The colour of environmental fluctuations associated with terrestrial animal population dynamics

Abstract

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.

Can temporal covariation and autocorrelation in demographic rates affect population dynamics in a raptor species?

“…These intervals were large and included 0 in all cases. This result is consistent with those from Gilljam et al () who stressed that uncertainty associated with the estimation of correlations is generally high and the type II error frequent. In our case, low precision is partly due to the length of the time series (15 years) and to the error propagation from the estimates of the vital rates to subsequent estimates of covariation and autocorrelation in the joint model.…”

“…Another reason of the limited empirical investigation of covariation and autocorrelation in vital rates is the long-term data needed (Doak, Gross, et al, 2005a). At least 10 or 16 years of continuous monitoring on different vital rates seems required according to Swanson (1998) and Gilljam et al (2019), respectively.…”

Temporal correlations among demographic parameters are ubiquitous but highly variable across species

“…Although the data sets we analysed are among the most comprehensive individual‐based long‐term monitoring available, uncertainty in correlation estimates was large and most of them had 95% CRI overlapping 0. This considerable uncertainty associated with correlation estimates has also been reported in previous studies (Compagnoni et al, 2016; Fay et al, 2020) and shows that precise estimation of temporal correlations is challenging and requires large sample size (Gilljam et al, 2019; Riecke et al, 2019). It is therefore unsurprising that many studies did not detect any correlation among demographic parameters (Jongejans et al, 2010), but this does not necessarily mean that correlations are non‐existent or even negligible.…”

“…First, it requires individual‐based monitoring in which individuals are marked and tracked. Second, precise estimates of annual demographic parameters and temporal correlations require large sample size, with hundreds of individuals monitored over several decades (Gilljam et al, 2019; Riecke et al, 2019). These requirements strongly limit the number of data sets adequate for the investigation of temporal correlations in demographic parameters.…”

How does temporal variation in habitat connectivity influence metapopulation dynamics?

“…thermal regime) may be becoming more strongly positively autocorrelated (Wang andDillon 2014, Di Cecco andGouhier 2018). A recent meta-analysis suggests that over long durations red environmental noise translates into red population trajectories (Gilljam et al 2019), which may be accompanied by heightened extinction risk (Ruokolainen et al 2009). In terms of the drivers of disconnection, Jaeger et al (2014), for example, show that under future climate change streamflow regimes in the western US may reduce the duration of flow by up to 20% and hence shift what are currently perennial streams to being intermittent.…”