The covariance of heterozygosity as a measure of linkage disequilibrium between blocks of linked and unlinked sites in Hapmap.

The covariance of heterozygosity serves as a measure of linkage disequilibrium (LD) between genes at two loci, although one that does not have as much information as a parameter such as r2. However, it may be extended to blocks of loci (single nucleotide polymorphisms, SNPs) along a chromosome. This has two advantages when searching for significant associations between different chromosomal regions. Calculations for a data set such as Hapmap are complicated by the large number of pairs of loci (SNPs) that need to be considered. For example, a search for significant associations between SNPs on different chromosomes involves around 1012 calculations for a single population. Furthermore, this may not be an efficient way of detecting associations since r2 values calculated from neighbouring pairs will not be independent of each other. The covariance of heterozygosity provides an average measure of association between blocks of any size, and reduces the number of calculations by a factor of b2, where b is the block size. Unlike the calculation of r2, the covariance of heterozygosity uses just diploid data and is not biased by sample size. Calculations using a block size of 50 have been used to look for associations in the Hapmap data set between regions within and between chromosomes. Within chromosomes, a signal is detected up to around 10 cM. No obviously significant associations have been detected between regions on different chromosomes, although there is a low level of association consistent with departures from random mating.