Figure 4.

The expectation of the mean X-chromosomal and autosomal admixture fractions over time, with their associated limits, for constant ongoing admixture. (A) Male-biased admixture from population $S_1.$ (B) Female-biased admixture from population $S_1.$ The initial condition is $\left(s_{1,0}^{\mathrm{f}},s_{1,0}^{\mathrm{m}},s_{2,0}^{\mathrm{f}},s_{2,0}^{\mathrm{m}}\right)=\left(0.5,0.5,0.5,0.5\right).$ The autosomal admixture is constant over time because $s_{1,0}=s_{2,0}=1/2$ and $s_1=s_2;$ it is the same in both A and B because it does not depend on the sex-specific contributions. The X-chromosomal admixture is different in females and males; it is smaller than the autosomal mean for male-biased admixture from population 1 and larger for female-biased admixture. The X-chromosomal mean is plotted using Equations 17–20. The autosomal mean uses equation 37 from Goldberg et al. (2014).