MATHEMATICAL MODELS AND UNDERSTANDING IN ECOLOGY

Abstract Of all possible mathematical models, only “conceptual” models, i.e., models which are understandable, manageable, and capable of being fully explored, can be of help in attaining an understanding of ecological systems and processes. However, the hitherto promulgated “philosophy” of conceptual mathematical modelling was not in a position to convince empiricists of the possibilities afforded by mathematical models on the one hand, and on the other to prevent theorists from becoming so engrossed in their theories as to neglect the testability of their hypotheses. The goal of this paper is to reveal the shortcomings of this “philosophy” of mathematical modelling and to outline a more promising strategy for creating models. It recommends choosing “patterns” actually existing in ecological systems, rather than questions of a general nature, as a point of departure for conceptual models. In this way, the advantages of conceptual models can be utilized without having to relinquish the testability of the hypotheses proposed with the aid of the models.

[1]  C. Wissel,et al.  A Model for the Mosaic-Cycle Concept , 1991 .

[2]  Simon A. Levin,et al.  The Role of Theoretical Ecology in the Description and Understanding of Populations in Heterogeneous Environments , 1981 .

[3]  D. Mueller‐Dombois.  Natural Dieback in Forests , 1987 .

[4]  Peter Turchin,et al.  Complex Dynamics in Ecological Time Series , 1992 .

[5]  D. Tilman.  The Importance of the Mechanisms of Interspecific Competition , 1987, The American Naturalist.

[6]  E. C. Pielou.  The Usefulness of Ecological Models: A Stock-Taking , 1981, The Quarterly Review of Biology.

[7]  Denis Mollison,et al.  Modelling biological invasions: chance, explanation, prediction , 1986 .

[8]  Florian Jeltsch,et al.  Oscillating dispersal patterns of tephritid fly populations , 1992 .

[9]  Daniel Simberloff,et al.  Competition Theory, Hypothesis-Testing, and Other Community Ecological Buzzwords , 1983, The American Naturalist.

[10]  Charles A. S. Hall,et al.  AN ASSESSMENT OF SEVERAL OF THE HISTORICALLY MOST INFLUENTIAL THEORETICAL MODELS USED IN ECOLOGY AND OF THE DATA PROVIDED IN THEIR SUPPORT , 1988 .

[11]  Charles J. Krebs,et al.  The experimental approach to rodent population dynamics , 1988 .

[12]  C Loehle,et al.  Hypothesis Testing in Ecology: Psychological Aspects and the Importance of Theory Maturation , 1987, The Quarterly Review of Biology.

[13]  A. Seitz,et al.  Modelling effects of toxicants on pelagic food-webs: many problems — some solutions , 1994 .

[14]  H. Remmert,et al.  The Mosaic-Cycle Concept of Ecosystems — An Overview , 1991 .

[15]  Christian Wissel,et al.  Aims and limits of ecological modelling exemplified by island theory , 1992 .

[16]  Nutrient gradients and spatial structure in tropical forests : a model study , 1991 .

[17]  Mark A. Burgman,et al.  Building Models for Conservation and Wildlife Management , 1987 .

[18]  LISTENING TO A SYMPOSIUM - A SUMMARY AND PROSPECTUS , 1981 .

[19]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[20]  H. Caswell.  THEORY AND MODELS IN ECOLOGY: A DIFFERENT PERSPECTIVE , 1988 .

[21]  C. Wissel,et al.  Modelling Factors Which May Cause Stand-Level Dieback in Forest , 1993 .

[22]  Charles A. S. Hall,et al.  An idiosyncratic assessment of the role of mathematical models in environmental sciences , 1991 .

[23]  J. Uchmański,et al.  Differentiation and frequency distributions of body weights in plants and animals. , 1985, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[24]  G. Salt.  Roles: Their Limits and Responsibilities in Ecological and Evolutionary Research , 1983, The American Naturalist.

[25]  D. L. Scarnecchia,et al.  Fundamentals of Ecological Modelling , 1995 .

[26]  Jonathan Roughgarden,et al.  Competition and Theory in Community Ecology , 1983, The American Naturalist.

[27]  Peter Kareiva,et al.  5. Renewing the Dialogue between Theory and Experiments in Population Ecology , 1989 .

[28]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[29]  Christian Wissel,et al.  On the application of stability concepts in ecology , 1992 .