PHYSICAL AND BIOLOGICAL MECHANISMS IN ANIMAL MOVEMENT PROCESSES

1. We have analysed a large set of animal locations from a telemetry study of a herd of domestic sheep, Ovis aries, in order to test an alternative model for area-utilization functions. Our model incorporates the special effects emerging from complex movement patterns, which have made the traditional home range demarcation protocols so difficult to employ. 2. The telemetry location plots approached a statistically self-similar fractal pattern with dimension 1.5 as the overall plot density (n) increased. 3. The home range area expanded on average as a function of n without any ap-parent asymptotic approach to a 'true' home range area. The regression of log(area) versus log(n) was approximately linear, with slope 0-5 for samples of 10-1433 coordinate plots. 4. This 'power law' expansion was time-independent: the average area from n position plots was the same when n was sampled from a short and a long time interval. In other words, the observed area utilization expanded as a function of n rather than time. We show that this did not seem to be due to insufficient sample size from a stationary function for area utilization distribution. 5. This curious result has potentially far-reaching practical consequences. The classical a priori assumption that an individual's true home range is equal to a given area utilization distribution from which our location samples are selected, could be a misleading approach. Alternatively, one can model an individual's area utilization as a dispersal process similar to random walk (mainly autocorrelated locations) or random walk on a random walk (a larger part with non-autocorrelated locations) in statistical mechanics. From these neutral models, testable ecological hypotheses can emerge from significant deviations from the log-linear area expansion, and from the y-intercept value in the log(area)/log(n) regression. 6. We discuss specific conditions where one would expect to find an area asymptote, or a true home range, from an expanding set of locations. These conditions should be regarded as special cases rather than the general rule.