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Scale and Scaling in Ecological and Economic Systems

  • Conference paper
The Economics of Non-Convex Ecosystems

Part of the book series: The Economics of Non-Market Goods and Resources ((ENGO,volume 4))

Abstract

We review various aspects of the notion of scale applied to natural systems, in particular complex adaptive systems. We argue that scaling issues are not only crucial from the standpoint of basic science, but also in many applied issues, and discuss tools for detecting and dealing with multiple scales, both spatial and temporal. We also suggest that the techniques of statistical mechanics, which have been successful in describing many emergent patterns in physical systems, can also prove useful in the study of complex adaptive systems.

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References

  • Amaral, L., S. Buldyrev, S. Havlin, H. Leschhon, P. Maas, H. E. Stanley and M. Stanley (1997), ‘Scaling Behavior in Economics. I. Empirical Results for Company Growth’, Journal de Physique 7, 621–633.

    Google Scholar 

  • Andow, D. A., P. M. Kareiva, S. A. Levin and A. Okubo (1990), ‘Spread of Invading Organisms’, Landscape Ecology 4, 177–188.

    Article  Google Scholar 

  • Arnol’d., V. I. (1986), Catastrophe Theory. Berlin: Springer-Verlag, 108 pp.

    Google Scholar 

  • Arrhenius, O. (1921), ‘Species and Area’, Journal of Ecology 9, 95–99.

    Google Scholar 

  • Arrow, K., G. Daily, P. Dasgupta, S. Levin, K.-G. Maler, E. Maskin, D. Starrett, T. Sterner and T. Toetenberg (2000), ‘Managing Ecosystem Resources’, Environmental Science and Technology 34, 1401–1406. Website http://dx.doi.org/10.1021/ES990672T.

    Article  CAS  Google Scholar 

  • Bak, P. and K. Sneppen (1993), ‘Punctuated Equilibrium and Criticality in a Simple Model of Evolution’, Physical Review Letters 71, 4083–4086.

    Article  CAS  ADS  PubMed  Google Scholar 

  • Bak, P., C. Tang and K. Wiesenfeld (1988), ‘Self-organized Criticality’, Physical Review A 38, 364–374.

    Article  ADS  PubMed  MathSciNet  Google Scholar 

  • Barabási, A.-L., S. V. Buldyrev, H. E. Stanley and B. Suki (1996), ‘Avalanches in the Lung: A Statistical Mechanical Model’, Physical Review Letters 76, 2192–2195.

    ADS  PubMed  Google Scholar 

  • Batchelor, G. K. (1953). The Theory of Homogeneous Turbulence. Cambridge University Press.

    Google Scholar 

  • Binney, J. J., N. J. Dowrick, A. J. Fisher and M. E. J. Newman (1992), The Theory of Critical Phenomena-An Introduction to the Renormalization Group. Oxford: Oxford Science Publications, Clarendon Press, 464 pp.

    Google Scholar 

  • Bogoliubov, N. N. (1946), Studies in Statistical Mechanics, in J. de Boer and G. E. Uhlenbeck, eds. Amsterdam: North-Holland Publishing Company.

    Google Scholar 

  • Bogoliubov, N. N. and D. V. Shirkov (1959), Introduction to the Theory of Quantized Fields. New York: Interscience Publishers, 720 pp.

    Google Scholar 

  • Bouchaud, J.-P. and M. Potters (2000), Theory of Financial Risks. Cambridge University Press.

    Google Scholar 

  • Broadbent, S. R. and J. M. Hammersley (1957), ‘Percolation Processes’, Proceedings of the Cambridge Philosophical Society 53, 629–645.

    CAS  MathSciNet  Google Scholar 

  • Brock (1999), ‘Scaling in Economics: A Reader’s Guide’, Industrial and Corporate Change 8, 409–446.

    Article  MathSciNet  Google Scholar 

  • Brown, J. H. and M. V. Lomolino (1998), Biogeography. Sinauer: Sunderland Mass.

    Google Scholar 

  • Buttel, L., R. Durrett and S. Levin (2002), ‘Competition and Species Packing in Patchy Environments’, Theoretical Population Biology 61, 265–276.

    Article  PubMed  Google Scholar 

  • Calder III, W. A. (1984), Size, Function, and Life History. Cambridge Mass: Harvard University Press.

    Google Scholar 

  • Carpenter, S. R., D. Ludwig and W. A. Brock (1999), ‘Management of Eutrophication for Lakes Subject to Potentially Irreversible Change’, Ecological Applications 9, 751–771.

    Google Scholar 

  • Chave, J., M. Dubios and B. Riéra (2001), ‘Estimation of Biomass in a Neotropical Forest of French Guiana: Spatial and Temporal Variability’, Journal of Tropical Ecology 17, 79–96.

    Article  Google Scholar 

  • Chave, J., H. Muller-Landau and S. Levin (2002), ‘Comparing Classical Community Models: Theoretical Consequences for Patterns of Diversity’, American Naturalist 159, 1–23.

    Google Scholar 

  • Clark, J. S. C. Fastie, G. Hurtt, S. T. Jackson, C. Johnson, G. King and M. Lewis (1998) ‘Reid’s Paradox of Rapid Plant Migration’, BioScience 48, 13–24.

    Google Scholar 

  • Clark, J. S. (1998), ‘Why Trees Migrate So Fast: Confronting Theory with Dispersal Biology and the Paleorecord’, American Naturalist 152, 204–224.

    Article  Google Scholar 

  • Connor, E. F. and E. D. McCoy (1979), ‘The Statistics and Biology of the Species-area Relationship’, American Naturalist 113, 791–833.

    Article  MathSciNet  Google Scholar 

  • Crawley, M. J. and J. E. Harral (2001), ‘Scale Dependence in Plant Biodiversity’, Science 291, 864–868.

    Article  CAS  ADS  PubMed  Google Scholar 

  • Durlauf, S. (1993), ‘Nonergodic Economic Growth’, Review of Economic Studies 60, 349–366.

    MATH  Google Scholar 

  • Durrett, R. and S. Levin (1994), ‘Stochastic Spatial Models: A User’s Guide to Ecological Applications’, Philosophical Transactions of the Royal Society of London B 343, 329–350.

    ADS  Google Scholar 

  • Durrett, R. and S. A. Levin (1996), ‘Spatial Models for Species-area Curves’, Journal of Theoretical Biology 179, 119–127.

    Article  Google Scholar 

  • Earn, D., S. Levin and P. Rohani (2000), ‘Coherence and Conservation’, Science 290, 1360–1363.

    Article  CAS  ADS  PubMed  Google Scholar 

  • Enquist, B. J., J. H. Brown and G. H. West (1998), ‘Allometric Scaling of Plant Energentics and Population Density’, Nature 395, 163–165.

    Article  CAS  Google Scholar 

  • Ferziger, J. H. and H. G. Kaper (1972), Mathematical Theory of Transport Processes in Gas. Amsterdam, London: North-Holland Publishing Company, 579 pp.

    Google Scholar 

  • Fisher, F. M. and A. Ando (1971), ‘Two Theorems on “Ceteris Paribus” in the Analysis of Dynamic Systems’, in H. M. Blalock Jr., ed., Causal Models in the Social Sciences (pp. 190–199). Chicago: Aldine Publishing Co.

    Google Scholar 

  • Flierl, G., D. Grünbaum, S. Levin and D. Olson (1999), ‘From Individuals to Aggregations: The Interplay between Behavior and Physics’, Journal of Theoretical Biology 196, 397–454.

    Article  CAS  PubMed  Google Scholar 

  • Fortuin, C. M. and P. W. Kastelyn (1972), ‘On the Random Cluster Model, I. Introduction and Relation to Other Models’, Physica 57, 536–564.

    Article  MathSciNet  Google Scholar 

  • Fragoso, J. (1997), ‘Tapir-generated Seed Shadows: Scale-dependent Patchiness’, Journal of Ecology 85, 519–529.

    Google Scholar 

  • Frisch, U. (1995), Turbulence: The Legacy of A.N. Kolmogorov. Cambridge: Cambridge University Press, 296 pp.

    Google Scholar 

  • Gell-Mann, M. (1994), The Quark and the Jaguar. New York: Freeman and Co.

    Google Scholar 

  • Gentry, A. H. (1992), ‘Tropical Forest Diversity: Distributional Patterns and Their Conservational Significance’, Oikos 63, 19–28.

    Google Scholar 

  • Grassberger, P. and A. de la Torre (1979), Reggeon Field Theory (Schlogl’s First Model) on a Lattice: Monte-Carlo Calculations of Critical Behaviour’, Annals of Physics 122, 373.

    Article  CAS  Google Scholar 

  • Guckenheimer, J. (2000), Numerical computation of canards. Website http://www.cam.cornell.edu/guckenheimer/timescale.html.

  • Harris, T. E. (1974), ‘Contact Interactions on a Lattice’, Annals of Probability 2, 969.

    MATH  Google Scholar 

  • Harte, J., A. Kinzig and J. Green (1999), ‘Self-similarity in the Abundance of Species’, Science 284, 334–336.

    Article  CAS  ADS  PubMed  Google Scholar 

  • Hastings, H. M. and G. Sugihara (1993), Fractals. A User’s Guide for the Natural Sciences. Oxford: Oxford Science Publications, Oxford University Press, 235 pp.

    Google Scholar 

  • Haury, L. R., J. A. McGowan and P. H. Wiebe (1978), ‘Patterns and Processes in the Time-space Scales of Plankton Distributions’, in J. H. Steele, ed., Spatial Pattern in Plankton Communities (pp. 277–327). New York, U.S.A.: Plenum.

    Google Scholar 

  • Hinrichsen, H. (2000), ‘Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States’, Advances of Physics 49, 815. Available online at http://xxx.lanl.gov (Los Alamos e-archive), section Condensed Matter, number cond-mat/0001070, 153 pp.

    CAS  ADS  Google Scholar 

  • Horn, H. S. (2000), ‘Twigs, Trees, and the Dynamics of Carbon in the Landscape’, in J. H. Brown and G. B. West, eds., Scaling in Biology (pp. 199–220). Santa Fe Institute, Oxford University Press, 352 pp.

    Google Scholar 

  • Hubbell, S. P. (1997), ‘A Unified Theory of Biogeography and Relative Species Abundance and Its Application to Tropical Rain Forests and Coreal Reefs’, Coral Reefs 16, S9–S21.

    Article  Google Scholar 

  • Ijiri, Y. (1971), ‘Fundamental Queries in Aggregation Theory’, Journal of the American Statistical Association 66, 766–782.

    MATH  Google Scholar 

  • Ijiri, Y. and H. Simon (1977), Skew Distributions and the Size of Business Firms. Amsterdam: North Holland.

    Google Scholar 

  • Iwasa, Y., S. A. Levin and V. Andreasen (1987), ‘Aggregation in Model Ecosystems. I. Perfect Aggregation’, Ecological Modelling 37, 287–302.

    Article  Google Scholar 

  • Iwasa, Y., S. A. Levin and V. Andreasen (1989), ‘Aggregation in Model Ecosystems. II. Approximate Aggregation’, IMA Journal of Mathematics Applied in Medicine 6, 1–23.

    MathSciNet  Google Scholar 

  • Jacob, F. (1977), ‘Evolution and Tinkering’, Science 196, 1161–1166.

    CAS  ADS  PubMed  Google Scholar 

  • Kadanoff, L. P. (1966), ‘Scaling Laws for Ising Models near T c ’, Physics 2, 263.

    Google Scholar 

  • Kauffman, S. (1993), The Origins of Order. Oxford: Oxford University Press.

    Google Scholar 

  • Kesten, H. (1980), ‘The Critical Probability for Bond Percolation on the Square Lattice Equals 1/2’, Communications in Mathematical Physics 74, 41–59.

    Article  MATH  MathSciNet  Google Scholar 

  • Kinzig, A. P., S. A. Levin, J. Dushoff and S. W. Pacala (1999), ‘Limiting Similarity, Species Packing, and System Stability for Hierarchical Competition-colonization Models’, American Naturalist 153, 371–383.

    Google Scholar 

  • Kolmogorov, A. N. (1941), ‘The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Number’, Comptes Rendus Académie des Sciences URSS 30, 301.

    MATH  Google Scholar 

  • Levin, S. A. (1979), ‘Non-uniform Stable Solutions to Reaction-diffusion Equations: Applications to Ecological Pattern Formation’, in H. Haken, ed., Pattern Formation by Dynamic Systems and Pattern Recognition (pp. 210–222). Berlin: Springer-Verlag.

    Google Scholar 

  • Levin, S. A. and L. A. Segel (1985), ‘Pattern Generation in Space and Aspect’, SIAM Review 27, 45–67.

    Article  MathSciNet  Google Scholar 

  • Levin, S. A. (1991), ‘The Problem of Relevant Detail’, in S. Busenberg and M. Martelli, eds., Differential Equations. Models in Biology, Ecology, and Epidemiology (pp. 9–15). Springer Verlag.

    Google Scholar 

  • Levin, S. A. (1992), ‘The Problem of Pattern and Scale in Ecology’, Ecology 73, 1943–1967.

    Google Scholar 

  • Levin, S. A. (1993), ‘Concept of Scale at the Local Level’, in J. R. Ehlringer and C. B. Field, eds., Scaling Physiological Processes. Leaf to Globe (pp. 7–19). Academic Press, 388 pp.

    Google Scholar 

  • Levin, S. A. (2000), ‘Complex Adaptive Systems: Exploring the Known, the Unknown and the Unknowable’, in F. Browder, ed., Mathematical Challenges of the XXIth Century. American Mathematical Society, Providence RI.

    Google Scholar 

  • Levin, S. A., A. Morin and T. H. Powell (1989), ‘Patterns and Processes in the Distribution and Dynamics of Antartic Krill’, in Scientific Committee for the Conservation of Antarctic Marine Living Resources-Selected Scientific Papers, Part 1, SC-CAMLR-SSp/5 (pp. 281–299). Australia: Hobart, Tasmania.

    Google Scholar 

  • Levin, S. A. and S. W. Pacala (1997), ‘Theories of Simplification and Scaling of Spatially Distributed Processes’, in D. Tilman and P. Kareiva, eds., Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions (pp. 271–296). Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Levin, S. A. (1999), Fragile Dominion. Massachussets: Helix Books, Perseus Reading.

    Google Scholar 

  • Levins, R. (1968), Evolution in Changing Environments. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Li, G. and H. Rabitz (1991a), ‘A General Lumping Analysis of a Reaction System Coupled with Diffusion’, Chemical Engineering Science 46, 2041.

    CAS  Google Scholar 

  • Li, G. and H. Rabitz (1991b), ‘A General Analysis of Lumping’, in G. Astarita and S. I. Sandler, eds., Chemical Kinetics, in Kinetic and Thermodynamic Lumping of Multicomponent Mixtures (pp. 49–62). Amsterdam: Elsevier Science Publishers B.V.

    Google Scholar 

  • Lin, C. C. and L. A. Segel (1974), Mathematics Applied to Deterministic Problems in the Natural Sciences. New York: Macmillan.

    Google Scholar 

  • Ludwig, D. and C. J. Walters (1985), ‘Are Age-structured Models Appropriate for Catch-effort Data?’, Canadian Journal of Fish Aquatic Science 42, 1066–1072.

    Google Scholar 

  • Ludwig, D., D. D. Jones and C. S. Holling (1978), ‘Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest’, Journal of Animal Ecology 47, 315–332.

    Google Scholar 

  • MacAuley, F. R. (1922), ‘Pareto’s Laws and the General Problem of Mathematically Describing the Frequency of Income’, Income in the United States: Its Amount ands Distribution 1909–1919. New York: National Bureau of Economic Research.

    Google Scholar 

  • Major, J. Endemism (a botanical perspective), In A. A. Myers and P. S. Giller, eds., Analytical Biogeography-An Integrated Approach to the Study of Animal and Plant Distributions (pp. 117–146). London: Chapman and Hall.

    Google Scholar 

  • Makse, H. A., S. Havlin and H. E. Stanley (1995), ‘Modelling Urban Growth Patterns’, Nature 377, 608–612.

    Article  CAS  ADS  Google Scholar 

  • Malamud, B. D., G. Morein and D. L. Turcotte (1998), ‘Forest Fires: An Example of Self-organized Critical Behavior’, Science 281, 1840–1842.

    Article  CAS  ADS  PubMed  Google Scholar 

  • Mandelbrot, B. B. (1963), ‘New Methods in Statistical Economics’, Journal of Political Economy 71, 421–440.

    Google Scholar 

  • Mandelbrot, B. B. (1975), Les Objets Fractals. Forme, Hasard et Dimension. Flammarion, Paris: Nouvelle Bibliothèque Scientifique, 190 pp.

    Google Scholar 

  • Mandelbrot, B. B. (1997), Fractals and Scaling in Finance. Springer-Verlag.

    Google Scholar 

  • May, R. M. (1974), ‘Biological Populations with Non-overlapping Generations: Stable Points, Stable Cycles, and Chaos’, Journal of Theoretical Biology 49, 511–524.

    Google Scholar 

  • May, R. M. and P. F. Stumpf (2000), ‘Species-area Relationships for Tropical Forests’, Science 290, 2084–2086.

    CAS  PubMed  Google Scholar 

  • McMahon, T. A. (1975), ‘The Mechanical Design of Trees’, Scientific American 233, 93–102.

    Google Scholar 

  • Mills, T. C. (1999), The Econometric Modelling of Financial Time Series. Cambridge University Press, 372 pp.

    Google Scholar 

  • Mollison, D. and S. A. Levin (1995), ‘Spatial Dynamics of Parasitism’, in B. T. Greenfell and A. P. Dobson, eds., Ecology of Infectious Diseases in Natural Populations (pp. 384–398). Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Nathan, R., U. N. Safriel, I. Noy-Meir and G. Schiller (2000), ‘Spatiotemporal Variation in Seed Dispersal and Recruitment near and Far From Pinus Halepensis Trees’, Ecology 81, 2156–2161.

    Google Scholar 

  • Nathan, R. (2001), ‘Dispersal Biogeography’, in S. Levin, ed., Encyclopedia of Biodiversity (pp. 127–152). Academic Press.

    Google Scholar 

  • Niklas, K. (1992), Plant Biomechanics: An Engineering Approach to Plant Form and Function. Chicago and London: University of Chicago Press, 607 pp.

    Google Scholar 

  • O’Brien, S. T., S. P. Hubbell, P. Spiro, R. Condit and R. B. Foster (1995), ‘Diameter, Height, Crown and Age Relationships in Eight Neotropical Tree Species’, Ecology 76, 1926–1939.

    Google Scholar 

  • Okubo, A. and S. A. Levin (1989), ‘A Theoretical Framework for Data Analysis of Wind Dispersal of Seeds and Pollen. Ecology 70, 329–338.

    Google Scholar 

  • Pareto, V. (1896), Cours d’Economie Politique. Reprinted in Pareto. Oeuvres Complètes. Droz, Geneva, 1965.

    Google Scholar 

  • Peters, R. H. (1983), The Ecological Implications of Body Size. Cambridge: Cambridge University Press, 324 pp.

    Google Scholar 

  • Pitman N. C. A., J. Terborgh, M. R. Silman and P. V. Nuñez (1999), ‘Tree Species Distribution in an Upper Amazonian Forest’, Ecology 80, 2651–2661.

    Google Scholar 

  • Plotkin J. B., M. D. Potts, D. W. Yu, S. Bunyavejchewin, R. Condit, R. Foster, S. Hubbell, J. LaFrankie, N. Manokaran, L. Hua Seng, R. Sukumar, M. A. Nowak and P. S. Ashton (2000), ‘Predicting Species Diversity in Tropical Forests’, Proceedings of the National Academy of Sciences U.S.A. 97, 10850–10854.

    CAS  ADS  Google Scholar 

  • Plotkin, J. B., J. Chave and P. S. Ashton (2002), ‘Cluster Analysis of Spatial Patterns in Malaysian Tree Species’, American Naturalist 60, 629–644.

    Google Scholar 

  • Prance, G. T. (1973), ‘Phytogeographic Support for the Theory of Pleistocene Forest Refuges in the Amazon Basin, Based on Evidence from Distribution Patterns in Caryocaraceae, Chrysobalanaceae, Dichapetalaceae and Lecythidaceae’, Acta Amazônica 3, 5–28.

    Google Scholar 

  • Prance, G. T. (1978), ‘Floristic Inventory of the Tropics: Where Do We Stand?’, Annals of the Missouri Botanical Garden 64, 659–684.

    Google Scholar 

  • Prance, G. T. (1994), ‘A Comparison of the Efficacy of Higher Taxa and Species Numbers in the Assessment of Biodiversity in the Tropics’, Philosophical Transactions of the Royal Society of London B 345, 89–99.

    ADS  Google Scholar 

  • Reynolds, P. J., W. Klein and H. E. Stanley (1977), ‘A Real-space Renormalization Group for Site and Bond Percolation’, Journal of Physics C 10, L167.

    CAS  ADS  Google Scholar 

  • Rodríguez-Iturbe, I. and A. Rinaldo (1997), Fractal River Basins. Chance and Self-Organization. Cambridge: Cambridge University Press, 547 pp.

    Google Scholar 

  • Schmidt-Nielsen, K. (1984), Scaling. Why is Animal Size so Important? Cambridge: Cambridge University Press, 241 pp.

    Google Scholar 

  • Segel, L. A. and S. A. Levin (1976), ‘Applications of Nonlinear Stability Theory to the Study of the Effects of Diffusion on Predator Prey Interactions’, in R. A. Piccirelli, ed., Topics in Statistical Mechanics and Biophysics: A Memorial to Julius L. Jackson. AIP New York.

    Google Scholar 

  • Shinozaki, K., K. Yoda, K. Hozumi and T. Kira (1964), ‘A Quantitative Analysis of Plant Form-The Pipe Model Theory I. Basic Analyses’, Japanese Journal of Ecology 14, 97–105.

    Google Scholar 

  • Simon, H. A. and A. Ando (1961), ‘Aggregation of Variables in Dynamic Systems’, Econometrica 29, 111–138.

    Google Scholar 

  • Skellam, J. G. (1951), ‘Random Dispersal in Theoretical Populations’, Biometrika 38, 196–218.

    CAS  MATH  PubMed  MathSciNet  Google Scholar 

  • Sornette, A. and D. Sornette (1989), ‘Self-organized Criticality and Earthquakes’, Europhysics Letters 9, 197–202.

    ADS  Google Scholar 

  • Stanley, H. E. (1971), Introduction to Phase Transitions and Critical Phenomena. Oxford: Oxford Science Publications, Clarendon Press.

    Google Scholar 

  • Stull, R. B. (1988), An Introduction to Boundary Layer Meteorology. Dordrecht, Boston, London: Atmospheric Sciences Library, Kluwer Academic Publishers, 670 pp.

    Google Scholar 

  • Thom, R. (1983), Mathematical Models of Morphogenesis. New York: Halsted Press, 305 pp.

    Google Scholar 

  • Turing, A. (1952), ‘The Chemical Basis of Morphogenesis’, Philosophical Transactions of the Royal Society of London B 237, 37–72.

    ADS  Google Scholar 

  • Tykhonov, A. N. (1952), Systems of Differential Equations Containing Small Parameters Multiplying the Derivatives. Mat.

    Google Scholar 

  • Vogel, S. (1994), Life in Moving Fluids. Princeton, NJ: Princeton University Press, 467 pp.

    Google Scholar 

  • West, G. B., J. H. Brown and B. J. Enquist (1997), ‘A General Model for the Origin of Allometric Scaling Laws in Biology’, Science 276, 122–126.

    Article  CAS  PubMed  Google Scholar 

  • Whittaker, R. J., M. B. Bush and K. Richards (1989), ‘Plant Recolonization and Vegetation Succession on the Krakatau Islands, Indonesia’, Ecological Monographs 59, 59–123.

    Google Scholar 

  • Williams, C. B. (1964), Patterns in the Balance of Nature and Related Problems in Quantitative Ecology. New York: Academic Press.

    Google Scholar 

  • Wilson, K. G. and J. Kogut (1974), ‘The Renormalization Group and the ε-expansion’, Physics Reports 12C, 75–200.

    ADS  Google Scholar 

  • Yeomans, J. M. (1992), Statistical Mechanics of Phase Transitions. Oxford: Oxford Science Publications, Clarendon Press, 153 pp.

    Google Scholar 

  • Zipf, G. K. (1949), Human Behavior and the Principle of Least Effort. Addison Wesley.

    Google Scholar 

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Author notes

  1. Jérôme Chave

    Present address: Laboratoire Evolution et Diversité Biologique, CNRS UMR 5174, 118 route de Narbone, F31062, Toulouse, France

Authors and Affiliations

  1. Department of Ecology and Evolutionary Biology, Guyot Hall, Princeton University, Princeton, NJ, 08544-1003, USA

    Simon Levin

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  1. Jérôme Chave
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Editors and Affiliations

  1. Faculty of Economics, Cambridge University, Cambridge, UK

    Partha Dasgupta

  2. Beijer International Institute of Ecological Economics, Royal Swedish Academy of Sciences, Stockholm, Sweden

    Karl-Göran Mäler

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Chave, J., Levin, S. (2004). Scale and Scaling in Ecological and Economic Systems. In: Dasgupta, P., Mäler, KG. (eds) The Economics of Non-Convex Ecosystems. The Economics of Non-Market Goods and Resources, vol 4. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2515-7_2

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  • DOI: https://doi.org/10.1007/1-4020-2515-7_2

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