Alexander B. Medvinsky

Spatiotemporal Complexity of Plankton and Fish Dynamics

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.

Numerical study of plankton–fish dynamics in a spatially structured and noisy environment

Abstract The effects of mobile fish schools and noisy zooplankton mortality on the plankton dynamics are described, using a minimal model of the nutrients–plankton–fish food chain. The space is divided into three habitats of different phytoplankton growth, a first with high productivity, connected to the second with productivity, linearly decreasing down to the level of the third habitat. The plankton growth, interactions and transport are modeled with reaction–diffusion equations whereas, the fish school motion is discrete and rule-based, depending on the local zooplankton density as well as on spatial position, previous direction and maximum residence time.

Will transgenic plants adversely affect the environment

Transgenic insecticidal plants based onBacillus thuringiensis (Bt) endotoxins, on proteinase inhibitors and on lectins, and transgenic herbicide tolerant plants are widely used in modern agriculture. The results of the studies on likelihood and non-likelihood of adverse effects of transgenic plants on the environment including: (i) effects on nontarget species; (ii) invasiveness; (iii) potential for transgenes to ‘escape’ into the environment by horizontal gene transfer; and (iv) adverse effects on soil biota are reviewed. In general, it seems that large-scale implementation of transgenic insecticidal and herbicide tolerant plants do not display considerable negative effects on the environments and, moreover, at least some transgenic plants can improve the corresponding environments and human health because their production considerably reduces the load of chemical insecticides and herbicides.

Pattern formation in models of plankton dynamics. A synthesis

The history of modelling plankton dynamics is already quite long and has been initiated by fishery science in the early 20th century. The main aim of modelling population dynamics is to improve the understanding of the functioning of food chains and webs and their dependence on internal and external conditions. Hence, mathematical models of biological population dynamics have not only to account for growth and interactions but also for spatial processes like random or directed and joint or relative motion of species as well as the variability of the environment. Early attempts began with physicochemical diffusion, exponential growth and Lotka-Volterra type interactions. These approaches have been continuously refined to more realistic descriptions of the development of natural populations. The aim of this paper is to give an extensive introduction to the subject and the bibliography. The fascinating variety of spatio-temporal patterns in such systems and the governing mechanisms of their generation and further dynamics are described and related to plankton.

Effects of seasonal perturbations on a model plankton community

The dynamic behaviour of a model plankton community is described by solutions of a generalized predator‐prey model. The qualitative changes due to variations of parameters are considered and the existence of multistability and catastrophic behaviour is noted. Local and global bifurcations of the system are displayed. A seasonal variation of a parameter is introduced and the resulting dynamics are considered, such as quasiperiodic solutions or chaotic attractors.

Chaos and fractals in fish school motion, II

Abstract It is shown that the turning angle distribution of a modelled moving fish school affects the fractal properties of the school trajectories. The multifractal spectrum is shifted to higher Holder exponents.

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.

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

This is 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.

Fish and Plankton Interplay Determines Both Plankton Spatio-Temporal Pattern Formation and Fish School Walks: A Theoretical Study

The fascinating variety of spatio-temporal patterns in aquatic ecosystems and the understanding of the governing mechanisms of its generation and further dynamics requires ongoing experimental and theoretical studies. After introducing a certain hybrid mathematical model, this paper makes an attempt to demonstrate that the predation of a mobile planktivorous fish school on zooplankton can initiate both plankton pattern formation and fish school walks. Nonlinear interactions in the model of a fish-zooplankton-algae trophic chain prevent a simple intuitive understanding of the system dynamics. It is shown that the fish school predation and motion can give rise to plankton spiral waves. In the course of the spiral wave formation, the amplitudes of the spatially averaged plankton density oscillations are decreasing dramatically. Fish school walks are shown to resemble a fractional Brownian motions with a Hurst exponent depending on the fish predation rate.

The role of periodic boundary forcing in plankton pattern formation

We consider one and two-dimensional minimal models in plankton dynamics. The influence of oscillating boundary forcing functions as agents for triggering pattern formation is discussed. In particular it is found that in these conditions population waves arise for one dimensional models, while for two dimensional models, different amplitudes and frequencies in the boundary forcing generate definite patterns, mimicking the boundary term. This happens even though the model we investigate is very simple. The emergence of these features is an interesting metaphor for the fundamental biological problem of how pattern formation processes may be inevitable in natural heterogeneous ecosystems.