  The breeder's equation is a cornerstone of quantitative genetics and is
widely used in evolutionary modeling. The equation which reads R=h^{2}S relates
response to selection R (the mean phenotype of the progeny) to the selection
differential S (mean phenotype of selected parents) through a simple
proportionality relation. The validity of this relation however relies strongly
on the normal (Gaussian) distribution of parent's genotype which is an
unobservable quantity and cannot be ascertained. In contrast, we show here that
if the fitness (or selection) function is Gaussian, an alternative, exact
linear equation in the form of R'=j^{2}S' can be derived, regardless of the
parental genotype distribution. Here R' and S' stand for the mean phenotypic
lag behind the mean of the fitness function in the offspring and selected
populations. To demonstrate this relation, we derive the exact functional
relation between the mean phenotype in the selected and the offspring
population and deduce all cases that lead to a linear relation between these
quantities. These computations, which are confirmed by individual based
numerical simulations, generalize naturally to the multivariate Lande's
equation \Delta\mathbf{\bar{z}}=GP^{-1}\mathbf{S} .
