Performance of the maximum likelihood, neighbor joining, and maximum parsimony methods when sequence sites are not independent

The Felsenstein zone of various tree reconstruction methods for a four-species tree was evaluated for two models of sequence evolution. The first model assumes correlated sequence sites, as suggested by Schoniger and von Haeseler (1994, Mol. Phylogenet. Evol. 3:240-247), thereby preserving the nonoverlapping doublet correlations (e.g., within base-paired nucleotides of stem regions of ribosomal RNA). The second model was proposed by Hasegawa, Kishino, and Yano (1985, J. Mol. Evol. 22:160-174) and assumes that the nucleotide sites are evolving independently of each other. The methods examined are maximum likelihood, maximum parsimony, and neighbor joining with uncorrected, Jukes-Cantor-corrected, and Kimura-corrected distances. All methods, including maximum likelihood, are inconsistent for certain model trees. Maximum likelihood only shows a Felsenstein zone if sequence sites are not evolving independently. The location of the border of the Felsenstein zone indicates that maximum likelihood is very robust against violation of the independence assumption. The other tree reconstruction methods are more sensitive to violation of this assumption. Moreover, the addition of dependence to a model of sequence evolution does not change the boundary of the Felsenstein zone very much if tree reconstruction methods that are already inconsistent for certain model trees are applied.