Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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).


  1. Milne, B. T. in Wildlife and Landscape Ecology: Effects of Pattern and Scale (ed. Bissonette, J. A.) 32–69 (Springer, New York, 1997)

    Book  Google Scholar 

  2. Peters, R. H. The Ecological Implications of Body Size (Cambridge Univ. Press, New York, 1983)

    Book  Google Scholar 

  3. Calder, W. A. Size, Function, and Life History (Dover, Mineola, New York, 1996)

    Google Scholar 

  4. West, G. B., Brown, J. H. & Enquist, B. J. A general model for the origin of allometric scaling laws in biology. Science 276, 122–126 (1997)

    CAS  Article  Google Scholar 

  5. Damuth, J. Home range, home range overlap, and species energy use among herbivorous mammals. Biol. J. Linn. Soc. 15, 185–193 (1981)

    Article  Google Scholar 

  6. Holling, C. S. Cross-scale morphology, geometry, and dynamics of ecosystems. Ecol. Monogr. 62, 447–502 (1992)

    Article  Google Scholar 

  7. Reiss, M. Scaling of home range size: body size, metabolic needs and ecology. Trends Ecol. Evol. 3, 85–88 (1988)

    CAS  Article  Google Scholar 

  8. Belovsky, G. E. in Viable Populations for Conservation (ed. Soule, M. E.) (Cambridge Univ. Press, Cambridge, 1987)

    Google Scholar 

  9. McNab, B. K. Bioenergetics and the determination of home range size. Am. Nat. 97, 133–140 (1963)

    Article  Google Scholar 

  10. Swihart, R. K., Slade, N. A. & Bergstrom, B. J. Relating body size to the rate of home range use in mammals. Ecology 69, 393–399 (1988)

    Article  Google Scholar 

  11. Whiting, L. The body mass allometries as evolutionarily determined by the foraging of mobile organisms. J. Theor. Biol. 177, 129–137 (1995)

    Article  Google Scholar 

  12. Armstrong, J. T. Breeding home range in the nighthawk and other birds: its evolutionary and ecological significance. Ecology 46, 619–629 (1965)

    Article  Google Scholar 

  13. Schoener, T. W. Sizes of feeding territories among birds. Ecology 49, 123–141 (1968)

    Article  Google Scholar 

  14. Gompper, M. E. & Gittleman, J. L. Home range scaling: Intraspecific and comparative trends. Oecologia 87, 343–348 (1991)

    ADS  Article  Google Scholar 

  15. Harestad, A. S. & Bunnell, F. L. Home range and body weight—A reevaluation. Ecology 60, 389–482 (1979)

    Article  Google Scholar 

  16. Owen-Smith, R. N. Megaherbivores: The Influence of Very Large Body Size on Ecology (Cambridge Univ. Press, New York, 1992)

    Google Scholar 

  17. Lindstedt, S. L., Miller, B. J., Buskirk, S. W. Home range, time and body size in mammals. Ecology 67, 413–418 (1986)

    Article  Google Scholar 

  18. Kelt, D. A. & VanVuren, D. Energetic constraints and the relationship between body size and home range area in mammals. Ecology 80, 337–340 (1999)

    Article  Google Scholar 

  19. Lawton, J. H. Are there general laws in ecology? Oikos 84, 177–192 (1999)

    Article  Google Scholar 

  20. Ritchie, M. E. Scale-dependent foraging and patch choice in fractal environments. Evol. Ecol. 12, 309–330 (1998)

    Article  Google Scholar 

  21. Ritchie, M. E. & Olff, H. Spatial scaling laws yield a synthetic theory of biodiversity. Nature 400, 557–560 (2000)

    ADS  Article  Google Scholar 

  22. Lawler, G., Schramm, O. & Werner, W. The dimension of the planar brownian frontier is 4/3. Math. Res. Lett. 8, 13–25 (2001)

    MathSciNet  Article  Google Scholar 

  23. Milne, B. T. Spatial aggregation and neutral models in fractal landscapes. Am. Nat. 139, 32–57 (1992)

    Article  Google Scholar 

  24. Kunin, W. E. Extrapolating species abundance across spatial scales. Science 281, 1513–1515 (1998)

    ADS  CAS  Article  Google Scholar 

  25. Mandelbrot, B. B. The Fractal Geometry of Nature (Freeman, New York, 1982)

    MATH  Google Scholar 

  26. Olff, H. & Ritchie, M. E. Fragmented nature: consequences for biodiversity. Landscape Urban Planning 858, 1–10 (2001)

    Google Scholar 

  27. Kotler, N. B. & Wiens, J. A. Multiple scales of patchiness and patch structure: a hierarchical framework for the study of heterogeneity. Oikos 59, 253–260 (1990)

    Article  Google Scholar 

  28. Poole, A. & Gill, F. (eds) The Birds of North America (The Birds of North America, Philadelphia, 1996–2000)

  29. Dunning, J. B. CRC Handbook of Avian Body Masses (CRC, Boca Raton, 1993)

    Google Scholar 

  30. Brown, J. H. in Experimental Ecology (eds Resetarits, W. J. Jr & Bernardo, J.) 71–95 (Oxford Univ. Press, New York, 1998)

    Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to John P. Haskell.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing