Differentiating the L\'evy walk from a composite correlated random walk

TL;DR

This paper introduces a statistical method to reliably distinguish between Le9vy walks and composite correlated random walks, two key models in animal movement ecology, using likelihood functions and hidden Markov models.

Contribution

The authors develop a novel likelihood-based approach, including hidden Markov models, to differentiate between Le9vy walks and composite correlated random walks in movement data.

Findings

Method accurately differentiates models in simulations

Applicable to complex real-world movement data

Facilitates research on animal search strategies

Abstract

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.