A restriction on the space of genetic relationships

It was pointed out by Trustrum (1961) that even for non-inbred pairs of relatives it is possible for all four cross-parental kinship coefficients to be non-zero, and hence that the expression often assumed for the correlation between such relatives is not completely general. Van Aarde (1975) has recently made the same comment. We derive a restriction on the space of attainable Cotterman coefficients for a relationship between two arbitrary non-inbred relatives. This restriction implies that the form of the expression for the correlation is in fact general, although the components cannot always be interpreted as parental kinships.