Unbiased Estimation of Linkage Disequilibrium from Unphased Data

Linkage disequilibrium (LD) is used to infer evolutionary history, to identify genomic regions under selection, and to dissect the relationship between genotype and phenotype. In each case, we require accurate estimates of LD statistics from sequencing data. Unphased data present a challenge because multilocus haplotypes cannot be inferred exactly. Widely 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 unbiased statistics are particularly well suited to estimate effective population sizes from unlinked loci in small populations. We develop a simple inference pipeline and use it to refine estimates of recent effective population sizes of the threatened Channel Island Fox populations.