Table 1. Linkage disequilibrium and genetic diversity measures.
| Description | Definition of measuresa |
|---|---|
| 1. Single locus homozygosity (F) and heterozygosity (H)b | FA = ∑i pAi2, HA = 1 − FA |
| 2. Haplotype-specific homozygosity (HSF)c | FA/Bj = ∑i (fij / pBj)2, FB/Ai = ∑j (fij / pAi)2 |
| 3. Overall weighted HSF values FA/B and FB/A | FA/B = ∑j (FA/Bj) (pBj), FB/A = ∑i (FB/Ai) (pAi) |
| 4. Multiallelic ALD squared (overall asymmetric LD squared) | WA/B2 = (FA/B−FA) / (1−FA) = [∑i ∑j (Dij2 / pBj)] / (1−FA) WB/A2 = (FB/A−FB) / (1−FB) = [∑i ∑j (Dij2 / pAi)] / (1−FB) |
In all cases, ∑i indicates summation over all i = 1, 2, …, kA, and similarly ∑j over all j = 1, 2, …, kB, where kA and kB are the number of alleles at the A and B loci, respectively, with ∑i pAi = 1, and ∑j pBj = 1. ∑i ∑j Dij = 0, ∑i Dij = 0, ∑j Dij = 0, ∑i ∑j fij = 1, ∑j fij = pAi, ∑i fij = pBj. For biallelic data: D11 = −D12 = −D21 = D22 = D. Alternate expressions are given in the Appendix along with biallelic results.
The values of FA and HA (FA + HA = 1) are those expected under Hardy–Weinberg proportions.
The HSFA/Bj values are the extension of the single-locus FA values but now restricted to haplotypes containing the allele Bj (similarly for HSFB/Ai). Haplotype-specific heterozygosity values are HSHA/Bj = 1–HSFA/Bj, and HSHB/Ai = 1–HSFB/Ai.