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premium than ever before on “cleverness in producing a model from which analytic insights can be gained” (Hastings, p. 501). There will definitely be no Lecture Notes in Biomathematics. The series has passed away, and Springer has held its wake in style. However, an exciting new era of biomathematics has already begun and, to quote Levin (p. 387) again, “The challenge is great for a new and powerful body of theory.”

In other words: Biomathematics is dead. Long live biomathematics!

MICHAEL MESTERTON-GIBBONS Department of Mathematics

Florida State University Tallahassee, FL 32306-3027, U.S.A.

SSDI: 0092-8240(95)00320-P

Predictability and Nonlinear Modelling in Natural Sciences and Economics, edited by Johan Grasman and Gerrit van Straten, Kluwer Academic Pub- lishers, Dordrecht, 1994. $256, 653 pp.

Since the dawn of digital computing, governments and businesses have used complicated simulation models to predict the behavior of complex systems ranging from the economy to the weather. Often, these simulation models are large assemblages of interacting nonlinear dynamical systems whose predictions are confounded by uncertainty in model parameters, in external forcings and even in the structure of the governing equations themselves. The accuracy of long-range forecasts may also be limited by the sensitive dependence on initial conditions which characterizes chaotic systems. The current debate over the possible effects of global climate change is in part fueled by the output of such models; it is also evidence that decisions based on the predictions of these models can have potentially large economic and political impacts. Therefore, understanding how uncertainty can interact with nonlinearity to diminish predictability, particularly in large complex systems, is an important if extremely difficult task.

In an admirable attempt to address this issue, a conference was held in 1993 at the Wageningen Agricultural University which brought together “scientists who are modelling the dynamics of natural and economic pro- cesses on the one hand, with systems analysts and mathematicians who develop methods for quantifying the characteristic features of such models on the other.” The proceedings of that conference are reported in the book we review here.

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In general, conference proceedings are, to quote Forrest Gump’s mother, “like a box of chocolates: you never know what you’re going to get,” and so it is with Nonlinear Modelling in the Natural Sciences and Economics. The proceedings are divided into chapters on geophysics, agriculture, population biology, systems sciences, environmental sciences and economics. (This division in and of itself points to the difficulty the conference organizers must have had in trying to establish common ground among the partici- pants.) The chapter on geophysics contains nine articles on meteorology and climatology. Of the five articles composing the chapter on agriculture, three use simulation models to study the effects of uncertainty in the climate on predictions of crop yields. The chapter on population biology includes nine papers on topics ranging from measles to fish schooling behavior. The chapter on systems science (12 papers) focuses on sensitivity and risk analyses of complex systems with a few examples. The 11 articles in Chapter 5, on environmental sciences, are characterized by the use of Monte Carlo methods to evaluate prediction uncertainty in large ecosystem models. The final chapter presents eight papers, half of which examine the nonlinear dynamics of relatively simple deterministic models of economic processes.

In the Introduction, the editors outline the conference’s formidable goal as “the cross-fertilization of ideas between the different disciplines that share the objective of making forecasts of dynamical processes.” Unfortu- nately, if any transdisciplinary unification of prediction and nonlinear modelling techniques occurred at the conference, it is not reflected in this book. Instead, these proceedings are a collection of 55 loosely related articles by 95 authors from 18 countries assembled into one book.

As mathematical ecologists, we had hoped to see how the nonlinear modelling and prediction techniques used in other fields could be applied to problems in population or community ecology and vice versa. We were, on the whole, disappointed, mainly because the liberal use of jargon rendered “out-of-field” chapters largely inaccessible. Most of the articles are written for specialists and present a number of obstacles to the neophyte. A serious hurdle to our comprehension of many articles was the lack of an explicit description of the model under consideration. One must either be familiar with the derivation of a discipline-specific model (e.g. “the quasigeostrophic barotropic potential vorticity equation”) or be satis- fied with vague statements like: “We built a matrix in which the columns represent the type of weather.. . .” In many cases the model description consists entirely of an acronym (CLEANER, SWACOM, DEMO, SENECA, SMOES, UNCSAM, SIM-PEL, SMART, EMEP, IMAGE, etc.) and a reference to the literature.

Rather than illuminating common ground, these proceedings demon- strate the large gap between research on deterministic models of idealized

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systems and attempts to understand and manage highly complex natural systems. They also highlight the difficulty scientists from different fields often encounter when trying to communicate with each other.

There are, however,.a few articles that stand out, if only for the fact that we could understand them without specialized training. One well written article on the evaluation of forecasts, by A. H. Murphy and M. Ehrendor- fer, distinguishes and explores the relationship between the quality of a forecast and its value. Ehrendorfer also contributed an interesting article on the use of the Liouville equation to describe the evolution of uncertainty in initial conditions under the operation of a nonlinear dynamical system. Another notable paper, by R. Engbert and F. R. Drepper, is on chaotic transients in a model for childhood disease epidemics. In this article, the authors modify a traditional epidemiological model to include immigration. They then simulate a stochastic version of the model and demonstrate that demographic stochasticity can shorten the duration of chaotic transients. Finally, R. A. Fleming’s and C. A. Shoemaker’s use of a simulation model of spruce budworm-forest dynamics to illustrate a method of validating the component parts of a complex model deserves mention.

This book could have been improved in several ways. A preface to each chapter is desperately needed to unify that chapter’s articles and introduce at least the terminology of the field. We cannot help but note that this book is unaffordable for all but the most well endowed of the “research workers at universities and (semi-) governmental institutes” whom the publisher claims as the book’s audience. (At $256-nearly 4Oc per page-this is the highest priced set of proceedings that has been reviewed in this journal over the past two years [n = 41.) Finally, the frequency and magnitude of typographical errors is irritating and, in some cases, seriously reduces readability.

MICHAEL NEUBERT and SARAH LITTLE Biology Department

Woods Hole Oceanographic Institution Woods Hole, MA 02543, U.S.A.

SSDI: 0092-8240(95)00330-4

Air and Water: The Biology and Physics of Life’s Media, Mark W. Denny, Princeton University Press, Princeton, 1993. $39.50 (cloth), xvii + 341~~.

Air and Water: The Biology and Physics of Life’s Media by Mark W. Denny is intended for biologists and physical scientists. It is a wonderful book