TwoLocus Likelihoods under Variable Population Size and FineScale Recombination Rate Estimation
Abstract
Twolocus sampling probabilities have played a central role in devising an efficient composite likelihood method for estimating finescale recombination rates. Due to mathematical and computational challenges, these sampling probabilities are typically computed under the unrealistic assumption of a constant population size, and simulation studies have shown that resulting recombination rate estimates can be severely biased in certain cases of historical population size changes. To alleviate this problem, we develop here new methods to compute the sampling probability for variable population size functions that are piecewise constant. Our main theoretical result, implemented in a new software package called LDpop, is a novel formula for the sampling probability that can be evaluated by numerically exponentiating a large but sparse matrix. This formula can handle moderate sample sizes ($n \leq 50$) and demographic size histories with a large number of epochs ($\mathcal{D} \geq 64$). In addition, LDpop implements an approximate formula for the sampling probability that is reasonably accurate and scales to hundreds in sample size ($n \geq 256$). Finally, LDpop includes an importance sampler for the posterior distribution of twolocus genealogies, based on a new result for the optimal proposal distribution in the variablesize setting. Using our methods, we study how a sharp population bottleneck followed by rapid growth affects the correlation between partially linked sites. Then, through an extensive simulation study, we show that accounting for population size changes under such a demographic model leads to substantial improvements in finescale recombination rate estimation. LDpop is freely available for download at https://github.com/popgenmethods/ldpop
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.06017
 Bibcode:
 2015arXiv151006017K
 Keywords:

 Quantitative Biology  Populations and Evolution;
 Mathematics  Probability
 EPrint:
 32 pages, 13 figures