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Interdisciplinary Applied Mathematics #14: Diffusion and Ecological Problemsby Akira Okubo
Synopses & Reviews
This substantially expanded and updated version of the classic 1980 book by the late Akira Okubo traces the developments that have flowed from the original work, building on detailed notes he left for revision. The first edition was a comprehensive treatment of the use of diffusion models in ecology that integrated rigorous mathematical theory and substantive applications. Enormous in scope, covering a wide variety of topics and including models of spread, critical patch size, and grouping, it has remained one of the most popular books in mathematical biology and has stimulated extensive research in the two decades since its publication. In this volume, friends and disciples of Okubo incorporate a wide range of results from their own fields that build upon the framework he first established.
Surveying a wide variety of mathematical models of diffusion in the ecological context, this book is written with the primary intent of providing scientists, particularly physicists but also biologists, with some background of the mathematics and physics of diffusion and how they can be applied to ecological problems. Equally, this is a specialized text book for graduates interested in mathematical ecology — assuming no more than a basic knowledge of probability and differential equations. Each chapter in this new edition has been substantially updated by appopriate leading researchers in the field and contains much new material covering recent developments.
This book surveys a wide variety of mathematical models of diffusion in the ecological context. It is written with the primary intent of providing scientists, particularly physicists but also biologists, with some background of the mathematics and physics of diffusion and how they can be applied to ecological problems. The secondary intent is to provide a specialized text book for graduate students, who are interested in mathematical ecology. The reader is assumed to have a basic knowledge of probability and differential equations. Each chapter in this new edition is substantially updated by appopriate leading researchers in the field and contains much new material covering developments in the field in the last 20 years.
Table of Contents
1 Introduction: The Mathematics of Ecological Diffusion * 2 The Basics of Diffusion * 3 Passive Diffusion in Ecosystems * 4 Diffusion of "Smell" and "Taste": Chemical Communication * 5 Mathematical Treatment of Biological Diffusion * 6 Some Examples of Animal Diffusion * 7 The Dynamics of Animal Grouping * 8 Animal Movements in Home Range * 9 Patchy Distribution and Diffusion * 10 Population Dynamics in Temporal and Spatial Domains * References * Author Index * Subject Index
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