Name And Address Supplied wrote:

> > JE:-
> > If the Peer review process had worked
> > correctly Hamilton's absurd logic would not have invaded
> > evolutionary theory over the last 50 years, along
> > with many other misused oversimplified models.

> NAS:- 
> I think this is telling. Your impression of the peer review process is
> based on the assumption that Hamilton's logic is absurd. *Given* that
> it is absurd, and given that it is established convention within the
> peer-reviewed literature, then you logically infer that there is
> something chronically wrong with the peer review process.

JE:-
I am only proposing a simple "IF THEN" deductive
proposition. I am allowed to do so in a free
county. IF Hamilton's rule does contain a 
basic error i.e. only constitutes an absurdity, 
THEN the current peer review process has been 
proven to have failed. 


My critique of the Hamilton's Rule 
is in two distinct parts:

1) Proof of a basic error.
2) An attempt to remove it.

Please note that 2 remains independent of 1, 
i.e. any attempt by myself (or others) to remove 
Hamilton's error has no bearing on the existence 
of a proven error.

Hamilton's rule:

		rb>c ...(1)

(1) Not a single constant is represented within
the rule. The terms r,b and c are just variables. 
Thus the rule has absolutely no frame of reference, 
i.e. it is logical but not rational. Within the 
sciences any rational mathematical expression must 
refer back to at least one constant term in order
to make any sense. Hamilton's rule remains 
employed as a STAND ALONE fitness 
accounting device that does not refer back
to any constant term to provide this missing 
frame of reference. As an example, E=Mc^2
just becomes meaningless when the constant c is 
oversimplified to become yet another variable. 
Only the constant c (maximum velocity of the
speed of light in a vacuum) provides a frame
of reference for Einstein's famous equation.

Mathematical expressions that do not include
at least one constant term are just over simplified 
models which are absolutely required to refer back 
to a logic that does contain at least one constant term
in order to represent a rational proposition. 
Hamilton's Rule, as it has been employed
for over 50 years is not rational.


(2) Because Hamilton's rule is logical but 
not rational it can only measure a relative 
difference between rb and c. It is impossible 
to deduce the total fitness of the actor from 
only this difference. Note that a baseline 
fitness (m) has been absolutely deleted from the 
rule, i.e. included on both sides of the inequality
and deleted.  Without the total fitness of the actor
included within the rule no frame of 
reference for a rational fitness measure can
exist. The first step towards obtaining this missing
total is putting all of the deleted baseline fitness m, 
back into Hamilton's rule.

A frame of reference is absolutely required
for any rule to be able to measure when OFA can 
evolve. None exist in Hamilton's rule. The net 
result is that the  sign of c (which alone is 
used to diagnose OFA from OFM its logical 
contradiction) remains  arbitrary. This 
has been confirmed by Dr Bob O'Hara who claims
to be a professional in the field. His only 
comment was, the rule was never designed to be used 
to support OFA after group selection failed
to be able to do so. Indeed. However, that
is the only use of the rule.

(3) With only a relative measure to go by,
just a single case exists within the rule 
that can prove OFA:-

	     rb > cmax

The value cmax represents the maximal cost c
to the actor. This cost represents a constant
(not just a variable) because it is
the maximum fitness cost of supplying b. 
This cost is equivalent to the total organism 
fitness of that actor. When cmax is paid nothing 
is left over for the actor to reproduce with 
so the actor remains fertile
but only has resources left to reproduce zero 
offspring. All reproductive resources
have been handed over as b units of fitness 
within the rule. Only this one case is proof 
of OFA within Hamilton's otherwise arbitrary rule 
because only this one case includes ALL the 
fitness of the actor. Every other case MAY OR MAY 
NOT be OFA. No way exists to differentiate
OFA from its contradiction, OFM in any of these 
other cases via the rule.

(4) If K is the missing total fitness of the
actor where K = cmax, then OFA can only
proven when:

	    rb > K

Clearly, m (an absolutely deleted baseline 
fitness) cannot be > K where c+m = K if
Hamilton's fitness books are to balance.
If c+m < K then some fitness has not been
accounted for within Hamilton's fitness accounting 
rule and if c+m>K then fitness has only been 
added from nowhere that cannot be accounted 
for via the rule.

Since:

	K = c+m

For OFA to be proven:

	rb > K

Substituting (c+m) for K:


	rb > c+m

	rb-c > m


CONCLUSION:

Hamilton's Rule:

	rb-c > 0

remains in error by the large amount, m.
The entirely missing variable m constitutes most 
of the representative fitness of the actor. 
Consequently, a selfish gene can now be 
argued to be selected via a relative gain 
at just an absolute (total) fitness cost.
Such an event is just an absurdity.
This absurdity allows both Hamilton's 
selfish gene  and an altruistic in fitness 
body to evolve to mutual extinction. Any 
rational evolutionary theory cannot allow  
extinction to be selected FOR.

> NAS:- 
> Well, I have in the past invested some of my time into examining your
> reasons for this crucial assumption, and was not persuaded in the
> slightest. What I saw was gross mischaracterisation and ignorance of
> current social evolutionary thought.

JE:-
It is always irrational to propose a
rule that suggests x is true when 
the condition A>B is met if
A and B are only variables.

Suppose that A and B are
company profits such that A>B
represents a proposed investment 
rule that measures when to invest 
in A. Unless A and B are constants,
e.g. end of financial year 
totals, the rule is not rational.
Investing in a company A instead
of B only because A is ahead 
of B in sub total profits, i.e.
profits measured at just any moment
in time, does not constitute a 
rational comparison of these 
two companies. Completed totals over 
time represent competing constants 
which are an essential basic for rational 
thinking.

A financial year time period
is only a convention. However,
business could not operate without
it. Note that the time period necessary 
to complete one Darwinian fitness 
total is NOT just a convention. I have
provided a definition of total Darwinian
fitness and demonstrated 
how classic Darwinism  always implied 
this exact fitness total. I have outlined
an experimental test (not just a model) to
refute this concept satisfying a 
minimal Popperian standard for the
sciences. I wish I could say the
same about Neo Darwinism. 


I have shown that total
Darwinian fitness represents an
epistatic gene fitness where all
epistasis has been artificially deleted 
from Hamilton's rule because of Fisher's
dictum of what is proposed to be
heritable within population genetics. 
I have provided an amended rule where 
epistasis (e) is now included:

	r^eb > c

If selfish genes attempt to sexually
selectively mate with the same genome
e.g. using  Dawkins "Green Beard" marker 
gene, then Hamilton's rule becomes inoperable
because the number of recipients required increases
geometrically as e increases. Thus Hamilton's
rule is hopelessly restricted to random mating. 

I have also pointed out that C. H. Waddington
altered Haldane's basic population genetics
equations to include an extra variable:
developed in x. Waddington's revision allowed
a token for heritable gene fitness epistasis
to now exist within Haldane's basic population
genetics equations. Waddington's revision
remains ignored even after Haldane's Dilemma
was resolved via the human genome size.
Our tiny genome refuted Fisher's
proposition of what is heritable.
In short, deleted epistasis
(and pleiotropic effects: please refer
to the post re: slime mould slug formation)
which alone allows Hamilton's independent gene 
level of selection only constituted a simplified 
model misuse.


I find it interesting that NAS, who
introduced the excellent term "maximand" to 
this discussion freely admits that gene
centric Neo Darwinism (typified by
Hamilton's rule) does not have a 
a proposed maximand fitness (refutable or 
otherwise). OTOH I have provided a refutable 
Darwinian  fitness maximand and an experiment 
required to refute it. This provides proof that
Hamiltonian logic is just an over simplification
of Darwinian logic where the Darwinian maximand
which determines all evolutionary theory to this
day, has been deleted for just Neo Darwinian 
modelling convenience.

_____________________________________________
I am very happy to debate any of the points
I have listed above as long as all questions are
answered and not evaded (by both myself and 
others).

I welcome any refutation of my argument because 
it IS refutable. Please note: the Neo Darwinian 
proposition remains NON refutable. Not only 
that, the entire process of refutation has
been thrown out by gene centric Neo Darwinism.
The Popperian umpire has been allowed to be shot 
inviting Neo Darwinists to conveniently delegate
themselves to referee competing 
ideas while competition has becomes 
restricted to just their own peer 
review. It is called cultural group selection. 
_____________________________________________ 
 


> NAS:-
> But say (for the sake of argument) that I, and the rest of the experts
> in this field, are wrong. I don't see how a properly laid-out argument
> against Hamilton could be hindered by the peer review process.

JE:-
Dr Hoelzer advised me that such a "negative" 
paper is unlikely to be acceptable. 

> NAS:-
> Reviewers have to give reasons for rejecting a paper, and these are
> made available to the author. A while back I suggested that you
> prepare a manuscript and submit to Journal of Theoretical Biology,
> which seems most appropriate for such a work, and is where Hamilton
> published his classic 1964 papers. Did you pursue this at all? I'd be
> interested to hear about the results.

JE:-
I am preparing a paper that is not based on
just a negative critique of Hamilton's rule. 
However it does include an evaluation of Hamilton's
basic error: deleting the fitness total of
the actor from the rule allowing just an
arbitrary fitness accounting device to
incorrectly determine when OFA can or
cannot evolve within nature.

I have posted for over 4 years that simplified
models have been consistently misused  within
Neo Darwinism. Discussion here has done nothing
to remove my fear this has indeed, been the case.
In almost all cases the critical questions asked
of the professional Neo Darwinists that post here
have been evaded. Evasion speaks for itself.

Regards,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

edser{at}tpg.com.au
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