Stochastic models for toxicant-stressed populations
- 54 Downloads
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.
KeywordsStochastic Differential Equation Positive Equilibrium Intrinsic Growth Rate Invariant Distribution Differential Equation Model
Unable to display preview. Download preview PDF.
- Gard, T. C. 1988.Introductions to Stochastic Differential Equations. New York: Marcel Dekker.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
- Rosenzweig, M. 1971. The paradox of enrichment: destabilization of exploitation ecosystems in ecological time.Science 171, 385–387.Google Scholar