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We consider the problem of inferring the evolutionary tree of a set of n species. We propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence. Let Q be a set of resolved quartets defined on the studied species, the method computes the unique maximum subset Q^* of Q which is equivalent to a tree and outputs the corresponding tree as an estimate of the species'' phylogeny. We use a characterization of the subset Q^* due to (Bandelt86) to provide an O(n^4) incremental algorithm for this variant of the NP-hard quartet consistency problem. Moreover, when chosing the resolution of the quartets by the Four-Point Method (FPM) and considering the Cavender-Farris model of evolution, we show that the convergence rate of the Q^* method is at worst polynomial when the maximum evolutive distance between two species is bounded. We complete these theoretical results by an experimental study on real and simulated data sets. The results show that (i) as expected, the strong combinatorial constraints it imposes on each edge leads the Q^* method to propose very few incorrect edges; (ii) more surprisingly, the method infers trees with a relatively high degree of resolution.

Inferring evolutionary trees with strong combinatorial evidence