Spectral color, synchrony, and extinction risk

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.