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Galled Tree-Child Networks

Authors Yu-Sheng Chang , Michael Fuchs , Guan-Ru Yu

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LIPIcs.AofA.2024.8.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Distribution functions
Keywords
  • Phylogenetic Network
  • galled Network
  • tree-child Network
  • asymptotic Enumeration
  • Limit Law
  • Lagrange Inversion

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Abstract

We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asymptotic) counting results and stochastic results have been proved with very different methods. We show that a counting result for the class of galled tree-child networks follows with similar tools as used for galled networks, however, the result has a similar pattern as the one for tree-child networks. In addition, we also consider the (suitably scaled) numbers of reticulation nodes of random galled tree-child networks and show that they are asymptotically normal distributed. This is in contrast to the limit laws of the corresponding quantities for galled networks and tree-child networks which have been both shown to be discrete.

Cite As Get BibTex

Yu-Sheng Chang, Michael Fuchs, and Guan-Ru Yu. Galled Tree-Child Networks. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.AofA.2024.8

Author Details

Yu-Sheng Chang
  • Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan
Michael Fuchs
  • Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan
Guan-Ru Yu
  • Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan

Funding

  • Chang, Yu-Sheng: NSTC-111-2115-M-004-002-MY2.
  • Fuchs, Michael: NSTC-111-2115-M-004-002-MY2.
  • Yu, Guan-Ru: NSTC-110-2115-M-017-003-MY3.

Acknowledgements

We thank the three reviewers for positive feedback and useful suggestions. This paper is dedicated to Hsien-Kuei Hwang on the occasion of his 60th birthday.

References

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