Speed of expansion and extinction in experimental populations.

Although the causes of population extinction are well understood, the speed at which populations decline to extinction is not. A testable, counter-intuitive prediction of stochastic population theory is that, on average, for any interior interval of the domain of biologically attainable population sizes, the expected duration of increase equals the expected duration of decline. Here we report the first empirical tests of this hypothesis. Using data from two experiments in which replicate populations of Daphnia magna were observed to go extinct under different experimental conditions, we failed to reject the null hypothesis of no difference between the growth and decline phases in populations under constant conditions and conditions with modest environmental variability, but find strong evidence to reject equal first passage time in highly variable environments. These results confirm the prediction of equal passage times entailed by diffusion models of population dynamics, supporting continued application in both population theory and conservation decision making under the restricted conditions where the approximation can be expected to hold.