Abstract
In this essay, I examine the role of induction in developing vegetation models. Falsification is a necessary component of model building but is not itself sufficient. Induction provides a necessary complement and one that dethrones the null hypothesis from its privileged state. After examining the role of description and environment, I examine several possible criteria useful for valorising models so that we may choose the ‘best’. These criteria include fit, simplicity, precision and interest. Predictability, which is given overwhelming importance in a falsification approach, is found to be ambiguous. It may be obtained by using multiple models without regard to the processes active in the real system. In addition movement towards a model which does reflect the ‘real’ processes can result in loss of predictivity. Finally, some comments are made on what we can infer and how this relates to our understanding of living systems.
Article PDF
Similar content being viewed by others
Abbreviations
- MML:
-
Minimum message length
- GUHA:
-
General Unary Hypothesis Automaton
References
Adomavicius, G. and A. Tuzhilin. 1997. Discovery of actionable patterns in databases: the action hierarchy approach. In: D. Heckerman, H. Mannila, D. Pregibon and R. Uthurusamy (eds.), Proc. Third International Conference on Knowledge Discovery and Data Mining. AAA1, pp. 111–114.
Akaike, H. 1977. On entropy maximization principles. In: P. K. Krishnaiah (ed.), Applications of Statistics North Holland, Amsterdam. pp 27–41.
Anand, M. 1997. The fundamental nature of vegetation dynamics -a chaotic synthesis. Coenoses 12: 55–62.
Anand, M. 2000. Fundamentals of vegetation change: complexity rules. Acta Biotheoretica 48: 1–14.
Anand, M. and Orlóci, L. 1996. Complexity in plant communities: the notion and quantification. J. theoret. Biol. 179:179–186.
Anderson, C. W. and G. E. McMaster. 1982. Computer assisted modelling of affective tone in written documents. Comput. Humanit. 16: 1–9.
Antonelli, P. L. 1990. Applied Volterra-Hamilton systems of the Finsler type: increased species diversity as a non-chemical defense for coral against crown-of-thorns. In: R. H. Bradbury (ed.), Acanthaster and the Coral Reef A Theoretical Perspective, Lecture Notes in Biomathematics 88. Springer-Verlag, Berlin pp. 220–235.
Abarbanel, H. D. I., R. Brown and M. B. Kennel. 1992. Local Lyapunov Exponents Computed from Observed Data. Journal of Nonlinear Science 2:343–365.
Austin, M. P. 1970. An applied ecological example of mixed data classification, in: R. S. Anderssen and M. R. Osborne (eds.), Data Representation. University of Queensland Press, Brisbane. pp. 113–117.
Badii, R. and A. Politi. 1997 Hierarchical Structure and Scaling in Physics. Cambridge University Press, Cambridge.
Barsalou, L. W. 1995. Deriving categories to achieve goals. In:. A. Ram and D. B. Leake (eds.), Goal Directed Learning. MIT Press, Cambridge MA. pp. 121–176.
Beeston, G. R. and M. B. Dale. 1975. Multiple predictive analysis: a management tool. Proceedings of the Ecological Society of Australia 9: 172–181.
Boerlijst, M. and P. Hogeweg. 1991. Spiral wave structure in prebiotic evolution: hypercycles stable against parasites. Physica D 48: 17–28.
Brokaw, N. and R. T. Busing. 2000. Niche versus chance in tree diversity in forest gaps. TREE 15: 183–188.
Carley, K. and M. Palmquist. 1992. Extracting, representing and analyzing mental models. Social Forces 70: 601–636.
Chambers, W. V. 1991. Inferring formal causation from corresponding regressions. The Journal of Mind and Behavior 12:49–70.
Crutchfield, J. P. and C. R. Shalizi. 1999. Thermodynamic depth of causal states: when paddling around in Occam’s pool, shallowness is a virtue. Physical Review E 59: 275–283.
Crutchfield, J. P. and K. Young. 1989. Inferring statistical complexity, Physical Review Letters 63: 105–108.
Dale, M. B. 1970. Systems analysis and ecology. Ecology 51: 2–16.
Dale, M. B. 1980. A syntactic basis for classification. Vegetatio 42: 93–98.
Dale, M. B. 1988. Some fuzzy approaches to phytosociology: ideals and instances. Folia Geobotanica Phytotaxonomica 23: 239–274.
Dale, M. B. 1994. Straightening the horseshoe: a Riemannian resolution? Coenoses 9: 43–53.
Dale, M. B. 1999. The dynamics of diversity: mixed strategy systems. Coenoses 13:105–113
Dale, M. B. 2000. Mt Glorious revisited: Secondary succession in subtropical rainforest Community Ecol. 1: 181–193
Dale, M. B. and Barson, M. M. 1989. Grammars in vegetation analysis. Vegetatio 81: 79–94.
Dale, M. B., R. Courts and P. E. R. Dale. 1988. Landscape classification by sequences: a study of Toohey Forest. Vegetatio 29: 113–129.
Dale, M. B., P. E. R. Dale and T. Edgoose. 2002a. Markov models for incorporating temporal dependence Acta Oecologica 23: 261–269.
Dale, M. B., P. E. R. Dale, C. Li and G. Biswas. 2002b. Assessing impacts of small perturbations using a model-based approach Ecological Modelling 156: 185–199.
Dale, M. B. and Hogeweg, P. 1998. The dynamics of diversity: a cellular automaton approach. Coenoses 13:3–15.
Dale, P., K. Hulsman, B. R. Jahnke and M. B. Dale. 1984. Vegetation and nesting preferences of Black Noddies at Masthead Island, Great Barrier Ree. Part 1. Patterns at the macro scale. Australian Journal of Ecology 9: 335–341.
Dale, M. B., L. Salmina and L. Mucina. 2001. Minimum message length clustering: an explication and some applications to vegetation data. Community Ecol. 2:231–247.
Dennett, D. 1991. Real patterns. J. Philosophy 88:27–51.
Devaney. R. L. 1985. An Introduction to Chaotic Dynamical Systems. Benjamin/Cummings, Menlo Park.
Domingos, P. 1996. Two-way induction. Intematl. J. Artificial Intelligence Tools 5: 113–125.
Domingos, P. 1998. When and how to combine predictive and causal learning. Proc NIPS-98 Workshop on Integrating Supervised and Unsupervised Learning, Breckonridge, CO. NIPS Foundation.
Domingos P. 1999. The role of Occam’s Razor in knowledge discovery. Data Mining and Knowledge Discovery 3: 409–425
Eco, U. 1980. II Nome della Rosa. Gruppe Editoriale Fabbri-Bompianni, Sonzogno, Etas S. p. A.
Edgoose, T. and L. Allison. 1999. MML Markov classification of sequential data. Statistics and Computing 9: 269–278.
Farrands, J. L. 1990. On modelling. In: R. H. Bradbury (ed.), Acan thaster and the Coral Reef: A Theoretical Perspective Lecture Notes in Biomathematics 88. Springer-Verlag, Berlin, pp. 1–5.
Fisher, D. 1992. Pessimistic and optimistic induction. TR CS-92–12 Dept. Comput. Sei., Vanderbilt Univ.
Forster, M. P. and E. Sober. 1994. Key concepts in model selection: performance and generalization. Brit. J. Philosophy Sei. 45:1–35.
Gell-Mann, M. 1994. The Quark and the Jaguar, W. H. Freeman, San Francisco.
Georgeff, M. P. and C. S. Wallace. 1984. A general criterion for inductive inference. In: T. O’Shea (ed.), Proc. 6th European Conf. Artificial Intelligence, Elsevier, Amsterdam.
Grassberger, P. 1989. Problems in quantifying self-generated complexity. Helvetica Physica Acta 62: 489–511.
Grassberger, P. 1991. Information and complexity measures in dynamical systems. In: H. Atmanspacher and H. Scheingraber (eds.), Information Dynamics. Plenum Press. New York, pp. 15–33.
Grassberger, P. and F. Procaccia. 1983. Estimation of the Kolmogorov entropy for a chaotic signal. Phys. Rev. A 28: 2591.
Gunther, R., B. Shapiro and P. Wagner. 1994. Complex systems, complexity measures, grammars and model inferring, Chaos, Solitons and Fractals 4: 635–651.
Hájek, P., I. Havel and M. Chytil. 1966. GUHA – the method of systematical hypotheses searching. Kybernetika (Prague) 2:31–39.
Hájek, P. and T. Havránek. 1977. On generation of inductive hypotheses. International. J. Man-Mach. Stud. 9: 415–438.
Herman, G. T. and Rozenberg, G. 1975. Developmental Systems and Languages, North-Holland, American Elsevier, Amsterdam.
Hilderman, R. J. and Hamilton, H.J. 1999. Heuristics for ranking the interestingness of discovered knowledge. Proc. 3rd Pacific-Asia Conf. Knowledge Discovery PKDD’99, Beijing, Springer-Verlag, Berlin, pp. 204–209.
Hoeting, J., D. Madigan, A. E. Raftery and C. T. Volinsky. 1998. Bayesian model averaging: atutorial. Statist. Sei. 14: 382–417.
Hogeweg, P. 2002. Computing an organism: on the interface between informatic and dynamic processes. BioSystems 64: 97–109.
Howard, E. and N. Oakley. 1994. The application of genetic programming to the investigation of short, noisy, chaotic data series. In: T C. Fogarty (ed.), Evolutionary Computing. Lecture Notes in Computer Science 865, Springer-Verlag, Berlin, pp. 320–332.
Hume, D. 1999. An Enquiry Concerning Human Understanding. Oxford Philosophical Texts, Oxford University Press, Oxford.
Iba, W., Wogulis, J. and Langley, P. 1988. Trading off simplicity and coverage in incremental concept learning. Proc. 5th Internatl. Conf. Machine Learning, Ann Arbor, Morgan Kaufman, CA. pp. 73–86.
Ivakhnenko, A. G. 1971. Polynomial theory of complex systems I. E. E. E. Trans. Syst. Man Cybern. SMC 1: 364–378.
Jöreskog, K. G. 1966. Some contributions to maximum likelihood factor analysis. Research Bulletin RB-66–41, Educational Testing Service, Princeton, N. J.
Kaufman, S. 2001. Investigations. Oxford University Press, Oxford.
Kelley, H. 1971. Causal schemata and the attribution process. In: E. Jones, D. Kanouse, H. Kelley, N. Nisbett, S. Valins and B. Weiner (eds.). Attribution: Perceiving the causes of behavior. General Learning Press, Morristown, NJ. pp 151–174.
Klemettinen, M., H. Mannila, P. Ronkainen, H. Toivonen and A. I. Verkamo. 1994. Finding interesting rules from large sets of discovered association rules. In: N. R. Adam, B. K. Bhargavaand Y. Yesha (eds.), Third Internatl. Conf. Information and Knowledge Management CIKM’94, ACM Press Association, pp. 401–407,
Kohavi, R. 1995. A study of cross-validation and bootstrap for accuracy estimation and model selection, Proc. International Joint Conference Artificial Intelligence.
Kolmogorov, A. N. 1965. Three approaches to the quantitative description of information. Prob. Inform. Transmission 1: 4–7 (translation)
Kontkainen, P., P. Myllymäki, T. Silander and H. Tirri. 1999. On stochastic complexity approximation. In: A Gammerman (ed.) Causal Systems and Intelligent data Management., Springer-Verlag, Berlin, pp. 120–136.
Lekkas, G. and N. Avouris. 1994. Case-Based Reasoning in Environmental Monitoring. Applied Artificial Intelligence 8: 359–376.
Li, C. and G. Biswas. 1999. Temporal pattern generation using hidden Markov model based unsupervised classification. Lecture Notes in Computer Science 1662. pp. 245–257.
Lloyd, S. and H. Pagels. 1988. Complexity as thermodynamic depth. Ann. Physics 188:186–212.
Löfgren, L. 1974. Complexity of descriptions of systems: A foundational study. International Journal of General Systems 3: 197–214.
Lux, A. and F. A. Bemmerlein-Lux. 1998. Two vegetation maps of the same island: floristic units versus structural units. Applied Vegetation Science 1: 201–210.
Mac Nally, R. 2000. Regression and model-building in conservation biology, biogeography and ecology: The distinction between -and reconciliation of -’predictive’ and ‘explanatory’ models Biodiversity and Conservation 9: 655–671.
Mackay, D. M. 1969. Recognition and action. In: S. Watanabe (ed.), Methodologies of Pattern Recognition, Academic Press, London, pp. 409–416.
May, R. M 1995. Necessity and chance: deterministic chaos in ecology and evolution. Bull. Amer. Math. Soc. 32: 291–308.
Murphy, G.L. and P. D. Allopenna. 1994. The locus of knowledge effects in concept learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19: 203–222.
Neil, J. R. and K. B. Korb. 1998. The MML evolution of causal models Tech. Rep. 98/17 School of Computer Science and Software Engineering, Monash University, Clayton, Victoria 3168, Australia.
Niven, B. S. 1992. Formalization of some basic concepts of plant ecology. Coenoses 7: 103–113.
Noble, I. R. and R. O. Slatyer. 1980. The use of vital attributes to predict successional changes in plant communities subject to recurrent disturbances. Vegetatio 43: 5–21.
Oates, T. and D. Jensen 1998. Large datasets lead to overly complex models: an explanation and a solution. KDD-98 Proc. 4th Internatl. Conf. Knowledge Discovery and Datamining. pp. 294–298.
Osledec. V. I. 1968 A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19: 197–231.
Padmanabhan, B. and A. Tuzhilin. 1999. Unexpectedness as a measure of interestingness in knowledge discovery. Decision Support Systems, 27. from http://citeseer.nj.nec.compadmanabhan99unexpectedness.html
Pagie, L. and P. Hogeweg. 1997. Evolutionary consequences of coevolving targets. Evolutionary Computation 5: 401–418.
Palus, M. 1996a. Detecting nonlinearity in multivariate time series. Physics Letters A 213: 1387.
Palus, M. 1996b. Coarse-grained entropy rates for characterisation of complex time series Physica D 93: 64–77.
Palus, M. 1997. Kolmogorov entropy from time series using information-theoretic functionals. Neural Network World 7: 269–292.
Pazzani, M. J. and D. Kibler. 1992. The utility of knowledge in inductive learning. Machine Learning 9: 57–94.
Pazzani, M., S. Mani and W. R. Shankle. 1997. Comprehensible knowledge discovery in databases. In: M. G. Shafto and P. Langley, (eds.), Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society, Lawrence Erlbaum, pp. 596–601.
Pillar, V. D. 1999a On the identification of optimal plant functional types. J. Veg.Sci. 10:631–640.
Pillar, V. D. 1999b The bootstrap ordination revisited. J. Veg. Sci. 10:895–902.
Popper, K. R. 1968. The Logic of Scientific Discovery. Harper, New York.
Posse, C. 1995. Projection pursuit exploratory data analysis. C amputat. Statist. Data Anal. 20: 669–687.
Provost, F., T. Fawcett and R. Kohavi. 1998. The Case Against Accuracy Estimation for Comparing Induction Algorithms. Presented at ICML-98 (15th Internatl. Conf. on Machine Learning).
Reich, Y. 1993. A model of aesthetic judgment in design. Artif. Intell. in Engineering 8:141–153
Reichenbach, H. 1950. The Rise of Scientific Philosophy. Univ. California Press, Los Angeles.
Riddle, R. R. and D. J. Hafner. 1999. Species as unit of analysis in ecology and biogeography: time to take the blinkers off. Global Ecology and Biogeography 8: 433–441.
Rigoutsos, I. and A. Floratos. 1998. Motif discovery without alignment or enumeration. Proc. 2nd. Ann. ACM Internatl. Conf. Computational Molecular Biology (RECOMB 98). New York, NY.
Rissanen, J. 1995. Stochastic complexity in learning. In: P. Vitányi (ed.), Computational Learning Theory Lecture Notes in Computer Science 904. Springer-Verlag, Berlin, pp. 196–201.
Rychlak, J.F. 1988. The Psychology of Rigorous Humanism. New York University Press, New York.
Savill, N. J., P. Rohani and P. Hogeweg. 1997. Self-reinforcing spatial patterns enslave evolution in a host-parasitoid system. J. theoret. Biol. 188:11–20.
Schmidhuber, J. 1994. Discovering solutions with low Kolmogorov complexity and high generalization ability. Tech. Rep. FKI-194–94 Faculty of Information, Technical University, Munich.
Schwarz, G. 1978. Estimating dimension of a model. Ann. Statist. 6: 461–464.
Shalizi, C. R. and J. P. Crutchfield. 1999 Computational mechanics: pattern and prediction, structure and simplicity. Sante Fe Institute Working paper 99–07-044.
Shipley, B. and P. A. Keddy. 1987. The individualistic and community-unit concepts as falsifiable hypotheses. Vegetatio 69: 47–55.
Simberloff, D. 1980. A succession of paradigms in ecology: Essentialism to materialism and probabilism. Synthese 43:3–29.
van den Bosch A. P. M. 1997. Simplicity and Prediction. Available electronically at http://tcw2.ppsw.rug.nl~vdbosch/simple.ps
Vapnik, V. N. and A. Chervonenkis. 1971. On the uniform convergence of relative frequencies of events to their probabilities. Theory Probability Appl. 16: 264–280.
Viswanathan, M., C. S. Wallace, D. L. Dowe and K. B. Korb. 1999. Finding outpoints in noisy binary sequences: a revised empirical examination. In: N. Foo (ed.), A1–99 Lecture Notes in Artificial Intelligence 1747. Springer-Verlag, Berlin, pp. 405–416.
Wackerbauer, R., A., Witt, H. Altmanspracher, J. Kurths and H. Scheingraber. 1994. A comparative classification of complexity measures based on distinguishing partitions in phase space as well as structural v. dynamic elements. Chaos, Solitons and Fractals 4: 133–173.
Wallace, C. S. 1995. Multiple factor analysis by MML estimation. Tech. Rep. 95/218, Dept Computer Science, Monash University, Clayton Victoria 3168, Australia.
Wallace, C. S. 1996. MML Inference of predictive trees, graphs and nets. In: A. Gammerman (ed.), Computational Learning and Probabilistic Reasoning. John Wiley. New York. pp. 43–66.
Wallace, C. S. 1998. Intrinsic classification of spatially-correlated data. Comput. J. 41: 602–611.
Wallace, C. S. and D. L. Dowe. 2000. MML clustering of multi-state, Poisson, von Mises circular and Gaussian distributions. Statistics and Computing 10: 73–83.
Wallace, C. S. and P. R. Freeman. 1987. Estimation and inference by compact coding. J. Roy. Statist. Soc. Ser. B 49: 240–252.
Wallace, C. S., K. B. Korb and H. Dai. 1996. Causal discovery via MML. Tech. Rep. 96/254 Dept. Computer Science, Monash University, Clayton, Victoria 3168, Australia.
Watanabe, S. 1969. Knowing and Guessing. Wiley, New York.
Webb, G. I. 1994. Generality is more significant than complexity: Toward alternatives to Occam’s razor. In: C. Zhang, J. Debenham and D. Lukose (eds.), AI’94 - Proceedings of the Seventh Australian Joint Conference on Artificial Intelligence. World Scientific, Armidale. pp. 60–67.
Webb, G. I. 1996. Further experimental evidence against the utility of Occam’s Razor. J. Artific. Intell. Res. 4:387–417.
Webb, L. J., J. G. Tracey and W. T. Williams. 1976. The value of structural features in tropical forest typology. Austral. J. Ecol. 1:3–28.
Williams, W. T. 1972. The problem of pattern. Austral. Mathem. Teacher 28:103–109.
Williams, W. T., J. M. Lambert and G. N. Lance. 1966. Multivariate methods in plant ecology V. Similarity analysis and information analysis. J. Ecol. 54:427–445.
Williams, W. T., G. N. Lance, L. J. Webb, J. G. Tracey and M. B. Dale. 1969. Studies in the numerical classification of complex rain-forest communities III. The analysis of successional data. J. Ecol. 57:515–535.
Wilson, J., A. D. Q. Agnew and T. R. Partridge. 1994. Carr texture in Britain and New Zealand: community convergence compared with a null model. J. Veg. Sci. 5:109–116.
Wisheu, I. and P. A. Keddy. 1992. Competition and centrifugal organisation of plant communities: theory and tests. J. Veg. Sci. 3: 147–156.
Wittgenstein, L. 1995. Tractacus Logico-Philosophicus. (trans) 5:3631 Routledge, Keagan & Paul, London.
Wolpert, D. H. and W. G. Macready. 1997. Self-dissimilarity: an empirically observable complexity measure. In: Y. Bar-Yam (ed.), Proc. International. Conf. Complex Systems, New England Complex Systems Inst. pp. 1–8.
Wright, S. 1934. The method of path coefficients. Ann. Mathem. Statist. 5:161–215.
Yamada, H. and S. Amaroso. 1971. Structural and behavioural equivalences of tessellation automata. Information and Control 18:1–31.
Yee, C. N. and L. Allison. 1993. Reconstruction of strings past. J. Comp. Appl. BioSci. 9: 1–7.
Acknowledgements
I would like to thank Sanyi Bartha and Pat Dale for many helpful comments made after reading earlier drafts.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Dale, M.B. Models, measures and messages: an essay on the role for induction. COMMUNITY ECOLOGY 3, 191–204 (2002). https://doi.org/10.1556/ComEc.3.2002.2.6
Published:
Issue Date:
DOI: https://doi.org/10.1556/ComEc.3.2002.2.6