joe{at}removethispart.gs.washington.edu wrote 

> >> OK.  So first we define a situation and then pause to see if
> >> McGinn is willing to accept it.  A simple model case, not a general
> >> case -- the interest is to see whether Hamilton's result emerges, or
> >> whether some totally different rule is correct.
> >> 
> >> We have
> >>   1.  An infinite population
> >>   2.  Diploid
> >>   3.  One sex (hermaphrodites)
>  [ 8 more deleted to save space]
>  12.  There is a locus with two alleles, A and a.  A is rare.
> >>       This locus is one (in our model case the only one) whose
> >>       genotype affects the probability that the Donor engages in the
> >>       behavior.
> >>
> >> Now we need to hear from McGinn whether by assuming this situation we
> >> are OK, so that he is willing to hear about the algebra that results.
> >
>  [McGinn]
> >Situation?
> >
> >I read your points, 1 thru 12 above, and found them 
> >unacceptable.  If you want to discuss why I found 
> >them unacceptable I guess we could approach that on 
> >a point by point basis.  But, to be honest, I'm 
> >wondering why you need (or think you need) special 
> >considerations in order to make your case?
> 
> Well, I should have guessed that the offer of $1000 for a successful
> proof was not likely to materialize ...  ;-)

The offer still stands.  Moreover I extend the 
challenge to anybody else.  Anybody that things 
they can make sense of Hamilton's rule is hereby 
invited to take a shot at it.

> 
> Model, it's a simple model.  I said "a simple model case, not a general
> case".  That's why all the assumptions.  You use these assumptions to
> set up something that can be analyzed mathematically.  Then you can see
> whether the condition for increase of some allele is  r b > c.
> 
> If McGinn is unhappy with some (or all) of the assumptions,
> he has to replace them by some assumptions

Well, I am, in the least, encouraged by the fact 
that you are not denying that these are 
assumptions.  (It seemed you were trying to pass 
this off by referring to it all as a, 
"situation.")

> that set up a simple case that can
> be analyzed mathematically, as this one can.  Or else he should not
> have agreed to the examination of a simple model case.  

Simple model case?  I agreed?

> He should either
> (1) withdraw his objections to the 12 assumptions, or (2) withdraw his
> agreement to having me analyze a simple model, or (3) suggest replacement
> assumptions that preserve mathematical analyzability.

I don't have any suggestions for what assumptions 
you could include in your model.  I myself, in my 
own models, am very careful not to include 
assumptions other than those that are verifiably 
part of nature/reality.  The reason I'm so careful 
about this is because I've found that the most 
common mistake that many theorists make in their 
evolutionary models is to include assumptions that 
are not well grounded in evidence.  Hamilton rule 
is a perfect example of the confusion that ensues 
when such care is not taken.


Jim
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