A Two-Stage Pruning Algorithm for Likelihood Computation for a Population Tree

RoyChoudhury, Arindam; Felsenstein, Joseph; Thompson, E. A.

doi:10.1534/genetics.107.085753

Cited by 49 publications

(95 citation statements)

References 20 publications

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“…It may be fruitful to adapt the Bayesian framework presented here to infer the historical relationships between the sampled populations. For example, the drift on different branches of a tree of populations could be approximated by normal deviations, which would allow rapid calculation of the branch lengths (see RoyChoudhury et al 2008 for a recent presentation of the problem). However, the pairwise covariance of allele frequencies across populations can be used only to learn about the average coalescent times within and between pairs of populations (Slatkin 1991) and so this approach could not be directly used to distinguish between isolation models and migration models (see McVean 2009, for discussion).…”

Section: Discussionmentioning

confidence: 99%

Using Environmental Correlations to Identify Loci Underlying Local Adaptation

Coop

Witonsky²,

Rienzo³

et al. 2010

Genetics

646

903

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Loci involved in local adaptation can potentially be identified by an unusual correlation between allele frequencies and important ecological variables or by extreme allele frequency differences between geographic regions. However, such comparisons are complicated by differences in sample sizes and the neutral correlation of allele frequencies across populations due to shared history and gene flow. To overcome these difficulties, we have developed a Bayesian method that estimates the empirical pattern of covariance in allele frequencies between populations from a set of markers and then uses this as a null model for a test at individual SNPs. In our model the sample frequencies of an allele across populations are drawn from a set of underlying population frequencies; a transform of these population frequencies is assumed to follow a multivariate normal distribution. We first estimate the covariance matrix of this multivariate normal across loci using a Monte Carlo Markov chain. At each SNP, we then provide a measure of the support, a Bayes factor, for a model where an environmental variable has a linear effect on the transformed allele frequencies compared to a model given by the covariance matrix alone. This test is shown through power simulations to outperform existing correlation tests. We also demonstrate that our method can be used to identify SNPs with unusually large allele frequency differentiation and offers a powerful alternative to tests based on pairwise or global F ST . Software is available at http://www. eve.ucdavis.edu/gmcoop/.

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Section: Discussionmentioning

confidence: 99%

Using Environmental Correlations to Identify Loci Underlying Local Adaptation

Coop

Witonsky²,

Rienzo³

et al. 2010

Genetics

646

903

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show abstract

“…We have used a pruning algorithm similar to other species tree computations (9,(40)(41)(42)(43)(44) that evaluate a quantity at a parent node in terms of corresponding values for daughter nodes. In previous applications of this idea, the states recorded at a node are generally simpler than our input and output states.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, we eliminate the past restriction (4) that the lineages whose monophyly is examined all derive from the same population. This generalization is analogous to the assumption that in computing the probability of a binary evolutionary character (40)(41)(42), one or both character states can appear in multiple species. Our approach uses a pruning algorithm, generalizing the two-species formula in a conceptually similar manner to other recursive coalescent computations on arbitrary trees (9,(40)(41)(42)(43)(44).…”

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confidence: 99%

The probability of monophyly of a sample of gene lineages on a species tree

Mehta

Bryant

Rosenberg

2016

Proc. Natl. Acad. Sci. U.S.A.

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Monophyletic groups-groups that consist of all of the descendants of a most recent common ancestor-arise naturally as a consequence of descent processes that result in meaningful distinctions between organisms. Aspects of monophyly are therefore central to fields that examine and use genealogical descent. In particular, studies in conservation genetics, phylogeography, population genetics, species delimitation, and systematics can all make use of mathematical predictions under evolutionary models about features of monophyly. One important calculation, the probability that a set of gene lineages is monophyletic under a two-species neutral coalescent model, has been used in many studies. Here, we extend this calculation for a species tree model that contains arbitrarily many species. We study the effects of species tree topology and branch lengths on the monophyly probability. These analyses reveal new behavior, including the maintenance of nontrivial monophyly probabilities for gene lineage samples that span multiple species and even for lineages that do not derive from a monophyletic species group. We illustrate the mathematical results using an example application to data from maize and teosinte. Since early in the development of coalescent theory and phylogeography, coalescent formulas and related simulations have contributed to a probabilistic understanding of the shapes of multispecies gene trees (1-3), enabling novel predictions about gene tree shapes under evolutionary hypotheses (4, 5), new ways of testing hypotheses about gene tree discordances (6, 7), and new algorithms for problems of species tree inference (8, 9) and species delimitation (10, 11). A "multispecies coalescent" model, in which coalescent processes on separate species tree branches merge back in time as species reach a common ancestor (12), has become a key tool for theoretical predictions, simulation design, and evaluation of inference methods, and as a null model for data analysis.A fundamental concept in genealogical studies is that of monophyly. In a genealogy, a group that is monophyletic consists of all of the descendants of its most recent common ancestor (MRCA): every lineage in the group-and no lineage outside it-descends from this ancestor. Backward in time, a monophyletic group has all of its lineages coalesce with each other before any coalesces with a lineage from outside the group.The phylogenetic and phylogeographic importance of monophyly traces to the fact that monophyly enables a natural definition of a genealogical unit. Such a unit can describe a distinctive set of organisms that differs from other groups of organisms in ways that are evolutionarily meaningful. Species can be delimited by characters present in every member of a species and absent outside the species, and that therefore can reflect monophyly (13,14). In conservation biology, monophyly can be used as a prioritization criterion because groups with many monophyletic loci are likely to possess unique evolutionary features (15). Reciprocal monophyly, in whic...

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“…The expectations of various quantities can be derived under a model without migration (Wakeley and Hey, 1997), and the likelihood of a particular configuration of allele counts at a locus may be computed analytically for a model with no migration and where mutation since divergence can be ignored (e.g. Nielsen and Slatkin, 2000;Nicholson et al, 2002;RoyChoudhury et al, 2008), or alternatively can be estimated accurately under more general models using coalescent simulations.…”

Section: Types Of Datamentioning

confidence: 99%

An approximate likelihood for genetic data under a model with recombination and population splitting

Davison¹,

Pritchard²,

Coop³

2009

Theoretical Population Biology

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We describe a new approximate likelihood for recombining population genetic data under a model in which a single ancestral population has split into two daughter populations. The approximate likelihood is based on the 'Product of Approximate Conditionals' likelihood and 'copying model' of Stephens (2003 Genetics 165:2213). The approach developed here may be used for efficient approximate likelihood-based analyses of unlinked data. However our copying model also considers the effects of recombination. Hence, a more important application is to looselylinked haplotype data, for which efficient statistical models explicitly featuring non-equilibrium population structure have so far been unavailable. Thus, in addition to the information in allele frequency differences about the timing of the population split, the method can also extract information from the lengths of haplotypes shared between the populations. There are a number of challenges posed by extracting such information, which makes parameter estimation difficult. We discuss how the approach could be extended to identify haplotypes introduced by migrants.

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A Two-Stage Pruning Algorithm for Likelihood Computation for a Population Tree

Cited by 49 publications

References 20 publications

Using Environmental Correlations to Identify Loci Underlying Local Adaptation

Using Environmental Correlations to Identify Loci Underlying Local Adaptation

The probability of monophyly of a sample of gene lineages on a species tree

An approximate likelihood for genetic data under a model with recombination and population splitting

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