NATURE|VOL 410|5 APRIL 2001|www.nature.com 655articlesInvariant scaling relations acrosstree-dominated communitiesBrian J. Enquist* & Karl J. Niklas²* Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona 85721, USA; National Center for Ecological Analysis and Synthesis,University of California, Santa Barbara, California, USA²Department of Plant Biology, Cornell University, Ithaca, New York 14853, USA............................................................................................................................................................................................................................................................................Organizing principles are needed to link organismal, community and ecosystem attributes across spatial and temporal scales.Here we extend allometric theoryÐhow attributes of organisms change with variation in their sizeÐand test its predictionsagainst worldwide data sets for forest communities by quantifying the relationships among tree size±frequency distributions,standing biomass, species number and number of individuals per unit area. As predicted, except for the highest latitudes, thenumber of individuals scales as the -2 power of basal stem diameter or as the -3/4 power of above-ground biomass. Also aspredicted, this scaling relationship varies little with species diversity, total standing biomass, latitude and geographic samplingarea. A simulation model in which individuals allocate biomass to leaf, stem and reproduction, and compete for space and lightobtains features identical to those of a community. In tandem with allometric theory, our results indicate that manymacroecological features of communities may emerge from a few allometric principles operating at the level of the individual.Despite insights from ecological theory and experimental manip-ulation, mechanistic connections among important characteristicsof ecological communities across diverse ecosystems have remainedelusive1±7. Variation in species diversity has been explained interms of a subdivision of community niche space with apresumed concomitant change in total standing biomass andproductivity2,3,8,9. Yet, the ecological properties of communities orecosystems accounting for this remain contentious2,5,10±13.One promising mechanistic approach interrelating many orga-nismal, community and ecosystem properties is to focus on size-dependent (allometric) relationships that demonstrably cut acrossphyletically disparate species6±7,14±25. One of the most prevalentallometric patterns observed for both plant and animal commu-nities is the inverse relationship between body mass andabundance23,26,27. Because this relationship re¯ects how biomassand productivity are partitioned among individuals, it offers con-siderable insight into the mechanisms structuring ecological com-munities across varying environments. However, relatively little isknown about how community size±frequency distributions varyacross different environments or how they vary among commu-nities differing in species composition. Here we provide a broadtheoretical framework for the size±frequency distributions of plantcommunities. We also show how the allometric constraints onresource use and plant form in¯uence many of the macroscopicproperties of tree-dominated communities.Extending allometric theory to plant communitiesAllometric theory16predicts that the total number of individuals, N,in any size class m, equals CmM-3/4, where Cmis the number ofindividuals per unit area normalized to a given size class m, and M isthe total body mass in class m. This relationship is predicted to holdtrue when all available space is occupied such that the total rate ofresource use of all individuals within a community QTo t(which isproportional to rates of gross primary production17) approximatesthe rate of resource supply from the environment R (that is,QTo t< R)16. Biomechanical and allometric theory14,15also predictsthat M is proportional to the 8/3 power of stem diameter D ofany size class (that is, M ~ D8/3), such that N will scale as N~ M-3/4~ D-2.If these scaling laws hold for entire communities, organismaltraits can be used to link to larger-scale properties of communitiesacross different ecosystems. For example, extensions of allometricand biomechanical theory predict that total standing communitybiomass will be invariant with respect to species composition andthus latitude. Furthermore, the intrinsic capacity to produce bio-mass on an annual basis will vary little across communities. Notethat total standing community biomass, MTo t, is given by theformulaMTot Cm#baM2 3=4dM  4CmM1=4a M1=4b1where the subscripts a and b denote maximum and minimum bodymass within a given community, respectively. As both the minimumand maximum body sizes are largely insensitive to species composi-tion or latitude14(see also results below), any variation in MTo twillbe determined by variation in Cm. For closed canopy forest,however, both theory and observation suggest that Cmvaries little,such that MTo tis expected to vary little across communities.Speci®cally, for any given size class, Rm< Qm< CmBm, where themetabolic rate Bm= CBAm. Here, Amis leaf or root area, and CBis therate of resource use per unit area, which can vary across species.Because allometric theory and empirical data14,16±18show thatAm= CA(M/r)3/4, where r is the bulk tissue density and CAis aconstant of proportionality re¯ecting the species-speci®c amount ofleaves or roots per individual per unit area, we derive the formulaCm<RmCACBMm=r3=42which quantitatively shows how numerous factors can in¯uenceplant population density per size class. Nonetheless, biometric andphysiological data indicate no signi®cant differences in the meanvalues of CB, CAand r across tropical and temperate tree species orwith variation in species richness16,17,20±22(see also Methods). Thisinvariance indicates that total community biomass is likely to beinsensitive to species diversity, even though Cmcan vary becauseof the many environmental factors (such as temperature andprecipitation) known to in¯uence Rm.Variation in species diversity might also independently in¯uenceRm, the quantity of resources used per size class per unit time. Inparticular, variation in Rmmight result either from an increase intotal niche volume occupied or as a consequence of synergisticeffects from increased diversity