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Effects of toxicants on populations: a qualitative approach II. First order kinetics. (English) Zbl 0548.92019

[For part I see the preceding review, Zbl 0548.92018.]
The effects of a chronic or of an acute dose of a toxicant in the environment on a population is studied by formulating a mathematical model. The state variables of the model are the concentration of toxicant in the environment of the population, the concentration of toxicant in an organism and the population biomass. It is assumed a logistic population model, a toxicant uptake from the environment following first order kinetics, and a linear dose-response function describing the toxicant- population interaction.
In terms of the model parameter it is phrased whether the population is persistent or goes to extinction. For a special case of the model for which no organismic concentration loss to environment and no environmental degeneration of toxicant are assumed it is shown for the case of acute dosage of toxicant that there is a threshold value of terminal organismic concentration, dependent on the dose-response formulation, which determines persistence or extinction of the population.
Reviewer: J.Peil

MSC:

92D40 Ecology
92D25 Population dynamics (general)
93C15 Control/observation systems governed by ordinary differential equations

Citations:

Zbl 0548.92018
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References:

[1] Branson, D. R., Blau, G. E., Alexander, H. C., Neely, W. B.: Bioconcentration of 2, 2’, 4, 4’, tetrachlorobiphenyl in rainbow trout as measured by an accelerated test. Trans. Amer. Fish Soc. 104, 785–792 (1975) · doi:10.1577/1548-8659(1975)104<785:BOTIRT>2.0.CO;2
[2] Butler, G. C.: Principles of ecotoxicology, Scope 12, 350 pp. New York: Wiley 1978
[3] Coppel, W. A.: Stability and asymptotic behavior of differential equations, 166 pp, Boston: Heath 1965 · Zbl 0154.09301
[4] Curtis, E. H., Beauchamp, J. J., Blaylock, B. G.: Applications of various mathematical models to data from the uptake of methylmercury in bluegill sunfish (Lepomis Macrochirus). Ecol. Modelling 3, 273–284 (1977) · doi:10.1016/0304-3800(77)90008-4
[5] Filov, V. A., Golubev, A. A., Liublina, E. I., Tolokonstev, N. A.: Quantitative toxicology, 462 pp. New York: Wiley 1979
[6] Hallam, T. G., Clark, C. E., Lassiter, R. R.: Effects of toxicants on populations: A qualitative approach I. Equilibrium environmental exposure. Ecol. Modelling 18, 291–304 (1983) · Zbl 0548.92018 · doi:10.1016/0304-3800(83)90019-4
[7] Lakshmikantham, V., Leela, S.: Differential and integral inequalities, Vol. I. New York: Academic Press 1969 · Zbl 0177.12403
[8] Lassiter, R. R., Baughman, G. L., Burns, L. A.: Fate of toxic organic substances in the aquatic environment. In: State-of-the-Art in Ecological Modelling (S. E. Jorgensen, ed.) Int. Soc. Ecol. Mod. Copenhagen, pp. 219–245 (1978)
[9] Norstrom, R. J., McKinnon, A. E., deFreitas, A. S. W.: A bioenergetics-based model for pollutant accumulation by fish.. Simulation of PCB and methylmercury residue levels in Ottawa River yellow perch (Perca flauecens). J. Fish. Res. Board Can. 33, 248–267 (1976) · doi:10.1139/f76-035
[10] Thomann, R. V.: Equilibrium model of fate of microcontaminants in diverse aquatic food chains. Can. J. Fish. Aquat. Sci. 38, 280–296 (1981) · doi:10.1139/f81-040
[11] Veith, G. D., DeFoe, D. L., Bergstedt, B. V.: Measuring and estimating the bioconcentration factor of chemicals in fish. J. Fish. Res. Board. Can. 36, 1040–1048 (1979) · doi:10.1139/f79-146
[12] Webster, J. R., Crossley, D. A., Jr.: Evaluation of two models for predicting elemental accumulation by arthropods. Environ. Entomol. 7, 411–417 (1978)
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