Fundamentals of Model Scaling in Forest Ecology

  • Matthias LangensiepenEmail author
Part of the Ecological Studies book series (ECOLSTUD, volume 212)


Coping with disturbances of forest systems which result from increasing fluctuations of physical and human environments requires a better quantitative understanding of forest ecological processes at different scales. Examples of applied scaling in forest ecology are initially discussed to stress the practical relevance of scaling studies. Model-based reasoning serves as a starting point of any scaling activity. Initial cognitive processes play an important role in model conceptualizing and are thus briefly summarized. Statistical techniques for scale identification are outlined and the establishment of mathematical scaling laws explained. Structure and function are emphasized as important concepts for understanding tree responses to changing environments. Methods of translating models across spatial scales are categorized in the concluding section.


Allometric Scaling Stomatal Control Leaf Area Density Allometric Relation Canopy Scale 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I gratefully acknowledge the support of this work through the European COST action “Forest Management and the Water Cycle”.


  1. Alon U (2007) An introduction to systems biology. Chapman & Hall, LondonGoogle Scholar
  2. Aloy P, Russell RB (2006) Structural systems biology: modelling protein interactions. Nat Rev 7:188–197CrossRefGoogle Scholar
  3. Barabasi AL, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev 5:101–114CrossRefGoogle Scholar
  4. Barenblatt G (2003) Scaling. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  5. Barenblatt GI, Chorin AJ (1998) New perspectives in turbulence: scaling laws, asymptotics, and intermittency. SIAM Rev 40:265–291CrossRefGoogle Scholar
  6. Becker P, Gribben RJ, Lim CM (2000) Tapered conduits can buffer hydraulic conductance from path-length effects. Tree Physiol 20:965–967CrossRefGoogle Scholar
  7. Boulton A, Panizoon D, Prior J (2005) Explicit knowledge structures as a tool for overcoming obstacles to interdisciplinary research. Conserv Biol 19:2026–2029CrossRefGoogle Scholar
  8. Boysen Jensen P (1932) Die Stoffproduktion der Pflanzen. Gustav Fischer, JenaGoogle Scholar
  9. Brutasert W (2005) Hydrology. Cambridge University Press, CambridgeGoogle Scholar
  10. Cacuci DG (2003) Sensitivity and uncertainty analysis. Chapman & Hall, LondonCrossRefGoogle Scholar
  11. Campbell GS, Norman JM (1998) An Introduction to Environmental Biophysics (2nd ed.). New York: Springer-Verlag. 286 ppCrossRefGoogle Scholar
  12. Cates S, Gittlemen J (1997) Reading between the lines – is allometric scaling useful? Tree 12:338–339PubMedGoogle Scholar
  13. Cermak J, Riguzzi F, Ceulemans R (1998) Scaling up from the individual tree to the stand level in Scots pine: I. Needle distribution, overall crown and root geometry. Ann Sci For 55:63–88CrossRefGoogle Scholar
  14. Chelle M (2005) Phylloclimate or the climate perceived by individual plant organs: what is it? How to model it? What for? New Phytol 166:781–790PubMedCrossRefGoogle Scholar
  15. Cruiziat P, Cochard H, Ameglio T (2002) Hydraulic architecture of trees: main concepts and results. Ann For Sci 59:723–752CrossRefGoogle Scholar
  16. Dale M (1999) Spatial pattern analysis in plant ecology. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  17. De Boer A, Volkov V (2003) Logistics of water and salt transport through the plant: structure and functioning of the xylem. Plant Cell Environ 26:87–101CrossRefGoogle Scholar
  18. Dehaene S (1997) The number sense: how the mind creates mathematics. Oxford University Press, OxfordGoogle Scholar
  19. Enquist B, Brown J, West G (1998) Allometric scaling of plant energetics and population density. Nature 395:163–165CrossRefGoogle Scholar
  20. Enquist B, West G, Charnov E, Brown J (1999) Allometric scaling of production and life-history variation in vascular plants. Nature 401:907–911CrossRefGoogle Scholar
  21. Ferrari P (2003) Abstraction in mathematics. Phil Trans R Soc Lond B 358:1225–1230CrossRefGoogle Scholar
  22. Finnigan JJ, Raupach M (1987) Transfer processes in plant canopies in relation to stomatal characteristics. In: Zeiger E, Farqhuar G, Cowan I (eds) Stomatal function. Stanford University Press, Stanford, CA, pp 385–444Google Scholar
  23. Gadkar K, Gunawan R, Doyle F (2005) Iterative approach to model identification of biological networks. BMC Bioinformatics 6:155. doi: 10.1186/1471-2105/6/155 PubMedCrossRefGoogle Scholar
  24. Godin C (2000) Representing and encoding plant architecture: A review. Ann. For. Sci. 57: 413–438PubMedCrossRefGoogle Scholar
  25. Haefner JW (2005) Modeling biological systems. Springer, New YorkGoogle Scholar
  26. Hatton T, Wu H (1995) Scaling theory to extrapolate individual tree water use to stand water useful? Hydrol Process 9:527–540CrossRefGoogle Scholar
  27. Hirose T (2005) Development of the Monsi-Saeki theory on the canopy structure and function. Ann Bot 95:483–494PubMedCrossRefGoogle Scholar
  28. Holland J, Holyoak K, Nisbett R, Thagard P (1986) Induction – processes of inference, learning, and discovery. MIT Press, CambridgeGoogle Scholar
  29. Holyoak K, Morrison R (2005) Cambridge handbook of thinking and reasoning. Cambridge University Press, CambridgeGoogle Scholar
  30. Huxley J (1932) Problems of relative growth. Methuea, MethueaGoogle Scholar
  31. Johnson-Laird P (2001) Mental models and deduction. Trends Cogn Sci 5:434–442PubMedCrossRefGoogle Scholar
  32. Kaimal J, Finnigan J (1994) Atmospheric boundary layer flows. Oxford University Press, New YorkGoogle Scholar
  33. Karlik J, McKay A (2002) Leaf area index, leaf mass density, and allometric relationships derived from harvest of blue oaks in a California Oak Savanna. USDA Forest Service Gen. Tech. rep. PSW-GTR-184Google Scholar
  34. Kimmis J (2008) From science to stewardship: harnessing forest ecology in the service of society. For Ecol Manage 256:1625–1635CrossRefGoogle Scholar
  35. King A (1991) Translating models across scales in the landscapes. In: Turner M, Gardner R (eds) Quantitative methods in landscape ecology. Springer, BerlinGoogle Scholar
  36. Kitano H (2002) Systems biology: a brief overview. Science 295:1662–1664PubMedCrossRefGoogle Scholar
  37. Konar K (2005) Computational intelligence: principles. techniques and applications. Springer, New YorkGoogle Scholar
  38. Kozlowski J, Weiner J (1997) Interspecific allometries are by-products of body size optimization. Am Nat 149:352–380CrossRefGoogle Scholar
  39. Kurth W (1994) Growth grammar interpreter GROGRA 2.4: A Software for the 3-Dimensional Interpretation of Stochastic, Sensitive Growth Grammar in the Context of Plant Modeling, Introduction and Reference Manual. Technical ManualGoogle Scholar
  40. Langensiepen M (2008) Scaling transpiration from leaves and canopies. In: Trimble S, Stewart B Howell T (eds) Encyclopedia of water science. Marcel Dekker, New YorkGoogle Scholar
  41. Li B, Wu H, Zou G (2000) Self-thinning rule: a causal interpretation from ecological field theory. Ecol Model 132:167–173CrossRefGoogle Scholar
  42. Lonsdale W (1990) The self-thinning rule: dead or alive? Ecology 71:1373–1388CrossRefGoogle Scholar
  43. McNaughton K, Jarvis P (1991) Effects of spatial scale on stomatal control of transpiration. Agric For Meteorol 54:279–301CrossRefGoogle Scholar
  44. Meentemeyer V, Box E (1987) Scale effects in landscape studies. In: Turner M (ed) Landscape heterogeneity and disturbance. Springer, New YorkGoogle Scholar
  45. Meinzer F (2002) Co-ordination of vapour and liquid phase water transport properties in plants. Plant Cell Environ 25:265–274PubMedCrossRefGoogle Scholar
  46. Meinzer F, Bond BJ, Warren J, Woodruff D (2005) Does water transport scale universally with tree size? Funct Ecol 19:558–565CrossRefGoogle Scholar
  47. Mencuccini M (2003) The ecological significance of long-distance water transport: short-term regulation, long-term acclimation and the hydraulic costs of stature across plant life forms. Plant Cell Environ 26:163–182CrossRefGoogle Scholar
  48. Mencuccini M (2002) Hydraulic constraints in the functional scaling of trees. Tree Physiol 22:553–565PubMedCrossRefGoogle Scholar
  49. Minorsky P (2003) Achieving the in Silicio Plant. Systems biology and the future of plant biological research. Plant Physiol 132:404–409CrossRefGoogle Scholar
  50. Monsi M, Saeki T (1952) Über den Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung für die Stoffproduktion. Jpn J Bot 14:22–52Google Scholar
  51. Mosley M, McKerchar A (1993) Streamflow. In: Maidment D (ed) Handbook of hydrology. McGraw-Hill, ColumbusGoogle Scholar
  52. Mäkelä A, Valentine H (2006) The quarter-power law scaling model does not imply size-invariant hydraulic resistance in plants. J Theor Biol 243:283–285PubMedCrossRefGoogle Scholar
  53. Nersessian N (2002) The cognitive basis of model-based reasoning in science. In: Carruthers P, Stich S, Siegal M (eds) The cognitive basis of science. Cambridge University Press, CambridgeGoogle Scholar
  54. Nersessian NJ (1999) Model-based reasoning in conceptual change. In: Magnani L, Nersessian NJ, Thagard P (eds) Model-based reasoning in conceptual change. Model-based reasoning in scientific discovery. Kluwer, New YorkGoogle Scholar
  55. Noy-Meir I, Anderson D (1971) Multiple pattern analysis, or multiscale ordination: towards a vegetation hologram? In: Patil G, Pielou E, Water W (eds) Many species populations, ecosystems and systems analysis. Pennsylvania State University Press, University Park, PAGoogle Scholar
  56. Oreskes N (2003) The role of quantitative models in science. In: Canham CD, Cole JJ, Lauenroth WK (eds) Models in ecosystem science. Princeton University Press, Princeton, NJGoogle Scholar
  57. Passioura J (1996) Simulation models: science, snake oil, education, or engineering? Agron J 88:690–694CrossRefGoogle Scholar
  58. Paul M, Foyer C (2001) Sink regulation of photosynthesis. J Exp Bot 52:1383–1400PubMedCrossRefGoogle Scholar
  59. Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, CambridgeGoogle Scholar
  60. Press W, Teukolsky S, Vetterling W, Flannery B (2007) Numerical recipes: the art of scientific computing. Cambridge University Press, CambridgeGoogle Scholar
  61. Pretzsch H, Mette T (2008) Linking stand-level self-thinning allometry to the tree-level leaf biomass alloetry. Trees 22:611–622CrossRefGoogle Scholar
  62. Prusinkiewicz P, Lindenmayer A (1990) The Algorithmic Beauty of Plants. Springer, New YorkCrossRefGoogle Scholar
  63. Raupach M (2001) Inferring biogeochemical sources and sinks from atmospheric concentrations: general considerations and application in vegetation canopies. In: In Schulze ED, Heiman M, Harrison S, Holland E, Lloyd J, Prentice IC, Schimel D (eds) Global biogeochemical cycles in the climate system. Academic, San Diego, CAGoogle Scholar
  64. Refsgaard J, Henriksen H (2004) Modeling guidelines – terminology and guiding principles. Adv Water Resour 27:71–82CrossRefGoogle Scholar
  65. Roderick M, Barnes B (2004) Self-thinning of plant populations from a dynamic viewpoint. Funct Ecol 18:197–203CrossRefGoogle Scholar
  66. Rodgers N (2000) Learning to reason: an introduction to logic, sets, and relations. Wiley, New YorkCrossRefGoogle Scholar
  67. Sackville Hamilton NR, Matthew C, Lemaire G (1995) In defence of the –3/2 boundary rule: a re-evaluation of self-thinning concepts and status. Annals of Botany 76: 569–577CrossRefGoogle Scholar
  68. Schneider D (2001) The rise of the concept of scale in ecology. BioScience 51:545–554CrossRefGoogle Scholar
  69. Schulze ED (1991) Water and nutrient interactions with plant water stress. In: Mooney H, Winner W, Pell E (eds) Response of plants to multiple stresses. Academic, New YorkGoogle Scholar
  70. Snyman J (2005) Practical mathematical optimization: an introduction to basic optimization theory and classical and new gradient-based algorithms. Springer, BerlinGoogle Scholar
  71. Sole R, Bascompte J (2006) Self-organization in complex ecosystems. Princeton University Press, Princeton, NJGoogle Scholar
  72. Spelke ES (2005) Sex differences in intrinsic aptitude for mathematics and science? Am Psychol 60:950–958PubMedCrossRefGoogle Scholar
  73. Srivastava L (2002) Plant growth and development. Academic, San Diego, CAGoogle Scholar
  74. Steiner G (2001) Grammars of creation. Yale University Press, New Haven, CT and LondonGoogle Scholar
  75. Stitt M (1994) Flux control at the level of the pathway: studies with mutants and transgenic plants having a decreased activity of enzymes involved in photosynthesis partitioning. In: Schulze ED (ed) Flux control in biological systems. Academic, San Diego, CAGoogle Scholar
  76. Stitt M, Fernie A (2003) From measurements of metabolites to metabolomics: an ‘on the fly’ perspective illustrated by recent studies of carbon-nitrogen interactions. Curr Opin Biotechnol 14:136–145PubMedCrossRefGoogle Scholar
  77. Stitt M, Müller C, Matt P, Gibon Y, Carillo P, Morcuende R, Scheible W, Krapp A (2002) Steps towards an integrated view of nitrogen metabolism. J Exp Bot 53:959–970PubMedCrossRefGoogle Scholar
  78. Sweetlove L, Fernie A (2005) Regulation of metabolic networks: understanding metabolic complexity in the systems biology era. New Phytol 168:9–24PubMedCrossRefGoogle Scholar
  79. Thagard P, Zhu R (2003) Acupuncture, incommensurability, and conceptual change. In: Sinatra G, Pintrich P (eds) Intentional conceptual change. Lawrence Erlbaum Associates, Mahwah, NJGoogle Scholar
  80. Thomas A, Benson M (1975) Generalization of streamflow characteristics from drainage basin characteristics. U.S. Geological Survey. Water-Supply PaperGoogle Scholar
  81. Turner M, Dale V, Gardner R (1989) Predicting across scales: theory development and testing. Landscape Ecol 3:245–252CrossRefGoogle Scholar
  82. Turner S, O’Neill R, Conley W, Conley M, Humphries H (1991) Pattern and scale: statistics for landscape ecology. In: Turner M, Gardner R (eds) Quantiative methods in landscape ecology. Springer, BerlinCrossRefGoogle Scholar
  83. Uetz P, Finley R (2005) From protein networks to biological systems. FEBS Lett 579:1821–1827PubMedCrossRefGoogle Scholar
  84. Varley R, Siegal M (2000) Evidence for cognition without grammar from causal reasoning and theory of mind in an agrammatic aphasic patient. Curr Biol 10:723–726PubMedCrossRefGoogle Scholar
  85. Ver Hoef J, Glenn-Lewin D (1989) Multiscale ordination: a method for detecting pattern at several scales. Vegetatio 82:59–67Google Scholar
  86. Weller D (1991) The self-thinning rule: dead or unsupportable? – a reply to Donsdale. Ecology 72:747–750CrossRefGoogle Scholar
  87. West G, Brown J (2005) 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 208:1575–1592PubMedCrossRefGoogle Scholar
  88. West G, Brown J, Enquist B (1999) A general model for the structure and allometry of plant vascular system. Nature 400:664–667CrossRefGoogle Scholar
  89. West G, Brown J, Enquist B (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122–126PubMedCrossRefGoogle Scholar
  90. White J (1981) The allometric interpretation of the self-thinning rule. J Theor Biol 89:475–500CrossRefGoogle Scholar
  91. Wiens J (2000) Ecological heterogeneity: an ontogeny of concepts and approaches. In: Hutchings M, John E, Stewart A (eds) The ecological consequences of environmental heterogeneity. Blackwell, OxfordGoogle Scholar
  92. Yoda K, Ogawa KH, Hozumi K (1963) Self-thinning in overcrowded pure stands under cultivated and natural conditions (Intraspecific competition among higher plants XI). Journal of Biology Osaka City University 14:107–129CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Faculty of Agriculture, Institute of Crop Science and Resource Protection, Crop Science GroupUniversity of BonnBonnGermany

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