Forest gap dynamics and the Ising model

Robert Schlicht, Yoh Iwasa

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


The vegetation height in forest ecosystems is spatially heterogeneous. Canopy gaps (sites with low vegetation) are formed by treefalls, and they recover to canopy sites (with high vegetation) either by growth of small trees or by branch extension of surrounding trees. The dynamics of canopy gaps have been studied using a spatial Markov chain with nearest neighbor interaction. (1) If the canopy recovery rate is constant and if the gap formation rate for a site increases exponentially with the number of neighboring gap sites, the equilibrium distribution is the same as the one generated by the Ising model in statistical mechanics. Here, we extend the equivalence to the situation in which both the gap formation and canopy recovery depend on the neighborhood, as shown in recent forest data. (2) We develop a statistical test of whether a given spatial pattern is a random sample from the Ising model. The test is based on the conditional probability of configurations on a partial lattice. We apply the method to vegetation height data from the Ogawa forest reserve, Japan, measured on a 5×5m grid in 1976, 1981, 1986, and 1991. The spatial pattern of the original forest data deviates significantly from the Ising model. We examine whether a larger sampling distance or the removal of the effects of the topography can reduce this deviation.

Original languageEnglish
Pages (from-to)65-75
Number of pages11
JournalJournal of Theoretical Biology
Issue number1
Publication statusPublished - Sept 7 2004

All Science Journal Classification (ASJC) codes

  • General Immunology and Microbiology
  • Applied Mathematics
  • General Biochemistry,Genetics and Molecular Biology
  • General Agricultural and Biological Sciences
  • Statistics and Probability
  • Modelling and Simulation


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