空间相互作用广义 Lotka–Volterra 生态系统中对无序具有鲁棒性的模式
Patterns robust to Disorder in spatially-interacting Generalized Lotka-Volterra Ecosystems
AI总结：
该研究构建可扩散、非局域相互作用的空间广义 Lotka–Volterra 模型，揭示均匀态失稳判据、BBP 谱转变与空间模式形成，并给出小无序下密度平均场方程的显式不动点解。
摘要：
物种之间的相互作用如何影响其在生态系统中的空间分布？为回答这一问题，我们引入一个空间扩展的广义 Lotka–Volterra 型生态系统，其中物种可以扩散，且相互作用是非局域的。我们计算了空间均匀生态系统丧失稳定性的判据，并表明均匀态的稳定性关键取决于最丰富的物种，以及一个物种世代内的空间探索与相互作用范围之间的相互影响。通过关注由物种丰度加权的相互作用矩阵的谱，我们识别出一次 Baik–Ben Arous–Péché 转变，该转变转化为物种重新分布的最终模式中的转变。最后，在假设无序较小的情况下，我们给出了物种种群密度动力学平均场方程的一个显式解，该解作为非局域 Fisher–Kolmogorov–Petrovski–Piskounov 方程的不动点得到。我们的工作为未来在活性物质与无序系统交叉领域的联合方法铺平了道路，以期更好地理解细菌群落等复杂生态系统。
英文摘要：
How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka-Volterra type, where species can diffuse and interactions are nonlocal. We compute the criterion for the loss of stability of the spatially homogeneous ecosystem, and we show that the stability of the uniform state crucially depends on the most abundant species, and on the interplay between space exploration during one species generation and the interaction range. Focusing on the spectrum of the interaction matrix weighted by the species abundances, we identify a Baik-Ben Arous-Péché transition that translates into a transition in the final patterns of the species repartition. Finally assuming that the disorder is small, we exhibit an explicit solution of the dynamical mean-field equation for the species density, obtained as the fixed point of a nonlocal Fisher-Kolmogorov-Petrovski-Piskounov equation. Our work paves the way of future combined approaches at the frontier of active matter and disordered systems, with the hope of better understanding complex ecosystems like bacterial communities.
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