phillip smith wrote:
> in article cllqtu$1tsk$1{at}darwin.ediacara.org, Anon. at
> bob.ohara{at}NOSPAM.helsinki.fi wrote on 27/10/04 4:36 AM:
> 
> 
>>Your point that several genetic architectures is one I had not thought
>>about, but is a good one.  It just makes the maths more complex (as you
>>have to sum over all of the routes to bipedalism).
> 
> 
> 
> What do you mean by sum over all the routes to bipedalism. I'm no
> mathematician. 
> 
Sorry for not replying yesterday: I was a bit short of time, because we 
have a PhD thesis defnece.  And party....

The idea is straightforward.  Imagine that we observe that 5 mutations 
(A, B, C, D and E) have become fixed in a population, and we want to 
know the probability that this happened.  If we could assume that they 
were independent, then we could calculate the probability as the product 
of the individual probabilities.  But if the fixation depended on the 
order in which the mutations became fixed, then this won't work. 
Instead, we have to calculate the probabilties for all of the possible 
orders, and sum them.  So, for the order A B C D E we calculate

P(A).P(B|A).P(C|A B).P(D|A B C).P(E|A B C D)

(where P(x|y) is the probability of x given y) and then just take the sum.

Bob

-- 
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

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