3D trajectories and corresponding curvatures of 30 bat pairs

Social animals exhibit collective behavior wherein they negotiate to reach an agreement, for example to coordinate motion. Bats are unique that they use active sensory echolocation or “bio-sonar”, wherein they emit ultrasonic waves and sense echoes to navigate surroundings. In real bat swarms, understanding navigational leadership roles in light of their unique sensing capabilities is a challenge, and quantitative assessment of leadership has not been explored rigorously. Given the broadcast nature of bio-sonar, the active sensing of one individual can directly influence the motion of others, making the directionality of leadership unclear. Here, we seek to understand navigational leadership from direct observation of other bats in flight and formally measure the strength of influence of one individual on another by quantifying directional coupling using tools from dynamical systems and information theory. Pairs of bats were continuously tracked in a mountain cave in Shandong Province, China, from which three-dimensional path points were extracted and converted to one-dimensional curvature time series. Results demonstrate the evidence of information exchange between flying bat pairs. We find the identified coupling-relationships between bats are sensitive to the selected mathematical tools, their parameters and the bat behavior.