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SCALING FROM TREES TO FORESTS: TRACTABLE MACROSCOPIC EQUATIONS FOR FOREST DYNAMICS

Authors

  • Nikolay Strigul,

    Corresponding author
    1. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08540 USA
    2. Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07020 USA
    3. Microsoft Research, Cambridge CB3 0FB United Kingdom
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  • Denis Pristinski,

    1. National Institute of Standards and Technology, Gaithersburg, Maryland 20899 USA
    2. Microsoft Research, Cambridge CB3 0FB United Kingdom
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  • Drew Purves,

    1. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08540 USA
    2. Microsoft Research, Cambridge CB3 0FB United Kingdom
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  • Jonathan Dushoff,

    1. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08540 USA
    2. Microsoft Research, Cambridge CB3 0FB United Kingdom
    3. Department of Biology, McMaster University, Hamilton, Ontario L8S 4L8 Canada
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  • Stephen Pacala

    1. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08540 USA
    2. Microsoft Research, Cambridge CB3 0FB United Kingdom
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  • Corresponding Editor: A. M. Ellison.

Abstract

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.

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