Mathematical Modelling in Studying Spatial Aspects of Population Dynamics

Dear Colleagues,

Classical theory of mathematical ecology began with population dynamics models that were built and validated on data collected from experiments performed with small laboratory microcosms. However, the understanding of the crucial role played by various spatial aspects in the functioning of population systems came quite soon, partly owing to the results obtained with the help of mathematical modelling. In turn, this understanding stimulated the development of new modelling approaches to the mathematical description of biophysical phenomena related to spatial factors.

The spatial extension of habitats is a key feature distinguishing natural ecosystems from small-scale laboratory microcosms that allow a modeler to admit the hypotheses of the well-mixed environment, random encounters, and unpurposive movements of animals. Taking into account the patchy distribution and directed movements of animals qualitatively alters the dynamics of population models and thus their response to external impacts. In other words, the inclusion of spatial factors into a population model can change the model’s prediction. Thus, the solution of applied or theoretical problems of biological population management should be based on adequate modeling tools correctly describing the interrelated processes of spatiotemporal population dynamics and spatial behavior of species. That is how modelling helped reveal the relationships between characteristics of spatiotemporal chaos and predictability of the population dynamics and spatial activity of phytophagous insects; its successful application for the biological control of weeds; the acclimatization of adventive invaders and their capability of spatial expansion by forming solitary population waves; the swarming behavior of fish and their vulnerability to predator attacks; the collective hunting of predators; and the emergence of the predator interference at the population level.

The purpose of this Special Issue is to gather a collection of articles presenting recent research dealing with spatial phenomena in biological populations and communities, obtained with models based on various mathematical techniques: ODE and PDE systems, integro-differential equations, difference equations (mapping), individual-based models, box models, matrix models, Markov models, and others.

Prof. Dr. Yuri V. Tyutyunov
Guest Editor

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• population dispersal
• animal movements
• predator–prey
• trophic community
• spatiotemporal heterogeneity
• pattern formation
• spatial behavior
• swarming
• emergent properties
• taxis–diffusion–reaction
• bifurcation
• spatiotemporal chaos