Figure 1

Description of the two problems. (1) A gene tree (the "initial tree") for the gene family {c, b 1, b 2, a 1, a 2} is shown with small red nodes and single thin red edges. It is reconciled with the phylogeny of the three species A, B and C shown with large green nodes and hollow edges represented by a pair of parallel black lines. Duplication nodes of the reconciled gene tree are squared, while speciation nodes and leaves are dots. (2) The two neighbors of b 1 on genome B and of a 1 on genome A are inferred to be orthologous according to their lowest common ancestor in their respective gene trees (not shown). This is an argument for infering orthology between b 1 and a 1, which is in contradiction with the information provided by the initial tree: their lowest common ancestor is a duplication, and thus they are inferred to be paralogous. (3) A solution to the GOC problem, that is a gene tree of minimum RF distance with the initial tree verifying the constraint of b 1 and a 1 being orthologous. (4) A solution to the COC problem, that is a reconciled tree in which the clade {b 1, b 2, a 1, a 2} of d in the initial tree is rather rooted by a speciation node in the corrected tree. This is an example where the optimal solutions to the two problems differ.