Movement in a confined space: Estimating path tortuosity

Tortuosity of an animal's path may be defined in the most general sense as departure of the path from straightness and is closely related to the animal‘s behavior. For example, movement toward a destination is straighter and hence less tortuous than foraging behavior where the animal is searching locally. It has been studied most often under the assumption that an animal has complete freedom of motion, i.e. there are no constraints on the choices it makes at each step. Almost all domestic or captive wild animals, however, are constrained in their movements in that they move within bounded regions such as pens. What distinguishes animals in confined space is that the boundaries are impermeable. We perform several simulation studies to compare several measures of tortuosity or movement for a path generated by the motion of an individual subject, in a bounded region. We show that established measures, such as fractal dimension and maximum distance traveled, behave differently for confined paths when compared to unconstrained movements. We also introduce new measures of the crookedness or movement of paths. These new measures are sensitive to the shape of the bounded region in which the path is confined, and to the distribution of turning angles for the path. In fact, all of the studied measures of tortuosity were affected by the shape of the enclosure and the magnitude of turning angles, but in different ways. Of the previously defined measures, fractal dimension and mean resultant length are sensitive to simulation model parameters, have low coefficients of variation, are uncorrelated with other measures, and change little with sample size. Of the new measures of tortuosity introduced, relative loop complexity is not only informative, but also uncorrelated with current measures of tortuosity. It has greater variability than some of the other measures; however, the variance decreases with increasing sample size. One measure, straightness index, is not recommended. It has high variability, is sensitive to sample size, and cannot distinguish among levels of any of the factors under study.