Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach

Xu, Li; Patterson, Denis; Staver, Ann Carla; Levin, Simon Asher; Wang, Jin

Abstract

The frequency distributions can characterize the population-potential landscape related to the stability of ecological states. We illustrate the practical utility of this approach by analyzing a forest–savanna model. Savanna and forest states coexist under certain conditions, consistent with past theoretical work and empirical observations. However, a grassland state, unseen in the corresponding deterministic model, emerges as an alternative quasi-stable state under fluctuations, providing a theoretical basis for the appearance of widespread grasslands in some empirical analyses. The ecological dynamics are determined by both the population-potential landscape gradient and the steady-state probability flux. The flux quantifies the net input/output to the ecological system and therefore the degree of nonequilibriumness. Landscape and flux together determine the transitions between stable states characterized by dominant paths and switching rates. The intrinsic potential landscape admits a Lyapunov function, which provides a quantitative measure of global stability. We find that the average flux, entropy production rate, and free energy have significant changes near bifurcations under both finite and zero fluctuation. These may provide both dynamical and thermodynamic origins of the bifurcations. We identified the variances in observed frequency time traces, fluctuations, and time irreversibility as kinematic measures for bifurcations. This framework opens the way to characterize ecological systems globally, to uncover how they change among states, and to quantify the emergence of quasi-stable states under stochastic fluctuations.

Citation

Xu, L., Patterson, D., Staver, A. C., Levin, S. A., & Wang, J. (2021). Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach. Proceedings of the National Academy of Sciences, 118(24), Article e2103779118. https://doi.org/10.1073/pnas.2103779118

• Journal Article Type: Article
• Acceptance Date: Apr 23, 2021
• Online Publication Date: Jun 11, 2021
• Publication Date: Jun 15, 2021
• Deposit Date: May 9, 2024
• Publicly Available Date: May 10, 2024
• Journal: Proceedings of the National Academy of Sciences
• Print ISSN: 0027-8424
• Electronic ISSN: 1091-6490
• Publisher: National Academy of Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 118
• Issue: 24
• Article Number: e2103779118
• DOI: https://doi.org/10.1073/pnas.2103779118
• Public URL: https://durham-repository.worktribe.com/output/2435827
• Related Public URLs: https://arxiv.org/abs/2103.08198