Productivity and Development Dynamics of Intensive and Superintensive Industrial Gardens: Mathematical Modeling and Forecast

The primary purpose of modern horticulture is to increase the yield capacity and intensity of industrial gardens. Today, the garden intensity degree is understood to be the number of trees per unit area. However, agricultural science is still lacking a set of tools making it possible to quantify intensity parameters of industrial gardens of various types. Mathematical relationships approximated by sigmoid logistic functions are proposed as a solution to this problem. These functions were used for mathematical modeling and analysis of the yield capacity and productivity of industrial apple orchards in central Russia. It is established that an increase in planting density from 1481 trees/ha (4.5 × 1.5 m) to 9524 trees/ha (1.5 × 0.7 m) results in an almost twofold increase in the maximum yield capacity and intensity and concurrently reduces the time required to enter the maximum yield mode. In the maximum growth and decline modes, the yield capacity of industrial apple orchards increases from 25.45 t/ha (planting pattern 4.5 × 1.5 m) to 44.56 t/ha (planting pattern 1.5 × 0.7 m) with the maximum yields of 35.25 and 70.00 t/ha, respectively. The yield values and intensity and productivity coefficients computed for industrial gardens using sigmoid logistic functions can be used to design new orchards and forecast the development dynamics of existing industrial gardens. A strong quantitative relationship between the intensity of industrial gardens and the productivity of trees has been identified.