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The frequency spectrum of structured discrete time population models: its properties and their ecological implications
Author(s) -
Greenman J. V.,
Benton T. G.
Publication year - 2005
Publication title -
oikos
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.672
H-Index - 179
eISSN - 1600-0706
pISSN - 0030-1299
DOI - 10.1111/j.0030-1299.2005.13652.x
Subject(s) - noise (video) , autocorrelation , statistical physics , environmental noise , filter (signal processing) , spectral density , computer science , population , eigenvalues and eigenvectors , nonlinear system , population cycle , discrete time and continuous time , biological system , control theory (sociology) , mathematics , ecology , physics , statistics , telecommunications , acoustics , artificial intelligence , biology , demography , control (management) , quantum mechanics , sociology , image (mathematics) , computer vision , sound (geography)
Much research effort has been devoted to the study of the interaction between environmental noise and discrete time nonlinear dynamical systems. A large part of this effort has involved numerical simulation of simple unstructured models for particular ranges of parameter values. While such research is important in encouraging discussion of important ecological issues it is often unclear how general are the conclusions reached. However, by restricting attention to weak noise it is possible to obtain analytical results that hold for essentially all discrete time models and still provide considerable insight into the properties of the noise‐dynamics interface. We follow this approach, focusing on the autocorrelation properties of the population fluctuations using the power (frequency) spectrum matrix as the analytic framework. We study the relationship between the spectral peak structure and the dynamical behaviour of the system and the modulation of this relationship by its internal structure, acting as an “intrinsic” filter and by colour in the noise acting as an “extrinsic” filter. These filters redistribute “power” between frequency components in the spectrum. The analysis emphasises the importance of eigenvalues in the identification of resonance, both in the system itself and in its subsystems, and the importance of noise configuration in defining which paths are followed on the network. The analysis highlights the complexity of the inverse problem (in finding, for example, the source of long term fluctuations) and the role of factors other than colour in the persistence of populations.