Appendix A. Methodological details.

*Power-law tail probability density function*

After setting the maximum step length for a particular simulation (e.g., 100 km), the power-law tail probability density function for a particular step length *l _{i}* was:

(A.1) |

where = 1 (normalizing constant), * µ* = 2 (idealized Lévy flight power exponent), *l _{i}* = a step length value in the 1…

*Track simulation*

To simulate an animal’s movement track based on the power-law tail probability density function described above, we first set the number of days of tracking (e.g., 365) and assumed that each step length sampled from Pr(*l _{i}*) represented a daily movement. For each day, we sampled with replacement a

(A.2) |

where = turn angle in radians. *R *code (R Development Core Team 2004) for this procedure is provided in the Supplement.

*Calculating *µ

Because the estimation of * µ* is highly sensitive to the histogram binning procedure used in comparing the log_{10} of the step length bin frequency and the log_{10} of the step length (Sims et al. In press), we modified the binning procedure such that the bin widths were set to increase exponentially relative to the number of *k* bins; here, the vector of bin widths = 2* ^{k}* (Viswanathan et al. 1996, Newman 2005):

(A.3) |

where [*w*_{1} … *w _{k}*] = the width-adjusted histogram bin vector and

*Incorporating location error*

Errors associated with each tracking technology (Table 1, main text) were incorporated into the track simulations using a random normal deviate based on a mean = 1 and the standard deviation estimated for each error level. The true *x*,*y* co-ordinate for each time step was simulated as outlined above, but in this case the appropriate random normal deviate (north-south or east-west) was added to each *x *and * y *co-ordinate to generate a new (incorrect) location. The new error-blurred step length was then calculated using the Pythagorean Theorem:

(A.4) |

where

Newman, M. E. J. 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics **46**:323–351.

R Development Core Team. 2004. R: A language and environment for statistical computing. *in*. R Foundation for Statistical Computing, Vienna, Austria.

Sims, D. W., D. Righton, and J. W. Pitchford. *In press*. Minimising errors in identifying Lévy flight behavior of organisms. Journal of Animal Ecology.

Viswanathan, G. M., V. Afanasyev, S. V. Buldyrev, E. J. Murphy, P. A. Prince, and H. E. Stanley. 1996. Levy flight search patterns of wandering albatrosses. Nature **381**:413–415.