Re: Kin Selection contradiction?
From: John Edser (edser_at_tpg.com.au)
Date: 06/17/04
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Date: Thu, 17 Jun 2004 05:15:16 +0000 (UTC)
JM:-
>snip<
4. In 1964, the symbol "r" is first used to represent Wright's
coefficient of relationship, and it is observed that this coefficient
is equal to the expected fraction of genes IBD in a relative in
a non-inbred population. But later, "r" is said to be the expected
fraction IBD. It is not clear to me whether Hamilton is using IBD
(noting that it is approximated by the familiar Wright coefficient)
or whether he is using Wright (noting it is approximated by the
conceptually simple IBD). In a response to Edser about a year ago,
NAS corrected Edser's statement about IBD saying that Hamilton's
"r" in "rb>c" is Wright's coefficient. And, I had assumed that
NAS was correct until this most recent rereading of Hamilton. But
now, I am no longer sure. It seems that the 1964 "r" really is
IBD in the case of inbred populations.
>snip<
JE:-
All this argument about what r is exactly is immaterial
to the fact that Hamilton's rule only measures a relative
fitness difference and not an absolute fitness change.
Since the rule failed to include any measure of total
Darwinian fitness for the actor it remains impossible
to distinguish between Darwinian organism fitness altruism
(OFA) and organism fitness mutualism (OFM) within it,
where these states are absolutely self exclusive, i.e.
contradictions. This means the rule remains _unintelligible_
without the inclusion of a specific general term within it
which represents the total Darwinian fitness of the actor.
This missing term will have the value cmax, i.e. the maximal
cost possible for the actor.
It does not matter if r was actually Wright's
coefficient or relatedness IBD which was in fact
only an approximation something else. All that matters
is that Hamilton specifically regarded relatedness r
to mean the probability that a nominated somatic gene
(a gene within a Darwinian body) was reproduced from
a PARENTAL GENE within a different body. Hamilton's
slight of hand was to make just a heuristic parent gene
equal to its Darwinian biological parent so that he could
delete that biological parent allowing just a
heuristic gene centric level of selection to now operate.
Once he had moved the level of selection from the fertile
organism level down to the gene level he was able to
suppose that selfish geneism could cause organism altruism.
This was his intention all along. He and many others
were looking for any mechanism that could justify
organism fitness altruism (OFA) within nature because
group selection had failed to do so. This would
be fine except for gene _fitness_ epistasis
(which is a special case of genetic epistasis) which
Hamilton et al deleted in the process via their
modelling "over simplifications". Dawkins included a
fitness epistatic "green beard" gene in a vain attempt
to put his finger in Hamilton's dyke. It fails when
genomes are not just randomly selected (which
in Dawkins green beard case they were not)
because:
r^eb>c
For just one green beard gene allowing e=2 (and
not just 1 so e could be deleted form the rule),
r=0.5, 4b related 0.5 becomes equal to one normal
reproduction and not 2b. As the number of non
randomly selected _fitness_ epistatic genes increases,
the b number required to become equivalent to the
reproduction of just one biological soma, increases
_geometrically_ making almost all inclusive fitness
a very expensive luxury even within just a gene centric
heuristic. Meanwhile, the biological fact that
ALL somatic genes are _fitness_ epistatic to one
fertile soma is just, very quietly, forgotten....
Best Wishes,
John Edser
Independent Researcher
PO Box 266
Church Pt
NSW 2105
Australia
edser@tpg.com.au
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