Equation or Algorithm: Differences and Choosing Between Them
 C. Gaucherel,
 S. Bérard,
 F. Munoz
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The issue of whether formal reasoning or a computingintensive approach is the most efficient manner to address scientific questions is the subject of some considerable debate and pertains not only to the nature of the phenomena and processes investigated by scientists, but also the nature of the equation and algorithm objects they use. Although algorithms and equations both rely on a common background of mathematical language and logic, they nevertheless possess some critical differences. They do not refer to the same level of symbolization, as equations are based on integrated concepts in a denotational manner, while algorithms specifically break down a complex problem into more elementary operations, in an operational manner. They may therefore be considered as suited to the representation of different phenomena. Specifically, algorithms are by nature sufficient to represent weak emergent phenomena, but not strong emergent patterns, while equations can do both. Finally, the choice between equations and algorithms are by nature sufficient to represent weak emergent phenomena, but not strong emergent patterns, while equations behave conversely. We propose a simplified classification of scientific issues for which both equation and/or algorithmbased approaches can be envisaged, and discuss their respective pros and cons. We further discuss the complementary and sometimes conflicting uses of equations and algorithms in a context of ecological theory of metapopulation dynamics. We finally propose both conceptual and practical guidelines for choosing between the alternative approaches.
 Title
 Equation or Algorithm: Differences and Choosing Between Them
 Journal

Acta Biotheoretica
Volume 59, Issue 1 , pp 6779
 Cover Date
 201103
 DOI
 10.1007/s1044101091194
 Print ISSN
 00015342
 Online ISSN
 15728358
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Emergence
 Ecology
 Metapopulation
 Modeling
 Semantics
 Spatial dynamics
 Theory
 Authors

 C. Gaucherel ^{(1)}
 S. Bérard ^{(2)}
 F. Munoz ^{(2)}
 Author Affiliations

 1. INRA—EFPA, UMR AMAP, TAA.51/PS2, 34398, Montpellier, Cedex 5, France
 2. Université Montpellier 2, UMR AMAP, TAA.51/PS2, 34000, Montpellier, France