ORIGINAL PAPER Spectral color, synchrony, and extinction risk Frida Lögdberg & Uno Wennergren Received: 9 June 2010 /Accepted: 14 October 2011 # The Author(s) 2012. This article is published with open access at Springerlink.com Abstract The autocorrelation of environmental variation, also called noise color, influences the population dynamics and the probability of extinction risk. Increasing the distance, the variations over time for two sites will become more unsynchronized. Thus, both degree of synchrony and noise color are parts of the same environmental variation affecting population dynamics in a spatial setting. We present a novel method of generating environmental noise controlling for its noise color and synchrony. We apply these time series to the carrying capacity (K) or (indirectly) to the growth rate (r) and altered the population regulation response between over- and under-compensatory. A novel finding is that the qualitative effects of noise color on extinction risk do not differ with degree of synchrony. Our results for the highly responsive dynamics (large growth rates and over-compensatory dynamics) agree with previous non-spatial studies by showing that the redder the noise, the lower the extinction risk. The results for the less responsive dynamics are more complex, indicating that intermediate noise color causes a larger extinction risk compared with a whiter or a redder color. To explain this hump-shaped response, we use classical descriptions of how means and variances of population density depend on noise color. These results allow a new straightforward interpretation of how extinction risk depends on the population dynamics, noise color, and synchrony. Keywords Noise color . Synchrony . Extinction risk . Subdivided population . Temporal correlation . Spatial model Introduction In conservation biology, and in ecology in general, it is important to correctly understand the causes of increased risk of extinction. Accordingly, estimates of temporal fluctuations in population density are essential because they constitute a major factor determining the persistence of a population (e.g., Inchausti and Halley 2003). The mix between variance and mean has a marked impact on the extinction risk and is often measured as the coefficient of variation. Still, temporal fluctuations have other properties that may influence the probability of extinction, one of which is autocorrelation. Several investigations of natural abiotic and biotic time series have shown positively autocorrelated variation referred to as red noise (Steele 1985; Pimm and Redfearn 1988; Pimm 1991; Halley 1996; Inchausti and Halley 2002; Vasseur and Yodzis 2004). In theoretical and empirical studies, the autocorrelation in time series of population densities is usually measured using a spectral representation obtained by applying a Fourier transform. The spectral representation of a time series without any autocorrelation has an equal mixture of all inherent frequencies, and it is termed white noise in analogy to white light. A time series that is (positively) autocorrelated is dominated by low frequencies and is denoted red noise. In theoretical studies, either autoregressive (AR) or spectral methods are used to generate colored time series of environmental noise, and the environmental noise is included in models of population growth that generate fluctuations in population densities. Most investigations of noise affecting population fluctuations use models in which Electronic supplementary material The online version of this article (doi:10.1007/s12080-011-0145-x) contains supplementary material, which is available to authorized users. F. Lögdberg : U. Wennergren (*) IFM, Theory and Modelling, Linköping University, Linköping, Sweden e-mail: unwen@ifm.liu.se Theor Ecol DOI 10.1007/s12080-011-0145-x