The VFractal: a new estimator for fractal dimension of animal movement paths

Fractal measurements of animal movement paths have been used to analyze how animals view habitats at different spatial scales. One problem has been the absence of error estimates for fractal d estimators. To address this weakness, I present and test 4 new estimators for measuring fractal dimension at different spatial scales, along with estimates of their variation. The estimators are based on dividing the movement path into pairs of steps, forming V's, and then estimating various statistics from each V.I measured the performance of these estimators by comparing them to the traditional divider d method, using data generated by two different animal movement models. The estimator based on the net distance between the two steps and the cos turning angle was most accurate, giving estimates similar to those of the traditionally-used divider d method. Precision increased with longer and straighter paths.Strengths of this new estimator are that it can estimate fractal d at different spatial scales, give an estimate of variation, and combine data from many separate path segments which have been gathered at various spatial scales.