TY - JOUR

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

AU - Halley, John M.

AU - Iwasa, Yoh

N1 - Funding Information:
We thank Professor Joel E. Cohen, whose advice was very helpful. We also thank Dr. William Kunin, Dr. Simon Wood, and Professor John Lawton for their comments. This work was supported in part (JMH) by an EEC MAST grant and was carried out during several summer visits of Y.I. to the NERC Centre for Population Biology. Y. I. wishes to acknowledge financial assistance from the Ministry of Education, Science and Culture of Japan, and from CREST (Core Research for Evolutional Science and Technology) of the Japan Science and Technology Corporation (JST).

PY - 1998/2

Y1 - 1998/2

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.

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U2 - 10.1006/tpbi.1997.1336

DO - 10.1006/tpbi.1997.1336

M3 - Article

C2 - 9500907

AN - SCOPUS:0032001656

SN - 0040-5809

VL - 53

SP - 1

EP - 15

JO - Theoretical Population Biology

JF - Theoretical Population Biology

IS - 1

ER -