"Perplexed in Peoria"  wrote in
message news:cpde12$24kf$1{at}darwin.ediacara.org...
> If you insist on using no statistical tools more complicated than
> simple averages, then here is a version of Hamilton's rule that
> satisfies your requirements:
>
> (r_IBD - r_IBD_hat) * b > c
>
> where
>  r_IBD is the IBD relatedness between donor organism and recipient
>  r_IBD_hat is the average IBD relatedness between donor and a
>    member of the general population
>  b is the difference between the actual fitness of the donor and the
>    hypothetical fitness it would have if it did not act altruistically
>  c is the difference between the actual fitness of the recipient and
>    the hypothetical fitness it would have if it did not receive the
>    beneficience.
>
> The rule is to be interpreted thus:  IF the inequality holds, averaged
> over all instances of the behavior, THEN the heritable behavior will
> increase in frequency within the population.
>
> An alternative (equivalent) interpretation:  Behaviors that we encounter
> in nature are likely to satisfy the inequality.  If we encounter a
> behavior that apparently does not satisfy the inequality, then either
> the behavior is in decline, or we don't really understand the behavior
> to the extent that we should.
>
> NOTES:
>
> 0. This rule is my own invention.  It seems roughly correct to me, but
> I may be completely off base.
> [snip]

After further thought, I think I was slightly off base.  Here is my revised
rule:

(r_IBD - r_IBD_hat) * b > (1 - r_IBD_hat) * c

One can even give a kind of heuristic justification for this rule.  One counts
the costs only to the extent that one is unique.  One takes credit for the
benefits only to the extent that the beneficiary is uniquely like oneself.
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