Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2024 / Paper 1 / C5 / b

Count the number of descendant leaves on each branch during each phylogenetic epoch. From the tips backward, both topologies have branch-size lists $(1,1,1,1)$ during $T_4$, then $(2,1,1)$ during $T_3$. During $T_2$, type A has $(3,1)$ and type B has $(2,2)$.

Let $L_j$ be the total length of branches carrying $j$ descendant leaves. Adding the relevant phylogenetic epoch durations givesFor example, type A has one external branch and one three-descendant branch throughout $T_2$, while type B has two two-descendant branches. In either case the total expected branch length is $4E_4+3E_3+2E_2$, a useful accounting check. The stem above the common root is excluded because mutations there would be shared by all four samples.