A basic question in molecular evolution - (Mar/14/2006 )

I'm having trouble understanding the following issue in molecular evolution. I hope the question is clear enough (at least it should be if you know your way around molecular evolution algorithms).

An article I've read have briefly mentioned how to calculate the likelihood of a sequence data set given the genealogy tree that connects the sequences, when the sequences are at the leaves.
The article states that under the infinite site mutation model, the number of mutations along a branch of the tree with length t is poisson distributed with rate theta*t/2. I can understand why this is true.
Next the article says that the likelihood computation is simply a product of poisson variables. This is where I'm missing the point. I assume it is talking about using Felsenstein's algorithm for phylogenetic trees, but I'm not sure how it is done for the genealogy tree.

I would be grateful for any help from anyone who can figure this out.

perhaps posting a link to this article would be a prudent move.

The article reference is:

Nielsen R, Wakeley J.
Distinguishing migration from isolation: a Markov chain Monte Carlo approach.
Genetics. 2001 Jun;158(2):885-96.


A direct link is: http://www.genetics.org/cgi/content/full/158/2/885


It talks about a whole different subject (markov chains) but mentions the likelihood computation of a geneological tree briefly at the beginning of the section titled "Markov Chain Monte Carlo" when explaining how to calculate f(X|theta, G). I'm trying to figure out how this calculation is made, but I can't find any references that explain the poisson variable model.