4.10 Measuring LD with \(r^2\)

\(\mathbf{r^2}\) is the most common statistic for measuring LD. Its value ranges from [0, 1], where 1 indicates maximum LD.

\[ r^2 = \frac{D^2}{p_1 (1-p_1) p_2 (1-p_2)} \]

Although it looks similar to the formulas for \(D\) and \(D'\), \(r^2\) is actually derived from the correlation coefficient of the frequencies of SNP1 and SNP2, and has a slightly different interpretation:

\(D\) and \(D'\) measure whether recombination has occurred between two alleles
\(r^2\) measures how well we can predict the allele at one locus if given the allele at the other locus

Calculate \(r^2\) for our two SNPs of interest.

r2 <- D^2 / (p1*(1-p1)*p2*(1-p2))
r2

## [1] 0.3773631

\(r^2 = 0.38\), indicating that these SNPs are in moderate LD.