Locus-aware decomposition of gene trees with respect to polytomous species trees

An example of locus trees for G = ((a1, b2), (b3, c4)) with two decompositions F1 and F2 consistent with S = (a, (b, c), d). These decompositions are created by cuts indicated with red color. MX:G → S is shown for every set of cuts X (for internal nodes). Here, Λ(F1, S) = Λ(F2, S) = 0, Δ(F1) = 2 · GAIN and Δ(F2) = 3 · GAIN, i.e., F1 is optima