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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.