American Scientist

Chance in Biology: Using Probability to Explore Nature. Mark W. Denny and Steven Gaines. xiv + 291 pp. Princeton University Press, 2000. $39.50.

As a colleague of mine who teaches statistics is fond of saying, "The teaching of the importance of randomness shouldn't be left to chance." As if in response to that mantra, Mark Denny and Steven Gaines have produced this lively, well-written text, in which they explore the meaning of chance in biology. With the caveat that the book is not about inferential statistics per se, they express the hope that the reader "will come away with a glimpse of joy to be had in bringing order out of chaos, the feeling of achievement in making an important biological prediction based on the intrinsic variability of nature."

The plan of the book is well-conceived. In chapter 2, "Rules of Disorder," boomer biologists will be delighted, as I was, to find Venn diagrams like those from our grade school years. These analyze in a nontrivial manner the genetics of bipolar smuts (parasitic fungi) and the ethology of sarcastic fringeheads (a marine fish). The use of Bayesian statistics to determine probabilities relating to HIV testing is also illustrated.

In chapters 3 and 4, discrete and continuous patterns of disorder are presented in a distinctive Socratic style, forcing the reader to participate in the discoveries. The authors impart a deep appreciation for the normal distribution and the utility of the Central Limit Theorem.

Chapters 5 and 6 address diffusion in biology, from the molecular level to the macroscopic, with a grateful nod to Howard Berg's pithy Random Walks in Biology (Princeton, 1983). Topics discussed include the limits to size and speed in aquatic microorganisms; how receptors and ion channels on cell surfaces are affected by scale; problems of dispersal and fertilization in marine larvae; and how genetic drift and fixation of alleles, rubber elasticity in biomaterials (including the limits to energy storage), and protein configurations can all be understood as diffusion problems.

In chapter 7, the authors explore situations in which the extreme values of a property are important rather than the average. Cocktail-party acoustics (could sound waves from the festivities damage your eardrum?), the human life span (is there an absolute upper limit?) and baseball statistics (the analysis of winning streaks is applicable to predator-prey interactions) are the real-world situations they use to illustrate how the statistics of extremes can be applied.

But the page-turner for me was chapter 8, which demonstrates how random noise has constrained—and enhanced(!)—the nervous system in animals. Four heuristic examples are explored: vision in low light, the threshold of sensitivity for hearing, the effects of channel noise on neurons and the recent excitement engendered by stochastic resonance, whereby randomness itself causes unexpected system behavior when nonlinearities are present. Fans of allometry will learn why frog ears are so big, and neurobiologists will get a tantalizing glimpse of how nervous noise might be "a boon to (rather than the bane of) signal detection in animals."

Throughout, the authors show the important algebra and calculus, without omitting the steps that often mystify a mathematically rusty biologist. A student who reads this book closely will come away with a much deeper appreciation for the universality of diffusion mechanics in science, the deep connections between the distributions central to inferential statistics, the importance of extreme events and how to deal with them analytically, and, most importantly, the power and limitations inherent in the underpinning of the inferential statistics that the student has learned elsewhere, usually in a recipe-style course. Accordingly, Chance in Biology has earned a place on my list of required reading for students preparing for the Ph.D. qualifying exam.

Denny and Gaines greatly increased the book's value for students at any level by including quantitative problems after each chapter; detailed solutions can be found in chapter 9. The problems vary quite a bit in difficulty, so mathematical sophisticates and tyros will both be served well. The problems are invariably well-posed, interesting in their own right and directly solvable by diligent (sometimes subtle) application of the preceding chapter's principles. Examples include figuring out paternity using Bayesian statistics, calculating time for diffusive transport across ocean basins and determining the number of amino acids found in the rubbery protein of tropical versus arctic jellyfish.

My factual quibbles, and suggestions for improvement in any future editions of this marvelous text, are few and far between: Euler's equation (invoked in the proof of the Central Limit Theorem in chapter 4) isn't merely a definitional relation as indicated, it's a hard-won jewel linking algebra and geometry. In explaining the derivation of the limits to size for single cells in chapter 5, the authors missed an opportunity to introduce metabolic scaling exponents (which would subtly change the result proffered). Also, most phytoplankton take up carbon dioxide preferentially to bicarbonate (although it's true that bicarbonate dominates at seawater pH, and some phytoplankton have enzymes to disequilibrate the seawater status quo). The authors could perhaps use their talent for enlightening explanations to further illuminate the distinction between stochastic processes and chaos and to expand on the mechanistic implications of noise in nonlinear systems. By the time a second edition comes out, the menagerie of stochastic-resonance phenomena will probably have swelled to include not just neurobiology and geophysics but also other disciplines of interest to biologists, including population biology. I also wish they would expose the dirty secret that the mathematics used to model diffusive phenomena predict infinite propagation speed (meaning that at an infinitesimal time after release, there is an infinitesimal detection of the diffusing quantity at infinite distance from the source), even though it's possible to use random-walk theory to calculate the eminently reasonable "time to capture" of a diffusive particle in a container with absorbing walls.

In the meantime, this book has already diffused off my bookshelf through the hands of several students and a colleague or two, proof that the "time to capture" of the authors' work by active minds is wonderfully short.—Mark R. Patterson, School of Marine Science, Virginia Institute of Marine Science, College of William & Mary