Logistic Model of Population Toxicodynamics

Abstract

The effect of pollutant in water on a population of aquatic organisms as a function of exposure time is studied. Natural assumptions are formulated regarding the character of this process, primarily, the linear relationship between the rate of decrease in the population, on the one hand, and the population size and the number of organisms killed by intoxication, on the other hand. The formulated assumptions are used to construct a model of population toxicodynamics, which describes the kinetics of suppression of the population by a logistic function. The results of model calculations are shown to agree with the available experimental data, thus justifying the formulated assumptions regarding the character of the intoxication process. An extension of the model is proposed through the incorporation of the dependence of the result of intoxication on pollutant concentration by the well-known Haber’s formula. The developed model was used to propose an equation of regulated toxicodynamics for organization of water use without violation of the regime of natural functioning of ecosystems. The obtained specification of the notions of the mechanisms of intoxication process is necessary for the substantiation of hygienic standards on the concentration of chemicals in water, forecasts of biodiversity, and the choice of measures for supporting weak components of trophic chains in aquatic ecosystems.