Reconciling multiple genes trees via segmental duplications and losses

Note that if G consists of one tree, this definition coincides with the usual one given in the literature (first formally defined in [24]). We say that α is an LCA-mapping if, for each internal node u ∈ V ( G ) with children u 1 , u 2 , α r ( u ) = L C A S ( α r ( u 1 ) , α r ( u 2 ) ) . Note that there may be more than one LCA-mapping, since the S and D events on internal nodes can vary. The number of duplications of α , denoted by d ( α ) is the number of nodes u of G such that α e ( u ) = D . For counting the losses, first define for y ≤ x the distance dist(x, y) as the number of arcs on the path from x to y. Then, for every internal node u with children { u 1 , u 2 } , the number of losses associated with u in a reconciliation α , denoted by l α ( u ) , is defined as follows