The colour of environmental fluctuations associated with terrestrial animal population dynamics

Aim: The temporal structure (colour) of environmental variation influences population fluctuations, extinction risk and community stability. However, it is unclear whether environmental covariates linked to population fluctuations are distinguishable from a purely random process (white noise). We aimed to estimate colour coefficients and relative support for three models commonly representing coloured stochastic processes, in environmental series linked to terrestrial animal population fluctuations.

Location: North America and Eurasia.

Time period: 1901–2002.

Major taxa studied: Birds, insects and mammals.

Methods: We analysed multiple abiotic environmental covariates, comparing point estimates and confidence intervals of temporal structure in competing models fitted using white noise, autoregressive [AR(1)] and 1/f processes in the time domain and the frequency domain (where time series were analysed after decomposition into different sinusoidal frequencies and their relative powers). All animal time series were sampled annually for ≤ 50 years, potentially inflating type II errors. We also considered 101‐year series of matched environmental covariates, performing a statistical power analysis evaluating our ability to draw robust conclusions.

Results: Temperature‐related variables were associated with the largest fraction of population fluctuations. Ninety‐three per cent of shorter environmental series were indistinguishable from white noise, limited by time‐series length and associated with wide confidence intervals. The longer environmental series analysed in the time domain offered sufficiently high statistical power to identify correctly colour estimates ≥ |0.27|, indicating that 20% of series were best described by a slightly reddened noise process.

Main conclusions: Focusing on the short time‐scales typically available for ecologists, most environmental variables associated with terrestrial animal population fluctuations are best characterized by white noise processes, although type II errors are common. The correct detection of intermediately coloured noise with power 0.8 requires ≥ 16 data points in the time domain or ≥ 47 points in the frequency domain. Over longer time‐scales, where type II errors are less likely, one‐fifth of populations are associated with coloured (often reddened) variables.