A generalised treatment of the use of diallel crosses in quantitative inheritance

Abstract

IN problems of quantitative inheritance it has been customary to make genetic analysis of populations using covariances between relatives, the method outlined in the classical paper by Fisher (1918). Associated with this approach is the notion of partitioning the total genotypic variance into additive and non-additive genetic components. The importance of this treatment of quantitative inheritance to the genetical theory of natural selection has been made clear by Fisher (1930), and the practical applications of these concepts to plant and animal improvement have been increasingly realised. In recent years techniques involving "diallel crosses" have been used in problems which concern quantitative inheritance. The methods used and problems attacked by this technique have been diverse. Sprague and Tatum (1942), Henderson (1948, 1952), and Griffing (i) have defined and applied the notions of general and specific combining ability to plant and animal experimental material using a variety of diallel crossing methods, but without an exact generalised genetic interpretation of the combining ability effects and variances. Hull (1946, 1952), Griffing (1950), Jinks (i4) and Hayman (I9Ma, i954b), again using diallel crossing systems, have given procedures for estimating other genetic parameters in terms of restricted gene models.