Journal of Mathematical Biology

, Volume 70, Issue 1, pp 329–341

Implications of the spatial dynamics of fire spread for the bistability of savanna and forest


DOI: 10.1007/s00285-014-0757-z

Cite this article as:
Schertzer, E., Staver, A.C. & Levin, S.A. J. Math. Biol. (2015) 70: 329. doi:10.1007/s00285-014-0757-z


The role of fire in expanding the global distribution of savanna is well recognized. Empirical observations and modeling suggest that fire spread has a threshold response to fuel-layer continuity, which sets up a positive feedback that maintains savanna–forest bistability. However, modeling has so far failed to examine fire spread as a spatial process that interacts with vegetation. Here, we use simple, well-supported assumptions about fire spread as an infection process and its effects on trees to ask whether spatial dynamics qualitatively change the potential for savanna–forest bistability. We show that the spatial effects of fire spread are the fundamental reason that bistability is possible: because fire spread is an infection process, it exhibits a threshold response to fuel continuity followed by a rapid increase in fire size. Other ecological processes affecting fire spread may also contribute including temporal variability in demography or fire spread. Finally, including the potential for spatial aggregation increases the potential both for savanna–forest bistability and for savanna and forest to coexist in a landscape mosaic.


Theoretical ecologySavanna–forest bistabilityFire-vegetation feedbacksPercolation

Mathematics Subject Classification (2000)

Primary 92D40Secondary 92D25

Supplementary material

285_2014_757_MOESM1_ESM.pdf (1014 kb)
Supplementary material 1 (pdf 1015 KB)

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.UPMC Univ. Paris 06, Laboratoire de Probabilités et Modèles Aléatoires, CNRS UMR 7599ParisFrance
  2. 2.Collège de France, Center for Interdisciplinary Research in Biology, CNRS UMR 7241ParisFrance
  3. 3.Department of Ecology, Evolution and Environmental BiologyColumbia UniversityNew YorkUSA
  4. 4.Department of Ecology and Evolutionary BiologyPrinceton UniversityPrincetonUSA