Re: Perpetually Perplexed
From: John Edser (edser_at_tpg.com.au)
Date: 01/21/05
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Date: Thu, 20 Jan 2005 23:53:58 -0500 (EST)
Joe Felsenstein wrote:-
> >> GH:-
> >> Yes. Let me try to be more precise about the meaning of
> >> Hamilton's Rule
> >> that I implied here. If you take the Rule to indicate that a mutation
> >> creating an altruism allele will tend to selectively increase
> >> in frequency,
> >> then I am arguing that the dispensing of altruism is assumed
> >> to be perfectly
> >> graded. To the extent that the grading of altruism with kinship is not
> >> perfect, then too much personal fitness is lost through
> >> altruism toward more
> >> distant relatives and/or too little inclusive fitness is lost
> >> by failing to
> >> be optimally altruistic toward closer relatives. Whatever the
> >> suboptimal
> >> mix, the conditions for selective frequency increase would be
> >> more stringent
> >> than indicated by Hamilton's Rule.
> > JM:-
> >Edser has occasionally written to the effect that there is a herd
> >behavior among professional biologists in which they will not attack
> >one of their own, but will cooperate in defense against outsiders.
> >I am going to succumb to the temptation to give no response to your
> >post and see what happens. You have provided an excellent opportunity
> >for refuting John's hypothesis.
> >I will also follow Edser's lead and explicitly challenge Joe Felsenstein
> >on this.
> JF:-
> OK, yes, I disagree with Guy. Hamilton's argument uses the quantity
> r for the average degree of relationship between the altruist and the
> recipients.
JE:-
The "average degree of relationship between
the altruist and the recipients" is not
sufficient to calculate any one _specific_
comparison of rb with c, just a population
average of such comparisons within which
all specific selective action is lost. Since
relatedness forms a major component of
Hamilton's incomplete fitness total rb it
must be measured specifically for each comparison
of rb with c and not just generally over
many comparisons via a mean value of
r.
> JF:-
> The altruist can be simply being nice to the neighbors,
> who happen to partly be its relatives.
JE:-
The selective motivation for such behaviour
can be mutualistic OR altruistic. In
fact, it is predicted that mutualism (which
requires no altruism via proxy reproduction)
can more easily evolve within families and
extended families simply because they are
more likely to remain in close contact
with each other. In the eusocials, mammals
or insect, this closeness along with a pheromonal
control of offspring fertility via enclosed
nest spaces allowed fertile parents to be
selected to maintain an army of sterile
offspring to act as slaves to their own
parents. Once again no Darwinian altruism
was involved. Mutualism between fertile parents
allowed genes to be selected and passed to offspring
that maintained most of these in a sterile state.
Sterile offspring act as modular body
parts to their parents. Hamilton et al
maintain an opposing causative theory.
Offspring sterility evolved via
selection operating at an independent
gene level of selection within the bodies
of sterile forms forcing these forms to
100% donate their own fitness to their
parents. One key observation that may
separate these contesting theories
is any documented observation in nature
of the reproduction of a fully fertile
form that never normally reproduces
itself becoming sterile and remaining
sterile until it dies of old age.
Does Dr Hunt have such a documented
example within the eusocials?
Most illustrations of 0.5 IBD relatedness
using Hamilton's Rule incorrectly employ
Haldane's Pub rule where the recipients are
helped directly. Here b would represent the
number of recipients helped. In Hamilton's
Rule b helps the offspring of these recipients
which is one more generation removed. This
means the maximum relatedness IBD can be for
any reproduction by proxy using Hamilton's
Rule is 0.25 and not 0.5. Within Hamilton's
Rule all maximal 0.5 relatedness must refer
to each parents specific relatedness
to just their own offspring which is not
a mean gene relatedness but not a mean
organism relatedness. Normal reproduction
is not altruistic and provides no proxy
wastage. Felsenstein (below) calculates an example
of this enormous wastage which must be paid
by every proxy reproductive act, i.e. every
time relatedness < 0.5 within Hamilton's
Rule (the maximal organism specific IBD
relatedness possible using normal sex).
> JF:-
> If, say, the neighbors were
> half of them first cousins of the altruist then the appropriate
> value of r is (1/2)x(1/16) where 1/16 is the r value for cousins.
> This adjustment of r (the factor of 1/2) above takes care of the
> dispensing of altruism to some non-relatives.
JE:-
This value of "1/2" only constitutes a needless
waste that is not evident if the parents
normally reproduce because all of your own
offspring are related 0.5 to yourself with normal
sex producing no such waste. Helping 16 cousins where you
cannot tell what their relatedness is to you, so you
needlessly waste your finite resources helping (most
probably, Hamilton's competitive wildtype non
altruistic allele!) cannot compete against
helping just 2 of your own reproductives
related 0.5 because you save the "1/2" within
Felsenstein's (1/2)x(1/16) calculation, i.e.
a massive "buy one and get one free" 50%
saving..
> JF:-
> There is no assumption in Hamilton's work that the altruist recognizes
> kin. This is a common misconception about the kin selection argument.
JE:-
Why doesn't Felsenstein explain why
it remains an absolute _necessity_ that
the altruist cannot recognize the kin?
When the same genomes seek each
other out to mate to just linearly
reduce Felsenstein's needless 50% waste
(indicated by the "1/2" within (1/2)x(1/16)
above) they suddenly rediscover the geometric
cost of previously deleted epistasis. The
best known example is Dawkins Green Beard
model which still remains accepted within
the literature. The gains of such non random sexual
selection (Hamilton only specified random mating)
are always less than the geometric rising cost of
previously _mathematically_ deleted epistasis:
(r^e)b > c
where e is the number of independent
epistatic loci that code for the organism
altruistic phenotype. For Dawkins Green Beard
model e=2. This e value represents just
the minimal cost of epistasis yet it
provides the reason as to why the rule fails.
I have been posting this for over a year.
Felsenstein even thanked me for it.
However NAS, EK, BOH etc continue to just
ignore it.
___________________________________________
Hamilton's mathematical deletion of genetic
epistasis by only using r=1 remains fatal
to Hamilton's Rule because Hamilton's
selfish allele cannot have any lineal
i.e. INDEPENDENT fitness without it.
When you set r = 1 it remains "gone but
not forgotten".
___________________________________________
In a sense, Hamilton's organism altruism
gene is addicted to e = 1 because without
it his selfish gene is forced to have a
DEPENDENT fitness at Darwin's organism
level. In this situation forcing organism
altruism must reduce selfish gene
fitness as well as organism fitness
so it cannot be selected for.
Allowing e=1 removes fitness dependency
at the cost of every gene within one genome
now being forced to compete against every
other at Hamilton's heuristic independent
genome level of selection. Now one Darwinian
organism fitness must be the simple sum
of the fitness of each independent gene
fitness within one genome. Such an event
has never been documented in nature because
it remains biologically absurd. In fact not
one single linear gene fitness has ever
been documented within nature. Yet,
Hamilton et al see fit to assign such a
fitness to their selfish gene. Hamilton's
organism altruistic gene is dammed if it
does and dammed if it doesn't.
Relatedness always remains:
r^e
where e=1 using Hamilton's simplification
of e was allowed by Fisher. Only by deleting
all epistasis in this way can Hamilton create
for himself his own heuristic (dare I say
it "Mad Hatter") world within which altruism
CAN evolve but by only supposing a genome
composed of just one locus with two alleles.
This is because only this massively
simplified selectee allows one gene
to become equivalent to one Darwinian
individual. As soon as you
make it more real by adding just one
more locus, unless these alleles always
freely compete against each other within
Hamilton's genomic level (which in turn
must compete against Darwin's
single Darwinian fertile organism
level of selection) they cannot
become kin selected because kin selecting 2
or more genes reduces r^e geometrically
so rb cannot compete with c (non kin selection).
In order to keep all these genomic genes freely
competing instead of only tightly cooperating
to produce just THE ONE Darwinian fitness
total at a higher fitness level all genetic
epistasis must remain deleted.
The amazing thing is rb does not care
a less about the organism phenotypic and
its fitness, it only cares about a better
100% relative way to reproduce, on just a gene
by gene basis, *ANY* gene. The fact that these
genes have a real phenotypic fitness remains
central to Darwinism but is simply deleted by
Hamilton et al. In Darwinism reproducing genes
becomes an effect of another cause: selection acting
by comparing each parents total Darwinian
fitness within one population. In Hamiltonian
reasoning the reproduction of genes over
organism generations now becomes the selected
cause so that any Darwinian phenotypic fitness
is just reduced to an effect of this new cause,
i.e. cause and effect were allowed to be entirely
reversed within Hamilton's heuristic model.
In the Darwinian view genes can only be selected
to promote organism reproduction but within the
Hamiltonian view organisms are only selected to
promote gene replication note however: over just
organism and not gene generations. Both cannot
be correct can they! Is this why Prof. Felsenstein
still refuses to discuss cause and effect within
the biological sciences?
My most sincere regards,
John Edser
Independent Researcher
PO Box 266
Church Pt
NSW 2105
Australia
edser@tpg.com.au
- Next message: John Edser: "Re: Washburn's fallacy"
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- Maybe in reply to: Jim McGinn: "Perpetually Perplexed"
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