The Physics of Foraging: An Introduction to Random Searches and Biological Encounters,

In 1996 H. Eugene “Gene” Stanley, his graduate student Gandhimohan Viswanathan, and collaborators at Boston University and the British Antarctic Survey published a paper partly inspired by Yossi Klafter and Michael Shlesinger’s stimulating suggestion that animal foraging might be modeled by non-Brownian, superdiffusive, random walks. The paper reported that a set of flight times of the wandering albatross followed a power-law distribution *t*^{-μ}, with *μ* ≈ 2, and proposed several tentative explanations including that albatrosses forage in fractally structured natural environments, including the turbulent atmosphere and oceans. In a second paper in 1999, Viswanathan and colleagues proposed something even bolder: They related their power law to a Lévy foraging hypothesis, which stated that foraging behavior based on the *μ* = 2 scaling exponent is optimal in some instances, and that natural selection would thus have evolved to exploit it.

Viswanathan (now a professor in Brazil at the Federal University of Rio Grande do Norte), Stanley, and their collaborators, Marcos da Luz and Ernesto Raposo, have now published their ideas in *The Physics of Foraging: An Introduction to Random Searches and Biological Encounters*, which aims to synthesize anomalous diffusion and animal foraging. As with previous texts written (or co-written) by Stanley, this book provides many clear explanations of nonintuitive concepts as evidenced by the lucid presentation of random walks and critical phenomena in the first three chapters. Another example of the text’s clarity is the discussion in chapter 4 of the difference between large values drawn from a power law distribution and classical outliers.

*The Physics of Foraging* is strong in its discussion of the development, during the past 10 years, of the Lévy foraging hypothesis, in which foraging can be viewed biologically or more generically as a random search problem. Chapters 5 through 8 of the book are devoted to the early experimental evidence, foraging by animals and humans, and the quality of collected data. The final 6 chapters focus on theory, particularly variants of the superdiffusive random walk and the notions of optimality behind the Lévy foraging hypothesis.

Unfortunately the book presents only seven figures drawn from experimental data; it also makes at least one error of fact in its presentation in chapter 4 of a 2007 paper revisiting the albatross data set, coauthored by Andrew Edwards, then at the British Antarctic Survey, this book’s authors, me, and others. The book correctly notes that the longest “flights” in that data set were spurious, but mistakenly lays the blame on the idea that the birds “had remained for some time in captivity prior to release.” In fact, the spurious “flights” were a result of the sometimes long intervals between attaching the tracking devices to the birds and their subsequent take-offs or between the birds’ landings and the devices’ subsequent removal.

I would also have preferred to see a wider variety of literature referenced in the book. Partially stimulated by the reexamination of the albatross data set, some recent papers on non-Brownian models of foraging present strikingly different viewpoints on simulation, data analysis, and statistical inference: A very recent example of which is the 2011 *Journal of the Royal Society Interface* paper “Assessing Lévy walks as models of animal foraging,” by Alex James, Michael Plank, and Edwards. I also think the appendix on maximum-likelihood estimation, which discusses best practices for statistical inference of power laws, would have benefited from an explicit reference to, and discussion of, the 2009 *SIAM Review* paper, “Power-law distributions in empirical data,” by Aaron Clauset, Cosma Shalizi, and Mark Newman.

Another unfortunate weakness is inadequate proofreading. The back cover, for example, suggests that the book will interest “ecologists with little familiarity with the concepts and methods of statistical physics,” whereas the first page refers instead to ecologists “already familiar” with the same. Occasionally one finds apt neologisms, like a reference to “statistically coercive” quantities, though more often the proofreading misses typos like “VHS” radio waves or a reference to the albatrosses of “southern (instead of “South”) Georgia.” Hopefully such mistakes will be fixed in a future edition.

Despite those problems, I think *The Physics of Foraging* is useful and will find a place in the literature of the physics and ecology communities. Over the past 40 years, Stanley has given us a number of excellent books. His *Introduction to Phase Transitions and Critical Phenomena* (Oxford University Press, 1971) remains a classic. Three other books co-written or co-edited by Stanley are among a select few that have inspired many scientists, myself included, to pursue criticality-based approaches to the study of complex systems. They are *On Growth and Form: Fractal and Non-Fractal Patterns in Physics* co-edited with Nicole Ostrowsky (Springer, 1985); *Fractal Concepts in Surface Growth* with Albert-László Barabási (Cambridge University Press, 1995); and *Introduction to Econophysics: Correlations and Complexity in Finance* with Rosario Mantegna (Cambridge University Press, 2000).

As the exciting, cross-disciplinary field of complex-systems science develops, it faces the twin challenges of analyzing rich new data sets (see Stanley’s review of *Complex Webs: Anticipating the Improbable* in PHYSICS TODAY, November 2011, page 58) and, at the same time, incorporating the relevant prior knowledge and expertise of existing disciplines. I expect to use *The Physics of Foraging* as part of that process. For advanced courses, the book could be supplemented by Klafter and Igor Sokolov’s excellent new book on anomalous diffusion, *First Steps in Random Walks: From Tools to Applications* (Oxford University Press, 2011); both books would stimulate learning and debate among graduate students and postdocs.