Mixed model with spatial variance–covariance structure for accommodating of local stationary trend and its influence on multi-environmental crop variety trial assessment

Abstract

The most common procedure for analyzing multi-environmental trials is based on the assumption that the residual error variance is homogenous across all locations considered. However, this may often be unrealistic, and therefore limit the accuracy of variety evaluation or the reliability of variety recommendations. The objectives of this study were to show the advantages of mixed models with spatial variance-covariance structures, and direct implications of model choice on the inference of varietal performance, ranking and testing based on two multi-environmental data sets from realistic national trials. A model comparison with a χ 2 -test for the trials in the two data sets (wheat data set BW00RVTI and barley data set BW01RVII) suggested that selected spatial variance-covariance structures fitted the data significantly better than the ANOVA model. The forms of optimally-fitted spatial variance-covariance, ranking and consistency ratio test were not the same from one trial (location) to the other. Linear mixed models with single stage analysis including spatial variance-covariance structure with a group factor of location on the random model also improved the real estimation of genotype effect and their ranking. The model also improved varietal performance estimation because of its capacity to handle additional sources of variation, location and genotype by location (environment) interaction variation and accommodating of local stationary trend.

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

“…Costa et al (2005) found no significant differences between the spherical, exponential and Gaussian models for the estimates of variance components. However, Duarte & Vencovsky (2005), evaluating the efficiency of spatial statistical analysis in the selection of soybean genotypes, found similar results to those of experiment 7, significant spatial autocorrelation by the DW test, and best fit for the exponential model with a range of 20.4 m. In the study of Negash et al (2014), the exponential model also showed the best quality fit for most of the evaluated trials.…”

“…Thus, the randomized blocks design may not be effective to control the spatial variability present in trials of genetic evaluation. Negash et al (2014) pointed out that several factors contribute to the spatial variability in experimental areas used for genetic evaluation of plants, including fertility changes, pH, soil structure and incidence of diseases and pests. The authors carried out a very detailed study addressing the advantages of using mixed models, considering the data's spatial structure, in trials of plant genetic evaluation in different environments.…”

“…Several studies in plant breeding have evaluated the efficiency of analyses that consider spatial dependence of errors in both annual and perennial plants. In most of these studies, the spatial analysis was more efficient or similar to traditional analyses that assume independence of errors and neglect the location of the observations used in the analyses (Zimmerman & Harville, 1991;Yang et al, 2004;Costa et al, 2005;Duarte & Vencovsky, 2005;Resende et al, 2006;Candido et al, 2009;Yang & Juskiw, 2011;Maia et al, 2013;Negash et al, 2014).…”

Prediction Accuracy and Consistency in Cultivar Ranking for Factor‐Analytic Linear Mixed Models for Winter Wheat Multienvironmental Trials

“…The R ij matrix was modeled by a spatial covariance structure based on the decompositions of error effects ε ij separately for the j th location in the i th year into a spatially dependent residual ξ ij and a spatially independent residual η ij (noise effects). For ξ ij , we assumed a separable autoregressive covariance structure (AR1 × AR1) in rows and columns (Cullis et al, 1998; Negash et al, 2014; Stefanova et al, 2009): where is the variance of spatially correlated residuals ξ ij for the j th location in the i th year, is the variance of independent residuals η ij for the j th location in the i th year, I is the identity matrix, and AR1 (Φ col ) and AR1 (Φ row ) are the first‐order autoregressive correlation matrices with autocorrelation parameters Φ col and Φ row , respectively.…”

“…The R ij matrix was modeled by a spatial covariance structure based on the decompositions of error effects e ij separately for the jth location in the ith year into a spatially dependent residual x ij and a spatially independent residual h ij (noise effects). For x ij , we assumed a separable autoregressive covariance structure (AR1 ´ AR1) in rows and columns (Cullis et al, 1998;Negash et al, 2014;Stefanova et al, 2009):…”