A smorgasbord of stochastic dynamics: Stochastic Population Dynamics in Ecology and Conservation by Russ Lande, Steinar Engen and Bernt-Erik Saether. Oxford University Press, 2003. £60.00/£27.50 hbk/pbk (222 pages) ISBN 0 19 852524 9/0 19 852525 7

View Large Image | Download PowerPoint SlideRuss Lande, Steinar Engen and Bernt-Erik Saether have been using stochastic models to understand ecological communities for a combined total of nearly 60 years, individually and in collaboration. Their new book, Stochastic Population Dynamics in Ecology and Conservation, presents a broad sampling of these efforts, and is a smorgasbord that will be palatable to mathematically proficient readers, or to those willing to take some of the results on faith.The book covers a wide range of topics that are relevant to both basic and applied ecology: linear and nonlinear population growth, extinction dynamics, population viability analysis, sustainable harvesting, biodiversity metrics, and neutral theories in community ecology, among others. The authors prefer simple models, aiming for general conclusions rather than mathematical rigor. They rightly criticize overdependence on simulations, but use them where appropriate to extend the conclusions of analytical models. Lande et al. follow in the tradition of ecological modelers such as Nisbet and Gurney [1xNisbet, R.M and Gurney, W.S.C. See all References[1], emphasizing the power and applicability of linear approximations rather than the complexities of strongly nonlinear models. They also sensibly eschew discrete models, such as branching processes, which achieve realism by following the fates of discrete individuals but pay a high price in flexibility and tractability. The authors show that the continuous-population alternative, stochastic partial differential equations, are a powerful framework for answering a broad spectrum of ecological questions (they wisely sweep the difficult mathematical assumptions that underlie these models under the rug).The drawback of the tremendous breadth of the book is that it prevents it from being a solid introduction to any particular topic. I was hoping to find an introductory text on stochastic dynamics (complementary to Denny and Gaines' excellent Chance [2xDenny, M and Gaines, S. See all References[2]), but this book doesn't fill that niche. The authors do introduce the basics of stochastic dynamics in the first chapter, and generally present modeling frameworks, such as diffusion approximations, early and return them in later chapters. However, the style assumes a high mathematical comfort level, and the book sometimes glosses over the deeper context of the methods: the assurance of the Introduction that readers need only a working knowledge of elementary calculus and statistics is technically correct, but optimistic. For this reason, Stochastic Population Dynamics will work best as a sampler of applications for mathematically inclined ecologists who can then go back to the primary literature for more detail.The authors challenge their theories with empirical data, weighing in on a variety of current topics. For example, they point out that temporal autocorrelation in population dynamics, often taken as a proxy for density dependence, can also arise from lags implicit in the life history of an organism. They present a straightforward method, based on simulating population dynamics with bootstrapped parameters, to address recent concerns [3xWhen is it meaningful to estimate an extinction probability?. Fieberg, J and Ellner, S.P. Ecology. 2000; 81: 2040–2047CrossrefSee all References[3] that population viability analysis fails to incorporate uncertainty in parameters. (Although I like their approach, I was disappointed by their rote dismissal of Bayesian approaches. I also disagree with their recommendation to present only the upper confidence limit of the extinction probability, which leads to the conclusion that any poorly understood species is endangered. Isn't it more honest to say that the confidence limits on extinction probability are 1–99% than to say only that there is a chance that extinction rate could be as high as 99%?) The authors also showcase their recent work on the roles of dispersal and environmental variation in driving spatial synchrony in population fluctuations. Finally, they use a new approach to partitioning metrics of biodiversity, which I initially took to be of theoretical interest only, as a platform to test (and reject) Hubbell's neutral theory of community assembly [4xHubbell, S.P. See all References[4] for a community of tropical butterflies.Stochastic Population Dynamics provides a snapshot of research into stochastic population dynamics by some of the best workers in the field. It gives the flavor of the authors' accomplished and well balanced approach to stochastic dynamic modeling, but it is definitely a sampler rather than a practical introduction to the methods. It will appeal to ecologists who are up for a mathematical challenge and who want to see the variety of theoretical and applied questions that one can answer by clever application of stochastic models to ecological systems.