Phylogenetic Reconstruction Algorithms Based on Weighted 4-Trees

Abstract

Quartet methods first compute 4-taxon trees (or 4-trees) then use a combinatorial algorithm to infer a phylogeny that closely respects the inferred 4-trees. This article focuses on the special case involving weighted 4-trees. The sum of the weights of the 4-trees induced by the inferred phylogeny is a natural measurement of the fit between this phylogeny and the 4-tree set. In order to measure the fit of each edge of the inferred tree, we propose a new criterion that takes the weights of the 4-trees along with the way they are grouped into account. However, finding the tree that optimizes the natural criterion is NP-hard [10], and optimizing our new criterion is likely not easier. We then describe two greedy heuristic algorithms that are experimentally efficient in optimizing these criteria and have an O(n ⁴) time complexity (where n is the number of studied taxa). We use computer simulations to show that these two algorithms have better topological accuracy than QUARTET PUZZLING [12], which is one of the few quartet methods able to take 4-trees weighting into account, and seems to be widely used.