Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Rate of tree carbon accumulation increases continuously with tree size


Forests are major components of the global carbon cycle, providing substantial feedback to atmospheric greenhouse gas concentrations1. Our ability to understand and predict changes in the forest carbon cycle—particularly net primary productivity and carbon storage—increasingly relies on models that represent biological processes across several scales of biological organization, from tree leaves to forest stands2,3. Yet, despite advances in our understanding of productivity at the scales of leaves and stands, no consensus exists about the nature of productivity at the scale of the individual tree4,5,6,7, in part because we lack a broad empirical assessment of whether rates of absolute tree mass growth (and thus carbon accumulation) decrease, remain constant, or increase as trees increase in size and age. Here we present a global analysis of 403 tropical and temperate tree species, showing that for most species mass growth rate increases continuously with tree size. Thus, large, old trees do not act simply as senescent carbon reservoirs but actively fix large amounts of carbon compared to smaller trees; at the extreme, a single big tree can add the same amount of carbon to the forest within a year as is contained in an entire mid-sized tree. The apparent paradoxes of individual tree growth increasing with tree size despite declining leaf-level8,9,10 and stand-level10 productivity can be explained, respectively, by increases in a tree’s total leaf area that outpace declines in productivity per unit of leaf area and, among other factors, age-related reductions in population density. Our results resolve conflicting assumptions about the nature of tree growth, inform efforts to undertand and model forest carbon dynamics, and have additional implications for theories of resource allocation11 and plant senescence12.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Example model fits for tree mass growth rates.
Figure 2: Aboveground mass growth rates for the 403 tree species, by continent.
Figure 3: Aboveground mass growth rates of species in our data set compared with E. regnans and S. sempervirens.


  1. 1

    Pan, Y. et al. A large and persistent carbon sink in the world’s forests. Science 333, 988–993 (2011)

    CAS  ADS  Article  Google Scholar 

  2. 2

    Medvigy, D., Wofsy, S. C., Munger, J. W., Hollinger, D. Y. & Moorcroft, P. R. Mechanistic scaling of ecosystem function and dynamics in space and time: Ecosystem Demography model version 2. J. Geophys. Res. 114, G01002 (2009)

    ADS  Google Scholar 

  3. 3

    Caspersen, J. P., Vanderwel, M. C., Cole, W. G. & Purves, D. W. How stand productivity results from size- and competition-dependent growth and mortality. PLoS ONE 6, e28660 (2011)

    CAS  ADS  PubMed  PubMed Central  Google Scholar 

  4. 4

    Kutsch, W. L. et al. in Old-Growth Forests: Function, Fate and Value (eds Wirth, C., Gleixner, G. & Heimann, M. ) 57–79 (Springer, 2009)

  5. 5

    Meinzer F. C., Lachenbruch B., Dawson T. E., eds. Size- and Age-Related Changes in Tree Structure and Function (Springer, 2011)

  6. 6

    Enquist, B. J., West, G. B., Charnov, E. L. & Brown, J. H. Allometric scaling of production and life-history variation in vascular plants. Nature 401, 907–911 (1999)

    CAS  ADS  Google Scholar 

  7. 7

    Sillett, S. C. et al. Increasing wood production through old age in tall trees. For. Ecol. Manage. 259, 976–994 (2010)

    Google Scholar 

  8. 8

    Mencuccini, M. et al. Size-mediated ageing reduces vigour in trees. Ecol. Lett. 8, 1183–1190 (2005)

    CAS  PubMed  Google Scholar 

  9. 9

    Drake, J. E., Raetz, L. M., Davis, S. C. & DeLucia, E. H. Hydraulic limitation not declining nitrogen availability causes the age-related photosynthetic decline in loblolly pine (Pinus taeda L.). Plant Cell Environ. 33, 1756–1766 (2010)

    CAS  PubMed  Google Scholar 

  10. 10

    Ryan, M. G., Binkley, D. & Fownes, J. H. Age-related decline in forest productivity: pattern and process. Adv. Ecol. Res. 27, 213–262 (1997)

    Google Scholar 

  11. 11

    Thomas, S. C. in Size- and Age-Related Changes in Tree Structure and Function (eds Meinzer, F. C., Lachenbruch, B. & Dawson, T. E. ) 33–64 (Springer, 2011)

    Google Scholar 

  12. 12

    Thomas, H. Senescence, ageing and death of the whole plant. New Phytol. 197, 696–711 (2013)

    PubMed  Google Scholar 

  13. 13

    Carey, E. V., Sala, A., Keane, R. & Callaway, R. M. Are old forests underestimated as global carbon sinks? Glob. Change Biol. 7, 339–344 (2001)

    ADS  Google Scholar 

  14. 14

    Phillips, N. G., Buckley, T. N. & Tissue, D. T. Capacity of old trees to respond to environmental change. J. Integr. Plant Biol. 50, 1355–1364 (2008)

    CAS  PubMed  Google Scholar 

  15. 15

    Piper, F. I. & Fajardo, A. No evidence of carbon limitation with tree age and height in Nothofagus pumilio under Mediterranean and temperate climate conditions. Ann. Bot. 108, 907–917 (2011)

    PubMed  PubMed Central  Google Scholar 

  16. 16

    Weiner, J. & Thomas, S. C. The nature of tree growth and the “age-related decline in forest productivity”. Oikos 94, 374–376 (2001)

    Google Scholar 

  17. 17

    Jenkins, J. C., Chojnacky, D. C., Heath, L. S. & Birdsey, R. A. Comprehensive Database of Diameter-based Biomass Regressions for North American Tree Species General Technical Report NE-319, (USDA Forest Service, Northeastern Research Station, 2004)

    Google Scholar 

  18. 18

    Niklas, K. J. & Enquist, B. J. Canonical rules for plant organ biomass partitioning and annual allocation. Am. J. Bot. 89, 812–819 (2002)

    PubMed  Google Scholar 

  19. 19

    Thomas, S. C. Photosynthetic capacity peaks at intermediate size in temperate deciduous trees. Tree Physiol. 30, 555–573 (2010)

    PubMed  Google Scholar 

  20. 20

    Steppe, K., Niinemets, Ü. & Teskey, R. O. in Size- and Age-Related Changes in Tree Structure and Function (eds Meinzer, F. C., Lachenbruch, B. & Dawson, T. E. ) 235–253 (Springer, 2011)

    Google Scholar 

  21. 21

    Gilmore, D. W. & Seymour, R. S. Alternative measures of stem growth efficiency applied to Abies balsamea from four canopy positions in central Maine, USA. For. Ecol. Manage. 84, 209–218 (1996)

    Google Scholar 

  22. 22

    Kaufmann, M. R. & Ryan, M. G. Physiographic, stand, and environmental effects on individual tree growth and growth efficiency in subalpine forests. Tree Physiol. 2, 47–59 (1986)

    PubMed  Google Scholar 

  23. 23

    Coomes, D. A., Holdaway, R. J., Kobe, R. K., Lines, E. R. & Allen, R. B. A general integrative framework for modelling woody biomass production and carbon sequestration rates in forests. J. Ecol. 100, 42–64 (2012)

    CAS  Google Scholar 

  24. 24

    Binkley, D. A hypothesis about the interaction of tree dominance and stand production through stand development. For. Ecol. Manage. 190, 265–271 (2004)

    Google Scholar 

  25. 25

    Pretzsch, H. & Biber, P. A re-evaluation of Reineke’s rule and stand density index. For. Sci. 51, 304–320 (2005)

    Google Scholar 

  26. 26

    Kashian, D. M., Turner, M. G., Romme, W. H. & Lorimer, C. G. Variability and convergence in stand structural development on a fire-dominated subalpine landscape. Ecology 86, 643–654 (2005)

    Google Scholar 

  27. 27

    Munné-Bosch, S. Do perennials really senesce? Trends Plant Sci. 13, 216–220 (2008)

    PubMed  Google Scholar 

  28. 28

    Jump, A. S., Hunt, J. M. & Peñuelas, J. Rapid climate change-related growth decline at the southern range edge of Fagus sylvatica. Glob. Change Biol. 12, 2163–2174 (2006)

    ADS  Google Scholar 

  29. 29

    Lindenmayer, D. B., Laurance, W. F. & Franklin, J. F. Global decline in large old trees. Science 338, 1305–1306 (2012)

    CAS  ADS  PubMed  Google Scholar 

  30. 30

    Enquist, B. J., West, G. B. & Brown, J. H. Extensions and evaluations of a general quantitative theory of forest structure and dynamics. Proc. Natl Acad. Sci. USA 106, 7046–7051 (2009)

    CAS  ADS  PubMed  Google Scholar 

  31. 31

    Condit, R. et al. Tropical forest dynamics across a rainfall gradient and the impact of an El Niño dry season. J. Trop. Ecol. 20, 51–72 (2004)

    Google Scholar 

  32. 32

    Condit, R. et al. The importance of demographic niches to tree diversity. Science 313, 98–101 (2006)

    CAS  ADS  PubMed  Google Scholar 

  33. 33

    Rüger, N., Berger, U., Hubbell, S. P., Vieilledent, G. & Condit, R. Growth strategies of tropical tree species: disentangling light and size effects. PLoS ONE 6, e25330 (2011)

    ADS  PubMed  PubMed Central  Google Scholar 

  34. 34

    Chave, J. et al. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia 145, 87–99 (2005)

    CAS  ADS  PubMed  Google Scholar 

  35. 35

    Sibly R. M., Brown J. H., Kodric-Brown A., eds. Metabolic Ecology: A Scaling Approach (John Wiley & Sons, 2012)

  36. 36

    Zanne, A. E. et al. Data from: Towards a worldwide wood economics spectrum. In Dryad Digital Data Repository, (2009)

  37. 37

    Enquist, B. J. & Niklas, K. J. Global allocation rules for patterns of biomass partitioning in seed plants. Science 295, 1517–1520 (2002)

    CAS  ADS  PubMed  Google Scholar 

  38. 38

    Niklas, K. J. Plant allometry: is there a grand unifying theory? Biol. Rev. 79, 871–889 (2004)

    PubMed  Google Scholar 

  39. 39

    Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)

    CAS  ADS  Google Scholar 

  40. 40

    Rüger, N., Huth, A., Hubbell, S. P. & Condit, R. Determinants of mortality across a tropical lowland rainforest community. Oikos 120, 1047–1056 (2011)

    Google Scholar 

  41. 41

    R Development Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2009)

  42. 42

    Hilborn, R. & Mangel, M. The Ecological Detective: Confronting Models with Data (Princeton Univ. Press, 1997)

    Google Scholar 

  43. 43

    Chambers, J. Q., Dos Santos, J., Ribeiro, R. J. & Higuchi, N. Tree damage, allometric relationships, and above-ground net primary production in central Amazon forest. For. Ecol. Manage. 152, 73–84 (2001)

    Google Scholar 

  44. 44

    Baskerville, G. L. Use of logarithmic regression in the estimation of plant biomass. Can. J. For. Res. 2, 49–53 (1972)

    Google Scholar 

  45. 45

    Canham, C. D. et al. Neighborhood analyses of canopy tree competition along environmental gradients in New England forests. Ecol. Appl. 16, 540–554 (2006)

    PubMed  Google Scholar 

  46. 46

    Coates, K. D., Canham, C. D. & LePage, P. T. Above- versus below-ground competitive effects and responses of a guild of temperate tree species. J. Ecol. 97, 118–130 (2009)

    Google Scholar 

  47. 47

    Pretzsch, H. & Biber, P. Size-symmetric versus size-asymmetric competition and growth partitioning among trees in forest stands along an ecological gradient in central Europe. Can. J. For. Res. 40, 370–384 (2010)

    Google Scholar 

  48. 48

    Gómez-Aparicio, L., García-Valdés, R., Ruíz-Benito, P. & Zavala, M. A. Disentangling the relative importance of climate, size and competition on tree growth in Iberian forests: implications for forest management under global change. Glob. Change Biol. 17, 2400–2414 (2011)

    ADS  Google Scholar 

  49. 49

    Das, A. The effect of size and competition on tree growth rate in old-growth coniferous forests. Can. J. For. Res. 42, 1983–1995 (2012)

    Google Scholar 

  50. 50

    Zianis, D., Muukkonen, P., Makipaa, R. & Mencuccini, M. Biomass and stem volume equations for tree species in Europe. Silva Fennica Monogr. 4, 1–63 (2005)

    Google Scholar 

Download references


We thank the hundreds of people who have established and maintained the forest plots and their associated databases; M. G. Ryan for comments on the manuscript; C. D. Canham and T. Hart for supplying data; C. D. Canham for discussions and feedback; J. S. Baron for hosting our workshops; and Spain’s Ministerio de Agricultura, Alimentación y Medio Ambiente (MAGRAMA) for granting access to the Spanish Forest Inventory Data. Our analyses were supported by the United States Geological Survey (USGS) John Wesley Powell Center for Analysis and Synthesis, the USGS Ecosystems and Climate and Land Use Change mission areas, the Smithsonian Institution Global Earth Observatory—Center for Tropical Forest Science (CTFS), and a University of Nebraska-Lincoln Program of Excellence in Population Biology Postdoctoral Fellowship (to N.G.B.). In addition, X.W. was supported by National Natural Science Foundation of China (31370444) and State Key Laboratory of Forest and Soil Ecology (LFSE2013-11). Data collection was funded by a broad range of organizations including the USGS, the CTFS, the US National Science Foundation, the Andrews LTER (NSF-LTER DEB-0823380), the US National Park Service, the US Forest Service (USFS), the USFS Forest Inventory and Analysis Program, the John D. and Catherine T. MacArthur Foundation, the Andrew W. Mellon Foundation, MAGRAMA, the Council of Agriculture of Taiwan, the National Science Council of Taiwan, the National Natural Science Foundation of China, the Knowledge Innovation Program of the Chinese Academy of Sciences, Landcare Research and the National Vegetation Survey Database (NVS) of New Zealand, the French Fund for the Global Environment and Fundación ProYungas. This paper is a contribution from the Western Mountain Initiative, a USGS global change research project. Any use of trade names is for descriptive purposes only and does not imply endorsement by the USA government.

Author information




N.L.S. and A.J.D. conceived the study with feedback from R.C. and D.A.C., N.L.S., A.J.D., R.C. and S.E.R. wrote the manuscript. R.C. devised the main analytical approach and wrote the computer code. N.L.S., A.J.D., R.C., S.E.R., P.J.B., N.G.B., D.A.C., E.R.L., W.K.M. and N.R. performed analyses. N.L.S., A.J.D., R.C., S.E.R., P.J.B., D.A.C., E.R.L., W.K.M., E.Á., C.B., S.B., G.C., S.J.D., Á.D., C.N.E., O.F., J.F.F., H.R.G., Z.H., M.E.H., S.P.H., D.K., Y.L., J.-R.M., A.M., L.R.M., R.J.P., N.P., S.-H.S., I-F.S., S.T., D.T., P.J.v.M., X.W., S.K.W. and M.A.Z. supplied data and sources of allometric equations appropriate to their data.

Corresponding author

Correspondence to N. L. Stephenson.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Fitted model parameters for each species have been deposited in USGS’s ScienceBase at

Extended data figures and tables

Extended Data Figure 1 Summary of model fits for tree mass growth rates.

Bars show the percentage of species with mass growth rates that increase with tree mass for each bin; black shading indicates percentage significant at P ≤ 0.05. Tree masses increase with bin number. a, Species fitted with one bin (165 species); b, Species fitted with two bins (139 species); c, Species fitted with three bins (56 species); and d, Species fitted with four bins (43 species).

Extended Data Figure 2 Log–log model fits of mass growth rates for 381 tree species, by continent.

Trees with growth rates ≤ 0 were dropped from the analysis, reducing the number of species meeting our threshold sample size for analysis. a, Africa (33 species); b, Asia (123 species); c, Australasia (22 species); d, Central and South America (73 species); e, Europe (41 species); and f, North America (89 species). Trunk diameters are approximate values for reference, based on the average diameters of trees of a given mass.

Extended Data Figure 3 Aboveground mass growth rates for 41 tree species in the absence of competition.

The ‘+’ or ‘−’ symbol preceding each species code indicates, respectively, species with mass growth rates that increased continuously with tree size or species with mass growth rates that declined in the largest trees. Sources of the diameter growth equations used to calculate mass growth were: a, ref. 45; b, ref. 46; c, ref. 48; d, ref. 47; and e, ref. 49. ABAM, Abies amabilis; ABBA, Abies balsamea; ABCO, Abies concolor; ABLA, Abies lasiocarpa; ABMA, Abies magnifica; ACRU, Acer rubrum; ACSA, Acer saccharum; BEAL, Betula alleghaniensis; BELE, Betula lenta; BEPA, Betula papyrifera; CADE, Calocedrus decurrens; CASA, Castanea sativa; FAGR, Fagus grandifolia; FASY, Fagus sylvatica; FRAM, Fraxinus americana; JUTH, Juniperus thurifera; PIAB, Picea abies; PICO, Pinus contorta; PIHA, Pinus halepensis; PIHY, Picea hybrid (a complex of Picea glauca, P. sitchensis and P. engelmannii); PILA, Pinus lambertiana; PINI, Pinus nigra; PIPINA, Pinus pinaster; PIPINE, Pinus pinea; PIRU, Picea rubens; PIST, Pinus strobus; PISY, Pinus sylvestris; PIUN, Pinus uncinata; POBA, Populus balsamifera ssp. trichocarpa; POTR, Populus tremuloides; PRSE, Prunus serotina; QUFA, Quercus faginea; QUIL, Quercus ilex; QUPE, Quercus petraea; QUPY, Quercus pyrenaica; QURO, Quercus robar; QURU, Quercus rubra; QUSU, Quercus suber; THPL, Thuja plicata; TSCA, Tsuga canadensis; and TSHE, Tsuga heterophylla.

Extended Data Figure 4 Residuals of predicted minus observed tree mass.

a, The allometric equation for moist tropical forests34—used for the majority of tree species—shows no evident systematic bias in predicted aboveground dry mass, M, relative to trunk diameter (n = 1,504 trees). b, In contrast, our simplest form of allometric equation—used for 22% of our species and here applied to nine temperate species—shows an apparent bias towards overestimating M for large trees (n = 1,358 trees). c, New allometries that we created for the nine temperate species removed the apparent bias in predicted M.

Extended Data Figure 5 Estimated mass growth rates of the nine temperate species of Extended Data Fig. 4.

Growth was estimated using the simplest form of allometric model [log(M) = a + blog(D)] (a) and our allometric models fitted with piecewise linear regression (b). Regardless of the allometric model form, all nine species show increasing G in the largest trees.

Related audio

Supplementary information

Supplementary Information

This file contains Supplementary Table 1 and additional references. (PDF 376 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Stephenson, N., Das, A., Condit, R. et al. Rate of tree carbon accumulation increases continuously with tree size. Nature 507, 90–93 (2014).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing