**Complex Population Dynamics: A Theoretical/Empirical Synthesis.** Peter Turchin. Monographs in Population Biology 35, Princeton University Press, Princeton, NJ, 2003. 536 pp. $29.95 (ISBN 0691090211 paper).

In the preface to this book, Peter Turchin clearly lays out its themes and functions: to review the current understanding of why populations oscillate, to synthesize the empirical and mathematical components of population ecology, to demonstrate that population ecology is on the “brink of maturity” in becoming a predictive science, and to communicate these themes to professional scientists and students alike. This is an ambitious undertaking, even though Turchin limits the scope of his themes by excluding both the spatial and the exogenous stochastic components of population processes. An additional intended function of the book, which becomes clear only toward its end, is to provide a decisive rejoinder to the fifth of seven principles laid out by Charles Krebs (1995) in analyzing the role of disease in population regulation: “Avoid mathematical models. They are more seductive than useful at this stage of the subject” (p. 9). Turchin pulls no punches in his criticisms of Krebs's work or of several other studies that he dissects in this book. This is good: It is what science is about. So I trust that Turchin will not object when I raise a few criticisms of his own approach to science.

But first some laudatory comments. Turchin certainly constructs a more thorough and persuasive argument for the maturity of population ecology as a predictive science than anyone else I have read. In doing so, he lays out a strong case for the importance of models in pushing forward the frontiers of population ecology. Turchin has as much experience as any quantitative scientist in melding theory and empiricism in population ecology, and he ably demonstrates this in the six chapters that constitute the section of his book titled “Case Studies.” This section is preceded by a three-chapter section on data, which in turn is preceded by a five-chapter section on theory.

In many ways Turchin's book is a *tour de force,* but it also has some notable weaknesses. These weaknesses do not detract from the book's importance as required reading for students and professionals in population ecology. But it is not the kind of text that the author promises in his preface, where he states, “I am assuming very little mathematical background on the part of the reader” (p. xii). True, chapters 3 and 4, “Single Species” and “Trophic Interactions,” do ease the reader into population modeling. The next three chapters, however— “Connecting Mathematical Theory to Empirical Dynamics” (chapter 5), “Empirical Approaches: An Overview” (chapter 6), and “Phenomenological Time Series Analysis” (chapter 7)—are more technical and much more difficult to understand for anyone without prior exposure to these topics. This is disappointing, given Turchin's express interest in having *Complex Population Dynamics* used as a textbook. Some additional background material on time series analysis, for example, is needed for chapter 7 to fulfill its promised didactic function.

A colleague and I assigned the book for a graduate course in population modeling this past spring. It was not nearly as successful a text as we had hoped on the basis of the promise in the preface. I would not use the book again as a core text for a graduate class or seminar, unless the students already had experience in fitting nonlinear data to dynamic models. One difficulty with the chapters in the “Case Studies” section is that they are packed with the results of regression analyses, and it is not always clear what methods Turchin used or whether the data or the output from models are being fitted to polynomial surfaces. In particular, some results were obtained through standard nonlinear regression techniques, while others were obtained through Turchin's own nonlinear time series modeling method, which is based on Box–Cox methods for fitting response surfaces. On the other hand, readers familiar with any of the case studies on the larch bud moth (chapter 9), the southern pine beetle (chapter 10), the red grouse (chapter 11), voles and other rodents (chapter 12), and the snowshoe hare (chapter 13) will surely be rewarded by Turchin's exquisite dissection of the best evidence to date about the endogenous ecological factors driving population processes in these species.

The case study on ungulates (chapter 14), however, is notably inferior to the others. The synthesis of ungulate models and data is dealt with in much more detail by Owen-Smith in his recent book, *Adaptive Herbivore Ecology* (2002). Further, although Turchin's chapter on trophic interactions is the most comprehensive review of its type, it does not discuss the class of metaphysiological models that underpin Owen-Smith's ungulate models. This is surprising, since this class of models deals directly with an issue raised by Turchin but then left unaddressed, namely, that “parameters of the logistic model combine individual-level parameters in subtle ways, and it is dangerous to modify them in a phenomenological fashion” (p. 62). (For more detailed discussion of this problem, see Ramos-Jiliberto [2002] and references therein.) Metaphysiological approaches also provide a natural way to build tritrophic models of the vole, lemming, snowshoe hare, and ungulate populations discussed by Turchin— models in which each of these species is simultaneously both a consumer of the vegetation below it and a resource for the predators above it. In concluding his chapter on ungulates, Turchin proposes “the ‘generic mammalian herbivore model’ (section 4.6) as an integrated framework for investigating cervid population dynamics” (p. 381). That other approaches are currently in vogue casts some doubt on Turchin's claim that population ecology really has the scientific maturity to adjudicate between modeling paradigms, at least in the area of ungulate dynamics. To my mind, even the heated debate over the functional response of consumers—whether this response should be resource-dependent or ratio-dependent—has not been satisfactorily resolved. Thus Turchin's criticism of Akcakaya's ratio-dependent approach (p. 350) may not be as decisive as he would have us believe.

This thought brings me to the nub of the book. Turchin poses the questions, “Is population ecology a mature science? Is it becoming a predictive science?” (p. 392) and concludes, “I believe that the answer is a resounding yes. In fact, my whole book can be taken as an extended answer to the this question” (p. 392). He certainly has taken a much more serious stab at answering this question than anyone else since Peters (1991) came to the opposite conclusion more than 12 years ago. It appears, however, that Turchin has been seduced into thinking that “population dynamics are underlaid by a set of foundational principles…which are analogous to laws in physics” (p. 393). Perhaps he overestimates the degree to which his models can reliably predict the future because his measures of model performance (set up in his equation 7.9) relate only to how well the next point in time is predicted rather than to prediction of some distant future time (an ability that is the hallmark of physical models). He appears to do so when, in a burst of exuberance on the penultimate page of his text, Turchin boldly states (in the context of modeling vole populations) that “there is no reason why a relatively simple oligofactorial model should be able to capture its dynamics. Yet it does” (p. 395). He invokes the ghost of physics envy past by adding parenthetically, “After writing this paragraph, I discovered that physicists have also been puzzled by the ‘unreasonable effectiveness of mathematics in natural sciences.’”

If you are a population biologist who believes in the Holy Grail of a set of population laws, or if you are willing to forgive this quirk, then you should buy Turchin's book and read it. You will need to be tolerant of a nonstandard approach to defining the order of a process (as opposed to defining it as the order of a difference or differential equation used to model that process). You will also need to accept an *ad hoc* approach to defining quasi-chaotic systems and a misappropriation of the term “quasi-stationary distribution.” (The latter has the well-defined meaning in stochastic process theory of a population distribution conditioned on not having entered an absorbing state such as extinction. Compare this with Turchin's use of the term to mean approximate stationarity over a finite interval of time.) Nonetheless, despite its faults, Turchin's book sets new standards in population ecology for monographs synthesizing theory and data. The book is, as Ilkka Hanski claims on its dust jacket, “a true landmark in the study of population ecology.”