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In the Introduction to Modelling Fluctuating Populations, published in 1982, we characterized the state-of-the-art in theoretical ecology as being that “at present we can make quantitative, testable models only of laboratory systems which are themselves caricatures of reality.” This unattractive situation no longer holds, as ecological theory has made spectacular advances over the past two decades. Thanks to new approaches to modelling, and to advances in time series analysis, mechanistically based models are now well-established tools for elucidating the dynamics of natural populations.

 

So why reprint a 20-year-old book?

 

The primary reason is that the 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.

 

Second, 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.

 

Third, 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 treatment of “demographic stochasticity”, the randomness that occurs because population change is caused by a sequence of individual births and deaths. We introduce the concept of “white noise” in a manner appropriate for ecologists, develop powerful approximate methods for predicting the intensity of fluctuating populations, and offer a systematic approach to modeling the probability of extinction."

 

“However, Modelling Fluctuating Populations is exceptional in more than one way and provided me with an unexpected pleasure; I enjoyed almost all of the book and found every chapter valuable.” Nature

 

“This is a splendid book which brings to the mathematically competent biologist, for the first time, a range of techniques which will enable him to construct and analyze more realistic models. “Biometrics

 

“A second reason is that this is the nest book on mathematical modelling of population growth in existence.” Natural Resource Modelling

 

“This excellent book gives a state-of-the-art account of our understanding of the dynamical behavior of biological populations. The book has been carefully designed to be read at several different levels: all ecologists -- no matter how empirical -- will benefit from dipping into it; while expert mathematicians will find it a valuable reference work.” Robert M. May in Acta Applicandae Mathematicae

 

“This book comes very close to the reviewers’ ideal of what a perfect textbook for an introductory course in the mathematical modeling of population growth should be.” Mathematical Biosciences