Consider a two locus two allele model in which the influence of epistatic
interaction on additive genetic effects is to be measured. The two loci are
called A and B, with 
and 
being the two alleles at the A locus and
analogously for the B locus. The genotypic value of the 
genotype
is written as 
. We denote the genotype specific physiological
effect (sensu Cheverud and Routman, 1995) of substituting 
by 
with 
, where the indices k and h denote the genotype at the B-locus.
This value is defined as 
of the difference in the genotypic values
and 
:
The genotypic value after gene substitution then is
Now let us consider how strongly the genetic background on the
B-locus affects the additive effect of the gene substitution at the
A-locus. For this purpose we declare the genotype 
as the reference
and compare the additive effect of 
in the 
and
background, i.e. we compare 
with 
.
The relative change of these values is the epistatic influence of a
gene substitution at the B-locus on the effect of a gene substitution at
the A-locus.
which is a dimension-less number. The genotype specific effect of a
substitution at the A-locus in the genetic background 
can be
written as
and the genotypic value of 
then is
This equation can be read as accounting first for the gene substitution
at the B-locus and then the gene substitution at the A-locus, who's effect
is now affected by the new genetic background at the B-locus:
Then substituting 
by 
leads to the above equation.
For symmetry reasons the genotypic value of 
can also be derived from the effect of a gene substitution at the
A-locus first and then a substitution at the B-locus. Now we have to take
into account the epistatic effects of the A locus on the B-locus.
with
Of course these two equations for 
have to yield the same value,
which implies a constraint on the epistatic coefficients
It is easy to show that this equation is always fulfilled. 
measures the
absolute epistatic effect: 
which is identical for both loci. This means that AxA interaction is a
strictly symmetrical relationship among loci, only the relative magnitude
of epistatic influence 
and 
can be different because the additive effects can be different.