Abstract
The ability of general scaling models to capture the central tendency or dispersion in biological data has been questioned. In fact, the appropriate domain of such models has never been clearly articulated and they have been supported and challenged using both interspecific and/or intraspecific data. Here, we evaluate several simplifying assumptions and predictions of two prominent scaling models: West, Brown and Enquist’s fractal model (WBE) and a null model of geometric similarity (GEOM). Using data for 53 herbaceous angiosperm species from the Songnen Grasslands of Northern China, we compared both the interspecific and intraspecific scaling relationships for plant geometry and biomass partitioning. Specifically, we considered biomass investment in shoots and leaves as well as related several traits not commonly collected in plant allometric analyses: shoot volume, leaf number, and mean leaf mass. At the interspecific level, we find substantial variation in regression slopes, and the simplifying assumptions of WBE and predictions of both the WBE and GEOM models do not hold. In contrast, we find substantial support for the WBE model at the intraspecific level, and to a lesser extent for GEOM. The differences between our results at interspecific and intraspecific levels are due to the fact that leaf size and stem tissue density vary considerably across species in contrast to the simplifying assumptions of WBE. These results highlight the domain within which simplifying model assumptions might be most appropriate, and suggest allometric models may be useful points of departure within some species, growth forms or taxonomic groups.
Similar content being viewed by others
References
Banavar JR, Maritan A, Rinaldo A (1999) Size and form in efficient transport networks. Nature 399:130–132
Banavar JR, Moses ME, Brown JH, Damuth J, Rinaldo A, Sibly RM, Maritan A (2010) A general basis for quarter-power scaling in animals. Proc Natl Acad Sci USA USA 107:15816–15820. doi:10.1073/pnas.1009974107
Bentley LP, Stegen JC, Savage VM, Smith DD, von Allmen EI, Sperry JS, Reich PB, Enquist BJ (2013) An empirical assessment of tree branching networks and implications for plant allometric scaling models. Ecol Lett 16:1069–1078. doi:10.1111/Ele.12127
Biewener AA (2005) Biomechanical consequences of scaling. J Exp Biol 208:1665–1676. doi:10.1242/jeb.01520
Bonser SP, Aarssen LW (2003) Allometry and development in herbaceous plants: functional responses of meristem allocation to light and nutrient availability. Am J Bot 90:404–412. doi:10.3732/ajb.90.3.404
Bonser SP, Aarssen LW (2006) Meristem allocation and life-history evolution in herbaceous plants. Can J Bot 84:143–150. doi:10.1139/b05-154
Brown JH, Gillooly JF, Allen AP, Savage VM, West GB (2004) Toward a metabolic theory of ecology. Ecology 85:1771–1789
Calder WA (1984) Size, function, and life history. Harvard University Press, Cambridge
Chave J, Coomes D, Jansen S, Lewis SL, Swenson NG, Zanne AE (2009) Towards a worldwide wood economics spectrum. Ecol Lett 12:351–366. doi:10.1111/j.1461-0248.2009.01285.x
Coomes DA (2006) Challenges to the generality of WBE theory. Trends Ecol Evol 21:593–596. doi:10.1016/j.tree.2006.09.002
Corner EJH (1949) The durian theory or the origin of the modern tree. Ann Bot Lond 13:367–414
Deng JM, Zuo WY, Wang ZQ, Fan ZX, Ji MF, Wang GX, Ran JZ, Zhao CM, Liu JQ, Niklas KJ, Hammond ST, Brown JH (2012) Insights into plant size-density relationships from models and agricultural crops. Proc Natl Acad Sci USA 109:8600–8605. doi:10.1073/pnas.1205663109
Enquist BJ, Brown JH, West GB (1998) Allometric scaling of plant energetics and population density. Nature 395(6698):163–165
Enquist BJ, West GB, Charnov EL, Brown JH (1999) Allometric scaling of production and life-history variation in vascular plants. Nature 401:907–911
Enquist B, Kerkhoff A, Stark S, Swenson N, McCarthy M, Price C (2007a) A general integrative model for scaling plant growth, carbon flux, and functional trait spectra. Nature 449:218–222. doi:10.1038/nature06061
Enquist BJ, Allen AP, Brown JH, Gillooly JF, Kerkhoff AJ, Niklas KJ, Price CA, West GB (2007b) Biological scaling: does the exception prove the rule? Nature 445:E9–E10. doi:10.1038/Nature05548
Falster DS, Westoby M (2005) Tradeoffs between height growth rate, stem persistence and maximum height among plant species in a post-fire succession. Oikos 111:57–66. doi:10.1111/j.0030-1299.2005.13383.x
Galilei G (1638) Discorsi e dimostrazioni matematiche, intorno a due nuove scienze. Appresso gli Elsevirii, Leida
Huo YL, Kassab GS (2012) Intraspecific scaling laws of vascular trees. J R Soc Interface 9:190–200. doi:10.1098/rsif.2011.0270
Huxley JS (1932) Problems of relative growth. Methuea, Methuea
Iida Y, Poorter L, Sterck FJ, Kassim AR, Kubo T, Potts MD, Kohyama TS (2012) Wood density explains architectural differentiation across 145 co-occurring tropical tree species. Funct Ecol 26:274–282. doi:10.1111/j.1365-2435.2011.01921.x
Jiang SC, He NP, Wu L, Zhou DW (2010) Vegetation restoration of secondary bare saline-alkali patches in the Songnen Plain, China. Appl Veg Sci 13:47–55. doi:10.1111/j.1654-109X.2009.01048.x
Kleiman D, Aarssen LW (2007) The leaf size/number trade-off in trees. J Ecol 95:376–382
Martinez-Cabrera HI, Schenk HJ, Cevallos-Ferriz SRS, Jones CS (2011) Integration of vessel traits, wood density, and height in Angiosperm shrubs and trees. Am J Bot 98:915–922. doi:10.3732/Ajb.1000335
McMahon T (1973) Size and shape in biology. Science 179:1201–1204. doi:10.1126/science.179.4079.1201
McMahon TA, Kronauer RE (1976) Tree structures: deducing the principle of mechanical design. J Theor Biol 59:443–466. doi:10.1016/0022-5193(76)90182-X
Meinzer FC, Bond BJ, Warren JM, Woodruff DR (2005) Does water transport scale universally with tree size? Funct Ecol 19:558–565. doi:10.1111/j.1365-2435.2005.01017.x
Mori S, Yamaji K, Ishida A, Prokushkin SG, Masyagina OV, Hagihara A, Hoque ATMR, Suwa R, Osawa A, Nishizono T, Ueda T, Kinjo M, Miyagi T, Kajimoto T, Koike T, Matsuura Y, Toma T, Zyryanova OA, Abaimov AP, Awaya Y, Araki MG, Kawasaki T, Chiba Y, Umari M (2010) Mixed-power scaling of whole-plant respiration from seedlings to giant trees. Proc Natl Acad Sci USA 107:1447–1451. doi:10.1073/pnas.0902554107
Muller-Landau HC, Condit RS, Chave J, Thomas SC, Bohlman SA, Bunyavejchewin S, Davies S, Foster R, Gunatilleke S, Gunatilleke N, Harms KE, Hart T, Hubbell SP, Itoh A, Kassim AR, LaFrankie JV, Lee HS, Losos E, Makana JR, Ohkubo T, Sukumar R, Sun IF, Supardi NMN, Tan S, Thompson J, Valencia R, Munoz GV, Wills C, Yamakura T, Chuyong G, Dattaraja HS, Esufali S, Hall P, Hernandez C, Kenfack D, Kiratiprayoon S, Suresh HS, Thomas D, Vallejo MI, Ashton P (2006a) Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests. Ecol Lett 9:575–588
Muller-Landau HC, Condit RS, Harms KE, Marks CO, Thomas SC, Bunyavejchewin S, Chuyong G, Co L, Davies S, Foster R, Gunatilleke S, Gunatilleke N, Hart T, Hubbell SP, Itoh A, Kassim AR, Kenfack D, LaFrankie JV, Lagunzad D, Lee HS, Losos E, Makana JR, Ohkubo T, Samper C, Sukumar R, Sun IF, Supardi NMN, Tan S, Thomas D, Thompson J, Valencia R, Vallejo MI, Munoz GV, Yamakura T, Zimmerman JK, Dattaraja HS, Esufali S, Hall P, He FL, Hernandez C, Kiratiprayoon S, Suresh HS, Wills C, Ashton P (2006b) Comparing tropical forest tree size distributions with the predictions of metabolic ecology and equilibrium models. Ecol Lett 9:589–602
Niinemets U, Portsmuth A, Tena D, Tobias M, Matesanz S, Valladares F (2007) Do we underestimate the importance of leaf size in plant economics? Disproportional scaling of support costs within the spectrum of leaf physiognomy. Ann Bot Lond 100:283–303. doi:10.1093/Aob/Mcm107
Niklas KJ (1994) Plant allometry: the scaling of form and process. University of Chicago Press, Chicago
Niklas KJ (1995) Plant height and the properties of some herbaceous stems. Ann Bot Lond 75:133–142. doi:10.1006/anbo.1995.1004
Niklas KJ (2004) Plant allometry: is there a grand unifying theory? Biol Rev 79:871–889
Niklas KJ (2005) Modelling below- and above-ground biomass for non-woody and woody plants. Ann Bot Lond 95:315–321
Niklas KJ, Owens T, Reich PB, Cobb ED (2005) Nitrogen/phosphorus leaf stoichiometry and the scaling of plant growth. Ecol Lett 8:636–642. doi:10.1111/j.1461-0248.2005.00759.x
Peng YH, Niklas KJ, Reich PB, Sun SC (2010) Ontogenetic shift in the scaling of dark respiration with whole-plant mass in seven shrub species. Funct Ecol 24:502–512. doi:10.1111/j.1365-2435.2009.01667.x
Poorter L, Rozendaal DMA (2008) Leaf size and leaf display of thirty-eight tropical tree species. Oecologia 158:35–46. doi:10.1007/s00442-008-1131-x
Pretzsch H, Dieler J (2012) Evidence of variant intra- and interspecific scaling of tree crown structure and relevance for allometric theory. Oecologia 169:637–649. doi:10.1007/s00442-011-2240-5
Price CA, Enquist BJ (2006) Scaling mass and morphology in plants with minimal branching: an extension of the WBE model. Funct Ecol 20:11–20
Price CA, Enquist BJ (2007) Scaling mass and morphology in leaves: an extension of the WBE model. Ecology 88:1132–1141
Price CA, Enquist BJ, Savage VM (2007) A general model for allometric covariation in botanical form and function. Proc Natl Acad Sci USA 104:13204–13209
Price CA, Ogle K, White EP, Weitz JS (2009) Evaluating scaling models in biology using hierarchical Bayesian approaches. Ecol Lett 12:641–651. doi:10.1111/j.1461-0248.2009.01316.x
Price CA, Weitz JS, Savage VM, Stegen J, Clarke A, Coomes DA, Dodds PS, Etienne RS, Kerkhoff AJ, McCulloh K, Niklas KJ, Olff H, Swenson NG (2012) Testing the metabolic theory of ecology. Ecol Lett 15:1465–1474. doi:10.1111/j.1461-0248.2012.01860.x
Price CA, Wright IJ, Ackerly D, Niinemets U, Reich PB, Veneklaas E (2014) Are leaf functional traits “invariant” with plant size, and what is “invariance” anyway? Funct Ecol 28:1330–1343. doi:10.1111/1365-2435.12298
Reich PB, Tjoelker MG, Machado JL, Oleksyn J (2006) Universal scaling of respiratory metabolism, size and nitrogen in plants. Nature 439:457–461. doi:10.1038/Nature04282
Savage VM, Deeds EJ, Fontana W (2008) Sizing up allometric scaling theory. PLoS Comput Biol. doi:10.1371/journal.pcbi.1000171
Savage VM, Bentley LP, Enquist BJ, Sperry JS, Smith DD, Reich PB, von Allmen EI (2010) Hydraulic trade-offs and space filling enable better predictions of vascular structure and function in plants. Proc Natl Acad Sci USA 107:22722–22727. doi:10.1073/pnas.1012194108
Thompson DW (1917) On growth and form. Cambridge University Press, Cambridge
Valladares F, Wright SJ, Lasso E, Kitajima K, Pearcy RW (2000) Plastic phenotypic response to light of 16 congeneric shrubs from a Panamanian rainforest. Ecology 81:1925–1936. doi:10.1890/0012-9658(2000)
Valladares F, Sanchez-Gomez D, Zavala MA (2006) Quantitative estimation of phenotypic plasticity: bridging the gap between the evolutionary concept and its ecological applications. J Ecol 94:1103–1116. doi:10.1111/j.1365-2745.2006.01176.x
Warton DI, Wright IJ, Falster DS, Westoby M (2006) Bivariate line-fitting methods for allometry. Biol Rev 81:259–291
West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122–126. doi:10.1126/science.276.5309.122
West GB, Brown JH, Enquist BJ (1999) A general model for the structure and allometry of plant vascular systems. Nature 400:664–667
Whitman T, Aarssen LW (2010) The leaf size/number trade-off in herbaceous angiosperms. J Plant Ecol 3:49–58. doi:10.1093/Jpe/Rtp018
Zheng HY, Li JD (1999) The saline vegetation and its restoration on the Songnen plains. Science Press, Beijing
Acknowledgments
YH is supported by the National Science Foundation of China (31570454) and the National Key Basic Research Special Foundation of China (2014FY210300). CAP is supported by Australian Research Council Discovery Early Career Research Award (DECRA) and a Sabbatical Fellowship at the National Institute for Mathematical and Biological Synthesis (NIMBioS, USA).
Author contribution statement
YH, MJL and DZ conceived and designed the experiments. YH performed the experiments. YH and CAP analyzed the data. YH, CAP and MJL wrote the manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Frederick C Meinzer.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Huang, Y., Lechowicz, M.J., Zhou, D. et al. Evaluating general allometric models: interspecific and intraspecific data tell different stories due to interspecific variation in stem tissue density and leaf size. Oecologia 180, 671–684 (2016). https://doi.org/10.1007/s00442-015-3497-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00442-015-3497-x