The Threshold of Survival for Systems in a Fluctuating Environment

Document Type


Publication Date


Journal / Book Title

Bulletin of Mathematical Biology


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.



Published Citation

Zhien, M., Baojun, S., & Hallam, T. G. (1989). The threshold of survival for systems in a fluctuating environment. Bulletin of Mathematical Biology, 51(3), 311-323.