"Perplexed in Peoria" 

> > > JM:-
> > > This is explained without much math in:
> > > "A geometric view of relatedness", Alan Grafen, 1985
> > > http://users.ox.ac.uk/~grafen/cv/oseb.pdf
> > > You don't even need to know what a regression coefficient is.

> > JE:-
> > Thank you for this reference. I have
> > read it and remain happy to debate its
> > content in another thread.

> JM:-
> Ok.  Your move.

JE:-
Jim this is not a game, it is just
an attempt to establish rational
MEANING within a supposed science
of biology. This requires mathematics
to make biological sense. You cannot
sacrifice biology to the god
of mathematics and keep biological 
science. Hamilton et al attempts
to do exactly, this.

Once again I urge you to complete
the form:

	"A DECLARATION OF MEANING"



> > JE:-
> > In BIOLOGICAL TERMS relatedness is
> > just genes held in in common.
> > How this can be measured remains a
> > problem. However the concept determines
> > what is to be measured, the measuring
> > system does NOT determine the concept.

> JM:-
> Agreed.  But ...
> We don't put concepts into mathematical "laws" such as
> Hamilton's rule.  We put measurements in.  

JE:-
This does NOT exclude the rule from
being able to _competently_ measure the
_concept_.

The rule is just a measuring tool. To be
a valid tool its has to be able to measure
what it is purported to measure, no exceptions. 
Hamilton's rule CANNOT measure what it is purported
to be able to measure: when organism fitness
altruism can be selected to evolve within
nature. Thus the rule is utterly misused
whenever it is suggested that it can do
so, i.e. it has been consistently misused
and has misrepresented evolutionary _theory_
from its inception (over 50 years).

> JM:-
> If we somehow
> came up with a measuring system for the concept of
> relatedness that was guaranteed to always give us a
> non-negative measurement, then perhaps we could reformulate
> Hamilton's rule to work with that method of measuring
> relatedness.  But the rule would then be more complicated
> algebraicly.

JE:-
It does not matter how you measure relatedness
-r is brain dead. You cannot sacrifice biology
on the alter of mathematics and still make biological
sense. EITHER the mathematical measure is up to
the concept or it is not. You do not chop off
the Darwinian foot to make the Neo Darwinian
shoe fit, you are REQUIRED to increase the size 
of the Neo Darwinian shoe. Hamilton et al act
like chopper happy mathematicians who are
biologically ignorant.

> JM:-
>snip<
> Arguing, based purely on philosophy, that Hamilton's rule
> can't be right because it uses a measuring scheme that
> allows negative relatedness is silly ..

JE:-
I argued: all cases of -r remain
invalid cases of Hamiltons rule.
I did _not_ agrue that all cases of
Hamilton's rule are invalid because
-r was invalid. 

>snip<

> > JE:-
> > Hamilton's rule attempts to
> > measure relatedness using a probability.

> JM:- 
> True only if you ASSUME that IBD is the intended concept
> to be measured.

JE:-
Incorrect. IBD is just a measuring 
tool that attempts to help measure the
_unnamed_ Hamiltonian total rb.


> > JE:-
> > IBD relatedness is only the probability that
> > you inherit a gene from a defined biological
> > source that is the same gene (i.e. is
> > not a mutation of that gene). Thus, -IBD
> > relatedness is nonsense. [snip]

> JM:-
> Agreed.  IBD relatedness is always positive (or zero if you
> allow truncation of the calculation, as my wife points out).
> IBD is never negative, and neither Hamilton, NAS, nor
> myself has ever said it could be negative.

JE:-
I have never suggested that Hamilton, NAS, nor
yourself has ever said it could be negative.
I suggested that all cases of the rule where
-r is negative are invalid. I aso said that
all -r measures produced by Price must be
reworked into a positive value of r before
relatedness can make any BIOLOGICAL sense.

_________________________________________
Please answer this:

MATEMATICALLY:		-r(-b)>c 

is eqivalent to:		rb>c

BUT:
ALL cases of -r are invalid.

THEREFORE:

Hamilton's rule is BOTH valid and invalid.
__________________________________________


> > JE:-
> > A regression coefficient is just a statistical
> > rework of reality just like any simple average is.

> JM:-
> Agreed.  A good analogy.

> > JE:-
> > If the average total fitness is 2.67, then absolutely
> > NOBODY can be average because the fraction is
> > BIOLOGICAL NONSENSE unless it is reworked into
> > some kind of a representation of a BIOLOGICAL
> > REALITY.

> JM:-
> Agreed that an individual fitness has to be an integer.
> But I disagree that an average of integers is going
> to be nonsense.  

JE:-
Any average of integers has to be reworked to
mean anything that is NOT just biological nonsense.
Any failure of the mathematics to make biological
sense is a failure of the mathematics and NOT A
FAILURE OF THE BIOLOGY. The concept has to be
adequately measured. Just because massses of
maths looks impressive does not mean that it
is adequate to measure the concept. Naturalists
I know shake their head in disbelief at
impressive but wholly inadequate mathematical 
models that seek to replace SIMPLE biological 
theory. At the same time a paternalistic 
attitute of model builders to biologists
who "cannot do maths", remains the norm...


> JM:-
> Sometimes it is the average value that
> is biologically causal rather than the integer individual
> value.  An example:
> Litter size in pigs is an integer.  A pig never gives
> birth to a litter of 3.57 piglets.  But it might well
> be the case that one population of pigs has an average
> litter size of 3.57 while another has an average litter
> size of 3.87.  Now, suppose we are trying to develop
> a theory relating the size of mammary fat deposits in
> pre-pubescent female pigs to litter size.  Is it the
> integer litter size of a particular litter that is
> causal here.  I think not.  Instead, it is the average
> litter size of the recent ancestors of the pig that
> created the selective environment for the adaptation
> of mammary fat deposits.

JE:-
Your model was misused. It was not "the average
litter size of the recent ancestors of the pig that
created the selective environment for the adaptation
of mammary fat deposits".  The average
litter size of the recent ancestors of the pig
can only be CORRELATED to an environment for the adaptation
of mammary fat deposits. ABOLUTELY no VALID causative 
theory was entertained in this model. All statistics
can do is provide a valid or invalid correlation.
A correlation is not a theory of causation it is
a documented observation that cries out for a
causative theory that must be testable in the
sciences.



> JE:-
> Yes, integer litter sizes may be the ultimate biological
> reality, but averages can be causal in biology,.. 

JE:-
Averages cannot be causal in 
biology only the averaged,
can be.

> > JE:-
> > This applies to any measure of -r.
> > It has to be reworked into zero or a positive number.

> JM:-
> My argument applies even more strongly to r.  The actual
> individual IBD r between donor and recipient is not
> causal in Hamilton's rule.  No part of the donor - not
> his brain, nor his hormones, nor his biochemistry - is
> making a calculation of IBD relationship before "deciding"
> whether to act altruistically.  It is Nature herself that
> "makes the calculation" and Nature is only concerned with
> averages.

JE:-
Incorrect. Nature is only concerned
with Darwinian fitness increases.
Altrusim can only be proven when
rb > Darwinian fitness.


> JM:-
> Or, to look at it another way, what really matters is whether
> the recipient actually shares the gene or not - not the
> probability that the gene is shared.  The recipient can
> share either 0, 1, or 2 copies of the gene.  Looked at in
> this way, it is integers that are causal, rather than
> probabilities.  Causal, not of behavior, but of changes in
> gene "populations". 

JE:-
Yes, the probability is only a stab
at a reality it attempts to measure.
Without the reality concept the tool
does not have a clue what it is required
to measure. "A Bad  workman blames his tools" 
is not as insane as "a bad workman does not 
even know which tool to choose". Neo Darwinians
have proven they are the latter. Hamilton's
rule is the classic case.


JM:-
> However, I would still claim that what
> matters in evolution is the long term trends, not the
> individual fluctuations, and thus we are back to probabilities
> and averages. 

JE:-
No, "what matters in evolution is the long term"
is whatver can be proven to cause shorter term
changes.

>snip<

> JM:-
> The important
> issue for deciding upon a measurement system for "relatedness"
> is not how well it captures the CONCEPT of relatedness.  It
> is in how well that measurement, as used in a "law", matches
> with empirical reality.

JE:-
It is nonsense to throw out meaningful
biology and replace it with meaningless
mathematics i.e. mathematics that
has no valid _biological_ interpretation.


> JM:-
> You may have a case for arguing that Hamilton's r should not
> be called "relatedness" if r is measured as Grafen suggests.
> But you can't argue on philosophical grounds that r should not
> be measured that way.  

JE:-
I argued: any -r must be reworked such that
it becomes +r within the science of biology.
Not to do so is to utterly misuse a model
-r.


> JM:-
> How r should be measured for use in the
> rule ought to be an empirical question, if the rule is taken
> to be a candidate law of nature. 

JE:-
The "empirical question" is the Popperian
question of refutability. This has been
ignored by Hamilton et al. When pressed
all they argue is that the rule is just a
"toy" model so it does not have to provide
any valid points of refutation. In the
next breath they allow this "toy" to compete
and win against Darwinian theory, i.e. they
have covertly treated the "toy" as if it 
were a contesting theory. 

> JM:-
> or, if Hamilton's rule is
> taken to be a derived theorem from a model, then the question
> is a mathematical one.

JE:-
No. The question is a BIOLOGICAL
ONE, always, if and only if the
rule is applied to the science of
biology. I know of no case of the
rule that is not applied to the
science of biology.

> JM:-
> So argue that r should be IBD, if you wish,
> by pointing that no clear-cut examples of Hamilton spite have
> been found in nature. 

JE:-
No. Here is the logic:

1) For IBD: -r is an invalid use
of a negative probability. It is
mathematically invalid. No proof
of biological invalidity is required.

2) For Price: Here -r is mathematically
valid but proof of biological
invalidity is still required.
Unless Prices model -r 
becomes reworked to become a positive 
or zero r value within a biological
theory, the -r model remains utterly 
misused within any science of biology.

Conclusion:
No value of -r is valid using
IBD, or anything else because
a biological form cannot be
less than zero related to 
any other biological form, no
exceptions.


Here is a definitive example of 
an application of the rule to 
the science of biology:


--------------quote----------------------

1) 22/01/2004:

JE:-
What is the difference between
a reduced positive c and a negative c?
If c was an abolute measure of fitness
then yes, a real difference exists. However
c is only a relative fitness cost and not
an absolute fitness cost, so what is the
difference?

BOH:-

As far as the rule is concerned, none.

----------- end quote --------------------

Please indicate if you agree or disagree
with Dr O'Hara's answer.

John Edser
Independent Researcher
PO Box 266
Church Pt
NSW 2105
Australia

edser{at}tpg.com.au
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