On the relation between temporal variability and persistence time in animal populations

Abstract

Summary 1.The relationship between temporal variability, spectral redness and population persistence for a large number of long-term time series was investigated. Although both intuition and theory suggest that more variability in population abundance would mean greater probability of extinction, previous empirical support for this view has not been conclusive. Possible reasons are the shortage of long-term data and the difficulties of adequately characterizing temporal variability, two issues that are explicitly addressed in this paper. 2. We examined the relationship between population variability and quasi-extinction time (measured as the time required to observe a 90% decline of population abundance) for a large set of data comprising 554 populations for 123 species that were censused for more than 30 years. Two aspects of temporal variability were considered in relation with the quasi-extinction time: a baseline value (coefficient of variation over a fixed, 30-year, time scale), and a measure of the rate of increase of the population variability over time (spectral exponent). 3. The results show that the quasi-extinction time was shorter for populations having higher temporal variability and redder dynamics. The relation between persistence time and population variability was compared for different taxa, trophic levels, habitat type (aquatic and terrestrial) and body sizes and compared with theoretical expectations.

Analysing multiple time series and extending significance testing in wavelet analysis

“…We propose a class of surrogates that models the underlying statistical structure of the time series as 1/ƒ noise (Halley 1996). Such a model is rather convenient as it allows for the 'more time, more variation' effect displayed by many ecological time series (Lawton 1988, Inchausti & Halley 2002, Vasseur & Yodzis 2004. This class of surrogates is thus adapted to ecological time series, as it is, in addition, designed to deal with short time series.…”

Poor environmental tracking can make extinction risk insensitive to the colour of environmental noise

“…Many abiotic environmental variables, such as temperature, are temporally autocorrelated (often showing a reddened spectrum [2,3]). Biotic environmental variables, such as resource or prey abundance, are also likely to have coloured noise properties, as many time-series of population size exhibit temporal autocorrelation [4,5]. Demographic rates depend on the environmental conditions and consequently coloured environmental noise can cause demographic rates also to be temporally autocorrelated, which in turn can affect population dynamics.…”

Life-History Variation Predicts the Effects of Demographic Stochasticity on Avian Population Dynamics

“…cific differences in population variability (Pimm 1991;Ariño and Pimm 1995;Inchausti and Halley 2002), we must therefore obtain a proper understanding of how the separate effects of demographic and environmental stochasticity are related to demographic variation across species. Theoretical analyses have shown that knowledge of demographic stochasticity is especially important for fluctuations of small populations (May 1973;Leigh 1981;Lande 1998;Lande et al 2003) that often are of management concern.…”