Chaos in Real Data. The Analysis of Non-Linear Dynamics from Short Ecological Time Series


  • Mike Bonsall

Joe N. Perry, Robert H. Smith, Ian P. Woiwod & David R. Morse (eds) (1999)
Chaos in Real Data. The Analysis of Non-Linear Dynamics from Short Ecological Time Series.
P. 225. Kluwer Academic Publishers, London. ISBN 0-412-79690-2.

As the quest for chaos in ecological time series continues unabated, the recent release of Chaos in Real Data (in the ‘Population and Community Biology’ Series) adds a strong string to the bow of the intrepid. The book is a tangible product of a workshop held in Leicester to examine a series of general questions about the application and interpretation of time-series methods to short ecological time series. The book is clearly aimed at those who wish to gain a good grounding in the approaches and techniques available for analysing ecological time series.

Methodological chapters provide an introduction into the philosophy, techniques and statistics associated with ecological time-series analysis. The first chapter (Ellner) is a detailed insight into the theory and range of statistical techniques applicable to short ecological time series. An understanding of deterministic chaos has now given way to the recognition that ecological dynamics are composed of both stochastic (noise) and non-linear (biotic) events. Ellner advocates the use of local, short-term responses to perturbations in understanding ecological population dynamics in order to disentangle noise from non-linearities. Local Lyapunov exponents are extensively reviewed together with brief excursions into metrics, including the divergence of the conditional mean and conditional distributions and forecasting error profiles as approaches for understanding the operational definition of chaos (sensitivity to initial conditions). The second chapter (Turchin and Ellner) reviews time-series analysis and concentrates on the full utilization of both mechanistic and phenomenological models as a pragmatic approach to this type of analysis. Using semi-mechanisitic approaches, the art of modelling a time series is outlined as fixing what is known biologically and using time-series statistics to explore that which remains unknown. Brief comments are made on appropriate model selection. It is clear that model selection still remains an ignored element in statistical ecology (and is equally, if not more, important than parameter estimation). Selecting a range of statistical models provides credence to inferences made about the dynamics and complexity of observed time series. This obviously remains a moot point in time-series analysis.

Chapters 3–7 form the test bed for time-series methodologies. Case studies centred around exemplary data sets on the dynamics of childhood measles (Bryan Grenfell), small rodents in Northern Fennoscandia (Heikki Henttonen and Ilkka Hanski), The Rothamsted Insect Survey (Ian Woiwod and colleagues), a host–parasitoid–pathogen interaction (Michael Begon and colleagues) and blowfly populations (Robert Smith and colleagues) aim to elucidate the central themes in ecological population regulation, stochasticity and chaos.

A detailed examination of measles cases in developed countries (Grenfell) reveals a wealth of dynamical complexity where the disease is influenced by both non-linear and stochastic events, driven in part by birth rates, age structure and vaccination. Discussions on the role of non-stationarity, noise and heterogeneity on the dynamics of measles are provided, and although the identification of chaos in measles cases remains arguable, the application of a range of methodologies (non-linear forecasting, stochastic and deterministic mechanistic models) provides a detailed understanding of the dynamics of measles epidemics.

Through the use of time-series analysis and mechanistic predator–prey models, Henttonen and Hanski reveal that in contrast to southern rodent populations, northern populations in Fennoscandia show marked delayed density dependence with the real possibility of chaotic dynamics. The role of shared enemy effects on complex multispecies interactions and how these may generate complex behaviours with sudden and dramatic changes in population dynamics are explored: the application of time-series methodologies to understanding complex species interactions still remain relatively novel. Woiwod and colleagues examine aphid and moth field data from The Rothamsted Insect Survey using response surfaces models. Detailed analyses reveal no evidence for non-linear dynamics in either the aphid or moth population series. Additionally, the role of measurement error in analysing the aphid series is briefly explored. This is a developing theme in the analysis of ecological time series.

The analysis by Begon and colleagues of the laboratory insect moth, parasitoid, pathogen system highlights again the importance of model selection in time-series analysis. Results from response surface models and non-parametric autoregressive techniques are compared. The application of these techniques reflects different motivations: response surface models define the complexity of the dynamics while detailed autoregressive methodologies address specific questions of the data. For example, is this pathogen a cause or a consequence of cycles in the host population? Analysis of control and metal-contaminated blowfly populations (Smith and colleagues) reveals that linear time-series analysis can distinguish broad differences in population dynamics. Control blowfly populations cycle with an increased periodicity when compared to the metal-contaminated populations. Again, it is the semi-mechanistic models that provide the most successful method for analysing the blowfly time series.

Inculcation is advocated throughout the book as the way in which time-series techniques are to be mastered and implemented and, in an unprecedented approach, a detailed glossary of specific terms associated with time-series analysis is included to aid the interpretation and accessibility of the book. However, in criticism, as time-series analysis is as much about graphical representation as quantitative analysis, a number of typesetting errors (e.g. the lack of colour on appropriate figures) mar what is otherwise a superlative book. With the data sets still readily accessible, adequate scope is left for extensions to the methodologies, interpretation of the ecologies and the continuity of that ever-elusive quest.