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.
Author(s): Frithjof Lutscher
Series: Interdisciplinary Applied Mathematics 49
Edition: 1
Publisher: Springer
Year: 2019
Language: English
Pages: 390
Tags: Ecology
Front Matter ....Pages i-xvi
Front Matter ....Pages 1-1
Models for Spatial Population Dynamics (Frithjof Lutscher)....Pages 3-7
Modeling with Integrodifference Equations (Frithjof Lutscher)....Pages 9-22
Critical Patch-Size (Frithjof Lutscher)....Pages 23-38
Positive Steady States (Frithjof Lutscher)....Pages 39-52
The Speed of Spatial Spread (Frithjof Lutscher)....Pages 53-73
Spatial Spread with Allee Effect (Frithjof Lutscher)....Pages 75-86
Modeling the Dispersal Process (Frithjof Lutscher)....Pages 87-104
Computational Aspects (Frithjof Lutscher)....Pages 105-115
Front Matter ....Pages 117-117
Dispersal Success (Frithjof Lutscher)....Pages 119-132
Approximations for Spread (Frithjof Lutscher)....Pages 133-143
The Shape of Spatial Spread (Frithjof Lutscher)....Pages 145-159
Applications (Frithjof Lutscher)....Pages 161-197
Front Matter ....Pages 199-199
Structured Populations (Frithjof Lutscher)....Pages 201-230
Two Interacting Populations (Frithjof Lutscher)....Pages 231-283
Spatial Variation (Frithjof Lutscher)....Pages 285-330
Temporal Variation (Frithjof Lutscher)....Pages 331-348
Further Topics and Related Models (Frithjof Lutscher)....Pages 349-361
Back Matter ....Pages 363-385
