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

Wilkinson‐Herbots, Hilde

doi:10.1016/j.tpb.2012.05.003

Cited by 47 publications

(50 citation statements)

References 51 publications

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“…Moreover, genomic regions of low interspecific divergence are spatially clustered (Figures 3C and S9), consistent with recent and ongoing introgression that is slowly broken down over generations of recombination. We point readers towards the recent work of Wilkinson-Herbots [43] for parameter inference from distributions like those in Figures 2B and 3B.…”

Section: Resultsmentioning

confidence: 88%

Speciation and Introgression between Mimulus nasutus and Mimulus guttatus

et al. 2014

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Mimulus guttatus and M. nasutus are an evolutionary and ecological model sister species pair differentiated by ecology, mating system, and partial reproductive isolation. Despite extensive research on this system, the history of divergence and differentiation in this sister pair is unclear. We present and analyze a population genomic data set which shows that M. nasutus budded from a central Californian M. guttatus population within the last 200 to 500 thousand years. In this time, the M. nasutus genome has accrued genomic signatures of the transition to predominant selfing, including an elevated proportion of nonsynonymous variants, an accumulation of premature stop codons, and extended levels of linkage disequilibrium. Despite clear biological differentiation, we document genomic signatures of ongoing, bidirectional introgression. We observe a negative relationship between the recombination rate and divergence between M. nasutus and sympatric M. guttatus samples, suggesting that selection acts against M. nasutus ancestry in M. guttatus.

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Section: Resultsmentioning

confidence: 88%

Speciation and Introgression between Mimulus nasutus and Mimulus guttatus

et al. 2014

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“…, in the case of symmetric gene flow and equal subpopulation sizes during the gene flow period), results 9 and 10 above simplify to the corresponding results in Wilkinson-Herbots (2012)—in this case, the coefficient

A_{i 3}

in the linear combination is zero for

i \in {1, 2, 3} .

…”

Section: Methodsmentioning

confidence: 78%

“…The equations 18 and 29 of Wilkinson-Herbots (2012) use this superimposition of processes to derive the distribution of S under a mathematically much simpler IIM model with symmetric migration and equal subpopulation sizes during the period of migration. These equations can now be adapted to obtain the probability mass function (PMF) of S under each of the migration scenarios dealt with in this article.…”

Section: Methodsmentioning

confidence: 99%

“…Their calculation of the likelihood of the number of nucleotide differences between pairs of sequences relies on the numerical computation of the coalescence time density at different points in time, which can be computationally expensive. IM models in which gene flow is allowed to cease at some point in the past—hereafter referred to as isolation-with-initial-migration (IIM) models—have also been considered by, for example, Teshima and Tajima (2002), Becquet and Przeworski (2009), Mailund et al (2012), Wilkinson-Herbots (2012), and Lohse et al (2015).…”

mentioning

confidence: 99%

“…In the present article, we apply matrix eigen-decomposition techniques to expand on the work of Wilkinson-Herbots (2012) on the IIM model, who derived explicit formulas for the distribution of the coalescence time of a pair of sequences, and the distribution of the number of nucleotide differences between them. These analytic results enable a very fast computation of the likelihood under an IIM model, given a data set consisting of observations on pairs of sequences at a large number of independent loci (Lohse et al 2015; Wilkinson-Herbots 2015; Janko et al 2016).…”

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confidence: 99%

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

Costa

Wilkinson‐Herbots

2017

Genetics

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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.

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Efficient computation in the IM model

2013

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In this paper we analyze the isolation-with-migration model in a continuous-time Markov chain framework, and derive analytical expressions for the probability densities of gene tree topologies with an arbitrary number of lineages. We combine these densities with both nucleotide-substitution and infinite sites mutation models and derive probabilities for use in maximum likelihood estimation. We demonstrate how to apply lumpability of continuous-time Markov chains to achieve a significant reduction in the size of the state-space under consideration. We use matrix exponentiation and spectral decomposition to derive explicit expressions for the case of two diploid individuals in two populations, when the data is given as alignment columns. We implement these expressions in order to carry out a maximum likelihood analysis and provide a simulation study to examine the performance of our method in terms of our ability to recover true parameters. Finally, we show how the performance depends on the parameters in the model.

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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

Cited by 47 publications

References 51 publications

Speciation and Introgression between Mimulus nasutus and Mimulus guttatus

Speciation and Introgression between Mimulus nasutus and Mimulus guttatus

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

Efficient computation in the IM model

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