Plankton lattices and the role of chaos in plankton patchiness

Spatiotemporal and interspecies irregularities in planktonic populations have been widely observed. Much research into the drivers of such plankton patches has been initiated over the past few decades but only recently have the dynamics of the interacting patches themselves been considered. We take a coupled lattice approach to model continuous-in-time plankton patch dynamics, as opposed to the more common continuum type reaction-diffusion-advection model, because it potentially offers a broader scope of application and numerical study with relative ease. We show that nonsynchronous plankton patch dynamics (the discrete analog of spatiotemporal irregularity) arise quite naturally for patches whose underlying dynamics are chaotic. However, we also observe that for parameters in a neighborhood of the chaotic regime, smooth generalized synchronization of nonidentical patches is more readily supported which reduces the incidence of distinct patchiness. We demonstrate that simply associating the coupling strength with measurements of (effective) turbulent diffusivity results in a realistic critical length of the order of 100 km, above which one would expect to observe unsynchronized behavior. It is likely that this estimate of critical length may be reduced by a more exact interpretation of coupling in turbulent flows

Effect of zooplankton growth rate on the spatiotemporal dynamics of plankton communities in heterogeneous environments

A conceptual mathematical model of the reaction-diffusion type was used to study the basic mechanisms underlying the patchy spatial distribution and intricate temporal behavior of plankton in an inhomogeneous medium. The model describes trophic interactions of the prey-predator type between phytoplankton, zooplankton, and fish in surface waters, assuming that plankton is passively driven by turbulent diffusion. Simulations suggest the different growth rates of phytoplankton in neighboring biotopes to be the cause of patch formation in the spatial distribution of plankton. Analysis of the model shows that the biomass of phytoplankton and zooplankton may exhibit regular temporal dynamics or vary chaotically with time. If the habitat conditions are heterogeneous, the spatiotemporal dynamics of plankton depends significantly on the rate of fish predation upon zooplankton.</p

Interrelation between spatial and temporal variations in plankton biomass: a study by mathematical modeling

Dynamics of aquatic biological communities in patchy environments is a topic of substantial interest in the study of interrelationships between phenomena of very different space and time scales. A simple reaction-diffusion model of trophic interactions between phytoplankton, zooplankton, and fish was used to examine how the intricate dynamics of plankton changes on varying the rate of fish predation upon zooplankton. In this study, plankton was assumed to be distributed between two biotopes, of which one contained no fish because of the hydrological conditions in that biotope. Varying the fish predation rate did not bias the correspondence between the scales of spatial patterning and temporal changes in its biomass. Specifically, plankton distributed in large patches exhibited regular temporal oscillations of its abundance. The formation of small patches was associated with chaotic oscillations. As in the case when the fish predation rate was fixed, the dynamic behavior of plankton was determined by the coexistence of a chaotic attractor with a limit cycle.</p

Chaos and regular dynamics in model multi-habitat plankton-fish communities

This work is focused on the role of diffusive interaction between separate habitats in a patchy environment in plankton pattern formation. We demonstrate that conceptual reaction-diffusion mathematical models constitute an appropriate tool for searching and understanding basic mechanisms of plankton pattern formation and complex spatio-temporal plankton dynamics.</p

On the correlation of time series in ecology of aquatic systems

Abstract: A method for estimating the mutual influence of short time series, which is based on extension of the concept of spectral entropy to the spectra of cross-correlation functions is developed. Algorithms of calculations and programs are given. The time series of plankton abundance in the lake ecosystem, which is situated in the Republic of Belarus, are analyzed in order to identify mutual correlations. Correlations between the bacterioplankton abundance and variations in seasonal temperature are identified. The peculiarities of interrelations between the abundances of zooplankton/phytoplankton and temperature depending on the reservoir are analysed.Note: Research direction:Mathematical modelling in actual problems of science and technic

Biological factors underlying regularity and chaos in aquatic ecosystems: simple models of complex dynamics

This work is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that reaction-diffusion mathematical models are an appropriate tool for searching and understanding basic mechanisms of complex spatio-temporal plankton dynamics and fractal properties of planktivorous fish school walks.</p