In the genetic study of a particular trait it is common practice to summarize the data by stating the frequencies with which the trait occurs among the various types of relatives of probands. Thus we find reported in the literature the proportion of sibs, parents, first cousins, etc., of probands who are affected with the trait. One method of analysis is then to consider the question, under a variety of genetic models,‘What is the probability that a relative of a proband be affected?’A comparison of these expected probabilities of being affected with the reported empirical proportions will then give a clue as to which genetic hypothesis is the most appropriate.

Li & Sacks (1954) introduced three basic stochastic matrices for the purpose of deriving the joint distribution and correlation between relatives, appropriate for monozygotic twins, children (or parents) and unrelated individuals respectively. These same matrices and others of a similar nature can be used to answer the question posed above. Each of these matrices has dimensions k x k, where Ic is the number of genotypes involved in the particular genetic hypothesis. For example, if the trait is due to the segregation of two alleles at one locus, k= 3; if three alleles at one locus are involved, k= 6. For two alleles at one autosomal locus, the 3 x 3 matrices for monozygotic twins, children (or parents) and unrelated individuals respectively are given by Li and Sacks as