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Modeling rate of adaptive trait evolution using Cox–Ingersoll–Ross process: An Approximate Bayesian Computation approach

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  • Jhwueng, Dwueng-Chwuan

Abstract

Over the past decades, Gaussian processes have been widely used to study trait evolution. In particular, two members of Gaussian processes, Brownian motion and the Ornstein–Uhlenbeck process, have been frequently applied for describing continuous trait evolution. Several models (OUBM, OUOU, OUBMBM, OUOUBM) have been proposed to study the impact on the optimum of a trait by other traits. Applying the Cox–Ingersoll–Ross (CIR) process on rate of evolution, which prevents rates from becoming negative, is a potentially useful extension developed here as the OUBMCIR and OUOUCIR models. Since the likelihood functions of the OUBMCIR and the OUOUCIR models are intractable, a heuristic algorithm for parameter estimation and inference under Approximate Bayesian Computation (ABC) is proposed. Simulation studies show that new models perform well. Empirical analysis using several data sets from literature also provides evidence of the validity and utility of the new models. The relevant data sets and R scripts developed for this project can be accessed through the link.11https://tonyjhwueng.info/ououcir.

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  • 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).
    • Handle: RePEc:eee:csdana:v:145:y:2020:i:c:s0167947320300153
    DOI: 10.1016/j.csda.2020.106924
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. Mark Pagel, 1999. "Inferring the historical patterns of biological evolution," Nature, Nature, vol. 401(6756), pages 877-884, October.
    4. Dwueng-Chwuan Jhwueng, 2013. "Assessing the Goodness of Fit of Phylogenetic Comparative Methods: A Meta-Analysis and Simulation Study," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-12, June.
    5. Paul Glasserman & Kyoung-Kuk Kim, 2011. "Gamma expansion of the Heston stochastic volatility model," Finance and Stochastics, Springer, vol. 15(2), pages 267-296, June.
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    Cited by:

    1. Dwueng-Chwuan Jhwueng, 2021. "Two Gaussian Bridge Processes for Mapping Continuous Trait Evolution along Phylogenetic Trees," Mathematics, MDPI, vol. 9(16), pages 1-14, August.

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