Peer-review: Yes - Open Access: Yes|http://science.thomsonreuters.com/cgi-bin/jrnlst/jlresults.cgi?PC=MASTER&ISSN=0018-067X

A diallel cross consists of all possible crosses between a number of varieties. Reciprocal crosses, and the selfed parents, may or maynot be omitted. Such a set of crosses is obviously of interest to the plant breeder, but the information obtained may not be worth the trouble of making the cross. In this paper the utility of such crosses is considered, using data available in the literature together with some new figures from an i8x i8 cross in tomatoes. The statistical analysis of a diallel cross has been described byYates (1947). It consists of fitting additive main effects for parents, and their interactions in the individual crosses. Such a main effect is sometimes called" general combining ability "or" additive genetical component" while an interaction may be referred to as "specific combining ability" or "non-additive genetical component ". The word interaction is used here in its purely statistical sense of a departure from additivity. It should not be confused with any form of genetical interaction between postulated "genes ". The interactions are part of the statistical description of the data, being the ups and downs which remain when the main effects have been taken out. The analysis is similar to that of factorial experiments, and merely assumes that the contributions of male and female parents are equally important. The exact mode of inheritance is not specified, and the analysis would be as effective for, say, blending inheritance as for Mendelian. There is no need for the parents to be inbred (or to have a uniform coefficient of inbreeding). It may be objected that a plant breeder is interestedin, say, the top 2 per cent. of each progeny, and so wishes to estimate not the mean a but j-+2a where a is the standard deviation. This, however, involves an adjustment in practice and not in principle. Inmany cases there will not be enough replication to give useful estimates of a for each particular cross and heterogeneity of variance will be undetectable. Main effects can, however, be fitted for log variance or standard deviation in the same way as for progeny means. This factorial method of analysis is to be judged by its success in describing the data.

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