Keystone predator and keystone intransitivity and the rescue of a competitively subdominant species.

Two significant complications in the structure of ecological communities are its dimensionality (many species interacting) and its network diversity (many ways to "wire" the interactions). Two classic concepts, the competitive exclusion principle and the keystone predator hypothesis, may frequently be embedded elements within that community structure and partially responsible for generating it. Other less-venerable concepts may be involved. In particular, for the current work, a keystone intransitivity and a behavioral higher-order effect are involved. We employ a strategic intersection of several particular network modalities-competitive hierarchy, keystone predator, keystone intransitivity, and higher-order trait-mediated effect-to examine the population dynamics of a real system, exploring the nature of its persistence (or extinction) based on the qualitative nature of its network structure. Because two of the dynamic structures, predation and intransitive competition, are both fundamentally oscillatory, the theoretical framework of coupled oscillators comes into play, a mathematical structure well known to be a major source of chaos. We use a set of natural history observations and measurements of a five-dimensional system, common in the coffee agroecosystems of Puerto Rico, to show how the unexpected persistence of a subdominant competitor in a competitive hierarchy may be contingent on a particular wiring of the system. It is notable that all five species are non-native and all are involved in a complex system of potential biological control of two significant pests.