Text 1322, 81 rader
Skriven 2005-01-04 20:31:00 av Joe Felsenstein (1:278/230)
Ärende: Re: McGinn's disproof of
================================


In article <crah9q$1hek$1@darwin.ediacara.org>,
Jim McGinn <jimmcginn@yahoo.com> wrote:
>Joe Felsenstein wrote:
>>
>> 1. An infinitely large diploid population.
>> 2. Discrete generations (an annual-plant-like life cycle)
>> 3. A single locus.
>> 4. Two alleles.
>> 5. Proportions of the three possible genotypes the same
>>    in both sexes, P, Q, and R  for AA, Aa, and aa.
>>
>Yes.  I accept these assumptions.  Now continue.
>
>(I can't wait till we get to the part where you try
>to include the assumption that altruistic genes will
>be (can be) rare in a population.  In another thread,
>entitled Hamilton's Nonsense, Perplexed in Peoria
>tried to assert this and ended up eating his words.)

McGinn has not noticed that here we're deriving Hardy-Weinberg
proportions, not anything about altruism.  (Also, as an
aside, I don't know how he knows that altruistic alleles
*can't* be rare, but that's another discussion so let that pass).

It is unexpectedly pleasant to have McGinn accept some model
assumptions.  OK.  More:

6. No immigration into the population
7. No differential emigration from the population
   (that is, no differences in the fraction of emigrants
    among genotypes).
8. No mutation.
9. No differences in viability between genotypes.
10. No differences between fertility between genotypes.
11. Random mating.

These are sufficient to go and derive that in the
next generation, among newborns, the proportions of
AA, Aa, and aa  will be  p^2, 2pq, and q^2, where

       p =   P + (1/2) Q
and
       q =   (1/2) Q + R

I can go throught the details of how we get from the
assumptions to the result.  Basically we make up a table of
possible mating types, work out the proportions of mating
types, work out the fractions of different offspring that come
from each, and find that they come out to be the above
proportions.  The assumptions about migration, mutation,
fertility and viability all function simply to say that all
offspring come from these matings, in proportion to their
numbers, and have the straightforward genotypes expected.

I can do that if McGinn accepts the above further assumptions
as reasonable, but feels there is going to be some problem
further down the line.  I can show there won't be any such problem,
once we are given those assumptions.  If he feels that it will all
work out then I am not sure why he agreed to discuss the derivation
of the Hardy-Weinberg proportions.  It would then at least
mean that he does accept some model arguments in theoretical
population genetics.  But if he objects to these assumptions it
would verify that his objections to Hamilton are generic
objections to models in theoretical population genetics.

Let's see which is his argument.


-- 
Joe Felsenstein         joe@removethispart.gs.washington.edu
 Department of Genome Sciences and Department of Biology,
 University of Washington, Box 357730, Seattle, WA 98195-7730 USA
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