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**Effects of toxicants on populations: a qualitative approach I. Equilibrium environmental exposure.**
*(English)*
Zbl 0548.92018

Ecol. Modelling 18, 291-304 (1983).

A preliminary theory of a qualitative character is suggested for the interactions of a dynamic population and a toxicant to examine the ecological effects of a toxic pollutant on an exposed population. The dynamics of the population density in absence of the toxicant is described by a logistic growth differential equation including the birth rate as well as the mortality rate of the population, and an intraspecific coefficient of competition.

A second differential equation is formulated for the dynamics of concentration of the toxicant. The interaction between concentration of toxicant and the dynamics of the population is assumed through a population level dose-response function as the intrinsic birth rate and the mortality rate are considered as functions of concentration of toxicant.

The qualitative analysis of the differential equation system is performed under the assumptions of density or of time dependent environmental concentrations of toxicant. For the first case it is shown that multiple stable equilibrium states may occur (whereas in the absence of the toxicant only a single stable equilibrium exists) or complete extinction may take place.

A second differential equation is formulated for the dynamics of concentration of the toxicant. The interaction between concentration of toxicant and the dynamics of the population is assumed through a population level dose-response function as the intrinsic birth rate and the mortality rate are considered as functions of concentration of toxicant.

The qualitative analysis of the differential equation system is performed under the assumptions of density or of time dependent environmental concentrations of toxicant. For the first case it is shown that multiple stable equilibrium states may occur (whereas in the absence of the toxicant only a single stable equilibrium exists) or complete extinction may take place.

Reviewer: J.Peil

### MSC:

92D40 | Ecology |

92D25 | Population dynamics (general) |

93C15 | Control/observation systems governed by ordinary differential equations |