Figure 3

Model of evolution with duplications. A duplication in the same species in each of the two gene trees leads to a duplication node with four children (white square) in the tree of possible adjacencies between the two gene trees. Immediately after a duplication event, the adjacency is broken for the duplicated branch (branch leading to the rightmost red node). The second duplication leads to the simultaneous apparition of two other branches (leading to left and middle red nodes). The adjacency is also broken at the beginning of these two branches. The probabilities of transition between the duplication node and its four children are then given by the (., 0, 0, 0) → (., ., ., .) components of P(t₁) ⊗ N¹¹(t₁). In the likelihood computation, all positions for the blue and red nodes are considered.