Figure 7:

Timing of admixture under assortative mating. The number of generations since admixture, g, for a single admixture event is plotted as a function of c_11,0 using the variance in autosomal admixture, eq. (51), with V ^A = 0.0625 and $s_{1,0}^s=s_{1,0}^m=0.5$. The plot traverses the range of possible c_11,0 values for g ≥ 0. Recalling that the values of the c_ij,0 are bounded such that the probability of each given parental pairing takes its values in the interval [0, 1], and such that each probability is no greater than the probability of one of its constituent components, for c_11,0 > 0, we have $c_{11,0}\le \text{min}\left(s_{1,0}^f,s_{1,0}^m\right)-s_{1,0}^f{s}_{1,0}^m$. In this case, c_11,0 ≤ 0.25. For c_11,0 < 0, we have $c_{11,0}\ge s_{1,0}^f{s}_{1,0}^m$. In this case, we have c_11,0 ≥ −0.25. However, g cannot be negative; therefore, in this case, we truncate the domain at the value of c_11,0 that produces g = 0. The value of g for a randomly mating population with the same contributions and variance is shown in the dashed line.