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.
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Within this Article
 Introduction
 Theoretical Context and Practical Issues
 Typology of Scientific Questions
 Application in Ecology
 Discussion
 References
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 Aubin D (1997) The withering immortality of Nicolas Bourbaki: a cultural connector at the confluence of mathematics. Sci Context 10:297–342
 Bascompte J (2001) Aggregate statistical measures and metapopulation dynamics. J Theor Biol 209:373–379 CrossRef
 Bascompte J (2003) Extinction threshold: insights from simple models. Ann Zool Fennici 40:99–114
 Bascompte J, Sole RV (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. J Anim Ecol 65(4):465–473 CrossRef
 Bedau MA (2008) Is weak emergence just in the mind? Mind Mach 18(4):443–459 CrossRef
 Berec L (2002) Techniques of spatially explicit individualbased models: construction, simulation, and meanfield analysis. Ecol Model 150(1–2):55–81 CrossRef
 Bolker B, Pacala SW (1997) Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theor Popul Biol 52:179–197 CrossRef
 Boogerd FC, Bruggeman FJ, Richardson RC, Stephan A, Westerhoff HV (2005) Emergence and its place in nature: a case study of biochemical networks. Synthese 145:131–164 CrossRef
 Broad CD (1919) Mechanical explanation and its alternatives. Proc Aristotelian Soc 19:86–124
 Broad CD (1925) In: Kegan Paul T (ed) The mind and its place in nature. Trubner & Co, London
 Buchberger B (1976) Theoretical basis for the reduction of polynomials to canonical forms. ACM SIGSAM Bull 10(3):19–29 CrossRef
 Burris SN, Sankappanavar HP (1981) A course in universal algebra. Springer Verlag, Berlin
 Church A (1941) The calculi of lambdaconversion. Princeton University Press, Princeton
 Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) (eds) Introduction to algorithms, 2nd edn. The Massasuchetts Institute of Technology, USA
 Dewdney AK (1985) Analog gadgets that solve a diversity of problems and raise an array of questions. Sci Am 252(5):18–24 CrossRef
 Epstein J (1999) Agentbased computational models and generative social science. Complexity 4(5):41–60 CrossRef
 Faugeras B, Maury O (2007) Modeling fish population movements: from an individualbased representation to an advectiondiffusion equation. J Theor Biol 247(4):837–848 CrossRef
 Gödel K (1931) Über formal unentscheidbare Sätze der principia mathematica und verwandter systeme. I. Monatshefte für Mathematik und Physik 38:173–198 CrossRef
 Gosselin F (1999) Test of mathematical assumptions behind the ‘incidence function’ estimation process of metapopulations’ dynamic parameters. Math Biosci 159(1):21–32 CrossRef
 Hales TC (2001) The honeycomb conjecture. Discrete Comput Geom 25(1):1–22
 Hanski I (1997) Predictive and practical metapopulation models: the incidence function approach. In: Tilman D, Kareiva P (eds) Spatial ecology—the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, pp 21–45
 Hanski I (1998) Metapopulation dynamics. Nature 396:41–49 CrossRef
 Hanski IA, Gilpin ME (eds) (1997) Metapopulation biology, vol 1. Academic Press, San Diego
 Hoare CAR (1999) A theory of programming: denotational, algebraic and operational semantics, in, http://www.research.microsoft.com/users/thoare/A_theory_of_programming.pdf
 Humphreys P (2004) Extending ourselves: computational science, empiricism, and scientific method. Oxford University Press, Oxford
 Humphreys P (2008) Synchronic and diachronic emergence. Mind Mach 18(4):431–442 CrossRef
 Huneman P (2008) Emergence made ontological? computational versus combinatorial approaches. Philos Sci 75(5):595–607 CrossRef
 Huneman P, Humphreys P (2008) Dynamical emergence and computation: an introduction. Mind Mach 18(4):425–430 CrossRef
 Keeling MJ (2002) Using individualbased simulations to test the Levins metapopulation paradigm. J Anim Ecol 71(2):270–279 CrossRef
 Lande R (1987) Extinction thresholds in demographic models of territorial populations. Am Nat 130:624–635 CrossRef
 Latour B (1987) Science in action, how to follow scientists and engineers through society. Harvard University Press, Cambridge Mass
 Law R, Murrell DJ, Dieckmann U (2003) Population growth in space and time: spatial logistic equations. Ecology 84(1):252–262 CrossRef
 Levi M (2009) The mathematical mechanic: using physical reasoning to solve problems. Princeton University Press, Princeton
 Levins R (1966) Strategy of model building in population biology. Am Sci 54(4):421
 Levins R (1969) Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull Entomol Soc Am 15:237–240
 Morin E (1982) Science avec conscience. Vol. (new edition). Collection Points, Fayard
 Munoz F, Cheptou PO, Kjellberg F (2007) Spectral analysis of simulated species distribution maps provides insights into metapopulation dynamics. Ecol Model 105:314–322 CrossRef
 Ovaskainen O, Sato K, Bascompte J, Hanski I (2002) Metapopulation models for extinction threshold in spatially correlated landscapes. J Theor Biol 215:95–108 CrossRef
 Peck SL (2004) Simulation as experiment: a philosophical reassessment for biological modeling. Trends Ecol Evol 19(10):530–534 CrossRef
 Plotkin GD (2004) A structural approach to operational semantics. J Log Algebraic Program 60–61:17–139
 Saccheri I, Kuussaari M, Kankare M, Vikman P, Fortelius W, Hanski I (1998) Inbreeding and extinction in a butterfly metapopulation. Nature 392
 Schmidt DA (1986) Denotational semantics. A methodology for language development. Allyn and Bacon, Inc., Boston
 Shapiro S (1997) Philosophy of mathematics: structure and ontology. Oxford University Press, Oxford
 Solé RV, Manrubia SC, Benton M, Kauffman S, Bak P (1999) Criticality and scaling in evolutionary ecology. Trends Ecol Evol 14(4):156–160 CrossRef
 Stephan A (1999) Varieties of emergentism. Evol Cogn 5(1):49–59
 Szpiro G (2003) Mathematics: does the proof stack up? Nature 424(6944):12–13 CrossRef
 Turing AM (1936) On computable numbers, with an application to the entscheidungsproblem. Proc Lond Math Soc 2(42):230–265
 Turner R, Eden AH (2007) The philosophy of computer science: introduction to the special issue. Mind Mach 17(2):129–133 CrossRef
 Vuorinen V, Peltomaki M, Rost M, Alava MJ (2004) Networks in metapopulation dynamics. Euro Phys J B 38(2):261–268 CrossRef
 Wigner E (1982) On science and its evolution. J Phys 43(NC8):435–438
 With KA, King AW (1999) Extinction thresholds for species in fractal landscapes. Conserv Biol 13(2):314–326 CrossRef
 Wolfram S (2002) A new kind of science. Wolfram media, Champaign
 Title
 Equation or Algorithm: Differences and Choosing Between Them
 Journal

Acta Biotheoretica
Volume 59, Issue 1 , pp 6779
 Cover Date
 20110301
 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