Stabilizing intransitive loops: self‐organized spatial structure and disjoint time frames in the coffee agroecosystem

It is familiar knowledge that population dynamics occur in both time and space. In this work, we incorporate three distinct but related theoretical schemata to qualitatively interrogate the complicated structure of part of a real agroecosystem. The three schemata are first, local dynamics translated into intransitive oscillators through spatial movement, second, stabilizing the system through spatial pattern, and third, formation of a self‐organized spatial pattern. The real system is the well‐studied autonomous pest control in the coffee agroecosystem, in which five insect species (one of which is a pest) are involved in creating a complex community structure that keeps the pest under control (the five species are an ant, Azteca sericeasur , a phorid fly parasitoid, Pseudacteon sp., a hymenopteran parasitoid, Coccophagus sp., a beetle predator, Azya orbigera , and the pest itself, the green coffee scale, Coccus viridis ). We use the qualitative framing of the three theoretical schemata to develop a cellular automata model that casts the basic predator/prey (natural enemy/pest) system as an intransitive oscillator, and then explore the interaction of the two basic predator/prey systems as coupled oscillators within this model framework. We note that Gause's principle of competitive exclusion is not violated with this basic framing (i.e., the two control agents cannot coexist theoretically), but that with a change in the spatial structure of the background habitat, coexistence can be maintained through the tradeoff between regional dispersal and local consumption. Finally, we explore how the other oscillator in the system (the ant and its phorid parasitoid) can act as a pilot system, creating the spatial structure in which the other two oscillators operate, but only in the context of disjoint time frames (between the two control agents and the pilot subsystem).