Is Fisher's model necessary for the theory of population improvement?

Summary It is shown here that genetic advance in one cycle of recurrent selection can be formulated directly in terms of covariances between relatives by application of the general statistical principle of linear prediction. For practical use of such formulae it is necessary to estimate the corresponding covariance between relatives from the mating design used. With General Combining Ability selection such estimation is direct. For other types of selection, it is necessary to derive associated covariances from other types of covariances but it is not necessary to use classical results of covariances between relatives in terms of genetic effects. Indeed, covariances can be derived without factorial decomposition of the genetic effects at one locus, i.e., without the concept of additivity and dominance. This approach allows a simple derivation of the genetic advance after n cycles of selection, followed by m generations of intercrossing, with a minimum of assumptions.