Analytic computation of the expectation of the linkage disequilibrium coefficient r2

Yun S. Song, Jun S. Song

Research output: Contribution to journalArticlepeer-review


The squared correlation coefficient r2 (sometimes denoted Δ2) is a measure of linkage disequilibrium that is widely used, but computing its expectation E [r2] in the population has remained an intriguing open problem. The expectation E [r2] is often approximated by the standard linkage deviation σd2, which is a ratio of two expectations amenable to analytic computation. In this paper, a method of computing the population-wide E [r2] 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 ρ approaches ∞, it is shown rigorously that the asymptotic behavior of E [r2] is given by 1 / ρ + O (ρ- 2), which, incidentally, is the same as that of σd2. A computer software that computes E [r2] numerically is available upon request.

Original languageEnglish (US)
Pages (from-to)49-60
Number of pages12
JournalTheoretical Population Biology
Issue number1
StatePublished - Feb 2007
Externally publishedYes


  • Diffusion approximation
  • Expectation
  • Genetic drift
  • Linkage disequilibrium
  • Recombination
  • Recurrent mutation
  • Squared correlation coefficient

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Ecology, Evolution, Behavior and Systematics


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