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Frequencies of twelve ascus-types and arrangement of three genes from tetrad data.

Equations expressing the theoretical frequencies of twelve ascus-types in the tetrad analysis of a triply heterozygous diploid are described. Using these equations, a mapping procedure for a gene X, is proposed. The procedure requires that two genes, X and Y, of the same phenotype be heterozygous and that the map position of Y be known, and that another standard gene, Z, show an independent phenotype from X and Y. This procedure does not require the laborious allelism test of the segregants to determine the allelic 2:2 segregation in tetrads for the X and Y genes, which is indispensable for mapping by the conventional procedure. The exact placement of the X gene on a chromosome is possible by the chi2 minimization procedure in comparison with the expected frequencies of the six ascus-types or four spore-types deduced from the twelve expected ascus-types to give the optimal fit with the observed data.