“…An equivalent constructive definition, based on a mapping, called the LCA mapping between the gene tree T and the species tree S, was formulated in [55,88] and widely used [20,39,44,54,77,86,87,88,128]. The LCA mapping between T and S, denoted by M , maps every vertex x of T to the Lowest Common Ancestor (LCA) of L(x) in S. This Interestingly, M (T, S) not only minimizes the duplication cost, but also minimizes the loss and mutation costs [28].…”