TY - JOUR

T1 - Covariance of pairwise differences on a multi-species coalescent tree and implications for FST

AU - Guerra, Geno

AU - Nielsen, Rasmus

N1 - Publisher Copyright: © 2022 Royal Society Publishing. All rights reserved.

PY - 2022

Y1 - 2022

N2 - The multi-species coalescent (MSC) provides a theoretical foundation for modern phylogenetics and comparative population genetics. Its theoretical properties have been heavily studied but there are still aspects of the MSC that are largely unknown, including the covariances in pairwise coalescence times, which are fundamental for understanding the properties oFSTatistics that combine data from multiple species, such as the fixation index (FST). The major contribution of this study is the derivation and implementation of exact expressions for the covariances of pairwise coalescence times under phylogenetic models with piecewise constant changes in population size, assuming no gene flow after species divergence. We use these expressions to derive the variance in average pairwise differences within and between populations. We then derive approximations for the expectation and bias of a sequence-based estimator of FST, a commonly used genetic measurement of population differentiation, when it is applied to a non-recombining region of the genome. We show that the estimator of FST is generally biased downward. A freely available software package is provided, STCov, to calculate the mean, variances and covariances in coalescence times presented here under user-defined piecewise-constant species trees. This article is part of the theme issue Celebrating 50 years since Lewontin's apportionment of human diversity'.

AB - The multi-species coalescent (MSC) provides a theoretical foundation for modern phylogenetics and comparative population genetics. Its theoretical properties have been heavily studied but there are still aspects of the MSC that are largely unknown, including the covariances in pairwise coalescence times, which are fundamental for understanding the properties oFSTatistics that combine data from multiple species, such as the fixation index (FST). The major contribution of this study is the derivation and implementation of exact expressions for the covariances of pairwise coalescence times under phylogenetic models with piecewise constant changes in population size, assuming no gene flow after species divergence. We use these expressions to derive the variance in average pairwise differences within and between populations. We then derive approximations for the expectation and bias of a sequence-based estimator of FST, a commonly used genetic measurement of population differentiation, when it is applied to a non-recombining region of the genome. We show that the estimator of FST is generally biased downward. A freely available software package is provided, STCov, to calculate the mean, variances and covariances in coalescence times presented here under user-defined piecewise-constant species trees. This article is part of the theme issue Celebrating 50 years since Lewontin's apportionment of human diversity'.

KW - covariance

KW - F

KW - Multi-species coalescent

KW - pairwise differences

KW - population differentiation

U2 - 10.1098/rstb.2020.0415

DO - 10.1098/rstb.2020.0415

M3 - Journal article

C2 - 35430886

AN - SCOPUS:85128380309

VL - 377

JO - Philosophical Transactions of the Royal Society B: Biological Sciences

JF - Philosophical Transactions of the Royal Society B: Biological Sciences

SN - 0962-8436

IS - 1852

M1 - 20200415

ER -