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When can we reconstruct the ancestral state? Beyond Brownian motion

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Abstract

Reconstructing the ancestral state of a group of species helps answer many important questions in evolutionary biology. Therefore, it is crucial to understand when we can estimate the ancestral state accurately. Previous works provide a necessary and sufficient condition, called the big bang condition, for the existence of an accurate reconstruction method under discrete trait evolution models and the Brownian motion model. In this paper, we extend this result to a wide range of continuous trait evolution models. In particular, we consider a general setting where continuous traits evolve along the tree according to stochastic processes that satisfy some regularity conditions. We verify these conditions for popular continuous trait evolution models including Ornstein–Uhlenbeck, reflected Brownian Motion, bounded Brownian Motion, and Cox–Ingersoll–Ross.

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Data Availability Statement

The R code for the simulations is available at https://github.com/lamho86/When-can-we-reconstruct-the-ancestral-state-Beyond-Brownian-motion.

Notes

  1. https://github.com/fcboucher/BBM.

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Acknowledgements

LSTH was supported by the Canada Research Chairs program, the NSERC Discovery Grant RGPIN-2018-05447, and the NSERC Discovery Launch Supplement DGECR-2018-00181. VD was supported by a startup fund from the University of Delaware, a University of Delaware Research Foundation’s Strategic Initiatives Grant, and National Science Foundation grant DMS- 1951474. The authors would like to thank Douglas Rizzolo for a helpful discussion that lead to the bounds for the Bounded Brownian Motion model.

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Author notes

  1. Nhat L. Vu and Thanh P. Nguyen have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada

    Nhat L. Vu & Lam Si Tung Ho

  2. AISIA Research Lab, Ho Chi Minh City, Vietnam

    Thanh P. Nguyen & Binh T. Nguyen

  3. Department of Computer Science, University of Science, Ho Chi Minh City, Vietnam

    Thanh P. Nguyen & Binh T. Nguyen

  4. Vietnam National University, Ho Chi Minh City, Vietnam

    Thanh P. Nguyen & Binh T. Nguyen

  5. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Vu Dinh

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  1. Nhat L. Vu
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  5. Lam Si Tung Ho
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Correspondence to Lam Si Tung Ho.

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Vu, N.L., Nguyen, T.P., Nguyen, B.T. et al. When can we reconstruct the ancestral state? Beyond Brownian motion. J. Math. Biol. 86, 88 (2023). https://doi.org/10.1007/s00285-023-01922-8

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  • DOI: https://doi.org/10.1007/s00285-023-01922-8

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