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Evolution of Shannon entropy in a fish system (European seabass, Dicentrarchus labrax) during exposure to sodium selenite
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1  Research Center for Experimental Marine Biology and Biotechnology - Plentziako Itsas Estazioa (PIE), University of the Basque Country UPV/EHU, Plentzia, Spain
2  Ikerbasque, Basque Foundation for Science, Bilbao, Spain.
3  Norwegian College of Fishery Science, Faculty of Biosciences, Fisheries and Economics, UiT The Arctic University of Norway, Tromsø, Norway


As part of our work on the development of on-line monitoring and early sensing and alarm systems in aquaculture, we are testing the suitability of the farmed fish as a biological warning system. This requieres the system to react in a quantifiable manner when exposed to perturbations. In this experiment European seabass (Dicentrarchus labrax) was exposed to sodium selenite (Na2Se, 10 μg/l) in order to i) test the methodology proposed by Eguiraun (doi: 10.3390/e16116133, Entropy, 2014, 16: 6133-51) and ii) to quantify the effect of the Na2Se on the fish system. Two experimental cases where performed: C1 (control) and C2 (Na2SeO3 exposure) for 7 days. Fish were monitored daily, in every video sequence the centroid of the group was calculated and its trajectory analized using Shannon Entropy (SE). The video sequences consisted of 3.5 minutes at 24 fps and 2 sequences were recorded per day in C1: basal (rest state) and event response (hit in the tank) while only one sequence was recorded in C2: the event response. Approximately every 2 days the water was changed in both tanks, which made visual conditions vary from one day to another due to differences in turbidity. All the images were obtained and processed following the same parameters. In C1 the SE of the basal (4.64) was lower than the SE of the event (5.32), and the empirical value of the latter coincided with that of previous works, while the SE of the event in C2 showed a lower value (5.09) than the control group. Accordingly, we believe that this methodology shows a real potential to i) effectively monitor European seabass and ii) confirm that exposure of the fish system to Na2SeO3 is quantifiable and decreases its SE in response to an event.

Keywords: Biological Warning System; Shannon entropy; Fish system; environmental monitoring, fish school trajectories, image analysis, motion patterns, contaminants, non linear dynamic
Comments on this paper
Francisco Chinesta
On the shannon entropy quantification
Dear auhthors,

Thanks for this very nice application,

In the paper you wrire

Shannon entropy of the fish system was measured ...

Can you give some more details on the entropy calcumation from the fish trajectories ?

Best regards,
Harkaitz Eguiraun
Dear Francisco:

If you can, please check the powerpoint presentation. It is explained there in a graphical and easier (I hope) way.

Briefly, we do not focus in individual behaviour. We want to analyze the fish as a shoal. Additionaly, we record a 3D enviroment while we only analize 2D image sequences. Thus, the methodology proposed detects all the elements within every image and calculates the centroid coordinates of all the images. No matter if there is a occlusion, a dirt or a shadow. Over the video sequence the centroid´s coordinates constitute two signals. Shannon entropy is measured in these two signals.

In case you what further info please feel free to contact again

Harkaitz Eguiraun
Francisco Chinesta
Thanks a lot, I'm checking with your presentation,
best regards,