Figure 5.

The expectation of the mean X-chromosomal and autosomal admixture fractions over time for constant admixture, with female-biased contributions from both source populations. 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 mean X-chromosomal admixture from $S_1,$ $\mathbb{E}\left[H_{1,g,\delta }^{\mathrm{X}}\right],$ is smaller than the mean autosomal admixture, $\mathbb{E}\left[H_{1,g,\delta }^{\mathrm{A}}\right],$ even though $S_1$ has an excess of females, $s_1^{\mathrm{f}}>s_1^{\mathrm{m}}.$ The expectation of X-chromosomal admixture is plotted using Equations 17 and 18. The autosomal mean uses equation 37 from Goldberg et al. (2014).