THE ESTIMATION OF GENE FREQUENCIES IN A RANDOM‐MATING POPULATION

1. The estimation of gene frequencies in a population is an important problem in human genetics and anthropology, especially where blood groups are concerned. Much work has already been done on this problem, notably by W. L. Stevens (1938), R. A. Fisher (1940, 1946), C. W. Cotterman (1947), D. J. Finney (1948a, b), W. C. Boyd (1954a, b ) , and others. Here we give a general procedure applicable (under very general conditions) both to samples of unrelated individuals and to families. This method is applied to data on blood groups collected from villages near the mouth of the River Po, in northern Italy, in the course of an investigation on microcythaemia (Bianco, Ceppellini, Silvestroni & Siniscalco, 1954). Experience shows that this new method of computation is reasonably rapid, except in the case of a rare, or fairly rare, recessive gene, or when such a gene is present in a series of alleles. It may also become laborious when there are complicated families and a system of several alleles; in this case, however, it seems possible to simplify the calculations, though with some sacrifice of information. Of course, in particular cases it may not be so rapid as methods specially designed for the case in question, as for example, Finney’s (1948a, b ) methods when there are only two alleles concerned and the families contain at most two generations. The new method will be shown to be equivalent to maximum likelihood, and therefore fully efficient in the statistical sense. 2. We assume that the population under investigation is large, with random mating, and without difference of fitness between the different genotypes, or any other form of selection. Thus the Hardy-Weinberg rule will hold, and the gene frequencies will not change from one generation to the next. There is assumed to be complete manifestation, so that the observed phenotypes depend only on the genotypes, and not on environmental conditions. It is well known that these assumptions hold remarkably well for most blood groups and most populations, though slight deviations will be introduced by inbreeding and by incompatibility between foetus and mother. We must also assume that. the sample chosen is not biased with regard to the character whose frequency is to be estimated. Thus the families from the Po delta were selected by the presence of microcythaemia in one or both parents. Since so far no association has been found between microcythaemia and the blood groups, except possibly for a linkage with Lewis, and also possibly with the secretor character (Bianco et al. 1954), it seems reasonable to consider this as a random sample in so far as the blood groups are concerned. Of course a linkage will not of itself introduce any bias in a sample of completely unrelated families. In the case of the Italian data the populations concerned are small, and the families are accordingly related in a complicated manner. This will accordingly influence the estimates, though it will have the effect rather of slightly increasing their standard error than of introducing a bias in the estimated frequencies themselves; this caution must be borne in mind in interpreting the results given below.