The univariate breeders equation is defined as,
$\ R = h^2 s$
where $\ R $ is the response, $\ h^2 $ is the heritability (additive genetic variation), $\ s $ is the selection differential. The multivariate equation is similar to this in principle but includes a multiple trait variance-covariance matrix and multiple selection differentials.
Essentially the breeders equation tells us how strong the response to selection will be as a result of the additive genetic variance within a trait (and between traits in the multivariate) and the selection applied to that variation ($\ s = cov (w,x) $ = the covariance between fitness ($w$) and the trait $x$).
For example, in trait $x$, $s$ = 0.8 and $h^2$ = 0.5 the value of the response for $x$ is $R$ = 0.4. Compared to another trait, $y$, where $s$ = 0.8 and $h^2$ = 0.1 and thus $R$ = 0.08.
My question is, if we look at a trait in a population, measure it's population mean and define $h^2$ and $s$ values, can we then predict the change in the population? IE. can we predict (with the values of $s, h^2$ and the population mean) what the mean population mean trait will be in the next generation directly from the result of the breeders equation? Does the value of $R$ give us anything of use?
Following from the example above, I examine a trait (wing length in chickens) and find the mean to be 24 cm. I select birds to start my next generation in a way that causes $s$ = 0.8. The additive genetic variance for the wing length is quite high, $h^2$ = 0.5. The predicted response is $R$ = 0.8 x 0.5 = 0.4. What does this tell me about the next generation?