Isolation-with-migration Model Research Articles

Assessing the impact of recombination on the estimation of isolation-with-migration models using genomic data: a simulation study.

Recombination events complicate the evolutionary history of populations and species and have a significant impact on the inference of isolation-with-migration (IM) models. However, several existing methods have been developed, assuming no recombination within a locus and free recombination between loci. In this study, we investigated the effect of recombination on the estimation of IM models using genomic data. We conducted a simulation study to evaluate the consistency of the parameter estimators with up to 1,000 loci and analyze true gene trees to examine the sources of errors in estimating the IM model parameters. The results showed that the presence of recombination led to biased estimates of the IM model parameters, with population sizes being more overestimated and migration rates being more underestimated as the number of loci increased. The magnitude of the biases tended to increase with the recombination rates when using 100 or more loci. On the other hand, the estimation of splitting times remained consistent as the number of loci increased. In the absence of recombination, the estimators of the IM model parameters remained consistent.

Divergence time estimation using ddRAD data and an isolation-with-migration model applied to water vole populations of Arvicola

Molecular dating methods of population splits are crucial in evolutionary biology, but they present important difficulties due to the complexity of the genealogical relationships of genes and past migrations between populations. Using the double digest restriction-site associated DNA (ddRAD) technique and an isolation-with-migration (IM) model, we studied the evolutionary history of water vole populations of the genus Arvicola, a group of complex evolution with fossorial and semi-aquatic ecotypes. To do this, we first estimated mutation rates of ddRAD loci using a phylogenetic approach. An IM model was then used to estimate split times and other relevant demographic parameters. A set of 300 ddRAD loci that included 85 calibrated loci resulted in good mixing and model convergence. The results showed that the two populations of A. scherman present in the Iberian Peninsula split 34 thousand years ago, during the last glaciation. In addition, the much greater divergence from its sister species, A. amphibius, may help to clarify the controversial taxonomy of the genus. We conclude that this approach, based on ddRAD data and an IM model, is highly useful for analyzing the origin of populations and species.

A maximum likelihood approach to infer demographic models

We present a new maximum likelihood approach to estimate demographic history using genomic data sampled from two populations. A demographic model such as an isolation-with-migration (IM) model explains the genetic divergence of two populations split away from their common ancestral population. The standard probability model for an IM model contains a latent variable called genealogy that represents gene-specific evolutionary paths and links the genetic data to the IM model. Under an IM model, a genealogy consists of two kinds of evolutionary paths of genetic data: vertical inheritance paths (coalescent events) through generations and horizontal paths (migration events) between populations. The computational complexity of the IM model inference is one of the major limitations to analyze genomic data. We propose a fast maximum likelihood approach to estimate IM models from genomic data. The first step analyzes genomic data and maximizes the likelihood of a coalescent tree that contains vertical paths of genealogy. The second step analyzes the estimated coalescent trees and finds the parameter values of an IM model, which maximizes the distribution of the coalescent trees after taking account of possible migration events. We evaluate the performance of the new method by analyses of simulated data and genomic data from two subspecies of common chimpanzees in Africa.

Exact Calculation of the Joint Allele Frequency Spectrum for Isolation with Migration Models.

Population genomic datasets collected over the past decade have spurred interest in developing methods that can utilize massive numbers of loci for inference of demographic and selective histories of populations. The allele frequency spectrum (AFS) provides a convenient statistic for such analysis, and, accordingly, much attention has been paid to predicting theoretical expectations of the AFS under a number of different models. However, to date, exact solutions for the joint AFS of two or more populations under models of migration and divergence have not been found. Here, we present a novel Markov chain representation of the coalescent on the state space of the joint AFS that allows for rapid, exact calculation of the joint AFS under isolation with migration (IM) models. In turn, we show how our Markov chain method, in the context of composite likelihood estimation, can be used for accurate inference of parameters of the IM model using SNP data. Lastly, we apply our method to recent whole genome datasets from African Drosophila melanogaster.

Inference of Gene Flow in the Process of Speciation: An Efficient Maximum-Likelihood Method for the Isolation-with-Initial-Migration Model.

The isolation-with-migration (IM) model is commonly used to make inferences about gene flow during speciation, using polymorphism data. However, it has been reported that the parameter estimates obtained by fitting the IM model are very sensitive to the model’s assumptions—including the assumption of constant gene flow until the present. This article is concerned with the isolation-with-initial-migration (IIM) model, which drops precisely this assumption. In the IIM model, one ancestral population divides into two descendant subpopulations, between which there is an initial period of gene flow and a subsequent period of isolation. We derive a very fast method of fitting an extended version of the IIM model, which also allows for asymmetric gene flow and unequal population sizes. This is a maximum-likelihood method, applicable to data on the number of segregating sites between pairs of DNA sequences from a large number of independent loci. In addition to obtaining parameter estimates, our method can also be used, by means of likelihood-ratio tests, to distinguish between alternative models representing the following divergence scenarios: (a) divergence with potentially asymmetric gene flow until the present, (b) divergence with potentially asymmetric gene flow until some point in the past and in isolation since then, and (c) divergence in complete isolation. We illustrate the procedure on pairs of Drosophila sequences from ∼30,000 loci. The computing time needed to fit the most complex version of the model to this data set is only a couple of minutes. The R code to fit the IIM model can be found in the supplementary files of this article.

Speciation with Gene Flow in North American Myotis Bats.

Growing evidence supports the idea that species can diverge in the presence of gene flow. However, most methods of phylogeny estimation do not consider this process, despite the fact that ignoring gene flow is known to bias phylogenetic inference. Furthermore, studies that do consider divergence-with-gene-flow typically do so by estimating rates of gene flow using a isolation-with-migration model (IM), rather than evaluating scenarios of gene flow (such as divergence-with-gene flow or secondary contact) that represent very different types of diversification. In this investigation, we aim to infer the recent phylogenetic history of a clade of western long-eared bats while evaluating a number of different models that parameterize gene flow in a variety of ways. We utilize PHRAPL, a new tool for phylogeographic model selection, to compare the fit of a broad set of demographic models that include divergence, migration, or both among Myotis evotis, $M$. thysanodes and M. keenii. A genomic data set consisting of 808 loci of ultraconserved elements was used to explore such models in three steps using an incremental design where each successive set was informed by, and thus more focused than, the previous set of models. Specifically, the three steps were to (i) assess whether gene flow should be modeled and identify the best topologies, (ii) infer directionality of migration using the best topologies, and (iii) estimate the timing of gene flow. The best model (AIC model weight ${\sim}0.98$) included two divergence events (($M$. evotis, $M$. thysanodes), M. keenii) accompanied by gene flow at the initial stages of divergence. These results provide a striking example of speciation-with-gene-flow in an evolutionary lineage. [Myotis bats; PHRAPL; P2C2M; phylogeographic model selection; speciation with gene flow.].

GPGA: GPU Accelerated Population Genetics Analyses.

BackgroundThe isolation with migration (IM) model is important for studies in population genetics and phylogeography. IM program applies the IM model to genetic data drawn from a pair of closely related populations or species based on Markov chain Monte Carlo (MCMC) simulations of gene genealogies. But computational burden of IM program has placed limits on its application.MethodologyWith strong computational power, Graphics Processing Unit (GPU) has been widely used in many fields. In this article, we present an effective implementation of IM program on one GPU based on Compute Unified Device Architecture (CUDA), which we call gPGA.ConclusionsCompared with IM program, gPGA can achieve up to 52.30X speedup on one GPU. The evaluation results demonstrate that it allows datasets to be analyzed effectively and rapidly for research on divergence population genetics. The software is freely available with source code at https://github.com/chunbaozhou/gPGA.

Molecular population genetics of male and female mitochondrial genomes in subarctic Mytilus trossulus

The doubly uniparental inheritance system allows for the use of two independent mitochondrial genomes for population history investigations. Under this system, two lineages of mitochondrial DNA (mtDNA) exist and males are typically heteroplasmic, having the additional, usually divergent, mitochondrial genome inherited from their male parent. This additional mtDNA typically evolves faster, potentially allowing for insight into more recent events in population history. Few studies did explore this possibility in marine mussels Mytilus showing its usefulness. Recent observations of the Mytilus trossulus mussels who have retained their native mtDNA in European waters posed the question of their origin. Are they part of a population present, but previously undetected, or is this a potentially human mediated, ongoing spread of an invasive species? To tackle this question, we amplified with species-specific primers and sequenced an approximately 1,200-bp-long fragment spanning COIII and ND2 genes from both mitochondrial genomes of mussels sampled at five locations worldwide, covering the whole M. trossulus range. The overall pattern of polymorphisms is compatible with the entirely postglacial history of the whole species, indicating a very deep bottleneck at last glacial maximum, with possible retention of the whole species in a single refugium, and the effective population size of no more than a few thousands. Both analyses of molecular variance and isolation with migration (IM) models point at the West Atlantic as the source of the European M. trossulus mussels, at least the ones who retained their native mtDNA. The hypothesis that this is an ongoing, human-mediated process was considered. To this end, comparison with the well-known case: the introduction of congeneric mussel, Mytilus galloprovincialis, from Mediterranean Sea to Asia was used. This introduction occurred within the last 100 years. The results inferred by the IM model suggest that the timing and structure of transatlantic migration of M. trossulus differs significantly from the M. galloprovincialis case: it is more than 1,000 years old and involves a much larger fraction of the ancestral population. Therefore, most likely, this invasion is not a human-mediated process.

A General Method for Calculating Likelihoods Under the Coalescent Process

Analysis of genomic data requires an efficient way to calculate likelihoods across very large numbers of loci. We describe a general method for finding the distribution of genealogies: we allow migration between demes, splitting of demes [as in the isolation-with-migration (IM) model], and recombination between linked loci. These processes are described by a set of linear recursions for the generating function of branch lengths. Under the infinite-sites model, the probability of any configuration of mutations can be found by differentiating this generating function. Such calculations are feasible for small numbers of sampled genomes: as an example, we show how the generating function can be derived explicitly for three genes under the two-deme IM model. This derivation is done automatically, using Mathematica. Given data from a large number of unlinked and nonrecombining blocks of sequence, these results can be used to find maximum-likelihood estimates of model parameters by tabulating the probabilities of all relevant mutational configurations and then multiplying across loci. The feasibility of the method is demonstrated by applying it to simulated data and to a data set previously analyzed by Wang and Hey (2010) consisting of 26,141 loci sampled from Drosophila simulans and D. melanogaster. Our results suggest that such likelihood calculations are scalable to genomic data as long as the numbers of sampled individuals and mutations per sequence block are small.

On the nonidentifiability of migration time estimates in isolation with migration models

In recent years many studies have found evidence of gene flow between diverging populations by analyzing genetic data under an Isolation with Migration (IM) model (Pinho & Hey 2010). Given evidence of gene exchange, investigators often then wish to inquire of the time when gene flow occurred (e.g. Won & Hey 2005; Becquet & Przeworski 2009). For example, a model of divergence with gene flow would be suggested if gene flow occurred early or throughout the divergence process, whereas secondary contact would be the likely interpretation if gene flow was found to only have occurred after divergence had been ongoing for some time. Recently Strasburg & Rieseberg (2011) assessed the quality of estimates for the time of migration events using the method currently implemented in the IMA2 program (Hey 2010). They found that the credible intervals of estimated times were so wide as to make the method unsuitable for the question. These results suggest that some conclusions of previous studies that draw upon the posterior distribution for times of migration should be discounted (e.g. Won & Hey 2005; Strasburg et al 2008; Niemiller et al 2008; Nadachowska & Babik 2009). The Strasburg & Rieseberg (2011) study reports results from simulations. Here we examine, using the theory underlying the method implemented in the IMA2 program, the possible bases for their observations. We demonstrate that gene migration times are not fully identifiable using the general coalescent for genealogies in an IM model, as implemented in IMA2 and similar programs. In many respects the findings are general to methods that rely upon calculating the probabilities of genealogies under the coalescent, and so are of broader interest than any particular program. We note that the method implemented in IMA2 is the same as that in the IMA program (Hey & Nielsen 2007), and hereafter we refer simply to IMA.

Detecting late vs. early introgressions during speciation

There is a wide interest in estimating parameters of simple demographic models from DNA polymorphism data. Specifically, the isolation-with-migration (IM) model is commonly used in speciation and conservation biology research as it allows one to estimate the split time and level of gene flow between two populations or species. However, enduring debate in evolutionary biology centers around the question of whether the early stages of speciation can occur in the presence of gene flow. To help resolve this question we develop a new method to estimate parameters of extensions of the IM model that use genomic scale data sets more efficiently than available methods.

Care of the dying.

Analysis of genomic data requires an efficient way to calculate likelihoods across very large numbers of loci. We describe a general method for finding the distribution of genealogies: we allow migration between demes, splitting of demes [as in the isolation-with-migration (IM) model], and recombination between linked loci. These processes are described by a set of linear recursions for the generating function of branch lengths. Under the infinite-sites model, the probability of any configuration of mutations can be found by differentiating this generating function. Such calculations are feasible for small numbers of sampled genomes: as an example, we show how the generating function can be derived explicitly for three genes under the two-deme IM model. This derivation is done automatically, using Mathematica. Given data from a large number of unlinked and nonrecombining blocks of sequence, these results can be used to find maximum-likelihood estimates of model parameters by tabulating the probabilities of all relevant mutational configurations and then multiplying across loci. The feasibility of the method is demonstrated by applying it to simulated data and to a data set previously analyzed by Wang and Hey (2010) consisting of 26,141 loci sampled from Drosophila simulans and D. melanogaster. Our results suggest that such likelihood calculations are scalable to genomic data as long as the numbers of sampled individuals and mutations per sequence block are small.