Figure 5.
Computation of the Estimate of Near Oceanian Ancestry pN(X)
The test population X is assumed to have arisen from a mixture of a proportion (1 − qX) of ancestry from ancestral East Asians E′ and (qX) of ancestral Near Oceanians N′. The Near Oceanians are, in turn, assumed to have received a proportion pX of their ancestry from the Denisovans (E and New Guinea are assumed to be unmixed descendants of these two). The expected value of f4(A,Australia; X, New Guinea) can be computed from the correlation in the allele frequency differences A − Australia (blue arrows) and X − New Guinea (red arrows). These paths only overlap along the proportion (1 − qX) of the ancestry of population X that takes the East Asian path, where the expected shared drift is (1 − pX)β+γ as shown in the figure. Thus, the expected value of the f4 statistic is (1 − qX)(1 − pX)β+γ. Because qX = 0 for the denominator of pN(X) (no Near Oceanian ancestry), the ratio of f4 statistics has an expected value of (1 − qX) and E[pN(X)] = qX.