"John Edser"  wrote in message
news:...
> "Perplexed in Peoria" 

> > 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. 

If by "-r" you mean "negative relatedness", then can
you please use
the latter, as this sloppiness can (and has) led to needless
misunderstandings, such as with the discussion of -c and +c. If
"negative relatedness" is too long winded, perhaps we can agree on a
short hand, say "-ve r", to be contrasted with "+ve r".

> 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.

Some quantity r has biological meaning in that it can be incorporated
into a rule r b > c to determine when traits will be favoured by
selection. Because the mathematically necessary definition of r does
not suit your intuition about some preconceived ideas of
'relatedness', you reject the entire theory. As Jim Menegay has said
before, perhaps 'relatedness' is a poorly chosen word to use in
relation to Hamilton's coefficient r. But if this is your only
objection, then it is rather petty and uninteresting. We biologists
are interested in biology, not word play.
 
> > 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. 

-ve r is not invalid. In a population of size N an actor is related to
a randomly chosen individual from the remainder of the population by
-1/(N-1) on average.

> >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.
> 

IBD attempts to measure relatedness using a probability. IBD is often
used in applications of Hamilton's rule because in most conditions it
will give approximately the correct answer. Hamilton's rule does not
attempt to measure relatedness using a probability.
 
> > > 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. 

What does "where -r is negative" mean? Surely you mean "where r is
negative"? John, this is obviously a conceptually difficult subject
for you, so please be more careful with your assertions.

> 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
> 

You need to be careful here, John. -r (-b) > c is equivalent to r b >
c. However, [-ve r]*[-ve b] > c is not equivalent to [+ve r]*[+ve b]>
c. Your confusing notation suggests the former, but your discussion
suggests the latter. However, in the above you have confusingly mixed
the two. The discussion is meaningless until you sort out this error.

True, [-ve r]*[-ve b] is positive and can be greater than +ve c, just
as the product of +ve r and +ve b is positive and can be greater than
+ve c. Thus, spite can be favoured, in a way that is analogous to
altruism, i.e. hurt to negative relations works, as does help to
positive relations.

> BUT:
> ALL cases of -r are invalid.

Assuming you mean -ve r, this is your assertion, and has not been
justified.
 
> THEREFORE:
> 
> Hamilton's rule is BOTH valid and invalid.

You have just destroyed your argument about negative relatedness
through reductio ad absurdum. Your assumption about negative
relatedness being invalid leads to self contradictory statements,
hence negative relatedness is valid.

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

But what if biological reality is statistical? 
  
> > > 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.  
 
We'd have to decide upon the proper measure of fitness before claiming
that it takes integer values.

> 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.

When I look at a mathematical proof, I see not "masses of maths" but a
clearly laid out, entirely unambiguous argument. Is your position
bourne out of maths fear or biological intuition?

> 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...

John, Hamilton's rule is framed in terms of pure maths, not any
simplistic model of evolution. If a naturalist shakes his head at
Hamilton's rule, then it is because he/she has not understood it.

> > 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.

Natural selection cares only about the correlation, and does not stop
to inquire as to the causation.

> > 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.

See above.
 
> > > 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.

Darwinian fitness = c? What?
 
> > 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.

I used a shoe this weekend to hammer a peg into the ground, and
obtained a satisfactory result.

> 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.

Maybe r has a proper biological meaning, and just needs a little more
time for you to get your head round. I know that I am comfortable with
it.
 
> > 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.

Why?

> > 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. 

Who claims that Hamilton's rule is a toy model? Certainly not me, and
certainly not Hamilton!
 
> > 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.

The mathematics of the rule can be applied more generally; however, by
referring to the b and c components in terms of fitness, the rule is
restricted to biology. Having said that, fitness can be applied more
generally, in an abstract sense. Building on Price, I can see that
Hamilton's rule could be applied to the tuning of radios.

> > 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.
> 

Right.

> 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.
>

Question: why does r have to be positive to be valid?
 
> 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.

Assertion.

> 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.

Is this amnesia?
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