The
Wahlund Effect
The
effect of population subdivision on genotypic frequencies was first
investigated
by S. Wahlund in 1928.The so-called
Wahlund Effect demonstrates the importance of population
structure
with respect to genetic variation.The
following account is drawn from Hedrick (1983), and a related account,
including the relationship to Wright's measure Fst,
is
found in Hartl (1988), p. 106-109.
Assume
that there are k demes...
Let
pi be the frequency of allele A in the ith deme
Let
qi be the frequency of allele a in the ith deme
The
mean allele frequency over all demes becomes:
 |
The
average frequencies of the three genotypes are:
 |
Now,
if the demes were merged into a single population at Castle - Hardy -
Weinberg
equilibrium, we would expect the frequencies of AA, Aa, and aa to be:
 |
respectively.
The
difference between the observed and expected frequencies is:
 |
 |
 |
 |
This
last term is the variance in the value of q (Vq) over the
demes.The
observed genotypic frequencies can now be written as:
 |
 |
 |
As
a result, the frequency of homozygotes is increased by Vq over what
would
be expected in a Castle - Hardy - Weinberg population.
The
following example will illustrate the phenomenon.Suppose
there are two demes:
_
q1
= 0.4 and q2 = 0.8, which means that q = 0.6
The
expected frequencies of AA, Aa, and aa are 0.16, 0.48, and 0.36.Even
if each deme is in Castle - Hardy - Weinberg equilibrium, however, the
average frequencies of these genotypes over the two demes are 0.2, 0.4,
and 0.4.The value of Vq
is 0.04.
_
The
effect of migration will be to make the values of p in each
deme
go to p, and the value of Vq will decline to 0.0.The
frequency of heterozygotes will increase.
Finally,
it should be noted that the effect of population subdivision will
result
in an excess of homozygotes if sampling is done across demes.This
will lead to the erroneous assumption that there is inbreeding in the
population,
when, in fact, each deme is in Castle - Hardy - Weinberg equilibrium.