A non-zero variance of Tajima's estimator for two sequences even for infinitely many unlinked loci

作者：King Leandra; Wakeley John; Carmi Shai^*

来源：Theoretical Population Biology, 2018, 122: 22-29.

DOI：10.1016/j.tpb.2017.03.002

• Coalescent theory
• Recombination
• Heterozygosity
• Effective population size
• Pedigrees
• Genealogies

The population-scaled mutation rate, theta, 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, the variance of Tajima's estimator ((theta) over cap), which is the average number of pairwise differences, does not vanish even as n -> infinity. The non-zero variance of (theta) over cap results from a (weak) correlation between coalescence times even at unlinked loci, which, in turn, is due to the underlying fixed pedigree shared by gene genealogies at all loci. 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 describe is small (Var [(theta) over cap] /theta(2) approximate to O (N-e(-1))), it is important to recognize this feature of statistical population genetics, which runs counter to commonly held notions about unlinked loci.

• 出版日期2018-7