Scaling from trees to forests: Tractable macroscopic equations for forest dynamics

Nikolay Strigul, Denis Pristinski, Drew Purves, Jonathan Dushoff, Stephen Wilson Pacala

Research output: Contribution to journalArticlepeer-review

162 Scopus citations


Individual-based forest simulators, such as TASS and SORTIE, are spatial stochastic processes that predict properties of populations and communities by simulating the fate of every plant throughout its life cycle. Although they are used for forest management and are able to predict dynamics of real forests, they are also analytically intractable, which limits their usefulness to basic scientists. We have developed a new spatial individual-based forest model that includes a perfect plasticity formulation for crown shape. Its structure allows us to derive an accurate approximation for the individual-based model that predicts mean densities and size structures using the same parameter values and functional forms, and also it is analytically tractable. The approximation is represented by a system of von Foerster partial differential equations coupled with an integral equation that we call the perfect plasticity approximation (PPA). We have derived a series of analytical results including equilibrium abundances for trees of different crown shapes, stability conditions, transient behaviors, such as the constant yield law and self-thinning exponents, and two species coexistence conditions.

Original languageEnglish (US)
Pages (from-to)523-545
Number of pages23
JournalEcological Monographs
Issue number4
StatePublished - Nov 2008

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics


  • Crown plasticity
  • Forest dynamics
  • Forest scaling
  • Individual-based forest simulator
  • Light competition
  • Macroscopic equations


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