Bounds and normalization of the composite linkage disequilibrium coefficient

The composite linkage disequilibrium (LD) measure is often calculated for two-locus genotypic data, especially when coupling and repulsion double heterozygotes cannot be distinguished. This measure was reported to have good statistical properties and was suggested for routine testing of LD, regardless of Hardy-Weinberg equilibrium at either of two loci. However, the bounds for this measure have not been yet reported. These bounds are derived here as functions of one-locus genotype or allele frequencies. They provide standardized measures of composite linkage disequilibrium, defined as the proportion of its maximum attainable value, given observed allele or genotype frequencies.