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Wald Space for Phylogenetic Trees

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Geometric Science of Information (GSI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12829))

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Abstract

The recently introduced wald space models phylogenetic trees from an evolutionary perspective. We show that it is a stratified space and propose algorithms to compute geodesics. In application we compute a Fréchet mean of three trees of different topologies that is fully resolved, unlike in BHV-space. Both, preliminary results on geodesics and on means suggest that wald space features less stickiness than BHV-space, making it an alternative model for statistical investigations.

Acknowledging DFG HU 1575/7, DFG GK 2088, DFG SFB 1465 and the Niedersachsen Vorab of the Volkswagen Foundation.

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References

  • Arnaudon, M., Nielsen, F.: On approximating the Riemannian 1-center. Computational Geometry 46(1), 93–104 (2013)

    Article  MathSciNet  Google Scholar 

  • Barden, D., Le, H., Owen, M.: Central limit theorems for Fréchet means in the space of phylogenetic trees. Electron. J. Probab 18(25), 1–25 (2013)

    MATH  Google Scholar 

  • Barden, D., Le, H., Owen, M.: Limiting behaviour of Fréchet means in the space of phylogenetic trees. Annals of the Institute of Statistical Mathematics 70(1), 99–129 (2016). https://doi.org/10.1007/s10463-016-0582-9

  • Bačák, M.: Computing Medians and Means in Hadamard Spaces. SIAM Journal on Optimization 24(3), 1542–1566 (2014)

    Article  MathSciNet  Google Scholar 

  • Billera, L., Holmes, S., Vogtmann, K.: Geometry of the space of phylogenetic trees. Advances in Applied Mathematics 27(4), 733–767 (2001)

    Article  MathSciNet  Google Scholar 

  • Brown, D. G. and M. Owen (2018, May). Mean and Variance of Phylogenetic Trees. arXiv:1708.00294 [math, q-bio, stat]. arXiv: 1708.00294

  • Garba, M.K., Nye, T.M., Boys, R.J.: Probabilistic Distances Between Trees. Systematic Biology 67(2), 320–327 (2018)

    Article  Google Scholar 

  • Garba, M. K., Nye, T. M. W., Lueg, J., Huckemann, S. F.: Information geometry for phylogenetic trees. Journal of Mathematical Biology 82(3), 1–39 (2021). https://doi.org/10.1007/s00285-021-01553-x

  • Garba, M. K., T. M. W. Nye, J. Lueg, and S. F. Huckemann (2021). Information metrics for phylogenetic trees via distributions of discrete and continuous characters. In: Nielsen, F., Barbaresco, F. (Eds.) GSI 2021, LNCS 12829, pp. 701–709 (2021). https://doi.org/10.1007/978-3-030-80209-7_75

  • Hotz, T., Huckemann, S., Le, H., Marron, J.S., Mattingly, J., Miller, E., Nolen, J., Owen, M., Patrangenaru, V., Skwerer, S.: Sticky central limit theorems on open books. Annals of Applied Probability 23(6), 2238–2258 (2013)

    Article  MathSciNet  Google Scholar 

  • Huckemann, S., Mattingly, J.C., Miller, E., Nolen, J.: Sticky central limit theorems at isolated hyperbolic planar singularities. Electronic Journal of Probability 20(78), 1–34 (2015)

    MathSciNet  MATH  Google Scholar 

  • Lang, S.: Fundamentals of Differential Geometry. Graduate Texts in Mathematics. Springer-Verlag, New York (1999)

    Book  Google Scholar 

  • Lueg, J., T. Nye, M. Garba, and S. F. Huckemann (2021). Phylogenetic wald spaces. manuscript

    Google Scholar 

  • Miller, E., Owen, M., Provan, J.S.: July). Polyhedral computational geometry for averaging metric phylogenetic trees. Advances in Applied Mathematics 68, 51–91 (2015)

    Article  MathSciNet  Google Scholar 

  • Moulton, V., Steel, M.: Peeling phylogenetic ‘oranges’. Advances in Applied Mathematics 33(4), 710–727 (2004)

    Google Scholar 

  • Nye, T. M., X. Tang, G. Weyenberg, and Y. Yoshida (2016). Principal component analysis and the locus of the Fréchet mean in the space of phylogenetic trees. arXiv preprint arXiv:1609.03045

  • Owen, M.: Computing geodesic distances in tree space. SIAM Journal on Discrete Mathematics 25(4), 1506–1529 (2011)

    Article  MathSciNet  Google Scholar 

  • Rokas, A., B. L. Williams, N. King, and S. B. Carroll (2003, October). Genome-scale approaches to resolving incongruence in molecular phylogenies. Nature 425(6960), 798–804

    Google Scholar 

  • Schmidt, Frank R., Clausen, Michael, Cremers, Daniel: Shape Matching by Variational Computation of Geodesics on a Manifold. In: Franke, Katrin, Müller, Klaus-Robert., Nickolay, Bertram, Schäfer, Ralf (eds.) DAGM 2006. LNCS, vol. 4174, pp. 142–151. Springer, Heidelberg (2006). https://doi.org/10.1007/11861898_15

    Chapter  Google Scholar 

  • Shiers, N., Zwiernik, P., Aston, J.A., Smith, J.Q.: The correlation space of gaussian latent tree models and model selection without fitting. Biometrika 103(3), 531–545 (2016)

    Article  MathSciNet  Google Scholar 

  • Sturm, K.: Probability measures on metric spaces of nonpositive curvature. Contemporary mathematics 338, 357–390 (2003)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences, Georg-August-Universität, Göttingen, Germany

    Jonas Lueg & Stephan F. Huckemann

  2. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Maryam K. Garba

  3. School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, UK

    Tom M. W. Nye

Authors
  1. Jonas Lueg
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  2. Maryam K. Garba
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  3. Tom M. W. Nye
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  4. Stephan F. Huckemann
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Corresponding author

Correspondence to Jonas Lueg .

Editor information

Editors and Affiliations

  1. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  2. THALES Land & Air Systems, Meudon, France

    Frédéric Barbaresco

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Lueg, J., Garba, M.K., Nye, T.M.W., Huckemann, S.F. (2021). Wald Space for Phylogenetic Trees. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_76

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  • DOI: https://doi.org/10.1007/978-3-030-80209-7_76

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-80208-0

  • Online ISBN: 978-3-030-80209-7

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