Re: Underestimating 'r'
- From: an588@xxxxxxxxxxxxxxxxxxx (Catherine Woodgold)
- Date: Sat, 15 Oct 2005 01:22:38 -0400 (EDT)
"Perplexed in Peoria" (jimmenegay@xxxxxxxxxxxxx) writes:
> In a haploid model, I can see that r is given by
> (p' - p) / (1 - p)
> where p' is the probability that the recipient has the "gene for altruism",
> 1 is the probability that the donor has it,
> and p is the probability that a random member of the population has it.
>
> And I see that it works for any locus where the probability that the
> donor has a particular allele is 1. That the focal gene is a "gene for
> altruism" is unnecessary.
Right, I get the same equation.
If it's the behaviour of an organism with Aa and
we want to discuss the effect of the behaviour
on the rate of A in the population, the
formula becomes:
(p' - p) / (0.5 - p)
where p' is the rate of A in the recipient
(e.g. 0, 0.5 or 1 for aa, Aa and AA)
or the expected value of this quantity according
to information available to the donor;
p is the rate of A in the general population;
and 0.5 is the rate of A in the Aa organism.
At one point in deriving this, both
sides of the inequality have to be divided
by an expression which may sometimes be
negative; in the cases where it's negative,
you have to switch the direction of the
inequality. I missed this first time through.
In any case, this produces a much more complicated
situation than the formula for the haploid or
AA case. It turns out that if the rate of A
in the population is high, then the best strategy
for the Aa organism if it wants to promote the
rate of A may be to commit suicide (or to
stay alive only if by doing so it can cause
a lot of harm to its relatives!) Genes that
actually promote such behaviour may be relatively
rare, but could be evolutionarily stable I think if A
does somehow gain a more than 0.5 rate in the
population to start with, and such genes if they
do occur may play a role in speciation, I suppose.
--
Cathy Woodgold
http://www.ncf.ca/~an588/par_home.html
We are all Iraqis now.
.
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