Biology and Philosophy

, Volume 21, Issue 5, pp 647–666 | Cite as

Loop analysis and qualitative modeling: limitations and merits

Original paper

Abstract

Richard Levins has advocated the scientific merits of qualitative modeling throughout his career. He believed an excessive and uncritical focus on emulating the models used by physicists and maximizing quantitative precision was hindering biological theorizing in particular. Greater emphasis on qualitative properties of modeled systems would help counteract this tendency, and Levins subsequently developed one method of qualitative modeling, loop analysis, to study a wide variety of biological phenomena. Qualitative modeling has been criticized for being conceptually and methodologically problematic. As a clear example of a qualitative modeling method, loop analysis shows this criticism is indefensible. The method has, however, some serious limitations. This paper describes loop analysis, its limitations, and attempts to clarify the differences between quantitative and qualitative modeling, in content and objective. Loop analysis is but one of numerous types of qualitative analysis, so its limitations do not detract from the currently underappreciated and underdeveloped role qualitative modeling could have within science.

Keywords

Complexity Idealization Loop analysis Perturbation Qualitative analysis Qualitative modeling Precision Sign digraph Stability 

References

  1. Athey S, Milgrom P, Roberts J (1998) Robust comparative statics. MonographGoogle Scholar
  2. Bassett L, Maybee J, Quirk J (1968) Qualitative economics and the scope of the correspondence principle. Econometrica 36:544–563CrossRefGoogle Scholar
  3. Boucher DH, James S, Keeler KH (1982) The ecology of mutualism. Annu Rev Ecol Syst 13:315–347CrossRefGoogle Scholar
  4. Brauer F, Nohel JA (1969) The qualitative theory of differential equations: an introduction. Dover Publications, New YorkGoogle Scholar
  5. Briand F, McCauley E (1978) Cybernetic mechanisms in lake plankton systems: how to control undesirable algae. Nature 273:228–230CrossRefGoogle Scholar
  6. Chesson PL, Case TJ (1986) Overview: nonequilibrium community theories: chance, variability, history, and coexistence. In: Diamond J, Case TJ (eds) Community ecology. Harper and Row, New York, pp 229–239Google Scholar
  7. Dambacher J, Luh H-K, Li H, Rossignol P (2003a) Qualitative stability and ambiguity in model ecosystems. Am Nat 161:876–888CrossRefGoogle Scholar
  8. Dambacher J, Li H, Rossignol P (2003b) Qualitative predictions in model ecosystems. Ecol Model 161:79–93CrossRefGoogle Scholar
  9. Desharnais RA, Costantino RF (1980) Genetic analysis of a population of tribolium. VII. Stability: response to genetic and demographic perturbations. Can J Genet Cytol 22:577–589Google Scholar
  10. Figuera J, Greco S, Ehrgott M (eds) (2005) Multiple criterion decision analysis: state of the art surveys. Springer, BerlinGoogle Scholar
  11. Flake RH (1980) Extension of Levins’ loop analysis to transient and periodic disturbances. Ecol Model 9:83–90CrossRefGoogle Scholar
  12. Gantmacher F (1960) Matrix theory, vol 2. Chelsea Publishing Company, New YorkGoogle Scholar
  13. Gasca AM (1996) Mathematical theories versus biological facts: a debate on mathematical population dynamics in the 1930s. Hist Stud Phys Biol Sci 26:347–403Google Scholar
  14. Hahn W (1963) Theory and application of Liapunov’s direct method. Prentice-Hall, Englewood CliffsGoogle Scholar
  15. Hale D, Lady G, Maybee J, Quirk J (1999) Nonparametric comparative statics and stability. Princeton University Press, PrincetonGoogle Scholar
  16. Haray F, Norman RZ, Cartwright D (1965) Structural models: an introduction to the theory of directed graphs. Wiley, New YorkGoogle Scholar
  17. Harsanyi J (1976) Essays on ethics, social behavior, and scientific explanation. Reidel, DordrechtGoogle Scholar
  18. Hastings A (1988) Food web theory and stability. Ecology 69:1665–1668CrossRefGoogle Scholar
  19. Justus J (2005) Qualitative scientific modeling and loop analysis. Philosophy of Science (in press)Google Scholar
  20. Justus J (in press) Ecological and Lyapunov stability. Presented at the Biennial meeting of the Philosophy of Science Association. VancouverGoogle Scholar
  21. Lancaster K (1962) The scope of qualitative economics. Rev Econ Stud 29:99–123CrossRefGoogle Scholar
  22. Lane P (1986) Symmetry, change, perturbation, and observing mode in natural communities. Ecology 67:223–239 CrossRefGoogle Scholar
  23. Lane P (1998) Assessing cumulative health effects in ecosystems. In: Rapport D, Contanza R, Epstein P, Gaudet C, Levins R (eds) Ecosystem health. Blackwell Science, Inc., Malden, pp 129–153Google Scholar
  24. Lane P, Levins R (1977) The dynamics of aquatic systems II. The effects of nutrient enrichment on model plankton communities. Limnol Oceanogr 22:454–471CrossRefGoogle Scholar
  25. Levine SH (1976) Competitive interactions in ecosystems. Am Nat 110:903–910CrossRefGoogle Scholar
  26. Levins R (1966) The strategy of model building in population biology. Am Sci 54:421–431Google Scholar
  27. Levins R (1968a) Evolution in changing environments. Princeton University Press, PrincetonGoogle Scholar
  28. Levins R (1968b) Ecological engineering: theory and technology. Q Rev Biol 43:301–305CrossRefGoogle Scholar
  29. Levins R (1970) Complex systems. In: Waddington CH (ed) Towards a theoretical biology, vol 3. Aldine Publishing, Chicago, pp 73–88Google Scholar
  30. Levins R (1974) Qualitative analysis of partially specified systems. Ann N Y Acad Sci 231:123–138CrossRefGoogle Scholar
  31. Levins R (1975a) Problems of signed digraphs in ecological theory. In: Levin SA (ed) Ecosystem analysis and prediction. Society for Industrial and Applied Mathematics, Philadelphia, pp 264–277Google Scholar
  32. Levins R (1975b) Evolution in communities near equilibrium. In: Cody M, Diamond J (eds) Ecology and evolution of communities. Belknap Press, Cambridge, pp 16–51Google Scholar
  33. Levins R (1998) Qualitative mathematics for understanding, prediction, and intervention in complex ecosystems. In: Rapport D, Contanza R, Epstein P, Gaudet C, Levins R (eds) Ecosystem health. Blackwell Science, Inc., Malden, pp 178–204Google Scholar
  34. Levins R, Schultz BB (1996) Effects of density dependence, feedback and environmental sensitivity on correlations among predators, prey and plant resources: models and practical implications. J Anim Ecol 65:802–812CrossRefGoogle Scholar
  35. Logofet D (1993), Matrices and graphs: stability problems in mathematical ecology. CRC Press, Ann ArborGoogle Scholar
  36. Lyapunov A ([1892], 1992) The general problem of the stability of motion. London: Taylor and FrancisGoogle Scholar
  37. Mason SJ (1953) Feedback theory: some properties of signal flow graphs. Proc Inst Radio Eng 41:1144–1156Google Scholar
  38. Maybee J (1966) Remarks on the theory of cycles in matrices. Mathematics Department, Purdue University. ManuscriptGoogle Scholar
  39. Orzack S (1990) The comparitive biology of second sex ratio evolution within a natural population of a parasitic wasp, Nasonia vetripennis. Genetics 124:385–396Google Scholar
  40. Orzack S, Sober E (1993) A critical assessment of Levins’s the strategy of model building in population biology (1966). Q Rev Biol 68:533–546CrossRefGoogle Scholar
  41. Puccia C, Levins R (1985) Qualitative modeling of complex systems. Harvard University Press, CambridgeGoogle Scholar
  42. Puccia C, Levins R (1991) Qualitative modeling in ecology: loop analysis, signed digraphs, and time averaging. In: Fishwick P, Luker P (eds) Qualitative simulation modeling and analysis. Springer-Verlag, New York, pp 119–143Google Scholar
  43. Quirk J, Ruppert R (1965) Qualitative economics and the stability of equilibrium. Rev Econ Stud 32:311–326CrossRefGoogle Scholar
  44. Roberts FS (1971) Signed digraphs and the growing demand for energy. Environ Plan 3:395–410CrossRefGoogle Scholar
  45. Roberts FS, Brown TA (1975) Signed digraphs and the energy crisis. Am Math Mon 82:577–594CrossRefGoogle Scholar
  46. Samuelson P (1947) Foundations of economic analysis. Harvard University Press, CambridgeGoogle Scholar
  47. Schmitz OJ (1997) Press perturbations and the predictability of ecological interactions in a food web. Ecology 78:55–69CrossRefGoogle Scholar
  48. Scudo F (1971) Vito volterra and theoretical ecology. Theor Popul Biol 2:1–23CrossRefGoogle Scholar
  49. Vandermeer J (1980) Indirect mutualism: variations on a theme by Stephen Levine. Am Nat 116:441–448CrossRefGoogle Scholar
  50. Walley P (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, New YorkGoogle Scholar
  51. Weirich P (1984) Interpersonal utility in principles of social choice. Erkenntnis 21:295–317CrossRefGoogle Scholar
  52. Weisberg M (2004) Qualitative modeling and chemical explanation. Philos Sci 71:1071–1081CrossRefGoogle Scholar
  53. Wiens JA (1984) On understanding a non-equilibrium world: myth and reality in community patterns and processes. In: Strong Jr DR, Simberloff D, Abele LG, Thistle AB (eds) Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, pp 439–457Google Scholar
  54. Wimsatt W (1970) Some problems with the concept of ‘Feedback’. In: PSA 1970, vol 1. Philosophy of Science Association, Boston, pp 241–256Google Scholar
  55. Wimsatt W (1987) False models as means to Truer theories. In: Nitecki M, Hoffman A (eds) Neutral models in biology. Oxford University Press, New York, pp 23–55Google Scholar
  56. Wright S (1921) Correlation and causation. J Agric Res 20:557–585Google Scholar

Copyright information

© Springer Science+Business Media, B.V. 2006

Authors and Affiliations

  1. 1.Philosophy DepartmentUniversity of TexasAustinUSA

Personalised recommendations