HOME RANGE - A FRACTAL APPROACH

Most current methods for describing animal home range assume that it may be represented as a Euclidean type shape such as a bell shaped curve or a closed polygon. Landscape ecology has increasingly shown that ecological objects are more often highly fragmented and irregular. A fractal approach to description of animal home range was thus developed. For each point where the animal was observed, a circle centered on this point was first laid down to represent the area searched for prey by the animal during a short time interval. In this way the behavior of the animal and differences between species can be represented. Next, a fine grid is laid over the map and the height of each grid square computed by the number of circles that overlap that square. Then, the fractal dimension of the resultant 3-D surface is calculated at several scales. From an analysis of data from a hawk, the existence of perching behavior can be inferred, as well as the observation that at coarse scales the hawk behavior is self-similar and resembles a random walk. The home range thus analyzed in no way resembles a closed figure such as a polygon because it is highly fragmented. Further analysis showed that the fractal measures are relatively insensitive to sample size and to measurement error. Code is included for performing the analyses.