Data from: A structural approach for understanding multispecies coexistence

Although observations of species-rich communities have long served as a primary motivation for research on the coexistence of competitors, the majority of our empirical and theoretical understanding comes from two-species systems. How much of the coexistence observed in species rich communities results from indirect effects among competitors that only emerge in diverse systems remains poorly understood. Resolving this issue requires simple, scalable, and intuitive metrics for quantifying the conditions for coexistence in multispecies systems, and how these conditions differ from those expected based solely on pairwise interactions. To achieve these aims, we develop a structural approach for studying the set of parameter values compatible with n-species coexistence given the geometric constraints imposed by the the matrix of competition coefficients. We derive novel mathematical metrics analogous to stabilizing niche differences and fitness differences that measure the range of conditions compatible with multispecies coexistence, incorporating the effects of indirect interactions emerging in diverse systems. We show how our measures can be used to quantify the extent to which the conditions for coexistence in multispecies systems differ from those that allow pairwise coexistence, and apply the method to a field system of annual plants. We conclude by presenting new challenges and empirical opportunities emerging from our structural metrics of multispecies coexistence.

尽管物种丰富群落的观测结果长期以来一直是竞争者共存研究的核心研究动机之一，但我们绝大多数的经验与理论认知都源自双物种种群系统。目前人们仍不清楚，在物种丰富的群落中观测到的共存现象，有多少源自仅在多样系统中才会显现的竞争者间间接效应。要解决这一问题，需要开发简洁、可扩展且直观的量化指标，用以衡量多物种种群系统的共存条件，以及这些条件与仅基于成对相互作用所预期的条件存在何种差异。为达成上述目标，我们提出了一种结构化研究方法，用于在竞争系数矩阵所施加的几何约束下，探究可实现n物种（n-species）共存的参数值集合。我们推导出了类似稳定生态位差异（stabilizing niche differences）与适合度差异（fitness differences）的全新数学指标，用于衡量与多物种种群共存兼容的条件范围，并纳入了多样系统中显现的间接相互作用效应。我们展示了如何利用所提出的指标，量化多物种种群系统的共存条件与允许成对共存的条件之间的差异程度，并将该方法应用于一年生植物的野外群落系统。最后，我们基于多物种种群共存的结构化指标，提出了一系列新的研究挑战与实证研究方向。