Simultaneous observation of intermittent locomotion of multiple fish by fine-scale spatiotemporal three-dimensional positioning

Larger yellow-phase Japanese eels show short-range homing in a freshwater river

The homing behavior and site fidelity to habitats in various fishes, including anguillid eels (genus Anguilla), are fascinating. However, little is known about how yellow-phase eels exhibit homing behavior and the sensory mechanisms involved. Using acoustic telemetry, we investigated the homing behavior of 18 Japanese eels, A. japonica, with total lengths ranging from 204 to 570 mm, in a narrow freshwater river in inland central Japan, where salinity gradient, tidal current, and magnetic sense cannot be used for their homing, but where olfaction could play a role. The tagged eels captured upstream and downstream were released downstream and upstream, respectively. The results showed that large eels, over approximately 400 mm in total length, exhibited homing behavior to their original sampling locations (likely to shelters and foraging sites, where they probably spent a longer time than in other locations and grew successfully) from outside their home ranges, predominantly during the dark period. Homing success was not affected by the two capture locations, indicating that eels did not use olfactory cues for short-range homing in freshwater rivers.

A simple intuitive method for seeking intersections of hyperbolas for acoustic positioning biotelemetry

We proposed a simple hyperbolic positioning method that does not require solving simultaneous quadratic equations. Moreover, we introduced the mathematical concept of a “pencil” into analytical calculations in the hyperbolic positioning method for a better understanding. In many recent studies using positioning biotelemetry, the specific procedure for intersection calculation of hyperbolas has rarely been described. This might be one of two major obstacles, with the other being clock synchronisation among receivers, for positioning biotelemetry users, including potential users. We focus only on the intersection calculation in this paper. Therefore, we propose a novel method and introduce the mathematical concept into analytical calculations. The computing performances of the novel method, an analytical method applying the concept of a pencil, and an approximating method using the Newton-Raphson method were compared regarding positioning correctness, accuracy, and calculation speed. In the novel method, hyperbolas were represented using the parameter θ, which was treated as a discrete variant. The finer the tick-width of the parameter θ, the more accurate was its positioning, but it took slightly longer to calculate. By setting the tick-width to 0.01°, a simulated trajectory was correctly and accurately localised, as in the analytical method which always correctly returned the accurate solution. The approximating method has a major limitation concerning correctness. It returns a single solution regardless of two intersections of hyperbolas; however, the positioning is accurate when the hyperbolas intersect at a single point. This study approached one major difficulty in positioning biotelemetry and will help biotelemetry users overcome this drawback with a simple and intuitive understanding of hyperbolic positioning.