Nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developments of late twentieth century mathematics and physics. The implications have changed our understanding of important phenomena in almost every field of science, including biology and ecology. This article investigates complexity and chaos in the spatiotemporal dynamics of aquatic ecosystems. The dynamics of these biological communities exhibit an interplay between processes acting on a scale from hundreds of meters to kilometers, controlled by biology, and processes acting on a scale from dozens to hundreds of kilometers, dominated by the heterogeneity of hydrophysical fields. We focus on how biological processes affect spatiotemporal pattern formation. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal plankton dynamics, fractal properties of planktivorous fish school movements, and their interrelationships.
Discovering why natural population densities change over time and vary with location is a central goal of ecological and evolutional disciplines. The recognition that even simple ecological systems can undergo chaotic behaviour has made chaos a topic of considerable interest among theoretical ecologists. However, there is still a lack of experimental evidence that chaotic behaviour occurs in the real world of coexisting populations in multi-species systems. Here we study the dynamics of a defined predator-prey system consisting of a bacterivorous ciliate and two bacterial prey species. The bacterial species preferred by the ciliate was the superior competitor. Experimental conditions were kept constant with continuous cultivation in a one-stage chemostat. We show that the dynamic behaviour of such a two-prey, one-predator system includes chaotic behaviour, as well as stable limit cycles and coexistence at equilibrium. Changes in the population dynamics were triggered by changes in the dilution rates of the chemostat. The observed dynamics were verified by estimating the corresponding Lyapunov exponents. Such a defined microbial food web offers a new possibility for the experimental study of deterministic chaos in real biological systems.
Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri- or monostability. Moreover, the disease can destabilize endemic equilibria and induce sustained oscillations. These disappear again for high transmissibilities, with eventually vanishing host population. Disease-induced extinction is thus possible for density-dependent transmission and without any alternative reservoirs. The overall complexity suggests that the system is very sensitive to perturbations and control methods, even in parameter regions with a basic reproductive ratio far beyond R(0) = 1. This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection.
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