Integrodifference Equations in Spatial Ecology

ISBN-13: 9783030292966 / Angielski / Miękka / 2020 / 385 str.

Opis

This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike.

Recenzje

“This well-written monograph is not only a successful introduction into the field of integrodifference equations as models in spatial ecology, it also surveys the present state of the art in this field. Its contents are interesting for both theoretical ecologists and applied mathematicians, from PhD students to established researchers.” (Christian Pötzsche, zbMATH 1445.45001, 2020)

“I would highly recommend this book both as an interesting setting for studying dynamical systems in their own right, and as a less-well-known, but plausibly very powerful, way to model population dynamics.” (MAA Reviews, March 7, 2020)

Spis treści

Models for Spatial Population Dynamics.- Modeling with Integrodifference Equations.- Critical Patch-Size.- Positive Steady States.- The Speed of Spatial Spread.- Spatial Spread with Allee Effect.- Modeling the Dispersal Process.- Computational Aspects.- Dispersal Success.- Approximations for Spread.- The Shape of Spatial Spread.- Applications.- Structured Populations.- Two Interacting Populations.- Spatial Variation.- Temporal Variation.- Further Topics and Related Models. 

O autorze

Frithjof Lutscher has worked at the interface between mathematics and biology throughout his career and has developed theory and applications of integrodifference equations for over 15 years. His research focuses on mechanistic models for ecological systems, in particular on population persistence and spread in fragmented landscapes. He is professor for applied mathematics at the University of Ottawa. He has published numerous articles in peer-reviewed journals, including Springer's Journal of Mathematical Biology, Bulletin of Mathematical Biology, and Theoretical Ecology.