Abstract

The objective of this work was evaluate multicollinearity effect and discard the variables which are based on multicollinearity reduction in diversity analysis of common bean genotypes, related to seeds physiological quality, in different salinity levels in germination substrate. The common bean seed germination test for six cultivars and seven landrace genotypes was performed in paper rolls (germitest), imbibed in NaCl solutions on the osmotic potentials of 0.0; -0.3 and -0.6 MPa, maintained in germinated Mangelsdorff type at temperature of 25 °C, on constant light. The experimental design was completely randomized in factorial arrangement 13 x 3 (genotype x osmotic potential), with four replications with 25 seeds, totaling 100 seeds per treatment. The carried out evaluations were: weight of a thousand seeds, germination mean time, primary root protrusion in five and nine days after seeding, normal seedling percentage, hypocotyl and primary root length and dry matter from aerial part and roots. The multicollinearity diagnosis was carried out on the phenotypic correlation matrix and the characteristic discard was preceded through the canonical variable technique. To evaluate the multicollinearity effect, the Tocher cluster method was used before and after the variables discard. The proposed discard methodology of variables is efficient on the multicollinearity reduction and the number of discarded physiological quality descriptors is higher on the potentials of -0.3 and -0.6 MPa, under salt stress conditions, need to be discarded three characteristics and in the absence of stress only two discarded, to became a weak condition of multicollinearity to follow with the cluster analysis. The common bean genotypes clusters are different on the severe and weak multicollinearity only under salt stress condition.

Highlights

  • The common bean (Phaseolus vulgaris L.) is a legume of the Fabaceae family, whose grain is much appreciated, being an important source of calories, proteins, carbohydrates (HADŽIû et al, 2013; PLANS et al, 2013), zinc (ROSA et al, 2010), iron (PEDROSA et al, 2015), and calcium (JOST et al, 2009), with a low lipid content (PEDROSA et al, 2015)

  • Salinisation reduces the productivity of various crops (ANDRÉO-SOUZA et al, 2010; MACHADO et al, 2007), including the bean (BEN-GAL et al, 2009), due to morphological changes caused by saline solutions, such as a reduction in germination (SAEIDI-SAR et al, 2013), during initial development (BOURGAULT et al, 2010) and in the vegetative growth attributed to osmotic stress; a result of the reduction in water potential of the medium and the toxic ion effect caused by the accumulation of ions in the tissues (AYDIN; KANT; TURAN, 2012; KHADRI; TEJERA; LLUCH, 2007; ROSALES et al, 2012), which modifies gene expression during salt stress (HERNÁNDEZ-LUCERO et al, 2014)

  • This is the high correlation between the set of explanatory characteristics of an experiment, which may reduce the efficiency of the multivariate techniques that use the residual covariance matrix (CRUZ; REGAZZI, 2001)

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Summary

Introduction

The common bean (Phaseolus vulgaris L.) is a legume of the Fabaceae family, whose grain is much appreciated, being an important source of calories, proteins, carbohydrates (HADŽIû et al, 2013; PLANS et al, 2013), zinc (ROSA et al, 2010), iron (PEDROSA et al, 2015), and calcium (JOST et al, 2009), with a low lipid content (PEDROSA et al, 2015). In Brazil, the bean is the fifth most-produced grain crop (CONAB, 2015), and in 2012 Brazil was the world’s third largest producer of the common bean, with a production of 2.94 million tonnes and a productivity of 1037.24 kg ha-1 (FAO, 2013). One of the factors which compromise the correct interpretation of clusters is multicollinearity. This is the high correlation between the set of explanatory characteristics of an experiment, which may reduce the efficiency of the multivariate techniques that use the residual covariance matrix (CRUZ; REGAZZI, 2001). The breeder can use techniques that help reduce multicollinearity, such as discarding redundant variables, so as to decrease time and manpower in future evaluations (CRUZ; REGAZZI, 2001)

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