Quantifying the difference between animal movements and Brownian motion: Why do we still fail?

Despite considerable research we still lack a satisfactory conceptual model of animal movement behavior. We offer a novel approach to this problem by combining statistical and mathematical modeling approaches. First, we present an integrated statistical framework for the analysis of animal space use data. Using data from mammal and bird species we address topics ranging from the allocation of field resources to data collection, to a spatially explicit decomposition of the variance in home range size into components due to variation in temporal, spatial, and individual-level processes. Second, we compare mathematical models of home range behavior, showing that most actually fail to accommodate real animal movement data. This is caused by an emphasis on the entropy present in movement data while ignoring its higher order properties. Traditionally, animal movement has been modeled as an essentially random process, with added structure created by dependence on previously visited locations or attraction to particular habitats.  We demonstrate, however, that these models predict that an animal's range will expand continually, which is contrary to home range behavior. The size of home ranges is often extremely small relative to the velocity of the animal. None of the existing modeling approaches predict the formation of stationary home ranges as an emergent property of animal movement paths. We propose possible solutions and conclude that a unified view of the progress in both areas represents an exciting opportunity for future field-based and theoretical studies.