Frequencies of reciprocally compatible single, three-way and double crosses as determined by the number of S-homozygotes, the number of lines per S-homozygote and the types of inheritance of incompatibility in cruciferous crops

Abstract

The low number of useful S-alleles in several species and varieties of cruciferous crops (Brassica, Raphanus) may hamper the set-up of a practical programme of hybrid breeding based on sporophytic one-locus incompatibility. Few S-alleles may considerably reduce the number of reciprocally compatible crosses and therefore restrict the possibilities of selection for combining ability and for suitable S-alleles. This problem is discussed in this article. General formulae are derived for calculating the maximum number of reciprocally compatible cross combinations for three types of crosses (singles, three-ways and doubles), four types of S-allele interactions (I, II, III, IV: table 1), different numbers of S-homozygotes (1,2.....n) and different numbers of genotypes per S-homozygote (equal: x; unequal: x1....k....xn).