The forest ecosystem is a common example of the functioning of open thermodynamic systems. The work analyzes the change in the entropy of an open thermodynamic system where the following processes can be realized: absorption of short-wave solar radiation – differentiation process; total biomass growth process associated with the consumption of resources for respiration and competition. As a result of these processes, the negative entropy flow enters the system, and the positive entropy is produced in the system. As the stand grows, its biomass reaches a maximum, which corresponds to the steady state in the ecosystem. It is shown that, in accordance with the Prigogine’s theorem, the specific entropy production in an open system takes on a minimum positive value. With a further increase in the age of the stand, the steady state of the open thermodynamic system evolves to an equilibrium state, at which a decrease in the plant biomass is observed, and the entropy tends to a maximum value in accordance with the 2nd law of thermodynamics (ecosystem decay). The analysis of the behavior of an open thermodynamic system forms the basis of a new ecological and physiological model of the stand growth dynamics. The model proposed uses the following parameters: the biomass of an individual tree and the number of trees per hectare. In order to model the biomass growth dynamics of an individual tree, the von Bertalanffy equation is used. It contains a dynamic equation describing growth of an individual due to resource uptake and limitation of growth due to resource consumption. The equation that characterizes the dynamics of stand size derives from the condition of reaching the maximum biomass of the stand during the stand’s growth. In general, the stand’s dynamics model has only three independent parameters. They are the onset time of the steady state, the resource consumption rate and the factor linking the area and biomass of the organism. The model verification is presented by calculating the biomass dynamics for full (normal) pine plantations of the first five quality classes (Ib, Ia, I, II, III). The model’s quality is assessed by the dimensionless Nash-Sutcliffe model efficiency coefficient, the value of which is usually greater than 0.95. This corresponds to a description of the data that is close to ideal.

Modelling the dynamics of forest ecosystems is an urgent task, as the volume of publications in the Russian and world press demonstrates. In the proposed work, a new ecological and physiological model of a mixed forest stand has considered. Basically, it proceeds from the ecological and physiological model of a single-breed forest stand, that had obtained from the analysis of the behavior of an open thermodynamic system, which is a forest ecosystem. Four differential equations are required to describe a two-species stand, with the mutual influence of species being expressed both in interspecific competition for a resource and in mutual ‘support’ in the growth of the trees. The model of mixed stand with two species contains 10 independent parameters that have a clear physical meaning. Six parameters relate to the dynamics of each species, and four ones take into account the interactions of the species during growth. The verification of the model is presented by calculating the biomass dynamics for full two-stage aspen-spruce stands of European part (middle taiga ecoregion) of the first appraisal area. The presented model of the dynamics of forest ecosystems can be used in practical forestry, especially in the transition from an extensive method of forestry to an intensive one.

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