mutation-drift-migration equilibrium more quickly, and because the spectra of mutants arriving in a population can be particularly distinct from the immigrants. We demonstrate this principle using a microsatellite data set from Mauritian skinks. The method identifies low gene flow between a putative new species and populations of its sister species, whereas the differentiation of two other populations is attributed to small population size. These distinct interpretations were not readily apparent from conventional measures of genetic differentiation and gene diversity. When the method is evaluated using simulated data sets, it correctly distinguishes low gene flow from small population size. Loci that are not at mutation-migration-drift equilibrium can distort the parameter estimates slightly. We discuss strategies for detecting and overcoming this effect.     

Influence of Gene Flow and Breeding Tactics on Gene Diversity within Populations

Expressions describing the accumulation of gene correlations within and among lineages and individuals of a population are derived. The model permits different migration rates by males and females and accounts for various breeding tactics within lineages. The resultant equations enable calculation of the probabilistic quantities for the fixation indices, rates of loss of genetic variation, accumulation of inbreeding, and coefficients of relationship for the population at any generation. All fixation indices were found to attain asymptotic values rapidly despite the consistent loss of genetic variation and accumulation of inbreeding within the population. The time required to attain asymptotic values, however, was prolonged when gene flow among lineages was relatively low (less than 20%). The degree of genetic differentiation among breeding groups, inbreeding coefficients, and gene correlations within lineages were found to be primarily functions of breeding tactics within groups rather than gene flow among groups. Thus, the asymptotic value of S. Wright's island model is not appropriate for describing genetic differences among groups within populations. An alternative solution is provided that under limited conditions will reduce to the original island model. The evolution of polygynous breeding tactics appears to be more favorable for promoting intragroup gene correlations than modification of migration rates. Inbreeding and variance effective sizes are derived for populations that are structured by different migration and breeding tactics. Processes that reduce the inbreeding effective population size result in a concomitant increase in variance effective population size.     

Gene flow among small populations of a self-incompatible plant: an interaction between demography and genetics

We assessed the effects of population size and genetic relatedness on rates of pollen gene flow into experimental populations of the insect-pollinated, self-incompatible plant Raphanus sativus. We created synthetic populations of sizes 2, 5, 10, and 20 with three genetic structures (full siblings, half siblings, and unrelated plants). Following pollination in a natural setting, we conducted a simple paternity exclusion analysis using the allozyme genotypes of progeny to measure apparent gene flow and Monte Carlo simulations to estimate total gene flow. Estimates of apparent pollen gene flow rates ranged from 0 to 100% and were similar in rank to estimates of total gene flow. There were significant effects of population size and relatedness on the rate of apparent gene flow, and there were significant population size by relatedness interactions. Populations of size 2 had higher gene flow rates than larger populations, gene flow being negatively associated with the level of cross-compatibility (as measured by hand pollinations). Gene flow into populations of size 2 was also negatively associated with the distance to the nearest population of size 10 or 20. These results suggest that interactions among demography (population size), genetics (cross-compatibility), and ecology (pollinator behavior) are important influences on pollen gene flow rates into small plant populations.     

Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations

Current estimators of gene flow come in two methods; those that estimate parameters assuming that the populations investigated are a small random sample of a large number of populations and those that assume that all populations were sampled. Maximum likelihood or Bayesian approaches that estimate the migration rates and population sizes directly using coalescent theory can easily accommodate datasets that contain a population that has no data, a so-called 'ghost' population. This manipulation allows us to explore the effects of missing populations on the estimation of population sizes and migration rates between two specific populations. The biases of the inferred population parameters depend on the magnitude of the migration rate from the unknown populations. The effects on the population sizes are larger than the effects on the migration rates. The more immigrants from the unknown populations that are arriving in the sample populations the larger the estimated population sizes. Taking into account a ghost population improves or at least does not harm the estimation of population sizes. Estimates of the scaled migration rate M (migration rate per generation divided by the mutation rate per generation) are fairly robust as long as migration rates from the unknown populations are not huge. The inclusion of a ghost population does not improve the estimation of the migration rate M; when the migration rates are estimated as the number of immigrants Nm then a ghost population improves the estimates because of its effect on population size estimation. It seems that for 'real world' analyses one should carefully choose which populations to sample, but there is no need to sample every population in the neighbourhood of a population of interest.     

Evolution of dispersal in density regulated populations: A haploid model

The evolution of dispersal is explored in a density-dependent framework. Attention is restricted to haploid populations in which the genotypic fitnesses at a single diallelic locus are decreasing functions of the changing number of individuals in the population. It is shown that migration between two populations in which the genotypic response to density is reversed can maintain both alleles when the intermigration rates are constant or nondecreasing functions of the population densities. There is always a unique symmetric interior equilibrium with equal numbers but opposite gene frequencies in the two populations, provided the system is not degenerate. Numerical examples with exponential and hyperbolic fitnesses suggest that this is the only stable equilibrium state under constant positive migration rates (m) less than . Practically speaking, however, there is only convergence after a reasonable number of generations for relatively small migration rates ( ). A migration-modifying mutant at a second, neutral locus, can successfully enter two populations at a stable migration-selection balance if and only if it reduces the intermigration rates of its carriers at the original equilibrium population size. Moreover, migration modification will always result in a higher equilibrium population size, provided the system approaches another symmetric interior equilibrium. The new equilibrium migration rate will be lower than that at the original equilibrium, even when the modified migration rate is a nondecreasing function of the population sizes. Therefore, as in constant viability models, evolution will lead to reduced dispersal.     

Inferring landscape resistance to gene flow when genetic drift is spatially heterogeneous

In connectivity models, land cover types are assigned cost values characterizing their resistance to species movements. Landscape genetic methods infer these values from the relationship between genetic differentiation and cost distances. The spatial heterogeneity of population sizes, and consequently genetic drift, is rarely included in this inference although it influences genetic differentiation. Similarly, migration rates and population spatial distributions potentially influence this inference. Here, we assessed the reliability of cost value inference under several migration rates, population spatial patterns and degrees of population size heterogeneity. Additionally, we assessed whether considering intra-population variables, here using gravity models, improved the inference when drift is spatially heterogeneous. We simulated several gene flow intensities between populations with varying local sizes and spatial distributions. We then fit gravity models of genetic distances as a function of (i) the ‘true’ cost distances driving simulations or alternative cost distances, and (ii) intra-population variables (population sizes, patch areas). We determined the conditions making the identification of the ‘true’ costs possible and assessed the contribution of intra-population variables to this objective. Overall, the inference ranked cost scenarios reliably in terms of similarity with the ‘true’ scenario (cost distance Mantel correlations), but this ‘true’ scenario rarely provided the best model goodness of fit. Ranking inaccuracies and failures to identify the ‘true’ scenario were more pronounced when migration was very restricted (<4 dispersal events/generation), population sizes were most heterogeneous and some populations were spatially aggregated. In these situations, considering intra-population variables helps identify cost scenarios reliably, thereby improving cost value inference from genetic data.     

Population genetic analysis identifies source-sink dynamics for two sympatric garter snake species (Thamnophis elegans and Thamnophis sirtalis)

Population genetic structure can be shaped by multiple ecological and evolutionary factors, but the genetic consequences of these factors for multiple species inhabiting the same environment remain unexplored. We used microsatellite markers to examine the population structures of two coexisting species of garter snake, Thamnophis elegans and Thamnophis sirtalis, to determine if shared landscape and biology imposed similar population genetic structures. These snakes inhabit a series of ponds, lakes and flooded meadows in northern California and tend to converge on prey type wherever they coexist. Both garter snakes had comparable effective population sizes and bidirectional migration rates (estimated using a maximum-likelihood method based on the coalescent) with low but significant levels of genetic differentiation (F(ST) = 0.024 for T. elegans and 0.035 for T. sirtalis). Asymmetrical gene flow revealed large source populations for both species as well as potential sinks, suggesting frequent extinction-recolonization and metapopulation dynamics. In addition, we found a significant correlation between their genetic structures based on both pairwise F(ST)s for shared populations (P = 0.009) and for bidirectional migration rates (P = 0.024). Possible ecological and evolutionary factors influencing similarities and differences in genetic structure for the two species are discussed. Genetic measures of effective population size and migration rates obtained in this study are also compared with estimates obtained from mark-recapture data.     

Joint estimation of contemporary seed and pollen dispersal rates among plant populations

There are few statistical methods for estimating contemporary dispersal among plant populations. A maximum-likelihood procedure is introduced here that uses pre- and post-dispersal population samples of biparentally inherited genetic markers to jointly estimate contemporary seed and pollen immigration rates from a set of discrete external sources into a target population. Monte Carlo simulations indicate that accurate estimates and reliable confidence intervals can be obtained using this method for both pollen and seed migration rates at modest sample sizes (100 parents/population and 100 offspring) when population differentiation is moderate (F(ST) ≥ 0.1), or by increasing pre-dispersal samples (to about 500 parents/population) when genetic divergence is weak (F(ST) = 0.01). The method exhibited low sensitivity to the number of source populations and achieved good accuracy at affordable genetic resolution (10 loci with 10 equifrequent alleles each). Unsampled source populations introduced positive biases in migration rate estimates from sampled sources, although they were minor when the proportion of immigration from the latter was comparatively low. A practical application of the method to a metapopulation of the Australian resprouter shrub Banksia attenuata revealed comparable levels of directional seed and pollen migration among dune groups, and the estimate of seed dispersal was higher than a previous estimate based on conservative assignment tests. The method should be of interest to researchers and managers assessing broad-scale nonequilibrium seed and pollen gene flow dynamics in plants.     

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.     

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.     

Effective Sizes for Subdivided Populations

Many derivations of effective population sizes have been suggested in the literature; however, few account for the breeding structure and none can readily be expanded to subdivided populations. Breeding structures influence gene correlations through their effects on the number of breeding individuals of each sex, the mean number of progeny per female, and the variance in the number of progeny produced by males and females. Additionally, hierarchical structuring in a population is determined by the number of breeding groups and the migration rates of males and females among such groups. This study derives analytical solutions for effective sizes that can be applied to subdivided populations. Parameters that encapsulate breeding structure and subdivision are utilized to derive the traditional inbreeding and variance effective sizes. Also, it is shown that effective sizes can be determined for any hierarchical level of population structure for which gene correlations can accrue. Derivations of effective sizes for the accumulation of gene correlations within breeding groups (coancestral effective size) and among breeding groups (intergroup effective size) are given. The results converge to traditional, single population measures when similar assumptions are applied. In particular, inbreeding and intergroup effective sizes are shown to be special cases of the coancestral effective size, and intergroup and variance effective sizes will be equal if the population census remains constant. Instantaneous solutions for effective sizes, at any time after gene correlation begins to accrue, are given in terms of traditional F statistics or transition equations. All effective sizes are shown to converge upon a common asymptotic value when breeding tactics and migration rates are constant. The asymptotic effective size can be expressed in terms of the fixation indices and the number of breeding groups; however, the rate of approach to the asymptote is dependent upon dispersal rates. For accurate assessment of effective sizes, initial, instantaneous or asymptotic, the expressions must be applied at the lowest levels at which migration among breeding groups is nonrandom. Thus, the expressions may be applicable to lineages within socially structured populations, fragmented populations (if random exchange of genes prevails within each population), or combinations of intra- and interpopulation discontinuities of gene flow. Failure to recognize internal structures of populations may lead to considerable overestimates of inbreeding effective size, while usually underestimating variance effective size.     

Population genetics and the evolution of geographic range limits in an annual plant

Abstract Theoretical models of species' geographic range limits have identified both demographic and evolutionary mechanisms that prevent range expansion. Stable range limits have been paradoxical for evolutionary biologists because they represent locations where populations chronically fail to respond to selection. Distinguishing among the proposed causes of species' range limits requires insight into both current and historical population dynamics. The tools of molecular population genetics provide a window into the stability of range limits, historical demography, and rates of gene flow. Here we evaluate alternative range limit models using a multilocus data set based on DNA sequences and microsatellites along with field demographic data from the annual plant Clarkia xantiana ssp. xantiana. Our data suggest that central and peripheral populations have very large historical and current effective population sizes and that there is little evidence for population size changes or bottlenecks associated with colonization in peripheral populations. Whereas range limit populations appear to have been stable, central populations exhibit a signature of population expansion and have contributed asymmetrically to the genetic diversity of peripheral populations via migration. Overall, our results discount strictly demographic models of range limits and more strongly support evolutionary genetic models of range limits, where adaptation is prevented by a lack of genetic variation or maladaptive gene flow.     

Effects of population size and isolation on heterosis, mean fitness, and inbreeding depression in a perennial plant

? In small isolated populations, genetic drift is expected to increase chance fixation of partly recessive, mildly deleterious mutations, reducing mean fitness and inbreeding depression within populations and increasing heterosis in outcrosses between populations. ? We estimated relative effective sizes and migration among populations and compared mean fitness, heterosis, and inbreeding depression for eight large and eight small populations of a perennial plant on the basis of fitness of progeny produced by hand pollinations within and between populations. ? Migration was limited, and, consistent with expectations for drift, mean fitness was 68% lower in small populations; heterosis was significantly greater for small (mean?=?70%, SE?=?14) than for large populations (mean?=?7%, SE?=?27); and inbreeding depression was lower, although not significantly so, in small (mean?=?-0.29%, SE?=?28) than in large (mean?=?0.28%, SE?=?23) populations. ? Genetic drift promotes fixation of deleterious mutations in small populations, which could threaten their persistence. Limited migration will exacerbate drift, but data on migration and effective population sizes in natural populations are scarce. Theory incorporating realistic variation in population size and patterns of migration could better predict genetic threats to small population persistence.     

Genetic diversity and structure of Pinus dabeshanensis revealed by expressed sequence tag-simple sequence repeat (EST-SSR) markers

Assessing patterns of genetic variation in rare endangered species is critical for developing both in situ and ex situ conservation strategies. Pinus dabeshanensis Cheng et Law is an endangered species endemic to the Dabieshan Mountains of eastern China. To obtain fundamental information of genetic diversity, population history, effective population size, and gene flow in this species, we explored patterns of genetic variation of natural populations, in addition to an ex situ conserved population, using expressed sequence tag-simple sequence repeats (EST-SSR) markers. Our results revealed moderate levels of genetic diversity (e.g., H_E = 0.458 vs. H_E = 0.423) and a low level of genetic differentiation (F_ST = 0.028) among natural and conserved populations relative to other conifers. Both contemporary and historical migration rates among populations were high. Bayesian coalescent-based analyses suggested that 3 populations underwent reductions in population size ca. 10,000 yr ago, and that two populations may have experienced recent genetic bottlenecks under the TPM. Bayesian clustering revealed that individuals from the ex situ population were largely assigned to the ‘red’ cluster. Additionally, our results identified private alleles in the natural populations but not in the ex situ population, suggesting that the ex situ conserved population insufficiently represents the genetic diversity present in the species. Past decline in population size is likely to be due to Holocene climate change. Based on the genetic information obtained for P. dabeshanensis, we propose some suggestions for the conservation and efficient management of this endangered species.     

Geographical patterns of adaptation within a species' range: interactions between drift and gene flow

We use individual-based stochastic simulations and analytical deterministic predictions to investigate the interaction between drift, natural selection and gene flow on the patterns of local adaptation across a fragmented species' range under clinally varying selection. Migration between populations follows a stepping-stone pattern and density decreases from the centre to the periphery of the range. Increased migration worsens gene swamping in small marginal populations but mitigates the effect of drift by replenishing genetic variance and helping purge deleterious mutations. Contrary to the deterministic prediction that increased connectivity within the range always inhibits local adaptation, simulations show that low intermediate migration rates improve fitness in marginal populations and attenuate fitness heterogeneity across the range. Such migration rates are optimal in that they maximize the total mean fitness at the scale of the range. Optimal migration rates increase with shallower environmental gradients, smaller marginal populations and higher mutation rates affecting fitness.     

Impacts of seed and pollen flow on population genetic structure for plant genomes with three contrasting modes of inheritance

The classical island and one-dimensional stepping-stone models of population genetic structure developed for animal populations are extended to hermaphrodite plant populations to study the behavior of biparentally inherited nuclear genes and organelle genes with paternal and maternal inheritance. By substituting appropriate values for effective population sizes and migration rates of the genes concerned into the classical models, expressions for genetic differentiation and correlation in gene frequency between populations can be derived. For both models, differentiation for maternally inherited genes at migration-drift equilibrium is greater than that for paternally inherited genes, which in turn is greater than that for biparentally inherited nuclear genes. In the stepping-stone model, the change of genetic correlation with distance is influenced by the mode of inheritance of the gene and the relative values of long- and short-distance migration by seed and pollen. In situations where it is possible to measure simultaneously Fst for genes with all three types of inheritance, estimates of the relative rates of pollen to seed flow can be made for both the short- and long-distance components of migration in the stepping-stone model.     

Differentiation with drift: a spatio-temporal genetic analysis of Galápagos mockingbird populations (Mimus spp.)

Small and isolated island populations provide ideal systems to study the effects of limited population size, genetic drift and gene flow on genetic diversity. We assessed genetic diversity within and differentiation among 19 mockingbird populations on 15 Galápagos islands, covering all four endemic species, using 16 microsatellite loci. We tested for signs of drift and gene flow, and used historic specimens to assess genetic change over the last century and to estimate effective population sizes. Within-population genetic diversity and effective population sizes varied substantially among island populations and correlated strongly with island size, suggesting that island size serves as a good predictor for effective population size. Genetic differentiation among populations was pronounced and increased with geographical distance. A century of genetic drift did not change genetic diversity on an archipelago-wide scale, but genetic drift led to loss of genetic diversity in small populations, especially in one of the two remaining populations of the endangered Floreana mockingbird. Unlike in other Galápagos bird species such as the Darwin''s finches, gene flow among mockingbird populations was low. The clear pattern of genetically distinct populations reflects the effects of genetic drift and suggests that Galápagos mockingbirds are evolving in relative isolation.     

Assessing natural introgression in 2 biomedical model species, the rhesus macaque (Macaca mulatta) and the long-tailed macaque (Macaca fascicularis)

Rhesus macaque (Macaca mulatta) and long-tailed macaque (Macaca fascicularis) are the 2 most commonly used primate model species in biomedical sciences. Although morphological studies have revealed a weak hybridization at the interspecific contact zone, in the north of Indochina, a molecular study has suggested an ancient introgression from rhesus to long-tailed macaque into the Indo-Chinese peninsula. However, the gene flow between these 2 taxa has never been quantified using genetic data and theoretical models. In this study, we have examined genetic variation within and between the parapatric Chinese rhesus macaque and Indo-Chinese long-tailed macaque populations, using 13 autosomal, 5 sex-linked microsatellite loci and mitochondrial DNA sequence data. From these data, we assessed genetic structure and estimated gene flow using a Bayesian clustering approach and the "Isolation with Migration" model. Our results reveal a weak interspecific genetic differentiation at both autosomal and sex-linked loci, suggesting large population sizes and/or gene flow between populations. According to the Bayesian clustering, Chinese rhesus macaque is a highly homogeneous gene pool that contributes strongly to the current Indo-Chinese long-tailed macaque genetic makeup, whether or not current admixture is assumed. Coalescent simulations, which integrated the characteristics of the loci, pointed out 1) a higher effective population size in rhesus macaque, 2) no mitochondrial gene flow, and 3) unilateral and male-mediated nuclear gene flow of approximately 10 migrants per generation from rhesus to long-tailed macaque. These patterns of genetic structure and gene flow suggest extensive ancient introgression from Chinese rhesus macaque into the Indo-Chinese long-tailed macaque population.     

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.