Fig. 2.

(A–C) Branch lengths in expected number of substitutions per site. (D–F) $N_{\mathrm{e}}$ values across nodes (including the leaves) relative to $N_{\mathrm{e}}$ at the root. From left to right: Simulation under the mutation–selection approximation (A, D), under a Wright–Fisher model accounting for small population size effects (5,000 individuals at the root), site linkage and short term fluctuation of $N_{\mathrm{e}}$ (B, E), and finally accounting for site epistasis in the context of selection for protein stability (C, F). The tree root is 150 My old, where the initial population starts with a mutation rate of ${10}^{-8}$ per site per generation and generation time of 10 years. These experiments confirm that signal in the placental mammalian tree can allow to reliably infer the direction of change in $N_{\mathrm{e}}$, even if linkage disequilibrium, short term fluctuation of $N_{\mathrm{e}}$ and finite population size effects are not accounted for in the inference framework. However, the presence of epistasis between sites is a serious threat to the inference of $N_{\mathrm{e}}$.