Topology weighting by iterative sampling of sub-trees

Topology weighting is a means to quantify relationships between taxa that are not necessarily monophyletic. It's a simple, descriptive method, designed for exploring how relationship vary across the genome using population genomic data.The relationship among a given set of taxa can be defined by a number of possible topologies. For example, for four taxa labelled A, B, C and D, there are three possible (unrooted) bifurcating topologies:Given a tree with any number of tips (or leaves), each belonging to a particular taxon, the weighting of each taxon topology is defined as the fraction of all unique sub-trees, in which each taxon is represented by a single tip, that match that topology. Topology weighting therefore reduces the complexity of the full tree to a number of values, each giving the proportionate contribution of a particular taxon tree to the full tree.This code implements the method Twisst (topology weighting by iterative sampling of sub-trees), which does what it says: it computes the weightings by iteratively sampling sub-trees from the full tree and checking their topology. This can be slow if there are many tips (e.g. 4 taxa with ten tips each gives 10 000 unique subtrees to consider. But there are some shortcuts to speed things up - see Weighting Method below.