Geometry applied to breeding common beans (Phaseolus vulgaris).

Area of Science:

• Plant Breeding
• Agronomy
• Genetics

Background:

• Common bean (Phaseolus vulgaris) grain yield is determined by pod number (X), grains per pod (Y), and grain weight (Z).
• Grafius's geometric model (1964) proposed maximizing yield by balancing X, Y, and Z contributions, analogous to a cube's volume.

Purpose of the Study:

• To evaluate the feasibility of selecting for an 'ideal plant' geometry that maximizes common bean yield.
• To estimate genetic parameters and correlations for yield components and geometric index (GI).

Main Methods:

• Evaluated individual plants and progenies from two common bean crosses ('Talismã' x 'L.59583' and 'Pérola' x 'ESAL 686').
• Estimated the geometric index (GI) as the sum of squares of deviations from the ideal plant.
• Calculated mean and variance genetic components, and genetic and phenotypic correlations between yield components.

Main Results:

• Observed good concordance between genetic and phenotypic correlations for yield components.
• Low heritability for the geometric index (GI) was found in both crosses (h(2)r = 6.7% and h(2) = 39.0%).
• Variability in the sum of yield components (X, Y, Z) among individuals limits selection for the ideal geometric plant.

Conclusions:

• Selection for an ideal geometric plant in common beans, aiming for balanced yield components, is unfeasible due to low GI heritability.
• The inherent variability in yield components prevents effective selection for the geometric cube model in common bean breeding.