Tortuosity Entropy: a measure of spatial complexity of behavioral changes in animal movement data

The goal of animal movement analysis is to understand how organisms explore and exploit the complex and varying environment. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviors to highly random ones. This is critical for assessing movement efficiency and strategies that are used to quantify and analyze movement trajectories. Here we introduce a tortuosity entropy (TorEn) based on comparison of parameters, e.g. heading, bearing, speed, of consecutive points in movement trajectory, which is a simple measure for quantifying the behavioral change in animal movement data in a fine scale. In our approach, the differences between pairwise successive track points are transformed inot symbolic sequences, then we map these symbols into a group of pattern vectors and calculate the information entropy of pattern vector. Tortuosity entropy can be easily applied to arbitrary real-world data-deterministic or stochastic, stationary or non-stationary. We test the algorithm on both simulated trajectories and real trajectories and show that both mixed segments in synthetic data and different phases in real movement data are identified accurately. The results show that the algorithm is applicable to various situations, indicating that our approach is a promising tool to reveal the behavioral pattern in movement data.