Skip to main content

Climate and competition: The effect of moving range boundaries on habitat invasibility

Abstract

Predictions for climate change include movement of temperature isoclines up to 1000 m/year, and this is supported by recent empirical studies. This paper considers effects of a rapidly changing environment on competitive outcomes between species. The model is formulated as a system of nonlinear partial differential equations in a moving domain. Terms in the equations decribe competition interactions and random movement by individuals. Here the critical patch size and travelling wave speed for each species, calculated in the absence of competition and in a stationary habitat, play a role in determining the outcome of the process with competition and in a moving habitat. We demonstrate how habitat movement, coupled with edge effects, can open up a new niche for invaders that would be otherwise excluded.

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

References

  • Abramowitz, M. and I. A. Stegun (Eds), (1965). Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, New York: Dover Publications.

    Google Scholar 

  • Aronson, D. and H. Weinberger (1975). Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in Lecture Notes in Mathematics, Springer, pp. 5–49.

  • Cantrell, R. S., C. Cosner and W. F. Fagan (1998). Competitive reversals inside ecological reserves: the role of external habitat degradation. J. Math. Biol. 37, 491–533.

    MathSciNet  Article  Google Scholar 

  • Clark, J. S. et al. (1998). Reid’s paradox of rapid plant migration. BioScience 48, 13–24.

    Article  Google Scholar 

  • Durret, R. (2002). Mutual Invadability Implies Coexistence in Spatial Models, Memoirs of the American Mathematical Society number 740.

  • Fagan, W. F., R. S. Cantrell and C. Cosner (1999). How habitat edges change species interactions. Am. Naturalist 153, 165–182.

    Article  Google Scholar 

  • Levin, S. A. (1974). Dispersion and population interactions. Am. Naturalist 108, 207–228.

    Article  Google Scholar 

  • Lewis, A. M., B. Li and H. F. Weinberger (2002). Spreading speed and linear determinacy for two-species competition models. J. Math. Biol. 45, 219–233.

    MathSciNet  Article  Google Scholar 

  • Ludwig, D., D. G. Aronson and H. F. Weinberger (1979). Spatial patterning of the spruce budworm. J. Math. Biol. 8, 217–258.

    MathSciNet  Google Scholar 

  • Malcolm, J. R. and A. Markham (2000). Global warming and terrestrial biodiversity decline. A Report Prepared for WWF (available online at http://panda.org/resources/publications/climate/speedkills).

  • Okubo, A. (1980). Diffusion and Ecological Problems: Mathematical Models, Berlin etc.: Springer.

    Google Scholar 

  • Parmesan, C. and G. Yohe (2003). A globally coherent fingerprint of climate change impacts across natural systems. Nature 421, 37–42.

    Article  Google Scholar 

  • Shigesada, N. and K. Kawasaki (1997). Biological Invasions: Theory and Practice, Oxford: Oxford University Press.

    Google Scholar 

  • Smith, H. L. and P. Waltman (1995). The Theory of the Chemostat, Cambridge: Cambridge University Press.

    Google Scholar 

  • Smoller, J. (1994). Shock Waves and Reaction-Diffusion Equations, NY etc.: Springer.

    Google Scholar 

  • Speirs, D. C. and W. S. C. Gurney (2001). Population persistence in rivers and estuaries. Ecology 82, 1219–1237.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. B. Potapov.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Potapov, A.B., Lewis, M.A. Climate and competition: The effect of moving range boundaries on habitat invasibility. Bull. Math. Biol. 66, 975–1008 (2004). https://doi.org/10.1016/j.bulm.2003.10.010

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1016/j.bulm.2003.10.010

Keywords

  • Lower Solution
  • Airy Function
  • Habitat Edge
  • Volterra Model
  • Dominant Eigenvalue