Prelude
to population structure: a thought experiment
In a single infinitely large population
not subject to selection, the expectation from the Hardy-Weinberg
theorem is that allele frequencies will remain
constant. When the infinite population is divided into a meta-population that comprises an
infinite number of smaller finite isolated
populations, genetic drift ensures that each
sub-population will eventually become fixed for one of the
alleles originally present. In a two-allele system with p
= (1-q) = f(A1) and (1-p)
= q = f(A2), a fraction (1-q)
of the sub-populations will become fixed for A1,
and a fraction q fixed for A2.
The overall allele frequencies are the same in the ideal
population and the meta-population, but the fraction of heterozygotes
in the meta-population goes to 2pq = 0 over
time. The deficiency of heterozygotes is thus a measure of population
structure.