Your PDF has successfully downloaded.

You may be interested in finding more content on these topics:


You are not currently logged in.

Access JSTOR through your library or other institution:


Log in through your institution.

Journal Article

Understanding Shifts in Wildfire Regimes as Emergent Threshold Phenomena

Richard D. Zinck, Mercedes Pascual and Volker Grimm
The American Naturalist
Vol. 178, No. 6 (December 2011), pp. E149-E161
DOI: 10.1086/662675
Stable URL:
Page Count: 13
Were these topics helpful?
See something inaccurate? Let us know!

Select the topics that are inaccurate.

  • Download PDF
  • Add to My Lists
  • Cite this Item
We're having trouble loading this content. Download PDF instead.


AbstractEcosystems driven by wildfire regimes are characterized by fire size distributions resembling power laws. Existing models produce power laws, but their predicted exponents are too high and fail to capture the exponent’s variation with geographic region. Here we present a minimal model of fire dynamics that describes fire spread as a stochastic birth-death process, analogous to stochastic population growth or disease spread and incorporating memory effects from previous fires. The model reproduces multiple regional patterns in fire regimes and allows us to classify different regions in terms of their proximity to a critical threshold. Transitions across this critical threshold imply abrupt and pronounced increases in average fire size. The model predicts that large regions in Canada are currently close to this transition and might be driven beyond the threshold in the future. We illustrate this point by analyzing the time series for large fires (>199 ha) from the Canadian Boreal Plains, found to have shifted from a subcritical regime to a critical regime in the recent past. By contrast to its predecessor, the model also suggests that a critical transition, and not self-organized criticality, underlies forest fire dynamics, with implications for other ecological systems exhibiting power-law-like patterns, in particular for their sensitivity to environmental change and control efforts.

Notes and References

This item contains 58 references.

Literature Cited
  • ['Amiro, B., B. Stocks, M. Alexander, M. Flannigan, and B. Wotton. 2001. Fire, climate change, carbon and fuel management in the Canadian boreal forest. International Journal of Wildland Fire 10:405–413.']
  • ['Bak, P., C. Tang, and K. Wiesenfeld. 1988. Self-organized criticality. Physical Review A 38:364–374.']
  • ['Bessie, W. C., and E. A. Johnson. 1995. The relative importance of fuels and weather on fire behavior in subalpine forests. Ecology 76:747–762.']
  • ['Bonachela, J. A., and M. A. Muñoz. 2009. Self-organization without conservation: true or just apparent scale-invariance? Journal of Statistical Mechanics: Theory and Experiment 2009:P09009.']
  • ['Bonachela, J. A., S. de Franciscis, J. J. Torres, and M. A. Muñoz. 2010. Self-organization without conservation: are neuronal avalanches generically critical? Journal of Statistical Mechanics: Theory and Experiment 2010:P02015.']
  • ['Bridge, S. R. J., K. Miyanishi, and E. A. Johnson. 2005. A critical evaluation of fire suppression effects in the boreal forest of Ontario. Forest Science 51:41–50.']
  • ['Canadian Forest Service. 1997. Canadian large fire database.']
  • ['Clauset, A., C. R. Shalizi, and M. E. J. Newman. 2009. Power-law distributions in empirical data. SIAM Review 51:661–703.']
  • ['Cuddington, K., and B. Beisner. 2005. Ecological paradigms lost: routes of theory change. Elsevier Academic, Burlington, MA.']
  • ['Cumming, S. G. 2005. Effective fire suppression in boreal forests. Canadian Journal of Forest Research 35:772–786.']
  • ['Drossel, B., and F. Schwabl. 1992. Self-organized critical forest-fire model. Physical Review Letters 69:1629.']
  • ['Earn, D. J., P. Rohani, B. M. Bolker, and B. T. Grenfell. 2000. A simple model for complex dynamical transitions in epidemics. Science 287:667–670.']
  • ['Flannigan, M., B. Stocks, M. Turetsky, and M. Wotton. 2009. Impacts of climate change on fire activity and fire management in the circumboreal forest. Global Change Biology 15:549–560.']
  • ['Grassberger, P. 1993. On a self-organized critical forest-fire model. Journal of Physics A 26:2081–2089.']
  • ['———. 2002. Critical behaviour of the Drossel-Schwabl forest fire model. New Journal of Physics 4:17.']
  • ['Grimm, V., E. Revilla, U. Berger, F. Jeltsch, W. M. Mooij, S. F. Railsback, H. Thulke, J. Weiner, T. Wiegand, and D. L. DeAngelis. 2005. Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–991.']
  • ['Henley, C. L. 1989. Self-organized percolation: a simpler model. Bulletin of the American Physical Society 34:838.']
  • ['Jansen, V. A. A., N. Stollenwerk, H. J. Jensen, M. E. Ramsay, W. J. Edmunds, and C. J. Rhodes. 2003. Measles outbreaks in a population with declining vaccine uptake. Science 301:804.']
  • ['Johnson, E. A., K. Miyanishi, and S. R. J. Bridge. 2001. Wildfire regime in the boreal forest and the idea of suppression and fuel buildup. Conservation Biology 15:1554–1557.']
  • ['Keane, R. E., G. J. Cary, I. D. Davies, M. D. Flannigan, R. H. Gardner, S. Lavorel, J. M. Lenihan, C. Li, and T. S. Rupp. 2004. A classification of landscape fire succession models: spatial simulations of fire and vegetation dynamics. Ecological Modelling 179:3–27.']
  • ['Kefi, S., M. Rietkerk, C. L. Alados, Y. Pueyo, V. P. Papanastasis, A. El Aich, and P. C. de Ruiter. 2007. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449:213–217.']
  • ['Krawchuk, M. A., M. A. Moritz, M.-A. Parisien, J. V. Dorn, and K. Hayhoe. 2009. Global pyrogeography: the current and future distribution of wildfire. PLoS ONE 4:e5102.']
  • ['Levina, A., J. M. Herrmann, and T. Geisel. 2009. Phase transitions towards criticality in a neural system with adaptive interactions. Physical Review Letters 102:118110.']
  • ['Malamud, B. D., G. Morein, and D. L. Turcotte. 1998. Forest fires: an example of self-organized critical behavior. Science 281:1840–1842.']
  • ['Malamud, B. D., J. D. A. Millington, and G. L. W. Perry. 2005. Characterizing wildfire regimes in the United States. Proceedings of the National Academy of Sciences of the USA 102:4694–4699.']
  • ['Moritz, M. A. 1997. Analyzing extreme disturbance events: fire in Los Padres National Forest. Ecological Applications 7:1252–1262.']
  • ['———. 2003. Spatiotemporal analysis of controls on shrubland fire regimes: age dependency and fire hazard. Ecology 84:351–361.']
  • ['Moritz, M. A., M. E. Morais, L. A. Summerell, J. M. Carlson, and J. Doyle. 2005. Wildfires, complexity, and highly optimized tolerance. Proceedings of the National Academy of Sciences of the USA 102:17912–17917.']
  • ['Newman, M. 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics 46:323–351.']
  • ['O’Neil, R. V., R. H. Gardner, M. G. Turner, and W. H. Romme. 1992. Epidemiology theory and disturbance spread on landscapes. Landscape Ecology 7:19–26.']
  • ['Pascual, M., and F. Guichard. 2005. Criticality and disturbance in spatial ecological systems. Trends in Ecology & Evolution 20:88–95.']
  • ['Pascual, M., M. Roy, F. Guichard, and G. Flierl. 2002. Cluster size distributions: signatures of self-organization in spatial ecologies. Philosophical Transactions of the Royal Society B: Biological Sciences 357:657–666.']
  • ['Peterson, G. D. 2002. Contagious disturbance, ecological memory, and the emergence of landscape pattern. Ecosystems 5:329–338.']
  • ['Pueyo, S. 2007. Self-organised criticality and the response of wildland fires to climate change. Climatic Change 82:131–161.']
  • ['Pueyo, S., P. de Alencastro Gra¸ca, R. Barbosa, R. Cots, E. Cardona, and P. Fearnside. 2010. Testing for criticality in ecosystem dynamics: the case of Amazonian rainforest and savanna fire. Ecology Letters 13:793–802.']
  • ['Ratz, A. 1996. A generic forest fire model: spatial patterns in forest fire ecosystems. PhD thesis. Phillips-Universität, Marburg.']
  • ['Reed, W. J., and K. S. McKelvey. 2002. Power-law behaviour and parametric models for the size-distribution of forest fires. Ecological Modelling 150:239–254.']
  • ['Rhodes, C. J., and R. M. Anderson. 1996. Power laws governing epidemics in isolated populations. Nature 381:600–602.']
  • ['Rhodes, C. J., H. J. Jensen, and R. M. Anderson. 1997. On the critical behaviour of simple epidemics. Proceedings of the Royal Society B: Biological Sciences 264:1639–1646.']
  • ['Rhodes, C. J., A. R. Butler, and R. M. Anderson. 1998. Epidemiology of communicable disease in small populations. Journal of Molecular Medicine 76:111–116.']
  • ['Ricotta, C., G. Avena, and M. Marchetti. 1999. The flaming sandpile: self-organized criticality and wildfires. Ecological Modelling 119:73–77.']
  • ['Ricotta, C., M. Arianoutsou, R. D´ıaz-Delgado, B. Duguy, F. Lloret, E. Maroudi, S. Mazzoleni, et al. 2001. Self-organized criticality of wildfires ecologically revisited. Ecological Modelling 141:307–311.']
  • ['Rohani, P., D. J. Earn, and B. T. Grenfell. 1999. Opposite patterns of synchrony in sympatric disease metapopulations. Science 286:968–971.']
  • ['Rothermel, R. 1972. A mathematical model for predicting fire spread in wildland fuels. Research paper INT-115. U.S. Forest Service, Intermountain Forest and Range Experiment Station, Ogden, UT.']
  • ['Roy, M., M. Pascual, and A. Franc. 2003. Broad scaling region in a spatial ecological system. Complexity 8:19–27.']
  • ['Scanlon, T. M., K. K. Caylor, S. A. Levin, and I. Rodriguez-Iturbe. 2007. Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature 449:209–212.']
  • ['Scheffer, M., S. Carpenter, J. A. Foley, C. Folke, and B. Walker. 2001. Catastrophic shifts in ecosystems. Nature 413:591–596.']
  • ['Song, W., F. Weicheng, W. Binghong, and Z. Jianjun. 2001. Self-organized criticality of forest fire in China. Ecological Modelling 145:61–68.']
  • ['Stephens, S. L., J. J. Moghaddas, C. Edminster, C. E. Fiedler, S. Haase, M. Harrington, J. E. Keeley, et al. 2009. Fire treatment effects on vegetation structure, fuels, and potential fire severity in western U.S. forests. Ecological Applications 19:305–320.']
  • ['Turcotte, D. L. 1999. Applications of statistical mechanics to natural hazards and landforms. Physica A 274:294–299.']
  • ['Turner, M. G. 2005. Landscape ecology: what is the state of the science? Annual Review of Ecology, Evolution, and Systematics 36:319–344.']
  • ['Turner, M. G., and W. H. Romme. 1994. Landscape dynamics in crown fire ecosystems. Landscape Ecology 9:59–77.']
  • ['Vandermeer, J., and I. Perfecto. 2006. A keystone mutualism drives pattern in a power function. Science 311:1000–1002.']
  • ['Wagner, C. V. 1977. Conditions for the start and spread of crown fire. Canadian Journal of Forest Research 7:23–34.']
  • ['Whelan, R. J. 1995. The ecology of fire. Cambridge University Press, Cambridge.']
  • ['Zinck, R. D., and V. Grimm. 2008. More realistic than anticipated: a classical forest fire model from statistical physics captures real fire shapes. Open Ecology Journal 1:8–13.']
  • ['———. 2009. Unifying wildfire models from ecology and statistical physics. American Naturalist 174:E170–E185.']
  • ['Zinck, R. D., K. Johst, and V. Grimm. 2010. Wildfire, landscape diversity and the Drossel-Schwabl model. Ecological Modelling 221:98–105.']
Part of Sustainability