Deep quantile regression for growth and maturation reaction norms

Abstract Understanding species' growth and maturation responses to anthropogenic and environmental pressures is crucial for tracking demographic shifts, phenotypic change and ensuring population sustainability. Traditional regression methods often focus on modelling the conditional mean of life‐history traits, potentially overlooking heterogeneity in ecological data. In this study, we developed quantile and binary quantile regression models using deep neural networks to investigate the growth and maturation schedules across multiple quantiles. By capturing different parts of the conditional distribution, our approach accommodates heterogeneity and improves predictive accuracy and robustness compared to conventional methods. We further propose novel quantile maturation reaction norms (QMRNs) to assess changes in age and size at maturation. QMRNs outperformed widely used probabilistic maturation reaction norms in simulated datasets, demonstrating greater reliability and robustness. Applying this framework to largehead hairtail ( Trichiurus japonicus ) revealed distinct growth and maturation patterns between the cooler northern and warmer southern coasts of Taiwan Island, achieving lower prediction errors and providing more detailed demographic insights than traditional approaches. Overall, our quantile framework enables a more nuanced characterization of growth and maturation heterogeneity, facilitating intraspecific comparisons of life‐history traits and evolutionary analyses of maturation schedules.