“…The statistical modeling approaches for the analyses of plant breeding in multi-environment trials continue evolving as more data with more complex structure are being collected in plant breeding programs (Crossa et al, 2021, Teixeira et al, 2011). For example, diverse set of methods are available for dealing with multi-dimensional data, such as the nonlinear approaches that are now being applied for modeling environmental relatedness using large-scale envirotyping data (Washburn et al, 2021; Rogers et al, 2021; Westhues et al, 2021; Costa-Neto et al, 2021a,b). Here were compared the conventional multi-environment GBLUP (M01, no enviromics) and two reaction-norm GBLUPs, the first using envirotyping data on a conventional linear kernel (M02, linear W-matrix, Jarquin et al, 2014) and the second using these data on a nonlinear Gaussian kernel (M03, nonlinear W-matrix, Costa-Neto et al, 2020b).…”