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A general quantitative theory of forest structure and dynamics

  1. Geoffrey B. Westa,
  2. Brian J. Enquista,b,1 and
  3. James H. Browna,c,1
  1. aSanta Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501;
  2. bDepartment of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721; and
  3. cDepartment of Biology, University of New Mexico, Albuquerque, NM 87131

  1. Contributed by James H. Brown, December 5, 2008 (received for review October 1, 2008)

Abstract

We present the first part of a quantitative theory for the structure and dynamics of forests at demographic and resource steady state. The theory uses allometric scaling relations, based on metabolism and biomechanics, to quantify how trees use resources, fill space, and grow. These individual-level traits and properties scale up to predict emergent properties of forest stands, including size–frequency distributions, spacing relations, resource flux rates, and canopy configurations. Two insights emerge from this analysis: (i) The size structure and spatial arrangement of trees in the entire forest are emergent manifestations of the way that functionally invariant xylem elements are bundled together to conduct water and nutrients up from the trunks, through the branches, to the leaves of individual trees. (ii) Geometric and dynamic properties of trees in a forest and branches in trees scale identically, so that the entire forest can be described mathematically and behaves structurally and functionally like a scaled version of the branching networks in the largest tree. This quantitative framework uses a small number of parameters to predict numerous structural and dynamical properties of idealized forests.

Footnotes

  • 1To whom correspondence may be addressed. E-mail: benquist{at}email.arizona.edu or jhbrown{at}unm.edu

  • Author contributions: G.B.W., B.J.E., and J.H.B. designed research; G.B.W. and B.J.E. performed research; B.J.E. analyzed data; and G.B.W., B.J.E., and J.H.B. wrote the paper.

  • The authors declare no conflict of interest.

  • This article contains supporting information online at www.pnas.org/cgi/content/full/0812294106/DCSupplemental.

  • ↵* For our notation we use superscript L to represent properties of a leaf and not an exponent.

  • ↵† The surface area of the canopy, acan, is essentially akin to the surface area that results from loosely wrapping the entire tree in a plastic sheet à la Christo and Jeanne-Claude (see www.christojeanneclaude.net/wt.shtml).

  • ↵‡ Statistics are for binned data (histogram) for frequency and branch radius based on the original data plots from the 1964 Shinozaki et al. article (46). While reasonable, given that only the histogram data are available, a more accurate assessment of our model for branch distributions should use the more rigorous statistical approach based on the raw (unbinned) data as discussed in White et al. (54).

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