Accounting for pseudo-replication of Linkage Disequilibrium for contemporary Ne estimation

The Linkage Disequilibrium (LD) of unlinked loci can be used to estimate contemporary effective population size (Ne) of one to a few generations ago. In genomic datasets loci on different chromosomes are considered unlinked, but there are many more pairs of unlinked loci than there are independent pairs of chromosomes, resulting to confidence intervals (C.I.) being too narrow if the non-independence is not taken into account. Simulations were run to investigate the correlation structure among LD of unlinked loci, which can be expressed by the LD of loci along the same chromosomes, based on a discovery of a novel Random Probe LD estimator. We classify the correlation into two categories: overlapping of loci and disjoint pairs. The former is induced from the same locus being considered twice and is the stronger form of correlation. These correlations feed into {rho}, a parameter to quantify the degree of pseudo-replication in a dataset, and further a correction formula from which C.I. can be properly inferred. We demonstrate the use of our method via an analysis of genomic data from the malaria-transmitting Anopheles gambiae s.s mosquitoes. Apart from the point and C.I. estimates, we find that Var((r^2 ) ) is inflated by about 550 times due to pseudo-replication, highlighting the danger of not handling genetic correlation properly.