Maze's Complexity Structure Index in Experiments to Assess Fishes' Learning Ability

The use of mazes has become a common method in fish behavior research, serving as an objective approach to assess mechanisms of spatial learning and memory. To study the possibilities of objective control over the learning process of fish Danio rerio, a small aquarium maze (35×25 cm with a 10 cm wall height) was designed. The specimens were fed for 10-12 days, measuring the time taken to reach the feeding location. It was found that the reduction in time from initial to final values for the fishes' passage through routes of different complexity followed an exponential function y=aebx with corresponding coefficients. A mathematical index of route complexity (IRC) is proposed, reflecting the product of the probability coefficients of the fish passing bifurcation points along the route, multiplied by a species coefficient. The latter is determined as the ratio of the length of the true path between the starting and finishing points and average speed of the biological subject. IRC indicates the minimal possible time to reach the goal, representing the initial time spent on the task before the learning process starts. The index of maze complexity (IMC) for fishes can be calculated as the sum of route index values under the non-intersecting and non-repeating corridors or by summarizing the probabilities of bifurcation points and the total corridor length. The data on feeding behavior and spatial orientation of the studied fish confirmed the positive correlation between the calculated IRC values for both simple and complex maze routes. Various aspects of fish intelligence can be studied by comparing mathematical parameters of maze complexity with task completion times.