Supplementary Methods 1 Definitions

Let a gene family be defined as the set of genes that are descendents of a single gene in the last common ancestor (LCA) of all n species in consideration. A genetic sequence can under go two types of evolution: micro-level (sequence mutation) and macro level (gene duplication, gene loss, horizontal transfer, etc.) [1]. Let T be a rooted phylogenetic tree of the a gene family. The leaf nodes of a gene-tree represent modern genes from modern species, where as the internal nodes represent ancestral genes from ancestral species. When there are no macro-level events, T will have the same topology as the species-tree. In such a case, the gene tree is said to be congruent. The edges of a rooted tree, often called branches, can be uniquely identified by the more recent of its two incident nodes. Using this convention, we can refer to a branch directly above node l as bl. From an alignment of the genes ’ sequences, we can estimate the number of substitutions (or length) along every branch of T using one of several methods, such as maximum likelihood [2] or least squared error [3, 4]. We will use bl to refer to not only the branch, but also its length as inferred from one of these methods. 1.1 Reconciliation The species of the modern genes is often a given. Although, the same is not true of ancestral genes, th