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Additional file 3: Detailed results for the four traits that did not show significant G × E interactions.

Additional file 2: Fig. S1. Density distribution of the estimated effects of contemporary groups. Fig. S2. Genetic correlations across environmental gradients using the optimal reaction norm models for the four traits without G × E interaction. Fig. S3. Heritability estimates using reaction norm models with homogenous (RNM1) and heterogeneous (RNM2) residual variances for the four traits without G × E interaction. Fig. S4. Genomic estimated breeding values using the optimal reaction norm models for 20 sires with the highest and lowest reaction norm slopes, respectively (for the four traits without G × E interaction). Fig. S5. Miami plots for the proportion of explained variance by 5-SNP sliding genomic windows for the four traits without clear G × E interaction. Fig. S6. Biological processes involved for all candidate genes identified in this study. Fig. S7. Five enriched terms of Human Phenotype Ontology for the number of piglets born alive (NBA). Fig. S8. Heritability estimates for the total number of piglets born (TNB) and number of piglets born alive (NBA) across environmental gradients using three scenarios regarding the X-chromosome markers.

Additional file 1: Table S1. Summary of the phenotypic records used in this study before data editing and quality control. Table S2. Selection of the fixed effects, covariates, and random effects included in the final mixed animal models. Table S3. Standard errors of variance components estimates based on the homogenous (RNM1) and heterogeneous (RNM2) residuals. Table S4. Spearman’s rank correlations of genomic estimated breeding values across three representative environmental gradients. Table S5. Genomic windows with the significantly explained variances and associated candidate genes for the four traits without clear G × E interaction. Table S6. Related quantitative trait loci (QTL) within relevant genomic regions for the four traits without clear G × E interaction. Table S7. Accuracies and reliabilities of genomic estimated breeding values for all animals. Table S8. Sample sizes and accuracies used for calculating the approximate genetic correlations (weighted Pearson coefficients). Table S9. Detailed information for the candidate genes found in this study.