Sampling Animal Movement Paths Causes Turn Autocorrelation
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Sampling Animal Movement Paths Causes Turn Autocorrelation Vilis O. Nams
Received: 7 May 2012 / Accepted: 27 February 2013 / Published online: 5 March 2013 Ó Springer Science+Business Media Dordrecht 2013
Abstract Animal movement models allow ecologists to study processes that operate over a wide range of scales. In order to study them, continuous movements of animals are translated into discrete data points, and then modelled as discrete models. This discretization can bias the representation of the movement path. This paper shows that discretizing correlated random movement paths creates a biased path by creating correlations between successive turning angles. The discretization also biases statistical tests for correlated random walks (CRW) and causes an overestimate in distances travelled; a correction is given for these biases. This effect suggests that there is a natural scale to CRWs, but that distance-discretized CRWs are in a sense, scale invariant. Perhaps a new null model for continuous movement paths is needed. Authors need to be aware of the biases caused by discretizing correlated random walks, and deal with them appropriately. Keywords
Correlated random walk Discretization Bias Scale-free
1 Introduction Animal movement is the glue that links individual behaviour to population dynamics. Spatially-explicit individual-based animal movement models allow ecologists to study processes that operate over a wide range of scales—from local to landscape. Most of these movement models are discrete, treating movement as discrete consecutive steps, yet often the animals being modelled show no naturallydefined steps. Thus we use a discrete model to represent a continuous process. It behoves us to ask how this discretization affects the representation of the movement V. O. Nams (&) Department of Environmental Sciences, Faculty of Agriculture, Dalhousie University, 50 Pictou Road, Box 550, Truro, NS B2N 5E3, Canada e-mail: [email protected]
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and thus our understanding of mechanisms driving the animal’s movement. For this paper I will focus on the correlated random walk (CRW) model, but the issue is important for all discrete movement models. The CRW is important because it has traditionally been used as a null model for movement—the model applied in the absence of knowledge of specific behavioural mechanisms (Lancaster et al. 2006; Schtickzelle et al. 2007; Turchin 1996). In addition, for the purposes of modelling, often the behavioural mechanism itself is ignored (except see Johnson et al. 2002). In a correlated random walk (CRW) an animal walks with discrete steps, and at each step turns with an angle that is independent of the previous turning angle (Kareiva and Shigesada 1983; McCulloch and Cain 1989). This has been the basis of the movement models for a variety of animals, such as leaf beetles [Cassida canaliculata; (Heisswolf et al. 2007)], African elephants [Loxodontia africana, (Dai et al. 2007)], gopher tortoises [Gopherus polyphemus; (Halstead et al. 2007)] and sperm whales [P
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