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The threshold of survival for systems in a fluctuating environment
Authors:Ma Zhien  Song Baojun  Thomas G Hallam
Institution:(1) Department of Mathematics, Xi'an Jiaotong Univeristy, Zi'an, People's Republic of China;(2) Department of Mathematics and Graduate Program in Ecology, University of Tennessee, 37996-1300 Knoxville, TN, USA
Abstract:Thresholds for survival and extinction are important for assessing the risk of mortality in systems exposed to exogeneous stress. For generic, rudimentary population models and the classical resource-consumer models of Leslie and Gallopin, we demonstrate the existence of a survival threshold for situations where demographic parameters are fluctuating, generally, in a nonperiodic manner. The fluctuations are assumed, to be generated by exogenous, anthropogenic stresses such as toxic chemical exposures. In general, the survival threshold is determined by a relationship between mean stress measure in organisms to the ratio of the population intrinsic growth rate and stress response rate. Research supported by the fund of Chinese Natural Science. Research supported in part by the U.S. Enviromental Protection Agency under cooperative agreement CR-813353-01-0.
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