Perplexed in Peoria wrote:

> >  PartialRegression[w,z|z'] +
> > PartialRegression[w,z'|z]*Regression[z',z]>0
> >
> > where z' is partner trait value. Since the three components above
are
> > the proper definitions of -c, b and r in Hamilton's rule, then we
have
> >
> >  rb>c
>
> Bravo.  Short, succinct, and correct.  However ...

Kings New Clothes

> Although I have been promoting the use of Regression[z', z] as the
> "right" definition of r, and although my Peshwari example promoted
> the PartialRegression definitions of "b" and "c",
I find the above
> derivation somewhat unsatisfying.  In trying to express the reasons
> for my dissatisfaction, I find myself using familiar phrases like
> "green beards and epistasis" and "good mathematics, but
bad biology".
> That is also disquieting, so I will try to be clear here.
>
> Hamilton's 1964 paper begins with the observation that parental care
> can be characterized as a kind of altruism to individuals with an
> IBD relatedness of 0.5,

That parental care can be characterized as a kind of
altruism to individuals (or, for that matter, as a form
of group behavior (and group selection) is reasonable.
That it can, supposedly, be respresented by, "IBD
relatedness of 0.5," is pure nonsense.  (Also, Hamilton's
above mentioned "observation," was not an observation, it
was an assumption.)

Nobody doubts that the parents of many species, some more
than others, tend to focus their assistance on offspring,
siblings on siblings, kin on kin, etc.  And nobody doubts
that this behavior is potentially explicable through
evolutinary biology.  But to say it has anything to do
with the provisioning path of genes, which is what IBD
literally measures, is ludicrous, pie-in-the-sky, wishful
thinking.  Biological phenomena is too complex to be
describable by such a simplistic notion.

> . . . and that therefore one is led to consider
> the adaptive character of altruism to siblings, who also have an
> IBD relatedness of 0.5.  He then proceeded to analyze the situation
> using a variant of Fisher's genetic models and came to the
quasi-normative
> conclusion that if organisms "should" be kind to their offspring,
then
> they "should" also be kind to close relatives.  For the same reasons.
> Of course, various biological assumptions and approximations were
built
> into this derivation.  But the result is, by and large, correct.

King's New Clothes.



> In this case,
> the rule seems to simply not work for the most natural definition of
the
> trait!  Probably I am missing some statistical subtlety here???
Now you're getting somewhere.

Jim
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