The Effect of Single Recombination Events on Coalescent Tree Height and Shape

Ferretti, Luca; Disanto, Filippo; Wiehe, Thomas

doi:10.1371/journal.pone.0060123

Cited by 18 publications

(22 citation statements)

References 27 publications

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“…Hence the imbalance measure Var(d) depends strongly on the root balance ω 1 , which has been previously recognised as a meaningful global measure of tree balance (Ferretti et al, 2013;Li and Wiehe, 2013), and on the imbalances of the first upper splits as well.…”

Section: The Mean Number Of Descendants Across All Branches From Levelmentioning

confidence: 97%

Decomposing the Site Frequency Spectrum: The Impact of Tree Topology on Neutrality Tests

et al. 2017

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We investigate the dependence of the site frequency spectrum (SFS) on the topological structure of genealogical trees. We show that basic population genetic statistics -for instance estimators of θ or neutrality tests such as Tajima's D -can be decomposed into components of waiting times between coalescent events and of tree topology. Our results clarify the relative impact of the two components on these statistics. We provide a rigorous interpretation of positive or negative values of an important class of neutrality tests in terms of the underlying tree shape. In particular, we show that values of Tajima's D and Fay and Wu's H depend in a direct way on a peculiar measure of tree balance which is mostly determined by the root * Email: luca.ferretti@gmail.com 1 arXiv:1510.06748v2 [q-bio.PE] 12 Jan 2017 balance of the tree. We present a new test for selection in the same class as Fay and Wu's H and discuss its interpretation and power. Finally, we determine the trees corresponding to extreme expected values of these neutrality tests and present formulae for these extreme values as a function of sample size and number of segregating sites.

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Section: The Mean Number Of Descendants Across All Branches From Levelmentioning

confidence: 97%

Decomposing the Site Frequency Spectrum: The Impact of Tree Topology on Neutrality Tests

et al. 2017

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“…In particular, tree height and tree topology of closely linked trees are highly correlated. However, under conditions of the standard neutral model, correlation breaks down on short distances (Figure 3) [15]. Roughly recombination events in the sample history reduce correlation by about 50%.…”

Section: Resultsmentioning

confidence: 98%

“…In fact, given a shallow tree, recombination leads with high probability to an increase of tree height and to unbalanced trees [15]. Thus, recombination events next to the selected site tend to increase tree height (see sketch in Figure 1B and C) and to create a bias in favour of unbalanced trees, i.e.…”

Section: Resultsmentioning

confidence: 99%

“…More recently, it was shown that the (non-Markovian) ARG can well be approximated by a simpler, more tractable model, the so-called Sequential Markov Coalescent [12]–[14], which is of particular interest for the efficient simulation of genealogies across large genomic regions. How single recombination events reflect on tree shape under neutrality has recently been analyzed by Ferretti et al [15]. Here, we concentrate on tree shape in the vicinity of a selected locus.…”

Section: Introductionmentioning

confidence: 99%

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Coalescent Tree Imbalance and a Simple Test for Selective Sweeps Based on Microsatellite Variation

Wiehe

2013

PLoS Comput Biol

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Selective sweeps are at the core of adaptive evolution. We study how the shape of coalescent trees is affected by recent selective sweeps. To do so we define a coarse-grained measure of tree topology. This measure has appealing analytical properties, its distribution is derived from a uniform, and it is easy to estimate from experimental data. We show how it can be cast into a test for recent selective sweeps using microsatellite markers and present an application to an experimental data set from Plasmodium falciparum.

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“…Ferretti et al (2013) used another approach to investigate the correlation between the times to the most recent common ancestor at two neighboring loci. The authors approached the problem using coalescent arguments to quantify the changes recombination induces on the local trees, but it is unclear how to generalize their approach efficiently to the total length of the genealogical trees.…”

Section: Introductionmentioning

confidence: 99%

Computing the joint distribution of the total tree length across loci in populations with variable size

Miroshnikov

Steinrücken

2017

Theoretical Population Biology

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In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly useful for this type of inference. Due to the Markovian structure of these models, an essential building block is the joint distribution of local genealogical trees, or statistics of these genealogies, at two neighboring loci in populations of variable size. Here, we present a novel method to compute the marginal and the joint distribution of the total length of the genealogical trees at two loci separated by at most one recombination event for samples of arbitrary size. To our knowledge, no method to compute these distributions has been presented in the literature to date. We show that they can be obtained from the solution of certain hyperbolic systems of partial differential equations. We present a numerical algorithm, based on the method of characteristics, that can be used to efficiently and accurately solve these systems and compute the marginal and the joint distributions. We demonstrate its utility to study properties of the joint distribution. Our flexible method can be straightforwardly extended to handle an arbitrary fixed number of recombination events, to include the distributions of other statistics of the genealogies as well, and can also be applied in structured populations.

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The Effect of Single Recombination Events on Coalescent Tree Height and Shape

Cited by 18 publications

References 27 publications

Decomposing the Site Frequency Spectrum: The Impact of Tree Topology on Neutrality Tests

Decomposing the Site Frequency Spectrum: The Impact of Tree Topology on Neutrality Tests

Coalescent Tree Imbalance and a Simple Test for Selective Sweeps Based on Microsatellite Variation

Computing the joint distribution of the total tree length across loci in populations with variable size

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