Number of Mating Types required for Balance in Multipoint Linkage Programmes

Abstract

IN two-point linkage work it is advantageous to use coupling and repulsion back-crosses in approximately equal numbers, for, with equal numbers of progeny, disturbances due to differential viability need not affect the estimation of the recombination fraction between the two loci. In fact, it is only possible to allow for differential viability in all the segregating phenotypes by this method of ‘balance’, and it may be shown that the estimation of the recombination fraction is most efficient when the balance is exact. The minimum requirement for balance is that the numbers of progeny from the coupling and repulsion back-crosses must be equal; in other contexts the definition of balance may be narrower, but it is used here as defined by this minimum requirement. This idea is just as fruitful in multi-point linkage work, but it is not necessary to make up matings using all the possible genotypes of multiple heterozygotes in order to ensure a set balanced for all pairs of loci. The present problem is to determine the minimum number of mating types needed for making up a balanced set for any given number of loci.