Characterizing Species Interactions to Understand Press Perturbations: What Is the Community Matrix?

Mark Novak, Justin D. Yeakel, Andrew E. Noble, Daniel F. Doak, Mark Emmerson, James A. Estes, Ute Jacob, M. Timothy Tinker, J. Timothy Wootton

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)


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, and the Removal matrix are also discussed. Our synthesis highlights the empirical challenges that remain in using these tools to understand actual communities.

Original languageEnglish
Pages (from-to)409-432
Number of pages24
JournalAnnual Review of Ecology, Evolution, and Systematics
Early online date07 Sept 2016
Publication statusPublished - 01 Nov 2016


  • Indirect effects
  • Interaction strengths
  • Multiple stressors
  • Network dynamics
  • Prediction
  • Sensitivity analysis

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology


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