Population dynamics and the color of environmental noise: A study on a three‐species food chain system

Abstract

In the present study, the effect of ‘red’, ‘white’ and ‘blue’ environmental noise on population dynamics in a simple three‐species food chain system was analyzed. The ‘colored’ noise was superimposed on the three‐species food chain model first put forth by Rosenzweig in different ways and the resulting power spectra were investigated. We showed that the amplitude of environmental noise, the trophic level at which a population is positioned and whether a population is directly affected by environmental noise, are all important with respect to the way in which a population responds to noise with different colors. For the deterministic case, all population dynamics are ‘red’ irrespective of the system dynamics. When all species are sensitive to environmental noise, the top predator's dynamics always remain ‘red’ regardless of the color of the noise and its amplitude, whereas the dynamics of the intermediate species turn ‘blue’ under disturbances of any color with high amplitude, and those of the basal species may become ‘blue’ only under ‘blue’ noise. If only one species is sensitive to environmental noise, the dynamics of the insensitive species are always ‘red’, irrespective of the color of the noise and its amplitude. Unlike previous results obtained by studying single‐species models, our results have almost nothing to do with deterministic system dynamics. In other words, changing the deterministic system dynamics from stable via periodic to chaotic does not qualitatively change the outcome. Our results are of importance in determining how we interpret the ubiquitous ‘red’ power spectrum of natural ecological time series.