## 3 Results
### Correspondence Analysis  
To identify the associations between the _Aeromonas_ species and histopathological lesions and behavioral changes two correspondence analysis (CA) were implemented. CA is an exploratory analysis that reduces the complexity of the initial database while retaining most information and providing the graphical output's relationships, favoring their interpretation. Table 4 depicts the results of \(\chi^{2}\) analysis, which reveals a strong dependency (\(p<0.001\)) between _Aeromonas_ species with histopathological lesions and behavioral changes. To the histopathological lesions CA, the first and second dimensions account for 79.94 and 20.05 percent of inertia, respectively; both dimensions represent for 100 % of cumulative inertia, indicating that the totality of variability was explained by the information contained within the first two axis (Table 2). The CA focused on behavioral changes associates with \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Histopathological Lesions** & **Behavioral Changes** \\ \hline \(\chi^{2}\) (observed value) & 68.20 & 123.64 \\ \(\chi^{2}\) (critical value) & 31.41 & 31.41 \\ DF & 20 & 20 \\ \(p\)-value & 0.0001 & 0.0001 \\ \(\alpha\) & 0.05 & 0.05 \\ \hline \end{tabular}
\end{table} 
Table 4: Results of \(\chi^{2}\) analysis of histopathological lesions and behavioral changes observed in rainbow trout fingerlings infected with several _Aeromonas_ species. \begin{table}
\begin{tabular}{c c c c c} \hline \hline _Aeromonas_ & \multirow{2}{*}{**N**} & \multicolumn{4}{c}{**\% of Fish with Histopathological Lesions 1**} \\ \cline{3-5}
**Species** & & **Rosette** & **Telencephalon** & **Oblongata Medulla** \\ \hline _A._ & 90 & 30 & 3.3 & 1.1 \\ _allosacharophilia_ & & & & \\ _A. besiarum_ & 90 & 26.6 & _21.1_ & _40_ \\ _A. caviae_ & 90 & 28.8 & _22.2_ & 16.6 \\ _A. hylrophilia_ & 90 & 27.7 & _18.8_ & 22.2 \\ _A. lusitana_ & 90 & _50_ & _18.8_ & 22.2 \\ _A. media_ & 90 & 35.5 & _31.1_ & 22.2 \\ _A. popoffii_ & 90 & _7.7_ & 3.3 & 4.4 \\ _A. salmonicida_ & 90 & _41.1_ & _25.5_ & 15.5 \\ _A. sobria_ & 90 & 20 & _7.7_ & 12.2 \\ _A. veronii_ & 90 & 11.1 & 10 & 17.7 \\ Control group & 90 & 0 & 0 & 0 \\ \hline \hline \end{tabular}  
* Groups in italics within the same column are significantly different (\(p<0.05\)).  
\end{table} 
Table 3: _Aeromonas_ species and histopathological lesions observed in nasal epithelium or rosette, telencephalon, and oblongata medulla changes (%), observed in rainbow trout fingerlings infected with different _Aeromonas_ species. _Aeromonas_ species reveals that the two dimensions provides an adequate description of data. The first dimension accounts for 71.17 % and, for the second dimension, 28.82 % of inertia, together accounting for 100 % of the variability of analyzed data (Table 5). Figure 2a shows CA maps of histological lesions and the quality of representation in the row and columns of the first dimension. The most of _Aeromonas_ species are well represented, with the exception of _A. popoffii_, _A. sobria_, and _A. hydrophilis_. With respect to the site of lesions, the telencephalon category showed a low quality of representation; therefore, the first dimension explains most of the deviation from the expected values of categories oblongata medulla and nasal epithelium. This means that the variability of first component can be explained by differences between oblongata medulla and nasal epithelium. According to the level of contribution of column categories of CA map of behavioral changes, the first dimension can be explained by a negative correlation among _A. veronii_ and _A. salmonicida_ (allocated in negative pole) with _A. lusitana_ and _A. popoffii_ (allocated in positive pole). On other hand, _A. hydrophilis_ and _A. bestiarum_ showed a poor representation, had a lower contribution, and was allocated near to the centroid. The contribution of row to the definition of the first dimension is shown in Figure 2b. The category hyperpigmentation shows the highest contribution to define the first dimension.