To gain further insight into the patterns of positive selection that have shaped present-day mammalian genes, we devised a model that allows for probabilistic inferences about the selection histories of individual genes. A selection history is defined as an assignment to each branch of the phylogeny of one of two evolutionary modes: positive selection (each site evolves with v 0 ,1, v 0 = 1, or v 2 .1) or absence of positive selection (each site evolves with v 0 ,1 or v 0 = 1). The model allows a posterior distribution over selection histories to be inferred for each gene, and it allows for estimates of the number of genes under positive selection on individual branches and clades that consider uncertainty about selection histories. Unlike the branch-and clade-specific LRTs-which are simple one-sided hypothesis tests and are necessarily conservative about rejection of the null hypothesis-this model considers all candidate histories symmetrically, and allows for ''soft'' (probabilistic), rather than absolute, choices of history at each gene.