High Meadows Environmental Institute, Princeton University, Princeton, NJ, 08544, USA.
Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, 08544, USA.
Bull Math Biol. 2023 Nov 27;86(1):3. doi: 10.1007/s11538-023-01231-7.
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.
我们分析了一个著名的森林-草原动态模型的空间扩展版本，该模型呈现为一个非线性偏积分微分方程组系统，并研究了形成模式的分岔的必要条件。无论所考虑的各种空间过程的长度尺度如何，均匀解都主导着标准的森林-草原模型的动态。然而，在包括空间资源限制（如对水、土壤养分或食草动物效应的竞争）时，可能会出现几种不同的形成模式的情况。我们使用数值模拟和延续，研究了作为系统参数和长度尺度函数的所得模式的性质，揭示了亚临界模式形成分岔，并观察到了现实参数范围内多稳定性的显著区域。最后，我们根据现有的草原-森林建模工作讨论了我们的结果，并强调了在不同降雨量水平下为草原建立统一数学模型方面的持续挑战。
