Composite Brownian Walks Best Describe Livestock Mobility Patterns across Species

Abstract

In quantitative studies on animal movements and foraging, there has been ongoing debate over the relevance of Levy walk and related stochastic models to understanding mobility patterns of diverse organisms. In this study, we collected and analyzed a large number of GPS logs that tracked the movements of different livestock species in northwestern Kenya. Statistically principled analysis has only found limited evidence for the scale-free movement patterns of the Levy walk and its variants, even though most of the tracked movements clearly show super-diffusive behavior within the relevant temporal duration. Instead, the analysis has given strong support to composite exponential distributions (composite Brownian walks) as the best description of livestock movement trajectories in a wide array of parameter settings. Furthermore, this support has become overwhelming and near universal under an alternative criterion for model selection. These results illuminate the multi-scale and multi-modal nature of livestock spatial behavior. They also have broader theoretical and empirical implications for the related literature.