The use of the nonlinear models in the growth of pears of ‘Shinseiki’ cultivar

ABSTRACT: The goal of this study was to elucidate the growth and development of the Asian pear fruit, on the grounds of length, diameter and fresh weight determined over time, using the non-linear Gompertz and Logistic models. The specifications of the models were assessed utilizing the R statistical software, via the least squares method and iterative Gauss-Newton process (DRAPER & SMITH, 2014). The residual standard deviation, adjusted coefficient of determination and the Akaike information criterion were used to compare the models. The residual correlations, observed in the data for length and diameter, were modeled using the second-order regression process to render the residuals independent. The logistic model was highly suitable in demonstrating the data, revealing the Asian pear fruit growth to be sigmoid in shape, showing remarkable development for three variables. It showed an average of up to 125 days for length and diameter and 140 days for fresh fruit weight, with values of 72mm length, 80mm diameter and 224g heavy fat.

摘要：本研究以随时间序列测定的亚洲梨果长度、直径及鲜重为依据，采用非线性Gompertz模型（Gompertz Model）与Logistic模型（Logistic Model）阐释其生长发育过程。本研究借助R统计软件，通过最小二乘法与迭代高斯-牛顿法（DRAPER & SMITH, 2014）对模型的拟合性能进行评估，并采用残差标准差、调整决定系数及赤池信息准则（Akaike Information Criterion）对两类模型开展对比。针对长度与直径数据中存在的残差相关性问题，本研究通过二阶回归方法建模以实现残差的独立性。结果表明，Logistic模型对数据集的拟合效果极佳，揭示出亚洲梨果的生长呈S形曲线特征，三个观测变量均展现出显著的生长发育规律。其中，长度与直径的平均生长周期最长可达125天，鲜重的平均生长周期为140天，最终可分别达到72mm的长度、80mm的直径以及224g的鲜重。