A general approach to the concept of varietal ability for synthetic varieties

Genetic effects for varietal value are defined at the level of the population of k-parent synthetic varieties. A simple expression for the total variance among synthetics arises directly from these definitions. A general expression for the covariance among related synthetics is given. Genetic effects are also defined in a completely general way so as to allow for any system of testing and used to derive an expression for the genetic advance in recurrent selection for varietal value. Covariances between relatives evaluated in the system of testing and in varietal combination are introduced, allowing a direct expression of the genetic advance in varietal development when parents are selected either individually or in groups. Some general implications for plant breeding are outlined.