Scaling of Extinction Time With Habitat Size in Experimental Populations

Abstract

Theoretical models suggest that the mean time to extinction scales with habitat size through either exponential or power law relationships, depending on demographic and environmental stochasticity. Despite extensive theoretical work, empirical validation of these scaling relationships is limited. Here, we report a microcosm study of Daphnia magna populations in experimental chambers consisting of 1, 2, 4, 8, 16, or 32 patches, with a total of 35 populations monitored daily until extinction. We tested the scaling of extinction time with patch count using nonlinear regression models for both exponential and power law functions, comparing model fit with mean squared error. Overall, the data supported the power law over an exponential relationship (bootstrapped ) although the difference between the models is not evident when comparing some treatment levels. Our experiment provides the first empirical test of long-standing theoretical predictions and lays a foundation for future studies to expand the understanding of extinction dynamics in ecological systems.