"Perplexed in Peoria"  wrote in
message news:...



> I'm not sure how Hamilton thought of "r".  But someone else
on this thread
> seemed pretty convinced that WDH thought it was a regression coefficient.
> If I understand things correctly, that is exactly what the
"r" in my formula
> is.
> 

That "someone else" is me. Hamilton agreed. And you are absolutely
correct that your r (which is Hamilton's r) is a regression
coefficient. This view of r is agreed upon by the majority of experts
in the field of social evolution theory.



> I'm still not sure I understand the differences between Malecot's IBD
> and Wright's coefficient of relationship in populations with recent
> inbreeding.  

The two concepts are not rigorously related to eachother in a general
way. Wright was not entirely happy with Malecot's formalism because of
this lack of rigour. But, if we adopt the standard approach whereby
the components of Wright's r are expressed in terms of prob i.b.d.,
then even without inbreeding we get r equal to *twice* the prob i.b.d.
between individuals, so they are not even nearly equivalent.



> Actually, if "r" is calculated by my formula, I don't need to concede
> anything.  My formula gives the value of "r" as zero (or
actually -1/N)
> when there is only one carrier of the allele.  So Hamilton's rule still
> works.

You seem to be on the right track (i.e. your thinking does seem to be
consistent with conventional thought on the mathematics of kin
selection), however, if i understand what you are trying to do above,
-1/N should be -1/(N-1).

1/N + ((N-1)/N)*r = 0

=> r = -1/(N-1)

I think the problem might be that you had not included the focal
individual's allele frequency within the population allele frequency
p. Although, as I said, I might have misunderstood what you were
doing.
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