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Handbook of Statistical Bioinformatics pp 135–147Cite as

Mixture Tree Construction and Its Applications

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Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

A new method for building a gene tree from Single Nucleotide Polymorphism (SNP) data was developed by Chen and Lindsay (Biometrika 93(4):843–860, 2006). Called the mixture tree, it was based on an ancestral mixture model. The sieve parameter in the model plays the role of time in the evolutionary tree of the sequences. By varying the sieve parameter, one can create a hierarchical tree that estimates the population structure at each fixed backward point in time. In this chapter, we will review the model and then present an application to the clustering of the mitochondrial sequences to show that the approach performs well. A simulator that simulates real SNPs sequences with unknown ancestral history will be introduced. Using the simulator we will compare the mixture trees with true trees to evaluate how well the mixture tree method performs. Comparison with some existing methods including neighbor-joining method and maximum parsimony method will also be presented in this chapter.

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Acknowledgements

We thank National Science Foundation for the funding – Division of Mathematical Sciences 0714949 to Shu-Chuan Chen and Michael Rosenberg, and National Science Foundation – Division of Mathematical Sciences 0714839 to Bruce Lindsay. In addition, we also acknowledge the support of National Center for Theoretical Sciences (South), Taiwan.

Author information

Authors and Affiliations

  1. School of Math & Stat, Arizona State University, Tempe, U.S.A.

    Grace S. C. Chen & Mingze Li

  2. School of Life Sciences, Arizona State University, Tempe, U.S.A.

    Michael Rosenberg

  3. Department of Statistics, Penn State University, University Park, U.S.A.

    Bruce Lindsay

Authors
  1. Grace S. C. Chen
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  2. Mingze Li
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  3. Michael Rosenberg
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  4. Bruce Lindsay
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Corresponding author

Correspondence to Grace S. C. Chen .

Editor information

Editors and Affiliations

  1. , Institute of Statistics, National Chiao Tung University, Ta Hsueh Road 1001, Hsinchu, 30050, Taiwan, Taiwan R.O.C.

    Henry Horng-Shing Lu

  2. , Department of Empirical Inference, MPI for Intelligent Systems, Spemannstraße 38, Tübingen, 72076, Germany

    Bernhard Schölkopf

  3. School of Medicine, Dept. Epidemiology & Public Health, Yale University, College Street 60, New Haven, 06520, Connecticut, USA

    Hongyu Zhao

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Chen, G.S.C., Li, M., Rosenberg, M., Lindsay, B. (2011). Mixture Tree Construction and Its Applications. In: Lu, HS., Schölkopf, B., Zhao, H. (eds) Handbook of Statistical Bioinformatics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16345-6_7

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