The aim of the present study was to estimate heritabilities and evaluate the existence of genotype-environment interactions for growth curve parameters in quail fed diets containing different threonine:lysine ratios. A total of 4,441 body weight information from two genetic quail groups (LF1 and LF2) fed diets containing 0.66%, 0.71%, 0.76%, 0.81%, and 0.86% threonine:lysine ratios from hatching to 21 d of age were evaluated. From 22 to 35 d of age, quail received a single diet. The Gompertz model was used to estimate growth curve parameters. Genetic analyses were performed using random regression models, by Legendre polynomials of the second kind, considering homogeneity of residual variances. The following characteristics were evaluated: asymptotic weight, asymptotic growth rate, and inflection point. Increases in threonine:lysine ratios promoted higher heritability estimates for these variables in the LF1 genetic group compared to LF2, which indicates that the additive genetic variation was modified due to the environmental variation influenced by the evaluated amino acid ratios, with differences between both genetic groups. Thus, it is recommended that quail be selected in the 0.86% ratio in genetic group LF1 and 0.66% in genetic group LF2, where greater heritabilities were observed. Dispersion of individual breeding values along the environmental gradient was observed for all evaluated characteristics, in both genetic groups, suggesting the existence of genotype-environment interactions for these variables. The evaluated amino acid ratios should be considered in quail breeding programs, since breeding value predictions for a determined threonine:lysine ratio are not valid for other ratios.