A numerical example

For example, suppose we have two subpopulations of green lacewings, one of which occurs in forests the other of which occurs in adjacent meadows. Suppose further that within each subpopulation mating occurs completely at random, but that there is no mating between forest and meadow individuals. Suppose we've determined allele frequencies in each population at a locus coding for phosglucoisomerase ($PGI$), which conveniently has only two alleles. The frequency of $A_1$ in the forest is 0.4 and in the meadow in 0.7. We can easily calculate the expected genotype frequencies within each population, namely

	$A_1A_1$	$A_1A_2$	$A_2A_2$
Forest	0.16	0.48	0.36
Meadow	0.49	0.42	0.09

Suppose, however, we were to consider a combined population consisting of 100 individuals from the forest subpopulation and 100 individuals from the meadow subpopulation. Then we'd get the following:¹

	$A_1A_1$	$A_1A_2$	$A_2A_2$
From forest	16	48	36
From meadow	49	42	9
Total	65	90	45

So the frequency of $A_1$ is $(2(65) + 90)/(2(65 + 90 + 45)) = 0.55$. Notice that this is just the average allele frequency in the two subpopulations, i.e., $(0.4 + 0.7)/2$. Since each subpopulation has genotypes in Hardy-Weinberg proportions, you might expect the combined population to have genotypes in Hardy-Weinberg proportions, but if you did you'd be wrong. Just look.

	$A_1A_1$	$A_1A_2$	$A_2A_2$
Expected (from $p=0.55$)	(0.3025)200	(0.4950)200	(0.2025)200
	60.5	99.0	40.5
Observed (from table above)	65	90	45

The expected and observed don't match, even though there is random mating within both subpopulations. They don't match because there isn't random mating involving the combined population. Forest lacewings choose mates at random from other forest lacewings, but they never mate with a meadow lacewing (and vice versa). Our sample includes two populations that don't mix. This is an example of what's know as the Wahlund effect [2].