## Abstract

The squared correlation coefficient r^{2} (sometimes denoted Δ^{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 σ_{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 ρ approaches ∞, it is shown rigorously that the asymptotic behavior of E [r^{2}] is given by 1 / ρ + O (ρ^{- 2}), which, incidentally, is the same as that of σ_{d}^{2}. A computer software that computes E [r^{2}] numerically is available upon request.

Original language | English (US) |
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Pages (from-to) | 49-60 |

Number of pages | 12 |

Journal | Theoretical Population Biology |

Volume | 71 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2007 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics

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