查看文章

Modelling Fluctuating Populations, originally published in 1982, is a classic textbook because primarily, this book takes a distinctive approach to population dynamics, by emphasizing from the earliest chapters that all populations fluctuate continuously. Traditional themes in theoretical ecology such as equilibrium and population stability are linked to analyses of the response of a population to environmental fluctuations and to extinction probabilities. Thus, the book's approach confronts head-on one common criticism of simple ecological models - the mismatch between the mathematical mechanisms studied and the questions of top ecological concern. Secondly, the book demonstrates the power of techniques based on linear mathematics. It has become fashionable to emphasize the importance of nonlinearity in ecological models, and there are some situations, notably those involving competition in fluctuating environments, where fundamentally nonlinear phenomena are critical to ecological understanding. But the importance in the real world of other nonlinear phenomena that attract much excitement among theorists, such as deterministic chaos, is much more doubtful. Many properties of fluctuations in nonlinear systems are well described by mathematical approaches that use linear equations to describe dynamics in the vicinity of an equilibrium state. The book gives a thorough introduction to these approaches, with particular focus on methods that exploit Fourier analysis. Thirdly, chapters 6 and 7 of the book take an unconventional approach to the formulation and analysis of stochastic population models. The starting point is a rigorous …