Monday, June 19, 2006

Well I'll be damned...   posted by JP @ 6/19/2006 10:28:00 AM

I imagine regular readers of GNXP are pretty familiar with Hardy-Weinberg Equilibrium (HWE): if a population is in HWE and we have a two allele locus with allele frequencies p and q, then the frequencies of the two homozygote genotypes and the heterozygote genotype are p*p, q*q, and 2*p*q, respectively. To maintain HWE over time, textbooks generally list five necessary conditions:

1. Random mating
2. Large (read: infinite) population size
3. No mutation
4. No gene flow
5. No natural selection

Obviously, these conditions aren't met in any population, but a lot of times we can say "eh, close enough". But it turns out the first condition is actually not necessary at all. That is, certain non-random mating patterns lead to equilibrium as well.

This was brought to my attention by this paper, which shows that, in a single round of non-random mating, HWE can be achieved in a population without a change in allele frequencies. In it, the author references another paper by Li, which derives several patterns of non-random mating that maintain HWE. So, as the author says, "thus Li's contribution and this one completely remove the necessity of random mating as a requirement for the establishment and maintainence of HWE".

The practial import of this? Probably close to null. But an interesting fact nonetheless, and a revealing look at how slightly incorrect (random mating is still sufficient for HWE, just not necessary) information can get passed through the generations.