realistic amino acid subst. models

[Joe Felsenstein]

In article <3q6miv$gjk at agate.berkeley.edu>,
Karl W Broman <kbroman at stat.Berkeley.EDU> wrote:
>	Regarding Dayhoff...this model is assuming that substitutions
>occur independently across sites according to a *reversible* Markov
>chain.  (By reversible, I mean that the probability that an i changes
>to a j in time t is the same as the probability that a j changing to
>an i in time t.  This reversibility is very much suspect.  (For
>instance, it is hard to imagine what the reversibility assumption
>means physically.)  

As one who has used reversible models, I can testify that this property
is not invoked for biological reasons, but for mmathematical convenience.

By the way, the description above might lead people to think that it
is an assumption of symmetry.  It is, of course, not an assumption that
Prob(i, given j) = Prob(j, given i) but instead that 
      Prob(i) Prob(j, given i) = Prob(j) Prob(i, given j)
in other words, the probability of i before and j after equals the
probability of j before and i after.

It makes things simpler.  But probably it's not realistic.  The question
is, is there much difference between it and realistic models?

-----
Joe Felsenstein         joe at genetics.washington.edu     (IP No. 128.95.12.41)
 Dept. of Genetics, Univ. of Washington, Box 357360, Seattle, WA 98195-7360