John Edser wrote:
>>BOH:-
>>We also seem to disagree on whether anyone has tried to use Hamilton's 
>>rule to separate OFM from OFA.  You are claiming that it has, but have 
>>still not provided any evidence for this.  So, I'm asking you again - 
>>please provide the evidence.  Cite papers!  Books!
>>
>>JE:-
>>I can't imagine where you got that from!
>>I am NOT claiming that is HAS been separated
>>I am claiming that OFM and OFA cannot be separated
>>within Hamilton's rule unless K, the absolute
>>donor fitness which is numerically equivalent to
>>cmax, is appended to the rule thus:
> 
> 
> BOH:-
> But you are also claiming that Hamilton's rule HAS BEEN USED to make 
> this separation (by claiming that it has been mis-used).  Quite simply, 
> I want to see evidence for this.  So far none has been forthcoming.
> 
> JE:-
> The evidence is simply, the rule _was_ used to
> support OFA after classical group selection
> failed to do so. You agreed that this was the
> case. Unless the rule HAD BEEN USED to separate
> OFM from OFA such a claim would have been logically 
> impossible.
> 
Why?  The argument Hamilton developed to support OFA was that there were 
behaviours that reduced the direct fitness of individuals (i.e. c is 
positive), and he could then mathematically show some of the conditions 
under which this situation might evolve.

The point is that the first step was to see that c was positive - which 
means that OFM is impossible in this situation by definition.  c can be 
measured without reference to Hamilton's rule, so Hamilton's rule is not 
needed to separate out OFM from OFA.


>>>______________________________________
>>>Do you agree that you cannot use OFM to support
>>>OFA?
>>>_________________________________________
>>
> 
>>BOH:-
>>Of course - they are mutually exclusive (by definition).  This should be 
>>obvious.
> 
> 
>>JE:-
>>Then you have no option but to agree that
>>Hamilton's rule was utterly misused to
>>support OFA within nature after group
>>selection failed to do so 
>>because:
>>
>>   ..AT ALL TIMES, EITHER OFA OR OFM
>>   ARE OPERATING TO SUPPORT OFA.. 
> 
> 
> BOH:-
> I'm sorry, I don't have a clue what you mean when you write that OFM is 
> operating to support OFA.
> 
> JE:-
> You agreed:
> 
> 1) The sign of c remains arbitrary for all 
> cases of Hamilton's rule. 

This might be misleading - I have argued that the sign of c is arbitrary 
  within Hamilton's rule, because the rule works equally well with both. 
  However, the "for all cases" might be taken to mean that it is 
arbitrary every time that Hamilton's rule is applied, in which case it 
is not arbitrary (because there is a measurable value).


> 
> 2) The cost c exists within rule and not outside of it.
> 
No, I don't believe I've ever agreed with this.  If I have, it must have 
been a mistake.  I've been arguing consistently that c exists outside of 
the rule.

> 3) OFA and OFM can only be separated within the rule
> using the sign of c within the rule. Thus the sign 
> of c only represents "individual discretion or preference 
> or  sometimes impulse or caprice" within Hamilton's rule.
> 
> 4) The rule was used to support OFA within nature
> after classical group selection failed to be able
> to do so.
> 
> The cost c, at all times, is either + or -
> because the difference between rb and c is only
> a relative measure. This is why 1) is true.
> Thus at all points where OFA is supported, OFM
> was also supported, no exceptions. 

Rubbsh.  If OFA is supported (i.e. c is positive), then OFM is not, 
because it requires a negative c.  So, if OFA is supported, OFM cannot be.

Bob

-- 
Bob O'Hara

Dept. of Mathematics and Statistics
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/
Journal of Negative Results - EEB: http://www.jnr-eeb.org
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