An equal-tempered measure of linkage disequilibrium

Abstract

Linkage disequilibrium (LD), the association of alleles at two loci, is defined in multiple ways. Because LD measures depend on allele frequencies, it is difficult to compare LD values between populations or loci with different allele frequencies. Here, I consider a geometric interpretation of a commonly used LD measure $r^2$ which suggests a modification that is frequency-independent in the sense that equal evolutionary forces lead to the same effect at different frequencies. This new measure is a very simple expression that is known elsewhere as the Hamann coefficient and the G index of agreement; it is a linear transformation of the simple matching coefficient. I explore properties of this quantity in comparison with $D$ and $r^2$, and discuss its interpretation, advantages and disadvantages.