An optimized geometric scaling–force model for predicting critical swimming speed in freshwater Cyprinidae

This is the authors' abstract. We don't add key points for this paper.

Critical swimming speed ( U crit ) is a key ecological indicator of fish swimming performance. However, most existing predictive models rely on empirical fitting, which limits their physical interpretability and dimensional consistency. In this study, we developed a physics-based prediction framework for U crit by integrating thrust–resistance balance theory with dimensional analysis. Using five representative cyprinid species, we conducted controlled swimming and morphometric measurements, demonstrating that body dimensions follow geometric scaling with body length. The resulting model is formulated within a unified framework and involves a single dimensionless coefficient, which serves as an effective parameter that can be calibrated to account for species-specific morphological and physiological differences. Cross-validation revealed that the proposed model achieves high predictive accuracy across species and body sizes, maintaining consistent predictive performance across the observed juvenile and adult size ranges. Compared with existing empirical models, our model reduces parameter complexity while improving interpretability and providing more bounded predictions across the observed juvenile and adult size ranges. This study advances the theoretical understanding of fish swimming biomechanics and provides a rigorous methodological foundation for the ecological application of critical swimming speed, including in fishway design, habitat assessment, and aquatic biodiversity conservation.