All Title Author
Keywords Abstract

PLOS ONE  2008 

Trade-Offs between the Metabolic Rate and Population Density of Plants

DOI: 10.1371/journal.pone.0001799

Full-Text   Cite this paper   Add to My Lib


The energetic equivalence rule, which is based on a combination of metabolic theory and the self-thinning rule, is one of the fundamental laws of nature. However, there is a progressively increasing body of evidence that scaling relationships of metabolic rate vs. body mass and population density vs. body mass are variable and deviate from their respective theoretical values of 3/4 and ?3/4 or ?2/3. These findings questioned the previous hypotheses of energetic equivalence rule in plants. Here we examined the allometric relationships between photosynthetic mass (Mp) or leaf mass (ML) vs. body mass (β); population density vs. body mass (δ); and leaf mass vs. population density, for desert shrubs, trees, and herbaceous plants, respectively. As expected, the allometric relationships for both photosynthetic mass (i.e. metabolic rate) and population density varied with the environmental conditions. However, the ratio between the two exponents was ?1 (i.e. β/δ = ?1) and followed the trade-off principle when local resources were limited. Our results demonstrate for the first time that the energetic equivalence rule of plants is based on trade-offs between the variable metabolic rate and population density rather than their constant allometric exponents.


[1]  Kleiber M (1932) Body size and metabolism. Hilgardia 6: 315–332.
[2]  Peters RH (1983) The ecological implications of body size. Cambridge, UK: Cambridge University Press.
[3]  Brown JH, Gillooly JF, Allen PA, Savage VM, West GB (2004) Toward a metabolic theory of ecology. Ecology 85: 1771–1789.
[4]  Damuth J (1981) Population density and body size in mammals. Nature, 290: 699–700.
[5]  Damuth J (1987) Interspecific allometry of population-density in mammals and other animals: the independence of body-mass and population energy-use. Biol J Linn Soc 31: 193–246.
[6]  West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276: 122–126.
[7]  West GB, Brown JH, Enquist BJ (1999a) The fourth dimension of life: fractal geometry and allometric scaling of organism. Science, 284: 1677–1679.
[8]  West GB, Brown JH, Enquist BJ (1999b) A general model for the structure and allometry of plant vascular systems. Nature 400: 664–667.
[9]  Enquist BJ, Brown JH, West GB (1998) Allometric scaling of plants energetics and population density. Nature 395: 163–165.
[10]  Enquist BJ, Brown JH, West GB (1999) Plant energetics and population density. Nature 398: 573.
[11]  Enquist BJ, Niklas KJ (2001) Invariant scaling relations across tree-dominated communities. Nature 410: 655–660.
[12]  Niklas KJ, Midgley JJ, Enquist BJ (2003) A general model for mass-growth-density relations across tree-dominated communities. Evol Ecol Res 5: 459–468.
[13]  Dodds PS, Rothman DH, Weitz JS (2001) Re-examination of the “3/4-law”of metabolism. J Theor Biol 209: 9–27.
[14]  Kozlowski J, Konarzewski M (2004) Is West, Brown and Enquist's model of allometric scaling mathematically correct and biologically relevant? Funct Ecol 18: 283–289.
[15]  Kozlowski J, Konarzewski M (2005) West, Brown and Enquist's model of allometric scaling again: the same questions remain. Funct Ecol 19: 739–743.
[16]  O′Connor MP, Kemp ST, Agosta SJ, Hansen F, Sieg AE, et al. (2007) Reconsidering the mechanistic basis of the metabolic theory of ecology. Oikos 116: 1058–1072.
[17]  White CR, Seymour RS (2003) Mammalian basal metabolic rate is proportional to body mass2/3. Proc Natl Acad Sci U S A 100: 4046–4049.
[18]  White J (1980) Demographic factors in populations of plants. In: Solbrig OT, editor. Demography and evolution in plant populations. Berkeley, California, USA: University of California Press. pp. 21–48.
[19]  Hutchings MJ (1983) Ecology's law in search of a theory. New Scie 98: 765–767.
[20]  Deng JM, Wang GX, Morris EC, Wei XP, Li DX, et al. (2006a) Plant mass-density relationship along a moisture gradient in north-west China. J Ecol 94: 953–958.
[21]  Li HT, Han XG, Wu JG (2006) Variant scaling relationship for mass-density across tree-dominated communities. J Integr P Biol 48: 268–277.
[22]  Pretzsch H (2006) Species-specific allometric scaling under self-thinning: evidence from long-term plots in forest stands. Oecologia 146: 572–583.
[23]  Ricklefs RE (2003) Is rate of ontogenetic growth constrained by resource supply or tissue growth potential? A comment on West et al.'s model. Funct Ecol 17: 384–393.
[24]  Reich PB, Tjoelker MG, Machado JL, Oleksyn J (2006) Universal scaling of respiratory metabolism, size and nitrogen in plants. Nature 439: 457–461.
[25]  Duncan RP, Forsyth DM, Hone J (2007) Testing the Metabolic theory of ecology: allometric scaling exponents in mammals. Ecology 88: 324–333.
[26]  White CR, Cassey P, Blackburn TM (2007) Allometric exponents do not support a universal metabolic allometry. Ecology 88: 315–323.
[27]  Weller DE (1987) Self-thinning exponent correlated with allometric measures of plant geometry. Ecology 64: 813–821.
[28]  Lonsdale WM (1990) The self-thinning rule: dead or alive? Ecology 71: 1373–1388.
[29]  Morris EC (2002) Self-thinning lines differ with fertility level. Ecol Res 17: 17–28.
[30]  Roderick ML, Barnes B (2004) Self-thinning of plant populations from a dynamic viewpoint. Funct Ecol 18: 197–203.
[31]  Liu J, Wei L, Wang CM, Wang GX, Wei XP (2006) Effect of water deficit on self-thinning line in even-aged monocultures of spring wheat (Triticum aestivum L.). J Integr P Biol 48: 415–419.
[32]  Niklas KJ, Enquist BJ (2001) Invariant scaling relationships for interspecifc plant biomass production rates and body size. Proc Natl Acad Sci U S A 98: 2922–2927.
[33]  Niklas KJ, Enquist BJ (2002a) On the vegetative biomass partitioning of seed plant leaves, stems, and roots. Am Nat 5: 482–497.
[34]  Niklas KJ, Enquist BJ (2002b) Canonical rules for plant organ biomass partitioning and annual allocation. Am J Bot 89: 812–819.
[35]  Enquist BJ, Niklas KJ (2002) Global allocation rules for patterns of biomass partitioning in seed plants. Science 295: 1517–1520.
[36]  Enquist BJ (2003) Scaling the macroecological and evolutionary implications of size and metabolism within and across plant taxa. Birmingham, UK: Blackwell publishing.
[37]  Yoda K, Kira T, Ogawa H, Hozumi K (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions. (Intraspecific competition among higher plants XI). Journal of the Institute of Polytechnics, Osaka City University, Series D 14: 107–129.
[38]  White J, Harper JL (1970) Correlated changes in plant size and number in plant populations. J Ecol 58: 467–485.
[39]  Begon M, Harper JL, Townsend CR (1996) Ecology 3rd ed. Oxford, UK: Blackwell Science Ltd.
[40]  Bi HQ, Wan GH, Turvey ND (2000) Estimating the self-thinning boundary line as a density-dependent stochastic biomass frontier. Ecology 81: 1477–1483.
[41]  Price CA, Enquist BJ (2007) Scaling mass and morphology in leaves: an extension of the WBE model. Ecology 88: 1132–1141.
[42]  Weller DE (1991) The self-thinning rule: dead or unsupported? A reply to Londale. Ecology 72: 747–750.
[43]  Osawa A, Allen RB (1993) Allometric theory explains self-thinning relationships of mountain beech and red pine. Ecology 74: 1020–1032.
[44]  Reynolds JH, Ford ED (2005) Improving competition representation in theoretical models of self-thinning: a critical review. J Ecol 93: 362–372.
[45]  Wang G, Zhang DY (1996) Theories of biological competition. Intraspecific competition. Xi'an, Shanxi: Science and technology press. pp. 28–43.
[46]  Wang G, Yuan JL, Wang XZ, Xiao S, Huang WB (2004) Competitve regulation of plant allometry and a generalized model for the plnt self-thinning process. J Theor Biol 66: 1875–1885.
[47]  Bokma F (2004) Evidence against universal metabolic allometry. Funct Ecol 18: 184–187.
[48]  Cry H, Walker SC (2004) An illusion of Mechanistic understanding. Ecology 85: 1802–1804.
[49]  Anderson KJ, Jetz W (2005) The broad-scale ecology of energy expenditure of endotherms. Ecol lett 8: 310–318.
[50]  Loeuille N, Michel L (2006) Evolution of body size in food webs: does the energetic equivalence rule hold? Ecol Lett 9: 171–178.
[51]  Kleiman D, Aarssen LW (2007) The leaf size/number trade-off in trees. J Ecol 95: 376–382.
[52]  Long JN, Smith FW (1984) Relation between size and density in developing stands: a description and possible mechanisms. Fores Ecol Mana 7: 191–206.
[53]  Richards RA (1991) Crop improvement for temperate Australia: future opportunities. Field Crop Res 26: 141–169.
[54]  Zhang DY, Sun GJ, Jiang XH (1999) Donald's ideotype and growth redundancy: a game theoretical analysis. Field Crop Res 61: 179–187.
[55]  Banavar JR, Damuth J, Maritan A, Rinaldo A (2002) Supply-demand balance and metabolic scaling. Proc Natl Acad Sci U S A 99: 10506–10509.
[56]  Lyshede OB (1979) Xeromorphic features of three stem assimilating in relation to their ecology. Bot J Lin Soc 78: 85–98.
[57]  Gong CM, Gao XW, Cheng DL, Wang GX (2006) C4 photosynthetic characteristics and antioxidative protection of C3 desert shrub Hedysarum scoparium in northwest China. Pakistan J Bot 38: 647–661.
[58]  Chen BM, Wang GX, Cheng DL, Deng JM, Peng SL, et al. (2007) Vegetation change and soil nutrient distribution along an oasis-desert transitional zone in Northwestern China. J Integr P Biol 49: 1537–1547.
[59]  Luo TX (1996) Patterns of biological production and its mathematical 50 models for main forest types of China (in Chinese). Committee of Synthesis Investigation of Natural Resources, the Chinese Academy of Sciences, Beijing.
[60]  Deng JM, Zhang XY, Wang GX, Wei XP, Zhao CM (2006b) The relationship between the energy use and densities of spring wheat under the different moisture levels (In Chinese with English abstract). Acta Ecolpgica Sinaca 26: 2282–2287.


comments powered by Disqus