Maximum Likelihood Calculation of Rh Gene Frequencies in Pacific Populations

Abstract

IN general, the calculation of maximum likelihood^1,2 estimates of gene frequencies requires the preliminary calculation of trial values, followed by the computation of corrections to the trial values, by a method which is essentially Newton's method of successive approximations for getting a root of an equation. In many Pacific populations (Gilbertese, Fijians, etc.), only four or five Rh types CDe/C (R ₁ R ₁), CDe/c (R ₁ r), CDE/c (R ₁ R ₂), cDE (R ₂), and occasionally a little cDe (R ₀) are present³, and the composition of the population can be explained by assuming that only three genes, R ₁, R ₂, and R ₀, are present. For such cases the maximum likelihood equations can be solved explicitly, and the best estimates of the gene frequencies obtained without any process of successive approximations. If we designate the frequencies of the five phenotypes, in the order just mentioned, as H̄ K̄ P̄ T̄ and Q̄, the solution of the maximum likelihood equations gives the following formulæ: