phillip smith wrote:
> in article clh816$j0o$1{at}darwin.ediacara.org, Anon. at
> bob.ohara{at}NOSPAM.helsinki.fi wrote on 25/10/04 10:49 AM:
> 
> 
>>William Morse wrote:
>>
>>>"Anon."  wrote in
news:cl65sn$ave$1
>>>{at}darwin.ediacara.org:
>>
>>
>>
>>>John is something of a conundrum. He is neither stupid nor ignorant. But
>>>he is singularly single-minded, and has an unfortunate tendency (shared
>>>by many humans, including myself) to lapse into calumny when his
>>>arguments are challenged.  I gave up responding to John some time ago,
>>>even though he raises some good arguments, because of his single-
>>>mindedness. I suggest you do the same. What we need to do is get into
>>>some good arguments between ourselves so we can both satisfy our desire
>>>for intellectual discussion. I think this may be difficult  because we
>>>tend to agree, but here goes: bipedalism in humans is simply a result of
>>>drift - our ancestors could have as easily switched to knuckle-walking.
>>>
>>
>>What?  We're bipedal?  No wonder I've been getting funny looks!
>>
>>More seriously, I think the typical reaction to that would be "no way,
>>nothing that complex could evolve by chance".  Which leads me to wonder
>>what the chance is.
>>
>>In trhe following discussion, I will ignore any possible developmental
>>constraints: they could be included but the maths gets messy.
>>
>>For drift to be the explanation, we have to posit that all of the genes
>>involved in the shift to bipedalism have drifted to fixation.  So, we'll
>>need to know how many genes are involved, the probabilities of fixation
>>of neutral alleles (which depend on the population size and structure),
>>and the mutation rate of these alleles.  We'll also need to know the
>>time since the shift to bipedalism started.
>>
>>The probability of bipedalism evolving over that time scale is then the
>>product of the probabilities for each allele.  The probability for each
>>allele is approximately the probability of fixation divided by the
>>mutation rate.
>>
>>This is, of course, not what we want: we know that bipedalism has
>>evolved, and want to know whether it was by drift or something else.  To
>>estimate the probability that it was drift wot done it, we have to
>>calculate the probability that it some other factor than drift caused
>>bipedalism, and then use Bayes formula to invert the probabilities.  At
>>this point, I will only point out that probabilities of fixation of
>>alleles can be increased by giving them a positive selection coefficient
>>- we would need to know what the selection coefficients were to do the
>>calculations.
>>
>>After all that, I can give you a list of 57 different parameters that
>>are necessary for the calculation, but are impossible to estimate.
>>
>>There may be a different, and better approach to this analysis, if so
>>I'd be interested in hearing it.  One that needs only 32
>>impossible-to-estimate parameters would be fine.
>>
>>Bob
> 
> I would like to confuse the issue more by suggesting both selection and
> drift  occurred. There may have been selection for bipedalism as a
> phenotype. But there is a myriad of genomic changes (genes) that could give
> rise to that phenotype. The genomic organisation that eventually became
> fixed as the bipedal genome was probably settled upon by some stochastic
> process. For example it may have been the most probable change or it might
> have just been the first to occur. I think this genetic drift as the
> population that first had the bipedal gait probably was very small possibly
> N=1 so genetic drift and nearly neutral evolution must have played a role.
> 
Yep, you're making it more confused!

I agree that there must have been drift as well as selection, but in my
scheme that's in the calculation of the probability of fixation.

Your point that several genetic architectures is one I had not thought
about, but is a good one.  It just makes hte maths moer complex (as you 
have to sum over all of the routes to bipedalism).

Bob

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

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax:  +358-9-191 51400
WWW:  http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org
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