Bulletin of Mathematical Biology

, Volume 75, Issue 12, pp 2324–2345 | Cite as

A Population Model of Chaparral Vegetation Response to Frequent Wildfires

  • Timothy A. Lucas
  • Garrett Johns
  • Wancen Jiang
  • Lucie Yang
Original Article


The recent increase in wildfire frequency in the Santa Monica Mountains (SMM) may substantially impact plant community structure. Species of Chaparral shrubs represent the dominant vegetation type in the SMM. These species can be divided into three life history types according to their response to wildfires. Nonsprouting species are completely killed by fire and reproduce by seeds that germinate in response to a fire cue, obligate sprouting species survive by resprouting from dormant buds in a root crown because their seeds are destroyed by fire, and facultative sprouting species recover after fire both by seeds and resprouts. Based on these assumptions, we developed a set of nonlinear difference equations to model each life history type. These models can be used to predict species survivorship under varying fire return intervals. For example, frequent fires can lead to localized extinction of nonsprouting species such as Ceanothus megacarpus while several facultative sprouting species such as Ceanothus spinosus and Malosma (Rhus) laurina will persist as documented by a longitudinal study in a biological preserve in the SMM. We estimated appropriate parameter values for several chaparral species using 25 years of data and explored parameter relationships that lead to equilibrium populations. We conclude by looking at the survival strategies of these three species of chaparral shrubs under varying fire return intervals and predict changes in plant community structure under fire intervals of short return. In particular, our model predicts that an average fire return interval of greater than 12 years is required for 50 % of the initial Ceanothus megacarpus population and 25 % of the initial Ceanothus spinosus population to survive. In contrast, we predict that the Malosma laurina population will have 90 % survivorship for an average fire return interval of at least 6 years.


Chaparral Wildfire Population ecology 



We would like to acknowledge Stephen Davis who provided us with over 25 years of data from his studies of chaparral at Pepperdine University. We would also like to thank Andrea Bertozzi for her support of undergraduate research through the UCLA Applied Mathematics Research Experience for Undergraduates. This work was supported by the National Science Foundation through DMS-0601395 and DMS-1045536.


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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Timothy A. Lucas
    • 1
  • Garrett Johns
    • 1
  • Wancen Jiang
    • 1
  • Lucie Yang
    • 1
  1. 1.Mathematics DepartmentPepperdine UniversityMalibuUSA

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