标题： 具有非高斯相互作用的大系统种群动力学 显示英文标题

标题： Large system population dynamics with non-Gaussian interactions

摘要： 我们研究广义洛特卡-沃尔泰拉（GLV）方程，这是理论生态学中的核心模型，其中假设物种相互作用随时间固定且异质（淬火噪声）。 最近的研究表明，在最简单的场景中，大型无序GLV系统的稳定性特性以及丰富度分布仅取决于物种相互作用分布的均值和方差。 然而，经验社区偏离了这种普遍性。 在本文中，我们提出了一种适用于非高斯相互作用的动态平均场理论的广义版本，可以应用于各种模型，包括GLV方程。 我们的结果表明，广义平均场方程的解依赖于物种相互作用分布的所有累积量，导致普遍性的破坏。 我们利用这一有信息量的破坏，从密度的宏观分布中提取微观相互作用细节，这些结果与经验数据一致。 具体而言，在稀疏相互作用的情况下，我们进行了分析研究，建立了相互作用分布与物种种群密度分布之间的简单关系。 显示英文摘要

摘要： We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the stability properties and abundance distributions of large disordered GLV systems depend, in the simplest scenario, solely on the mean and variance of the distribution of species interactions. However, empirical communities deviate from this level of universality. In this article, we present a generalized version of the dynamical mean field theory for non-Gaussian interactions that can be applied to various models, including the GLV equations. Our results show that the generalized mean field equations have solutions which depend on all cumulants of the distribution of species interactions, leading to a breakdown of universality. We leverage on this informative breakdown to extract microscopic interaction details from the macroscopic distribution of densities which are in agreement with empirical data. Specifically, in the case of sparse interactions, which we analytically investigate, we establish a simple relationship between the distribution of interactions and the distribution of species population densities.