"John Edser"  wrote in message
news:cf0iao$1ncf$1{at}darwin.ediacara.org...
>
>
>  "Perplexed in Peoria" wrote:
>
> >> JE:-
> >> Any relative fitness is a comparison.
> >> Any subtraction is just a comparison.
> >> What was being compared is what was being
> >> subtracted.
>
> > JM:-
> > It is correct to say that a relative fitness is
> > a comparison - at least as most biologists use the
> > term "relative fitness".  It is a comparison between
> > two "absolute fitnesses".
> > However it is wrong to suggest that the comparison
> > is done by subtraction.  It is done by division.  At
> > least that is how it is done in population biology.
>
> JE:-
> The subject here is c within Hamilton's rule which
> is a comparison by simple subtraction between rb and c
> via a _hidden_ "baseline fitness" K which is not
> explicitly included anywhere within the rule.

Well, I thought that the subject was "Any relative fitness".
That is what you wrote in the quote I was responding to.

Regarding the rest of your paragraph, I'm afraid I don't
understand it - particularly the part about c being a
comparison between c and rb.  That HAS to be a typo.

> > JM:-
> > I did a Google on:
> >     "absolute fitness" "relative fitness"
> > I found many definitions of these terms.  There was
> > some variation in the definitions, particularly in
> > the definition of absolute fitness, but there was
> > near universal agreement that a relative fitness is
> > the ratio of two absolute fitnesses - not the difference.
> > Some examples: [snipped]
>
> JE:-
> Thanks for the references. IYO does any significant
> difference exist between additive (subtracted)
> and non additive (divided) absolute fitness
> comparisons within a science of biology?

Definitely!  Subtraction and division are different operations
and it is obvious that the results will be different when you
try to incorporate the comparison into some biological law.

Furthermore, though it may not be obvious, both operations
"throw away" some of the original information, though they
discard different parts of the original.  For example,
let A1 = 3.3, A2 = 3.0, A3 = 2.2, A4 = 2.0.  If you compare
A1 to A2 by division, you get the same answer as when you
compare A3 to A4 by division.  But if you do the same pairs
of comparisons by subtraction, the two comparisons do not
yield the same result.  Therefore, forming a ratio and taking
a difference are FUNDAMENTALLY different comparisons.

Forming a ratio between two absolute fitnesses yields a
relative fitness, and there are a variety of biological laws
that talk about or use relative fitnesses.  Taking the
difference between two absolute fitnesses is usually done
to determine a fitness cost or benefit.  There are a variety
(a completely different variety) of biological laws that
talk about or use fitness costs and benefits.

Here is another distinction between subtraction and division.
Dividing one absolute fitness by another to get a relative
fitness always yields a positive number.  But subtracting
two absolute fitnesses can yield either a positive or a
negative number.

I feel a little foolish spelling all this out.  I can only
hope that you feel equally foolish for asking. ;-)

> JM:-
> >However, subtraction IS involved in calculating Hamilton's c.
> >"c" and "b" are differences between fitnesses.
>
> JE:-
> No, the difference is between c
> and the multiple rb.

I agree that there is an implicit difference formed by subtraction
(rb - c) within Hamilton's rule.  However, before you can do that
subtraction, you have to say what b and c are.  As it happens,
they are *also* formed by subtraction.  "c" is defined as the
difference between the fitness of an organism that does
not act altruistically and the fitness of the same organism
in the same environment if it does act altruistically.  (Or
spitefully, mutualistically, selfishly, whatever.  The definition
of "c" is not limited to altruism.)  You can use either absolute
or relative fitnesses for calculating c, as long as you use the
same kind of fitness in calculating b.
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