There were 7 loci with significant additive effects and/or additive × environment interaction effects, and 2 pairs of loci with significant epistatic effect and/or epistasis × environment interaction effects on soybean flowering time in six environments (Table 5, Fig. 5, Additional file 8: Figure S5). Gm04_4497001, Gm04_42153936 and Gm15_11855585 had significant additive effect, indicating that the additive loci were stable in different environments, whereas Gm11_36124908, Gm16_30766209, Gm19_44042544 and Gm19_47514601 had both significant additive effects and additive × environment interactions, suggesting that these loci were sensitive to different environments. Among them, Gm11_36124908 was the most significant and had high heritability of additive effect (ha 2 = 6.73%) and additive × environment interaction (hae 2 = 31.96%). In addition, Gm04_4497001 interacted with two other loci (Gm11_36124908, Gm19_47514601) to control phenotypic variation of flowering time, and Gm04_4497001 and Gm19_47514601 had epistasis × environment interaction in the SP condition.Table 5The predicted genetic effects with significant heritability of the flowering time for soybeans in six environmentsLocusEffectPredicted value-Log10PHeritability (%)Candidate GenesGm04_4497001 a −2.145.820.33 Glyma04g06100 Gm04_42153936 a 3.6615.540.97 Glyma04g358100; Glyma04g35720 Gm11_36124908 a −9.6244.816.73 Glyma11g34250 ae1 8.306.467.99 ae2 −6.013.667.99 ae3 −10.149.337.99 ae4 8.366.547.99Gm15_11855585 a −2.658.610.51 Glyma15g15730; Glyma15g15400 Gm16_30766209 a −5.0011.791.81 Glyma16g26660; Glyma16g26690 ae1 5.913.288.61 ae3 −14.2616.218.61 ae4 6.293.658.61Gm19_44042544 a 4.7125.361.61Glyma19g36830 ae1 −4.043.843.07 ae3 8.5014.743.07 ae4 −4.103.953.07Gm19_47514601 a −3.3613.340.82 Glyma19g40980 ae2 −4.404.682.02Gm04_4497001 × Gm11_36124908 aa 3.787.5912.43Gm04_4497001 × Gm19_47514601 aa 1.934.823.23 aae2 3.783.9012.45a, additive effect; aa, epistasis effect; ae1, additive by environment interaction effect in 12 h day length in the spring sowing (SD + LT); ae2, additive by environment interaction effect in natural day treatment in the spring sowing (SP); ae3, additive by environment interaction effect in 16 h day length in the spring sowing (LD + LT); ae4, additive by environment interaction effect in 12 h day length in the summer sowing (SD + HT); aae2, epistasis by environment interaction effect in natural day treatment in the spring sowing (SP); -Log10P = minus log10(P-value); h2(%) = heritability(%) Fig. 5The plot of network of highly significant loci identified for soybean flowering time. The red dots represent the loci with additive effects; the blue dots represent the loci with both additive and environment-specific effects; red lines between two dots represent epistasis (aa); blue lines between two dots represent both epistasis (aa) and environment-specific epistasis (aae)