"Jim McGinn"  wrote in message
news:cp0pta$18qb$1{at}darwin.ediacara.org...
> "Perplexed in Peoria"  wrote
in message news:...
> > "Tim Tyler"  wrote in message
news:coebn2$1m04$1{at}darwin.ediacara.org...
> > > Jim McGinn  wrote or quoted:
> >  Someone wrote:
> > > > > ... Hamilton's rule is accepted because the majority
> > > > > of scientists who have taken a hard look at it
think it has some
> > > > > validity.
> > > >
> > > > Some validity?  What does this supposedly mean?
> > > > Either it is valid or it is invalid.  Sounds like
> > > > nothing more than an excuse for vagueness.
> > >
> > > It could be a reference to the fact that Hamilton's rule
> > > assumes that the relatedness of the actors is known to
> > > the participants - whereas in nature, that condition
> > > is rarely met exactly - and usually there is some measure
> > > of uncertainty which causes a mismatich between relatedness
> > > and percieved relatedness.
> >
> > Tim, allow me to join the chorus of people who point out that Hamilton's
> > rule makes no such assumption.  Hamilton's rule doesn't even assume a
> > correlation between recipients and relatives.
>
> correlation in what?

Correlation between being a recipient and being a relative.  Tim was saying
that it is assumed that the donor can distinguish relatives from non-relatives
and adjusts his behavior so that recipients are mostly relatives.  Tim is
correct in claiming that if the donor does this, then there will be a positive
"r" and the behavior will be favored by selection if the ratio of benefit
to cost is high enough.  I pointed out that the rule still applies even if the
donor bestows its altruism indiscriminately upon the general population
("r" of zero) or if the donor perversely bestows its altruism only on
non-relatives (slightly negative "r").  The rule still works - it
just doesn't
predict the spread of altruism in these cases.

> > If there is no correlation,
> > then "r" is zero.
>
> Uh, you sure about that?

Yes.  Well, to be more precise, it will be either zero or (-1/N), depending
on whether you count yourself as a member of the population for purposes of
calculating the correlation.

Once again, let me recommend the paper by Grafen entitled "A Geometric View
of Relatedness" for a clear description of what "r" means in
Hamilton's rule.

> > Hamilton's rule works in all cases.
>
> Don't tell us.  Show us.  If you can show us even one case where
> Hamilton's rule works (or if you can just describe it so that it makes
> sense) I will send you a check for 10 thousand dollars!

No thanks.  I have already provided my own original derivation of Hamilton's
rule in a dialog with Dr. Hoelzer a few months ago.  Explaining things in
terms that Guy understands was painful enough.  Explaining it so that YOU
would understand it, well ...

Would you consider raising the prize to $20 thousand?   ;-)

But better yet, let me give you 2 cents worth of advice.  Most of the posters
to this NG do not understand Hamilton.  That is, they don't even understand what
the rule *says*, let alone how it is derived.  And, to make it worse, the few
that do understand it will often describe it imprecisely.

Of those who do not understand it, most seem to accept it anyways, as I think
you have observed.  Some of these - notably Hoelzer and Tyler - accept it
with reservations.  Apparently, they think that this stance makes them appear
sophisticated.

But there are two people - you and John - who misunderstand what the rule
says, and who are smart enough and ornery enough to point out that the rule,
    **** as you misunderstand it ****
cannot possibly be derived correctly.

John's misunderstanding seems to be on the meaning of "b" and
"c".  Yours
appears to be regarding the meaning of "r".  My advice, sir, is that you
correct your misunderstanding, and keep the checkbook in the desk.  But
you are obviously not going to correct your misunderstanding here on sbe.
Attempting to do so will only deepen the misunderstanding.  Get a textbook.
I would recommend the one by Maynard Smith.  In it, you will find yet another
recommendation of the Grafen paper.
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