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

Citation: Phys. Today 65(1), 44 (2012); doi: 10.1063/PT.3.1401 View online: http://dx.doi.org/10.1063/PT.3.1401 View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v65/i1 Published by the American Institute of Physics.

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More and Different We also learn about interpersonal “Of course I am not religious—I relations at Bell Labs during its heroic don’t in fact see how any scientist Notes from a Thoughtful years. We are given Anderson’s defi- who thinks at all deeply can be Curmudgeon nitely non-postmodernist views on the so” (page 133). And, “We atheists science wars. We hear his altogether can . . . argue that, with the Philip W. Anderson modern revolution in attitudes World Scientific, Hackensack, NJ, admirable opinions on the politiciza- tion of science. We get a history of the toward homosexuals, we have 2011. $38.00 paper (243 pp.). become the only group that may ISBN 978-981-4350-13-6 theory of superconductivity as seen from the frontlines. We get his opin- not reveal itself in normal social ions—almost all respectful, but often discourse” (page 177). Reviewed by with an edge—about John Bardeen, N. David Mermin Hans Bethe, Leon Cooper, Richard “Consciousness [is] one of the When asked to review Feynman, Murray Gell-Mann, Stephen major deep problems, already Philip Anderson’s new Hawking, Brian Josephson, Lev Lan- apparent in the 20th century, book, I had expected dau, Bernd Matthias, Ilya Prigogine, which may take most of the 21st century to solve” (page 113). And the opportunity to fire J. Robert Schrieffer, William Shockley, “the greatest puzzle of all [is] the a few curmudgeonly and Eugene Wigner, among others. I emergence of consciousness” shots at the greatest curmudgeon to could easily have listed more if the book (page 138). (When I complained grace our profession over the past two- came with an index. to a very distinguished colleague thirds of a century. But I was wrong. In The only part of the collection I did that his Theory of Everything had More and Different: Notes from a Thought- not find a delight to read are Anderson’s nothing to say about conscious- ful Curmudgeon, Anderson has put attempts to convey to the general ness, he replied, “Consciousness together an entertaining and instructive reader the scientific content of some of is an illusion.”) collection of highly readable reviews, his own contributions. He is aware of columns, talks, and unpublished essays the problem: “I have elsewhere dis- “If there weren’t any solids we’d on science and the scientists he has avowed any ability [to explain technical have no way to measure space— known. He is rarely inappropriately scientific matters to laymen], and the so by breaking the symmetry of provocative, and he is a pleasure to read. reader—especially the true layman— space we have in a sense created One of Anderson’s recurrent themes will surely agree.” I would add that space as a new entity” (page 144). is his refutation of naive reductionism even a physicist from a different sub- (I was once charged in the pages going back at least 40 years to his field will find some of his explanations of PHYSICS TODAY with post- famous 1972 essay in Science, “More is a little terse. Just a touch of strictly ped- modernism for making similar different,” which unfortunately is not agogical reductionism might have remarks about time.) included here. Reductionism over- helped. looks emergence. In a section entitled I blame most shortcomings of the And, most engagingly, “All I can “Emergence as the God principle”—a book on the publisher. We are not told say to the younger theorists is: well-deserved swipe at Leon Leder- where or, more importantly, when most don’t trust anyone over 45, except man—Anderson eloquently defines of the more than 60 essays were pub- maybe me, and I’m not so sure emergence as “obedient to the laws of lished or written, which often requires about me” (p. 159). the more primitive level, but not con- the reader to deduce from internal evi- ceptually consequent from that level” dence the state of the issues at the time (page 90). Nobody contemplating the of Anderson’s critical discussion. Some- The Physics of Lagrangian of the electromagnetic and times an essay contains references to matter fields would have guessed that other articles in the unidentified collec- Foraging broken gauge symmetry was the key to tion from which that essay was taken. An Introduction to Random the phenomenon of superconductivity. And because many of the themes that Searches and Biological Even with the clue provided by the lab- interest Anderson are taken up in sev- oratory of Heike Kamerlingh Onnes, it eral essays over, one assumes, a span of Encounters took 32 years after the creation of quan- many years, I found the absence of an Gandhimohan M. Viswanathan, tum mechanics to discover the explana- index a frequent source of frustration. Marcos G. E. da Luz, Ernesto P. tion, which is consistent with, but not I conclude with just a few of the Raposo, and H. Eugene Stanley implied by, the quantum laws. many wonderful obiter dicta, which Cambridge U. Press, give More and Different a special charm: New York, 2011. $50.00 N. David Mermin, a retired professor of (164 pp.). “When we are all done, it will ISBN 978-1-107-00679-9 physics at Cornell University in Ithaca, New turn out that there is no exotic York, last wrote in PHYSICS TODAY about P. W. form of ‘dark matter’, merely a In 1996 H. Eugene “Gene” Anderson 30 years ago; in “E pluribus boojum: comedy of errors in a field where Stanley, his graduate stu- The physicist as neologist” (April 1981, it is practically de rigueur to dent Gandhimohan Vis- page 46) Anderson rescues “boojum” from underestimate one’s limits of wanathan, and collabora- the dustbin of rejected scientific terms. error” (page 107). tors at Boston University

44 January 2012 Physics Today www.physicstoday.org and the British Antarctic Survey pub- longest “flights” in that data set were some recent papers on non-Brownian lished a paper partly inspired by Yossi spurious, but mistakenly lays the blame models of foraging present strikingly Klafter and Michael Shlesinger’s stimu- on the idea that the birds “had different viewpoints on simulation, lating suggestion that animal foraging remained for some time in captivity data analysis, and statistical inference: might be modeled by non-Brownian, prior to release.” In fact, the spurious A very recent example of which is the superdiffusive, random walks. The “flights” were a result of the sometimes 2011 Journal of the Royal Society Interface paper reported that a set of flight times long intervals between attaching the paper “Assessing Lévy walks as models of the wandering albatross followed a tracking devices to the birds and their of animal foraging,” by Alex James, power-law distribution t-μ, with μ ≈ 2, subsequent take-offs or between the Michael Plank, and Edwards. I also and proposed several tentative expla- birds’ landings and the devices’ subse- think the appendix on maximum- nations including that albatrosses for- quent removal. likelihood estimation, which discusses age in fractally structured natural envi- I would also have preferred to see a best practices for statistical inference of ronments, including the turbulent wider variety of literature referenced in power laws, would have benefited from atmosphere and oceans. In a second the book. Partially stimulated by the an explicit reference to, and discussion paper in 1999, Viswanathan and col- reexamination of the albatross data set, of, the 2009 SIAM Review paper, leagues 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 from selection would thus have evolved to New and Forthcoming Titles Cambridge! exploit it. Viswanathan (now a professor in Atoms in Intense Now in Paperback! Brazil at the Federal University of Rio Laser Fields Grande do Norte), Stanley, and their Quantum Physics C. J. Joachain, Michel Le Bellac collaborators, Marcos da Luz and N. J. Kylstra, $65.00: Pb: 978-1-107-60276-2: and Ernesto Raposo, have now published R. M. Potvliege 606 pp. their ideas in The Physics of Foraging: An $135.00: Hb: 978-0-521-79301-8: Introduction to Random Searches and Bio- 580 pp. logical Encounters, which aims to syn- thesize anomalous diffusion and ani- Continuum Semiconductor mal foraging. As with previous texts Quantum Optics written (or co-written) by Stanley, this Mechanics and Thermodynamics Mackillo Kira book provides many clear explanations and Stephan W. Koch From Fundamental of nonintuitive concepts as evidenced $90.00: Hb: 978-0-521-87509-7: Concepts to Governing 658 pp. by the lucid presentation of random Equations walks and critical phenomena in the Ellad B. Tadmor, first three chapters. Another example of Ronald E. Miller, The German the text’s clarity is the discussion in and Ryan S. Elliott Physical Society chapter 4 of the difference between $80.00: Hb: 978-1-107-00826-7: in the Third Reich large values drawn from a power law 372 pp. Physicists between Autonomy distribution and classical outliers. and Accommodation The Physics of Foraging is strong in its Edited by Dieter Hoffmann and discussion of the development, during Modeling Materials Mark Walker $90.00: Hb: 978-1-107-00684-3: the past 10 years, of the Lévy foraging Continuum, Atomistic and Multiscale Techniques 482 pp. hypothesis, in which foraging can be Ellad B. Tadmor viewed biologically or more generically and Ronald E. Miller The Mathematical as a random search problem. Chapters $85.00: Hb: 978-0-521-85698-0: Language of 5 through 8 of the book are devoted to 786 pp. Quantum Theory the early experimental evidence, forag- From Uncertainty to ing by animals and humans, and the Entanglement quality of collected data. The final Optical Coatings Teiko Heinosaari 6 chapters focus on theory, particularly and Thermal and Mário Ziman variants of the superdiffusive random Noise in Precision $85.00: Hb: 978-0-521-19583-6: walk and the notions of optimality Measurement 340 pp. behind the Lévy foraging hypothesis. Edited by Unfortunately the book presents Gregory Harry, Thermal Physics only seven figures drawn from experi- Timothy P. Bodiya, Concepts and Practice mental data; it also makes at least one and Riccardo DeSalvo Allen L. Wasserman $140.00: Hb: 978-1-107-00338-5: $65.00: Hb: 978-1-107-00649-2: error of fact in its presentation in chap- 344 pp. 318 pp. ter 4 of a 2007 paper revisiting the alba- tross data set, coauthored by Andrew Edwards, then at the British Antarctic Prices subject to change. Survey, this book’s authors, me, and others. The book correctly notes that the www.cambridge.org/us/physics 800.872.7423 January 2012 Physics Today 45 books

“Power-law distributions in empirical The Shaping of Life sheets. Another favorite of Harrison’s data,” by Aaron Clauset, Cosma Shalizi, are the somatic embryos of conifers, and Mark Newman. The Generation of such as the hybrid larch Larix x lepto - Another unfortunate weakness is Biological Pattern europaea. As an embryo, Larix is a multi- inadequate proofreading. The back cellular organism accessible to obser - cover, for example, suggests that the Lionel G. Harrison vation in much the same way as book will interest “ecologists with little Cambridge U. Press, New York, 2011. Acetabularia. Despite its multi- familiarity with the concepts and meth- $99.00 (247 pp.). cellular nature, the develop- ISBN 978-0-521-55350-6 ods of statistical physics,” whereas the ment of outgrowths called first page refers instead to ecologists In 1917 D’Arcy Wentworth cotyledons from Larix embryos “already familiar” with the same. Thompson penned the classic greatly resembles the whorl Occasionally one finds apt neologisms, On Growth and Form (revised formation in the single-cell like a reference to “statistically coer- edition, Dover, 1992), in which Acetabularia and, indeed, can be cive” quantities, though more often the he argued, contrary to the Dar- modeled on a similar mathe- proofreading misses typos like “VHS” winian orthodoxy of the time, matical formalism. radio waves or a reference to the that structure originates before In the second half of the albatrosses of “southern (instead of function and that growth and form can book, Harrison turns the reader’s gaze “South”) Georgia.” Hopefully such be explained through mathematics and from plant development to animal mistakes will be fixed in a future physics. By the early 1950s, Alan Turing development. Here one learns about edition. would demonstrate how spatial pat- segmentation in the Drosophila egg, Despite those problems, I think The terns could arise through chemical amphibian heart development, the Physics of Foraging is useful and will instabilities inherent in a simple set of rearrangement of stripe patterns in find a place in the literature of the coupled reaction–diffusion equations. angelfish, vertebrate limb develop- physics and ecology communities. Turing patterns, as they came to be ment, the growth of slime molds, and Over the past 40 years, Stanley has known, are evident in nature; for exam- much more. The examples are highly given us a number of excellent books. ple, some resemble the spots on a leop- varied, some touched on in more His Introduction to Phase Transitions and ard, others the stripes on a zebra or detail than others, but taken together Critical Phenomena (Oxford University the complex fractal-like patterns on they clearly display that there is no Press, 1971) remains a classic. Three seashells. But it was not until the 1980s shortage of complex developmental other books co-written or co-edited by that chemists could actually set up behavior that can be understood Stanley are among a select few that reactions that would produce Turing through mathematics. have inspired many scientists, myself patterns. One notable omission, which Harri- included, to pursue criticality-based Though embraced by mathemati- son admits early on in the manuscript, approaches to the study of complex cians and physicists, Turing’s mathe- is any discussion about the genetics of systems. They are On Growth and matical approach to biological pattern development. That is fair; as Harrison’s Form: Fractal and Non-Fractal Patterns formation is hardly accepted by most numerous examples show, much can in Physics co-edited with Nicole experimental biologists. The late physi- be said about understanding complex Ostrowsky (Springer, 1985); Fractal cal chemist and theoretical biologist developmental behavior through Concepts in Surface Growth with Albert- Lionel Harrison laments such resis - course-grained mathematical models László Barabási (Cambridge University tance in The Shaping of Life: The Genera- of pattern formation at the level of Press, 1995); and Introduction to Econo- tion of Biological Pattern, which he abstraction presented in The Shaping of physics: Correlations and Complexity in drafted before his untimely death in Life. In fact, a mathematical approach to Finance with Rosario Mantegna (Cam- 2008 and which was completed by developmental modeling is the subject bridge University Press, 2000). friends and colleagues. Harrison pio- of numerous complementary books, As the exciting, cross-disciplinary neered a quantitative approach to including Biological Physics of the Devel- field of complex-systems science devel- developmental biology in the 1970s, an oping Embryo (Cambridge University ops, it faces the twin challenges of ana- era when few thought it was useful to Press, 2005) by Gabor Forgacs and lyzing rich new data sets (see Stanley’s mathematically model the complexities Stuart Newman and The Self-Made review of Complex Webs: Anticipating the of biological growth and development. Tapestry: Pattern Formation in Nature Improbable in PHYSICS TODAY, November The Shaping of Life makes the case for (Oxford University Press, 1999) by 2011, page 58) and, at the same time, simple coarse-grained mathematical Philip Ball. For a technical discussion of incorporating the relevant prior knowl- models in biology—simple, that is, in the genetic origin of bodily form, inter- edge and expertise of existing disciplines. comparison to models that explain the ested readers can consult Imaginal Discs: I expect to use The Physics of Foraging as phenomena at a genetic or systems The Genetic and Cellular Logic of Pattern part of that process. For advanced level. Many of the topics in the book’s Formation (Cambridge University Press, courses, the book could be supplemented first half are drawn from Harrison’s 2002) by Lewis Held Jr; for a more read- by Klafter and Igor Sokolov’s excellent own research on plant development. ily accessible popular account on the new book on anomalous diffusion, First His work had led him to investigate a same topic, readers can check out the Steps in Random Walks: From Tools to Appli- variety of novel creatures such as immensely pleasurable Endless Forms cations (Oxford University Press, 2011); Acetabularia, a seaweed that grows to Most Beautiful: The New Science of Evo both books would stimulate learning and several centimeters and generates mul- Devo and the Making of the Animal King- debate among graduate students and tiple whorls of hair-like filaments along dom (W. W. Norton, 2005) by Sean B. postdocs. its exterior. Those organisms are ideal Carroll. Nicholas Watkins laboratories for studying the dynamics Besides being a text about biological British Antarctic Survey of growth, since they are mostly trans- pattern formation, The Shaping of Life is Cambridge, UK parent and grow in two-dimensional an exposition on how human beings

46 January 2012 Physics Today www.physicstoday.org