John Edser wrote:
>  "Anon."  wrote:
> 
> 
>>>>>JE:-
>>>>>What I am arguing here is that Hamilton's logic can only work
>>>>>when the cost c remains _negative_ (in strictly Darwinian 
>>>>>fitness terms). This means that at all times, organism fitness 
>>>>>mutualism (OFM) and not organism fitness altruism (OFA) is
>>>>>operating in ALL valid cases of Hamilton's rule, no exceptions. 
>>>>>____________________________________________________________
>>>>>So that I am not misunderstood: all positive cases of c,
>>>>>within the rule are invalid. This is because
>>>>>all positive values of c remain  _ambiguous_ re: the 
>>>>>measuring OFA and OFM, as Dr O'Hara has reluctantly agreed.
>>>>>It is this point of logical ambiguity that nobody wishes to 
>>>>>discuss, not even Dr O'Hara who agrees that it does exist.
>>>>>____________________________________________________________
>>>>
> 
>>>>BOH:- 
>>>>John, please don't put words into my mouth.  
> 
> 
> JE:-
> I do not do anything of the sort. 
> 
I have never claimed that a positive value of c is ambiguous, so if you 
claim that I have, then you are putting words into my mouth.

> 
>>>>BOH:-
>>>>There is (in my mind at 
>>>>least) no ambiguity - a positive c is a positive c so that the 
>>>>behaviour 
>>>>under study is altruistic (this follows directly from the technical 
>>>>definition of altriusm).  Whether this behviour will invade a 
>>>>population 
>>>>is determined by Hamilton's rule.
> 
> 
> 
>>>JE:-
>>>If you wish to retract your reply below, 
>>>then please do so, _explicity_:
> 
> 
>>BOH:- 
>>No, I do not.  Please do not extrapolate from what I write and then 
>>claim that I agree with the extrapolation you make.
> 
> 
>>snip<
> 
> 
> JE:-
> If any "extrapolation" is logically 
> deductive from what you have said 
> then: 
> 
That's a big if, and I don't think your logic is correct.


> Please provide the missing logic that 
> proves it was invalid for me to just 
> deductively conclude that: IF no difference 
> exists within Hamilton's rule "between a 
> reduced  positive c and a negative c" THEN 
> the rule cannot measure the critical difference 
> between  mutualism and altruism for any case 
> of a positive c?
> 
Err, by definition a positive c cannot mean mutualism.

Bob

-- 
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gusfaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax:  +358-9-191 51400
WWW:  http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org
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