Mixture Tree Construction and Its Applications

  • Grace S. C. Chen
  • Mingze Li
  • Michael Rosenberg
  • Bruce Lindsay
Part of the Springer Handbooks of Computational Statistics book series (SHCS)


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.


Maximum Parsimony Neighbor Join Maximum Parsimony Tree Minimum Evolution Mixture Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Grace S. C. Chen
    • 1
  • Mingze Li
    • 1
  • Michael Rosenberg
    • 2
  • Bruce Lindsay
    • 3
  1. 1.School of Math & StatArizona State UniversityTempeU.S.A.
  2. 2.School of Life SciencesArizona State UniversityTempeU.S.A.
  3. 3.Department of StatisticsPenn State UniversityUniversity ParkU.S.A.

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