"William Morse"  wrote in message
news:cb2fdn$217i$1{at}darwin.ediacara.org...
> "Perplexed in Peoria"  wrote in
> news:car9d1$2lm6$1{at}darwin.ediacara.org:
> > Hamilton's rule is independent of p.
>
> This would be true if the benefit was independent of the allele
> frequency.

Yes.  It is a fundamental assumption that the ratio b/c is
independent of the allele frequency.  And it is fairly easy
to construct models in which b/c is not independent.

For example, consider a case in which the altruism has both
fixed and variable costs.  For example, we might consider
altruistic backscratching in which the fixed cost is growing
fingernails and the variable cost is the time spent actually
scratching backs.

You might think that the fixed cost can be rolled into variable
(or vise versa), but this makes the further assumption that the
number of altruistic acts that an organism engages in over its
lifetime is also independent of gene frequency.  But, if the
backscratching gene is rare, the altruist will have to scratch
everyone's back, whereas if it is common, other altruists will
share the backscratching load.  ;-)

> 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.

Unfortunately, I don't have a subscription.  However, from your
description, this sounds similar to the "g-e" idea that we
discussed elsewhere.

However, it is important to note that Hamilton's logic doesn't
say that the net benefit (or cost) of altruism is independent
of allele frequency - only that the sign is independent.  Also,
I have found that it is helpful in analyzing the high level of
altruism situation to turn the analysis around and ask what
happens to the rare selfish allele.  Assuming that "r" is still
operative, this rare selfish organism should be likely to interact
with moderately selfish relatives.  Hence, his fitness may be
lower than that of an altruist.
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