"Perplexed in Peoria"  wrote in
news:car9d1$2lm6$1{at}darwin.ediacara.org: 

> 
> "Guy Hoelzer"  wrote in message
> news:canf98$1b4t$1{at}darwin.ediacara.org...

>> For clarity, my use of "genealogically-based" in my
second definition
>> was meant to imply that the calculation should be done according to
>> IBD. 
 
> I don't think that that clarifies enough.  The issue isn't the
> methodology used in producing the estimate.  It is the meaning of the
> thing being estimated.
 
> Whatever method is used, the result has to be an "r" with the
> following property:  Randomly choose one of the two genes at any locus
> in the donor. Suppose that the frequency of this allele in the general
> population is "p". Now, randomly choose one of the two genes at the
> same locus in the recipient.  It must be the case that the probability
> that the two randomly selected genes are identical is (r + (1 - r)p). 
> That is, there is a probability r that they are identical IBD, but if
> not, then there is still a probability p that they are identical for
> other reasons - because the allele is fairly common in the population.
 
> Or, if like McGinn, you have an intuition that geneological history
> cannot be causal in this situation, ignore the IBD above.  "r" is
> simply a measure of how much more likely than "p" it is that the two
> genes are identical for whatever reason.  The key thing is that the
> formula (r + (1-r)p) gives the probability that the alleles are
> "shared". 
 
> Why is that particular formula so important?  Well, when you do the
> math, you will see that the average fitness of allele carriers will be
> greater than non-carriers, as long as the carriers direct their
> altruism to recipients of relatedness "r".  That is, average fitness
> of carriers will be higher as long as rb>c.  And the parameter "p"
> nicely cancels out of the equations.  Hamilton's rule is independent
> of p.  As long as "r" has the meaning above.


This would be true if the benefit was independent of the allele 
frequency. But for populations at or near the carrying capacity, in most 
cases as the allele becomes more common in the overall population (or if 
the population is viscous so interactions are mostly between kin), any 
benefit to a relative will be offset by a cost to another relative. 
Simply put, if the niche only has room for 100 individuals, if my sister 
has two more children then Joe will have two less children. In the case 
that the allele is common and my sister and Joe are both very likely to 
have the allele, there is no net benefit. An article that discusses this 
is: http://www.sciencemag.org/cgi/content/full/296/5565/, but you have to  
be a subscriber to Science. If not it is the April 2002 issue.  

Yours,

Bill Morse
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