TY - JOUR T1 - A non-zero variance of Tajima’s estimator for two sequences even for infinitely many unlinked loci JF - bioRxiv DO - 10.1101/069989 SP - 069989 AU - Léandra King AU - John Wakeley AU - Shai Carmi Y1 - 2016/01/01 UR - http://biorxiv.org/content/early/2016/08/17/069989.abstract N2 - The population-scaled mutation rate, θ, is informative on the effective population size and is thus widely used in population genetics. We show that for two sequences and n unlinked loci, Tajima’s estimator (), which is the average number of pairwise differences, is not consistent and therefore its variance does not vanish even as n → ∞. The non-zero variance of results from a (weak) correlation between coalescence times even at unlinked loci, which, in turn, is due to the underlying fixed pedigree shared by all genealogies. We derive the correlation coefficient under a diploid, discrete-time, Wright-Fisher model, and we also derive a simple, closed-form lower bound. We also obtain empirical estimates of the correlation of coalescence times under demographic models inspired by large-scale human genealogies. While the effect we de scribe is small , it is important to recognize this feature of statistical population genetics, which runs counter to commonly held notions about unlinked loci. ER -