Table 2 Akaike information criterion (AIC), estimated additive genetic variance (\( {\hat{\sigma}}_a^2 \)), additive direct genetic variance (\( {\hat{\sigma}}_{a_d}^2 \)), additive competition genetic variance (\( {\hat{\sigma}}_{a_c}^2 \)), dominance genetic variance (\( {\hat{\sigma}}_d^2 \)), check lot effect variance (\( {\hat{\sigma}}_s^2 \)), block effect variance (\( {\hat{\sigma}}_b^2 \)), plot effect variance (\( {\hat{\sigma}}_p^2 \)), environmental competition effects variance (\( {\hat{\sigma}}_{p_c}^2 \)), residual variance (\( {\hat{\sigma}}_e^2 \)), and single-site individual narrow- (\( {\hat{h}}_s^2 \) and\( {\hat{h}}_c^2 \)) and broad-sense (\( {\hat{H}}_s^2 \) and \( {\hat{H}}_c^2 \)) heritability for diameter at breast height (DBH), total tree height (TH), and normal score of stem straightness (NSTR) from the multi-environment standard (MSM) and competition (MCM) individual-tree mixed models of sites 1 and 2 (the lowest AIC are highlighted in bold)
Models | Site | Parameters | DBH | TH | NSTR |
|---|---|---|---|---|---|
MSM | AIC | 16,515 | 13,086 | 8,015 | |
1 | \( {\hat{\sigma}}_{a_1}^2 \) | 4.46 (2.09) | 1.05 (0.54) | 0.17 (0.05) | |
\( {\hat{\sigma}}_{d_1}^2 \) | 6.78 (3.23) | 0.44 (0.77) | 0.15 (0.06) | ||
\( {\hat{\sigma}}_{s_1}^2 \) | 46.38 (29.97) | 6.69 (4.65) | 0.07 (0.07) | ||
\( {\hat{\sigma}}_{b_1}^2 \) | 0.27 (0.28) | 0.96 (0.72) | 0.00 (0.00) | ||
\( {\hat{\sigma}}_{p_1}^2 \) | 0.70 (0.65) | 0.82 (0.27) | 0.03 (0.02) | ||
\( {\hat{\sigma}}_{e_1}^2 \) | 12.45 (2.60) | 5.47 (0.67) | 0.55 (0.06) | ||
\( {\hat{h}}_{s_1}^2 \) | 0.19 (0.08) | 0.15 (0.08) | 0.20 (0.06) | ||
\( {\hat{H}}_{s_1}^2 \) | 0.47 (0.12) | 0.21 (0.11) | 0.37 (0.06) | ||
2 | \( {\hat{\sigma}}_{a_2}^2 \) | 7.24 (2.15) | 1.07 (0.36) | 0.12 (0.04) | |
\( {\hat{\sigma}}_{d_2}^2 \) | 3.19 (1.55) | 0.71 (0.36) | 0.07 (0.03) | ||
\( {\hat{\sigma}}_{s_2}^2 \) | 49.87 (35.79) | 7.44 (4.93) | 0.19 (0.16) | ||
\( {\hat{\sigma}}_{b_2}^2 \) | 0.20 (0.18) | 0.21 (0.14) | 0.00 (0.00) | ||
\( {\hat{\sigma}}_{p_2}^2 \) | 0.06 (0.48) | 0.01 (0.11) | 0.00 (0.00) | ||
\( {\hat{\sigma}}_{e_2}^2 \) | 15.34 (1.78) | 3.89 (0.37) | 0.69 (0.04) | ||
\( {\hat{h}}_{s_2}^2 \) | 0.28 (0.07) | 0.19 (0.06) | 0.14 (0.04) | ||
\( {\hat{H}}_{s_2}^2 \) | 0.40 (0.08) | 0.31 (0.07) | 0.22 (0.05) | ||
MCM | AIC | 16,511 | 13,056 | 8,033 | |
1 | \( {\hat{\sigma}}_{a_{d1}}^2 \) | 4.91 (2.09) | 1.15 (0.50) | 0.18 (0.07) | |
\( {\hat{\sigma}}_{a_{c1}}^2 \) | 0.13 (0.80) | 0.20 (0.55) | 0.00 (0.00) | ||
\( {\hat{\sigma}}_{d_1}^2 \) | 6.99 (3.28) | 0.46 (0.63) | 0.14 (0.08) | ||
\( {\hat{\sigma}}_{s_1}^2 \) | 50.02 (32.96) | 5.70 (4.01) | 0.07 (0.06) | ||
\( {\hat{\sigma}}_{b_1}^2 \) | 0.33 (0.33) | 0.73 (0.58) | 0.00 (0.01) | ||
\( {\hat{\sigma}}_{p_1}^2 \) | 0.57 (0.66) | 0.12 (0.22) | 0.03 (0.02) | ||
\( {\hat{\sigma}}_{p_{c1}}^2 \) | 0.24 (5.33) | 1.81 (1.80) | 0.01 (0.02) | ||
\( {\hat{\sigma}}_{e_1}^2 \) | 11.77 (2.66) | 4.02 (0.60) | 0.54 (0.08) | ||
\( {\hat{h}}_{c_1}^2 \) | 0.21 (0.10) | 0.18 (0.10) | 0.21 (0.08) | ||
\( {\hat{H}}_{c_1}^2 \) | 0.50 (0.17) | 0.24 (0.13) | 0.37 (0.10) | ||
2 | \( {\hat{\sigma}}_{a_{d2}}^2 \) | 10.52 (2.41) | 1.05 (0.35) | 0.12 (0.04) | |
\( {\hat{\sigma}}_{a_{c2}}^2 \) | 0.29 (0.87) | 0.04 (0.24) | 0.00 (0.00) | ||
\( {\hat{\sigma}}_{d_2}^2 \) | 2.89 (1.44) | 0.66 (0.36) | 0.06 (0.04) | ||
\( {\hat{\sigma}}_{s_2}^2 \) | 43.25 (28.64) | 7.72 (5.11) | 0.19 (0.15) | ||
\( {\hat{\sigma}}_{b_2}^2 \) | 0.20 (0.18) | 0.20 (0.14) | 0.00 (0.00) | ||
\( {\hat{\sigma}}_{p_2}^2 \) | 0.05 (0.49) | 0.01 (0.13) | 0.00 (0.00) | ||
\( {\hat{\sigma}}_{p_{c2}}^2 \) | 0.13 (3.60) | 0.43 (0.89) | 0.01 (0.01) | ||
\( {\hat{\sigma}}_{e_2}^2 \) | 13.15 (1.84) | 3.51 (0.37) | 0.68 (0.05) | ||
\( {\hat{h}}_{c_2}^2 \) | 0.40 (0.09) | 0.19 (0.07) | 0.14 (0.05) | ||
\( {\hat{H}}_{c_2}^2 \) | 0.51 (0.10) | 0.31 (0.09) | 0.21 (0.06) |