Reducing the Number of Individuals to Monitor Shoaling Fish Systems – Application of the Shannon Entropy to Construct a Biological Warning System Model

The present study aims at identifying the lowest number of fish (European seabass) that could be used for monitoring and/or experimental purposes in small-scale fish facilities by quantifying the effect that the number of individuals has on the Shannon entropy (SE) of the trajectory followed by the shoal’s centroid. Two different experiments were performed: (i) one starting with 50 fish and decreasing to 25, 13, and 1 fish, and (ii) a second experiment starting with one fish, adding one new fish per day during 5 days, ending up with five fish in the tank. The fish were recorded for 1h daily, during which time a stochastic event (a hit in the tank) was introduced. The SE values were calculated from the images corresponding to three arbitrary basal (shoaling) periods of 3.5 min prior to the event, and to the 3.5 min period immediately after the event (schooling response). Taking both experiments together, the coefficient of variation (CV) of the SE among measurements was largest for one fish systems (CV 37.12 and 17.94% for the daily average basal and response SE, respectively) and decreased concomitantly with the number of fish (CV 8.6–10% for the basal SE of 2 to 5 fish systems and 5.86, 2.69, and 2.31% for the basal SE of 13, 25, and 50 fish, respectively). The SE of the systems kept a power relationship with the number of fish (basal: R(2)= 0.93 and response: R(2)= 0.92). Thus, 5–13 individuals should be the lowest number for a compromise between acceptable variability (<10%) in the data and reduction in the number of fish. We believe this to be the first scientific work made to estimate the minimum number of individuals to be used in subsequent experimental (including behavioral) studies using shoaling fish species that reaches a compromise between the reduction in number demanded by animal welfare guidelines and a low variability in the fish system’s response.