"Guy Hoelzer"  wrote in message
news:canf98$1b4t$1{at}darwin.ediacara.org...
>
>
>
> in article cadt61$1fir$1{at}darwin.ediacara.org, Perplexed in Peoria at
> jimmenegay{at}sbcglobal.net wrote on 6/11/04 8:26 PM:
>
> > "Name And Address Supplied"

wrote in
> > message news:cackku$11mc$1{at}darwin.ediacara.org...
> >> Guy Hoelzer  wrote in message
> > news:...
> >>> in article ca9vg4$4s2$1{at}darwin.ediacara.org, Name And
Address Supplied
> > at
> >>> name_and_address_supplied{at}hotmail.com wrote on 6/10/04 8:41 AM:
> >>>
> >>>> Guy Hoelzer  wrote in message
> >>>> news:... in article
> >>>> ca4lgv$1fvr$1{at}darwin.ediacara.org, Name And Address Supplied at
> >>>> name_and_address_supplied{at}hotmail.com wrote on 6/8/04
8:21 AM: Again,
what
> >>>> do you think that r actually is?
> >>>>
> >>>>> This is the first time you have asked.  The
parameter "r" represents
the
> >>>>> genealogically-based probability that two
individuals will share a
> >>>>> particular allele IBD.  It also represents a
genealogically-based
estimate
> >>>>> of the fraction of the alleles in the genome
shared by a pair of
> >>>>> individuals.
> >
> > When I first saw this, I thought that NAS would point out that Dr.
Hoelzer's
> > second definition is different from the first, as it omits the
"IBD".
> > The second definition, assuming that the omission of the IBD is
deliberate,
> > is definitely wrong, and seems similar to what McGinn has been saying.
>
> For clarity, my use of "genealogically-based" in my second
definition was
> meant to imply that the calculation should be done according to IBD.

I don't think that that clarifies enough.  The issue isn't the methodology
used in producing the estimate.  It is the meaning of the thing being
estimated.

Whatever method is used, the result has to be an "r" with the following
property:  Randomly choose one of the two genes at any locus in the donor.
Suppose that the frequency of this allele in the general population is "p".
Now, randomly choose one of the two genes at the same locus in the
recipient.  It must be the case that the probability that the two randomly
selected genes are identical is (r + (1 - r)p).  That is, there is a
probability r that they are identical IBD, but if not, then there is still
a probability p that they are identical for other reasons - because the
allele is fairly common in the population.

Or, if like McGinn, you have an intuition that geneological history cannot
be causal in this situation, ignore the IBD above.  "r" is simply a measure
of how much more likely than "p" it is that the two genes are identical
for whatever reason.  The key thing is that the formula (r + (1-r)p)
gives the probability that the alleles are "shared".

Why is that particular formula so important?  Well, when you do the math,
you will see that the average fitness of allele carriers will be greater
than non-carriers, as long as the carriers direct their altruism to
recipients of relatedness "r".  That is, average fitness of carriers
will be higher as long as rb>c.  And the parameter "p" nicely cancels
out of the equations.  Hamilton's rule is independent of p.  As long
as "r" has the meaning above.
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