Fig. 1.

Subfigure (a) shows the model admixture graph $(N^{*},{\mathbf{\Theta }}^{*})$ discussed in Section 3. We refer to this model as M1, and let ${\mathit{X}}^{*}$ denote the vector of f₂-statistics implied by this model. Subfigure (b) shows N₀: the ML (and NJ) tree for ${\mathit{X}}^{*}$ rooted at the outgroup E. Subfigure (c) shows N₁: the ML network in the edge addition neighborhood of N₀. Although $N^{*}$ has the highest likelihood of all networks with one admixture node, TreeMix and related STB-ML methods get stuck in a local optimum, returning N₁. Numerical parameters shown in subfigure (b) and (c) were computed using TreeMix. Log-likelihood scores, also computed using TreeMix, of N₀, N₁ and $N^{*}$ are −1 302 625, −366 944 and 83, respectively. Branch lengths are shown multiplied by 1000