Scaling rules for the final decline to extinction.

Space-time scaling rules are ubiquitous in ecological phenomena. Current theory postulates three scaling rules that describe the duration of a population's final decline to extinction, although these predictions have not previously been empirically confirmed. We examine these scaling rules across a broader set of conditions, including a wide range of density-dependent patterns in the underlying population dynamics. We then report on tests of these predictions from experiments using the cladoceran Daphnia magna as a model. Our results support two predictions that: (i) the duration of population persistence is much greater than the duration of the final decline to extinction and (ii) the duration of the final decline to extinction increases with the logarithm of the population's estimated carrying capacity. However, our results do not support a third prediction that the duration of the final decline scales inversely with population growth rate. These findings not only support the current standard theory of population extinction but also introduce new empirical anomalies awaiting a theoretical explanation.