"Perplexed in Peoria"  wrote:-

> > > JM:-
> > > Yes.  Well, to be more precise, it will be either zero or (-1/N),
> > > depending on whether you count yourself as a member of the population
> > > for purposes of calculating the correlation.

> > JE:-
> > The value r cannot be zero unless life was not decended
> > from just one common ancestor.

> JM:-
> There are two different versions of "r" being confused here.
> What you say is correct for "IBD_r".  I was referring to
> "regression_r", which can be zero or negative.  


JE:-
Regression does not help because
a negative r only remains biologically 
_meaningless_ and just a zero r means all
life is not descended from just the one
common ancestor no matter what mathematics
is that is employed to calculate r. EITHER we 
are all descended from just the one common ancestor 
or we are NOT. The rule of parsimony insists that 
we must assume that all life is descended from the 
one same ancestor until it is proven otherwise. To
ignore parsimony is to reduce the efficiency
of the biological sciences, i.e. waste time and 
money on pointless research (even if it is other
peoples money!).

> JM:-
> As Hamilton
> makes clear in his later writing, IBD_r is only a useful
> approximation to regression_r.  It is regression_r that should
> be used in Hamilton's rule.  For one thing, use of regression_r
> in the rule eliminates one annoying assumption - you no longer
> have to assume random mating.


JE:-
The use of regression does not reduce Hamilton's assumption
of random mating. Random mating was only assumed to evade
the _insurmountable_ problem of gene fitness epistasis which 
Hamilton et al simply deleted using the Neo Darwinian 
technique of over simplification. Hamilton required zero 
gene fitness epistasis because without it this critical
heuristic assumption a 100% independent gene level
of selection cannot exist. If this level does not exist
then selfish genes cannot force organism fitness altruism
because all genomic genes remain selectable at just the
ONE Darwinian fertile organism level of selection, i.e.
genomic genes are reduced to the biological reality of 
100% DEPENDENT selection. In this situation any selfish 
gene that reduces Total Darwinian Fitness must also reduce 
its own fitness, no exceptions no matter if Hamilton's
Rule cannot even measure such a basic. When gene fitness 
epistasis is put back into the rule so that selfish genes
can seek each other out and just mate with each other
(as in Dawkins Green Beard hypothesis) then the paltry
lineal gains to these selfish genes is LESS than the
cost of the geometric increase in the number of recipients 
that are now required to be helped:

		r^eb > c


> [snip]


> > JE:-
> > As I recently posted r =0.5 can only exist
> > for your own offspring when b applies to
> > fitness gains made over to recipients who
> > are the offspring of another parent and not
> > that other parent which is the case within
> > Hamilton's measure of b. Most people entirely confuse
> > "Haldane's Rule" with Hamilton's Rule because
> > they assume recipients who are not their own
> > offspring can be validly related  r = 0.5.
> > This is only possible within "Haldane's Rule"
> > where the beneficiary is the other parent and
> > _not_ the offspring of that other parent (one
> > entire generation difference). Refer to almost
> > any "authority" at random and you will see this
> > glaring error due to sloppy Neo Darwinistic
> > thinking.

> JM:-
> John, has anyone ever told you that your writing is not
> very clear?  


JE:-
Two rules historically exist and not just one:

1) Haldane's Rule

2) Hamilton's Rule.

These rules are different but remain
confused within the literature.

Haldane's Rule was derived
from Haldane's discussion in a pub
where he suggested he would sacrifice
himself for two brothers etc only because
2*0.5 = 1 where sibs are related 0.5. In 
this rule the help supplied as b is handed
over to the bothers and NOT their 
(the bothers) offspring. However within
Hamilton's Rule b is only handed over
to the offspring of the brothers
and not the brothers themselves.
Here r must measure the relatedness t
he bothers offspring and not the brothers 
themselves because b is donated one more generation
removed within Hamilton's Rule compared
to Haldane's rule. The _maximal_ possible 
relatedness any sibling has to the recipients
of b using normal sex is 0.5 via Haldane's rule 
but only 0.25 employing Hamilton's Rule. However, 
read almost any text and Hamilton's Rule assumes 
0.5 relatedness to inclusive fitness recipients of b. 
The only way  a recipient can be related 0.5 within 
Hamilton's Rule  is when that recipient is just the 
normal offspring of that actor. Helping your own 
offspring is hardly altruistic in Darwinian fitness 
terms.

Both Haldane and Hamilton's
argument make the same basic error:
they delete the total fitness of
he actor. Within Haldane's rule
it is _obvious_ that this error 
reduces Haldane's argument to
inanity because Haldane may have
lived to reproduce 5 if he had
not died for just two bothers where
5 would have represented Haldane's total 
Darwinian fitness which was simply deleted
by Haldane. The same logic holds for
Hamilton's Rule but here it is not so
obvious. Within Hamilton's
rule, without the total fitness of the
actor included the sign of c remains
arbitrary yet only this is used by the
rule to separate an altruistic donation 
by the actor from its nemesis a selfish 
investment.

Here is my challenge: Provide any rule
you like, I don't care what it specifically
refers to. If the rule is used as a stand 
alone measuring device as Hamilton's is,
then without at least one constant term
the rule may be logical but NOT 
RATIONAL. All rational things are logical
but not all logical things are rational.
My charge is that Hamilton's Rule is not
rational. It was and remains an irrational
fitness accounting device to measure when
organism fitness altruism can evolve within 
nature because it cannot separate organism
fitness altruism from its nemesis organism fitness
mutualism. Any accounting rule that remains 100%
relative will remain irrational. Enron accountants
attempted such a rule and ended up bankrupting
one of the USA's largest companies because
debits can become credits under any 100%
relative accounting rule, including Hamilton's.

> JM:-
> I had to read this paragraph six times
> before the light finally dawned - at least I think it is
> light.  Are you saying this? :  If I help my brother, and if
> my brother and I have not yet achieved sexual maturity,
> then the right way to account for this is to say that our
> father has helped our mother (and vice versa).

JE:-
The above remains BIOLOGICALLY true but is
an addition to what I was suggesting. I argued
that Hamilton's Rule is consistently confused
with Haldane's rule by an incompetent establishment.

> JM:-
> I'm guessing that this is what you are saying, because you
> think that immature me is a "fitness zombie" for my father
> and my immature sib is a not-yet-realized potential fitness
> element for our mother.
> Well, I agree, kind-of.  But this complication strikes me as yet
> one more reason why the "Edserian" definition of fitness is
> inferior to the standard one.

JE:-
It remains logically incorrect to suggest that infertile 
forms have any fitness of their own to donate. This 
being the case the only use that infertile forms have 
is as fitness slaves to their parents, i.e. they act as 
a modular extension of the parental soma. Eusocial forms
confirm this hypothesis more then they confirm Hamilton's.
The genes within infertile forms can only be selected for 
at the ONE parental Darwinian fitness level, as fitness 
epistatic genes to just the one, parental genome. The 
converse is  once infertile forms become fertile they 
must contest 100% every other fertile form in the same 
population no matter how closely related they are. 
Mutualised cooperation should firstly evolve between sibs 
not because these forms are more related but because sibs 
provide the first exposure to other forms for 
cooperation to even start, i.e. relatedness is not a cause 
of apparent altruism it is an effect based on mutualised
and nor altruistic, TOTAL fitness gains.

In conclusion I would suggest that over 99% of heritable
information is NON ADDITIVE, i.e. epistatic information.
All this information has simply been deleted from Hamilton's
Rule. If the vast majority of heritable information is epistatic
then suggesting that rb (where epistasis is deleted) constitutes 
some sort of rational measure of an alternative fitness to c 
which includes epistasis, is just aburd.

Regards,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

edser{at}tpg.com.au
---
þ RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info{at}bbsworld.com

---
 * RIMEGate(tm)V10.2áÿ* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 12/8/04 6:22:57 AM