Figure 1

Gene trees. Left: Example of an evolutionary scenario showing the evolution of a gene family. The corresponding true gene tree $\widehat{T}$ appears embedded in the true species tree $Ŝ$. The map $\widehat{\mu }$ is implicitly given by drawing the species tree superimposed on the gene tree. In particular, the speciation vertices in the gene tree (red circuits) are mapped to the vertices of the species tree (gray ovals) and the duplication vertices (blue squares) to the edges of the species tree. Gene losses are represented with "⊗" (mapping to edges in $Ŝ$). The observable species a b,..., f are the leaves of the species tree (green ovals) and extant genes therein are labeled with "⊙". Right: The corresponding gene tree T with observed events from the left tree. Leaves are labeled with the corresponding species.