Title: Population Dynamics and the Colour of Environmental Noise

Authors: Veijo Kaitala, Janica Ylikarjula, Esa Ranta and Per Lundberg

Status: Proceedings of the Royal Society of London, Series B, Biological Sciences 264, 1997, pp. 943-948

Keywords: Population dynamics, Environmental noise, Time series analysis, Population modelling, Chaos

The effect of red, white and blue environmental noise on discrete-time population dynamics is analysed. The coloured noise is superimposed on Moran-Ricker and Maynard Smith dynamics, the resulting power spectra are then examined. Time series dominated by short- and long-term fluctuations are said to be blue and red, respectively. In the stable range of the Moran-Ricker dynamics, environmental noise of any colour will make population dynamics red or blue depending on the intrinsic growth rate. Thus, telling apart the colour of the noise from the colour of the population dynamics may not be possible. Population dynamics subjected to red and blue environmental noise show, respectively, more red or blue power spectra than those subjected to white noise. The sensitivity to differences in the noise colours decreases with increasing complexity and ultimately disappears in the chaotic range of the population dynamics. These findings are duplicated with the Maynard Smith model for high growth rates when the strength of density dependence changes. However, for low growth rates the power spectra of the population dynamics with noise are red in stable, periodic and aperiodic ranges irrespective of the noise colour. Since chaotic population fluctuations may show blue spectra in the deterministic case, this implies that blue deterministic chaos may become red under any colour of the noise.