What Is Common between Ecology and Nuclear Physics: A Random Matrix Model for the Distribution of Trees in a Stand by Inventory Data

The interactions between trees in a forest are manifested in a decrease in phytomass growth and the weakening and disappearance of some trees. One of the ways to identify the nature of the relationship between trees in a forest is to study the current functions of distribution of trees in the stand in terms of height and trunk diameter. In this case, various functions are used for description: gamma function, normal and logarithmically normal functions, Weibull function, etc. To theoretically substantiate the choice of a particular distribution to describe the diameters and heights of trees in a stand, in this paper, it is proposed to use the Gaussian Orthogonal Ensemble (GOE) model used in nuclear physics to describe the distribution of energy levels of atomic nuclei and to characterize interactions in chaotic systems. It is shown that the interactions both in the atomic nucleus and in the forest stand can be described by a general model. To describe the taxation indicators of trees, the characteristics of reciprocal heights and diameters are introduced. The GOE model for the forest stand was verified according to the inventory data. It is shown that the parameters of the normalized GOE model do not depend on the age of the stand.