Lima J G, Ramalho M A P
Departamento de Biologia, Universidade Federal de Lavras, Lavras, MG, Brasil.
Genet Mol Res. 2016 Apr 26;15(2):gmr7873. doi: 10.4238/gmr.15027873.
The primary components of common bean (Phaseolus vulgaris) grain yield (W) are the number of pods (X), the number of grains per pod (Y), and the weight of the grains (Z). In 1964, Grafius suggested using geometry in plant breeding; W corresponds to the volume of a parallelepiped with three axes, X, Y, and Z. Because the cube is the largest parallelepiped by volume, maximum yield is obtained when the relative contributions of X, Y, and Z are the same. We evaluated individual plants of a 'Talismã' x 'L.59583' cross in two sowing periods. The sum of squares of deviations from the ideal plant (GI), i.e., the plant in which the X, Y, and Z contributions were the same, was estimated. Mean and variance genetic components, and genetic and phenotypic correlations between the characteristics were also estimated. Good concordance was observed in the magnitude and direction of the genetic and phenotypic correlation estimates of the paired characteristics. However, a low GI heritability (h(2)r = 6.7%) indicated that success due to selection should be small. Ninety-four progenies of 'Pérola' x 'ESAL 686' crosses were also evaluated, where X, Y, Z, and W were obtained and GI was estimated. The h(2) estimate was higher, but still low (h(2) = 39.0%). Therefore, the selection of individuals to obtain plants in which the X, Y, and Z products tend to the cube is unfeasible, because the sums of X, Y, and Z vary between individuals. In addition, the GI h2 value was low.
普通菜豆（Phaseolus vulgaris）籽粒产量（W）的主要构成要素是荚果数量（X）、每荚粒数（Y）和粒重（Z）。1964年，格拉菲乌斯建议在植物育种中运用几何学；W相当于一个以X、Y和Z为三个轴的平行六面体的体积。由于正方体是体积最大的平行六面体，当X、Y和Z的相对贡献相同时可获得最高产量。我们在两个播种期对一个‘塔利斯马’בL.59583’杂交组合的单株进行了评估。估算了与理想植株（GI）（即X、Y和Z贡献相同的植株）的偏差平方和。还估算了均值和方差遗传成分以及各性状之间的遗传和表型相关性。在成对性状的遗传和表型相关性估计值的大小和方向上观察到了良好的一致性。然而，GI的低遗传力（h(2)r = 6.7%）表明通过选择获得成功的可能性较小。还对‘佩罗拉’בESAL 686’杂交组合的94个后代进行了评估，测定了X、Y、Z和W并估算了GI。h(2)估计值较高，但仍然较低（h(2) = 39.0%）。因此，选择个体以获得X、Y和Z乘积趋于正方体的植株是不可行的，因为X、Y和Z的总和在个体之间存在差异。此外，GI的h2值较低。
