Extinction risk in a temporally correlated fluctuating environment.

Usually extinction risk due to environmental stochasticity is estimated under the assumption of white environmental noise. This holds for a sufficiently short correlation time tauc of the fluctuations compared to the internal time scale of population growth r-1 (tauc/r-1<<1). Using a time-discrete simulation model we investigate when the white noise approximation is misleading. Environmental fluctuations are related to fluctuations of the birth and death rates of the species and the temporal correlation of these fluctuations (coloured noise) is described by a first-order autoregressive process. We found that extinction risk increases rapidly with correlation time tauc if the strength of noise is large. In this case the white noise approximation underestimates extinction risk essentially unless temporal correlation is very small (tauc/r-1<<0.1). Extinction risk increases only slowly with correlation time if the strength of noise is small. Then the white noise approximation may be used even for stronger temporal correlations (tauc/r-1>/=0.1). Thus, the estimation of extinction risk on the basis of white or coloured noise must be justified by time scale and strength of the fluctuations. Especially for species that are sensitive to environmental fluctuations the applicability of the white noise approximation should be carefully checked.