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Survival or extinction of an endangered species is inherently stochastic. We develop statistical methods for estimating quantities related to growth rates and extinction probabilities from time series data on the abundance of a single population. The statistical methods are based on a stochastic model of exponential growth arising from the biological theory of age or stagestructured populations. The model incorporates the socalled environmental type of stochastic fluctuations and yields a lognormal probability distribution of population abundance. Calculation of maximum likelihood estimates of the two unknown parameters in this model reduces to performing a simple linear regression. We describe techniques for rigorously...