Abstract: [Objective] In order to comprehensively evaluate fast-growing, high-yielding and stability of Larix principis-rupprechtii families and discrimitiveness and representiveness of test sites, genotype main effect plus genotype-environmental interaction effect (GGE) biplot was applied to the analysis of 2017 annual growth data of the regional family trial.[Method] Based on the data of diameter at breast height (DBH) for 26 families of L. principis-rupprechtii at four experimental sites in north Hebei, three linear mixed effect models with the same fixed effects ("site" and "block at site") and the same residuals variance matrix (autoregression for row and column AR1×AR1,to be used for spatial effects analysis) were firstly fitted. A factor analysis model with two factors was used in random effects for Model 1 (FA model), while an unstructured matrix model (US model) was used in random effects for Model 2 (without measurement errors) and Model 3 (with measurement errors simultaneously). The optimal model was selected based on Akaike information criterion. Through the best linear unbiased prediction (BLUP), the BLUP data of DBH for each family at each site was obtained. Genotype main effect plus genotype-environmental interaction effect (GGE) biplot based on BLUP data of DBH was analyzed to evaluate families and sites.[Result] Model 3 (fitted by spatial effects with the unstructured matrix model including measurement errors (US model)) was selected as the optimal model based on Akaike information criterion. The sum of variance interpretation percentage for the first two principal components of GGE biplot based on BLUP data of DBH was 92.4%, which suggests that results were reliable. The four sites were divided into two groups. Group 1 included site L1 (Mayinggou of Chicheng), site L3 (Liutiaogou of Guyuan) and site L4 (Zhazi of Weichang), where family 111 had the largest DBH; while group 2 included site L2 (Yudaokou of Weichang), in which family 78 had the largest DBH. Site L3 (Liutiaogou of Guyuan) was relatively more effective in selecting families with characteristics of fast-growing, high-yielding and stability. The performance of each family varied at different sites. Overall, among the 26 families, family 111 had the largest DBH, followed by families 78, 72, 82, 76, 59, 100, 77, 56, 86 and 96. Family 1 had the smallest DBH, and the DBH of families 97, 116, 53, 35, 46, 66 and 49 were small too. The DBH of families 68 and 42 were close to the overall mean. Families 96, 86, 100 and 76 were fast-growing, high-yielding and stable. The stability of fast-growing and high-yielding families 111, 72 and 56 was moderate. The stability of families 78, 82 and 77 was below the average level. The fast-growing and high-yielding family 59 was unstable.[Conclusion] In this study, Model 3 (fitted by spatial effects with the unstructured matrix model including measurement errors (US model)) was more reliable than the other two models. Site L3 (Liutiaogou of Guyuan) with high discrimination and high representation can be used to effectively evaluate families. Families 96, 86, 100 and 76 with characteristics of fast-growing, high-yielding and stability can be widely promoted. GGE biplot based on BLUP data can be effectively used for evaluation of L. principis-rupprechtii families and test sites. This study can provide decision support for the selection and application of L. principis-rupprechtii families in north Hebei.

Key words: linear mixed-effects model, best linear unbiased prediction(BLUP), genotype main effect plus genotype-environmental interaction effect(GGE) biplot, Larix principis-rupprechtii, regional trial