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Journal Article

Evolutionary Trees From Gene Frequencies and Quantitative Characters: Finding Maximum Likelihood Estimates

Joseph Felsenstein
Evolution
Vol. 35, No. 6 (Nov., 1981), pp. 1229-1242
DOI: 10.2307/2408134
Stable URL: http://www.jstor.org/stable/2408134
Page Count: 14
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Evolutionary Trees From Gene Frequencies and Quantitative Characters: Finding Maximum Likelihood Estimates
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Abstract

The assumptions involved in maximum likelihood estimation of evolutionary trees from quantitative character data have been described. A strict maximum likelihood method applied to the case of two populations encounters singularities in the likelihood surface, and even when restrictions are placed on the parameters to avoid this the resulting estimate converges to the wrong value as more characters are considered. These problems arise because new "nuisance" parameters are introduced every time we add a new character. If the data are assumed to consist only of the differences between population phenotypes, and a maximum likelihood solution based on these transformed data is found, this restricted maximum likelihood (REML) method behaves well. An exact solution is given for the three-population case. Two computational techniques, the pruning algorithm and the pulley principle, have been described which allow rapid computation of the restricted likelihood. They allow construction of an iterative procedure for finding the maximum of the restricted likelihood within a given tree topology. Combined with an algorithm for searching among similar tree topologies, this allows construction of a computer program to find the REML estimate of the tree.

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