Re: Hamilton's rule
- From: Guy Hoelzer <hoelzer@xxxxxxx>
- Date: Wed, 19 Oct 2005 02:06:26 -0400 (EDT)
in article dj1v9k$1pcv$1@xxxxxxxxxxxxxxxxxxx, Catherine Woodgold at
an588@xxxxxxxxxxxxxxxxxxx wrote on 10/17/05 9:56 PM:
> Guy Hoelzer (hoelzer@xxxxxxx) writes:
>> Just for the record, I never argued that "r" is frequency dependent, and
>> that is not my position.
>
> If in the inequality instead of "r" you use "R", the
> ratio between cost and benefit below which the
> altruistic choice will increase the rate of the
> altruistic gene,
OK. I will pursue this model below, but it is entirely unrelated to
Hamilton's theory of kin selection. Your model now lies squarely in the
realm of pure Darwinian selection.
> then in a diploid species R is
> dependent on how common that gene is in the
> population. It even gets negative sometimes, I think.
I don't see why the result of a simple economical (cost/benefit) analysis
would necessarily be frequency dependent. As I said above, your model
simply assesses the net cost or benefit of a mutation, which could be either
positively or negatively frequency dependent, but need not be either.
If I apply your standard Darwinian model (natural selection will favor an
increase in the frequency of any mutation for which R<1) specifically to
mutations leading to altruistic behavior, which is I think what you
intended, then you have landed in the discrete prisoner's dilemma game. I
agree with you that analysis of this game suggests that the fitnesses
associated with alternative genotypes in this game are indeed likely to be
frequency dependent. If you are leading to the argument that this logic
should also apply in a population experiencing kin selection, I agree.
However, it is not necessarily the case that these two processes (kin
selection and ordinary Darwinian selection) would have some interesting sort
of interaction. My initial impression in thinking about the effects of both
processes is that they would have essentially additive effects (act
independently). Still, it might be that positive frequency dependent
selection could take over driving an altruism allele to higher frequency
when the effects of kin selection peter out under some conditions. Is this
what you had in mind?
Guy Hoelzer
.
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