Maximum-likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites

Felsenstein's maximum-likelihood approach for inferring phylogeny from DNAsequences assumes that the rate of nucleotide substitution is constant overdifferent nucleotide sites. This assumption is sometimes unrealistic, ashas been revealed by analysis of real sequence data. In the present paperFelsenstein's method is extended to the case where substitution rates oversites are described by the gamma distribution. A numerical example ispresented to show that the method fits the data better than do previousmodels.