Re: Hardy-Weinberg lawt

From: EKurtz (NoJunk_at_ForgetIt.com)
Date: 06/27/04 

Date: Sun, 27 Jun 2004 23:39:55 +0000 (UTC)

> >> > JE:-
> >> > Pedantic nonsense.
> >> > Do you deny or confirm that HW "law"
> >> > only represents a binomial _distribution_
> >> > of the alleles concerned so the HW "law"
> >> > is actually just a binomial distribution
> >> > of alleles, i.e. HW "law" only represents
> >> > a defined _zero_ state re: any _significant_
> >> > bias of a binomial distribution of the
> >> > alleles concerned?

The binomial formula in HWE refers not to the probability of alleles, but of
allele pairs in a diploid organism - ie of *genotypes*. The populational
proportion of alleles is assumed to be known prior to the calculation. The
resulting proportions are for an infinite population in a neutral model. It
is possible to reverse the calculation if the genotypes are known (eg
inferred from phenotypes).

Note: In population genetics, the population proportion of a given allele,
genotype, whatever and its resulting probability (ie the probability of it
being randomly selected) are used interchangably. In fact, the latter is
more common.

"Anon." <bob.ohara@SOD.OFF.Spammers.helsinki.fi> wrote
> >> (1) H-W is deterministic

In what sense? Since it depends on random mating, the outcome in a real,
finite population cannot be predicted.

> there is no distribution,

True, there is no distribution in the sense that there is no probability
density function for a continuous variable, as you might get for a
quantitative trait such a height. The introduction of the binomial
distribution into this discussion has generated much confusion.

(2)
> >> the binomial distribution only has two classes of events: "success" and
> >> "failure". H-W has three: two homozygotes and a heterozygote.

This is the simplest case, where the locus is biallelic, ie has only two
variants. In the HW formula, the locus can be a single base, a gene, a
microsatellite, whatever. This means that the number of variants at the
locus of interest can be >= 2.
In the simple two-variant form, the genotype probabilities are given by:

P^2, 2PQ, Q^2

If the locus has variants A1, A2, A3,...An with populational probabilities
P1, P2, P3...Pn, then, under the model outlined above, the probability of
homozygous genotype AiAi will be PiPi, and the probability of heterozygous
genotype AiAj will be 2PiPj.

The distribution is thus binomial only for the biallelic case; in all other
caes it is multinomial. Whether it is one or the other is actually
irrelevant.

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