Seasons and Chaos in Ecosystems

Rinaldi, S. (1992). Seasons and Chaos in Ecosystems. IIASA Research Report (Reprint). IIASA, Laxenburg, Austria: RR-94-004. Reprinted from Theoretical Population Biology, 43(2):159-183 [1993] and Bulletin of Mathematical Biology; 55(1):15-35 [1992]

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Abstract

This research report combines two journal articles on the relationships between seasons and chaos in ecosystems. They show that the strength of the seasons (i.e., the latitude) is a key factor for understanding the strange behavior of the ecosystem, and that chaos can be present in an assembly of different communities where the rhythm of the seasons suitably interferes with the endogenous rhythms of the biological processes. The first paper by Rinaldi et al. studies a general predator-prey model describing the behavior of two interacting populations in a periodic environment. Multiple attractors and catastrophic transitions are proved to exist and the two classical routes to chaos (torn destruction and cascade of period doublings) are numerically detected. The second paper by Doveri et al. presents a seasonally perturbed plankton-fish model composed by five compartments: nutrient, algae, zoo plankton, young fish, and adult fish. The bifurcation analysis of the model supports the conclusion that the dynamics of plankton communities can easily be chaotic provided that the strength of the season is sufficiently strong. In particular, the paper shows why large year-to-year differences in young fish survival need not always be attributable to external factors like interannual weather variability.

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