Space use by red deer in Norway recorded by aid of GPS, averaged over 18 individuals. (A) Lagrangian view; measuring parallel shift from increasing tobs by a factor of 10, from 1 hr to 10 hr. The similar magnitude of β and the magnitude of the parallel shift (blue arrow) both confirm scale-free movement, which may be LW-like (Markov-compliant) or MRW-like (memory-influenced). (B) Eulerian view; incidence log(I) as a function of sample size of fixes log(N) supports MRW over LW, since z = 0.41 <<1 and stable (implying a scale-free kind of site fidelity) over a substantial range of N. The plots show the average I(N) for 18 individuals (+/- 1 standard error), where each individual’s characteristic spatial scale parameter c has been normalized to c ≈ 1 by respective grid scale adjustments (Additional file1). This normalization does not need to be exact; it is trivial to estimate c = 1 [log(c) = 0] from a somewhat smaller or larger value given by the regression. The distribution of the actual c-estimates (magnitudes in m2) is shown in the inset.