"Perplexed in Peoria"  wrote:-

> > JE:-
> > My understanding is that the only point in replacing
> > IBD with regression analysis is to attempt to remove probability ...

> Your understanding is incorrect.  Regression does not remove
> probability.

JE:-
Then (as I argued) you cannot _validly_ compare
rb employing r as just a probability with the
cost c via subtraction because the relatedness
of the forms represented within c is the relatedness
of any natural sexual parent to its own offspring which
INCLUDES all epistatic information where this remains
deleted within rb. Hamilton's Rule is just
an irrational fitness gamble for something that
cannot even be measured because the gains/losses
are only relatively and NOT absolutely, measured.

Haldane's Dilemma refuted Fisher's dictum that
only additive heritable information, i.e. only
non epistatic information is heritable and thus
selectable. Since rb has all this epistatic
information deleted but c includes all of it
then Hamilton's comparison of rb to c using
simple subtraction to measure when organism
fitness altruism can evolve within _nature_
remains _hopelessly_ inaccurate. All Hamilton
et al are doing is comparing just their heuristic
fitness value rb to c, where c is NOT just
a non refutable heuristic it constitutes
refutable REALITY. This is because only cmax
(which remains deleted from Hamilton’s Rule)
allows the rule to be tested to refutation.
In the rule cmax = K where K is the total
Darwinian fitness of the actor. Such a
measure constitutes a maximand. The rule simply
deleted  this basic Darwinian maximand and failed
to replace it with another. Hence the rule is
totally irrational.





> JM:-
> The point of the replacement is that IBD is only
> an approximation to "r", whereas the regression is exact.

JE:-
My understanding is that this is definitely NOT
the case. Any probability remains an inexact
measure.  All regression does is provide the
mean relatedness of one population (whatever
that is supposed to mean!). Hamilton's actor
is now compared to just a mythical population relatedness mean.
That is all. Imagine measuring an investment to just the
mean earnings of each person within one entire population
(rb) instead of investing/donating using the known total
earnings of one company (c).  To attempt such an event
is just madness, yet Hamilton et al are supposing such
an event is somehow rational.

I will argue that IBD is more exact than regression
analysis for any INDEPENDENT GENE LEVEL selective event
that MUST delete epistatic gene fitness (which Hamilton et
al have done.) This is because IBD is the probability that
one parental genomic gene reproduced another gene over
organism generations of that gene (not gene generations).
For Hamilton's gene level of selection (the THEORY from
which Hamilton's mere MODEL was SIMPLIFIED) this makes more
sense than comparing a parental genomic gene to some
entirely mythical mean population relatedness measure.

> JM:-
> On the
> other hand, IBD is easy to measure (if you have good geneologies),
> whereas regression requires (in theory) taking a genetic sample from
> the entire population.


JE:-
What you are forgetting is that rb remains just a heuristic
but c is NOT. This simple point is all you need to know
to understand why Hamilton's model cannot do what it
claims to do: measure when organism fitness altruism
can evolve within _nature_. Amazingly, the professionals
that post here will not confirm or deny that the
rule has been misused to measure when organism fitness
altruism can evolve in nature. If you quiz say, Prof.
Felsenstein (who is a model buliding specialist) he will
just keep on restating that Hamilton's rule can
measure when Hamilton's supposed fitness
altruistic gene can (only) relatively spread compared
to the wildtype allele within the precepts of the model
(random mating, zero genetic epistasis etc) and just
leave it at that. He will not discuss the issue of
measuring when Hamilton’s supposed altruistic allele
can absolutely spread simply because this event cannot
even be measured by Hamilton’s model. Professional model
builder’s  attitude seems to be: I build the models I
don't apply them so application is none of my business!
None of them will take any responsibility re: how
the rule has been correctly/incorrectly applied within
the science of biology, as a stand alone fitness
accounting device to measure when organism fitness
altruism can or cannot evolve within _nature_, yet
this remains the ONLY application of the rule for
over 50 years! It is never a defence to suggest you
were only taking orders....



> JM:-
> If you insist on using no statistical tools more complicated than
> simple averages, then here is a version of Hamilton's rule that
> satisfies your requirements:
> (r_IBD - r_IBD_hat) * b > c
> where
>  r_IBD is the IBD relatedness between donor organism and recipient
>  r_IBD_hat is the average IBD relatedness between donor and a
>    member of the general population
>  b is the difference between the actual fitness of the donor and the
>    hypothetical fitness it would have if it did not act altruistically
>  c is the difference between the actual fitness of the recipient and
>    the hypothetical fitness it would have if it did not receive the
>    beneficience.

JE:-
Unless you can propose a exact mechanism to
measure  “the actual fitness of the donor”
your logic is remains irrational.

My Regards,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

edser{at}tpg.com.au
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