  An attempt to use phylogenetic invariants for tree reconstruction was made at
the end of the 80s and the beginning of the 90s by several authors (the initial
idea due to Lake and Cavender and Felsenstein in 1987. However, the efficiency
of methods based on invariants is still in doubt, probably because these
methods only used few generators of the set of phylogenetic invariants. The
method studied in this paper was first introduced by Casanellas, Garcia and
Sullivant and it is the first method based on invariants that uses the whole
set of generators for DNA data. The simulation studies performed in this paper
prove that it is a very competitive and highly efficient phylogenetic
reconstruction method, especially for non-homogeneous models on phylogenetic
trees.
