Abstract
AbstractIt 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).
Highlights
Ecological dynamics in space has been a major theme in ecology for some time (Tilman and Kareiva 1997, Cronin and Reeve 2005), employing a variety of theoretical approaches (Pacala and Levin 1997, Massol et al 2011)
A coffee bush may be free of the scale insect pest, or it may have populations of that pest on it, or the pest population may be in a state of undergoing attack from the hymenopteran parasitoid, Coccophagus sp
As we show in this model exercise, it is the spatial extension of the system that allows the two biological control elements to persist in the long run, effecting autonomous biological control over the scale insect over the entire farm, sacrificing a small percentage of the farm as effective spatial repositories of the pest, which keeps the biological control agents alive over the entire region
Summary
Ecological dynamics in space has been a major theme in ecology for some time (Tilman and Kareiva 1997, Cronin and Reeve 2005), employing a variety of theoretical approaches (Pacala and Levin 1997, Massol et al 2011). We propose a unique theoretical framing based on our qualitative understanding of a particular subcomponent of an ecosystem, the traditional shaded coffee agroecosystem. Our framing differs from previous literature in its qualitative nature based on observations and experiments in this real system over the past 25 yr (Perfecto and Vandermeer 2015), combining other well-known theoretical issues into a coherent framework that corresponds to the long-term observable dynamics in this system. The theory is formed from previous literature on (1) intransitive coupled oscillations, (2) spatial dynamics, and (3) self-organization of spatial pattern
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