The community matrix is among ecology's most important mathematical abstractions, formally encapsulating the interconnected network of effects that species have on one another's populations. Despite its importance, the term “community matrix” has been applied to multiple types of matrices that have differing interpretations. This has hindered the application of theory for understanding community structure and perturbation responses. Here, we clarify the correspondence and distinctions among the Interaction matrix, the Alpha matrix, and the Jacobian matrix, terms that are frequently used interchangeably as well as synonymously with the term “community matrix.” We illustrate how these matrices correspond to different ways of characterizing interaction strengths, how they permit insights regarding different types of press perturbations, and how these are related by a simple scaling relationship. Connections to additional interaction strength characterizations encapsulated by the Beta matrix, the Gamma matrix...

中文翻译：

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表征物种相互作用以了解媒体扰动：什么是社区矩阵？

群落矩阵是生态学最重要的数学抽象之一，正式封装了物种对彼此种群的相互影响网络。尽管它很重要，但术语“社区矩阵”已应用于具有不同解释的多种类型的矩阵。这阻碍了理论在理解群落结构和扰动响应方面的应用。在这里，我们澄清交互矩阵、Alpha 矩阵和雅可比矩阵之间的对应关系和区别，这些术语经常互换使用，并且与术语“社区矩阵”同义。我们说明了这些矩阵如何对应于表征交互强度的不同方式，它们如何允许洞察不同类型的新闻扰动，以及这些如何通过简单的缩放关系相关联。与由 Beta 矩阵、Gamma 矩阵封装的其他交互强度特征的连接......