Variational modelling theorems and algocoenoses functioning principles

Natural system structure modelling on the basis of category and functor theory makes it possible to formulate extremal principles of system modelling and to derive functionals for setting up variational problems in the ecology of communities. Variational modelling allows one to predict and understand many features of stationary states of communities of many species that consume mutually irreplaceable resources. A solution to the variational problem, that is, the species structure formula, allows one to calculate the abundance of a member species of a community as a function of the resources which restrict its development and the demands of individuals for these resources. It is also possible to solve the inverse problem: given the population abundances and the amounts of limiting resources, to estimate the demands. One can also calculate the partial consumption of any resource by each population, given its consumption by the whole community. Analytical consequences of the variational modelling also suggest interpretations and analogues of the functional to be extremized: entropy, free energy, exergy, complexity, information, self-organization, expansion, degree of structuredness, degree of stability, diversity and the limiting resources consumption. The origin and ecological meaning of the model constructs are discussed, including rank distributions, diversity indices and Lagrange multipliers. The adequate consequences of variational modelling have been verified by numerous experimental data on laboratory and natural (in vitro and in situ) algocoenoses.