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Pattern Formation in Mesic Savannas

Patterson, Denis; Levin, Simon; Staver, Ann Carla; Touboul, Jonathan

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Authors

Simon Levin

Ann Carla Staver

Jonathan Touboul



Abstract

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Homogeneous solutions dominate the dynamics of the standard forest-savanna model, regardless of the length scales of the various spatial processes considered. However, several different pattern-forming scenarios are possible upon including spatial resource limitation, such as competition for water, soil nutrients, or herbivory effects. Using numerical simulations and continuation, we study the nature of the resulting patterns as a function of system parameters and length scales, uncovering subcritical pattern-forming bifurcations and observing significant regions of multistability for realistic parameter regimes. Finally, we discuss our results in the context of extant savanna-forest modeling efforts and highlight ongoing challenges in building a unifying mathematical model for savannas across different rainfall levels.

Citation

Patterson, D., Levin, S., Staver, A. C., & Touboul, J. (2024). Pattern Formation in Mesic Savannas. Bulletin of Mathematical Biology, 86(1), https://doi.org/10.1007/s11538-023-01231-7

Journal Article Type Article
Acceptance Date Oct 29, 2023
Online Publication Date Nov 27, 2023
Publication Date Jan 1, 2024
Deposit Date Jan 10, 2024
Publicly Available Date Jan 10, 2024
Journal Bulletin of Mathematical Biology
Print ISSN 0092-8240
Electronic ISSN 1522-9602
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 86
Issue 1
DOI https://doi.org/10.1007/s11538-023-01231-7
Keywords 35B36, Spatial modeling, Vegetation dynamics, Pattern formation, Integro-differential equations, 45K05, 92F05, Savanna
Public URL https://durham-repository.worktribe.com/output/1965580

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Licence
http://creativecommons.org/licenses/by/4.0/

Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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