TY - JOUR

T1 - Extinction rate of a population under both demographic and environmental stochasticity

AU - Halley, John M.

AU - Iwasa, Yoh

PY - 1998/1/1

Y1 - 1998/1/1

N2 - We examined the asymptotic rate of population extinction β when the population experiences density-dependent population regulation, demographic stochasticity, and environmental stochasticity. We assume discrete-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 processes and fluctuation from catastrophes within a single scheme. We develop a new approximate method of calculating the asymptotic rate of population extinction per year, β = ∫0/(∞) exp(-x) u(x) dx, where u(x) is the stationary distribution of adult population size from the continuous-population model including environmental stochasticity and population-regulation but neglecting demographic stochasticity. The method can be regarded as a perturbation expansion of the transition operator for population size. For several sets of population growth functions and probability distributions of environmental fluctuation, the stationary distributions can be calculated explicitly. Using these, we compare the predictions of this approximate method with that using a full transition operator and with the results of a direct Monte Carlo simulation. The approximate formula is accurate when the intrinsic rate of population increase is relatively large, though the magnitude of environmental fluctuation is also large. This approximation is complementary to the diffusion approximation.

AB - We examined the asymptotic rate of population extinction β when the population experiences density-dependent population regulation, demographic stochasticity, and environmental stochasticity. We assume discrete-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 processes and fluctuation from catastrophes within a single scheme. We develop a new approximate method of calculating the asymptotic rate of population extinction per year, β = ∫0/(∞) exp(-x) u(x) dx, where u(x) is the stationary distribution of adult population size from the continuous-population model including environmental stochasticity and population-regulation but neglecting demographic stochasticity. The method can be regarded as a perturbation expansion of the transition operator for population size. For several sets of population growth functions and probability distributions of environmental fluctuation, the stationary distributions can be calculated explicitly. Using these, we compare the predictions of this approximate method with that using a full transition operator and with the results of a direct Monte Carlo simulation. The approximate formula is accurate when the intrinsic rate of population increase is relatively large, though the magnitude of environmental fluctuation is also large. This approximation is complementary to the diffusion approximation.

UR - http://www.scopus.com/inward/record.url?scp=0032001656&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032001656&partnerID=8YFLogxK

U2 - 10.1006/tpbi.1997.1336

DO - 10.1006/tpbi.1997.1336

M3 - Article

C2 - 9500907

AN - SCOPUS:0032001656

VL - 53

SP - 1

EP - 15

JO - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 1

ER -