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This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies.
Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems.
Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.
Table des matières
Elements of Probability Theory.- Introduction to Stochastic Processes.- Microscopic, Mesoscopic and Macroscopic Descriptions of Dispersal- Continuous-Time Random Walks and Anomalous Diffusion.- Reaction-Dispersal Models and Front Propagation.- Stochastic Optimal Foraging Theory.- Cell Motion and Chemotaxis.- Host-Pathogen Interactions.- Biological Invasions.- Random Search in Model Organisms.
Résumé
This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies.
Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems.
Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.
Texte suppl.
From the book reviews:
“This book … attempts to provide an overview of the essential mathematical, physical and modelling aspects which describe the motion of living entities at various scales. … This book is interdisciplinary, intuitive and versatile, bridging a gap between mathematics and ecology in a pedagogically sound and scientifically relevant manner, from which a broad audience may benefit.” (Paul Georgescu, zbMATH, Vol. 1295, 2014)
Commentaire
From the book reviews:
"This book ... attempts to provide an overview of the essential mathematical, physical and modelling aspects which describe the motion of living entities at various scales. ... This book is interdisciplinary, intuitive and versatile, bridging a gap between mathematics and ecology in a pedagogically sound and scientifically relevant manner, from which a broad audience may benefit." (Paul Georgescu, zbMATH, Vol. 1295, 2014)
