Identity-by-descent in large samples

Abstract

If two haplotypes share the same alleles for an extended gene tract, these haplotypes are likely to be derived identical-by-descent from a recent common ancestor. Identity-by-descent segment lengths are correlated via unobserved ancestral tree and recombination processes, which commonly presents challenges to the derivation of theoretical results in population genetics. We show that the proportion of detectable identity-by-descent segments around a locus is normally distributed when the sample size and the scaled population size are large. We generalize this central limit theorem to cover flexible demographic scenarios, multi-way identity-by-descent segments, and multivariate identity-by-descent rates. We use efficient simulations to study the distributional behavior of the detectable identity-by-descent rate. One consequence of non-normality in finite samples is that a genome-wide scan looking for excess identity-by-descent rates may be subject to anti-conservative control of family-wise error rates. HighlightsO_LIWe show the asymptotic normality of the detectable identity-by-descent rate, a mean of correlated binary random variables that arises in population genetics studies. C_LIO_LIWe generalize our main central limit theorem to cover scenarios of nonconstant population sizes, multi-way identity-by-descent segments, and identity-by-descent rates of multiple samples from the same population. C_LIO_LIIn enormous simulation studies, we use an efficient algorithm to characterize distributional properties of the detectable identity-by-descent rate. C_LI