Biophysics of communities of living organisms

This article reviews theoretical and experimental studies on fundamental problems of ecology. Theoretical study of the dynamics of ecosystems was initiated by the studies of V. Volterra, A. Lotka, A. N. Kolmogorov, and A. A. Lyapunov. These have been primarily models of point systems of the predatorprey type and models of competitive interrelationships between populations. The conclusions of the theory are illustrated by the experimental data of G. F. Gause, Nicholson, et al. It is shown how one might introduce the Lagrangian and Hamiltonian formalism to describe multispecies ecosystems. Considerable space is given to describing closed ecosystems whose development is limited by a biogenic element that constitutes the ecological minimum. It is shown that auto-oscillations can arise in such systems, while the stability of such ecosystems is determined by the diversity of species and some other factors, in particular, the specialization of species. Since real ecosystems consist of a large number of species, it becomes necessary to apply the methods of statistical mechanics to study these systems. Yet one cannot use the Gibbs method, owing to lack of ergodicity. The possibility is discussed of selecting macroparameters for describing ecosystems and constructing a Fokker-Planck equation for the populations.