## 3 Results and Discussion  
The non-invasive tool we wished to develop targeted the responses of the fish groups rather than that of individual fish both to reduce the computational effort and because the response of the group may be considered the result of integrating all the responses each individual fish, which may be influenced by the physiological status of the individual, its size, status in the school's hierarchy and other factors that are usually unknown in monitoring purposes. Also, the response to a stochastic event was measured instead of other behavioural aspects (swimming pattern, daily activity, feeding, aggressiveness, _etc._) because it permits to restrict the computational analysis in time to the duration of the response (three minutes was sufficient in our case, rather than observing the animals for longer periods of time where more variablesmay play a role) and to reproduce the event at will in other settings for comparison purposes. Longer periods of time were also analyzed but the discriminative power of the analyses did not improve (results not shown). Of the three cases examined, we expected C1 and C2 to behave similarly to each other and to be clearly different from C3 due to the methylmercury contamination in C3. The neurotoxic agent methylmercury was selected because of its increasing relevance as an environmentally ubiquitous pollutant that accumulates and biomagnifies in the trophic chain [63]. Although differences in fish stocking density between C1 and C2 (81 fish) vs C3 (41 fish) might have had an effect on the responses to the event, most probably they did not [26, 27]. Two of the three FD algorithms used, Higuchi and Katz's variation proposed by [PERSON] were able to differentiate C1, C2 and particularly C3, for the three sampling window lengths in both coordinates of the clusters' centers, X and Y in a 2D analysis, as shown in Figure 5. Since there was a correlation between the X and Y coordinates, the rest of the calculations were performed on only one of them, the X values. The almost constant and close to 1 value of the FD obtained by using the Katz algorithm is in agreement with the results of [PERSON] [64] and confirms [PERSON]'s note [51]. Indeed the modification proposed by [PERSON] was more sensitive to detect differences between the three cases than [PERSON], suggesting that for our particular application, it may be the most suitable algorithm. The median and the standard deviation of the FDs obtained for each case and window length for the Katz-Castiglioni algorithm on the X values are plotted in Figure 6 and shown in Table 2. C3 showed the highest FD median value for all three window lengths, with very similar values that were close to 2.5 (Table 2) but it also displayed the largest dispersion of values (Figure 6). C1 had the smallest dispersion of values (Figure 6) and they had a tendency to increase with increasing window length. The FD of C2 varied between 1.9 and 2.1. Increasing window length seemed to diminish the dispersion of the values in C1 and C2, but did not affect the degree of dispersion in C3 (Figure 6). Interestingly our results agree with those of [16] in spite of these authors using a different species (zebrafish, which is a freshwater species that prefers warmer water), only one individual and a different contaminant: the FD of the swimming trajectory of their zebrafish also trended to increasing concentrations of sodium hypochlorite contaminating its water, obtaining FD values of the swimming trajectories between 2.11 and 2.14. The value of the FD varies depending on the algorithm used for its calculation, on the different units composing the time series whether normalization has taken place or not as adressed by [PERSON] [65] and on the window length; with lower values of window length producing lower FD values. Optimization of the window length for our particular case produced FD values higher than 2, which is also in accordance with the results of [PERSON] and [PERSON] [16].