大型植物-传粉者随机网络的连续极限及若干应用
Continuous limits of large plant-pollinator random networks and some applications
AI总结：
该研究通过二分图构建植物-传粉者随机模型，分析其连续极限的确定性近似及长期行为，建立中心极限定理量化模型差异，发现嵌套群落会坍缩为单对物种共存。
摘要：
我们通过二分图研究了一个基于个体的植物与传粉者物种相互作用的随机模型：每个物种是图的一个节点，边表示物种对之间的相互作用。系统的动力学依赖于物种间和物种内的相互作用：昆虫传粉会提高植物繁殖率，但存在成本，该成本会根据传粉者密度增加植物死亡率；传粉者的繁殖率会因从植物获取的资源而提高。每个物种具有一个对应其泛化程度的特征，该特征决定了相互作用图的结构及物种间交换的资源量。我们的模型特别包含嵌套或模块化网络。当种群规模较大或图密集且可被图论（graphon）替代时，建立并研究了随机测度值过程通过常微分方程或积分微分方程的确定性近似。研究了这些极限的长期行为，并建立中心极限定理以量化离散随机个体模型与确定性近似之间的差异。最后，通过研究相互作用网络的连续极限及所得偏微分方程，我们发现嵌套的植物-传粉者群落预计会坍缩为单对植物与传粉者物种的共存状态。
英文摘要：
We study a stochastic individual-based model of interacting plant and pollinator species through a bipartite graph: each species is a node of the graph, an edge representing interactions between a pair of species. The dynamics of the system depends on the between- and within-species interactions: pollination by insects increases plant reproduction rate but has a cost which can increase plant death rate, depending on the densities of pollinators. Pollinators reproduction is increased by the resources harvested on plants. Each species is characterized by a trait corresponding to its degree of generalism. This trait determines the structure of the interaction graph and the quantities of resources exchanged between species. Our model includes in particular nested or modular networks. Deterministic approximations of the stochastic measure-valued process by systems of ordinary differential equations or integro-differential equations are established and studied, when the population is large or when the graph is dense and can be replaced with a graphon. The long-time behaviors of these limits are studied and central limit theorems are established to quantify the difference between the discrete stochastic individual-based model and the deterministic approximations. Finally, studying the continuous limits of the interaction network and the resulting PDEs, we show that nested plant-pollinator communities are expected to collapse towards a coexistence between a single pair of species of plants and pollinators.
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