A FUNDAMENTAL MODEL FOR OXYGEN CONSUMPTION OF ATLANTIC SALMON

Introduction

Predicting oxygen availability in Atlantic salmon farms is challenging, but digital simulations that couple bioenergetics and hydrodynamics show great promise. Robust simulations depend on reliable estimates of oxygen demand, yet previous empirical models offer limited accuracy. Here, we present a refined fundamental model for Atlantic salmon oxygen consumption rate (MO2) as a function of three readily measurable parameters: body weight, water temperature, and relative swimming speed (Morin et al., 2026).

Materials and Methods

Retaining the established framework of Grøttum and Sigholt (1998), we refined the model through an improved coefficient estimation approach and a methodologically rigorous dataset derived from group swim tunnel respirometry measurements on 718 fish across seven experiments. Model coefficients were re-estimated using log-linear regression fitted via nonlinear mixed-effects, substantially improving parameterisation and yielding a model that explains 80% of the observed variation in MO2.

Results

The log-linear regression fitted via nonlinear mixed-effects showed the strongest performance, with adjusted R² = 0.80 and root mean square error (RMSE) = 56.39, outperforming the model by Grøttum and Sigholt (1998) which had an adjusted R² = 0.68 and RMSE = 71.50. Our model is as follows:

MO2 = 79.7W^-0.141.04^T1.63^U , where MO2 is oxygen consumption rate (mg O2 kg^-1 h^-1), W is body weight (kg), T is water temperature (°C), and U is relative swimming speed (body lengths s^-1).

Discussion

Our refined fundamental model for oxygen consumption of Atlantic salmon represents a substantial advance over previous empirical models. It spans an extensive range of metabolic rates (60–700 mg O2 kg^-1 h^-1), fish sizes (0.2–3.38 kg), water temperatures (3–18 °C), and relative swimming speeds (0.31–2.84 BL s^-1), capturing the diversity of conditions in modern salmon aquaculture. This core formulation defines baseline MO2 for Atlantic salmon and serves as a foundational component within digital simulation frameworks. With broad utility in both research and industry, our model supports the development of more precise, data-driven strategies for modern salmon aquaculture.

Figure 1

Fig. 5: Three-dimensional surface contours illustrating oxygen consumption rate (MO2; mg O2 kg^-1 h^-1; z-axis) as a function of relative swimming speed (U; body lengths [BL] s^-1; y-axis) and water temperature (T; °C; x-axis). Results are displayed for two body weights (W; kg): (A) 0.5 kg and (B) 3.4 kg, selected as the most representative weights of our refined dataset. Surface contours are generated from our model developed using log-linear regression fitted via nonlinear mixed-effects: MO2 = 79.7W^-0.141.04^T1.63^U.

Acknowledgment

We thank Tina Oldham for her contributions to our dataset and Luke Barrett for his valuable input during the preparation of this manuscript.

References

Grøttum, J. A., & Sigholt, T. (1998). A model for oxygen consumption of Atlantic salmon (Salmo salar) based on measurements of individual fish in a tunnel respirometer. Aquacultural Engineering, 17(4), 241–251. https://doi.org/10.1016/S0144-8609(98)00012-0

Morin, A., Jacobsson, T., Dempster, T., Warren-Myers, F., Oppedal, F., & Hvas, M. (2026). A fundamental model for oxygen consumption of Atlantic salmon. Scientific Reports. https://doi.org/10.1038/s41598-026-47328-6