# Ensemble Modelling for Predicting Fish Mortality +
## 6 Conclusions  
This study presented a novel ensemble approach, combining Artificial Neural Networks (ANNs), Symbolic Regression (SR), and Decision Trees (DTs) for predicting fish mortality due to infectious diseases. The implemented models, built in two stages (intermediate and final), were designed to address the need for accurate prediction tools, which also provide interpretable insights into the interactions between influential factors. Our findings revealed that these hybrid models offer a notable improvement over the standalone ANN and SR models developed in our earlier work [11], as they achieved superior predictive accuracy across all the examined disease types. Specifically, the final stage ensemble models achieved an MAE of 52.18, 13.24, 2.95 and 1.27 for the diseases of Pasteurella, Vibrio Harveyi, Myxobacteria and Viral Nervous Necrosis, respectively. These values are lower  
Figure 6: Estimation (in the validation dataset) of the final stage ensemble model for the total number of fish deaths on the next day.  
Figure 7: A concise presentation of the Decision Tree of the DT model encompassed into the respective final-stage ensemble model. Variable \(Deaths\_i\) denotes the total number of fish deaths recorded \(i\) days ago.  
than those achieved by the standalone ANN and SR models of [11] in the corresponding diseases. Additionally, the intermediate-stage ensemble models also showed significant improvements, with MAEs of 58.55, 13.24, 2.98, and 1.54 for Pasteurella, Vibrio Harveyi, Myxobacteria and Viral Nervous Necrosis, respectively, demonstrating that both stages of the ensemble method enhance predictive accuracy compared to standalone models.  
By integrating the strengths of ANNs, SR, and DTs, our approach offers a powerful tool for aquaculture management, facilitating better decision-making and helping ensure the sustainability of global fish stocks. The capacity to predict and understand fish mortality due to infectious diseases could greatly aid in the development of preventive measures and effective treatments, which are of utmost importance in the rapidly growing field of aquaculture.  
Future work is to be devoted to the evaluation of more advanced ANN-based models, more sophisticated SR models (such as the \"AI Feynman\" [9]), and further exploration of the synergistic potential of DTs within the ensembles. Moreover, future research will aim to refine the developed ensemble models for more specific diseases and contexts, further enhancing their real-world applicability. As our knowledge of fish diseases expands, the models can be updated and improved to incorporate new findings, making them a versatile and evolving tool in fish health management.  
Conceptualization, I.H. and G.S.; Methodology, T.A. and I.H.; Software, T.A.; Validation, T.A.; Formal analysis, T.A. and I.H.; Investigation, T.A.; Resources, G.S.; Writing--original draft, T.A.; Writing--review & editing, I.H. and G.S.; Visualization, G.S.; Supervision, I.H. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The datasets presented in this article are not readily available due to confidentiality agreements with the fish-farming units from which the data were obtained. Requests to access the datasets should be directed to [PERSON] ([EMAIL_ADDRESS]).  
Author [PERSON] was employed by the company Kefalonia Fisheries S.A. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.