Nonlinear Physics of Ecosystems, Ehud Meron, CRC Press, 2015. $89.95 (344 pp.). ISBN 978-1-4398-2631-7 Buy at Amazon
Many concepts and methods from nonlinear physics have proved to be useful for addressing important problems in ecology. Indeed, a growing number of physicists are working with ecologists and are making significant contributions to ecology. Pattern formation and spatial ecology—how those patterns are related to ecological phenomena—are particular research areas that benefit from the interdisciplinary interactions. For example, field observations of vegetation patterns in arid and semiarid regions have revealed patterns similar to ones found in fluid dynamics and nonlinear optics.
Any book that attempts to bridge ecology and nonlinear physics would be welcomed by scientists who work at the intersection of both fields. In my own work, I have collaborated with ecologists to develop quantitative methods and models to address biodiversity dynamics and spatiotemporal early warning signals of catastrophic shifts in ecosystems. I have also taught courses for mixed audiences of agronomists, ecologists, and physicists.
I was greatly impressed by the variety of topics covered in Ehud Meron’s Nonlinear Physics of Ecosystems and by the depth in which they are discussed. The author’s introduction to each topic is clear, and the book’s overall organization makes it easily readable. At the beginning of each chapter is an outline of the major points treated, and at the end, a summary of the key ideas that were developed. The bibliography is extensive and comprehensive. I found few omissions. The most significant one would be James Murray’s classic text Mathematical Biology II: Spatial Models and Biomedical Applications (Springer, 2003), which, although it does not focus on spatial ecology, has substantial overlap with this book. Nonlinear Physics of Ecosystems also contains many figures and photos that help readers to visualize spatial patterns in real ecosystems. All that makes Meron’s book an important reference, particularly for researchers of spatial self-organization and spatial ecology.
The book is divided into three parts. The first begins with a quite standard presentation of the basics of self-organization in nonequilibrium systems. It then offers a qualitative review of spatial ecology and presents outstanding problems such as desertification and biodiversity loss. The concluding chapter for that section raises important and broadly relevant questions about ecosystem modeling: Why model? How should a model be set up? What is the significance of qualitative information? Such questions should be considered by anyone who conducts scientific research and uses models.
The second part is devoted to pattern formation theory, which, according to Meron, is a missing link in ecological research. In fact, the book’s main purpose is to fill that gap; in essence, part two is the book’s nucleus. The author presents basic and advanced methods related to the main types of pattern formation mechanisms. Among the plethora of structures are stripe and hexagonal patterns, scale-free patterns, and spiral waves.
The third part considers different applications of pattern formation theory to spatial ecology. The author explains the significance of self-organized vegetation patchiness to paramount ecological problems presented in the first part, including desertification and biodiversity loss in changing environments. I enjoyed reading the two final chapters—11 and 12—which cover topics I have been working on, namely, regime shifts, desertification, and species coexistence and diversity in plant communities. Particularly well done were the discussions on different early warning signals of regime shifts and their spatial aspects. I enjoyed the explanation of species coexistence induced by plants that act as ecosystem engineers by modifying their physical environment and in certain circumstances facilitating the growth of other species.
Nonlinear Physics of Ecosystems surely will contribute to the development of a newly emerging interdisciplinary research field at the interface of ecology and pattern formation. I would recommend it to graduate students who want to conduct research in mathematical ecology or physics applied to spatial-ecology problems. A minor caveat: I wish the book had included exercises to help students reinforce and test their understanding; maybe it will in the next edition.
Nonetheless, it could be used either as a main or supporting textbook in a one-semester course for advanced undergraduate or graduate students in physics or ecology or in a course with a mixed audience of students from both disciplines. I also warmly recommend the book for nonlinear physicists, applied mathematicians, and theoretical ecologists working on those cutting-edge environmental interdisciplinary problems.
Hugo Fort is head of the complex systems group at the University of the Republic in Montevideo, Uruguay. Since 2002 he has been conducting research in complex systems and physics applied to ecology and evolution.
