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Modeling the Phylogenetic Rates of Continuous Trait Evolution: An Autoregressive–Moving-Average Model Approach

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  • Dwueng-Chwuan Jhwueng

    (Department of Statistics, Feng-Chia University, Taichung 40724, Taiwan)

Abstract

The rates of continuous evolution plays a crucial role in understanding the pace at which species evolve. Various statistical models have been developed to estimate the rates of continuous trait evolution for a group of related species evolving along a phylogenetic tree. Existing models often assume the independence of the rate parameters; however, this assumption may not account for scenarios where the rate of continuous trait evolution correlates with its evolutionary history. We propose using the autoregressive–moving-average (ARMA) model for modeling the rate of continuous trait evolution along the tree, hypothesizing that rates between two successive generations (ancestor–descendant) are time-dependent and correlated along the tree. We denote PhyRateARMA ( p , q ) as a phylogenetic rate-of-continuous-trait-evolution ARMA( p , q ) model in our framework. Our algorithm begins by utilizing the tree and trait data to estimate the rates on each branch, followed by implementing the ARMA process to infer the relationships between successive rates. We apply our innovation to analyze the primate body mass dataset and plant genome size dataset and test for the autoregressive effect of the rates of continuous evolution along the tree.

Suggested Citation

  • Dwueng-Chwuan Jhwueng, 2024. "Modeling the Phylogenetic Rates of Continuous Trait Evolution: An Autoregressive–Moving-Average Model Approach," Mathematics, MDPI, vol. 13(1), pages 1-27, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:111-:d:1556930
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    References listed on IDEAS

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    1. D.-C. Jhwueng & V. Maroulas, 2016. "Adaptive trait evolution in random environment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2310-2324, September.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Luigi Spezia, 2024. "Bayesian prior modeling in vector autoregressions via the Yule-Walker equations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(14), pages 5230-5247, April.
    4. Neculai Andrei, 2022. "Modern Numerical Nonlinear Optimization," Springer Optimization and Its Applications, Springer, number 978-3-031-08720-2, December.
    5. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    6. Jhwueng, Dwueng-Chwuan, 2020. "Modeling rate of adaptive trait evolution using Cox–Ingersoll–Ross process: An Approximate Bayesian Computation approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
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