Loop analysis and qualitative modeling: limitations and merits

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.

[1]  A. M. Lyapunov The general problem of the stability of motion , 1992 .

[2]  Stephen H. Levine,et al.  Competitive Interactions in Ecosystems , 1976, The American Naturalist.

[3]  Norman,et al.  Structural Models: An Introduction to the Theory of Directed Graphs. , 1966 .

[4]  F. Briand,et al.  Cybernetic mechanisms in lake plankton systems: how to control undersirable algae , 1978, Nature.

[5]  Extension of Levins' Loop Analysis to transient and periodic disturbances , 1980 .

[6]  Mathematical theories versus biological facts: a debate on mathematical population dynamics in the 1930s. , 1996, Historical studies in the physical and biological sciences : HSPS.

[7]  John C. Harsanyi,et al.  Essays on ethics, social behavior, and scientific explanation , 1976 .

[8]  R. Levins,et al.  The dynamics of aquatic systems. 2. The effects of nutrient enrichment on model plankton communities1,2 , 1977 .

[9]  Patricia A. Lane,et al.  Symmetry, Change, Perturbation, and Observation Mode in Natural Communities , 1986 .

[10]  Daniel Simberloff,et al.  Ecological Communities: Conceptual Issues and the Evidence , 1984 .

[11]  P. Games Correlation and Causation: A Logical Snafu , 1990 .

[12]  R. Levins The strategy of model building in population biology , 1966 .

[13]  F. M. Scudo,et al.  Vito Volterra and theoretical ecology. , 1971, Theoretical population biology.

[14]  Kathleen H. Keeler,et al.  The Ecology of Mutualism , 1982 .

[15]  A. Hastings Food Web Theory and Stability , 1988 .

[16]  Jeffrey M. Dambacher,et al.  Qualitative predictions in model ecosystems , 2003 .

[17]  Mike Mannion,et al.  Complex systems , 1997, Proceedings International Conference and Workshop on Engineering of Computer-Based Systems.

[18]  Ja Wiens,et al.  On understanding a non-equilibrium world:myth and reality in community patterns and processes , 1984 .

[19]  Samuel J. Mason,et al.  Feedback Theory-Some Properties of Signal Flow Graphs , 1953, Proceedings of the IRE.

[20]  James Justus Ecological and Lyapunov Stability* , 2008, Philosophy of Science.

[21]  Kelvin Lancaster,et al.  The Scope of Qualitative Economics , 1962 .

[22]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[23]  Wolfgang Hahn,et al.  Theory and Application of Liapunov's Direct Method , 1963 .

[24]  Paul A. Luker,et al.  Qualitative Simulation Modeling and Analysis , 1991, Advances in Simulation.

[25]  A. Hoffman,et al.  Neutral models in biology , 1987 .

[26]  R. Levins,et al.  Effects of density dependence, feedback and environmental sensitivity on correlations among predators, prey and plant resources : models and practical implications , 1996 .

[27]  R. Levins Evolution in Changing Environments , 1968 .

[28]  F. Brauer,et al.  The Qualitative Theory of Ordinary Differential Equations: An Introduction , 1989 .

[29]  P. Walley Statistical Reasoning with Imprecise Probabilities , 1990 .

[30]  R. F. Costantino,et al.  GENETIC ANALYSIS OF A POPULATION OF TRIBOLIUM: VII. STABILITY: RESPONSE TO GENETIC AND DEMOGRAPHIC PERTURBATIONS , 1980 .

[31]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[32]  Elliott Sober,et al.  A Critical Assessment of Levins's The Strategy of Model Building in Population Biology (1966) , 1993, The Quarterly Review of Biology.

[33]  D. Hale Nonparametric Comparative Statics and Stability , 1999 .

[34]  P. Samuelson,et al.  Foundations of Economic Analysis. , 1948 .

[35]  David W. Lewis,et al.  Matrix theory , 1991 .

[36]  Charles J. Puccia,et al.  Qualitative modeling in ecology: loop analysis, signed digraphs, and time averaging , 1991 .

[37]  R Levins,et al.  DISCUSSION PAPER: THE QUALITATIVE ANALYSIS OF PARTIALLY SPECIFIED SYSTEMS , 1974, Annals of the New York Academy of Sciences.

[38]  R. Levins Ecological Engineering: Theory and Technology , 1968, The Quarterly Review of Biology.

[39]  James P. Quirk,et al.  Qualitative Economics and the Stability of Equilibrium , 1965 .

[40]  Michael Weisberg,et al.  Qualitative Theory and Chemical Explanation , 2004, Philosophy of Science.

[41]  Thomas A. Brown,et al.  Signed Digraphs and the Energy Crisis , 1975 .

[42]  Paul R. Milgrom,et al.  Robust Comparative Statics , 2002 .

[43]  James Justus,et al.  Qualitative Scientific Modeling and Loop Analysis , 2005, Philosophy of Science.

[44]  P. Weirich Interpersonal utility in principles of social choice , 1984 .

[45]  H. Luh,et al.  Qualitative Stability and Ambiguity in Model Ecosystems , 2003, The American Naturalist.

[46]  Oswald J. Schmitz,et al.  PRESS PERTURBATIONS AND THE PREDICTABILITY OFECOLOGICAL INTERACTIONS IN A FOOD WEB , 1997 .

[47]  C. H. WADDINGTON,et al.  Towards a Theoretical Biology , 1968, Nature.

[48]  William C. Wimsatt Some Problems with the Concept of ‘Feedback’ , 1970 .

[49]  Dmitriĭ Olegovich Logofet,et al.  Matrices and Graphs Stability Problems in Mathematical Ecology , 1993 .

[50]  Fred S. Roberts,et al.  Signed Digraphs and the Growing Demand for Energy , 1971 .

[51]  John Maybee,et al.  Qualitative Economics and the Scope of the Correspondence Principle , 1968 .

[52]  S. Orzack The comparative biology of second sex ratio evolution within a natural population of a parasitic wasp, Nasonia vitripennis. , 1990, Genetics.

[53]  John Vandermeer,et al.  Indirect Mutualism: Variations on a Theme by Stephen Levine , 1980, The American Naturalist.