John Edser wrote:
>>>>BOH:-
>>>>...So, I'll re-write Hamilton's Rule as rb-c>0, and
there you have 
>>>>it.  rb-c is a variable, and 0 is your missing constant.
>>>
> 
>>>>JE:-
>>>>This zero state has to represent
>>>>something within a testable theory
>>>>of nature. 
>>>
> 
>>>BOH:-
>>>Yes.  In this case, no difference between the costs and benefits of an 
>>>altruistic behaviour.
>>
> 
>>>JE:-
>>>Please replace the number "0" with a new 
>>>defined term, within Hamilton's rule.
>>
> 
>>BOH:-
>>Why?  Zero is zero in Hamilton's rule.  It's a constant.  
> 
> 
>>JE:-
>>This is _not_ a difficult ask. If you really
>>think you understand what zero represents
>>within the rule, then go ahead and replace it with 
>>an actual algebraic term that represents something 
>>within the science of biology! 
> 
> 
> BOH:-
> Why?  The zero does represent something biological.
> It's the point in the b/c tradeoff where there is no 
> difference in fitness between the 
> altruistic and non-altruistic phenotypes.
> 
> 
> JE:-
> No, it only represents a zero state of some biological
> _unknown_. 

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.


>>BOH:-
>>If the 
>>benefits are greater than the costs (i.e. if rb>c), then the altruistic 
>>trait can evolve.  Zero is the critical value here - it's this that rb-c 
>>is compared to.
> 
> 
>>JE:-
>>"If the benefits are greater than the costs" COMPARED
>>TO WHAT MISSING MAXIMAL VALUE? 
> 
> 
> BOH:-
> They are compared to each other.  There is no missing maximal value.
> 
> JE:-
> A zero ratio is simply not enough to make
> a rational argument. All you are suggesting
> is that when a defined relationship is zero, 
> then kin selection operates, 

No I'm not.  Hamilton's rule is an inequality.


>>JE:-
>>If kin fitness only makes
>>a relative benefit at just the gene level but decreases the 
>>number of organisms reproduced by doing so, then yes, the
>>gene spreads _relatively_, but also, yes, the gene 
>>becomes _absolutely_ extinct as the population 
>>constantly shrinks to zero. 
> 
> 
> BOH:-
> That's a very big "if" at the start, and Hamilton's rule says nothing 
> about the absolute numbers in the population. 
> 
> JE:-
> Exactly. Nobody can know, just using Hamilton's
> rule if such an absurd situation has indeed arisen 
> i.e. as rb-c>0 the population simply heads
> towards extinction. 

I've not seen any demostration that if rb-c>0 extinction is inevitable - 
it'll depend on much more than is in Hamilton's assumptions.

And if altruism does lead to extinction, then that's fine.  Nothing in 
evolutionary biology stops species evolving themselves to extinction.

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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