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研究长期以来一直是竞争者共存研究的核心动因，但当前绝大多数经验与理论认知均源于双物种系统。在物种丰富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接相互作用，这一问题目前仍不甚明晰。要解决这一问题，需要开发简便、可扩展且直观的量化指标，用以评估多物种种群共存的条件，以及该条件与仅基于两两相互作用（pairwise interactions）所预期的共存条件之间的差异。为达成上述目标，我们提出了一种结构化研究方法，可基于竞争系数矩阵（competition coefficients matrix）所施加的几何约束，探究与n物种共存（n-species coexistence）兼容的参数值集合。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）的新型数学指标，用于衡量与多物种种群共存兼容的条件范围，并整合了多样系统中涌现的间接相互作用效应。我们阐释了如何利用所提指标量化多物种种群共存条件与两两共存允许条件之间的差异程度，并将该方法应用于一年生植物（annual plants）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，提出了全新的研究挑战与经验研究契机。