Spatial dependence in experiments of progeny selection for bean ( Phaseolus vulgaris L.) yield

Abstract

ABSTRACT In field experiments, it is often assumed that errors are statistically independent, but not always this condition is met, compromising the results. An inappropriate choice of the analytical model can compromise the efficiency of breeding programs in preventing unpromising genotypes from being selected and maintained in the next selection cycles resulting in waste of time and resources. The objective of this study was to evaluate the spatial dependence of errors in experiments evaluating grain yield of bean progenies using analyses in lattice and randomized blocks. And also evaluate the efficiency of geostatistical models to describe the structure of spatial variability of errors. The data used in this study derived from experiments arranged in the lattice design and analyzed as lattice or as randomized blocks. The Durbin-Watson test was used to verify the existence of spatial autocorrelation. The theoretical semivariogram was fitted using geostatistical models (exponential, spherical and Gaussian) to describe the spatial variability of errors. The likelihood ratio test was applied to assess the significance of the geostatistical model parameters. Of the eight experiments evaluated, five had moderate spatial dependence for the randomized blocks analysis and one for both analyses, in lattice and randomized blocks. The area of the experiments was not a determinant factor of the spatial dependence. The spherical, exponential and Gaussian geostatistical models with nugget effect were suitable to represent the spatial structure in the randomized block analysis. The analysis in lattice was efficient to ensure the independence of errors.