Nutrient-Based Mathematical Models for Predicting Tilapia Growth

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By Milthon Lujan

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The aquaculture industry has experienced significant and sustained growth in recent years, underscoring the need for accurate mathematical models to estimate crucial production-related parameters.

Predicting factors such as fish growth, feed requirements, and waste production is essential to ensure the profitability and sustainability of aquaculture activities.

While bioenergetic models have been widely used to estimate growth based on energy budgets, they have limitations in not explicitly considering the mass balance of key macronutrients, such as proteins.

In contrast, nutrient-based models provide a more comprehensive approach, considering both energy and nutrient inputs, and simulate fish growth by tracking nutrient accumulation in the fish’s body.

Despite the existence of bioenergetic and nutrient-based models for predicting Nile tilapia growth in the literature, their suitability has often been questioned due to their development relying solely on uncertain or suboptimal calibration goodness-of-fit measures.

A Data-Driven Approach to Predicting Nile Tilapia Growth

A study published by researchers from the Abel Salazar Institute of Biomedical Sciences, the Interdisciplinary Center for Marine and Environmental Research at the University of Porto, and SPAROS Lda. reviewed a series of databases to enhance our understanding of Nile tilapia growth.

They compiled extensive datasets on Nile tilapia growth, covering a wide range of rearing conditions and food compositions from scientific literature sources. These datasets formed the basis of exploratory analysis, shedding light on the relationships between energy and protein intake and fish growth.

The analysis revealed several key findings:

  • A direct relationship was observed between digestible energy intake and energy gain.
  • Similarly, a direct relationship was identified between digestible protein intake and protein gain.
  • Protein gain demonstrated superior efficiency compared to energy gain, even at higher intake levels, without evidence of a saturation effect.
  • Digestible energy intake had a negative impact on energy retention efficiency, while digestible protein intake did not significantly affect protein retention efficiency.
  • Energy retention efficiency varied with fish body weight, whereas no such effect was observed for protein retention efficiency.
  • The ratio of digestible protein to digestible energy (DP/DE) appeared to negatively affect protein retention efficiency.

Development and Calibration of Growth Models

Armed with these insights, the researchers developed plausible growth models of varying complexity and calibrated them under a variety of assumptions. Additionally, they compared the performance of these models with two existing growth models for Nile tilapia previously published in scientific literature.

The results of their model evaluation were enlightening:

  • Energy-protein flux models (EP models) showed lower errors in predicting fish growth than pure bioenergetic models.
  • EP models demonstrated a Mean Absolute Percentage Error (MAPE) of approximately 9%, compared to around 13% for pure bioenergetic models.

Assuming fixed standard metabolic body weight exponents of 0.80 for energy and 0.70 for protein, rather than estimating them from the data, significantly improved the predictive accuracy of the models.


In conclusion, this study highlights the importance of coupling bioenergetic models with nutrient-based models for accurate prediction of Nile tilapia growth. By considering both energy and protein intake, these models provide a more precise representation of Nile tilapia growth and body composition over time.

“Our findings not only contribute to a better understanding of aquaculture sustainability but also offer practical tools for the industry to optimize production processes, reduce waste, and ensure the profitability and sustainability of Nile tilapia farming operations,” report the scientists.

As the aquaculture sector continues to evolve, embracing data-driven approaches and advanced modeling techniques will be crucial to meeting the growing global demand for fish products while minimizing environmental impact.

A.I.G. Raposo
Abel Salazar Institute of Biomedical Sciences
University of Porto,
Rua de Jorge Viterbo Ferreira, 228, 4050-313 Porto,
Email: andreiaraposo@sparos.pt

A.I.G. Raposo, F. Soares, A. Nobre, L.E.C. Conceição, L.M.P. Valente, T.S. Silva. 2023. Development of dynamic growth and body composition models for Nile Tilapia (Oreochromis niloticus): An exploratory approach to protein and energy metabolism, Aquaculture, 2023, 740032, ISSN 0044-8486, https://doi.org/10.1016/j.aquaculture.2023.740032.

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