Inbreeding within a subpopulation is caused by the nonrandom mating of the members of that subpopulation, in that mating occurs more often than by chance alone, between closely related individuals. As closely related individuals will contain a large proportion of the same alleles due to common descent, their offspring will have a higher level of homozygosity, and conversely, a lower level of heterozygosity then expected. A within subpopulations F-statistic can be estimated from a ratio of the observed to expected heterozygosity where,
where 
is the average expected heterozygosity estimated from each
subpopulation by,
and 
is the average observed heterozygosity,
for k subpopulations.
Population substructure will also lead to inbreeding-like effects, i.e.
a reduction in observed heterozygosity when compared to expected. This
effect is known as Wahlunds' effect. This relationship
shows that as allele frequencies in two subpopulations deviate, the
average expected heterozygosity in those populations will always be
less than that expected from the pooled allele frequencies 
.
An among subpopulations F-statistic can be estimated from this ratio.
where
and 
is the frequency of the ith allele averaged over all
subpopulations. It should be noted that as allele frequencies deviate,
the difference in 
and 
will increase and 
will
therefore also serve as a measure of genetic distance among
subpopulations.
The measure of the correlation of alleles for the entire population is thus a combination of both the within and among subpopulation effects, and can be estimated from,
Nei (1987) further developed 
so that data from many loci could
be combined. This estimate 
is calculated from
where 
and 
are averaged across all loci and then used
to estimate 
.
where 
is the frequency of the ith allele in the jth
population.
Weir and Cockerham (1984) have developed a variance based method for
estimation of F- statistics. 
can be thought of as the
correlation of pairs of alleles between individuals within a
subpopulation. If there is population structure then alleles found
within a subpopulation should be correlated (found more often together
than expected) with respect to all the alleles found in the entire
population. Weir and Cockerham (1984) describe a measure 
which
estimates the correlation of pairs of alleles between individuals
within a subpopulation through an analysis of the partitioning of
variance of allele frequency.
The total variance of allele frequency within a population 
is
equal to the sum of its components; between subpopulation variance in
allele frequency 
, between individuals within subpopulation
variance in allele frequency 
, and the between gametes within
individuals variance in allele frequency 
, i.e.
Given this 
can be estimated from
where the variances in allele frequency are summed over all alleles
i and all loci u. The precise formulae for the estimations of
the component of variance can be found in Weir and Cockerham (1984).
In the special case when both the sample sizes n and the number of
subpopulations sampled 
are very large, the estimation of 
can be reduced to
where 
and 
are the observed allele frequency and sample size
of the jth population, and 
and 
are the average allele
frequency and sample size for the entire population. From this
equation it can be seen that as the allele frequencies in the
subpopulation diverge, the value of the numerator will increase, and
the value of 
will approach 1.
