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

A phylogenetic epoch is a time interval between successive branching events during which the number of ancestral branches is constant. Read backward from the four sampled leaves: there are four branches until the first merger, then three until the next, then two until their common root. Write the random durations as $T_4,T_3,T_2$, with expected values $E_k=\mathbb{E}[T_k]$.

The original solution diagram below places time horizontally and labels each branch by its number of descendant leaves. Type A is the pectinate topology; type B is the balanced topology. The coloured time strips identify the three phylogenetic epochs; their drawn widths are schematic, not estimated times.