Extensions and evaluations of a general quantitativetheory of forest structure and dynamicsBrian J. Enquista,b,1, Geoffrey B. Westa, and James H. Browna,c,1aSanta Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501;bDepartment of Ecology and Evolutionary Biology, University of Arizona,Tucson, AZ 85721; andcDepartment of Biology, University of New Mexico, Albuquerque, NM 87131Contributed by James H. Brown, December 5, 2008 (sent for review October 1, 2008)Here, we present the second part of a quantitative theory for thestructure and dynamics of forests under demographic and resourcesteady state. The theory is based on individual-level allometricscaling relations for how trees use resources, fill space, and grow.These scale up to determine emergent properties of diverse for-ests, including size–frequency distributions, spacing relations, can-opy configurations, mortality rates, population dynamics, succes-sional dynamics, and resource flux rates. The theory uniquelymakes quantitative predictions for both stand-level scaling expo-nents and normalizations. We evaluate these predictions by com-piling and analyzing macroecological datasets from several tropicalforests. The close match between theoretical predictions and datasuggests that forests are organized by a set of very general scalingrules. Our mechanistic theory is based on allometric scaling rela-tions, is complementary to ‘‘demographic theory,’’ but is funda-mentally different in approach. It provides a quantitative baselinefor understanding deviations from predictions due to other factors,including disturbance, variation in branching architecture, asym-metric competition, resource limitation, and other sources of mor-tality, which are not included in the deliberately simplified theory.The theory should apply to a wide range of forests despite largedifferences in abiotic environment, species diversity, and taxo-nomic and functional composition.allometry 兩 mortality rate 兩 plant ecology 兩 size distribution 兩competitive thinningUnderstanding the key forces that shape the structure,function, and dynamics of ecosystems is a fundamentalgoal of ecology (1–6). Current approaches to plant commu-nities focus on questions such as what allows for speciescoexistence (7), why tropical sites have more species thantemperate ones (8), and what environmental factors determinethe structure, dynamics, and species composition of commu-nities (9). Detailed models have been developed to integratehow species-specific traits ‘‘scale-up’’ to influence communityand ecosystem dynamics (10, 11).Here, we present a complementary but alternative approach.We use a few key principles to show how variation in resourcesupply together with general cross-taxa patterns of plant archi-tecture and growth give rise to predictable emergent patterns ofresource use, spatial structure, and demography. In our previousarticle (12) we incorporated these principles to derive the firstpart of a general quantitative theory for the structure anddynamics of a single-species stand. In this article we evaluatethese predictions, using data from several tropical forests com-posed of multiple tree species including: (i) a 20-year recordfrom Costa Rica (13); (ii) a 10-year time series from Panama;(iii) a 40-year survey from a Malaysian forest dataset; (iv) and asuccessional sequence of Costa Rican forests ranging fromrecently abandoned pasture to mature uncut forests (14) (formethodology and additional detail, see supporting information(SI) Text). We also elaborate and extend the theory to show howthe critical assumption of resource and demographic steady stateleads to empirically supported predictions for growth, mortality,succession, and whole-stand resource flux.Our theory, which is an extension of a more general body oftheory termed ‘‘metabolic scaling theory’’ (13, 15–19), shows mech-anistically how plant growth and allometry influence size distribu-tions and stand dynamics (15, 20–23). It deliberately makes severalsimplifying assumptions. In particular, the forest (i) can be modeledas a stand with no recruitment limitation, where recruitment beginswith seedlings; (ii) is in resource (15) and demographic steady state(24), so that, on average, the total rate of resource use equals therate of resource supply, birth rates equal death rates, and there isa stable distribution of ages and sizes; (iii) is composed of ‘‘allo-metrically ideal’’ trees which obey previously derived quarter-powerallometric scaling laws (16) that govern how they use resources,occupy space, and grow.Empirical Results and Theoretical ExtensionsSize-Frequency Distributions.Prediction: Number of stems scales as aninverse square law.The theory predicts ⌬nk⬀ rk⫺2, where ⌬nkis thenumber of trees in the sample plot of standardized area in a givensize class or bin, k, and with a stem radius, rk, between rkand rk⫹⌬rk. With linear binning this gives the continuous frequencydistribution, f(r) ⬅ dn/dr ⬀ r⫺2(see equation 9 and supportinginformation in ref. 12). As shown in Fig. 1 and Fig. S1, thisinverse square law prediction is supported by data from CostaRica, Malaysia, and Panama. Note that the exponent remainsvery close to ⫺2 across several decades of time (see Table S1).Therefore, these forests remained close to demographic andresource steady state despite extensive turnover of individualsand substantial changes in species composition (see SI Text).Analysis of a large global dataset, for both temperate andtropical forests, also generally supports the ⫺2 prediction (17,25). Because stem radii exhibit the predicted scaling with mass,rk⬀ mk3/8(26, 27), these observations also confirm the predictedscaling of number of stems with mass: f(r) ⬀ m⫺3/4(see support-ing information in ref. 12). One caveat, discussed below, is thatthere are deviations from the exact predicted power function(17), especially for the largest trees.Energy Equivalence.Prediction: The total energy and resource flux of allstems within a size class is independent of plant size when binned linearly withrespect to stem radius.As shown previously, both theoretically (16)and empirically (15, 28), the xylem flux of a tree, Q˙k, scales as Q˙k⬀ rk2⬀ mk3/4. When combined with the inverse square law for thenumber of trees in a bin, ⌬nk⬀ rk⫺2⬀ mk⫺3/4, this predicts that thetotal resource flux per unit area per size class,Q˙ktot⫽ ⌬nkQ˙k⬀ rk0⬀ mk0[1]Author