Figure 2

Recursion to compute p ( G, l|θ, S ). Shows six possible scenarios of a gene tree evolving inside the species tree and how they relate to dynamic programming calculations. (A) A gene tree lineage starts and reaches y, where y is a leaf of an extant species. (B) An internal vertex of a gene tree cannot be mapped to a speciation vertex other than the least common ancestor of its children in species tree. (C) An internal vertex of a gene tree may be placed on a speciation node (the least common ancestor of its children in the species tree). (D) A gene subtree rooted at u, starts from x (a speciation vertex), duplicates at y and yields the subtree below. (E) A gene subtree rooted at u is placed at some discretization point on an edge of species tree. (F) A gene lineage starts from a discretization point on an edge of species tree, and yields the gene subtree rooted at u.