Evidence of Multiple Maximum Likelihood Points

227. B. B. Zhou, M. Tarawneh, D. Chu, P. Wang, C. Wang, A. Zomaya and R. P. Brent, Evidence of multiple maximum likelihood points for a phylogenetic tree, Proc. Sixth IEEE Symposium on Bioinformatics and Bioengineering (BIBE06), Arlington, Virginia, Oct 2006, 193-197.

Preprint: pdf (264K).


An interesting and important, but largely ignored question associated with the ML method is whether there exists a single maximum likelihood point for a given phylogenetic tree. Mike Steel [Syst. Biol. 43 (1994), 560-564] presented a simple analytical results to argue that the ML point is not unique. However, so far his view has attracted 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 a 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 globally optimal tree under the maximum likelihood criterion, this tree is not necessarily the correct phylogenetic tree. In this 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 more than one tree for a given problem.

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