A new approach for the identification of turns and steps in tortuous movement data

• Published in: Methods in Ecology and Evolution
• Main Authors: Humphries, N. E., Weimerskirch, Henri, Sims, David W
• Other Authors: The Laboratory (Marine Biological Association of the United Kingdom), Marine Biological Association of the United Kingdom (MBA), Marine Biology and Ecology Research Centre, Plymouth University, Centre d'études biologiques de Chizé (CEBC), Centre National de la Recherche Scientifique (CNRS), National Oceanography Centre Southampton (NOC), University of Southampton, Centre for Biological Sciences (University of Southampton)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2013
• Subjects: albatross; cell tracking; correlated random walk; fractal path analysis; Lévy flight; optimal foraging theory; power-law distribution; random walk; satellite tracking; scale-free movement; [SDE]Environmental Sciences; Wandering Albatross
• Online Access: https://hal.archives-ouvertes.fr/hal-00853663; https://doi.org/10.1111/2041-210X.12096

International audience 1. A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns. 2. Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data. 3. We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such. 4. By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3*5 orders of magnitude. 5. Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical ...