EXTINCTION RATE OF A POPULATION UNDER BOTH DEMOGRAPHIC AND ENVIRONMENTAL STOCHASTICITY

We examined the asymptotic rate of population extinction beta when the population experiences density-dependent population regulation, demog raphic stochasticity, and environmental stochasticity. We assume discr ete-generation population dynamics, in which some parameters fluctuate between years. The fluctuation of parameters can be of any magnitude, including both fluctuation traditionally treated as diffusion process es and fluctuation from catastrophes within a single scheme. We develo p a new approximate method of calculating the asymptotic rate of popul ation extinction per year, beta = integral(0)(infinity) exp(-x) u(x) d x, where u(x) is the stationary distribution of adult population size from the continuous-population model including environmental stochasti city and population-regulation but neglecting demographic stochasticit y, The method can be regarded as a perturbation expansion of the trans ition operator for population size. For several sets of population gro wth functions and probability distributions of environmental fluctuati on, the stationary distributions can be calculated explicitly. Using t hese, we compare the predictions of this approximate method with that using a full transition operator and with the results of a direct Mont e Carlo simulation, The approximate formula is accurate when the intri nsic rate of population increase is relatively large, though the magni tude of environmental fluctuation is also large, This approximation is complementary to the diffusion approximation. (C) 1998 Academic Press .