Population differentiation and migration: coalescence times in a two-sex island model for autosomal and X-linked loci

Abstract

Evolutionists have debated whether population-genetic parameters, such as effective population size and migration rate, differ between males and females. In humans, most analyses of this problem have focused on the Y chromosome and the mitochondrial genome, while the X chromosome has largely been omitted from the discussion. Past studies have compared F(ST) values for the Y chromosome and mitochondrion under a model with migration rates that differ between the sexes but with equal male and female population sizes. In this study we investigate rates of coalescence for X-linked and autosomal lineages in an island model with different population sizes and migration rates for males and females, obtaining the mean time to coalescence for pairs of lineages from the same deme and for pairs of lineages from different demes. We apply our results to microsatellite data from the Human Genome Diversity Panel, and we examine the male and female migration rates implied by observed F(ST) values.

Figure 1

The region in which the ratio M_f/M_m is positive, as computed from equations (14) and (15) for fixed values of r, with F_ST,X and F_ST,A varying on the interval [0,1]. The region is shaded in grey. The solid line is 2F_ST,A(2 − r)/[3+ F_ST,A(1 − 2r)], which F_ST,X must be greater than for M_m to be greater than zero. The dashed line is 4F_ST,A(2 − r)/[3 + F_ST,A(5 − r)], which F_ST,X must be less than for M_f to be greater than zero.

Figure 2

F_ST at X-linked and autosomal loci (equations (12) and (13)) as r, the female fraction of the population, varies on [0,1]. The dashed line is F_ST,X and the solid line is F_ST,A. A: M_f = N_f m_f = 1 migrant per generation, while the number of male migrants per generation is 0.01. B: M_m, the number of male migrants per generation, is equal to 1, while M_f = 0.01.

Figure 3

Global and regional estimates of the ratio of female to male migrants (the ratio of equation (14) to equation (15)) as r varies over [0.4, 0.6], based on F_ST values calculated using 952 individuals from the Human Genome Diversity Panel.