Molecular Biology and Evolution, Vol 12, 546-557, Copyright © 1995 by Society for Molecular Biology and Evolution
X Gu, YX Fu and WH Li
This paper presents a maximum likelihood approach to estimating the
variation of substitution rate among nucleotide sites. We assume that the
rate varies among sites according to an invariant+gamma distribution, which
has two parameters: the gamma parameter alpha and the proportion of
invariable sites theta. Theoretical treatments on three, four, and five
sequences have been conducted, and computer program have been developed. It
is shown that rho = (1 + theta alpha)/(1 + alpha) is a good measure for the
rate heterogeneity among sites. Extensive simulations show that (1) if the
proportion of invariable sites is negligible, i.e., theta = 0, the gamma
parameter alpha can be satisfactorily estimated, even with three sequences;
(2) if the proportion of invariable sites is not negligible, the
heterogeneity rho can still be suitably estimated with four or more
sequences; and (3) the distances estimated by the proposed method are
almost unbiased and are robust against violation of the assumption of the
invariant + gamma distribution.
ORIGINAL ARTICLE
Maximum likelihood estimation of the heterogeneity of substitution rate among nucleotide sites
Human Genetics Center, University of Texas, Houston 77225, USA.
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