Analytic computation of the expectation of the linkage disequilibrium coefficient r2

Theor Popul Biol. 2007 Feb;71(1):49-60. doi: 10.1016/j.tpb.2006.09.001. Epub 2006 Sep 23.


The squared correlation coefficient r(2) (sometimes denoted Delta(2)) is a measure of linkage disequilibrium that is widely used, but computing its expectation E[r(2)] in the population has remained an intriguing open problem. The expectation E[r(2)] is often approximated by the standard linkage deviation sigma(d)(2), which is a ratio of two expectations amenable to analytic computation. In this paper, a method of computing the population-wide E[r(2)] is introduced for a model with recurrent mutation, genetic drift and recombination. The approach is algebraic and is based on the diffusion process approximation. In the limit as the population-scaled recombination rate rho approaches infinity, it is shown rigorously that the asymptotic behavior of E[r(2)] is given by 1/rho+O(rho(-2)), which, incidentally, is the same as that of sigma(d)(2). A computer software that computes E[r(2)] numerically is available upon request.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Allelic Imbalance / genetics*
  • Genetic Drift*
  • Linkage Disequilibrium / genetics*
  • Models, Genetic
  • Recombination, Genetic*