Mathematical Model of Apple Fruit Growth and Correlation Analysis among Growth Indices

‘Fuji’ apple (Malus domestica‘Fuji’) was used as test material to determine dynamic changes in growth indices of fruit during the growth and development period. Five theoretical growth equations were adopted to fit vertical diameter, horizontal diameter, single fruit weight, single fruit volume and dry weight, and appropriate growth equations according to fitting results were selected to establish mathematical models of growth indices of fruit. Polynomial fitting was used to establish a mathematical model of dynamic change in fruit shape index. Correlation analysis was then conducted among growth indices of fruit. Results showed that the mathematical growth models of fruit vertical diameter and horizontal diameter were appropriately established with the Logistic equation, while mathematical growth models of single fruit weight, single fruit volume and dry weight were appropriate for the Gompertz equation, and fruit shape index for polynomial fitting. Correlation analysis among the growth indices of fruit showed that each correlation coefficient between two indices, containing fruit vertical diameter, horizontal diameter, single fruit weight, single fruit volume and dry weight, was significantly positive. Both fruit shape index and relative content of dry matter in fruit showed significant negative correlation with vertical diameter, horizontal diameter, single fruit weight, single fruit volume and dry weight. The density of fruit showed significant negative correlation with vertical diameter, horizontal diameter, single fruit weight, single fruit volume and dry weight, but significant positive correlation with fruit shape index and relative content of dry matter in fruit.