Mathematical Models

Models are coherent representations of systems and/or of the processes therein, and may consist of words (‘word models’), graphs or equations. Words alone can often describe complex systems or processes adequately, as in the case of natural selection (Darwin 1859).* Graphs can also make compelling cases, as did, for example, the trophic pyramid of Lindeman (1942). However, equations that capture essential aspects of systems or processes always outperform word or graph models, if only because the application of standard albebraic or other mathematical rules to these equations often leads to the discovery of unkonwn properties of the systems or processes in question. This non-intuitive, and in fact wondrous property of mathematical descriptions (Wigner 1960) has, moreover, the distinct advantage of allowing the testing of hypotheses about future states, or previoiusly unobserved features of ecosystems, besides allowing for testing the adequacy of the initial description (p. 212, Pauly & Christensen, 2002, Ecosystem Models, in Handbook of Fish Biology and Fisheries, vol. 2, Hart & Reynolds (eds.), pp. 211 – 227).

* See Pauly & Christensen (2002) for references.

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