Let 
be the genotypic value of the genotype comprised of gametes
i and j, and let 
be the average effect of a gamete i on
character 
, and finally let 
be the frequency of this gamete.
Then, under random mating, the mean genotypic value of character 1,
, is
With additive
effects, the genotypic values are simply the sum of the gametic effects.
Consequently, the mean genotypic value is two times the mean gametic effect
where
is a gametic effect on character 1.
Hence, the rate of change of the character mean of 
is twice the rate
of change of the mean gametic effect
where the rate of change in the gamete frequencies is given by
In this equation 
is the mean fitness of the gamete i, 
the mean fitness of the population and 
the increase or decrease of gamete frequency caused by recombination. The rate of evolution then
becomes
With additive effects the second term on the right hand side is always zero, because the re-distribution of alleles caused by recombination alone will not change the mean value of the character. Expanding the first term leads to
This is the 'seconday theorem' of Robertson (1966). The above derivation shows that it is exact for additive characters. Applying this formula to the fitness function of the corridor model, one obtains
An analogous formula
holds for discrete generations. The first term on the right hand side is
the classical result about the response to directional natural selection
(Lande, 1976). The second term concerns the interaction between evolution
of the first character and fitness effects of the second. It corresponds
to the term 
in Turelli's two character equation (Turelli, 1988a).
Note that this term is not the correlated selection response, as will be
shown below. The precise meaning of this term can only be explicated in
the context of an explicitly genetic model. It will be shown below, that
the term 
describes the effect of
stabilizing selection on the genetic variance of the second character.
This variance is linked via pleiotropic effects to the evolution of the
first character.