Abstract
Identity by descent (IBD) sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history. In this paper we provide a framework to estimate IBD sharing for a demographic model called two-population model with migration. We adopt the structured coalescent theory and use a continuous-time Markov jump process {X(t), t ≥ 0} to describe the genealogical process in such model. Then we apply Kolmogorov backward equation to calculate the distribution of coalescence time and develop a formula for estimating the IBD sharing. The simulation studies show that our method to estimate IBD sharing for this demographic model is robust and accurate.
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References
Browning, B.L., Browning, S.R. A fast, powerful method for detecting identity by descent. Am. J. Hum. Genet., 88(2): 173–182 (2011)
Browning, S.R., Browning, B.L. Accurate Non-parametric Estimation of Recent Effective Population Size from Segments of Identity by Descent. Am. J. Hum. Genet., 97(3): 404–418 (2015)
Browning, S.R., Browning, B.L. High-resolution detection of identity by descent in unrelated individuals. Am. J. Hum. Genet., 86(4): 526–539 (2010)
Durrett, R. Probability models for DNA sequence evolution. Springer Science and Business Media, 2008
Feller, W. An Introduction to Probability Theory, Vol. I, II. John Willey and Sons, 1968
Gusev, A., et al. Whole population, genome-wide mapping of hidden relatedness. Genome Res, 19(2): 318–326 (2009)
Hudson, R.R. Generating samples under a Wright-Fisher neutral model of genetic variation. Bioinformatics, 18(2): 337–338 (2002)
Moltke, I., Albrechtsen, A., Hansen, T.V., Nielsen, F.C., Nielsen, R. A method for detecting IBD regions simultaneously in multiple individuals-with applications to disease genetics. Genome. Res., 21(7): 1168–1180 (2011)
Ni, X., Guo, W., Yuan, K., Yang, X., Ma, Z., Xu, S., Zhang, S. A Probabilistic Method for Estimating the Sharing of Identity by Descent for Populations with Migration. IEEE ACM T. Comput. Bi., 13(2), 281–290 (2016)
Notohara, M. The coalescent and the genealogical process in geographically structured population. J. Math. Biol, 29(1): 59–75 (1990)
Palamara, P.F., Lencz, T., Darvasi, A., Pe’er, I. Length distributions of identity by descent reveal fine-scale demographic history. Am. J. Hum. Genet., 91(5): 809–822 (2012)
Palamara, P.F., Pe’er, I. Inference of historical migration rates via haplotype sharing. Bioinformatics, 29(13): i180–i188 (2013)
Purcell, S. et al. A tool set for whole-genome association and population-based linkage analyses. Am. J. Hum. Genet., 81(3): 559–575 (2007)
Acknowledgments
We thank Kai Yuan, Xiong Yang, Zhi-Ming Ma, Shuhua Xu, and Shihua Zhang for pleasant collaboration in our previous work[9] and for allowing us to use some idea of [9] to develop this work. In particular, the revised ms simulator (ms-IBD) introduced in [9] was employed for the simulation in this paper. We are grateful to Zhi-Ming Ma for his guidance and helpful discussions.
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This paper is supported by the Fundamental Research Funds for the Central Universities (2020RC001).
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Chen, X., Guo, W. & Ni, Xm. Markov Jump Processes in Estimating Sharing of Identity by Descent. Acta Math. Appl. Sin. Engl. Ser. 37, 183–191 (2021). https://doi.org/10.1007/s10255-021-0989-9
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DOI: https://doi.org/10.1007/s10255-021-0989-9