# Estimate of population extinction risk and its application to ecological risk management

Iwasa, Y., Hakoyama, H., Nakamaru, M. and Nakanishi, J.Environmental threats, such as habitat size reduction or environmental pollution, may not cause immediate extinction of a population but may shorten the expected time to extinction. We developed a method to estimate the mean time to extinction for a density-dependent population with environmental fluctuation and to compare the impacts of different risk factors. We first derived a formula of the mean extinction time for a population with logistic growth and environmental and demographic stochasticities expressed as a stochastic differential equation model (canonical model). The relative importance of different risk factors is evaluated by the decrease in the mean extinction time. We studied an approximated formula for the reduction in habitat size that enhances extinction risk by the same magnitude as a given decrease in survivorship caused by toxic chemical exposure. In a large population (large K) or in a slowly growing population (small r), a small decrease in survivorship can cause the extinction risk to increase, corresponding to a significant reduction in the habitat size. Finally, we studied an approximate maximum likelihood estimate of three parameters (intrinsic growth rate r, carrying capacity K, and environmental stochasticity σ2e) from time series data. By Monte Carlo sampling, we can remove the bias very effectively and determine the confidence interval. We discuss here how the reliability of the estimate changes with the length of time series. If we know the intrinsic rate of population growth r, the mean extinction time is estimated quite accurately even when only a short time series is available for parameter estimation.

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