Genetic modelling of the weekly weight of Japanese quails using orthogonal Legendre polynomials

In this study, Legendre polynomial random regression models (RRMs) of orders 2 to 6 were applied to estimate genetic parameters (heritability coefficients and genetic correlations) for weekly body weight (5745 records) from hatch up to 9 weeks of age in 575 Japanese quails (423 females and 152 males). Based on the Bayesian information criterion (BIC), the optimal RRM was of the fifth order and incorporated nine heterogeneous residual variance classes. The model demonstrated high predictive accuracy, yielding a symmetric mean absolute percentage error (SMAPE) of 2.6 % and a CV(RMSE) of 5.0 %. Heritability estimates ranged from 0.25 (at hatch) to 0.15 (at day 63), peaking at day 21 ( $h^2\approx 0.30$ ). Genetic parameter estimates from the optimal RRM were highly consistent with those from a multivariate analysis, showing that genetic correlations were highest between adjacent ages and decayed progressively as the time interval increased. Eigenfunction decomposition of the additive genetic covariance matrix identified two principal modes of variation: the first eigenfunction (84.8 %) represented uniform shifts across the entire growth trajectory, whereas the second (10.2 %) captured a genetic trade-off between early and late growth phases. Simulated selection targeting the top 10 % of birds based on estimated breeding values (EBVs) at early (1-14 d), middle (21-35 d), and late (42-63 d) growth stages differentially altered the genetic response curves, demonstrating the capacity to tailor selection strategies to specific breeding objectives. Overall, selection between 21 and 35 d of age provided the most balanced genetic response across the growth trajectory, identifying this period as the optimal selection window for Japanese quail breeding programmes.