Fractal Analyses of Animal Movement: A Critique

Several recent papers developed and applied a novel approach for the analysis of animal movement paths, based on calculating the paths' fractal dimensions. The estimated fractal dimension is used to describe the pattern of the interaction between animal movement and landscape heterogeneity, and possibly to extrapolate movement patterns of organisms across spatial scales. Here, I critically examine the key assumption of the fractal approach: that the estimated fractal dimension is constant over some biologically relevant range of spatial scales. Use of a correlated random walk as a null hypothesis for movement suggests that the fractal dimension should grade smoothly from near 1 at very small spatial scales to near 2 at very large spatial scales. Several empirical data sets exhibit a qualitative pattern in agreement with this prediction. I conclude that ecologists should avoid calculating and using the fractal dimension of movement paths, unless self—similarity (a constant fractal dimension) for some range of spatial scales is demonstrated. An alternative approach employing random—walk models provides a more powerful framework for translating individual movements in heterogeneous space into spatial dynamics of populations.