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Fractal geometry predicts varying body size scaling relationships for mammal and bird home ranges


Scaling laws that describe complex interactions between organisms and their environment as a function of body size offer exciting potential for synthesis in biology1,2,3,4. Home range size, or the area used by individual organisms, is a critical ecological variable that integrates behaviour, physiology and population density and strongly depends on organism size5,6,7. Here we present a new model of home range–body size scaling based on fractal resource distributions, in which resource encounter rates are a function of body size. The model predicts no universally constant scaling exponent for home range, but defines a possible range of values set by geometric limits to resource density and distribution. The model unifies apparently conflicting earlier results and explains differences in scaling exponents among herbivorous and carnivorous mammals and birds5,6,7,8,9,10,11,12,13,14,15,16,17,18. We apply the model to predict that home range increases with habitat fragmentation, and that the home ranges of larger species should be much more sensitive to habitat fragmentation than those of smaller species.

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Figure 1: Hypothetical average density h of resources per sampling volume encountered by species with different sampling volumes of length w on a fractal distribution of resources (black cells, fractal dimension F = 1.26).
Figure 2: Relationship between density and estimated fractal dimension for different distributions in a two-dimensional environment.
Figure 3: Comparison of model predictions and empirical estimates for home range–body mass scaling relationships (see also Table 1).


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We thank J. Brown, B. Enquist, J. Damuth and G. Belovsky. Work on this model began during the Fractals in Biology Meeting at the Santa Fe Institute, New Mexico. J.P.H. is supported by an NSF Graduate Research Fellowship.

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Correspondence to John P. Haskell.

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Haskell, J., Ritchie, M. & Olff, H. Fractal geometry predicts varying body size scaling relationships for mammal and bird home ranges. Nature 418, 527–530 (2002).

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