Figure 1

A birth and death process along the lineages of a phylogenetic tree. The branch lengths t s of the phylogenetic tree are given in millions of years. In the phylogenetic tree, (x _{i 1}, x _{i 2}, x _{i 3}, x _{i 4}, x _{i 5}) are the sizes of gene family i for species 1, 2, 3, 4, and 5, while (θ _i6 , θ _i7 , θ _i8 , θ _i9 ,) are the sizes of the internal nodes for gene family i.