Evolution of theoretical ecology in last decades: why did individual-based modelling emerge

Janusz Uchmański, Kamila Kowalczyk, Piotr Ogrodowczyk

DOI: http://dx.doi.org/10.12775/v10090-009-0002-3

Abstract


Mathematical models of classical theoretical ecology are state variable models. They use density of population as a state variable. Because such models posses equilibrium states and they are stable around them, classical theoretical ecology has been dominated by considerations about stability of ecological systems. Three factors observed in ecology in last decades had great influence on the gradual decline of the classical theoretical ecology: first one is development of evolutionary ecology and the stress it laid on individuals, the second one nonequlibrium way of thinking about dynamics of ecological systems and the third one various methodological doubts about application of difference and differential equations in ecology. Individual-based modeling has emerged as the result of this discussions. However, individual-based approach to modeling the dynamics of ecological systems has natural tendency to describe particular systems and to produce their detailed models. Much should be done in the future to solve general problems formulated by classical theoretical ecology using method of individual-based approach.

Keywords


classical theoretical ecology; computer simulation; difference equations; evolutionary ecology; mathematical models; species diversity; stability; spatial distribution

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References


Berger U. & Hildenbrandt H., 2000, A new approach to spatially explicit modelling of forest dynamics: spacing, ageing and neighborhood competition of mangrove trees, Ecological Modelling 132: 287 - 302.

Bulmer M., 1994, Theoretical evolutionary ecology, Sinauer Associates, Sunderland.

Connel T., 1978, Diversity in tropical rain forest and coral reefs, Science 199: 1302 - 1309.

Connell T., 1979, Tropical rain forest and coral reefs as open non-equilibrium systems, Symposia of the British Ecological Society 20: 141 - 163.

Czárán T., 1998, Spatiotemporal models of population and community dynamics, Chapman & Hall, London - Weinheim.

DeAngelis D. L. & Gross L. J. (eds.), 1992, Individual-based models and approaches in ecology: population, communities and ecosystems, Chapman & Hall, New York.

Grimm V., 2008, Individual-based models, [in:] S. E. Jørgensen & B. D. Fath (eds.), Elsevier, Oxford, Encyclopedia of ecology 3: 1959 - 1968.

Grimm V., Frank K., Jeltsch F., Brandl R. & Uchmański J., 1996, Pattern-oriented modeling in population ecology, Sciences of Total Environment 183: 151 - 166.

Grimm V., Wissel C., 1997, Babel, or the ecological stability discussion: an inventory and analysis of terminology and a guide for avoiding confusion, Oecologia 109: 323 - 334.

Grimm V. & Railsback F., 2005, Individual-based modeling and ecology, Princeton University Press, Princeton - Oxford.

Grimm V., Berger U., Bastiansen F., Eliassen S., Ginot V., Giske J., Goss-Gustard J., Grand T., Heinz S. K., Huse G., Huth A., Jepsen J. U., Jørgensen C., Mooij W. M., Müller B., Pe'er G., Piou C., Railsback S. F., Robbins A. M., Robbins M. M., Rossmanith E., Rüger N., Strand E., Souissi S., Stillman R. A., Vabø R., Visser U. & DeAngelis D. L., 2006, A standard protocol for describing individual-based and agent-based models, Ecological Modelling 198: 115 - 126.

Hara T., 1988, Dynamics of size structure in plant populations, Trends in Ecology and Evolution 3: 129 - 133.

Hofbauer J. & Sigmund K., 1990, Evolutionary games and population dynamics, Cambridge University Press, Cambridge - London.

Kaandorp J. A., 1994, Fractal modeling. Growth and form in biology, Springer-Verlag, Berlin - Heidelberg.

Kaandorp J. A. & Kübler J. E., 2001, The algorithmic beauty of seaweeds, sponges and corals, Springer-Verlag, Berlin - Heidelberg.

Kingsland S. E., 1995, Modeling nature. Episodes in the history of population ecology, The University of Chicago Press, Chicago - London.

Krebs J. R. & Davies N. B., 1993, An introduction to behavioural ecology, Third edition, Blackwell Scientific Publishers, Oxford - London.

Mangel M., 2006, The theoretical biologist's toolbox. Quantitative methods for ecology and evolutionary biology, Cambridge University Press, Cambridge - New York.

May R. M., 1972, Will a large complex system be stable?, Nature 238: 413 - 414.

May R. M., 1973, The stability and complexity in model ecosystems, Princeton University Press, Princeton.

May R. M., 1975, Patterns of species abundance and diversity, [in:] M. L. Cody & J. M. Diamond (eds.), Ecology and evolution of communities, The Belknap Press of Harvard University Press, Cambridge Mass. - London: 81 - 120.

May R. M. (ed.), 1981, Theoretical ecology. Principles and application, Blackwell, Oxford - London.

May R. M. & McLean A., 2007, Theoretical ecology. Principles and applications, Third edition, Oxford University Press, Oxford - New York.

Maynard Smith J., 1992, Evolution and the theory of games, Cambridge University Press, Cambridge - London.

Murray J. D., 2002, Mathematical biology. I: An introduction, Springer-Verlag, Berlin - Heidelberg.

Prusinkiewicz P. & Lindenmayer A., 1990, The algorithmic beauty of plant, Springer-Verlag, New York - Berlin.

Rice S. H., 2004, Evolutionary theory. Mathematical and conceptual foundations, Sinauer Associates, Sunderland.

Rhode K., 2005, Nonequilibrium ecology, Cambridge University Press, Cambridge - New York.

Romanovskij Y. M., Stiepanova N. V. & Černavskij D. S., 1975, Matematičeskoje modelirovanije v biofizikie, Nauka, Moskwa.

Scudo F. M. & Ziegler J. R., 1978, The golden age of theoretical ecology: 1923 - 1940, Lecture notes in biomathematics vol. 22, Springer-Verlag, Berlin - Heidelberg - New York.

Stearns S. C., 1992, The evolution of life histories, Oxford University Press, Oxford - New York.

Uchmański J., 2000, Resource partitioning among competing individuals and population persistence: an individual-based model, Ecological Modelling 131: 21 - 32.

Uchmański J. & Grimm V., 1996, Individual-based modeling in ecology: what makes the difference?, Trends in Ecology and Evolution 11: 437 - 441.

Uchmański J., Aikman E. D., Wyszomirski T. & Grimm V. (eds.), 1999, Individual-based modeling in ecology, Ecological Modelling 15, 2, 3 (special issue).

Volterra V., 1931, Leçons sur la théorie mathematique de la lutte pour la vie, Gauthier-Villars et Cie, Paris.




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