Re: Hamilton's rule


Perplexed in Peoria wrote:
> "Guy Hoelzer" <hoelzer@xxxxxxx> wrote in message news:dlh6sj$274$1@xxxxxxxxxxxxxxxxxxxxxx
> > in article dlft8t$2fog$1@xxxxxxxxxxxxxxxxxxx, Perplexed in Peoria at
> > jimmenegay@xxxxxxxxxxxxx wrote on 11/16/05 10:20 AM:

> > > This fact is a consequence of the definition of IBD 'r' and the assumption
> > > of random mating. This fact is all that is needed to establish Hamilton's
> > > rule.
> >
> > I'm going to have to apologize again for being dense, but I don't see how
> > your graph justifies HR at all.
>
> Well, the graph doesn't exactly justify HR. The relationship R = P +(D_P)r
> plus some simple reasoning justifies HR.

Simple reasoning?

<snip>

> > As you said, "this fact is a consequence of the
> > definition of IBD 'r' and the assumption of random mating." Because it
> > relies so fundamentally on the definition of IBD 'r', how can it justify the
> > use of IBD 'r'?

Well stated, Guy. IOW, it's tautological to suggest that the validity
of IBD 'r' justifies itself.

> You are beginning to sound like McGinn. The logic is that the definition
> of 'r' (IBD) and the assumption of random mating leads to the relationship
> R = P + (D-P)r. That relationship, leads (by a different line of reasoning)
> to Hamilton's rule. We use the IBD definition of 'r' because it leads
> to a nice (and correct) rule.

Can you explain to us the intellectual mechanics that brought you to
this conclusion?

Jim


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