Linkage Disequilibrium and r-squared

D=pAB−pA·pB compares the observed haplotype frequency with the frequency expected if the two alleles combined independently. D=0 means pAB equals the product of their marginal frequencies. This proves neither physical independence nor absence of linkage: recombination, population history and sample size affect the observed association. Alleles and haplotype phase must be clearly defined to calculate D. Define alleles, haplotype frequencies, population and estimation method. Small samples and uncertain phase can substantially distort r². Marker comparisons also require consistent variant coding and quality filters, given ascertainment, age structure and sequencing filters.

r² scales D² by the heterozygosities of both markers and equals the squared correlation of allele indicators. It ranges from 0 to 1 and describes how predictably one marker identifies the other. D instead retains direction and the absolute frequency deviation. r² is not D′; the measures answer different questions and respond differently to allele frequencies. High r² can help marker selection, but does not make a marker causal. Define alleles, haplotype frequencies, population and estimation method. Small samples and uncertain phase can substantially distort r². Marker comparisons also require consistent variant coding and quality filters, given ascertainment, age structure and sequencing filters.

Linkage disequilibrium is created and changed by recombination, drift, selection, mutation, migration, population mixture and sampling error. The same markers can therefore show different D and r² values across populations or cohorts. Rare alleles also constrain possible r² values. Report population, sample size, variants and phasing method. A single LD measure cannot establish a universal gene distance or causal effect. Define alleles, haplotype frequencies, population and estimation method. Small samples and uncertain phase can substantially distort r². Marker comparisons also require consistent variant coding and quality filters, given ascertainment, age structure and sequencing filters.

Reproduce the example calculation: Let pA=0.50, pB=0.40 and pAB=0.30. Linkage Disequilibrium and r-squared uses D = pAB−pA·pB; r² = D²/[pA(1−pA)pB(1−pB)]. In plain terms, d measures departure of two alleles from independent association; r-squared scales this association as a squared allele correlation. Unit check: Allele frequencies, D and r² are dimensionless; r² ranges from 0 to 1. Two biallelic loci with estimated haplotype frequencies; phase uncertainty and population mixture affect estimates. Values are comparable only when their definitions, denominators and periods match. Record these details next to the result so the reference group is clear. If the direction is implausible, check data preparation and the calculation basis before discussing biological causes.

A key limit of Linkage Disequilibrium and r-squared is this: Two biallelic loci with estimated haplotype frequencies; phase uncertainty and population mixture affect estimates. Do not use the metric without its reference; it is useful for Genetic mapping, marker selection and description of haplotype association in population-genetic datasets. D measures departure of two alleles from independent association; r-squared scales this association as a squared allele correlation. When comparing populations or experiments, check whether definitions, denominators and observation periods match. If the assumption is implausible, the result shows only what the simplified model calculates from its inputs; it is not a reliable estimate for the target population. State this limitation in the report, and do not infer a causal effect from the formula alone.