Environmental parameters such as temperature and rainfall have a positively autocorrelated variance structure which makes it likely that runs of good or bad conditions will occur. It has previously been demonstrated that autocorrelated environmental variance can increase the probability of extinction of populations not subject to density-dependent limitation (effects vary for populations with density-dependent regulation). In fact, some authors suggest that large positive autocorrelation in biologically important parameters such as temperature may be mimicked using an uncorrelated signal with higher variance. Increasing autocorrelation is therefore viewed as solely increasing extinction risk for populations with geometric growth. As a result, it has also been suggested that positive autocorrelation will decrease the probability that a species will establish in a novel location. We use a modeling approach to examine the effect of positively autocorrelated signals that alter the growth rate of density-independent populations (i.e., those with a very low density). We tightly control signal variance, and moreover, use spectral mimicry to ensure that populations are subject to exactly the same signal elements, rearranged to produce the appropriate level of autocorrelation. With this method we eliminate the possibility that results are driven by differences in the variance or the probability of extreme values across signals with different degrees of autocorrelation
Results/Conclusions
We find that where variance is low, positive autocorrelation can increase the probability of extinction and decrease the probability of invasive species establishment as previously predicted (where invasion is defined as lack of extinction in a given interval). However, where variance is high and the geometric mean of the population growth rate is low, autocorrelation increases invasion risk (where risk is defined as passing an upper threshold density), even when extinction probability is largely unaffected. This effect is particularly important since species classified as having low probability of invasion risk (0.1) on the basis of population growth rates measured in low variance environments, may actually have quite a substantial probability of establishing (0.4). The mechanism behind the effect seems to be the disproportionate influence of short runs of good conditions initially following introduction. Finally, we discuss appropriate definitions of invasion risk, and explain why a definition of “no extinction” in a given time period may be inappropriate.