Geometria aplicada ao melhoramento genético do feijoeiro

Abstract

The primary components of bean grain productivity (W) are number of pods (X), number of grains per pod (Y) and grain mass (Z). In 1964, Grafius proposed the employment of geometry for plant breeding. In his proposal, W would correspond to the volume of a parallelepiped of which the axes are X, Y and Z. Since the parallelepiped with the largest volume is the cube, the maximum productivity will be obtained when the relative contribution of X, Y and Z are the same. The present work was conduct ed with the objective of verifying the viability of applying geometry for bean breeding. We used crosses Talismã x L. 59583 and Pérola x ESAL 686. We evaluated individual plants of different crosses between Talismã x L. 59583 in two different sowing periods. We obtained X, Y and Z of each plant and estimated the sum of squares of the deviations in relation to the ideal plant (GI), that in which the contribution of X, Y and Z is the same. We also estimated mean and variance of genetic components, as well as genetic and phenotypic correlations between the traits. We observed good correlation for the magnitude and direction of the genetic and phenotypic correlations of the pairings of traits. However, the low heritability of GI (h 2 r = 6.7%) indicated a small possibility of success with selection. We also evaluated 94 progenies of the Pérola x ESAL 686 cross. We obtained X,Y and Z, and estimasted GI. The estimation of h 2 , in this case, was higher, however, remaining of low magnitude (h 2 = 39.0%). We infer that the selection of individuals aiming at obtaining plants of which the product of X, Y and Z tend to a cube is unfeasible, given that the sum of X, Y and Z varies between individuals, which makes the comparison difficult. In addition, the h 2 of GI presents low magnitude.