Dominance and Spatiotemporal Behavior in Cyclic Ecological Systems

Stiadle, Thomas Isaac

doi:https://doi.org/10.21985/n2-xb35-hv41

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Dominance and Spatiotemporal Behavior in Cyclic Ecological Systems

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Deterministic models are used to explain and predict the dynamics of ecosystems featuring cyclic competition schemes. The models are systems of reaction-diffusion partialdifferential equations that account for species mobility via Fickian diffusion and interspecies interactions according to the competition scheme. Length and temporal scales are chosen to be appropriate for an experimental bacterial community, qualitatively modeling observed E. coli bacterial systems, and behaviors reported from relevant experiments are reproduced by the models. Systems of two, three, and four species are examined and it is shown that direct interspecies competition, mobility, and initial spatial structure are relevant factors in the determination of the dominant species and long-term dynamics of cyclic systems. One- and two-dimensional domains are considered, modeling a community confined to a thin annulus and a petri dish, respectively. For three-species symmetric systems, when coexistence of all three species is unstable and interspecies competition is relatively weak, spatiotemporal chaotic behavior generally occurs. A mechanism for the development of chaos, patch splitting, is proposed. On the4 other hand, when interspecies competition is sufficiently strong, ordered patterns are often found. In 1D, traveling arrays of single-species patches, as well as modulated traveling waves, consisting of patches which periodically expand and contract (breather modes), can be found. In 2D, spirals, as well as localized patches that chase each other, can occur. In three-species asymmetric systems, the “survival of the weakest” phenomenon is often reproduced by the model. In three- and four-species systems with an exceptionally strong or weak competitor, behavior is dominated by transcritical bifurcations between (i) the coexistence state and (ii) partial alliance states involving competing species. Although the three- and four- species models admit very different solutions when all species are strong competitors, these transcritical bifurcations unify the behavior of the two systems in the case of a strong or weak exceptional species. The displacement of one state by another is discussed in the context of an invasion. For the displacement of unstable states, speeds of displacement are computed and compared to analytical estimates for pulled fronts. Finally, it is shown that for a one-dimensional three-species system involving a species that is less mobile than the others, the dynamics of the system become more complicated as the mobility of the exceptional species decreases.

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