Modeling On Structure Of Fish School

Mathematical modeling and computer simulation is the most important way to study the structure of fish schooling currently. In this project, a fish school of Hemigrammus rhodostomus in lab was recorded by a camera and the locations of fish individuals were logged; Calculated the speed, turning and Nearest neighbour distance, and then applied these results to a mathematical model; Finally, by adjusting the greatest visual ability to verify the reliability of the model.Hemigrammus rhodostomus, which is small in size and has significant characteristics of schooling, was applied in this paper. Fish was feed in a tank with dimensions of 100×50×50 cm3 and recorded by a camera. Extracted 89 images from a 9-second video; used Bitmap image software in Windows to track five individuals in the schooling. All the selected fish were distributed randomly in the school and far away from the edges of tank. Logged the horizontal and vertical coordinates of the five individuals’ snout and tail in each image. Calculate the speed and turning of the fish.The model in this paper has applied the concept of Individual Based Models and based on the models from Aoki, I., Huth A. and C. Wissel. The rule is founded by repulsion, parallel and attraction. Avoiding the collision will be considered as the prerequisite. Defined the reaction equation of fish according to the greatest visual ability of fish.In our model, the greatest visual ability of fish has been divided into five different ranges: 1) repulsive-reaction distance: according to the principle of avoiding collision, the main fish i will go away from its neighbor j when the distance between them is smaller than the nearest neighbor distance; 2) distance without a neutral reaction: the main fish will move with an average-group-speed in random directions; 3) parallel-orientation distance: fish i is moving with a target speed with a unchanged direction; 4) attractive-reaction distance: fish i will move toward its neighbor fish j; 5) no response distance: fish j is out of the visibility range of the main fish and it will not have any impact on fish i.Model a fish schooling in a rectangular tank with finite space. Applied Open GL and C++ to simulate the moving of schooling. In order to investigate the influence of the greatest visual ability on the structure of the fish schooling, a random factor was added in the mathematical model to keep the chaos and avoid ordered abnormal phenomenon.The results showed that schooling of Hemigrammus rhodostomus moved randomly but orderly and had evenly spacing among the individuals; the speed, orientation and turning of individuals were similar. The average speed of fish was 3.9 BL/S; the most frequency speed was 3.6BL/S which can refer to the target speed. The turning of fish was distributed between 0oand 30o, the average value and the maximum value was 18oand 70o, respectly. The nearest neighbor distance was distributed mostly between 1.5BL and 2.5BL, the minimum was 1.2BL.17 cases have been simulated by changing the greatest visual ability from 4 til 20. Simulation results showed that: when the value of r was small(from 4 to 7), the individual average swimming speed was small, the change of average turning was unstable; mean while individuals were affected by few neighbors in a small-scale, therefore, at the beginning of simulation there could be some dense groups or isolated individuals, after few minutes, the schooling became disordered; When the value of r was around 10, the simulated indivuals had an average speed of 3.9 BL/S and stable turning, at this time some ordered schooling which was similar with Hemigrammus rhodostomus recorded in tank occurred easily. When the value of r was large and between 18 and 20, the individuals moved at a higher speed and had unstable turning, in this case the fish was affected by many individuals in a large scale, therefore a larger and disordered schooling could be founded frequently. So the study showed mathematical model and simulation can help to describe some of the characteristics of the actual fish schooling.