One limitation of the way I've described things so far is that
doesn't provide a convenient way to compare population
structure from different samples. can be much larger
if both alleles are about equally common in the whole sample than if
one occurs at a mean frequency of 0.99 and the other at a frequency of
0.01. Moreover, if you stare at equations (4)-(6)
for a while, you begin to realize that they look a lot like some
equations we've already
encountered.
Namely, if we were to define ^{8} as
, then we could
rewrite equations (4)-(6) as

And it's not even completely artificial to define the way I did. After all, the effect of geographic structure is to cause matings to occur among genetically similar individuals. It's rather like inbreeding. Moreover, the extent to which this local mating matters depends on the extent to which populations differ from one another. is the maximum allele frequency variance possible, given the observed mean frequency. So one way of thinking about is that it measures the amount of allele frequency variance in a sample relative to the maximum possible.

There may, of course, be inbreeding within populations, too. But it's
easy to incorporate this into the framework, too.^{10} Let be the actual
heterozygosity in individuals within subpopulations, be the
expected heterozygosity within subpopulations assuming Hardy-Weinberg
within populations, and be the expected heterozygosity in the
combined population assuming Hardy-Weinberg over the whole
sample.^{11} Then thinking of as a measure of departure
from Hardy-Weinberg and assuming that all populations depart from
Hardy-Weinberg to the same degree, i.e., that they all have the same
, we can define

Let's fiddle with that a bit.

where is the inbreeding coefficient within populations, i.e., , and has the same definition as before.