Differentiating the L\'evy walk from a composite correlated random walk
  1. Understanding how to find targets with very limited information is a topic of interest in many disciplines. In ecology, such research has often focused on the development of two movement models: i) the L\'evy walk and; ii) the composite correlated random walk and its associated area-restricted search behaviour. Although the processes underlying these models differ, they can produce similar movement patterns. Due to this similarity and because of their disparate formulation, current methods cannot reliably differentiate between these two models.   2. Here, we present a method that differentiates between the two models. It consists of likelihood functions, including one for a hidden Markov model, and associated statistical measures that assess the relative support for and absolute fit of each model.   3. Using a simulation study, we show that our method can differentiate between the two search models over a range of parameter values. Using the movement data of two polar bears (\textit{Ursus maritimus}), we show that the method can be applied to complex, real-world movement paths.   4. By providing the means to differentiate between the two most prominent search models in the literature, and a framework that could be extended to include other models, we facilitate further research into the strategies animals use to find resources. 
Marie Auger-M\'eth\'e, Andrew E. Derocher, Michael J. Plank, Edward A.   Codling, Mark A. Lewis
q-bio.QM