Molecular Biology and Evolution, Vol 13, 93-104, Copyright © 1996 by Society for Molecular Biology and Evolution
J Felsenstein and GA Churchill
The method of Hidden Markov Models is used to allow for unequal and unknown
evolutionary rates at different sites in molecular sequences. Rates of
evolution at different sites are assumed to be drawn from a set of possible
rates, with a finite number of possibilities. The overall likelihood of
phylogeny is calculated as a sum of terms, each term being the probability
of the data given a particular assignment of rates to sites, times the
prior probability of that particular combination of rates. The
probabilities of different rate combinations are specified by a stationary
Markov chain that assigns rate categories to sites. While there will be a
very large number of possible ways of assigning rates to sites, a simple
recursive algorithm allows the contributions to the likelihood from all
possible combinations of rates to be summed, in a time proportional to the
number of different rates at a single site. Thus with three rates, the
effort involved is no greater than three times that for a single rate. This
"Hidden Markov Model" method allows for rates to differ between sites and
for correlations between the rates of neighboring sites. By summing over
all possibilities it does not require us to know the rates at individual
sites. However, it does not allow for correlation of rates at nonadjacent
sites, nor does it allow for a continuous distribution of rates over sites.
It is shown how to use the Newton-Raphson method to estimate branch lengths
of a phylogeny and to infer from a phylogeny what assignment of rates to
sites has the largest posterior probability. An example is given using
beta-hemoglobin DNA sequences in eight mammal species; the regions of high
and low evolutionary rates are inferred and also the average length of
patches of similar rates.
ORIGINAL ARTICLE
A Hidden Markov Model approach to variation among sites in rate of evolution
Department of Genetics, University of Washington, Seattle 98195, USA.
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