Capabilities and Limitations of Mathematical Models in Ecological Safety Forecasting

Abstract

The evolution of the mathematical models of ecosystems over the past century was reviewed, starting from the simplest schemes of biological oxygen uptake (Streeter–Phelps, 1925) and ending with modern space-time models including dozens of factors and important components. The principal shortcomings and limitations of statistical models were discussed. For models based on the systems of differential or differential-algebraic equations, it was demonstrated that increased computational power and more detailed treatment do not improve the prognostic qualities of the model. When choosing a space-time grid for solving the problems by the finite difference method, the kinetic picture for the significant components is more important than their spatial distribution, which asymptotically tends toward normal. The efficiency of the Crank–Nicolson scheme based on the tridiagonal elimination method was demonstrated once again, although it does not guarantee a stable forecast.