"Anon."  wrote in
message news:cetl72$lrj$1{at}darwin.ediacara.org...
> Jim Menegay wrote:
> > "Perplexed in Peoria" 
wrote in message news:...
> >
> >>PinP:-
> >>          |    Edserian       |
> >>Cat-egory | Count  | Fitness  |
> >>----------|--------|----------|
> >> HB       |    280 |  2.14    |
> >> HN       |    120 |  1.99    |
> >> NB       |    120 |  2.19    |
> >> NN       |    480 |  2.04    |
> >> XX       |      0 |  N/A     |
> >
> >>One of the team members claims that Hamilton's rule is not
> >>automatically applicable.  He claims that if our data had found only
> >>80 HB cats, for example, with counts unchanged for the other
> >>categories, then Hamilton's rule "would not work". 
Does this make any
> >>sense to you?
> >
> >>JM:-
> >>Yes, that is correct.  Hamilton's rule would not be applicable
> >>if the data were different in that way.  The reason is that such
> >>a pattern of data would indicate that the helpfulness trait is not
> >>determined by the genetics of the helper and that it is a kind of
> >>shared trait of the helper and the beneficiary.
> >
> >
> > I should probably expand upon this point.
> >
> > The counts listed above are based on a simple genetic model.  The
> > frequency of the helpful trait is 4/10.  Given that a cat is helpful,
> > the probability that its full sib is helpful should then be 7/10.
> > The above counts are then inevitable if the total population is 1000.
> > Changing the HB count without also making adjustments in the other
> > counts is impossible without violating this simple model.
> >
> What's the genetic model?  As it was apparently not a simple one, I
> decided that the frequencies could be explained by *some* genetic model.

I assumed that if I have a trait, then the probability that my full
sib also has the trait is (1/2 + p/2) where p is the frequency of the
trait in the population as a whole.  AFAICS, this formula works for
haploid genetics, for diploid genetics with the trait being dominant,
and for diploid genetics with the trait being recessive.  I assume
that it also works for more complicated genetic situations, though I have
never actually seen a statement or proof of this.  All of this assumes
random mating and perhaps other "independence" assumptions as well.

Perhaps I am using terminology incorrectly to call this formula a
"simple genetic model".
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