Table 6:

Description, usages, and mathematical properties of five LD measures for biallelic loci.

Statistic	Description	Noted usages in the literature	Mathematical properties
|D′|	Normalization of |D| by its theoretical maximum value for a given set of allele frequencies	Detecting “complete” LD (where one of the four haplotypes is absent), an indication of whether recombination has occurred between the two loci [11]	|D′| varies linearly as a function of pAB (Figure 5) Upper bound of 1 for all allele frequencies Assuming a uniform distribution of pAB over the range of values it can take, the mean and variance of |D′| are both constant values (eqs. 19 and 33)
r2	Squared correlation coefficient measure between allelic indicator variables	Testing for independence between a pair of loci by a χ2 test [16] Association studies, where a mathematical relationship exists between r2 and the sample size needed to detect association between a marker and disease phenotype [16]	r2 varies quadratically as a function of pAB (Figure 5) Low upper bound and small range of values if MAF is low (Figure 2A) Mean maximum value varies considerably as a function of the allele frequency distribution (Figure 4)
|d|	Difference in the proportions of disease and normal alleles found on the same haplotype with a particular marker allele	Association mapping for rare diseases in which case-control sampling is employed [9]	|d| varies linearly as a function of pAB (Figure 5) Upper bound has an intermediate value; measure still has a considerable range even at low MAF (Figure 2B) Mean maximum value relatively stable as a function of the allele frequency distribution (Figure 4)
ρ	Probability that a haplotype chosen at random descends without recombination from a population of haplotypes that excludes one of the four possible haplotypes	Mapping of marker association and localization of disease loci [19]	Identical to |D′| in the octants in which it can be applied
$r^2/r_{\max }^2$	Normalization of r2 by its theoretical maximum value for a given set of allele frequencies	If a range that is independent of allele frequency is desired, but the measure still maintains some connection to r2 [20]	$r^2/r_{\max }^2$ varies quadratically as a function of pAB (Figure 5) Upper bound of 1 for all allele frequencies Assuming a uniform distribution of pAB over the range of values it can take, the mean and variance of $r^2/r_{\max }^2$ both depend only on the locus with the larger MAF (eqs. 22 and 39)