Summary
Various approaches have been developed for modelling processes related to vegetation dynamics. Most of them are biogeographical models (empirical) or dynamical models. Recent development in dynamical systems analysis has led to the investigation of an original concept essentially motivated by vegetation migration. It is the so-called spreadability concept developed by El Jai et al. (1994). The purpose of this paper is to consider this new idea and to show how it can lead to dynamical models which describe the expansion of a vegetation area. We give some mathematical examples showing the migration of the system state and also present some results related to control and numerical implementation of such systems. These results are, at the moment, completely academic, but they can be usefully applied in the analysis of real ecosystems and the dynamics that govern the behaviour of these systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barkham, J. P., Hance, C. E., 1982: Population Dynamics of the wild daffodil III. Implication of a computer model of 1000 years of population change.J. Ecology 70, 323–344.
Brufau, H., 1995: Modélisation d'une dynamique de végétation. Thèse de Doctorat. France:Université de Perpignan.
Brufau, H., Soule, S., Fournier, M., Leyris, J. P., Maurissen, Y., 1994: Modélisation d'un procédé bioclimatologique. COMAGEP1. 4–6 Mai, Marrakech, Morrocco.
Brufau, H., Soule, S., Founier, M., Leyris, J. P., Maurissen, Y., 1995: Vegetation dynamics — A state space approach. (To appear).
Budyko, M. I., 1971:Climate and Life. Leningrad: Hydrometeoizdat, (Russian), 472 p.
Budyko, M. I., 1986:The Evolution of the Biosphere. Dordrecht: D. Reidel, 423 pp.
Colasanti, R. L., Grime, J. P., 1983: Resource dynamics and vegetation processes: a determistic model using two-dimensional cellular automata.Functional Ecology.,7, 169–176.
Crawley, M. J., May, R. M., 1987: Population dynamics and plant community structure: competition between annuals and perennials.J. Theoretical Biology 125: 1119–1145.
Delfour, M. C., 1990: Shape analysis and optimization in distributed parameter systems. In: El Jai A., Amouroux, M., (eds.)Fifth IFAC Symposium on the Control of Distributed Systems. IFAC Series No 3. Pergamon.
Delfour, M. C., Zolesio, J. P., 1990: Computation of the shape hessian by a Lagrangian method. In: El Jai A., Amouroux, M., (eds.)Fifth IFAC Symposium on the Control of Distributed Systems. IFAC Series No 3. Pergamon.
Dautray, R., Lions, J. L., 1988:Analyse mathématique et calcul numérique. France: Masson, Vol. 1–9.
Diaz, J. I., Lions, J. L., 1993:Mathematics Climate and Environment. France: Masson. (Serie RMA, No 27).
El Jai, A., Kassara, K., 1994: Spreadable Distributed Systems.Mathematical and Computer Modelling 20 (1), 47–64.
El Jai, A., Founier, M., Kassara, K., Noumare, B., 1994: A new System Analysis Concept related to Vegetation Dynamics. First GCTE Science Conference, Woods Hole, Massachussetts. USA. 23–27 May.
Horn, H. S., 1975: Forest Succession.Sc. Amer. 232, 90–98.
Horn, H. S., 1975: Markovian properties of forest succession. In: Cody, M. L., Diamond, J. M., (eds.)Ecology and Evolution in Communities. Cambridge: Harvard University Press.
Huston, M., De Angelis, D., Post, W., 1988: New computer models unify ecological theory.BioScience., 38, (10).
Kurnetov, Antonovsky, Biktashev, Aponina, 1994: A cross diffusion model of forest boundary dynamics.J. Math. Biology. (To appear).
Monserud, R. A., Tchebakova, N. M., Leemans, R., 1993: Global vegetation change predicted by the modified Budyko model.Climatic Change 25, 59–83.
Naot, O., Mahrer, Y., 1989: Modelling microclimate environment: verification study.Bound. Layer Meteor. 46, 333–354.
Prentice, I. C., Sykes, M. T., Cramer, W., 1991: The possible dynamics response of northern forests to global warming.Ecology and Biogeography letters 1, 129–135.
Shugart, H. H., 1984:A Theory of Forest Dynamics. New York: Springer.
Shugart, H. H., 1990: Modeling future Changes of Vegetation succession. Symposium on Global Change Systems and Climate Variation and Hydrology. Anaheim, California, Feb. 5–9, 1990.
Smith, T. M., Shugart, H. H., Bonan, G. B., Smith, J. B., 1992: Modeling the potential response of vegetation to global climate change.Advances in Ecological Research, 22.
Smith, T. M., Weishampel, H. H., Shugart, H. H., 1992: The response of terrestral C storage to change. Modeling C dynamics at varying temporal and spatial scales.Water, Air and Soil Pollution 64, 307–326.
Solomon, A. M., Shugart, H. H., (eds.), 1993:Vegetation Dynamics and Global Change. IIASA. Chapman and Hall. Library of Congress Cataloging in Publication Data.
Ucinski, D., El Jai, A., 1995: On weak spreadability of DPS and its achievement via LQ Control Techniques.IMA Journal on Control and Information Science. (To appear).
Watt, A. S., 1947: Pattern and process in the plant community.J. Ecolo. 35, 1–22.
Wolfram, S., 1984: Cellular automata as models of complexity.Nature 311, 419–424.
Author information
Authors and Affiliations
Additional information
With 6 Figures
Rights and permissions
About this article
Cite this article
El Jai, A., Fournier, M., Kassara, K. et al. Vegetation dynamics: A deterministic modelling approach using the concept of spreadability. Theor Appl Climatol 52, 241–249 (1995). https://doi.org/10.1007/BF00864047
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00864047