Unbiased estimation of linkage disequilibrium from unphased data

Linkage disequilibrium is used to infer evolutionary history and to identify regions under selection or associated with a given trait. In each case, we require accurate estimates of linkage disequilibrium from sequencing data. Unphased data presents a challenge because the co-occurrence of alleles at different loci is ambiguous. Commonly used estimators for the common statistics r 2 and D 2 exhibit large and variable upward biases that complicate interpretation and comparison across cohorts. Here, we show how to find unbiased estimators for a wide range of two-locus statistics, including D 2 , for both single and multiple randomly mating populations. These provide accurate estimates over three orders of magnitude in LD. We also use these estimators to construct an estimator for r 2 that is less biased than commonly used estimators, but nevertheless argue for using rather than r 2 for population size estimates.