Fig. 10

Illustration of a recursion step in BuildGeneTree (Algorithm 1). A The current vertex in the species tree, \(u_S\), is a leaf. B The current vertex in the species tree, \(u_S\), is an inner vertex. The connected components of \(H_1\), \(H_2\), and \(H_3\) are represented by the orange, green, and blue boxes, respectively. For simplicity, only those connected components of \(H_2\) and \(H_3\) are shown that are included in \(C_i\) and \(C_j\), respectively. Two vertices x and y must form an edge in (a) \(G_{_{>}}\) (wavy lines) if they are in distinct components of \(H_1\), (b) \(G_{_{>}}\) or \(G_{_{=}}\) (solid straight lines) if they are in the same component of \(H_1\) but distinct components of \(H_2\), and (c) \(G_{_{<}}\) (dashed lines) if they are in the same component of \(H_2\) but distinct components of \(H_3\). Below, the construction of the reconciliation map and the time map is illustrated. The half circles indicate that \(L'=L(T(\rho '))\), \(C_i=L(T(u_i))\), etc. if the respective vertex is not suppressed