Hamilton's Rule is Xeno's Paradox ( was Re: Underestimating 'r')



Catherine Woodgold wrote:-

> Question for John Edser:
> You've mentioned epistasis a number of times,
> and r^e. I'm trying to understand what you
> mean. If you answer this question, it may help.
> This is even more basic than the situation I
> mentioned in a post I posted a few hours ago.
> Suppose in a haploid organism, on average once
> in a lifetime each organism has the opportunity
> to do an act which reduces its fitness by 0.1
> (10% chance of dying) and increases the fitness
> of one of its full siblings (same mother and
> same father) by 0.21. Suppose aB, Ab and ab never
> carry out this act, but AB always does.
> I contend that the rate of A and B will tend to
> increase and will take over in many, many generations,
> while a and b will die out.
> What do you think will happen? Do you
> disagree with my contention?

I have two propositions that are required to address this issue which I will
call my MAIN PROPOSITION and my SECONDARY PROPOSITION. I firstly have to
address my main proposition which involves a logical analysis of empirical
events within HR which is something almost nobody here likes to do :-|

If you follow classical population genetics procedures and work out the gene
freq. changes using the Hardy-Weinberg Equilibrium Model which employed a
bi-nomial expansion of alleles at separate loci it will provide the answer
that AB will tend to increase.

http://anthro.palomar.edu/synthetic/synth_2.htm

Note that evolution now becomes redefined as just: "the SUM total of the
genetically inherited changes in the individuals who are the members of a
population's gene pool." [my capitalization of SUM]

MAIN PROPOSITION:
I claim that any relative increase in AB by altruism using HR is just a
mathematical illusion which has no basis in empirical reality. My argument
can be summed up this way: Hamilton's rationale represents another example
of Xeno's Paradox:

http://www.bbc.co.uk/dna/h2g2/alabaster/A524242


Mathematics is full of paradoxes because IT IS NOT empirically based :-(
OTOH science has no paradoxes because IT IS empirically based :-)

The reason why paradoxes exist is mostly always the same: no constant
algebraic term. This reduces any proposition to just an empirical absurdity
(just a contradiction). In Xeno's Paradox the algebraic constant "time" has
been deleted as an oversimplification. This reduces the mathematics to
become entirely, just a relative proposition within which the hare can never
actually catch up to the tortoise. Of course this is easily refuted
empirically. Einstein was one of the first to make explicit that any
rational proposition has to have a finite empirical frame of reference. This
was c within E=Mc^2. Within Newtonian Mechanics this constant is mass which
was absolutely required just to allow independent events within physics.
Newton's critical constant was reduced to just a variable by Einstein as a
formal refutation of Newton while c became elevated to become a new and very
surprising, constant.

Mathematically, a frame of reference is always provided by a constant term
which I call the "absolute assumption". In the sciences this cannot be just
an absolute dictate because the proffered constant must be empirically
refutable. Hamilton's Rule has no constant algebraic term so it can have no
frame of reference. Therefore any logician has to predict that only two
contrary WHY events exist with it. This prediction can be verified because
it can be proven that only "altruism" and "selfishness" can exist
unconditionally and therefore empirically within HR where these constitute
the only valid WHY propositions of HR. It will be proven that these two WHY
events remain insufficient.

Hamilton et al argued that four WHY events can exist so they included
"mutualism" and "spite" where however, all four remained _conditional_ to b.
Any conditional event is just a relative event so Hamilton's four
conditional WHY events can have no frame of reference so they must be
paradoxical. It can be proven that they are paradoxical because no
independent fitness events exist at all in HR if all WHY events are
conditional to b. I am happy to expand on this argument a bit later on. What
a logician is looking for are any UNCONDITIONAL WHY events as the key to the
rule simply because the rule is not just employed to explain HOW (the
comparison of rb to c) it is much more critically employed to explain WHY
(the conditional definitions of altruism, selfishness, mutualism and spite
), on however, an empirical basis. Within HR only two unconditional WHY
events actually exist: any positive c and any negative c. These represent
the following two contrary empirically based events:-

1) X resources move from actor to recipients as proactive action by the
actor. These resources become reprocessed into b reproductive gains as
however, just a recipient group selective total. Thus b MUST be multiplied
by r before these gains represent a valid (Hamiltonian) fitness. For this
group selective total to become non group selective rb/p where p = the
number of recipients. Please not that if rb is not group selective then the
rule fails.

2) X resources move from recipients to actor, again as proactive action by
the actor where these resources become reprocessed into A reproductive gains
for a NON group selected actor. Again they must be multiplied by r before
these gains represent a valid Hamiltonian fitness. Please note that this
event has never been accounted for, i.e. the gain in A units of fitness to
the selfish actor has never ever been credited to Hamilton's actor so
Hamilton's books do not balance. This provides a key as to why Hamilton's
gene is actually spreading: via hidden selfishness and not just altruism.

At all times HR was and remains just a medieval contest between individual
and group selection. This contest was proven in the 1960's to always resolve
in favor of individual selection. Note that the original intention of the
rule was to allow altruism to evolve in nature via organism selection and
not group selection because of this fact. IOW Hamilton's Rule was always
just a misrepresentation of a non group selective argument. It must be noted
here that comparing group selective events to individual selective events is
akin to comparing apples with oranges which of course is just meaningless
unless one can be converted into the other.

However, because c represented just another variable any WHY proposition
within Hamilton's Rule becomes reduced to just an absurdity: two contrary
events occurring simultaneously as described within the mathematically
equivalent rules: rb>c and -rb<-c.

Conclusion:
Since AB alleles only increase on just a relative basis no empirical way
exists to explain WHY they are increasing just HOW they are increasing which
of course is insufficient. Therefore it can be validly argued within HR that
Hamilton's alleles increase because of altruistic action OR selfish action
by the actor where no way exists to empirically discriminate between them
within HR.

MY SECONDARY PROPOSITION: r is empirically r^e where r>1.

Before I can move on to discussing this, the main proposition has to be
clear. By this I do not mean that you have to agree with it, simply, that
you understand it. I would like to point out that my main proposition
remains entirely refutable. All you have to do to refute it is provide an
entirely relative proposition that does not remain fatally ambiguous when
applied empirically, i.e. does not describe simultaneous contrary events,
e.g. empirically apply:

100<200


Regards,

John Edser
Independent Researcher

edser@xxxxxxxxxx











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Relevant Pages

  • Re: Issues: A Question Of Integrity (was: Issues)
    ... Altruism can only be diagnosed using the sign of c because it ... The term "altruism" is only applied to Hamilton's proactive actor ... group selection which failed to be able to do so (the fact that the rule ... The fitness of both Hamilton's actor and recipients (as just the one ...
    (sci.bio.evolution)
  • Re: Issues: A Question Of Integrity (was: Issues)
    ... >> simply b resources that limit fitness. ... The observation that when rb>c a gene may just REALATIVELY and not ... >> reproduced by the actor are selected on a Darwinian basis but the ... defined by them as "altruism") after group selection failed to be able ...
    (sci.bio.evolution)
  • Re: Hamiltons Rule In The Mirror
    ... >> fitness. ... > which impact on the fitness of individuals other than the actor. ... group selection over 40 years later? ... >> total increase in normal reproductions for the recipients helped, ...
    (sci.bio.evolution)
  • Re: The rebellion of the ant slaves
    ... I think you are rejecting the term "group selection" while advocating the ... If we regard each ant colony as a single fertile individual then each ... ant becomes reduced to just a fitness part of one fertile individual ... eusocial queens are almost entirely determined by the sterile casts ...
    (sci.bio.evolution)
  • Re: Hamiltons Rule In The Mirror
    ... a mutualised absolute fitness loss. ... This is why group selection cannot be selected for within nature. ... Unless the gene spreads because both the actor and recipients ...
    (sci.bio.evolution)
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