A comprehensive account of natural and anthropogenic factors affecting the growth and productivity of tree species in protective forest stands, in particular, pedunculate oak, due to their diversity, is a very difficult task. From a fundamental point of view, the totality of natural and anthropogenic factors is a multidimensional hypersurface, the detailed study of which is complicated by the complexity of its structure. We used mathematical models and methods that allowed us to take into account the impact on the growth of the petiolate oak of the most significant factors that allow for a mathematical description available for use: diameter, growth intensity index, cambium productivity.
H = b0 + b1D +b2P +b3K + b4DP +b5DK +b6PK +b7DPK, (3)
where, h is the height of the pedunculate oak, m; D is the diameter of the oak at chest height, cm; P is the indicator of growth intensity, cm/cm2; K is the productivity of cambium, dm3/m2; b0-b7 are the coefficients of multiple regression
The study of forestry and taxation parameters of tree species in protective forest stands on various parts of the slope showed a regular growth dynamics. With an increase in the steepness of the slope, the taxation indicators of tree species, primarily the oak bonitet, naturally decrease, which is associated with a drop-in soil fertility as a result of erosion [2,3]. The height of an oak tree with an increase in steepness by 1.9-2.3 times on southern chernozem and gray forest soil decreases by 6.9-11.3%, and the diameter-by 13.9-24.2 %. The index of oak growth intensity with an increase in the slope of the slope increases by 21.4-38.5%, and the productivity of the cambial tissue decreases by 14.1-23.6%. The same trends in the dynamics of forestry and taxation indicators are characteristic of related breeds. There is a high more than 71% vital state of tree species in protective plantings (Tables 1, 2).
The dynamics of growth in the height of the pedunculate oak, depending on the age, shows that in the first 4-6 years, the breed develops mainly the root system, and then the crown. The dependence of the growth rate in the height of the oak on the age is described by the equation of A. Mitcherlich (1) (Fig. 1,2).
For the three regression curves in Fig. 1, the parameters a2 = 0.2, a3 = 10, and the values of parameter a1 for the upper, middle and lower parts of the slope are 8.1, 7.7 and 7.3, respectively. For the three regression curves, Fig. 2 parameters a2 = 0.2, a3 = 40, and the values of parameter a1 for the upper, middle and lower parts of the slope are 17.1, 16.6 and 16.0, respectively.
Regression and correlation analysis showed that of the many natural and anthropogenic factors that affect the growth in height of the petiolate oak, an indicator of the growth intensity associated with the diameter of the rock and the productivity of the cambium, depending on the increments in diameter and height, have an effect. The coefficients of determination are 0.95-0.98, which indicates a close relationship of the studied features (Fig. 3,4).
Studies of the growth of pedunculate oak, conducted in the conditions of the Central Chernozem Region of Russia, have shown that the use of wide row spacing (2.5 m) in forest strips and the use of accompanying species in mixing with oak - holly maple and small-leaved linden, provides an increase in the taxation indicators of oak by 20% compared with the indicators of oak in forest strips with narrow row spacing (1.5 m) and without accompanying species (Mikhin V. I., Mikhina E. A., Tanyukevich V. V.). In our studies of the growth of pedunculate oak in the forest strips of the Volga Upland, the following indicators were used: the growth intensity index (IGI), the coefficient of competitive relations (CCR), the degree of plant stability (SUN) and the productivity of cambium, (PC) allowing for a deeper assessment of the growth and condition of the pedunculate oak in various growing conditions.
The results of the study were implemented in the farms " Lesnoye "of the Tatishchevsky district of the Saratov region (the steppe of the Volga Upland) and" Novoe Chemeevo " of the Morgaushsky district of the Chuvash Republic (the forest-steppe of the Volga Upland).
The area of protective forest stands on the slopes with the main oak species is 14.5 hectares, which protect 227 hectares of pasture land with a forest cover of 6.4% and an increase in the productivity of pasture grasses by 15-45%.