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Persistence and extinction of a population in a polluted environment. (English) Zbl 0714.92027
The authors investigate models of the persistence and extinction of a population in a polluted environment. They don’t make the unnatural assumption that the capacity of the environment is so large that the change of toxicant in the environment that comes from uptake and egestion by the organism can be neglected. The main results are some sufficient conditions on persistence or extinction. Additionally, the threshold between the two has been obtained for most situations of interest.
Reviewer: R.Manthey

Full Text: DOI
[1] Hallam, T. G.; De Luna, J. L.: Effects of toxicants on populations: a qualitative approach, III. Environmental and food chain pathways. J. theor. Biol. 109, 411-429 (1984)
[2] Hallam, T. G.; Ma, Z. E.: Persistence in population models with demographic fluctuations. J. math. Biol. 24, 327-339 (1986) · Zbl 0606.92022
[3] Hallam, T. G.; Ma, Z. E.: On density and extinction in continuous population models. J. math. Biol. 25, 191-201 (1987) · Zbl 0641.92011
[4] Hallam, T. G.; Clark, C. E.; Jordan, G. S.: Effects of toxicants on populations: a qualitative approach, II. First order kinetics. J. math. Biol. 18, 25-37 (1983) · Zbl 0548.92019
[5] Hallam, T. G.; Clark, C. E.; Lassiter, R. R.: Effects of toxicants on populations: a qualitative approach. I. equilibrium environmental exposure. Ecol. modeling 18, 291-304 (1983) · Zbl 0548.92018
[6] H.P. Liu and Z.E. Ma, The threshold of survival for Lotka-Volterra models in a polluted environment, to be published.
[7] Ma, Z. E.; Hallam, T. G.: Effects of parameter fluctuations on community survival. Math. biosci. 86, 35-49 (1987) · Zbl 0631.92019
[8] Ma, Z. E.; Song, B. J.; Hallam, T. G.: The threshold of survival for systems in a fluctuating environment. Bull. math. Biol. 51, No. 3, 311-323 (1989) · Zbl 0676.92010
[9] Z.E. Ma and W.D. Wang, Asymptotic behavior of Lotka-Volterra models,Appl. Anal., to appear.
[10] W.D. Wang and Z.E. Ma, Harmless delays for uniform persistence, Math. Anal. Appl., to appear. · Zbl 0731.34085