Majority-rule consensus of phylogenetic trees obtained by maximum- likelihood analysis

The maximum-likelihood (ML) approach is a powerful tool for reconstructing molecular phylogenies. In conjunction with the Kishino- Hasegawa test, it allows direct comparison of alternative evolutionary hypotheses. A commonly occurring outcome is that several trees are not significantly different from the ML tree, and thus there is residual uncertainty about the correct tree topology. We present a new method for producing a majority-rule consensus tree that is based on those aces that are not significantly less likely than the ML tree. Five types of consensus trees are considered. These differ in the weighting schemes that are employed. Apart from incorporating the topologies of alternative trees, some of the weighting schemes also make use of the differences between the log likelihood estimate of the ML tree and those of the other trees and the standard errors of those differences. The new approach is used to analyze the phylogenetic relationship of psbA proteins from four free-living photosynthetic prokaryotes and a chloroplast from green plants. We conclude that the most promising weighting scheme involves exponential weighting of differences between the log likelihood estimate of the ML tree and those of the other trees standardized by the standard errors of the differences. A consensus tree that is based on this weighting scheme is referred to as a standardized, exponentially weighted consensus tree. The new approach is a valuable alternative to existing tree-evaluating methods, because it integrates phylogenetic information from the ML tree with that of trees that do not differ significantly from the ML tree.