rate variation in ML models

[Joe Felsenstein]

Nicholas Galtier <galtier at acnuc.univ-lyon1.fr>
>I had reached somewhat different conclusions about rate variation among sites
>in usual implementations of the ML method. I understand that Felsenstein
>and Churchill's (1996) hidden Markov model relaxes the independance assumption
>for rates among sites, since some autocorrelation is assumed. However, my
>opinion about Yang's approach is that the iid assumption is on. The way
>I see present-day character states of any site are generated under Yang's 
>model assumptions is:
>
>    1- randomly draw a rate value in a (possibly discretized) Gamma distribution
>    2- make the site evolve according to the tree, branch lengths, other
>       substitution parameters (TI/TV ratios, etc...) AND the above chosen rate
>
>This "process" appears commonly assumed for all sites since sites are not assigned
>to a given category when the likelihood is computed. Therefore, the "identically
>distributed" assumption seems here. The likelihood of a data set is computed by
>multiplying the likelihoods of each site, suggesting that the "independant"
>assumption is also on. 

If you look at Yang's paper in Genetics in 1995:

Yang-Z.
   A space-time process model for the evolution of DNA sequences.
      Genetics.  1995 Feb.  139(2).  P 993-1005.
 
you will see him using an autocorrelated model which is somewhat different
from Gary's and my 1996 Hidden Markov Model approach (though it too is in
effect a Hidden Markov Model method).  It does not assume i.i.d.

-- 
Joe Felsenstein         joe at genetics.washington.edu
 Dept. of Genetics, Univ. of Washington, Box 357360, Seattle, WA 98195-7360 USA