The inferred rates of gain and loss are quite variable ( Figure 4A and Figure S2 ), with posterior means ranging from about 0.01 to 0.53. These rates are sharply reduced for the external branches of the tree, probably in large part because of diminished power to detect changes in selective mode on these branches. The number of genes inferred to be under selection also varies by branch, but not as dramatically, with expected values ranging between 207.9 and 393.9 and many 95% credible intervals overlapping ( Figure 4B ). Despite differences at individual branches, gains and losses appear to be roughly in equilibrium overall, with 61% of genes estimated to have been under selection at the root, and between 38% and 62% (averaging 50%) under selection at the leaves. The slight tendency to lose selection over time could reflect an ascertainment bias for genes that experienced selection early in mammalian evolution, which will tend to display signatures of selection on multiple long branches of the tree and therefore will be more easily detectable by the LRTs. The branches with the most genes under selection (such as those leading to the rodent and primate ancestors, and to dog and macaque) are generally long (see Figure 1A ), suggesting power may influence these estimates. Nevertheless, the unusually high rate of gain on the branch to the rodents, and the comparatively low rate of loss on that branch (both having fairly low posterior variance; Figure S2 ), suggest not just differences in power but a real tendency for a net gain of selection on this branch, perhaps due to larger population sizes in the rodents. Whether because of power or a genuine increase in selection, the rodent branch appears to play a major role in the identification of PSGs. An expected 72% of the 544 candidate PSGs are under selection on this branch.