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On joint subtree distributions under two evolutionary models

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  • Wu, Taoyang
  • Choi, Kwok Pui

Abstract

In population and evolutionary biology, hypotheses about micro-evolutionary and macro-evolutionary processes are commonly tested by comparing the shape indices of empirical evolutionary trees with those predicted by neutral models. A key ingredient in this approach is the ability to compute and quantify distributions of various tree shape indices under random models of interest. As a step to meet this challenge, in this paper we investigate the joint distribution of cherries and pitchforks (that is, subtrees with two and three leaves) under two widely used null models: the Yule–Harding–Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model. Based on two novel recursive formulae, we propose a dynamic approach to numerically compute the exact joint distribution (and hence the marginal distributions) for trees of any size. We also obtained insights into the statistical properties of trees generated under these two models, including a constant correlation between the cherry and the pitchfork distributions under the YHK model, and the log-concavity and unimodality of the cherry distributions under both models. In addition, we show that there exists a unique change point for the cherry distributions between these two models.

Suggested Citation

  • Wu, Taoyang & Choi, Kwok Pui, 2016. "On joint subtree distributions under two evolutionary models," Theoretical Population Biology, Elsevier, vol. 108(C), pages 13-23.
    • Handle: RePEc:eee:thpobi:v:108:y:2016:i:c:p:13-23
    DOI: 10.1016/j.tpb.2015.11.004
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    References listed on IDEAS

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    1. Zhu, Sha & Degnan, James H. & Steel, Mike, 2011. "Clades, clans, and reciprocal monophyly under neutral evolutionary models," Theoretical Population Biology, Elsevier, vol. 79(4), pages 220-227.
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    Cited by:

    1. Choi, Kwok Pui & Thompson, Ariadne & Wu, Taoyang, 2020. "On cherry and pitchfork distributions of random rooted and unrooted phylogenetic trees," Theoretical Population Biology, Elsevier, vol. 132(C), pages 92-104.
    2. Kaur, Gursharn & Choi, Kwok Pui & Wu, Taoyang, 2023. "Distributions of cherries and pitchforks for the Ford model," Theoretical Population Biology, Elsevier, vol. 149(C), pages 27-38.

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