On the relationship between mass and diameter distributions in tree communities.

It has been suggested that frequency distributions of individual tree masses in natural stands are characterized by power-law distributions with exponents near -3/4, and that therefore tree communities exhibit energetic equivalence among size classes. Because the mass of trees is not measured directly, but estimated from diameter, this supposition is based on the fact that the observed distribution of tree diameters is approximately characterized by a power-law with an exponent approximately -2. Here we show that diameter distributions of this form are not equivalent to mass distributions with exponents of -3/4, but actually to mass distributions with exponents of -11/8. We discuss the implications of this result for the metabolic theory of ecology and for understanding energetic equivalence and the processes structuring tree communities.

[1]  B. Enquist,et al.  On estimating the exponent of power-law frequency distributions. , 2008, Ecology.

[2]  R. May,et al.  Observations on related ecological exponents. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[3]  K J Niklas,et al.  Invariant scaling relationships for interspecific plant biomass production rates and body size , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[4]  D. Raffaelli,et al.  Three allometric relations of population density to body mass: theoretical integration and empirical tests in 149 food webs. , 2008, Ecology letters.

[5]  ANDREW J. KERKHOFF,et al.  The Implications of Scaling Approaches for Understanding Resilience and Reorganization in Ecosystems , 2007 .

[6]  David Kenfack,et al.  Comparing tropical forest tree size distributions with the predictions of metabolic ecology and equilibrium models. , 2006, Ecology letters.

[7]  S. Ross.  A First Course in Probability , 1977 .

[8]  James H. Brown,et al.  Toward a metabolic theory of ecology , 2004 .

[9]  James H. Brown,et al.  Quarter-power allometric scaling in vascular plants: functional basis and ecological consequences , 2000 .

[10]  T. Hara.  A stochastic model and the moment dynamics of the growth and size distribution in plant populations , 1984 .

[11]  D. Coomes,et al.  Challenges to the generality of WBE theory. , 2006, Trends in ecology & evolution.

[12]  On the conceptual basis of the self-thinning rule , 2001 .

[13]  K. Andersen,et al.  Asymptotic Size Determines Species Abundance in the Marine Size Spectrum , 2006, The American Naturalist.

[14]  T. Meehan.  Energy use and animal abundance in litter and soil communities. , 2006, Ecology.

[15]  David A. Coomes,et al.  Disturbances prevent stem size‐density distributions in natural forests from following scaling relationships , 2003 .

[16]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[17]  Evan P. Economo,et al.  Scaling metabolism from organisms to ecosystems , 2003, Nature.

[18]  Charles A Price,et al.  A general model for allometric covariation in botanical form and function , 2007, Proceedings of the National Academy of Sciences.

[19]  Jacob Weiner,et al.  Mechanisms determining the degree of size asymmetry in competition among plants , 1998, Oecologia.

[20]  R. Peters.  The Ecological Implications of Body Size , 1983 .

[21]  P. Marquet,et al.  Scaling and power-laws in ecological systems , 2005, Journal of Experimental Biology.

[22]  D. Sims,et al.  Minimizing errors in identifying Lévy flight behaviour of organisms. , 2007, The Journal of animal ecology.

[23]  David A. Coomes,et al.  Mortality and tree‐size distributions in natural mixed‐age forests , 2007 .

[24]  S. Ernest,et al.  Relationships between body size and abundance in ecology. , 2007, Trends in ecology & evolution.

[25]  James H. Brown,et al.  The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization , 2005, Journal of Experimental Biology.

[26]  Geoffrey B. West,et al.  Life's Universal Scaling Laws , 2004 .

[27]  J. Chave.  Study of structural, successional and spatial patterns in tropical rain forests using TROLL, a spatially explicit forest model , 1999 .

[28]  Stephanie A. Bohlman,et al.  Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests. , 2006, Ecology letters.

[29]  Karl J. Niklas,et al.  A general model for mass-growth-density relations across tree-dominated communities , 2003 .

[30]  Iain H. Woodhouse,et al.  Predicting backscatter-biomass and height-biomass trends using a macroecology model , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[31]  J. Damuth,et al.  Population density and body size in mammals , 1981, Nature.

[32]  N. Odling,et al.  Scaling of fracture systems in geological media , 2001 .

[33]  Stephen J. Wright,et al.  Light-Gap disturbances, recruitment limitation, and tree diversity in a neotropical forest , 1999, Science.

[34]  Mikael Akke,et al.  Global Allocation Rules for Patterns of Biomass Partitioning , 2002, Science.

[35]  Richard Condit,et al.  Tropical Forest Census Plots , 1998, Environmental Intelligence Unit.

[36]  James H. Brown,et al.  Allometric scaling of plant energetics and population density , 1998, Nature.

[37]  James H. Brown,et al.  The contribution of small individuals to density-body size relationships: examination of energetic equivalence in reef fishes , 2004, Oecologia.

[38]  J. Damuth.  Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy‐use , 1987 .

[39]  M. Lawes,et al.  Tree spacing and area of competitive influence do not scale with tree size in an African rain forest , 2008 .

[40]  J. Chambers,et al.  Tree allometry and improved estimation of carbon stocks and balance in tropical forests , 2005, Oecologia.

[41]  Robert M. May,et al.  The Search for Patterns in the Balance of Nature: Advances and Retreats , 1986 .

[42]  James H. Brown,et al.  A general model for the structure and allometry of plant vascular systems , 1999, Nature.

[43]  Karl J. Niklas,et al.  Botanical Scaling. (Book Reviews: Plant Allometry. The Scaling of Form and Process.) , 1994 .

[44]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[45]  Ethan P. White,et al.  Thermodynamic and metabolic effects on the scaling of production and population energy use , 2003 .

[46]  O. Phillips,et al.  Global Patterns of Plant Diversity: Alwyn H. Gentry's Forest Transect Data Set , 2002 .

[47]  P. Lachenbruch.  Mathematical Statistics, 2nd Edition , 1972 .

[48]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[49]  J. Downing,et al.  Population density and community size structure: Comparison of aquatic and terrestrial systems , 1997 .

[50]  Karl J. Niklas,et al.  Invariant scaling relations across tree-dominated communities , 2001, Nature.

[51]  S. Jennings,et al.  Measurement of body size and abundance in tests of macroecological and food web theory. , 2007, The Journal of animal ecology.

[52]  T. Kohyama,et al.  Size-structured tree populations in gap-dynamic forest-the forest architecture hypothesis for the stable coexistence of species , 1993 .

[53]  B. Enquist.  Universal scaling in tree and vascular plant allometry: toward a general quantitative theory linking plant form and function from cells to ecosystems. , 2002, Tree physiology.

[54]  A. Kerkhoff,et al.  Ecosystem allometry: the scaling of nutrient stocks and primary productivity across plant communities. , 2006, Ecology letters.