Jim Menegay wrote:
> August West  wrote in message
news:...
> 
> 
>>[Snip some good and wise stuff]
>>Yes, I was saying that Hamilton's rule is a mathematical relationship
>>that in itself is not subject to testing (provided, of course, that it
>>is internally consistent). I would say the same for natural selection,
>>except that it is more pure logic than mathematics. 
>>[Snip more good and wise stuff]
> 
> 
> I agree with everything said in this post and (despite my apparent
> complaint) in its predecesor.
> 
> But, to sharpen the focus a little on the epistemology - some comments
> and a question.
> 
> Consider the somewhat vague hypothesis "Genes that promote the 
> fitness of the organisms that contain them will proliferate".
> 
> This hypothesis certainly SEEMS to be testable - it is not pure
> mathematics.  But there are problems when we try to clarify the
> meaning of the key words "fitness" and "proliferate".
> 
> One possible issue with fitness is the old canard about "Natural
> Selection is a tautology."  Ignore this - I don't want to go into
> this issue.
> 
I think you might end up there anyway!  I'll just point out that fitness 
is defined to be specific to the environment, so if the environment 
changes, so might fitness.

> A second issue is whether "fitness" should be inclusive fitness.
> I'm going to ignore this one too.  Let John deal with it.
> 
> In this post, I am going to focus on how "proliferate" should be
> clarified.  I will list four possible meanings and ask which one
> is "correct".
> 
> 1. Proliferation means an increase in allele population over the
> short term.  (i. e. Absolute)
> 
This would be absolute fitness.  It has problems because you need to 
know about the demographics of the whole population, so you have to know 
about whether the population is at carrying capacity, for example.

> 2. Proliferation means an increase in allele frequency over the
> short term.  (i. e. Relative to the allele's competitors)
> 
This is the way it's usually used.  Note that now if the relative 
fitness is independent of density, then you can largely ignore 
demographics (OK, as long as extinction isn't likely!).

> 3. Proliferation means an increase in allele population over the
> long term.  
> 
> 4. Proliferation means an increase in allele frequency over the
> long term.  
> 
These two will without doubt include a lot of environmental variation, 
so hte best you can do is work with mean fitness.

> Which of these is correct?  That is, which of these things is Nature
> trying to increase?  

None of them, Nature just is!

We're trying to describe Nature, so the question is which one of these 
provides the best description.  There's nothing wrong with trying to use 
the different concepts at different times, as long as you're clear about 
which one you're using.  if you use the wrong oneat the wrong time, I'm 
sure someone will point it out.

Bob

-- 
Bob O'Hara

Rolf Nevanlinna Institute
P.O. Box 4 (Yliopistonkatu 5)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 23743
Mobile: +358 50 599 0540
Fax:  +358-9-191 22 779
WWW:  http://www.RNI.Helsinki.FI/~boh/
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