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Aiming the “unreasonable effectiveness of mathematics” at ecological theory

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  • Ginzburg, Lev R.
  • Jensen, Christopher X.J.
  • Yule, Jeffrey V.

Abstract

A good theory is focused without being blurred by extraneous detail or overgenerality. Yet ecological theories frequently fail to achieve this desirable middle ground. Here, we review the reasons for the mismatch between what theorists seek to achieve and what they actually accomplish. In doing so, we argue on pragmatic grounds against mathematical literalism as an appropriate constraint to mathematical constructions: such literalism would allow mathematics to constrain biology when the biology ought to be constraining mathematics. We also suggest a method for differentiating theories with the potential to be “unreasonably effective” from those that are simply overgeneral. Simple axiomatic assumptions about an ecological system should lead to theoretical predictions that can then be compared with existing data. If the theory is so general that data cannot be used to test it, the theory must be made more specific.

Suggested Citation

  • Ginzburg, Lev R. & Jensen, Christopher X.J. & Yule, Jeffrey V., 2007. "Aiming the “unreasonable effectiveness of mathematics” at ecological theory," Ecological Modelling, Elsevier, vol. 207(2), pages 356-362.
    • Handle: RePEc:eee:ecomod:v:207:y:2007:i:2:p:356-362
    DOI: 10.1016/j.ecolmodel.2007.05.015
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    References listed on IDEAS

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    1. Schizas, Dimitrios & Stamou, George, 2007. "What ecosystems really are—Physicochemical or biological entities?," Ecological Modelling, Elsevier, vol. 200(1), pages 178-182.
    2. Edward McCauley & Roger M. Nisbet & William W. Murdoch & Andre M. de Roos & William S. C. Gurney, 1999. "Large-amplitude cycles of Daphnia and its algal prey in enriched environments," Nature, Nature, vol. 402(6762), pages 653-656, December.
    3. Christina M. K. Kaunzinger & Peter J. Morin, 1998. "Productivity controls food-chain properties in microbial communities," Nature, Nature, vol. 395(6701), pages 495-497, October.
    4. Aumann, Craig A., 2007. "A methodology for developing simulation models of complex systems," Ecological Modelling, Elsevier, vol. 202(3), pages 385-396.
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    Cited by:

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    2. Sakanoue, Seiichi, 2009. "A resource-based approach to modelling the dynamics of interacting populations," Ecological Modelling, Elsevier, vol. 220(11), pages 1383-1394.

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