John Edser wrote:
>>>>JE:-
>>>>...[zero] only represents a zero state of some biological
>>>>_unknown_. 
>>>
> 
>>>BOH:-
>>>Would you care to demostrate why my statement is wrong, rather than just 
>>>ignoring the content of what I wrote?  I can't accept your statements 
>>>without you persuading me that my ideas are wrong.  And I can't do that 
>>> if you don't try and say what are wrng with my ideas.
>>
> 
>>>JE:-
>>>When rb-c=0 what is left?
>>
> 
>>BOH:-
>>What is left from what?
> 
> 
>>JE:-
>>Hamilton's rule is supposed
>>to be a fitness road map. Suddenly 
>>no road map exists, i.e. we have gone 
>>off the map because zero fitness is
>>represented. However a real fitness 
>>still remains. What biological fitness 
>>actually remains when rb-c=0?
> 
> 
> BOH:-
> The fitnesses of the two behaviours.  
> But now they're equal.
> 
> JE:-
> You failed to mention the two equal
> fitnesses are logically _opposed_.
> If both fitnesses are equal but 
> logically opposed, as Hamilton's rule
> insists that they are, then _relatively_
> no fitness, i.e. just a zero fitness exists 
> within Hamilton's rule when rb-c. 

"no fitness" and "zero fitness" are not the same
things.  A temperature 
of zero degrees Celcius does not mean no temperature.


> 
> BOH:-
> If I want to find out if I'm taller than you, I do it by measuring my 
> height and your height, and taking the difference.  IF we're both 188cm 
> tall, then the difference is zero.  But that doesn't mean that neither 
> of us has no height at all.
> 
> JE:-
> Exactly, but the above is my argument _against_
> Hamilton. Two and not just one, height concepts 
> exist in your argument: relative and absolute
> height. In biology two concepts of fitness
> exist, relative and absolute fitness. When you just 
> compare heights you are only using a relative concept of 
> height so that when they are equal but opposed, the
> absolute concept of height must remain otherwise
> no such comparison was possible. Likewise, when rb-c=0, 
> absolute fitness remains within the science of biology
> but remains absent from Hamilton's rule.
> 
Because it doesn't need to be there.  If the question is "Am I taller 
than you?", then if I'm 1cm taller, it doesn't matter if I'm 54cm tall 
or 724km tall - the answer is still "yes".

Recently there has been quite a bit of work on the dynamics of 
populations, but none of it (as far as I'm aware) invalidates Hamilton's 
rule.

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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