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Table 2 Results of the mixed linear model applied to each population for each trait considering all trials and N conditions as confounded (multi-environment model (1)), \( {\boldsymbol{P}}_{\boldsymbol{i}\boldsymbol{jklm}} = \boldsymbol{\mu} +\underline {{\boldsymbol{G}}_{\boldsymbol{i}}} + {\boldsymbol{N}}_{\boldsymbol{j}} + \underline {{\boldsymbol{T}}_{\boldsymbol{l}}}+\underline {{\boldsymbol{T}}_{\boldsymbol{l}}\left({\boldsymbol{R}}_{\boldsymbol{k}}\right)} + \underline {{\boldsymbol{G}}_{\boldsymbol{i}}\times {\boldsymbol{N}}_{\boldsymbol{j}}}+\underline {{\boldsymbol{G}}_{\boldsymbol{i}} \times {\boldsymbol{T}}_{\boldsymbol{l}}} + {\underline {{\boldsymbol{G}}_{\boldsymbol{i}}\times {\boldsymbol{N}}_{\boldsymbol{j}}\times \boldsymbol{T}}}_{\boldsymbol{l}} + \underline {{\boldsymbol{e}}_{\boldsymbol{i}\boldsymbol{jklm}}} \)

From: Genetic basis of nitrogen use efficiency and yield stability across environments in winter rapeseed

     T N G G × N G × T G × N × T h2 (c)
   Mean values ± standard error Number of trials (a) Var (b) pvalue Var pvalue Var pvalue Var pvalue Var pvalue Var pvalue  
DTF WOSR 96.32 ± 10.29 7 83.62 *** 16.86 *** 7.15 *** <10−16 NS 2.56 *** 0.27 *** 0.94
AM-DH 85.25 ± 6.55 4 29.9 *** 7.65 *** 16.42 *** <10−16 NS 3.16 *** 9.30.10−2 * 0.95
DK-DH 83.87 ± 5.64 2 28.85 *** 14.65 *** 15.13 *** <10−16 NS 3.21 *** 7.54.10−2 NS 0.90
SY WOSR 2.75 ± 1.07 7 0.66 *** 0.12 *** 0.31 *** 1.01.10−3 NS 0.11 *** 1.79.10−2 ** 0.92
AM-DH 3.32 ± 0.66 5 2.41 *** 5.05 *** 0.5 *** <10−16 NS 0.23 *** 0.44 *** 0.85
DK-DH 2.68 ± 0.63 2 1.85 *** 9.32 *** 0.62 *** <10−16 NS 0.51 *** 0.25 *** 0.63
TSW WOSR 4.64 ± 0.54 7 4.45.10−2 *** 9.40.10−3 *** 0.17 *** 2.56.10−3 ** 2.56.10−2 *** 6.47.10−3 *** 0.97
AM-DH 4.37 ± 0.70 5 0.75 *** 0.19 ** 4.52.10−2 *** <10−16 NS 1.69.10−2 *** 3.85.10−3 *** 0.92
DK-DH 3.67 ± 0.58 2 0.51 *** 0.25 NS 3.20.10−2 *** 1.07.10−3 NS 2.01.10−2 *** 7.10.10−4 NS 0.73
SN WOSR 59,925 ± 24,740 7 3.36.108 *** 5.95.107 *** 1.66.108 *** 1.13.10−6 NS 5.74.107 *** 7.48.106 * 0.92
AM-DH 75,428 ± 18,007 5 2.35.108 *** 3.97.107 *** 2.80.107 *** <10−16 NS 1.47.107 *** 3.39.107 *** 0.84
DK-DH 73,614 ± 16,275 2 7.46.106 ** 1.03.107 *** 7.41.107 *** 2.58.106 NS 3.65.107 *** 9.65.106 NS 0.73
Pr WOSR 18.61 ± 2.59 7 4.87 *** 0.74 *** 1.48 *** <10−16 NS 0.32 *** 0.16 *** 0.94
AM-DH 19.93 ± 2.27 5 4.89 *** 0.99 *** 0.25 *** 2.97.10−14 NS 4.53.10−2 * 0.16 *** 0.90
DK-DH 19.08 ± 3.04 2 - - - - - - - - - - - - -
O WOSR 49.26 ± 2.43 7 1.83 *** 0.31 *** 2.17 *** 8.49.10−3 NS 0.58 *** 0.12 *** 0.94
AM-DH 47.94 ± 3.36 5 14.11 *** 2.87 *** 0.6 *** <10−16 NS 0.19 *** 0.18 *** 0.91
DK-DH 48.73 ± 4.09 2 - - - - - - - - - - - - -
O/Pr WOSR 2.71 ± 0.46 7 0.11 *** 1.75.10−2 *** 5.81.10−2 *** <10−16 NS 1.72.10−2 *** 7.32.10−3 *** 0.95
AM-DH 2.46 ± 0.45 5 0.22 *** 4.49.10−2 *** 8.66.10−3 *** <10−16 NS 3.44.10−3 *** 2.68.10−3 *** 0.87
DK-DH 2.65 ± 0.60 2 - - - - - - - - - - - - -
  1. The significance of the genotype (G), nitrogen level (N), trial (T) and their interactions (G × N, G × T, G × N × T) was assessed for each population
  2. (***, p-value < 0.001; **, 0.01 < p-value < 0.001; *, 0.05 < p-value; NS, non-significant; '-', not available)
  3. (a)Number of trials considered for evaluation of the different effects
  4. (b)Var: Variance components
  5. (c)Heritabilities (h2) were calculated according to model (2): \( {\mathrm{h}}^2=\frac{{\sigma^2}_G}{{\sigma^2}_G+\frac{{\sigma^2}_G\kern0.1em \mathrm{x}\kern0.1em \mathrm{N}}{\mathrm{n}}+\frac{{\sigma^2}_G\kern0.1em \mathrm{x}\kern0.1em \mathrm{T}}{\mathrm{T}}+\frac{{\sigma^2}_{\mathrm{e}}}{\mathrm{t}\;\mathrm{x}\;\mathrm{n}\;\mathrm{x}\;\mathrm{r}}} \) for each population; all environments (N × T) were considered as confounded