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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alon U (2007) An introduction to systems biology. Chapman & Hall, London
Aloy P, Russell RB (2006) Structural systems biology: modelling protein interactions. Nat Rev 7:188–197
Barabasi AL, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev 5:101–114
Barenblatt G (2003) Scaling. Cambridge University Press, Cambridge
Barenblatt GI, Chorin AJ (1998) New perspectives in turbulence: scaling laws, asymptotics, and intermittency. SIAM Rev 40:265–291
Becker P, Gribben RJ, Lim CM (2000) Tapered conduits can buffer hydraulic conductance from path-length effects. Tree Physiol 20:965–967
Boulton A, Panizoon D, Prior J (2005) Explicit knowledge structures as a tool for overcoming obstacles to interdisciplinary research. Conserv Biol 19:2026–2029
Boysen Jensen P (1932) Die Stoffproduktion der Pflanzen. Gustav Fischer, Jena
Brutasert W (2005) Hydrology. Cambridge University Press, Cambridge
Cacuci DG (2003) Sensitivity and uncertainty analysis. Chapman & Hall, London
Campbell GS, Norman JM (1998) An Introduction to Environmental Biophysics (2nd ed.). New York: Springer-Verlag. 286 pp
Cates S, Gittlemen J (1997) Reading between the lines – is allometric scaling useful? Tree 12:338–339
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
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
Cruiziat P, Cochard H, Ameglio T (2002) Hydraulic architecture of trees: main concepts and results. Ann For Sci 59:723–752
Dale M (1999) Spatial pattern analysis in plant ecology. Cambridge University Press, Cambridge
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
Dehaene S (1997) The number sense: how the mind creates mathematics. Oxford University Press, Oxford
Enquist B, Brown J, West G (1998) Allometric scaling of plant energetics and population density. Nature 395:163–165
Enquist B, West G, Charnov E, Brown J (1999) Allometric scaling of production and life-history variation in vascular plants. Nature 401:907–911
Ferrari P (2003) Abstraction in mathematics. Phil Trans R Soc Lond B 358:1225–1230
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
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
Godin C (2000) Representing and encoding plant architecture: A review. Ann. For. Sci. 57: 413–438
Haefner JW (2005) Modeling biological systems. Springer, New York
Hatton T, Wu H (1995) Scaling theory to extrapolate individual tree water use to stand water useful? Hydrol Process 9:527–540
Hirose T (2005) Development of the Monsi-Saeki theory on the canopy structure and function. Ann Bot 95:483–494
Holland J, Holyoak K, Nisbett R, Thagard P (1986) Induction – processes of inference, learning, and discovery. MIT Press, Cambridge
Holyoak K, Morrison R (2005) Cambridge handbook of thinking and reasoning. Cambridge University Press, Cambridge
Huxley J (1932) Problems of relative growth. Methuea, Methuea
Johnson-Laird P (2001) Mental models and deduction. Trends Cogn Sci 5:434–442
Kaimal J, Finnigan J (1994) Atmospheric boundary layer flows. Oxford University Press, New York
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
Kimmis J (2008) From science to stewardship: harnessing forest ecology in the service of society. For Ecol Manage 256:1625–1635
King A (1991) Translating models across scales in the landscapes. In: Turner M, Gardner R (eds) Quantitative methods in landscape ecology. Springer, Berlin
Kitano H (2002) Systems biology: a brief overview. Science 295:1662–1664
Konar K (2005) Computational intelligence: principles. techniques and applications. Springer, New York
Kozlowski J, Weiner J (1997) Interspecific allometries are by-products of body size optimization. Am Nat 149:352–380
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
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
Li B, Wu H, Zou G (2000) Self-thinning rule: a causal interpretation from ecological field theory. Ecol Model 132:167–173
Lonsdale W (1990) The self-thinning rule: dead or alive? Ecology 71:1373–1388
McNaughton K, Jarvis P (1991) Effects of spatial scale on stomatal control of transpiration. Agric For Meteorol 54:279–301
Meentemeyer V, Box E (1987) Scale effects in landscape studies. In: Turner M (ed) Landscape heterogeneity and disturbance. Springer, New York
Meinzer F (2002) Co-ordination of vapour and liquid phase water transport properties in plants. Plant Cell Environ 25:265–274
Meinzer F, Bond BJ, Warren J, Woodruff D (2005) Does water transport scale universally with tree size? Funct Ecol 19:558–565
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
Mencuccini M (2002) Hydraulic constraints in the functional scaling of trees. Tree Physiol 22:553–565
Minorsky P (2003) Achieving the in Silicio Plant. Systems biology and the future of plant biological research. Plant Physiol 132:404–409
Monsi M, Saeki T (1952) Über den Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung für die Stoffproduktion. Jpn J Bot 14:22–52
Mosley M, McKerchar A (1993) Streamflow. In: Maidment D (ed) Handbook of hydrology. McGraw-Hill, Columbus
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
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
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
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
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
Passioura J (1996) Simulation models: science, snake oil, education, or engineering? Agron J 88:690–694
Paul M, Foyer C (2001) Sink regulation of photosynthesis. J Exp Bot 52:1383–1400
Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, Cambridge
Press W, Teukolsky S, Vetterling W, Flannery B (2007) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge
Pretzsch H, Mette T (2008) Linking stand-level self-thinning allometry to the tree-level leaf biomass alloetry. Trees 22:611–622
Prusinkiewicz P, Lindenmayer A (1990) The Algorithmic Beauty of Plants. Springer, New York
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
Refsgaard J, Henriksen H (2004) Modeling guidelines – terminology and guiding principles. Adv Water Resour 27:71–82
Roderick M, Barnes B (2004) Self-thinning of plant populations from a dynamic viewpoint. Funct Ecol 18:197–203
Rodgers N (2000) Learning to reason: an introduction to logic, sets, and relations. Wiley, New York
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
Schneider D (2001) The rise of the concept of scale in ecology. BioScience 51:545–554
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
Snyman J (2005) Practical mathematical optimization: an introduction to basic optimization theory and classical and new gradient-based algorithms. Springer, Berlin
Sole R, Bascompte J (2006) Self-organization in complex ecosystems. Princeton University Press, Princeton, NJ
Spelke ES (2005) Sex differences in intrinsic aptitude for mathematics and science? Am Psychol 60:950–958
Srivastava L (2002) Plant growth and development. Academic, San Diego, CA
Steiner G (2001) Grammars of creation. Yale University Press, New Haven, CT and London
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
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
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
Sweetlove L, Fernie A (2005) Regulation of metabolic networks: understanding metabolic complexity in the systems biology era. New Phytol 168:9–24
Thagard P, Zhu R (2003) Acupuncture, incommensurability, and conceptual change. In: Sinatra G, Pintrich P (eds) Intentional conceptual change. Lawrence Erlbaum Associates, Mahwah, NJ
Thomas A, Benson M (1975) Generalization of streamflow characteristics from drainage basin characteristics. U.S. Geological Survey. Water-Supply Paper
Turner M, Dale V, Gardner R (1989) Predicting across scales: theory development and testing. Landscape Ecol 3:245–252
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
Uetz P, Finley R (2005) From protein networks to biological systems. FEBS Lett 579:1821–1827
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
Ver Hoef J, Glenn-Lewin D (1989) Multiscale ordination: a method for detecting pattern at several scales. Vegetatio 82:59–67
Weller D (1991) The self-thinning rule: dead or unsupportable? – a reply to Donsdale. Ecology 72:747–750
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
West G, Brown J, Enquist B (1999) A general model for the structure and allometry of plant vascular system. Nature 400:664–667
West G, Brown J, Enquist B (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122–126
White J (1981) The allometric interpretation of the self-thinning rule. J Theor Biol 89:475–500
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
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
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
Corresponding author
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-90-481-9834-4_21
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9833-7
Online ISBN: 978-90-481-9834-4
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)