Abstract We present and analyze a model aiming at recovering, as dynamical outcomes of fire-mediated tree–grass interactions, the wide range of vegetation physiognomies observable in the savanna biome along rainfall gradients at regional/continental scales. The model is based on two ordinary differential equations (ODE), for woody and grass biomass. It is parameterized from literature with respect to the African context and retains mathematical tractability, since we restricted it to the main processes, notably tree–grass asymmetric interactions (either facilitative or competitive) and the grass-fire feedback. We used a fully qualitative analysis to derive all possible long term dynamics and express them in a bifurcation diagram in relation to mean annual rainfall and fire frequency. We delineated domains of monostability (forest, grassland, savanna), of bistability (e.g. forest–grassland or forest–savanna) and even tristability. Notably, we highlighted regions in which two savanna equilibria may be jointly stable (possibly in addition to forest or grassland). We verified that common knowledge about decreasing woody biomass with increasing fire frequency is verified for all levels of rainfall, contrary to previous attempts using analogous ODE frameworks. Thus, our framework appears able to render more realistic and diversified outcomes than often thought of regarding ODE. Our model can help figure out the ongoing dynamics of savanna vegetation in large territories for which local data are sparse or absent. To explore the bifurcation diagram with different combinations of the model parameters, we have developed a user-friendly R-Shiny application freely available at : https://gitlab.com/cirad-apps/tree-grass .

中文翻译：

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稀树草原生物群落植被地貌的简约模型

摘要 我们提出并分析了一个模型，该模型旨在恢复作为火介导的树-草相互作用的动态结果，沿着区域/大陆尺度的降雨梯度在热带稀树草原生物群落中可观察到的广泛植被地貌。该模型基于木本和草本生物量的两个常微分方程 (ODE)。它从与非洲背景相关的文献中参数化并保留了数学易处理性，因为我们将其限制在主要过程中，特别是树 - 草不对称相互作用（促进或竞争）和草火反馈。我们使用完全定性分析来推导出所有可能的长期动态，并在与年平均降雨量和火灾频率相关的分叉图中表达它们。我们划定了单稳态域（森林、草原、稀树草原），双稳态（例如森林-草地或森林-稀树草原）甚至三稳态。值得注意的是，我们强调了两个稀树草原平衡可能共同稳定的区域（可能除了森林或草原）。我们验证了关于随火灾频率增加而减少木质生物量的常识在所有降雨量水平上都得到了验证，这与之前使用类似 ODE 框架的尝试相反。因此，我们的框架似乎能够呈现比 ODE 经常想到的更现实和多样化的结果。我们的模型可以帮助确定当地数据稀少或不存在的大面积稀树草原植被的持续动态。为了探索具有不同模型参数组合的分叉图，我们开发了一个用户友好的 R-Shiny 应用程序，可在以下网址免费获得：https://gitlab。