"John Edser"  wrote in message
news:...
> Name And Address Supplied wrote:-
> 
> > > >>JE:-
> > > >>Here we go 'round  the mulberry bush....
> > > >>
> > > >>--------------quote----------------------
> > > >>
> > > >>1) 22/01/2004:
> > > >>
> > > >>JE:-
> > > >>What is the difference between
> > > >>a reduced positive c and a negative c?
> > > >>If c was an abolute measure of fitness
> > > >>then yes, a real difference exists. However
> > > >>c is only a relative fitness cost and not
> > > >>an absolute fitness cost, so what is the
> > > >>difference?
> > > >>
> > > >>BOH:-
> > > >>
> > > >>As far as the rule is concerned, none.
> > > >>
> > > >>----------- end quote --------------------
> > > >>For the 6th (?) time and counting:
> > > >>Do you agree or disagree with the
> > > >>answer Dr O'Hara provided? A simple
> > > >>YES or NO will suffice.
>  
> > > > NAS:-
> > > > No, a simple yes or no will not suffice to your
question as it has
> > > > been put 
> > > > My answer is: I disagree with Dr O'Hara.
>  
> > > BOH:-
> > > Oh!  The point behind the statement I made there was that the 
> > > rule still 
> > > holds whether c is positive or negative, i.e. it can still be used to 
> > > decide whether a behaviour will invade a population.  Obviously 
> > > changing 
> > > the value of c may change the prediction, but the rule would still be 
> > > used.  Therfore as far as the rule is concerned, there is no 
> > > difference, 
> > > even if there would be a diffeence in a particular application 
> > > of the rule.
>  
> > NAS:-
> > Right, I agree with this. I would say that the sign of c makes no
> > difference to the validity of Hamilton's rule (which is always valid,
> > as it is a mathematical truism) but it does make a difference for the
> > interpretation.
> 
> JE:-
> The Mad Hatter "mathematical truism" is 
> now giving away (absolutely) free gifts
> to almost everybody he likes at
> his famous Dept Of Biology Tea Party. 
> His gift: everybody remains correct 
> except (of course) JE who remains
> a Neo Darwinistic tribal outcast
> (with thanks).

Pure mathematics - not ad hoc, simplified models, but pure mathematics
- shows that you are wrong. Hamilton's rule is a correct mathematical
statement. Only lunatics chase after disproofs of mathematical
theorems.
 
> NAS and BOH _seriously_ maintain that
> as long as the mathematics remains valid, 
> the biology (the "application") doesn't 
> matter. 

So long as that application of the rule is correct. Of course, if your
application of the rule involves redefining its components - for
instance, r as a convenient probability measure - then, yes, you will
run into difficulties.

> ERGO: No matter if the critical
> case of the rule that allows organism
> fitness altruism is proven biologically 
> meaningless, it remains valid mathematics 
> and that is ALL that matters. Their
> argument demeans the science of biology.

I haven't seen any demonstration of biological meaninglessness in
Hamilton's rule.

> > NAS:-
> > For example, if we have a positive b then positive c
> > is associated with altruism, and negative c with mutualism.
> 
> JE:-
> Yes, it does not matter at all to
> the science of biology that the
> rule cannot measure any difference
> between just a reduced donation
> and an investment cost by the actor. 

Be explicit. Do you mean

reduced donation: c < 0

investment cost: c > 0

or what?

> Did anybody here have shares in 
> Enron?
> 
> Dear oh dear..

I'd concentrate on the logic of your argument before drawing such
parallels, John. This only serves to betray a fundamental ignorance in
relation to your grasp of Hamilton's rule.
---
þ RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info{at}bbsworld.com

---
 * RIMEGate(tm)V10.2áÿ* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 8/8/04 9:57:34 PM