Long term behaviors of stochastic single-species growth models in a polluted environment

Thresholds for extinction and persistence are important for assessing the risk of mortality in systems exposed to toxicant. In this paper, three single-species models with random perturbation in a polluted environment are proposed and investigated. One is the generalized logistic model and the other two are the stochastic resource–consumer models of Leslie and Gallopin. For each model, the survival threshold is obtained in some cases. In general, each threshold is determined by intensity of the random noise, the mean stress measure in organisms, the population intrinsic growth rate and the stress response rate.