Figure 1.

S is a species tree for Σ = {1, 2, 3}; H represents a history, consistent with (i.e. embedded in) the species tree S, with one duplication event preceding the speciation event leading to genomes 2 and 3. Speciation events appear as bifurcations at obtuse angles, while duplication events appear at right angles. We represent the information on isorthology by positioning the retainer of parental function directly under the parental gene. Moreover, we label isorthologs with the same letter (all a's are pairwise isorthologous, and all b's are pairwise isorthologous); P is the phylogeny for the gene family Γ = {a₁,a₂,a₃,b₂,b₃} corresponding to H; it is the same tree as H, embedded differently (uncross edges). G is the gene tree respecting the isolocalization property that is likely to be obtained for the gene family Γ that evolved according to H. Internal node labels of S,G, and P correspond to the LCA mapping, and squares mark duplication nodes, and circles mark speciations resulting from the mapping. R is the reconciliation corresponding to the mapping. The loss has a dotted line indicating the lost lineage.