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MultiWaver 2.0: modeling discrete and continuous gene flow to reconstruct complex population admixtures

European Journal of Human Geneticsvolume 27pages133139 (2019) | Download Citation


Our goal in developing the MultiWaver software series was to be able to infer population admixture history under various complex scenarios. The earlier version of MultiWaver considered only discrete admixture models. Here, we report a newly developed version, MultiWaver 2.0, that implements a more flexible framework and is capable of inferring multiple-wave admixture histories under both discrete and continuous admixture models. MultiWaver 2.0 can automatically select an optimal admixture model based on the length distribution of ancestral tracks of chromosomes, and the program can estimate the corresponding parameters under the selected model. Specifically, for discrete admixture models, we used a likelihood ratio test (LRT) to determine the optimal discrete model and an expectation–maximization algorithm to estimate the parameters. In addition, according to the principles of the Bayesian Information Criterion (BIC), we compared the optimal discrete model with several continuous admixture models. In MultiWaver 2.0, we also applied a bootstrapping technique to provide levels of support for the chosen model and the confidence interval (CI) of the estimations of admixture time. Simulation studies validated the reliability and effectiveness of our method. Finally, the program performed well when applied to real datasets of typical admixed populations, such as African Americans, Uyghurs, and Hazaras.

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  1. 1.

    Yuan K, Zhou Y, Ni X, Wang Y, Liu C, Xu S. Models, methods and tools for ancestry inference and admixture analysis. Quant Biol. 2017;5:236–50.

  2. 2.

    Xu S, Huang W, Qian J, Jin L. Analysis of genomic admixture in Uyghur and its implication in mapping strategy. Am J Hum Genet. 2008;82:883–94.

  3. 3.

    Patterson N, Moorjani P, Luo Y, Mallick S, Rohland N, Zhan Y et al. Ancient admixture in human history. Genetics. 2012; 192:1065–93.

  4. 4.

    Loh PR, Lipson M, Patterson N, Moorjani P, Pickrell JK, Reich D et al. Inferring admixture histories of human populations using linkage disequilibrium. Genetics. 2013;193:1233–54.

  5. 5.

    Pickrell JK, Patterson N, Loh PR, Lipson M, Berger B, Stoneking M et al. Ancient west Eurasian ancestry in southern and eastern Africa. Proc Natl Acad Sci U S A. 2014;111:2632–7.

  6. 6.

    Zhou Y, Yuan K, Yu Y, Ni X, Xie P, Xing E et al. Inference of multiple-wave population admixture by modeling decay of linkage disequilibrium with polynomial functions. Heredity. 2017;118:503–10.

  7. 7.

    Pugach I, Matveyev R, Wollstein A, Kayser M, Stoneking M. Dating the age of admixture via wavelet transform analysis of genome-wide data. Genome Biol. 2011;12:R19.

  8. 8.

    Jin W, Li R, Zhou Y, Xu S. Distribution of ancestral chromosomal segments in admixed genomes and its implications for inferring population history and admixture mapping. Eur J Hum Genet. 2014;22:930–7.

  9. 9.

    Jin W, Wang S, Wang H, Jin L, Xu S. Exploring population admixture dynamics via empirical and simulated genome-wide distribution of ancestral chromosomal segments. Am J Hum Genet. 2012;91:849–62.

  10. 10.

    Gravel S. Population genetics models of local ancestry. Genetics 2012;191:607–19.

  11. 11.

    Pool JE, Nielsen R. Inference of historical changes in migration rate from the lengths of migrant tracts. Genetics. 2009;181:711–9.

  12. 12.

    Hellenthal G, Busby GB, Band G, Wilson JF, Capelli C, Falush D. et al. A genetic atlas of human admixture history. Science. 2014;343:747–51.

  13. 13.

    Ni X, Yang X, Guo W, Yuan K, Zhou Y, Ma Z et al. Length Distribution of Ancestral Tracks under a General Admixture Model and Its Applications in Population History Inference. Sci Rep. 2016;6:20048.

  14. 14.

    Pugach I, Matveev R, Spitsyn V, Makarov S, Novgorodov I, Osakovsky V et al. The Complex Admixture History and Recent Southern Origins of Siberian Populations. Mol Biol Evol. 2016;33:1777–95.

  15. 15.

    Feng QD, Lu Y, Ni XM, Yuan K, Yang YJ, Yang X et al. Genetic History of Xinjiang's Uyghurs Suggests Bronze Age Multiple-Way Contacts in Eurasia. Mol Biol Evol. 2017;34:2572–82.

  16. 16.

    Kidd JM, Gravel S, Byrnes J, Moreno-Estrada A, Musharoff S, Bryc K et al. Population genetic inference from personal genome data: impact of ancestry and admixture on human genomic variation. Am J Hum Genet. 2012;91:660–71.

  17. 17.

    Baharian S, Barakatt M, Gignoux CR, Shringarpure S, Errington J, Blot WJ et al. The Great Migration and African-American Genomic Diversity. PLoS Genet. 2016;12:e1006059.

  18. 18.

    Moorjani P, Patterson N, Hirschhorn JN, Keinan A, Hao L, Atzmon G et al. The history of African gene flow into Southern Europeans, Levantines, and Jews. PLoS Genet. 2011;7:e1001373.

  19. 19.

    Price AL, Patterson N, Yu F, Cox DR, Waliszewska A, McDonald GJ et al. A genomewide admixture map for Latino populations. Am J Hum Genet. 2007;80:1024–36.

  20. 20.

    Tian C, Hinds DA, Shigeta R, Adler SG, Lee A, Pahl MV et al. A genomewide single-nucleotide-polymorphism panel for Mexican American admixture mapping. Am J Hum Genet. 2007;80:1014–23.

  21. 21.

    Wang S, Ray N, Rojas W, Parra MV, Bedoya G, Gallo C et al. Geographic patterns of genome admixture in Latin American Mestizos. PLoS Genet. 2008;4:e1000037.

  22. 22.

    Xu S, Jin L. A genome-wide analysis of admixture in Uyghurs and a high-density admixture map for disease-gene discovery. Am J Hum Genet. 2008;83:322–36.

  23. 23.

    Lipson M, Loh PR, Patterson N, Moorjani P, Ko YC, Stoneking M et al. Reconstructing Austronesian population history in Island Southeast Asia. Nat Commun. 2014;5:4689.

  24. 24.

    Bryc K, Durand EY, Macpherson JM, Reich D, Mountain JL. The genetic ancestry of African Americans, Latinos, and European Americans across the United States. Am J Hum Genet. 2015;96:37–53.

  25. 25.

    Ni X, Yuan K, Yang X, Feng Q, Guo W, Ma Z et al. Inference of multiple-wave admixtures by length distribution of ancestral tracks. Heredity. 2018:1.

  26. 26.

    International HapMap C, Altshuler DM, Gibbs RA, Peltonen L, Altshuler DM, Gibbs RA et al. Integrating common and rare genetic variation in diverse human populations. Nature. 2010;467:52–8.

  27. 27.

    Li JZ, Absher DM, Tang H, Southwick AM, Casto AM, Ramachandran S et al. Worldwide human relationships inferred from genome-wide patterns of variation. Science. 2008;319:1100–4.

  28. 28.

    Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;6:461–4.

  29. 29.

    Wit E, van den Heuvel E, Romeijn JW. ‘All models are wrong…’: an introduction to model uncertainty. Stat Neerl. 2012;66:217–36.

  30. 30.

    Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B.1977:39:1−38.

  31. 31.

    Yang X, Ni X, Zhou Y, Guo W, Yuan K, Xu S. AdmixSim: a forward-time simulator for various and complex scenarios of population admixture. bioRxiv. 2016:037135.

  32. 32.

    Delaneau O, Marchini J, Zagury JF. A linear complexity phasing method for thousands of genomes. Nat Methods. 2012;9:179–81.

  33. 33.

    Price AL, Tandon A, Patterson N, Barnes KC, Rafaels N, Ruczinski I et al. Sensitive detection of chromosomal segments of distinct ancestry in admixed populations. PLoS Genet. 2009;5:e1000519.

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This work was supported by the Strategic Priority Research Program (XDB13040100) and Key Research Program of Frontier Sciences (QYZDJ-SSW-SYS009) of the Chinese Academy of Sciences (CAS), the Fundamental Research Funds for the Central Universities (2017JBM071, 2017YJS197), the National Natural Science Foundation of China (NSFC) (91731303, 31771388, 11426237, and 31711530221), the National Science Fund for Distinguished Young Scholars (31525014), the Program of Shanghai Academic Research Leader (16XD1404700), the National Key Research and Development Program (2016YFC0906403), and Shanghai Municipal Science and Technology Major Project (2017SHZDZX01), the China Postdoctoral Science Foundation (2017M620595), the National Center for Mathematics and Interdisciplinary Sciences of CAS. SX also gratefully acknowledges the support of the National Program for Top-Notch Young Innovative Talents of the “Wanren Jihua” Project.

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Author notes

  1. These authors contributed equally: Xumin Ni, Kai Yuan.


  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, China

    • Xumin Ni
    •  & Zhiming Ma
  2. Chinese Academy of Sciences (CAS) Key Laboratory of Computational Biology, Max Planck Independent Research Group on Population Genomics, CAS-MPG Partner Institute for Computational Biology (PICB), Shanghai Institute of Nutrition and Health, Shanghai Institutes for Biological Sciences, CAS, Shanghai, 200031, China

    • Kai Yuan
    • , Chang Liu
    • , Qidi Feng
    • , Lei Tian
    •  & Shuhua Xu
  3. University of Chinese Academy of Sciences, Beijing, 100049, China

    • Kai Yuan
    • , Chang Liu
    • , Qidi Feng
    • , Lei Tian
    • , Zhiming Ma
    •  & Shuhua Xu
  4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    • Zhiming Ma
  5. School of Life Science and Technology, ShanghaiTech University, Shanghai, 201210, China

    • Shuhua Xu
  6. Center for Excellence in Animal Evolution and Genetics, Chinese Academy of Sciences, Kunming, 650223, China

    • Shuhua Xu
  7. Collaborative Innovation Center of Genetics and Development, Shanghai, 200438, China

    • Shuhua Xu


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The authors declare that they have no conflict of interest.

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Correspondence to Zhiming Ma or Shuhua Xu.

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