Noise colour and the risk of population extinctions

A recurrent problem in ecology and conservation biology is to estimate the risk of population extinctions. Extinction probabilities are not only imperative for conservation and management, but may also elucidate basic mechanisms of the regulation of natural populations. The usual way of modelling stochastic influence on population dynamics has been to assume that the external noise is uncorrelated. This means that each and every randomly drawn noise value is totally independent on previous ones. This is what is generally called 'white' noise. However, the noise itself can be temporally autocorrelated. That is, the values of the random numbers used in the noise process will depend on previous ones. Here we show that the autocorrelation, or colour, of the external noise assumed to influence population dynamics strongly modifies estimated extinction probabilities. For positively autocorrelated ('red') noise, the risk of extinction clearly decreases the stronger the autocorrelation is. Negatively autocorrelated ('blue') noise is more ambiguously related to extinction probability. Thus, the commonly assumed white noise in population modelling will severely bias population extinction risk estimates. Moreover, the extinction probability estimates are also significantly dependent on model structure which calls for a cautious use of traditional discrete-time models