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Stochastic models for toxicant-stressed populations

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Abstract

We obtain conditions for the existence of an invariant distribution on (0, ∞) for stochastic growth models of Ito type. We interpret the results in the case where the intrinsic growth rate is adjusted to account for the impact of a toxicant on the population. Comparisons with related results for ODE models by Hallamet al. are given, and consequences of taking the Stratonovich interpretation for the stochastic models are mentioned.

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Literature

  • Butler, G., H. I. Freedman and P. Waltman. 1986. Uniformly persistent systems.Proc. Am. math. Soc. 96, 425–430.

    Article  MATH  MathSciNet  Google Scholar 

  • DeAngelis, D. L., R. A. Goldstein and R. V. O'Neill. 1975. A model for trophic interaction.Ecology 56, 881–982.

    Article  Google Scholar 

  • Gallopin, G. C. 1971. A generalized model of a resource-population system: I. General properties. II. Stability analysis.Oecologia 7, 382–413;7, 414–432.

    Article  Google Scholar 

  • Gard, T. C. 1988.Introductions to Stochastic Differential Equations. New York: Marcel Dekker.

    Google Scholar 

  • Gard, T. C. 1990. A stochastic model for the effects of toxicants on population.Ecol. Modelling 51, 273–280.

    Article  Google Scholar 

  • Goel, N. S. S. C. Maitra and E. W. Montroll. 1971 On the Volterra and other nonlinear models of interacting populations.Rev. Mod. Phys. 43, 231–276.

    Article  MathSciNet  Google Scholar 

  • Gompertz, B. 1925. On the nature of the function expressive of the law of human mortability.Phil. Trans. 115, 513–585.

    Google Scholar 

  • Hallam, T. G. 1986. Population dynamics in a homogeneous environment. InMathematical Ecology, T. G. Hallam and S. A. Levin (Eds). Berlin: Springer-Verlag.

    Google Scholar 

  • Hallam, T. G. and Ma Zhien. 1986. Persistence in population models with demographic fluctuations.J. math. Biol. 24, 327–339.

    MATH  MathSciNet  Google Scholar 

  • Ma Zhien Song Baojun and T. G. Hallam. 1989. The threshold of survival for systems in a fluctuating environment.Bull. math. Biol. 51 311–323.

    Article  Google Scholar 

  • Rosenzweig, M. 1971. The paradox of enrichment: destabilization of exploitation ecosystems in ecological time.Science 171, 385–387.

    Google Scholar 

  • Smith, F. E. 1963. Population dynamics in Daphnia magna and a new model for population growth.Ecology 44, 651–663.

    Article  Google Scholar 

  • Vance, R. R. 1990. Population growth in a time-varying environment.Theor. Pop. Biol. 37, 438–454.

    Article  MATH  MathSciNet  Google Scholar 

  • Vance R. R. and E. A. Coddington. 1989. A nonautonomous model of population growth.J. math. Biol. 27, 491–506.

    Article  MATH  MathSciNet  Google Scholar 

  • Wong, E. and M. Zakai. 1965. On the convergence of ordinary integrals to stochastic integrals.Ann. math. Stat. 36, 1560–1564.

    MATH  MathSciNet  Google Scholar 

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  1. Department of Mathematics, The University of Georgia, 30602, Athens, GA, USA

    Thomas C. Gard

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  1. Thomas C. Gard
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Gard, T.C. Stochastic models for toxicant-stressed populations. Bltn Mathcal Biology 54, 827–837 (1992). https://doi.org/10.1007/BF02459932

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