Diffusion and ecological problems: Modern perspectives.
This book is the second edition of the popular and very influential book of \textit{A. Okubo}, Diffusion and ecological problems: Mathematical models. (1980; Zbl 0422.92025). Stimulated by notes intended for an updated version left by Okubo at his untimely death in 1996, S. A. Levin gathered together a dozen leading researchers in the field of diffusion problems in ecology to produce the updated book that Okubo was unable to complete. Each chapter was adopted by an expert in the chapter's topics who amended Okubo's notes and added new material. The goal of the new version was not necessarily to provide a comprehensive coverage of this vast field, but to trace the influence of the original book, which was immense. The book can be divided roughly into two parts. The first part deals with passive diffusion of chiefly abiotic objects. There is a chapter on the mathematical basics of diffusion modeling and two chapters that treat a wide variety of examples and applications, including diffusion within and above (terrestrial and aquatic) plant canopies, diffusion of spores, diffusion of nutrients in oceans, the dispersal of gametes, and the diffusion of chemicals associated with smell, taste, and communication. The second part of the book deals with what Okubo calls active diffusion, i.e., the diffusion of objects (such as animals) that perform motion by themselves. Of course, it is recognized that both passive and active diffusion can be important in modeling the dispersal of animals (particularly those of small size). There is a second chapter that expands further on the mathematical treatment of diffusion processes for biological organisms. The remaining chapters deal with numerous examples and applications of animal diffusion and dispersal, grouping (swarming and schooling), movements within home ranges, and problems associated with patchiness (e.g., in plankton communities). Birth and death (reaction-diffusion) processes, including multi-species interactions such as predator-prey relationships, are treated in the final chapter. The reader will find a great deal of biological interpretation and discussion (including references) in addition to mathematical derivations and analyses. A valuable asset of the book is the reference list that contains well over one thousand literature citations. S. Levin and his colleagues are to be commended and congratulated on this volume, which undoubtedly will continue well into the future to hold its legendary status in the field of diffusion processes in biology.
scientific article; zbMATH DE number 1745054