Re: Hamilton's rule
- From: "John Edser" <edser@xxxxxxxxxx>
- Date: Wed, 23 Nov 2005 17:55:52 -0500 (EST)
"Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx>
> > > > Jim McGinn wrote:-
> > > > I thought all
> > > > organisms received all their genes from their parents. Now your
> > > > saying that some of them come from, "the general population." What
> > > > do you mean by this, and how would you apply it, ...
>
> > > A nicely asked question. Ok. A fraction 'r' of the typical
> recipient's
> > > genes (on average) come from the common ancestors that the recipient
> > > shares with the donor AND they are identical (by descent) with the
> > > genes that the donor received from the same ancestors. I described
> this
> > > using the shorthand language that these genes 'come from' the donor.
> > JE:-
> > Incorrect. You are required to be _absolutely_ correct on this most
> critical
> > of matters within HR: A fraction 'r' of the typical recipient's genes
> (on
> > average) come from the common ancestors that the recipient shares with
> the
> > donor AS JUST A PROBABILITY where an average is just that, only an
> average.
> >
> > All averages and probabilities are required to be VERY CAREFULLY
> interpreted
> > in evolutionary theory otherwise you may incorrectly use them to convert
> one
> > level of fitness into another or even worse, entirely fail to conserve a
> > critical level of fitness throughout within the mathematics.
> I agree that it is important to get it right. But you have gotten it
> wrong.
> The probability 'r' does not measure the recipient genes that come from
> the common ancestor.
JE:-
I never argued that it did. Within HR "r" is only the probability that
exactly ONE allele within exactly one of a total of n organism recipients
had been replicated from exactly just the ONE parent organism over exactly
organism generations of that allele and NOT allele generations of it
(required to measure any real gene centric fitness count) and NOT organism
group generations of it (required to measure any real group centric fitness
count). This makes Hamilton's "r" just an oversimplified organism centric
relatedness probability which was and remains to this very day
oversimplified from the empirically based Darwinian fertile organism centric
theory but has been allowed to become incorrectly known as "gene centric".
> 'r' involves the product of two probabilities -
> the probability that the ancestral gene goes to the donor and the
> probability
> that the same ancestral gene goes to the recipient.
JE:-
The "probability that the ancestral gene goes to the donor and the
probability that the same ancestral gene goes to the recipient" from exactly
WHO?
For the donor's natural children using normal sex the IBD probability is 0.5
for one allele as long as meiosis produces a random distribution which in
most cases it does but not in all cases e.g. the t allele in mice (which
refuted the proposition that meiosis was a random process). If two alleles
at two different loci become involved and they are on separate chromosomes
so they independently segregate then the probability for each must be
_multiplied_ which is this case is 0.5*0.5 = 0.25. Since all alleles on all
chromosomes that exist in nature remain entirely fertile organism fitness
dependent then the minimum number of alleles that can be heuristically
supposed within HR is equal to the haploid number of chromosomes in the
actor.
> > > The remainder (fraction (1-r)) of the recipient's genes come from
> > > sources that don't provide genes to the donor.
> > JE:-
> > Who exactly are "they" and how do they "provide genes" to the
> recipients?
> By 'they' I suppose you mean the 'other sources'. Well, for the most part
> they are unshared ancestors.
JE:-
How can "unshared ancestors" provide genes if they were "unshared"?
You appear to me to be confusing just the probability of provisioning with
actual provisioning while at the same time evading the critical centricity
of 1-r. Is 1-r, organism centric, group centric or gene centric?
>snip<
> > > These genes are expected
> > > (on average) to have the same allele frequencies as the general
> > > population.
> > > I used the shorthand language of saying that these genes come from
> > > the general population.
> > JE:-
> > Why are these genes "expected (on average) to have the same allele
> > frequencies as the general population?"
> Well, what other frequency would they have?
JE:-
In this instance the average hides away all the critical selective events
for all fitness counts at all selective levels that were just averaged so
averages it can be badly misused.
> If you followed the attempts
> of Felsenstein to clear up Tim Tyler's misunderstanding of 'r', the
> 'general population' that I am talking about is the same as the 'base
> population' that Felsenstein was talking about. That is, it is the
> population a few generations back, not the current generation.
JE:-
Biologically the base population was and remains, the one population into
which each parent (fertile form) reproduces itself (reproduces another
fertile form i.e. the allele count was and remains EMPIRICALLY fertile form
centric) where that specific parent cannot reproduce itself into a past
population. This also applies to the reproduction of that parent by proxy
because x resources cannot be donated by any here-and-now actor to a past
population. This is why IBD must restart all-over-again at every fertile
organism generation where the probability remains entirely relative to
Hamilton's ONE DARWINIAN organism actor who is donating in _real_ time, i.e.
is not donating into the past or into the future.
> Not that
> this distinction makes much difference. Hamilton (and for that matter,
> B.J. Williams) often mention that they are talking about gene frequencies
> in the absense of selection as a way of tieing current gene frequencies
> to the frequencies in the base population.
JE:-
I realize that Darwinian natural selection operating at the fertile organism
level causes inclusive fitness at Hamilton's heuristic gene centric level
(which was and remains to this very day just an oversimplified Darwinian
fertile organism centric level because Hamilton's allele is actually counted
over fertile organism generations) to FAIL so it was deleted within HR. The
reason WHY was and remains entirely ignored by Hamilton et al. Hamilton's
single allele, after it has successfully passed the _heuristic_ inclusive
fitness level when rb>c must also pass the Darwinian _empirical_ level in
biological _reality_. This is indicated by rb/n > c causing the rule to fail
in every case of n>1. When n is defined to be just 1 allowing the rule to
function in a 100% relative capacity then the only viable option for
Hamilton's actor is to inclusively select itself which of course represents
normal non proxy reproduction making Hamilton's tautology turn full circle.
Your own and Felsenstein's derivation of HR remains based on tautological
premises so both derivations are biologically invalid. You employed the
"Woodgold trick" to keep the population at the same size allowing rb to vary
with Rb within just a static population where all selection at Darwin's
fertile organism kevel has been heuristically deleted. Here your reasoning
becomes rb varies with Rb only because Rb varies with rb which is just a
circular argument (a tautology). When a constant is mathematically derived
to break your circular reasoning:
rb = Rb*k
what you did by employing the "Woodgold trick" was define k = 1 to stop the
population expanding or contracting providing just the one case which can
only trivially verify HR. Your error was to incorrectly argue that this one
case can be generalized to all cases, i.e. your error was inductive. It
cannot. Unless k is > 1 your reasoning remains utterly tautological and
therefore biologically invalid but when k > or < 1 your derivation fails.
Regards,
John Edser
Independent Researcher
edser@xxxxxxxxxx
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