Table 1. Components of the 8 models included in this study. Each of these models is fitted with the linear kernel (GB) and the Gaussian kernel (GK).

Model	General mean	Fixed environmental effect	Main genetic effect of line across environments	Genotype × environment interaction (G×E)	Random intercept of the lines	Unstructured G×E	Random residual
MM	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$	${\mathit{Z}}_g\mathit{g}$				$\mathit{\epsilon }$ (${\sigma }^2)$
MM$\mathit{l}$	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$	${\mathit{Z}}_g\mathit{g}$		${\mathit{Z}}_g\mathit{l}$ (${\sigma }_l^2)$		$\mathit{\epsilon }$ (${\sigma }^2)$
MDs	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$	${\mathit{Z}}_g\mathit{g}$	$\mathit{ge}$ (${\sigma }_{ge}^2$)			$\mathit{\epsilon }$ (${\sigma }^2)$
MDs$\mathit{l}$	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$	${\mathit{Z}}_g\mathit{g}$	$\mathit{ge}$ (${\sigma }_{ge}^2$)	${\mathit{Z}}_g\mathit{l}$ (${\sigma }_l^2)$		$\mathit{\epsilon }$ (${\sigma }^2)$
MDe	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$	${\mathit{Z}}_g\mathit{g}$	${\mathit{g}}_E$ (${\sigma }_{g_{E_j}}^2$for each environment)			$\mathit{\epsilon }$ (${\sigma }^2)$
MDe$\mathit{l}$	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$	${\mathit{Z}}_g\mathit{g}$	${\mathit{g}}_E$ (${\sigma }_{g_{E_j}}^2$for each environment)	${\mathit{Z}}_g\mathit{l}$ (${\sigma }_l^2)$		$\mathit{\epsilon }$ (${\sigma }^2)$
MUC	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$		$\mathit{u}$ (${\mathit{U}}_E\otimes \mathit{K})$			$\mathit{\epsilon }$ ($\Sigma \otimes \mathit{I})$
MUC$\mathit{f}$	$\mu 1$	${\mathit{Z}}_E{\mathit{\beta }}_E$		$\mathit{u}$ (${\mathit{U}}_E\otimes \mathit{K})$		$\mathit{f}$ (${\mathit{F}}_E\otimes \mathit{I})$	$\mathit{\epsilon }$ ($\Sigma \otimes \mathit{I})$