Do Life History Traits Affect the Accuracy of Diffusion Approximations for Mean Time to Extinction?

Estimating the risk of extinction is one of the central foci of conservation biology, but such estimates are often constrained by the available data. In the face of limited data, several authors have suggested using diffusion approximations to estimate the mean time to extinction as a means of quantifying the risk of extinction. However, the accuracy of the diffusion approximation for characterizing extinction processes has not been well tested. We develop a simulation model that includes life history parameters and incorporates both demographic and environmental stochasticity in population dynamics. We use the simulation model to study the effects of stochasticity on the accuracy of the diffusion approximation across different life history strategies. Our results show that predictions for mean time to extinction from the diffusion approximation may differ significantly from simulated ones, and that the amount and direction of the error in the approximation is not systematic. Given that this error is unpredictable and may be very sensitive to the exact demographic rates, we believe that the diffusion approximation should be used with caution as a basis for assessing extinction risk or making management decisions.