Skip to main content

Home range formation in wolves due to scent marking


Social carnivores, such as wolves and coyotes, have distinct and well-defined home ranges. During the formation of these home ranges scent marks provide important cues regarding the use of space by familiar and foreign packs. Previous models for territorial pattern formation have required a den site as the organizational center around which the territory is formed. However, well-defined wolf home ranges have been known to form in the absence of a den site, and even in the absence of surrounding packs. To date, the quantitative models have failed to describe a mechanism for such a process. In this paper we propose a mechanism. It involves interaction between scent marking and movement behavior in response to familiar scent marks. We show that the model yields distinct home ranges by this new means, and that the spatial profile of these home ranges is different from those arising from the territorial interactions with den sites.

This is a preview of subscription content, access via your institution.


  • Aronson, D. G. (1985). The role of diffusion in mathematical population biology: Skellam revisited, in Mathematics in Biology and Medicine, V. Capaso, E. Grosso and S. L. Paveri-Fontana (Eds), Berlin: Springer-Verlag, pp. 2–6.

    Google Scholar 

  • Lewis, M. A. (1994). Spatial coupling of plant and herbivore dynamics: the contribution of herbivore dispersal to transient and persistent “waves” of damage. Theor. Popul. Biol. 45, 277–312.

    MATH  Article  Google Scholar 

  • Lewis, M. A. and J. D. Murray (1993). Modelling territoriality and wolf-deer interactions. Nature 366, 738–740.

    Article  Google Scholar 

  • Lewis, M. A., K. A. J. White and J. D. Murray (1997). Analysis of a model for wolf territories. J. Math. Biol. 35, 749–774.

    MathSciNet  Article  Google Scholar 

  • Mech, D. L. (1991). The Way of The Wolf, Stillwater, MN: Voyageur Press.

    Google Scholar 

  • Merti-Millhollen, A. S., P. A. Goodmann and E. Klinghammer (1986). Wolf scent marking with raised-leg urination. Zoo Biol. 5, 7–20.

    Article  Google Scholar 

  • Moorcroft, P. R., M. A. Lewis and R. L. Crabtree (1999). Analysis of coyote home ranges using a mechanistic home range model. Ecology 80, 1656–1665.

    Article  Google Scholar 

  • Murray, J. D. (1989). Mathematical Biology, Biomathematics 19, Berlin: Springer-Verlag.

    Google Scholar 

  • Okubo, A. (1980). Diffusion and Ecological Problems: Mathematical Models, Biomathematics 10, Berlin: Springer-Verlag.

    Google Scholar 

  • Parrish, S. (1998). Analysis of a home range model: pattern formation from scent-marking, Master’s thesis, University of Utah.

  • Peters, R. P. (1974). Wolf sign: scents and space in a wide-ranging predator, PhD thesis, University of Michigan, Ann Arbor, MI.

    Google Scholar 

  • Peters, R. P. (1979). Mental maps in wolf territoriality, in The Behavior and Ecology of Wolves, E. Klinghammer (Ed.), New York, NY: Garland Press, pp. 119–152.

    Google Scholar 

  • Peters, R. P. and L. D. Mech (1975). Scent marking in wolves. Am. Scientist 63, 628–637.

    Google Scholar 

  • Rothman, R. J. and L. D. Mech (1979). Scent-marking in lone wolves and newly formed pairs. Anim. Behav. 27, 750–760.

    Article  Google Scholar 

  • Turchin, P. (1989). Population consequences of aggregative movement. J. Anim. Ecol. 58, 75–100.

    Google Scholar 

  • White, K. A. J., M. A. Lewis and J. D. Murray (1996). A model for wolf-pack territory formation and maintenance. J. Theor. Biol. 178, 29–43.

    Article  Google Scholar 

  • White, K. A. J., M. A. Lewis and J. D. Murray (1998). On Wolf Territoriality and Deer Survival, Chap. 6, Springer Verlag, pp. 105–126.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Mark A. Lewis.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Briscoe, B.K., Lewis, M.A. & Parrish, S.E. Home range formation in wolves due to scent marking. Bull. Math. Biol. 64, 261–284 (2002).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:


  • Dispersion Relation
  • Home Range
  • Steady State Solution
  • Movement Behavior
  • Scent Mark