Evidence of multiple maximum likelihood points for a phylogenetic tree

An interesting and important, but largely ignored question associated with the ML method is whether there exists only a single maximum likelihood point for a given phylogenetic tree. Mike Steel presented a simple analytical result to argue that the ML point is not unique [11]. However, his view so far attracts only little attention. Though many researchers believe that multiple maximum likelihood points may exist for certain phylogenetic trees, most existing phylogenetic construction programs only produce a single best tree under the ML criterion and in practice many researchers still use only the ML values to make judgment on the quality of different trees for a given problem. In this paper we present some experimental results from a large number of synthetic test data sets and show that it is quite common that certain incorrect trees can have likelihood values at least as large as that of the correct tree. A significant implication of this is that even if we are able to find a truly globally optimal tree under the maximum likelihood criterion, this tree may not necessarily be the correct phylogenetic tree. In the paper we also show that our newly developed algorithm can perform much better in terms of accuracy than well known algorithms such as FASTDNAML and PHYML by constructing only a few more trees for a given problem.