An attempt to use phylogenetic invariants for tree reconstruction was made at the end of the 80s and the beginning of the 90s by Lake and Cavender-Felsenstein. However, the efficiency of the methods based on invariants was not obvious ([Huelsenbeck, 1995]), probably because they only used few generators of the set of phylogenetic invariants. Results and simulation studies about the performance of a new method of phylogenetic reconstruction based on invariants ([Casanellas et al., 2005]) are presented in this talk. These simulations show that it is very competitive and highly efficient, especially for nonhomogeneous phylogenetic trees. Recent improvements for this method using algebraic geometry techniques are also discussed. Part of these results has appeared in [Casanellas and Fernandez-Sanchez, 2007].
References: [Casanellas and Fernandez-Sanchez, 2007] Casanellas, M and Fernandez-Sanchez, J. (2007). Performance of a new invariants method method on homogeneous and nonhomogeneous quarted trees. Mol Biol Evol 24 :288-293.
[Casanellas et al., 2005] Casanellas, M; Garcia, L and Sullivant, S (2005). Catalog of small trees. In Pachter, L. and Sturmfels, B., editors, Algebraic Statistics for computational biology, chapter 15. Cambridge University Press.
[Huelsenbeck, 1995] Huelsenbeck, J. (1995). Performance of phylogentic methods in simulation. Syst. Biol., 44:17–48.
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