Estimating a geographically explicit model of population divergence

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

The distribution of the coalescence time and the number of pairwise nucleotide differences in a model of population divergence or speciation with an initial period of gene flow

This paper is concerned with a model of “isolation with an initial period of migration”, where a panmictic ancestral population split into n descendant populations which exchanged migrants symmetrically at a constant rate for a period of time and subsequently became completely isolated. In the limit as the population split occurred an infinitely long time ago, the model becomes an “isolation after migration” model, describing completely isolated descendant populations which arose from a subdivided ancestral population. The probability density function of the coalescence time of a pair of genes and the probability distribution of the number of pairwise nucleotide differences are derived for both models. Whilst these are theoretical results of interest in their own right, they also give an exact analytical expression for the likelihood, for data consisting of the numbers of nucleotide differences between pairs of DNA sequences where each pair is at a different, independent locus. The behaviour of the distribution of the number of pairwise nucleotide differences under these models is illustrated and compared to the corresponding distributions under the “isolation with migration” and “complete isolation” models. It is shown that the distribution of the number of nucleotide differences between a pair of DNA sequences from different descendant populations in the model of “isolation with an initial period of migration” can be quite different from that under the “isolation with migration model”, even if the average migration rate over time (and hence the total number of migrants) is the same in both scenarios. It is also illustrated how the results can be extended to other demographic scenarios that can be described by a combination of isolated panmictic populations and “symmetric island” models.     

Recent behavioural and population genetic divergence of an invasive ant in a novel environment

Aim Invasive species frequently exhibit high temporal and spatial variation in abundance. Although ecological aspects undoubtedly affect this variation, genetic factors may also play a part. The invasive unicolonial yellow crazy ant Anoplolepis gracilipes exhibits considerable variation in abundance throughout its extensive distribution in Australia’s Northern Territory, where it was first detected in the 1980s. First, we aimed to determine whether A. gracilipes variation in abundance was associated with behavioural and genetic differentiation of the population and to determine whether one or more introductions occurred. Second, we investigated whether the A. gracilipes population was genetically and behaviourally heterogeneous to determine whether population divergence has occurred since introduction. Location Tropical monsoonal savanna in Arnhem Land, Northern Territory, Australia. Methods Ant abundances were assessed at 13 sites throughout the study region. We used mitochondrial DNA sequences and microsatellite molecular markers to determine population genetic structure, which we correlated with abundance. Behavioural differentiation was assayed using aggression trials and analysed together with genetic data to investigate population divergence. Results Although we found considerable variation in abundance, we found no association between population structure and differences in abundance. Our analyses suggest that A. gracilipes ants in Arnhem Land resulted from a single introduction. The population is not homogeneous, however, as aggression scores varied over both genetic and geographic distance. We also found a positive relationship between genetic and geographic distance. Main conclusions The variation in abundance in the Arnhem Land population of A. gracilipes is clearly not owing to invasion by ants from different sources. The genetic and behavioural differentiation we observed is suggestive of incipient genetic and behavioural divergence, which may be expected over time when an invasive species enters in a new environment.     

Weak genetic divergence suggests extensive gene flow at the northeastern range limit of a dioecious Ficus species

Genus Ficus (Moraceae) plays a critical role in the sustainability and biodiversity in tropical and subtropical ecosystems. Ficus species and their host specific pollinating fig wasps (Agaonidae) represent a classic example of obligate mutualism. The genetic consequence of range expansion and range shift is still under investigation, but extensive gene flow and subsequently low level of genetic divergence may be expected to occur among the populations at the poleward range limit of some Ficus species due to long distance gene flow in the genus. In the present study, we focused on populations of F. sarmentosa var. henryi at its northeastern range limit in southeast China to test whether edge populations were genetically fragile. Consistent with our hypothesis, high level of genetic diversity and weak genetic structure were revealed in Ficus sarmentosa var. henryi populations, suggesting extensive gene flow at the plant's range limit. Long-distance movements of both pollinators and frugivorous birds were likely to be frequent and thereby predominantly contributed to the extensive gene flow at large scale despite of some magnificent landscape elements like huge mountains.     

The shapes of neutral gene genealogies in two species: probabilities of monophyly,paraphyly, and polyphyly in a coalescent model

Abstract.— The genealogies of samples of orthologous regions from multiple species can be classified by their shapes. Using a neutral coalescent model of two species, I give exact probabilities of each of four possible genealogical shapes: reciprocal monophyly, two types of paraphyly, and polyphyly. After the divergence that forms two species, each of which has population size N , polyphyly is the most likely genealogical shape for the lineages of the two species. At ∼ 1.300 N generations after divergence, paraphyly becomes most likely, and reciprocal monophyly becomes most likely at ∼1.665 N generations. For a given species, the time at which 99% of its loci acquire monophyletic genealogies is ∼5.298 N generations, assuming all loci in its sister species are monophyletic. The probability that all lineages of two species are reciprocally monophyletic given that a sample from the two species has a reciprocally monophyletic genealogy increases rapidly with sample size, as does the probability that the most recent common ancestor (MRCA) for a sample is also the MRCA for all lineages from the two species. The results have potential applications for the testing of evolutionary hypotheses.     

The probability of fixation of a single mutant in an exchangeable selection model

The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection. The probability of fixation of a mutant type is studied under the assumption of weak selection. An exact formula for the derivative of this probability with respect to the intensity of selection is deduced, and developed in the case of a single mutant. This formula is expressed in terms of mean coalescence times under neutrality assuming that the coefficient of selection for the mutant type has a derivative with respect to the intensity of selection that takes a polynomial form with respect to the frequency of the mutant type. An approximation is obtained in the case where this derivative is a continuous function of the mutant frequency and the population size is large. This approximation is consistent with a diffusion approximation under moment conditions on the number of descendants of a single individual in one time step. Applications to evolutionary game theory in finite populations are presented.      

Ecological and life history characteristics predict population genetic divergence of two salmonids in the same landscape

Ecological and life history characteristics such as population size, dispersal pattern, and mating system mediate the influence of genetic drift and gene flow on population subdivision. Bull trout (Salvelinus confluentus) and mountain whitefish (Prosopium williamsoni) differ markedly in spawning location, population size and mating system. Based on these differences, we predicted that bull trout would have reduced genetic variation within and greater differentiation among populations compared with mountain whitefish. To test this hypothesis, we used microsatellite markers to determine patterns of genetic divergence for each species in the Clark Fork River, Montana, USA. As predicted, bull trout had a much greater proportion of genetic variation partitioned among populations than mountain whitefish. Among all sites, FST was seven times greater for bull trout (FST = 0.304 for bull trout, 0.042 for mountain whitefish. After removing genetically differentiated high mountain lake sites for each species FST, was 10 times greater for bull trout (FST = 0.176 for bull trout; FST = 0.018 for mountain whitefish). The same characteristics that affect dispersal patterns in these species also lead to predictions about the amount and scale of adaptive divergence among populations. We provide a theoretical framework that incorporates variation in ecological and life history factors, neutral divergence, and adaptive divergence to interpret how neutral and adaptive divergence might be correlates of ecological and life history factors.     

Inferring the evolutionary history of divergence despite gene flow in a lizard species,Scincella lateralis (Scincidae), composed of cryptic lineages

Although recent radiations are fruitful for studying the process of speciation, they are difficult to characterize and require the use of multiple loci and analytical methods that account for processes such as gene flow and genetic drift. Using multilocus sequence data, we combine hierarchical cluster analysis, coalescent species tree inference, and isolation‐with‐migration analysis to investigate evolutionary relationships among cryptic lineages of North American ground skinks. We also estimate the extent that gene flow has accompanied or followed diversification, and also attempt to account for and minimize the influence of gene flow when reconstructing relationships. The data best support seven largely parapatric populations that are broadly concordant with mitochondrial (mt)DNA phylogeography throughout most of the species range, although they fail to fully represent extensive mtDNA divergence along the Gulf Coast. Relationships within and among three broad geographical groups are well supported, despite evidence of gene flow among them. Rejection of an allopatric divergence model partially depends on the inclusion of samples from near parapatric boundaries in the analyses, suggesting that allopatric divergence followed by recent migration may best explain migration rate estimates. Accounting for geographical variation in patterns of gene flow can improve estimates of migration–divergence parameters and minimize the influence of contemporary gene flow on phylogenetic inference. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.     

Cryptic population genetic structure: the number of inferred clusters depends on sample size

Clustering methods have been used extensively to unravel cryptic population genetic structure. We investigated the effect of the number of individuals sampled in each location on the resulting number of clusters. Our study was motivated by recent results in Arabidopsis thaliana: studies in which more than one individual was sampled per location apparently have led to a much higher number of clusters than studies where only one individual was sampled in each location, as is generally done in this species. We show, using computer simulations and microsatellite data in A. thaliana, that the number of sampled individuals indeed has a strong impact on the number of resulting clusters. This effect is smaller if the sampled populations have a hierarchical structure. In most cases, sampling 5–10 individuals per population should be enough. The results argue for abandoning the concept of ‘accessions’ in partially selfing organisms.     

The breakdown of genomic ancestry blocks in hybrid lineages given a finite number of recombination sites

When a lineage originates from hybridization genomic blocks of contiguous ancestry from different ancestors are fragmented through genetic recombination. The resulting blocks are delineated by so called junctions, which accumulate with every generation that passes. Modeling the accumulation of ancestry block junctions can elucidate processes and timeframes of genomic admixture. Previous models have not addressed ancestry block dynamics for chromosomes that consist of a finite number of recombination sites. However, genomic data typically consist of informative markers that are interspersed with fragments for which no ancestry information is available. Hence, repeated recombination events may occur between markers, effectively removing existing junctions. Here, we present an analytical treatment of the dynamics of the mean number of junctions over time, taking into account the number of recombination sites per chromosome, population size, genetic map length, and the frequency of the ancestral species in the founding hybrid swarm. We describe the expected number of junctions using equidistant molecular markers and estimate the number of junctions using random markers. This extended theory of junctions thus reflects properties of empirical data and can serve to study the genomic patterns following admixture.     

A population genetic assessment of taxonomic species: The case of Lake Malawi cichlid fishes

Organisms sampled for population‐level research are typically assigned to species by morphological criteria. However, if those criteria are limited to one sex or life stage, or the organisms come from a complex of closely related forms, the species assignments may misdirect analyses. The impact of such sampling can be assessed from the correspondence of genetic clusters, identified only from patterns of genetic variation, to the species identified using only phenotypic criteria. We undertook this protocol with the rock‐dwelling mbuna cichlids of Lake Malawi, for which species within genera are usually identified using adult male coloration patterns. Given high local endemism of male colour patterns, and considerable allele sharing among species, there persists considerable taxonomic uncertainty in these fishes. Over 700 individuals from a single transect were photographed, genotyped and separately assigned: (a) to morphospecies using photographs; and (b) to genetic clusters using five widely used methods. Overall, the correspondence between clustering methods was strong for larger clusters, but methods varied widely in estimated number of clusters. The correspondence between morphospecies and genetic clusters was also strong for larger clusters, as well as some smaller clusters for some methods. These analyses generally affirm (a) adult male‐limited sampling and (b) the taxonomic status of Lake Malawi mbuna, as the species in our study largely appear to be well‐demarcated genetic entities. More generally, our analyses highlight the challenges for clustering methods when the number of populations is unknown, especially in cases of highly uneven sample sizes.     

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

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

Detecting populations in the 'ambiguous' zone: kinship-based estimation of population structure at low genetic divergence

Identifying population structure is one of the most common and important objectives of spatial analyses using population genetic data. Population structure is detected either by rejecting the null hypothesis of a homogenous distribution of genetic variation, or by estimating low migration rates. Issues arise with most current population genetic inference methods when the genetic divergence is low among putative populations. Low levels of genetic divergence may be as a result of either high ongoing migration or historic high migration but no current, ongoing migration. We direct attention to recent developments in the use of the tempo-spatial distribution of closely related individuals to detect population structure or estimate current migration rates. These 'kinship-based' approaches complement more traditional population-based genetic inference methods by providing a means to detect population structure and estimate current migration rates when genetic divergence is low. However, for kinship-based methods to become widely adopted, formal estimation procedures applicable to a range of species life histories are needed.     

The Kuroshio Current influences genetic diversity and population genetic structure of a tropical seagrass,Enhalus acoroides

Information on genetic diversity and differentiation of seagrass populations is essential for the conservation of coastal ecosystems. However, little is known about the seagrasses in the Indo‐West Pacific Ocean, where the world's highest diversity of seagrasses occurs. The influence of sea currents on these populations is also unknown. We estimated the genetic diversity and population genetic structure and identified reproductive features in Enhalus acoroides populations from the Yaeyama Islands, Hainan Island and the Philippines. The Philippines are situated at the centre of the E. acoroides range, Yaeyama and Hainan are peripheral populations, and the Yaeyama population is at the northern limit of the species range. The powerful Kuroshio Current flows from the Philippines to Yaeyama. Genetic analyses using nine microsatellite markers indicated that reproduction of E. acoroides is mostly sexual. Clonal diversity does not decrease in northern populations, although genetic diversity does. However, the genetic diversity of the Yaeyama populations is greater than that of the Hainan populations. Significant genetic differentiation among most populations was evident; however, the Yaeyama and north‐east Philippines populations were genetically similar, despite being separated by ~1100 km. An assignment test suggested that recruitment occurs from the north‐east Philippines to Yaeyama. The strong current in this region is probably responsible for the extant genetic diversity and recruitment patterns.     

Phylogenetic divergence in a local population of the ectomycorrhizal fungus Cenococcum geophilum

Cenococcum geophilum is a widely distributed mycorrhizal species associated with diverse gymnosperm and angiosperm hosts. In previous studies, a significant amount of genetic and genotypic diversity has been detected in this species, despite the fact that C. geophilum is not thought to reproduce by meiotic or mitotic spores. We conducted a phylogenetic analysis of 103 C. geophilum isolates from a California oak woodland and seven non-California isolates using a glyceraldehyde 3-phosphate dehydrogenase gene. In addition, a subset of isolates was analyzed using sequences from ITS-rDNA, a Group I intron located in the 3' end of the SSU-rDNA and a portion of the mitochondrial SSU-rDNA. Phylogenetically distinct lineages, or cryptic species, of C. geophilum were detected at the scale of a single soil sample within our field site. As much genetic diversity was found within a soil sample as was found for isolates collected across the USA. Our results help explain the large amount of physiological, phenotypic, and genetic differences reported among isolates of C. geophilum from similar as well as diverse geographic regions. The ecological role that these sympatric cryptic species play remains to be determined.     

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.     

The influence of gene flow and drift on genetic and phenotypic divergence in two species of Zosterops in Vanuatu

Colonization of an archipelago sets the stage for adaptive radiation. However, some archipelagos are home to spectacular radiations, while others have much lower levels of diversification. The amount of gene flow among allopatric populations is one factor proposed to contribute to this variation. In island colonizing birds, selection for reduced dispersal ability is predicted to produce changing patterns of regional population genetic structure as gene flow-dominated systems give way to drift-mediated divergence. If this transition is important in facilitating phenotypic divergence, levels of genetic and phenotypic divergence should be associated. We consider population genetic structure and phenotypic divergence among two co-distributed, congeneric (Genus: Zosterops) bird species inhabiting the Vanuatu archipelago. The more recent colonist, Z. lateralis, exhibits genetic patterns consistent with a strong influence of distance-mediated gene flow. However, complex patterns of asymmetrical gene flow indicate variation in dispersal ability or inclination among populations. The endemic species, Z. flavifrons, shows only a partial transition towards a drift-mediated system, despite a long evolutionary history on the archipelago. We find no strong evidence that gene flow constrains phenotypic divergence in either species, suggesting that levels of inter-island gene flow do not explain the absence of a radiation across this archipelago.     

The distribution of species diversity across a flora's component lineages: dating the Cape's 'relicts'

The Cape Floristic Region is exceptionally species-rich both for its area and latitude, and this diversity is highly unevenly distributed among genera. The modern flora is hypothesized to result largely from recent (post-Oligocene) speciation, and it has long been speculated that particular species-poor lineages pre-date this burst of speciation. Here, we employ molecular phylogenetic data in combination with fossil calibrations to estimate the minimum duration of Cape occupation by 14 unrelated putative relicts. Estimates vary widely between lineages (7-101 Myr ago), and when compared with the estimated timing of onset of the modern flora's radiation, it is clear that many, but possibly not all, of these lineages pre-date its establishment. Statistical comparisons of diversities with lineage age show that low species diversity of many of the putative relicts results from a lower rate of diversification than in dated Cape radiations. In other putative relicts, however, we cannot reject the possibility that they diversify at the same underlying rate as the radiations, but have been present in the Cape for insufficient time to accumulate higher diversity. Although the extremes in diversity of currently dated Cape lineages fall outside expectations under a constant underlying diversification rate, sampling of all Cape lineages would be required to reject this null hypothesis.