# Ensemble Modelling for Predicting Fish Mortality +
## 5 Results and Discussion  
To demonstrate the derived results, Table 2 is first reported, which, for each infectious disease under consideration, presents the Mean Absolute Error (MAE) obtained by the corresponding final stage ensemble model in the validation dataset. For the sake of comparison, Table 2 also presents the corresponding MAEs of the intermediate stage ensemble models, as well as of the ANN and SR models developed in our previous work [11] (recall that VNN was not studied in [11]). It is evident that, for each of the diseases Pasteurella, Vibrio Harveyi and Myxobacteria, the corresponding ensemble models achieved a lower MAE than the corresponding standalone ANN and SR models of [11]. Specifically, for Pasteurella, the final stage ensemble model reduced the MAE to 52.18 from 60 (ANN) and 65.1 (SR), representing improvements of approximately 13% and 20%, respectively. The intermediate stage ensemble model also showed improvement over the standalone models of [11], with an MAE of 58.55, though not as significant as the final stage model. In the case of Vibrio Harveyi, the final stage ensemble model achieved an MAE of 13.13, compared to 18 (ANN) and 20 (SR), marking reductions of about 27% and 34%, respectively. The intermediate stage ensemble model's MAE was 13.24, showing significant improvement as well, but slightly higher than the final stage model, indicating a minor difference. For Myxobacteria, the final stage ensemble model's MAE of 2.95 is lower than the ANN's MAE of 3 and significantly better than the SR's MAE of 9.13, showcasing a minor improvement over ANN and a substantial 68% reduction over SR. The intermediate stage ensemble model had an MAE of 2.98, indicating consistent performance improvement over the standalone models of [11], but with a marginal difference compared to the final stage model. Overall, the comparison between intermediate and final stage ensemble models reveals that, while both stages offer significant improvements over the standaloneML models of [11], the final stage ensemble models consistently achieve slightly better MAE values than the corresponding intermediate stage models. Thereafter, for each one of the examined diseases, Figure 4 depicts the estimation of the intermediate and final stage ensemble models in the validation dataset for the number of fish deaths on the 3 rd forthcoming day. Firstly, it is evident that the estimations of the intermediate and final stage ensemble models for Pasteurella and VNN display no significant visual differences; in contrast, the intermediate and final stage ensemble models for Vibrio Harveyi and Myxobacteria demonstrate noticeable visual variations. In general, the ensemble models for Pasteurella, Myxobacteria, and VNN demonstrate a close alignment between real and estimated data points, indicating a high degree of model accuracy. Particularly noteworthy are the models for Myxobacteria, which nearly perfectly capture the actual spike, suggesting exceptional predictive precision. However, the models for Vibrio Harveyi show a significant discrepancy during peak events, where the models underestimate the severity of the impact. Let us now turn to the symbolic knowledge of the SR models encompassed in the trained (intermediate and final stage) ensemble models. Accordingly, we subsequently present the mathematical expressions encoded into each SR model developed for the estimation of fish deaths caused by Pasteurella, Vibrio Harveyi, Myxobacteria and VNN (Due to the randomness characterizing the construction of the SR models, not all runs converge into exact mathematical expressions. The mathematical expressions shown herein are indicative. The units of measurement for all variables involved in the equations are identical to those of the available data, discussed in Section 3).