{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/two-locus-likelihoods-under-variable","title":"Two-Locus Likelihoods under Variable Population Size and Fine-Scale Recombination Rate Estimation","arxiv_id":"1510.06017","date":"2016-04-10","proceeding":null,"authors":[],"abstract":"Two-locus sampling probabilities have played a central role in devising an\nefficient composite likelihood method for estimating fine-scale recombination\nrates. Due to mathematical and computational challenges, these sampling\nprobabilities are typically computed under the unrealistic assumption of a\nconstant population size, and simulation studies have shown that resulting\nrecombination rate estimates can be severely biased in certain cases of\nhistorical population size changes. To alleviate this problem, we develop here\nnew methods to compute the sampling probability for variable population size\nfunctions that are piecewise constant. Our main theoretical result, implemented\nin a new software package called LDpop, is a novel formula for the sampling\nprobability that can be evaluated by numerically exponentiating a large but\nsparse matrix. This formula can handle moderate sample sizes ($n \\leq 50$) and\ndemographic size histories with a large number of epochs ($\\mathcal{D} \\geq\n64$). In addition, LDpop implements an approximate formula for the sampling\nprobability that is reasonably accurate and scales to hundreds in sample size\n($n \\geq 256$). Finally, LDpop includes an importance sampler for the posterior\ndistribution of two-locus genealogies, based on a new result for the optimal\nproposal distribution in the variable-size setting. Using our methods, we study\nhow a sharp population bottleneck followed by rapid growth affects the\ncorrelation between partially linked sites. Then, through an extensive\nsimulation study, we show that accounting for population size changes under\nsuch a demographic model leads to substantial improvements in fine-scale\nrecombination rate estimation. LDpop is freely available for download at\nhttps://github.com/popgenmethods/ldpop","url_abs":"http://arxiv.org/abs/1510.06017v2","url_pdf":"http://arxiv.org/pdf/1510.06017v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"two-locus-likelihoods-under-variable","repo_url":"https://github.com/popgenmethods/ldpop","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}