Sufficient number of experiments for the adaptability and stability analyses of maize using the Eberhart and Russell method

Abstract: The objective of this work was to determine the sufficient number of experiments (environments) for the adaptability and stability analyses of maize cultivars, using the Eberhart and Russell method. Grain yield data from 63 trials of maize cultivars from six groups of experiments were used. In each group, new data files were formed from all experiments (n), for the combinations of 3, 4, ..., n-1 experiments, totaling 10,381 files. Mean and estimates of the adaptability (b) and stability (S2d) parameters were obtained for each cultivar, in each file. A power function was adjusted for the amplitudes of b and S2d (dependent variables) in each cultivar, as a function of the number of experiments (independent variable), totaling 290 equations (145 cultivars × two dependent variables). For each equation, the value was determined on the abscissa axis (Xs, sufficient number of experiments), corresponding to the point of maximum curvature. The highest value among the 290 estimates of Xs, rounded up to the nearest integer, was assumed to be the sufficient number of experiments for the analyses. Seven experiments are sufficient to analyze the adaptability and stability of maize cultivars using the Eberhart and Russell method.

摘要：本研究旨在利用埃伯哈特-拉塞尔法（Eberhart and Russell method）确定玉米品种适应性与稳定性分析所需的足够试验环境数量。本研究采用了源自6组试验的63个玉米品种籽粒产量试验数据集。在每组试验中，针对该组内全部n个试验的3、4、…、n-1个试验的组合，生成新的数据文件，总计生成10381个数据文件。针对每个数据文件中的每个品种，计算其籽粒产量均值以及适应性参数b与稳定性参数S²d的估计值。以试验数量为自变量，以各品种的b和S²d幅值为因变量，拟合幂函数，共计得到290个方程（145个品种 × 2个因变量）。针对每个方程，确定其横坐标上曲率最大点对应的横坐标值（Xs，即足够试验数量）。将290个Xs估计值中的最大值向上取整至最近整数，以此作为本分析所需的足够试验数量。结果表明，利用埃伯哈特-拉塞尔法开展玉米品种适应性与稳定性分析时，7个试验环境即已满足分析需求。