Abstract
AbstractAimThe 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.LocationNorth America and Eurasia.Time period1901–2002.Major taxa studiedBirds, insects and mammals.MethodsWe 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.ResultsTemperature‐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 conclusionsFocusing 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.
Highlights
A major issue in population biology concerns how the colour of en‐ vironmental variation interacts with population dynamics to drive observed patterns of population fluctuations (e.g., Dillon et al, 2016; Halley, 1996; Ruokolainen, Lindén, Kaitala, & Fowler, 2009; Steele, 1985)
Longer environmental series (L, 101 years) showed a larger fraction of estimates being significantly different from zero (Figure 3d–f) compared with short series (Figure 3a–c); the estimates that were distinguishable from white noise processes tended to be reddened (Figure 3d–f)
We have shown that the majority (93%) of environmental variables that have previously been linked to terrestrial animal population fluctuations do not appear to show any recognizable temporal structure, when estimated over a maximum of 50 years
Summary
A major issue in population biology concerns how the colour of en‐ vironmental variation interacts with population dynamics to drive observed patterns of population fluctuations (e.g., Dillon et al, 2016; Halley, 1996; Ruokolainen, Lindén, Kaitala, & Fowler, 2009; Steele, 1985). Given the short time‐scales typically available for ecological time‐series data, two important questions in population biology are : (a) what model form (e.g., white noise, autoregressive or 1/f process) best characterizes, and (b) what statistical power do we have for correctly detecting autocorrelation in the environmental variables that drive natural population fluctuations? We assessed the level of statisti‐ cal support and power in natural environmental time series for three models commonly used to characterize or simulate (coloured) sto‐ chastic processes: white noise (a purely random process without any temporal structure), AR(1) and 1/f models Support for these meth‐ ods was assessed by analysis in both the frequency and time domains (Chatfield, 1996; Dillon et al, 2016) to allow meaningful comparison across the methods. We recorded the frequency of different environmental coefficient estimates (including their confidence intervals) to (a) establish the evidence for different coloured environmental covariates associated with population fluc‐ tuations in different animal taxa, and (b) assess whether results are characterized by lack of statistical power using the relatively short (≤ 50‐year) length of available animal population time series through comparison with longer (101‐year) versions of the same associated en‐ vironmental series
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