Summary: This paper concentrates on studying the long-term behavior of a single species in a polluted closed environment. We improve the rudimentary population model of Hallam [see T. G. Hallam
et al., J. Math. Biol. 24, 327–339 (1986; Zbl 0606.92022
); Ecol. Modelling 8, 291–304 (1983)] and the classical G. C. Gallopin
[Oecologia 7, 382–413, 414–432 (1971)] resource-consumer model, assuming that a born organism takes with it a quantity of internal toxicant, and the amount of toxicant stored in each living organism which dies is drifted into the environment. Sufficient criteria for persistence or extinction of the consumer population are obtained. The threshold between persistence and extinction will be established in some cases.