Unexpected dominance of high frequencies in chaotic nonlinear population models

Abstract

BECAUSSE water has a higher heat capacity than air, large bodies of water fluctuate in temperature more slowly than does the atmosphere¹. Marine temperature time series are 'redder' than atmospheric temperature time series by analogy to light: in red light, low-frequency variability has greater amplitude than high-frequency variability, whereas in white light all frequencies have the same amplitude². Differences in the relative importance of high-and low-frequency variability in different habitats affect the population dynamics of individual species and the structure of ecological communities^3–9. Population dynamics of individual species are thought to be dominated by low-frequency fluctuations, that is, to display reddened fluctuations¹⁰. Here I report, however, that in eight nonlinear, iterative, deterministic, autonomous, discrete-time population models, some of which have been used to model real biological populations, the power spectral densities of chaotic trajectories are neither white nor reddened but are notably blue, with increasing power at higher frequencies.