Arguments for a stochastic model

The exact definition of the model will be done very easily using the metalanguage of formal reaction kinetics. The stochastic model of the reaction to be defined below will be the stochastic model of the phenomena of eutrophication. Therefore the only questions worth treating here are  

Deterministic models (most commonly systems of nonlinear differential equations) have been used to model the dynamics of lake ecosystems (Park et ai, 1974 Chen Orlob, 1975 Joergensen, 1976 Di Toro et ai, 1979). These models have been satisfactory to describe the main trends of ecological phenomena however, deterministic models are not capable of reflecting the inherently random behaviour of ecosystems. This source of uncertainty is/ especially important in large multiparameter models. / 

The cases when there are qualitative differences between a deterministic model and the corresponding stochastic one have been enumerated previously. A single viewpoint should be emphasised here. 

Models in general are aimed at describing the investigated phenomena, and making predictions of the behaviour of the system under different conditions. In terms of Schofield Krutchkoff s (1974, p. 1) statement it is possible for the instantaneous pollution concentrations to be at ecologically dangerous levels, while the means or deterministic concentrations remain at acceptable levels. We are interested in how far the evolution of a variable is reproducible under essentially the same conditions. 

In general the method of confidence intervals (Zacks, 1971, Ch. 10) may be suggested for approaching a problem of this kind. As it follows from the nature of the stochastic model, an increase in input load of phosphorus does not necessarily lead to an acceleration of the eutrophication process. The same input load, however, may lead to a major increase in algae biomass (as was probably the case in 1982). 

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