Skip to main content

Fundamentals of Model Scaling in Forest Ecology

  • Chapter
  • First Online:
Forest Management and the Water Cycle

Part of the book series: Ecological Studies ((ECOLSTUD,volume 212))

  • 1448 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alon U (2007) An introduction to systems biology. Chapman & Hall, London

    Google Scholar 

  • Aloy P, Russell RB (2006) Structural systems biology: modelling protein interactions. Nat Rev 7:188–197

    Article  CAS  Google Scholar 

  • Barabasi AL, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev 5:101–114

    Article  CAS  Google Scholar 

  • Barenblatt G (2003) Scaling. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Barenblatt GI, Chorin AJ (1998) New perspectives in turbulence: scaling laws, asymptotics, and intermittency. SIAM Rev 40:265–291

    Article  Google Scholar 

  • Becker P, Gribben RJ, Lim CM (2000) Tapered conduits can buffer hydraulic conductance from path-length effects. Tree Physiol 20:965–967

    Article  Google Scholar 

  • Boulton A, Panizoon D, Prior J (2005) Explicit knowledge structures as a tool for overcoming obstacles to interdisciplinary research. Conserv Biol 19:2026–2029

    Article  Google Scholar 

  • Boysen Jensen P (1932) Die Stoffproduktion der Pflanzen. Gustav Fischer, Jena

    Google Scholar 

  • Brutasert W (2005) Hydrology. Cambridge University Press, Cambridge

    Google Scholar 

  • Cacuci DG (2003) Sensitivity and uncertainty analysis. Chapman & Hall, London

    Book  Google Scholar 

  • Campbell GS, Norman JM (1998) An Introduction to Environmental Biophysics (2nd ed.). New York: Springer-Verlag. 286 pp

    Book  Google Scholar 

  • Cates S, Gittlemen J (1997) Reading between the lines – is allometric scaling useful? Tree 12:338–339

    PubMed  CAS  Google Scholar 

  • 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 55:63–88

    Article  Google Scholar 

  • Chelle M (2005) Phylloclimate or the climate perceived by individual plant organs: what is it? How to model it? What for? New Phytol 166:781–790

    Article  PubMed  Google Scholar 

  • Cruiziat P, Cochard H, Ameglio T (2002) Hydraulic architecture of trees: main concepts and results. Ann For Sci 59:723–752

    Article  Google Scholar 

  • Dale M (1999) Spatial pattern analysis in plant ecology. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • De Boer A, Volkov V (2003) Logistics of water and salt transport through the plant: structure and functioning of the xylem. Plant Cell Environ 26:87–101

    Article  Google Scholar 

  • Dehaene S (1997) The number sense: how the mind creates mathematics. Oxford University Press, Oxford

    Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  • Ferrari P (2003) Abstraction in mathematics. Phil Trans R Soc Lond B 358:1225–1230

    Article  Google Scholar 

  • 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 385–444

    Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Godin C (2000) Representing and encoding plant architecture: A review. Ann. For. Sci. 57: 413–438

    Article  PubMed  Google Scholar 

  • Haefner JW (2005) Modeling biological systems. Springer, New York

    Google Scholar 

  • Hatton T, Wu H (1995) Scaling theory to extrapolate individual tree water use to stand water useful? Hydrol Process 9:527–540

    Article  Google Scholar 

  • Hirose T (2005) Development of the Monsi-Saeki theory on the canopy structure and function. Ann Bot 95:483–494

    Article  PubMed  CAS  Google Scholar 

  • Holland J, Holyoak K, Nisbett R, Thagard P (1986) Induction – processes of inference, learning, and discovery. MIT Press, Cambridge

    Google Scholar 

  • Holyoak K, Morrison R (2005) Cambridge handbook of thinking and reasoning. Cambridge University Press, Cambridge

    Google Scholar 

  • Huxley J (1932) Problems of relative growth. Methuea, Methuea

    Google Scholar 

  • Johnson-Laird P (2001) Mental models and deduction. Trends Cogn Sci 5:434–442

    Article  PubMed  Google Scholar 

  • Kaimal J, Finnigan J (1994) Atmospheric boundary layer flows. Oxford University Press, New York

    Google Scholar 

  • 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-184

    Google Scholar 

  • Kimmis J (2008) From science to stewardship: harnessing forest ecology in the service of society. For Ecol Manage 256:1625–1635

    Article  Google Scholar 

  • King A (1991) Translating models across scales in the landscapes. In: Turner M, Gardner R (eds) Quantitative methods in landscape ecology. Springer, Berlin

    Google Scholar 

  • Kitano H (2002) Systems biology: a brief overview. Science 295:1662–1664

    Article  PubMed  CAS  Google Scholar 

  • Konar K (2005) Computational intelligence: principles. techniques and applications. Springer, New York

    Google Scholar 

  • Kozlowski J, Weiner J (1997) Interspecific allometries are by-products of body size optimization. Am Nat 149:352–380

    Article  Google Scholar 

  • 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 Manual

    Google Scholar 

  • Langensiepen M (2008) Scaling transpiration from leaves and canopies. In: Trimble S, Stewart B Howell T (eds) Encyclopedia of water science. Marcel Dekker, New York

    Google Scholar 

  • Li B, Wu H, Zou G (2000) Self-thinning rule: a causal interpretation from ecological field theory. Ecol Model 132:167–173

    Article  Google Scholar 

  • Lonsdale W (1990) The self-thinning rule: dead or alive? Ecology 71:1373–1388

    Article  Google Scholar 

  • McNaughton K, Jarvis P (1991) Effects of spatial scale on stomatal control of transpiration. Agric For Meteorol 54:279–301

    Article  Google Scholar 

  • Meentemeyer V, Box E (1987) Scale effects in landscape studies. In: Turner M (ed) Landscape heterogeneity and disturbance. Springer, New York

    Google Scholar 

  • Meinzer F (2002) Co-ordination of vapour and liquid phase water transport properties in plants. Plant Cell Environ 25:265–274

    Article  PubMed  Google Scholar 

  • Meinzer F, Bond BJ, Warren J, Woodruff D (2005) Does water transport scale universally with tree size? Funct Ecol 19:558–565

    Article  Google Scholar 

  • 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 26:163–182

    Article  Google Scholar 

  • Mencuccini M (2002) Hydraulic constraints in the functional scaling of trees. Tree Physiol 22:553–565

    Article  PubMed  Google Scholar 

  • Minorsky P (2003) Achieving the in Silicio Plant. Systems biology and the future of plant biological research. Plant Physiol 132:404–409

    Article  CAS  Google Scholar 

  • Monsi M, Saeki T (1952) Über den Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung für die Stoffproduktion. Jpn J Bot 14:22–52

    Google Scholar 

  • Mosley M, McKerchar A (1993) Streamflow. In: Maidment D (ed) Handbook of hydrology. McGraw-Hill, Columbus

    Google Scholar 

  • Mäkelä A, Valentine H (2006) The quarter-power law scaling model does not imply size-invariant hydraulic resistance in plants. J Theor Biol 243:283–285

    Article  PubMed  Google Scholar 

  • 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, Cambridge

    Google Scholar 

  • 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 York

    Google Scholar 

  • 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, PA

    Google Scholar 

  • 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, NJ

    Google Scholar 

  • Passioura J (1996) Simulation models: science, snake oil, education, or engineering? Agron J 88:690–694

    Article  Google Scholar 

  • Paul M, Foyer C (2001) Sink regulation of photosynthesis. J Exp Bot 52:1383–1400

    Article  PubMed  CAS  Google Scholar 

  • Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, Cambridge

    Google Scholar 

  • Press W, Teukolsky S, Vetterling W, Flannery B (2007) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge

    Google Scholar 

  • Pretzsch H, Mette T (2008) Linking stand-level self-thinning allometry to the tree-level leaf biomass alloetry. Trees 22:611–622

    Article  Google Scholar 

  • Prusinkiewicz P, Lindenmayer A (1990) The Algorithmic Beauty of Plants. Springer, New York

    Article  Google Scholar 

  • 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, CA

    Google Scholar 

  • Refsgaard J, Henriksen H (2004) Modeling guidelines – terminology and guiding principles. Adv Water Resour 27:71–82

    Article  Google Scholar 

  • Roderick M, Barnes B (2004) Self-thinning of plant populations from a dynamic viewpoint. Funct Ecol 18:197–203

    Article  Google Scholar 

  • Rodgers N (2000) Learning to reason: an introduction to logic, sets, and relations. Wiley, New York

    Book  Google Scholar 

  • 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: 569–577

    Book  Google Scholar 

  • Schneider D (2001) The rise of the concept of scale in ecology. BioScience 51:545–554

    Article  Google Scholar 

  • 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 York

    Google Scholar 

  • Snyman J (2005) Practical mathematical optimization: an introduction to basic optimization theory and classical and new gradient-based algorithms. Springer, Berlin

    Google Scholar 

  • Sole R, Bascompte J (2006) Self-organization in complex ecosystems. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Spelke ES (2005) Sex differences in intrinsic aptitude for mathematics and science? Am Psychol 60:950–958

    Article  PubMed  Google Scholar 

  • Srivastava L (2002) Plant growth and development. Academic, San Diego, CA

    Google Scholar 

  • Steiner G (2001) Grammars of creation. Yale University Press, New Haven, CT and London

    Google Scholar 

  • 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, CA

    Google Scholar 

  • 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 14:136–145

    Article  PubMed  CAS  Google Scholar 

  • 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 53:959–970

    Article  PubMed  CAS  Google Scholar 

  • Sweetlove L, Fernie A (2005) Regulation of metabolic networks: understanding metabolic complexity in the systems biology era. New Phytol 168:9–24

    Article  PubMed  CAS  Google Scholar 

  • Thagard P, Zhu R (2003) Acupuncture, incommensurability, and conceptual change. In: Sinatra G, Pintrich P (eds) Intentional conceptual change. Lawrence Erlbaum Associates, Mahwah, NJ

    Google Scholar 

  • Thomas A, Benson M (1975) Generalization of streamflow characteristics from drainage basin characteristics. U.S. Geological Survey. Water-Supply Paper

    Google Scholar 

  • Turner M, Dale V, Gardner R (1989) Predicting across scales: theory development and testing. Landscape Ecol 3:245–252

    Article  Google Scholar 

  • 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, Berlin

    Chapter  Google Scholar 

  • Uetz P, Finley R (2005) From protein networks to biological systems. FEBS Lett 579:1821–1827

    Article  PubMed  CAS  Google Scholar 

  • Varley R, Siegal M (2000) Evidence for cognition without grammar from causal reasoning and theory of mind in an agrammatic aphasic patient. Curr Biol 10:723–726

    Article  PubMed  CAS  Google Scholar 

  • Ver Hoef J, Glenn-Lewin D (1989) Multiscale ordination: a method for detecting pattern at several scales. Vegetatio 82:59–67

    Google Scholar 

  • Weller D (1991) The self-thinning rule: dead or unsupportable? – a reply to Donsdale. Ecology 72:747–750

    Article  Google Scholar 

  • 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 208:1575–1592

    Article  PubMed  Google Scholar 

  • West G, Brown J, Enquist B (1999) A general model for the structure and allometry of plant vascular system. Nature 400:664–667

    Article  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • White J (1981) The allometric interpretation of the self-thinning rule. J Theor Biol 89:475–500

    Article  Google Scholar 

  • 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, Oxford

    Google Scholar 

  • 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 14:107–129

    Article  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matthias Langensiepen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Langensiepen, M. (2010). Fundamentals of Model Scaling in Forest Ecology. In: Bredemeier, M., Cohen, S., Godbold, D., Lode, E., Pichler, V., Schleppi, P. (eds) Forest Management and the Water Cycle. Ecological Studies, vol 212. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9834-4_21

Download citation

Publish with us

Policies and ethics