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Dynamic allometric scaling of tree biomass and size

Nature Plants volume 7, pages 42–49 (2021)Cite this article

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Abstract

Allometric scaling laws critically examine structure–function relationships. In estimating the forest biomass carbon and its response under climate change, the issue of scaling has resulted in difficulties when modelling the biomass for different-sized trees, especially large ones, and has not yet been solved in either theory or practice. Here, we propose the concept of a dynamic allometric scaling relationship between stem biomass and above-ground biomass The allometric curve approaches an asymptote with an increase in tree size. An asymptotic allometric equation is presented that has a better fit to the data than the simple power-law allometric equation. The non-constant exponent is determined by the change in the biomass ratio for different organs and is governed by the dynamic allometric coefficient. This study presents a methodological framework to theoretically characterize allometric relationships and provides new insights in understanding the general scaling pattern and carbon sequestration capacity of large trees across global forests.

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Fig. 1: The nonlinear issues that resulted in dynamic allometric scaling.
Fig. 2: Allometric relationship between SB and AGB with a dynamic scaling coefficient at the plot level.
Fig. 3: Curve fittings for allometric equations.
Fig. 4: Testing the model that includes two independent variables (SB and foliage and branch biomass (FBB)).

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Data availability

The dataset of tree biomass measurements used here is available in the Supplementary Information.

References

  1. Weiskittel, A. R. et al. A call to improve methods for estimating tree biomass for regional and national assessments. J. For. 113, 414–424 (2015).

    Google Scholar 

  2. Huang, H., Liu, C., Wang, X., Zhou, X. & Gong, P. Integration of multi-resource remotely sensed data and allometric models for forest aboveground biomass estimation in China. Remote Sens. Environ. 221, 225–234 (2019).

    Article  Google Scholar 

  3. Zianis, D. & Seura, S. Biomass and stem volume equations for tree species in Europe. Silva Fenn. Monogr. 4, 1–63 (2005).

    Article  Google Scholar 

  4. Henry, M. et al. Estimating tree biomass of sub-Saharan African forests: a review of available allometric equations. Silva Fenn. 45, 477–569 (2011).

    Article  Google Scholar 

  5. Jenkins, J. C., Chojnacky, D. C., Heath, L. S. & Birdsey, R. A. Comprehensive Database of Diameter-Based Biomass Regressions for North American Tree Species (USDA Forest Service, 2003).

  6. Yuen, J. Q., Fung, T. & Ziegler, A. D. Review of allometric equations for major land covers in SE Asia: uncertainty and implications for above- and below-ground carbon estimates. For. Ecol. Manag. 360, 323–340 (2016).

    Article  Google Scholar 

  7. Liu, C. et al. Separating regressions for model fitting to reduce the uncertainty in forest volume–biomass relationship. Forests 10, 658 (2019).

    Article  Google Scholar 

  8. Niklas, K. J. A phyletic perspective on the allometry of plant biomass-partitioning patterns and functionally equivalent organ-categories. New Phytol. 171, 27–40 (2006).

    Article  PubMed  Google Scholar 

  9. Smith, J. E., Heath, L. S. & Jenkins, J. C. Forest Volume-to-Biomass Models and Estimates of Mass for Live and Standing Dead Trees of U.S. Forests (USDA Forest Service, 2003).

  10. Jalkanen, A., Mäkipää, R., Ståhl, G., Lehtonen, A. & Petersson, H. Silviculture-driven vegetation change in a European temperate deciduous forest. Ann. For. Sci. 62, 313–323 (2005).

    Article  Google Scholar 

  11. Guo, Z., Fang, J., Pan, Y. & Birdsey, R. Inventory-based estimates of forest biomass carbon stocks in China: a comparison of three methods. For. Ecol. Manag. 259, 1225–1231 (2010).

    Article  Google Scholar 

  12. Chave, J. et al. Improved allometric models to estimate the aboveground biomass of tropical trees. Glob. Change Biol. 20, 3177–3190 (2014).

    Article  Google Scholar 

  13. Ishihara, M. I. et al. Efficacy of generic allometric equations for estimating biomass: a test in Japanese natural forests. Ecol. Appl. 25, 1433–1446 (2015).

    Article  PubMed  Google Scholar 

  14. Xiang, W. et al. General allometric equations and biomass allocation of Pinus massoniana trees on regional scale in southern China. Ecol. Res. 26, 697–711 (2011).

    Article  Google Scholar 

  15. Parresol, B. R. Assessing tree and stand biomass: a review with examples and critical comparisons. For. Sci. 45, 573–593 (1999).

    Google Scholar 

  16. Wirth, C., Schumacher, J. & Schulze, E.-D. Generic biomass functions for Norway spruce in Central Europe—a meta-analysis approach toward prediction and uncertainty estimation. Tree Physiol. 24, 121–139 (2004).

    Article  PubMed  Google Scholar 

  17. Rutishauser, E. et al. Generic allometric models including height best estimate forest biomass and carbon stocks in Indonesia. For. Ecol. Manag. 307, 219–225 (2013).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Gonzalez-Benecke, C. A. et al. Local and general above-stump biomass functions for loblolly pine and slash pine trees. For. Ecol. Manag. 334, 254–276 (2014).

    Article  Google Scholar 

  20. Sileshi, G. W. A critical review of forest biomass estimation models, common mistakes and corrective measures. For. Ecol. Manag. 329, 237–254 (2014).

    Article  Google Scholar 

  21. Picard, N., Rutishauser, E., Ploton, P., Ngomanda, A. & Henry, M. Should tree biomass allometry be restricted to power models? For. Ecol. Manag. 353, 156–163 (2015).

    Article  Google Scholar 

  22. Sheil, D. et al. Does biomass growth increase in the largest trees? Flaws, fallacies and alternative analyses. Funct. Ecol. 31, 568–581 (2017).

    Article  Google Scholar 

  23. Muller-Landau, H. C. et al. Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests. Ecol. Lett. 9, 575–588 (2006).

    Article  PubMed  Google Scholar 

  24. Schafer, J. L. & Mack, M. C. Growth, biomass, and allometry of resprouting shrubs after fire in scrubby flatwoods. Am. Midl. Nat. 172, 266–284 (2014).

    Article  Google Scholar 

  25. Poorter, H. et al. How does biomass distribution change with size and differ among species? An analysis for 1200 plant species from five continents. New Phytol. 208, 736–749 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  26. Smith, R. J. Rethinking allometry. J. Theor. Biol. 87, 97–111 (1980).

    Article  CAS  PubMed  Google Scholar 

  27. Dassot, M. et al. Terrestrial laser scanning for measuring the solid wood volume, including branches, of adult standing trees in the forest environment. Comput. Electron. Agric. 89, 86–93 (2012).

    Article  Google Scholar 

  28. Disney, M. I. et al. Weighing trees with lasers: advances, challenges and opportunities. Interface Focus 8, 201700484 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Sarrus, P. F. & Rameaux, J.-F. Application des sciences accessoires et principalement des mathématiques à la physiologie générale. Bull. Acad. R. Méd. 3, 1094–1100 (1838).

    Google Scholar 

  30. Huxley, J. S. & Teissier, G. Terminology of relative growth. Nature 137, 780–781 (1936).

    Article  Google Scholar 

  31. Gayon, J. History of the concept of allometry. Am. Zool. 40, 748–758 (2000).

    Google Scholar 

  32. Rubner, M. Über den einfluss der körpergrösse auf stoff- und kraftwechsel. Z. Biol. 19, 536–562 (1883).

    Google Scholar 

  33. von Bertalanffy, L. General System Theory: Foundations, Development, Applications (George Braziller, 1973).

  34. Kleiber, M. Body size and metabolism. Hilgardia 6, 315–353 (1932).

    Article  CAS  Google Scholar 

  35. West, G. B., Brown, J. H. & Enquist, B. J. A general model for the origin of allometric scaling laws in biology. Science 276, 122–126 (1997).

    Article  CAS  PubMed  Google Scholar 

  36. West, G. B., Brown, J. H. & Enquist, B. J. A general model for ontogenetic growth. Nature 413, 628–631 (2001).

    Article  CAS  PubMed  Google Scholar 

  37. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. Toward a metabolic theory of ecology. Ecology 85, 1771–1789 (2004).

    Article  Google Scholar 

  38. Bokma, F. Evidence against universal metabolic allometry. Funct. Ecol. 18, 184–187 (2004).

    Article  Google Scholar 

  39. Dodds, P. S., Rothman, D. H. & Weitz, J. S. Re-examination of the “3/4-law” of metabolism. J. Theor. Biol. 209, 9–27 (2001).

    Article  CAS  PubMed  Google Scholar 

  40. Kozłowski, J. & Konarzewski, M. Is West, Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant? Funct. Ecol. 18, 283–289 (2004).

    Article  Google Scholar 

  41. Henry, M. et al. Wood density, phytomass variations within and among trees, and allometric equations in a tropical rainforest of Africa. For. Ecol. Manag. 260, 1375–1388 (2010).

    Article  Google Scholar 

  42. Satoo, T. Notes on Kittredge’s method of estimation of amount of leaves of forest stand. Jpn. J. For. 44, 267–272 (1962).

    Google Scholar 

  43. Ruark, G. A., Martin, G. L. & Bockheim, J. G. Comparison of constant and variable allometric ratios for estimating populus tremuloides biomass. For. Sci. 33, 294–300 (1987).

    Google Scholar 

  44. Mori, S. et al. Mixed-power scaling of whole-plant respiration from seedlings to giant trees. Proc. Natl Acad. Sci. USA 107, 1447–1451 (2010).

    Article  CAS  PubMed  Google Scholar 

  45. Tjørve, E. Shapes and functions of species-area curves (II): a review of new models and parameterizations. J. Biogeogr. 36, 1435–1445 (2009).

    Article  Google Scholar 

  46. Luo, Y., Wang, X., Zhang, X. & Lu, F. Biomass and Its Allocation of Forest Ecosystems in China [in Chinese] (Chinese Forestry Publishing House, 2013).

  47. Stovall, A. E. L., Shugart, H. H., Stovall, A. E. L. & Anderson-Teixeira, K. J. Assessing terrestrial laser scanning for developing non-destructive biomass allometry. For. Ecol. Manag. 427, 217–229 (2018).

    Article  Google Scholar 

  48. Packard, G. C. Is logarithmic transformation necessary in allometry? Biol. J. Linn. Soc. 109, 476–486 (2013).

    Article  Google Scholar 

  49. Mascaro, J., Litton, C. M., Hughes, R. F., Uowolo, A. & Schnitzer, S. A. Is logarithmic transformation necessary in allometry? Ten, one-hundred, one-thousand-times yes. Biol. J. Linn. Soc. 111, 230–233 (2014).

    Article  Google Scholar 

  50. Sprugel, D. G. Correcting for bias in log-transformed allometric equations. Ecology 64, 209–210 (1983).

    Article  Google Scholar 

  51. Peichl, M. & Arain, M. A. Allometry and partitioning of above- and belowground tree biomass in an age-sequence of white pine forests. For. Ecol. Manag. 253, 68–80 (2007).

    Article  Google Scholar 

  52. Wolf, A., Field, C. B. & Berry, J. A. Allometric growth and allocation in forests: a perspective from FLUXNET. Ecol. Appl. 21, 1546–1556 (2011).

    Article  PubMed  Google Scholar 

  53. Litton, C. M., Raich, J. W. & Ryan, M. G. Carbon allocation in forest ecosystems. Glob. Change Biol. 13, 2089–2109 (2007).

    Article  Google Scholar 

  54. Vallet, P., Dhôte, J. F., Moguédec, G. L. E., Ravart, M. & Pignard, G. Development of total aboveground volume equations for seven important forest tree species in France. For. Ecol. Manag. 229, 98–110 (2006).

    Article  Google Scholar 

  55. Cannell, M. G. R. World Forest Biomass and Primary Production Data (Academic Press, 1982).

  56. Usoltsev, V. A. Forest Biomass and Primary Production Database for Eurasia (Ural State Forest Engineering Univ., 2013).

  57. West, G. B. & Brown, J. H. The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. J. Exp. Biol. 208, 1575–1592 (2005).

    Article  PubMed  Google Scholar 

  58. Reich, P. B. et al. Universal scaling of respiratory metabolism, size and nitrogen in plants. Nature 439, 457–461 (2006).

    Article  CAS  PubMed  Google Scholar 

  59. Li, H., Han, X. & Wu, J. Lack of evidence for 3/4 scaling of metabolism in terrestrial plants. J. Integr. Plant Biol. 47, 1173–1183 (2005).

    Article  Google Scholar 

  60. Zhou, X. et al. Correcting the overestimate of forest biomass carbon on the national scale. Method Ecol. Evol. 7, 447–455 (2016).

    Article  Google Scholar 

  61. Enquist, B. J., Brown, J. H. & West, G. B. Allometric scaling of plant energetics and population density. Nature 395, 163–165 (1998).

    Article  CAS  Google Scholar 

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Acknowledgements

This study was supported financially by the National Natural Science Foundation of China (41901117), the Outstanding Youth Project of Hunan Provincial Education Department (18B001) and the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant.

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Authors and Affiliations

  1. College of Resources and Environmental Science, Hunan Normal University, Changsha, China

    Xiaolu Zhou, Mingxia Yang, Zelin Liu, Peng Li, Binggeng Xie & Changhui Peng

  2. Department of Biology Sciences, University of Québec at Montreal, Montreal, Québec, Canada

    Changhui Peng

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Contributions

X.Z. and C.P. conceived of the study idea. X.Z. led and carried out all of the analyses, derived models and predictions with input from C.P., M.Y., Z.L., P.L. and B.X. M.Y. analysed the data. X.Z., M.Y. and C.P. wrote the first draft of the manuscript. All authors interpreted the results, revised the text and provided critical feedback.

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Correspondence to Xiaolu Zhou or Changhui Peng.

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The authors declare no competing interests.

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Peer review information Nature Plants thanks Wenhua Xiang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Zhou, X., Yang, M., Liu, Z. et al. Dynamic allometric scaling of tree biomass and size. Nat. Plants 7, 42–49 (2021). https://doi.org/10.1038/s41477-020-00815-8

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