In this, the first of a series of communications on the application of the study of polymorphic enzyme and protein systems to gene location on a trisomic chromosome, the theoretical implications are considered. Mathematical models for the expected phenotype shift have been examined, and have been expanded to include a three‐allele locus and a three‐allele locus with one allele being of the ‘silent’ variety. Some modifications in the existing mathematical models were necessary due to possible failure of electrophoretic and immuno‐electrophoretic separations to differentiate between some heterozygote forms. The mathematical models have been applied to a series of hi‐allelic polymorphic systems and one tri‐allelic system to determine the minimum number of subjets with trisomy that would be required to establish the presence or absence of a phenotype shift. The additional use of the techniques for estimating the position of the gene with respect to the centromere, and estimating the timing of the non‐disjunction are discussed.
The application of Haldane's log ratio test (1956) involving the combining of the homozygous Corms is considered and applied to the phenotype data on the serum haptoglobins of 254 subjects with Down's syndrome and 853 mentally retarded control subjects.