Ecological Archives E090-064-A3

Yannis P. Papastamatiou, Christopher G. Lowe, Jennifer E. Caselle, and Alan M. Friedlander. 2009. Scale-dependent effects of habitat on movements and path structure of reef sharks at a predator-dominated atoll. Ecology 90:996–1008.

Appendix C. Description of fractal analysis.

A range of dividers are used to determine the length of a movement path, with path length decreasing as divider size increases (Mandelbrot 1967, Doerr and Doerr 2004). A log-log plot of divider size versus path length is then generated, which yields a line with slope 1-D, and can be described by L(G) = kG1-D, where L(G) is path length, k is a constant and G is divider size. If the movement path is more tortuous and has a greater number of turns, then the slope of the line will also increase, and the path has a higher fractal D. Fractal D also incorporates replication by measuring path length twice for each divider size, by running the dividers both forward and backward along the path, which reduces bias associated with previous Fractal D measures (Nams 2006).

Doerr, V. A. J., and E. D. Doerr. 2004. Fractal analysis can explain individual variation in dispersal search paths. Ecology 85:1428–1438.

Mandelbrot, B. B. 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636–638.

Nams, V. O. 2006. Improving accuracy and precision in estimating fractal dimension of animal movement paths. Acta. Biotheoretica. 54:1–11.

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