EAI Endorsed Transactions on Complex Systems 13(2): e2

Research Article

Power-law of Aggregate-size Spectra in Natural Systems

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  • @ARTICLE{10.4108/trans.cs.1.2.e2,
        author={Matteo Convertino and Filippo Simini and Filippo Catani and Igor Linkov and Gregory A. Kiker},
        title={Power-law of Aggregate-size Spectra in Natural Systems},
        journal={EAI Endorsed Transactions on Complex Systems},
        keywords={aggregate-size, fractal dimension, river basins, networks, systems, allometry},
  • Matteo Convertino
    Filippo Simini
    Filippo Catani
    Igor Linkov
    Gregory A. Kiker
    Year: 2013
    Power-law of Aggregate-size Spectra in Natural Systems
    DOI: 10.4108/trans.cs.1.2.e2
Matteo Convertino1,2,3,4, Filippo Simini5, Filippo Catani6, Igor Linkov2,7, Gregory A. Kiker1,3,4
  • 1: Department of Agricultural and Biological Engineering - IFAS, University of Florida, Gainesville, FL, USA
  • 2: Florida Climate Institute, c/o University of Florida, and Sustainable-UF, Gainesville, FL, USA
  • 3: Contractor of the US Army Corps of Engineers at the Risk and Decision Science Team, Engineer Research and Development
  • 4: Center (ERDC), Concord, MA, USA
  • 5: Center for Complex Network Research (Barabasi Lab), Department of Physics, Northeastern University, Boston, MA
  • 6: Engineering Geology and Geomorphology Unit, Department of Earth Sciences, Università di Firenze, Firenze, IT
  • 7: Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA, USA


Patterns of animate and inanimate systems show remarkable similarities in their aggregation. One similarity is the double-Pareto distribution of the aggregate-size of system components. Different models have been developed to predict aggregates of system components. However, not many models have been developed to describe probabilistically the aggregate-size distribution of any system regardless of the intrinsic and extrinsic drivers of the aggregation process. Here we consider natural animate systems, from one of the greatest mammals - the African elephant (Loxodonta africana) - to the Escherichia coli bacteria, and natural inanimate systems in river basins. Considering aggregates as islands and their perimeter as a curve mirroring the sculpting network of the system, the probability of exceedence of the drainage area, and the Hack’s law are shown to be the the Korˇcak’s law and the perimeter-area relationship for river basins. The perimeter-area relationship, and the probability of exceedence of the aggregate-size provide a meaningful estimate of the same fractal dimension. Systems aggregate because of the influence exerted by a physical or processes network within the system domain. The aggregate-size distribution is accurately derived using the null-method of box-counting on the occurrences of system components. The importance of the aggregate-size spectrum relies on its ability to reveal system form, function, and dynamics also as a function of other coupled systems. Variations of the fractal dimension and of the aggregate-size distribution are related to changes of systems that are meaningful to monitor because potentially critical for these systems.