Rapidly Computing the Phylogenetic Transfer Index

Given trees T and T_o on the same taxon set, the transfer index phi(b,T_o) is the number of taxa that need to be ignored so that the bipartition induced by branch b in T is equal to some bipartition in T_o. Recently, Lemoine et al. [Lemoine et al., 2018] used the transfer index to design a novel bootstrap analysis technique that improves on Felsenstein’s bootstrap on large, noisy data sets. In this work, we propose an algorithm that computes the transfer index for all branches b in T in O(n log^3 n) time, which improves upon the current O(n^2)-time algorithm by Lin, Rajan and Moret [Lin et al., 2012]. Our implementation is able to process pairs of trees with hundreds of thousands of taxa in minutes and considerably speeds up the method of Lemoine et al. on large data sets. We believe our algorithm can be useful for comparing large phylogenies, especially when some taxa are misplaced (e.g. due to horizontal gene transfer, recombination, or reconstruction errors).