Re: Hardy-Weinberg law

From: Tim Tyler (tim_at_tt1lock.org)
Date: 06/26/04 

Date: Sat, 26 Jun 2004 04:56:29 +0000 (UTC)

Perplexed in Peoria <jimmenegay@sbcglobal.net> wrote or quoted:
>
> "Tim Tyler" <tim@tt1lock.org> wrote in message
> news:cbf259$3tt$1@darwin.ediacara.org...
>
> > You cannot simply talk about ratios between two infinite quantities.
>
> Agreed.
>
> > so - unqualified mention of allele frequency in an infinite population
> > makes no sense.
>
> Your inference is valid only if you make the auxiliary assumption that
> "frequency" is defined using a ratio. It need not be. It can be
> defined directly as a probability. Then ratios come in (via the
> law of large numbers) only indirectly and only for finite samples
> or populations.

If you are picking samples from a population and looking at the
limit as the sample size tends to infinity, you *still* need to
specify how you are choosing your sample.

Different approaches to taking samples are likely to lead to different
ratios.

You can't just say something like "sample at random" - since sampling
at random from an infinite population is not normally a well-defined
operation either.

> Returning to Hardy-Weinberg, you will notice that the derivation of
> the law uses frequencies as probabilities (i.e. random mating) -
> ratios never enter into it, since large quantities N*p never come
> into it.

While it makes sense in finite populations, "random mating" is not a
coherent concept in an infinite population. Nor can you sensibly
discuss the probability of organisms having a particular genome -
*unless* you specify a sampling strategy.

I have no problem with Hardy-Weinberg - provided it is expressed as
a limit as N -> oo. 

-- 
__________
 |im |yler  http://timtyler.org/  tim@tt1lock.org  Remove lock to reply.

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