On the consistency of the minimum evolution principle of phylogenetic inference

The goal of phylogenetic inference is the reconstuction of the evolutionary history of various biological entities (taxa) such as genes, proteins, viruses or species. Phylogenetic inference is of major importance in computational biology and has numerous applications ranging from the study of biodiversity to sequence analysis. Given a matrix of pairwise distances between taxa, the minimum evolution (ME) principle consists in selecting the tree whose length is minimal, where the tree length is estimated within the least-squares framework. The ME principle has been shown to be statistically consistent when using the ordinary least-squares criterion (OLS) and inconsistent with the more general weighted least-squares criterion (WLS). Unfortunately, OLS+ME inference method can provide poor results since the variances of the input data are not taken into account. Here we study a model which lies between OLS and WLS, classical in statistics and data analysis, and we prove that the ME principle is statistically consistent within this model. Our proof is inductive and relies on a time optimal recursive algorithm for estimating edge lengths. As a corollary, we obtain a different and simpler proof of the consistency result for OLS+ME.

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