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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.

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Land‐use and climate change are two of the primary drivers of the current biodiversity crisis. However, we lack understanding of how single‐species and multispecies associations are affected by interactions between multiple environmental stressors.We address this gap by examining how environmental degradation interacts with daily stochastic temperature variation to affect individual life history and population dynamics in a host–parasitoid trophic interaction, using the Indian meal moth, Plodia interpunctella, and its parasitoid wasp Venturia canescens.We carried out a single‐generation individual life‐history experiment and a multigeneration microcosm experiment during which individuals and microcosms were maintained at a mean temperature of 26°C that was either kept constant or varied stochastically, at four levels of host resource degradation, in the presence or absence of parasitoids.At the individual level, resource degradation increased juvenile development time and decreased adult body size in both species. Parasitoids were more sensitive to temperature variation than their hosts, with a shorter juvenile stage duration than in constant temperatures and a longer adult life span in moderately degraded environments. Resource degradation also altered the host's response to temperature variation, leading to a longer juvenile development time at high resource degradation. At the population level, moderate resource degradation amplified the effects of temperature variation on host and parasitoid populations compared with no or high resource degradation and parasitoid overall abundance was lower in fluctuating temperatures. Top‐down regulation by the parasitoid and bottom‐up regulation driven by resource degradation contributed to more than 50% of host and parasitoid population responses to temperature variation.Our results demonstrate that environmental degradation can strongly affect how species in a trophic interaction respond to short‐term temperature fluctuations through direct and indirect trait‐mediated effects. These effects are driven by species differences in sensitivity to environmental conditions and modulate top‐down (parasitism) and bottom‐up (resource) regulation. This study highlights the need to account for differences in the sensitivity of species’ traits to environmental stressors to understand how interacting species will respond to simultaneous anthropogenic changes.

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