Tim Tyler 

> TT:-
> Hamilton phrased his original argument with the question of whether
> an organism could be expected to sacrifice itself to save three brothers
> [1].
> He suggested that orgainsms could reasonably be expected to do this.

JE:-
You have to distinguish between Hamilton's Rule and Haldane's
implied Rule. Haldane's pub discussion calculation was: 
"I'd sacrifice myself for two siblings or 4 cousins"
only because they all add up to r = 1. Of course
had Haldane not sacrificed himself he may have raised 
more than just one offspring to fertile adulthood :-)
Haldane's argument remains inane without his total
Darwinian fitness (the total number of fertile
forms reproduced by Haldane within one population).

Any of Haldane's genes has a 0.5 chance  of ending 
up  in one of his sperm cells. Thus Haldane's 
sibling has on average half of his own genes 
(irrespective of what these genes do); his first cousin, 
0.25. Haldane is providing help to relatives whereas Hamilton's
actor only provides help direct to the reproductives of
the same relative. This is one generation removed compared to 
Haldane so it makes a big difference. In Haldane's
case only the IBD relatedness of the relatives is calculated
and not the IBD relatedness of their offspring. This makes
a mockery of most suppositions using Hamilton's Rule that
purports to supply b help to r = 0.5 related recipients
because only your own offspring can be related to you
0.5 using Hamilton's logic. The offspring of your nearest 
relative (a sibling) in normal sexually reproducing species 
is 0.25 and not 0.5.  

> TT:-
> Much the same argument suggests that organisms should sacrifice 
> themselves to save six aunts.

JE:-
For Hamilton the relatedness of your mother's or fathers
sisters (aunts) _offspring_ must be calculated but for 
Haldane the relatedness of just an aunt is sufficient. 
Since aunts are related 0.25 to Hamilton's actor then the
relatedness of any of the actors aunts offspring is 0.125.
Six of them totals 0.75. Using Hamilton's rule, sacrificing one 
of your own offspring related 0.5 produces a net gain
for the genes but an absolute loss to your own total Darwinian 
fitness. This being the case AN UNKNOWN DARWINIAN TOTAL 
FITNESS is being _selected_ to be _reduced_ via just an 
increase in fitness at Hamilton's supposed independently 
selectable gene level. Hence the term "selfish geneism" being 
supposed to cause organism fitness altruism. The fly in 
Hamilton's ointment is that the gene level is NOT independently 
selectable. Not a single documented observation within 
nature of genomic genes having just a polygenetic
fitness (a fitness whereby the fitness of a group
of genomic genes is just the simple addition of each gene)
exists. OTOH the Darwinian maximand fitness (which is
just deleted from Hamilton's rule and is equal to
cmax, the maximum cost to the actor) has been observed,
can be refuted but has remained non refuted for over
150 years. 
______________________________________________________
Genes are forced to compete for selection
at just the one, same, Darwinian fertile organism 
level  of selection and not at Hamilton's heuristic 
independently selectable gene level within 
refutable biological reality.
This being the case, Hamilton's selfish genes are
only selectable at the fertile organism level.
Therefore any fertile organism centric sacrifice
that is heritable reduces the absolute fitness
of the genes that code for it forcing these
genes to select for their own (and everybody
else's) extinction. Hamilton's logic remains
biologically absurd. 
_______________________________________________________

Any genes that are selected to force a reduction in
the TOTAL fitness of their parent organism as Hamilton's hapless 
actor is, can only produce a relative gain for just an absolute 
loss, i.e. like Enron accountants Hamilton et al have been playing 
silly buggers with Darwin's fitness books. A relative gain 
for an absolute loss is just another absolute loss. Unless 
the total fitness is put back into the rule Hamilton's logic
will continue to send everyone and everything it touches into
intellectual bankruptcy. Hamilton's error constitutes a gross 
misuse of an over simplified model. This error has become 
endemic within evolutionary theory as ignorant 
mathematicians run amok in Darwin's china shop.


> TT:- 
> However this might not be such a good deal.  Indeed it might be
> a very *bad* deal - if the aunts are much past child-bearing age.
> To this extent, the health, fitness and expected reproductive
> success of the altruism recipient needs to be factored in in
> some way.
> How much an organism's fitness is improved by an act that benefits
> them can be considered to be a function of their state of health.
> [1] The Evolution of Altruistic Behaviour, WDH, 1963.

JE:-
Yes all of them are good points but the 
most salient points remain:

1) The total fitness of the actor representing a
refutable Darwinian maximand fitness has been
deleted from the rule via just the modelling over
simplification process.

2) No independent genomic gene level of fitness
exists.

I might add that any brother
is related more than a sister because
brothers have one entire X chromosome of 
genes that his sister cannot not have. 

Hamilton's rule contains such a mass
of deletions that it bears no relationship
to any known biological reality. Thus it remains
entirely misused as a stand alone fitness
accounting device to measure when organism
fitness altruism can evolve within nature.
Yet this was and remains, its only use.


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 12/6/04 6:36:09 AM