The present study was conducted using phenotypic records of weekly body weights obtained from Japanese quails reared at the Quail Breeding Unit, Isparta University of Applied Sciences. Therefore, it did not require any ethical approval.

As shown in Table 1, increasing the LP order from 2 to 6 progressively improved model fit, yielding higher log L values and lower AIC values, while BIC decreased up to the fifth order. The largest gains occurred at lower orders, with improvements tapering off at higher degrees. While the sixth-order model maximized log L, its marginal improvement over the fifth-order model did not justify the estimation of 14 additional parameters (65 vs. 51). Furthermore, the fifth-order model minimized the BIC, indicating an optimal compromise. Consequently, the fifth-order model was selected for all subsequent analyses as it provided the best balance between goodness of fit and parsimony.

The fifth-order LP accurately described quail growth, as shown in Fig. 1 and Table 2. At all ages, there were no significant differences between observed (μO) and predicted (μP) mean weights, as their 95 % confidence intervals overlapped (Table 2). The model's predictive performance was also confirmed by low SMAPE (2.62 %) and CV(RMSE) (4.98 %) values.

Predicted weights (μP) were derived from the optimal fifth-order RRM.

Heritability estimates obtained from the optimal RRM and MV analyses were generally consistent, both showing a peak around 21 d of age followed by a decline at later ages (Table 3). However, the MV analysis tended to yield slightly higher heritability estimates after 42 d. Similarly, permanent environmental effects (c2) followed comparable trends in both approaches, although RRM estimates were generally higher at later ages. Overall, the close agreement between methods supports the robustness of the results.

Figure 2 illustrates the genetic and phenotypic correlations for the trait across the time trajectory, estimated using RRM and MV analyses. In both models, genetic correlations showed a distinct pattern of increasing strength with age with weak or even negative correlations between early time points and markedly stronger between later time points. A clear temporal pattern emerged with correlations being highest between adjacent ages and progressively decreasing as the interval between measurements increases. Phenotypic correlations closely followed the same temporal trend as genetic correlations, with higher correlations at later ages and between adjacent time points. Comparing the models, the RRM consistently yielded higher correlations than the MV analysis for both genetic and phenotypic estimates and provided smoother estimates over time.

Table 4 presents estimates of heritability (h2) and permanent environmental effects (c2) from the optimal RRM in males and females. Based on the Wilcoxon signed-rank test, heritability estimates (h2) did not differ significantly between sexes (p=0.4922). In contrast, permanent environmental effects (c2) were found to significantly differ (p=0.0371) between sexes. Nevertheless, given the small sample size (particularly within the male group) and the associated elevated sampling variance of estimates, these findings must be treated with caution.

Figure 3 indicates a more stable genetic correlation structure across ages in males, characterized by consistently positive correlations throughout the growth period. In contrast, genetic correlations between hatch weight (w₀) and subsequent body weights in females were generally weaker and occasionally negative. Nevertheless, these sex-specific differences warrant cautious interpretation due to the high sampling variance of the estimates in both groups, and particularly within the male group (where standard errors of genetic correlations ranged from 0.28 to 0.68; results not shown).

Figure 4 shows the first two additive genetic variance eigenfunctions, explaining jointly 95 % of the total genetic variance. The first eigenfunction (blue line) accounted for most of the additive genetic variation and remained relatively constant across ages, indicating the presence of a general genetic growth factor affecting body weight uniformly throughout development. This component can be interpreted as a scale effect, where some individuals are genetically predisposed to maintain consistently higher body weights across all growth stages. In contrast, the second eigenfunction (orange line) changed sign across age, shifting from negative values at early growth stages to positive values at later ages. This pattern suggests a genetic trade-off between early and late growth performance, reflecting differences in growth timing or developmental allocation strategies among individuals.

The consequences of applying selection at different stages of growth are illustrated in Fig. 5. Note that the top 10 % selection pool (n=68) per growth phase was derived from the 681 pedigree animals (out of 705 total) with available EBVs, including both phenotyped birds (n=575) and unrecorded relatives. Selection based on EBVs during the early growth period resulted in high genetic merit at young ages, followed by a plateau or slight decline after the intermediate stage. This pattern suggests that birds selected for superior early growth tend to exhibit rapid juvenile development but do not necessarily maintain a proportional growth advantage later in life. In contrast, selection during the intermediate growth period produced more balanced EBV trajectories, with favourable genetic performance expressed throughout both the early and late stages of development. Selection based on EBVs at later ages generated a different pattern, characterized by relatively modest EBVs during the juvenile period followed by a continuous increase toward the end of the growth trajectory. These birds exhibited slower early growth but possessed greater genetic potential for achieving high final body weight.

Figure 6 presents an UpSet plot illustrating the overlap among animals ranked within the top 10 % based on phase-specific estimated breeding values (EBVs) during the early, intermediate, and late growth phases. Each phase-specific selection group contained 68 animals (top 10 % of the 681 animals with EBV estimates). In total, 84 unique animals appeared in at least one of the three top 10 % selection groups, indicating substantial overlap among phase-specific selections. The largest intersection comprised 53 animals that were simultaneously ranked among the top animals in all three growth phases, corresponding to 77.9 % of each phase-specific selection group. This substantial overlap indicates a high degree of stability in EBV rankings throughout development and suggests the presence of a large group of birds with consistently superior genetic merit.

Nevertheless, several animals exhibited phase-specific superiority. Eight animals were selected in both the early and intermediate phases but not in the late phase, whereas six animals were common to the intermediate and late phases only. Seven, one, and nine animals were uniquely selected in the early, intermediate, and late phases, respectively, while no animals were shared exclusively between the early and late phases.

Overall, these results demonstrate that although a large proportion of top-ranked animals maintain superior genetic merit throughout development, a smaller subset exhibits age-specific genetic advantages that may be exploited when selection objectives target particular growth stages.

The current study confirms the value of LP-based RRMs in modelling longitudinal growth with heterogeneous residual variance structures in the Japanese quail. A fifth-order polynomial was identified as optimal for weekly BW from hatch to 9 weeks, providing the best balance between goodness of fit and model complexity. The selected model adequately captured the major changes in growth dynamics, particularly the transition from rapid juvenile growth to the later stabilization phase, whereas lower-order polynomials tended to oversmooth the trajectory. Although the sixth-order model produced slightly better fit statistics, the improvement was marginal relative to the increased parameterization, suggesting limited biological and practical benefit. Similar findings have been reported in previous studies. Pavan et al. (2024) recommended fifth- and sixth-order polynomials for additive genetic and permanent environmental effects, respectively, in meat-type quail. Akbaş et al. (2004) and Gonçalves et al. (2012) favoured sixth-order models, with Gonçalves also incorporating six residual variance classes, and Bonafé et al. (2011) found that higher-order models generally improved model fit. In contrast, Karami et al. (2017) and Alkan et al. (2012) adopted more parsimonious third-order models, and studies by da Costa Caetano et al. (2017) and Mota et al. (2018) demonstrated that second- to fourth-order polynomials could also provide adequate fit, particularly when combined with heterogeneous residual variances. These findings suggest that the optimal polynomial order depends on the structure of the dataset and the complexity of the growth trajectory being modelled.

The RRM revealed an age-specific trend in h2 estimates, ranging from 0.25 at hatch, peaking at day 21 (h2≈0.30), and declining thereafter to approximately 0.14–0.15 at later ages. The peak in heritability around day 21 may reflect a stage at which maternal and incubation-related influences have largely diminished, while additive genetic differences in growth potential become more fully expressed. The subsequent decline may result from the increasing contribution of cumulative environmental effects and individual variation in resource allocation during later growth stages. Similar time-dependent patterns have been reported in Japanese quail, although the shape of the trajectory varies among studies. Akbaş et al. (2004) observed an increase in h2 up to week 4, followed by a moderate decline, whereas Gonçalves et al. (2012) and El-Attrouny et al. (2020) reported a progressive decrease throughout growth. In contrast, Alkan et al. (2012) and Karami et al. (2017) found heritability to increase with age. Intermediate patterns characterized by a mid-growth peak followed by a decline, similar to the present results, were reported by Bonafé et al. (2011) and Pavan et al. (2024). In meat-type quail, Mota et al. (2018) and Silva et al. (2013) also reported moderate to high heritability estimates for body weight, with values generally declining after the period of rapid growth. Heritability estimates obtained from the MV analysis followed a similar overall pattern, although values tended to be slightly higher at later ages.

The relatively high estimates of permanent environmental effects estimated herein may reflect a broad set of non-additive and non-residual sources of variation that repeatedly affect the same individual across ages. In the present study, such effects may have originated from conditions established during the pre- and early post-hatch period, including egg-related maternal influences, incubation environment, early nutritional status, brooding conditions, social interactions, and cage-level management differences. These factors can create persistent differences among individuals that are maintained throughout the growth trajectory and may thus inflate the proportion of phenotypic variance attributed to permanent environmental effects. Consequently, the relatively high c2 estimates highlight the importance of controlling early management conditions and, where possible, explicitly modelling maternal or common environmental effects in future studies.

The present study revealed strong positive genetic correlations, particularly between adjacent time points, with a progressive decline in correlation strength as the temporal distance between ages increased. Similar patterns have been reported in previous studies on Japanese quail. Akbaş et al. (2004), Gonçalves et al. (2012), Karami et al. (2017), and Alkan et al. (2012) consistently observed high genetic correlations among adjacent ages and lower correlations as the interval between ages increased. An interesting finding of the present study was the negative genetic correlation between hatch weight and body weight at day 7 (-0.13), together with near-zero or low positive correlations between hatch weight and subsequent body weights. Similar results have been reported by Dionello et al. (2008) and Alkan et al. (2012), who also found negative genetic associations between hatch weight and later growth performance. These findings suggest that hatch weight may be under partly different genetic control than post-hatch growth and therefore may have limited value as a selection criterion for improving body weight at later ages. Moreover, hatch weight is known to be strongly influenced by maternal and early environmental effects (Faraji-Arough et al., 2022; Lotfi et al., 2012). Phenotypic correlations closely mirrored the genetic correlations, exhibiting higher values between adjacent ages and lower values between more distant ages. Similar trends have been reported by Akbaş et al. (2004), Gonçalves et al. (2012), Alkan et al. (2012), Silva et al. (2013), and Karami et al. (2017). In agreement with theoretical expectations, phenotypic correlations were generally lower than the corresponding genetic correlations (Roff, 1996).

Although both approaches produced broadly similar estimates, RRMs offer several practical advantages over MV analyses. RRMs require fewer parameters, provide smooth covariance functions across the trajectory, accommodate unequally spaced observations, and allow prediction of genetic parameters at intermediate ages. These properties make RRMs particularly attractive for routine genetic evaluation of longitudinal growth traits.

Heritability (h2) and permanent environmental effects (c2) showed some numerical differences between sexes across ages. Statistical analysis showed that h2 estimates did not differ significantly, suggesting that the genetic contribution to body weight was generally similar in males and females throughout growth. Supporting this, studies in broilers using large datasets, such as the work of Maniatis et al. (2013) based on approximately 200 000 body weight records, also reported no sex-based differences in direct heritability estimates for body weight at 35 d of age. On the other hand, c2 differed significantly between sexes, with higher values in males, especially during the early growth period. Such differences could reflect sex-specific sensitivity to environmental stress in early life, as males and females are known to respond differently in terms of behaviour, physiology, and gene expression. These variations may lead to longer-term effects on growth and other traits, especially in males (Elfwing et al., 2015). Genetic correlations were consistently higher in males but more variable in females. Nevertheless, due to the high sampling variance of estimates in the male group, the current findings should be interpreted with caution, and no general inference could be made.

To investigate the principal modes of additive genetic variation underlying growth in Japanese quails, eigenfunction decomposition of the additive genetic covariance matrix was performed. This approach enabled a comprehensive characterization of the genetic architecture governing growth throughout the developmental period. The identification of two biologically meaningful eigenfunctions indicated that body weight development is influenced by multiple genetic processes, including overall growth potential and age-specific patterns of growth expression. The first eigenfunction described uniform genetic variation across the entire growth trajectory, effectively distinguishing genetically fast- and slow-growing individuals at all ages. In contrast, the second eigenfunction revealed antagonistic genetic effects between early and late growth, indicating age-dependent differences in the expression of genetic potential. These results suggest that some individuals are genetically predisposed to rapid juvenile growth, whereas others exhibit greater genetic potential for growth during later developmental stages. Consequently, selection conducted at different ages may target partially distinct genetic mechanisms. Similar age-dependent growth patterns and early–late growth trade-offs have been reported in beef cattle (Nobre et al., 2003) and sheep (Fischer et al., 2004).

The practical implications of these findings were explored through a hypothetical selection scenario based on the top 10 % of birds ranked according to estimated breeding values (EBVs) within early, intermediate, and late growth stages. Selection during early growth may reduce generation interval and recording costs while achieving appreciable genetic gain. However, the corresponding EBV trajectories indicated that selection at young ages may preferentially identify birds exhibiting rapid juvenile growth without necessarily maintaining superior performance later in life.

Selection during the intermediate growth stage (21–35 d of age) produced more balanced EBV profiles across the entire growth trajectory, suggesting that this period represents a favourable compromise between early growth performance and sustained later development. In contrast, selection at later ages yielded the greatest expected response for final body weight but would require longer evaluation periods and increased maintenance costs before selection decisions could be implemented.

Therefore, the optimal age for selection depends on the breeding objective. Programmes aiming to improve early market weight and accelerate genetic turnover may benefit from earlier selection, whereas breeding schemes focused on maximizing mature body weight may require selection at later ages. Overall, the present results suggest that selection between 21 and 35 d of age offers the most advantageous balance among prediction accuracy, overall growth response, and generation interval, making this interval a particularly attractive selection window for practical breeding programmes. In conclusion, the application of the RRM facilitated the estimation of age-specific EBVs throughout the growth trajectory, providing greater flexibility in identifying superior animals and optimizing the timing of selection decisions.

This study was not without limitations. Potential confounding effects arising from non-modelled environmental sources of variation, such as micro-environmental heterogeneity within cages, as well as maternal genetic and permanent environmental effects, were not considered and may have influenced parameter estimates, particularly during early growth (Faraji-Arough et al., 2022; Lotfi et al., 2012; Maniatis et al., 2013). Future studies could benefit from explicitly accounting for these factors or incorporating genomic information to improve the accuracy of genetic parameter estimation. In addition, although LPs provided a flexible framework for modelling growth trajectories, alternative basis functions, such as B-splines, may also be worth investigating (Mota et al., 2018). Furthermore, the relatively moderate population size and the limited depth of the pedigree may have constrained the precision of variance component estimates and the ability to fully capture long-range genetic relationships. Deeper pedigrees, larger populations, or genomic relationship matrices could provide more accurate estimates of genetic parameters and breeding values.

In conclusion, a fifth-order LP RRM provided the best fit for quail growth trajectories. Eigenfunction analysis revealed a general growth factor and an antagonism between early and late growth. Selection between 21 and 35 d of age produced the most balanced genetic response across the growth trajectory, suggesting this period as an optimal selection window for Japanese quail breeding programmes.