苹果果实生长的数学模型及各生长指标间的相关性分析

以富士苹果(Malus domestica‘Fuji’)为试材,测定其果实生长发育期间各生长指标的动态变化,选择5种理论生长方程对纵径、横径、单果重、体积、干重进行拟合,并根据拟合结果确定合适的生长方程建立各生长指标的数学模型,采用多项式拟合建立果形指数变化的数学模型,同时对果实各生长指标之间进行相关性分析。结果表明,果实纵径、横径生长适合选择Logistic方程,单果重、体积、干重适合选择Gompertz方程,果形指数的变化适合采用多项式拟合;果实纵径、横径、单果重、体积、干重两两之间均呈显著正相关,果形指数、果实干物质相对含量均与纵径、横径、单果重、体积、干重之间呈显著负相关,果实密度与纵径、横径、单果重、体积、干重之间呈显著负相关,而与果形指数、果实干物质相对含量之间呈显著正相关。

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.