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.     

The effect on neutral gene flow of selection at a linked locus

The effect on gene flow at a neutral locus of a selective cline at a linked locus is investigated. A diffusion approximation for a two-locus island model is derived in which only one locus is subject to selection. The moments of the stationary distribution are obtained and compared to the corresponding moments from a one-locus, neutral island model. This comparison yields an effective migration rate. The effective migration rate is always less than the actual migration rate, but this effect is seen to be small for weak selection and loose linkage in the case of adult migration. The importance of selection at linked loci to the question of genetic differentiation in a subdivided population is discussed.     

Patterns of inbreeding depression and architecture of the load in subdivided populations

Inbreeding depression is a general phenomenon that is due mainly to recessive deleterious mutations, the so-called mutation load. It has been much studied theoretically. However, until very recently, population structure has not been taken into account, even though it can be an important factor in the evolution of populations. Population subdivision modifies the dynamics of deleterious mutations because the outcome of selection depends on processes both within populations (selection and drift) and between populations (migration). Here, we present a general model that permits us to gain insight into patterns of inbreeding depression, heterosis, and the load in subdivided populations. We show that they can be interpreted with reference to single-population theory, using an appropriate local effective population size that integrates the effects of drift, selection, and migration. We term this the "effective population size of selection" (NS(e)). For the infinite island model, for example, it is equal to NS(e) = N1 + m/hs, where N is the local population size, m the migration rate, and h and s the dominance and selection coefficients of deleterious mutation. Our results have implications for the estimation and interpretation of inbreeding depression in subdivided populations, especially regarding conservation issues. We also discuss the possible effects of migration and subdivision on the evolution of mating systems.     

Temporal changes in allele frequencies but stable genetic diversity over the past 40 years in the Irish Sea population of thornback ray, Raja clavata

Rays and skates are an unavoidable part of the by-catch in demersal fisheries. Over the past 40 years, the thornback ray (Raja clavata) has decreased in numbers and even disappeared in some areas, leading to concerns about genetic risk. For this reason, the effective population size (N(e)), the migration rate (m) and temporal changes in the genetic diversity were estimated for the population of thornback rays in the Irish Sea and Bristol Channel. Using genotyped, archived and contemporary samples (1965 and 2003-2004), N(e) was estimated at 283 individuals (95% CI=145-857), m at 0.1 (95% CI=0.03-0.25) and the N(e)/N ratio between 9 x 10(-5) and 6 x 10(-4). Although these results must be treated with caution, due to the small sample sizes, this is the first attempt to estimate N(e) in an elasmobranch species. The low N(e)/N ratio suggests that relatively few individuals contribute to the next generation. The combined effect of sex bias, inbreeding, fluctuations in population size and, perhaps most important, the variance in reproductive success may explain the low N(e)/N ratio. In addition, the relatively high gene flow between Irish Sea population and other source populations is likely to have had an impact on our estimate, which may be more relevant at the metapopulation scale. No significant loss of genetic diversity was found over the 40-year timeframe and long-term maintenance of the genetic diversity could be due to gene flow.     

Reconciling extremely strong barriers with high levels of gene exchange in annual sunflowers

In several cases, estimates of gene flow between species appear to be higher than we might predict given the strength of interspecific barriers separating these species pairs. However, as far as we are aware, detailed measurements of reproductive isolation have not previously been compared with a coalescent-based assessment of gene flow. Here, we contrast these two measures in two species of sunflower, Helianthus annuus and H. petiolaris. We quantified the total reproductive barrier strength between these species by compounding the contributions of the following prezygotic and postzygotic barriers: ecogeographic isolation, reproductive asynchrony, niche differentiation, pollen competition, hybrid seed formation, hybrid seed germination, hybrid fertility, and extrinsic postzygotic isolation. From this estimate, we calculated the probability that a reproductively successful hybrid is produced: estimates of P(hyb) range from 10(-4) to 10(-6) depending on the direction of the cross and the degree of independence among reproductive barriers. We then compared this probability with population genetic estimates of the per generation migration rate (m). We showed that the relatively high levels of gene flow estimated between these sunflower species (N(e) m= 0.34-0.76) are mainly due to their large effective population sizes (N(e) > 10(6)). The interspecific migration rate (m) is very small (<10(-7)) and an order of magnitude lower than that expected based on our reproductive barrier strength estimates. Thus, even high levels of reproductive isolation (>0.999) may produce genomic mosaics.     

Relationships between migration rates and landscape resistance assessed using individual-based simulations

Linking landscape effects on gene flow to processes such as dispersal and mating is essential to provide a conceptual foundation for landscape genetics. It is particularly important to determine how classical population genetic models relate to recent individual-based landscape genetic models when assessing individual movement and its influence on population genetic structure. We used classical Wright-Fisher models and spatially explicit, individual-based, landscape genetic models to simulate gene flow via dispersal and mating in a series of landscapes representing two patches of habitat separated by a barrier. We developed a mathematical formula that predicts the relationship between barrier strength (i.e., permeability) and the migration rate (m) across the barrier, thereby linking spatially explicit landscape genetics to classical population genetics theory. We then assessed the reliability of the function by obtaining population genetics parameters (m, F(ST) ) using simulations for both spatially explicit and Wright-Fisher simulation models for a range of gene flow rates. Next, we show that relaxing some of the assumptions of the Wright-Fisher model can substantially change population substructure (i.e., F(ST) ). For example, isolation by distance among individuals on each side of a barrier maintains an F(ST) of ～0.20 regardless of migration rate across the barrier, whereas panmixia on each side of the barrier results in an F(ST) that changes with m as predicted by classical population genetics theory. We suggest that individual-based, spatially explicit modelling provides a general framework to investigate how interactions between movement and landscape resistance drive population genetic patterns and connectivity across complex landscapes.     

Gene flow among populations of the malaria vector, Anopheles gambiae, in Mali, West Africa

The population structure of the Anopheles gambiae complex is unusual, with several sibling species often occupying a single area and, in one of these species, An. gambiae sensu stricto, as many as three "chromosomal forms" occurring together. The chromosomal forms are thought to be intermediate between populations and species, distinguishable by patterns of chromosome gene arrangements. The extent of reproductive isolation among these forms has been debated. To better characterize this structure we measured effective population size, N(e), and migration rates, m, or their product by both direct and indirect means. Gene flow among villages within each chromosomal form was found to be large (N(e)m > 40), was intermediate between chromosomal forms (N(e)m approximately 3-30), and was low between species (N(e)m approximately 0.17-1.3). A recently developed means for distinguishing among certain of the forms using PCR indicated rates of gene flow consistent with those observed using the other genetic markers.     

Contemporary gene flow and the spatio-temporal genetic structure of subdivided newt populations (Triturus cristatus, T. marmoratus)

Gene flow and drift shape the distribution of neutral genetic diversity in metapopulations, but their local rates are difficult to quantify. To identify gene flow between demes as distinct from individual migration, we present a modified Bayesian method to genetically test for descendants between an immigrant and a resident in a nonmigratory life stage. Applied to a metapopulation of pond-breeding European newts (Triturus cristatus, T. marmoratus) in western France, the evidence for gene flow was usually asymmetric and, for demes of known census size (N), translated into maximally seven reproducing immigrants. Temporal sampling also enabled the joint estimation of the effective demic population size (Ne) and the immigration rate m (including nonreproductive individuals). Ne ranged between 4.1 and 19.3 individuals, Ne/N ranged between 0.05 and 0.65 and always decreased with N; m was estimated as 0.19-0.63, and was possibly biased upwards. We discuss how genotypic data can reveal fine-scale demographic processes with important microevolutionary implications.     

The expected number of heterozygous sites in a subdivided population.

A simple, exact formula is derived for the expected number of heterozygous sites per individual at equilibrium in a subdivided population. The model of infinitely many neutral sites is posited; the linkage map is arbitrary. The monoecious, diploid population is subdivided into a finite number of panmictic colonies that exchange gametes. The backward migration matrix is arbitrary, but time independent and ergodic (i.e., irreducible and aperiodic). With suitable weighting, the expected number of heterozygous sites is 4Neu, where Ne denotes the migration effective population number and u designates the total mutation rate per gene (or DNA sequence). For diploid migration, this formula is a good approximation if Ne >> 1.     

Genetic estimates of contemporary effective population size: what can they tell us about the importance of genetic stochasticity for wild population persistence?

Genetic stochasticity due to small population size contributes to population extinction, especially when population fragmentation disrupts gene flow. Estimates of effective population size ( N _e) can therefore be informative about population persistence, but there is a need for an assessment of their consistency and informative relevance. Here we review the body of empirical estimates of N _e for wild populations obtained with the temporal genetic method and published since Frankham's (1995 ) review. Theoretical considerations have identified important sources of bias for this analytical approach, and we use empirical data to investigate the extent of these biases. We find that particularly model selection and sampling require more attention in future studies.
We report a median unbiased N _e estimate of 260 (among 83 studies) and find that this median estimate tends to be smaller for populations of conservation concern, which may therefore be more sensitive to genetic stochasticity. Furthermore, we report a median N _e/ N ratio of 0.14, and find that this ratio may actually be higher for small populations, suggesting changes in biological interactions at low population abundances. We confirm the role of gene flow in countering genetic stochasticity by finding that N _e correlates strongest with neutral genetic metrics when populations can be considered isolated. This underlines the importance of gene flow for the estimation of N _e, and of population connectivity for conservation in general. Reductions in contemporary gene flow due to ongoing habitat fragmentation will likely increase the prevalence of genetic stochasticity, which should therefore remain a focal point in the conservation of biodiversity.     

植物三种不同遗传方式基因的地理家系谱理论与应用初探

将已知用于从地理空间上离散或连续分布群体随机抽取基因样本的基因家系谱理论推广到两性异交植物上。由于存在不同的群体间基因多率,地３种不同遗传方式的植物基因组（核、叶绿体和线粒体ＤＮＡ）分别进行了研究。理论上证明对于不同遗传方式的基因,通过相应调整有效群体大小和迁移率,现有的基因家系谱理论可直接应用于植物群体上,其中一个结论就是当从离散分布群体中随机抽取ｎ个基因样本时,亚群体间的花粉流和种子流的相对比     

Geography of genetic processes in populations: gene migrations in Siberia and Far East

A map of gene migration rate m in the indigenous population of Siberia and the Russian Far East was constructed on the basis of data obtained from questionnaires of 1960 to 1990. The mean gene migration rate weighted with respect to the region area and averaged over 3951 grid nodes was m = 0.0083. Weighting with respect to population density yielded a significantly lower rate (m = 0.0053), which reflected a more intense gene exchange in less populous regions of traditional nomadism. The association between gene migration rate m and genetically effective population size Ne was analyzed. The parameter Nem, which characterizes the interpopulation gene diversity, was used to identify regions where this parameter is autoregulated and those where the autoregulatory mechanisms were disrupted. A tree of ethnolinguistic types was constructed. Its analysis did not reveal any association between migration structure and linguistic characteristics, suggesting that the spreading of cultural elements is not necessarily associated with migration. The tree was also used to construct a map of ethnos-forming migration; its major element reflected migration from the Baikal and Altai regions to the ethnic region of modern Yakuts.     

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.     

Comparative estimation of effective population sizes and temporal gene flow in two contrasting population systems

Estimation of effective population sizes (N(e)) and temporal gene flow (N(e)m, m) has many implications for understanding population structure in evolutionary and conservation biology. However, comparative studies that gauge the relative performance of N(e), N(e)m or m methods are few. Using temporal genetic data from two salmonid fish population systems with disparate population structure, we (i) evaluated the congruence in estimates and precision of long- and short-term N(e), N(e)m and m from six methods; (ii) explored the effects of metapopulation structure on N(e) estimation in one system with spatiotemporally linked subpopulations, using three approaches; and (iii) determined to what degree interpopulation gene flow was asymmetric over time. We found that long-term N(e) estimates exceeded short-term N(e) within populations by 2-10 times; the two were correlated in the system with temporally stable structure (Atlantic salmon, Salmo salar) but not in the highly dynamic system (brown trout, Salmo trutta). Four temporal methods yielded short-term N(e) estimates within populations that were strongly correlated, and these were higher but more variable within salmon populations than within trout populations. In trout populations, however, these short-term N(e) estimates were always lower when assuming gene flow than when assuming no gene flow. Linkage disequilibrium data generally yielded short-term N(e) estimates of the same magnitude as temporal methods in both systems, but the two were uncorrelated. Correlations between long- and short-term geneflow estimates were inconsistent between methods, and their relative size varied up to eightfold within systems. While asymmetries in gene flow were common in both systems (58-63% of population-pair comparisons), they were only temporally stable in direction within certain salmon population pairs, suggesting that gene flow between particular populations is often intermittent and/or variable. Exploratory metapopulation N(e) analyses in trout demonstrated both the importance of spatial scale in estimating N(e) and the role of gene flow in maintaining genetic variability within subpopulations. Collectively, our results illustrate the utility of comparatively applying N(e), N(e)m and m to (i) tease apart processes implicated in population structure, (ii) assess the degree of continuity in patterns of connectivity between population pairs and (iii) gauge the relative performance of different approaches, such as the influence of population subdivision and gene flow on N(e) estimation. They further reiterate the importance of temporal sampling replication in population genetics, the value of interpreting N(e)or m in light of species biology, and the need to address long-standing assumptions of current N(e), N(e)m or m models more explicitly in future research.     

Density-dependent migration and human population structure in historical Massachusetts

Studies of population structure often focus on the effects of population size and migration rates on genetic variation. Few studies, however, have investigated the relationship between these two factors. The purpose of this paper is to determine the extent to which migration (and gene flow) is density-dependent (that is, affected by population size) for populations in historical Massachusetts. Data from 4,859 marriage records were analyzed from four populations in north-central Massachusetts during the time period 1741 to 1849. These data were placed into 29 samples defined in terms of population and time cohort. Within each cohort the overall exogamy rate was computed along with three estimates of gene flow based on marital migration: local migration (k), long-distance migration (m), and effective migration rate (me). Three samples show unusually low rates that reflect the history of settlement. Regression analyses were used with the remaining samples, and they show nonlinear density-dependent migration that is unrelated to temporal trends. Migration is highest in samples with small population sizes (less than 800) and large population sizes (greater than 1,600). Migration is lowest in medium-sized populations. Two processes are suggested to explain this curvilinear relationship of migration and population size. In small populations, the lack of suitable potential mates and/or availability of settled land leads to an increase in migration into the population. As population size increases, this migration decreases. After populations reach a certain size, migration increases again, most likely reflecting the economic pull of larger populations. These patterns could act to enhance, or counter, genetic drift, depending on the direction of density dependence.     

Variation of female and male lineages in sub-Saharan populations: the importance of sociocultural factors

In this paper, we present a study of genetic variation in sub-Saharan Africa, which is based on published and unpublished data on fast-evolving (hypervariable region 1 of mitochondrial DNA and six microsatellites of Y chromosome) and slow-evolving (haplogroup frequencies) polymorphisms of mtDNA and Y chromosome. Our study reveals a striking difference in the genetic structure of food-producer (Bantu and Sudanic speakers) and hunter-gatherer populations (Pygmies, Kung, and Hadza). In fact, the ratio of mtDNA to Y-chromosome Nupsilon is substantially higher in food producers than in hunter-gatherers as determined by fast-evolving polymorphisms (1.76 versus 0.11). This finding indicates that the two population groups differ substantially in female and male migration rate and/or effective size. The difference also persists when linguistically homogeneous populations are used and outlier populations are eliminated (1.78 vs 0.19) or when the jacknife procedure is applied to a paired population data set (1.32 to 7.84 versus 0.14 to 0.66). The higher ratio of mtDNA to Y-chromosome Nnu in food producers than in hunter-gatherers is further confirmed by the use of slow-evolving polymorphisms (1.59 to 7.91 versus 0.12 to 0.35). To explain these results, we propose a model that integrates demographic and genetic aspects and incorporates ethnographic knowledge. In such a model, the asymmetric gene flow, polyginy, and patrilocality play an important role in differentiating the genetic structure of sub-Saharan populations. The existence of an asymmetric gene flow is supported by the phylogeographic features of mtDNA and Y-chromosome haplogroups found in the two population groups. The role of polyginy and patrilocality is sustained by the evidence of a differential pressure of genetic drift and gene flow on maternal and paternal lineages of food producers and hunter-gatherers that is revealed through the analysis of mitochondrial and Y-chromosomal intrapopulational variation.     

The effect of unequal migration rates on FST

Using the structured coalescent model, it is shown that unequal migration rates between different pairs of subpopulations can increase the value of Wright's coefficient F(ST) and its dependence on the mutation rate, and decrease the effective level of gene flow. Two specific models of population structure are considered: (i) an 'island model with barrier' where migration rates between subpopulations on the same side of the barrier are higher than migration rates between subpopulations on opposite sides of the barrier, and (ii) the two-dimensional stepping-stone model with unequal migration rates in the two dimensions of the model.     

CLINAL VARIATION AT MICROSATELLITE LOCI REVEALS HISTORICAL SECONDARY INTERGRADATION BETWEEN GLACIAL RACES OF COREGONUS ARTEDI (TELEOSTEI: COREGONINAE)

Abstract Classical models of the spatial structure of population genetics rely on the assumption of migration‐drift equilibrium, which is seldom met in natural populations having only recently colonized their current range (e.g., postglacial). Population structure then depicts historical events, and counfounding effects due to recent secondary contact between recently differentiated lineages can further counfound analyses of association between geographic and genetic distances. Mitochondrial polymorphisms have revealed the existence of two closely related lineages of the lake cisco, Coregonus artedi, whose significantly different but overlaping geographical distributions provided a weak signal of past range fragmentation blurred by putative subsequent extensive secondary contacts. In this study, we analyzed geographical patterns of genetic variation at seven microsatellite loci among 22 populations of lake cisco located along the axis of an area covered by proglacial lakes 12,000–8000 years ago in North America. The results clearly confirmed the existence of two genetically distinct races characterized by different sets of microsatellite alleles whose frequencies varied clinally across some 3000 km. Equilibrium and nonequilibrium analyses of isolation by distance revealed historical signal of gene flow resulting from the nearly complete admixture of these races following neutral secondary contacts in their historical habitat and indicated that the colonization process occurred by a stepwise expansion of an eastern (Atlantic) race into a previously established Mississippian race. This historical signal of equilibrium contrasted with the current migration‐drift disequilibrium within major extant watersheds and was apparently maintained by high effective population sizes and low migration regimes.     

Multilocus coalescent analysis of haemoglobin differentiation between low- and high-altitude populations of crested ducks (Lophonetta specularioides)

Hypoxia is a key factor determining survival, and haemoglobins are targets of selection in species native to high-altitude regions. We studied population genetic structure and evaluated evidence for local adaptation in the crested duck (Lophonetta specularioides). Differentiation, gene flow and time since divergence between highland and lowland populations were assessed for three haemoglobin genes (α(A) , α(D) , β(A) ) and compared to seven reference loci (six autosomal introns and mtDNA). Four derived amino acid replacements were found in the globin genes that had elevated Φ(ST) values between the Andean highlands and Patagonian lowlands. A single β(A) -globin polymorphism at a site known to influence O(2) affinity was fixed for different alleles in the two populations, whereas three α(A) - and α(D) -globin polymorphisms exhibited high heterozygosity in the highlands but not in the lowlands. Coalescent analyses supported restricted gene flow for haemoglobin alleles and mitochondrial DNA but nonzero gene flow for the introns. Simulating genetic data under a drift-migration model of selective neutrality, the β(A) -globin fell outside the 95% confidence limit of simulated data, suggesting that directional selection is maintaining different variants in the contrasting elevational environments, thereby restricting migration of β(A) -globin alleles. The α(A) - and α(D) -globins, by contrast, did not differ from the simulated values, suggesting that variants in these genes are either selectively neutral, or that the effects of selection could not be differentiated from background levels of population structure and linkage disequilibrium. This study illustrates the combined effects of selection and population history on inferring levels of population divergence for a species distributed across an altitudinal gradient in which selection for hypoxia resistance has likely played an important role.     

Estimating effective population size and migration rates from genetic samples over space and time

In the past, moment and likelihood methods have been developed to estimate the effective population size (N(e)) on the basis of the observed changes of marker allele frequencies over time, and these have been applied to a large variety of species and populations. Such methods invariably make the critical assumption of a single isolated population receiving no immigrants over the study interval. For most populations in the real world, however, migration is not negligible and can substantially bias estimates of N(e) if it is not accounted for. Here we extend previous moment and maximum-likelihood methods to allow the joint estimation of N(e) and migration rate (m) using genetic samples over space and time. It is shown that, compared to genetic drift acting alone, migration results in changes in allele frequency that are greater in the short term and smaller in the long term, leading to under- and overestimation of N(e), respectively, if it is ignored. Extensive simulations are run to evaluate the newly developed moment and likelihood methods, which yield generally satisfactory estimates of both N(e) and m for populations with widely different effective sizes and migration rates and patterns, given a reasonably large sample size and number of markers.