The Mathematical Institute, University of Oxford, Eprints Archive

The effect of sampling rate on observed statistics in a correlated random walk

Rosser, G and Fletcher, A G and Maini, P. K. and Baker, R. E. (2013) The effect of sampling rate on observed statistics in a correlated random walk. The Journal of the Royal Society Interface, 10 (83). pp. 1742-5662.

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Tracking the movement of individual cells or animals can provide important information about their motile behaviour, with key examples including migrating birds, foraging mammals and bacterial chemotaxis. In many experimental protocols, observations are recorded with a fixed sampling interval and the continuous underlying motion is approximated as a series of discrete steps. The size of the sampling interval significantly affects the tracking measurements, the statistics computed from observed trajectories, and the inferences drawn. Despite the widespread use of tracking data to investigate motile behaviour, many open questions remain about these effects. We use a correlated random walk model to study the variation with sampling interval of two key quantities of interest: apparent speed and angle change. Two variants of the model are considered, in which reorientations occur instantaneously and with a stationary pause, respectively. We employ stochastic simulations to study the effect of sampling on the distributions of apparent speeds and angle changes, and present novel mathematical analysis in the case of rapid sampling. Our investigation elucidates the complex nature of sampling effects for sampling intervals ranging over many orders of magnitude. Results show that inclusion of a stationary phase significantly alters the observed distributions of both quantities.

Item Type:Article
Uncontrolled Keywords:correlated random walk sampling rate tracking animal migration bacterial motility
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1709
Deposited By: Philip Maini
Deposited On:29 Jun 2013 07:52
Last Modified:29 May 2015 19:24

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