Diffusion and Ecological Problems

The story of this edition is a testament to an almost legendary gure in theoretical ecology and to the in uence his work and charisma has had on the eld. It is also a story that can only be told by a trip back in time, to the genesis of the First Edition and before. Akira kubo and I were students together, but never knew it at the time. He was a graduate student at The ohns Hopkins niversity, where I was an undergraduate in mathematics. e both studied modern physics, taught by Dino Franco asetti, and we decided years later that we must have been in the same class. Akira was then a chemical oceanographer, but ship time and his stomach did not agree. Sohe turned to theory,and the rest is history. His impact has been phenomenal, and the First Edition of this book was his most in uential work. Building on his famous work with dye-di¤usion e periments, he turned his attention to organisms and created a unique melding of ideas from physics and biology.

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.