The solution surface of the Li-Stephens haplotype copying model

Algorithms for Molecular Biology

Research

Yifan Jin¹  Jonathan Terhorst¹ 

[1] Department of Statistics, University of Michigan, 1085 South University Avenue, 48103, Ann Arbor, MI, USA;

关键词: Li-Stephens model;    Haplotype copying model;    Solution path;   

DOI  :  10.1186/s13015-023-00237-z

 received in 2023-03-29, accepted in 2023-07-30,  发布年份 2023

来源: Springer

【 摘 要 】

The Li-Stephens (LS) haplotype copying model forms the basis of a number of important statistical inference procedures in genetics. LS is a probabilistic generative model which supposes that a sampled chromosome is an imperfect mosaic of other chromosomes found in a population. In the frequentist setting which is the focus of this paper, the output of LS is a “copying path” through chromosome space. The behavior of LS depends crucially on two user-specified parameters, θ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta $$\end{document} and ρ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho $$\end{document}, which are respectively interpreted as the rates of mutation and recombination. However, because LS is not based on a realistic model of ancestry, the precise connection between these parameters and the biological phenomena they represent is unclear. Here, we offer an alternative perspective, which considers θ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta $$\end{document} and ρ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho $$\end{document} as tuning parameters, and seeks to understand their impact on the LS output. We derive an algorithm which, for a given dataset, efficiently partitions the (θ,ρ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\theta ,\rho )$$\end{document} plane into regions where the output of the algorithm is constant, thereby enumerating all possible solutions to the LS model in one go. We extend this approach to the “diploid LS” model commonly used for phasing. We demonstrate the usefulness of our method by studying the effects of changing θ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta $$\end{document} and ρ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho $$\end{document} when using LS for common bioinformatic tasks. Our findings indicate that using the conventional (i.e., population-scaled) values for θ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta $$\end{document} and ρ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho $$\end{document} produces near optimal results for imputation, but may systematically inflate switch error in the case of phasing diploid genotypes.

【 授权许可】

CC BY   
© BioMed Central Ltd., part of Springer Nature 2023

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