Second-Order Moments of Segregating Sites Under Variable Population Size

Abstract

The identification of genomic regions that have been exposed to positive selection is a major challenge in population genetics. Since selective sweeps are expected to occur during environmental changes or when populations are colonizing a new habitat, statistical tests constructed on the assumption of constant population size are biased by the co-occurrence of population size changes and selection. To delimit this problem and gain better insights into demographic factors, theoretical results regarding the second-order moments of segregating sites, such as the variance of segregating sites, have been derived. Driven by emerging genomewide surveys, which allow the estimation of demographic parameters, a generalized version of Tajima's D has been derived that takes into account a previously estimated demographic scenario to test single loci for traces of selection against the null hypothesis of neutral evolution under variable population size.

The Total Branch Length of Sample Genealogies in Populations of Variable Size

“…For the particular case k ¼ 1 our result corresponds to an expression derived by Austerlitz et al (1997) and Slatkin (1996) and also to the result obtained by summing Equation 1 in Zivkovic and Wiehe (2008). For k ¼ 2, the coefficients d n;;j1;j2 are tabulated in Figure A1 in the appendix for small values of n. In general, the nested integrals in Equation 20 cannot be simplified further; their form expresses the correlations of the times t j due to population-size variations.…”

“…In a population of constant size, the variables t j are mutually independent. In general this is not the case: Zivkovic and Wiehe (2008), for example, calculated t i t j for a time-varying population (Equations 2 and 3 in their article), using Equation 6.…”

Genetic hitchhiking versus background selection: the controversy and its implications

“…A more conceptual problem of these analyses has been that these summary statistics were oriented towards the standard neutral model, but did not take deviations such as demography and population structure into account. Efforts alleviating this problem by-for instance-calculating Tajima's D for nonequilibrium populations of varying size are relatively recent (Innan & Stephan 2000;Zivkovic & Wiehe 2008), but have not yet been fully exploited in data analyses.…”

Linkage Disequilibrium Under Recurrent Bottlenecks

“…When demographic fluctuations are much slower than the coalescent timescale, they can be ignored and the effective population size can be approximated by the initial population size (Sjödin et al 2005). In the opposite case of rapid demographic fluctuations, it has been argued (Wright 1938;Crow and Kimura 1970) that genetic variation is well described in terms of a population with effective population size N eff , given by the harmonic average of the population size: et al (2010) have shown how to compute moments of the distribution of the total branch lengths of gene genealogies at a single locus, conditional on a given demographic history (see also Zivkovic and Wiehe 2008). In summary, the effect of population-size fluctuations upon genetic variation at a single locus is well understood.…”

“…By contrast, when both timescales are of the same order, it has been shown (Kaj and Krone 2003;Nordborg and Krone 2002;Sjödin et al 2005;Eriksson et al 2010) that the distribution of total branch lengths in samples of single-locus gene genealogies does not in general agree with that predicted by the standard coalescent approximation. But Eriksson et al (2010) have shown how to compute moments of the distribution of the total branch lengths of gene genealogies at a single locus, conditional on a given demographic history (see also Zivkovic and Wiehe 2008). In summary, the effect of population-size fluctuations upon genetic variation at a single locus is well understood.…”