The linkage detection problem.

Linkage data in man are usually analysed on families lacking a full set of grandparents on the assumption that there is one locus relating to an abnormal phenotype, the test locus. The basic problems of establishing linkage of this locus to another locus, the marker locus, with a defined likelihood and of estimating the recombination fraction were resolved by Morton (1955). However, the likelihood ratio derived after estimating the most likely recombination fraction is widely misunderstood to be a direct measure of the likelihood of linkage while the bias of estimates conditional on some likelihood criterion derived from the same data is usually ignored. Since data are limited this tolerance of excessive confidence in detecting linkages and a consistent tendency to underestimate recombination fractions is justified but the expected errors are not small and they are readily magnified when multiple loci are involved. Multiple markers provide further opportunities for detecting false linkages although the corrections required are known. The problems imposed by multiple loci at which mutations lead to a common phenotype have so far had little consideration. As most proteins are multimers whose units are not necessarily coded for by neighbouring loci, and as disturbances to any of several enzymes acting in series may lead to similar consequences, the assumption of a one-to-one relationship between a locus and a phenotype will usually be wrong.