University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, Vienna, 1090, Austria; Parthenope University of Naples, Department of Engineering, Centro Direzionale - Isola C4, Naples, 80143, Italy.
Utrecht University, Copernicus Institute of Sustainable Development, Environmental Sciences Group, Utrecht, 3508 TC, The Netherlands; National Research Council of Italy, Institute of Atmospheric Sciences and Climate (CNR-ISAC), Corso Fiume 4, Torino, 10133, Italy; National Biodiversity Future Center, Piazza Marina, 61, Palermo, 90133, Italy.
Math Biosci. 2024 Feb;368:109128. doi: 10.1016/j.mbs.2023.109128. Epub 2023 Dec 20.
The emergence and maintenance of tree species diversity in tropical forests is commonly attributed to the Janzen-Connell (JC) hypothesis, which states that growth of seedlings is suppressed in the proximity of conspecific adult trees. As a result, a JC distribution due to a density-dependent negative feedback emerges in the form of a (transient) pattern where conspecific seedling density is highest at intermediate distances away from parent trees. Several studies suggest that the required density-dependent feedbacks behind this pattern could result from interactions between trees and soil-borne pathogens. However, negative plant-soil feedback may involve additional mechanisms, including the accumulation of autotoxic compounds generated through tree litter decomposition. An essential task therefore consists in constructing mathematical models incorporating both effects showing the ability to support the emergence of JC distributions. In this work, we develop and analyse a novel reaction-diffusion-ODE model, describing the interactions within tropical tree species across different life stages (seeds, seedlings, and adults) as driven by negative plant-soil feedback. In particular, we show that under strong negative plant-soil feedback travelling wave solutions exist, creating transient distributions of adult trees and seedlings that are in agreement with the Janzen-Connell hypothesis. Moreover, we show that these travelling wave solutions are pulled fronts and a robust feature as they occur over a broad parameter range. Finally, we calculate their linear spreading speed and show its (in)dependence on relevant nondimensional parameters.
热带森林中树种多样性的出现和维持通常归因于简-康奈尔（Janzen-Connell，JC）假说，该假说指出，在同种成年树附近，幼苗的生长受到抑制。因此，由于密度依赖的负反馈，会出现 JC 分布，表现为同种幼苗密度在离亲树中等距离处最高的（瞬态）模式。一些研究表明，这种模式背后所需的密度依赖反馈可能来自树木和土壤传播病原体之间的相互作用。然而，负的植物-土壤反馈可能涉及其他机制，包括通过树木凋落物分解产生的自毒性化合物的积累。因此，一个重要的任务是构建包含这两种效应的数学模型，以展示支持 JC 分布出现的能力。在这项工作中，我们开发并分析了一个新的反应扩散-ODE 模型，该模型描述了不同生命阶段（种子、幼苗和成年树）的热带树种之间的相互作用，这些相互作用是由负的植物-土壤反馈驱动的。特别是，我们表明，在强烈的负的植物-土壤反馈下，存在传播波解，产生与简-康奈尔假说一致的成年树和幼苗的瞬态分布。此外，我们表明这些传播波解是拉动前沿，是一个稳健的特征，因为它们在广泛的参数范围内出现。最后，我们计算了它们的线性传播速度，并表明其对相关无量纲参数的（不）依赖性。
