One reason why classical phylogenetic reconstruction methods fail to
correctly infer the underlying topology is because they assume oversimplified
models. In this paper we propose a topology reconstruction method consistent
with the most general Markov model of nucleotide substitution, which can also
deal with data coming from mixtures on the same topology. It is based on an
idea of Eriksson on using phylogenetic invariants and provides a system of
weights that can be used as input of quartet-based methods. We study its
performance on real data and on a wide range of simulated 4-taxon data (both
time-homogeneous and nonhomogeneous, with or without among-site rate
heterogeneity, and with different branch length settings). We compare it to the
classical methods of neighbor-joining (with paralinear distance), maximum
likelihood (with different underlying models), and maximum parsimony. Our
results show that this method is accurate and robust, has a similar performance
to ML when data satisfies the assumptions of both methods, and outperforms all
methods when these are based on inappropriate substitution models or when both
long and short branches are present. If alignments are long enough, then it
also outperforms other methods when some of its assumptions are violated.Comment: 32 pages; 9 figure