  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.
