Abstract
One-hump maps as single species pioneer and climax ecological models confirm the expected pioneer exclusion in an uninterrupted two dimensional discrete pioneer-climax competition model. Other dynamic situations occur in such models. In particular a mutual exclusion principle is presented as a mathematical theorem.
Similar content being viewed by others
References
Comins, H. N., Hassell, M. P.: Predation in multi-prey communities. J. Theor. Biol. 62, 93–114 (1976)
Franke, J., Yakubu, A.: Geometry of exclusion principles in discrete systems. J. Math. Anal. Appl. 168 No. 2, 385–400 (1992)
Franke, J. Yakubu, A.: Global attractors in competitive systems. Nonlin. Anal. Theory Meth. Appl. 16, 111–129 (1991)
Franke, J. Yakubu, A.: Mutual exclusion versus coexistence for discrete competitive systems. J. Math. Biol. 30, 161–168 (1991)
Franke, J. Yakubu, A.: Exclusion principles for density dependent discrete pioneer-climax models. J. Math. Anal. Appl. (in press)
Hallam, T., Levin, S.: Mathematical ecology: an introduction. In: Biomathematics. 17 Berlin Heidelberg New York: Springer 1986
Harper, J.: Population Biology of Plants. New York: Academic Press 1977
Hassell, M., Comins, H.: Discrete time models for two-species competition. Theor. Popul. Biol. 9, 202–221 (1976)
Hofbauer, J., Hutson, V., Jansen, W.: Coexistence for systems governed by difference equations of Lotka-Volterra type. J. Math. Biol. 25, 553–570 (1987)
Jiang, H., Rogers, T.: The discrete dynamics of symmetric competition. J. Math. Biol. 25, 573–596 (1987)
May, R. M.: Biological populations obeying difference equations: stable points, stable cycles, and chaos, Science 186: 645–647 (1974)
May, R. M.: Simple mathematical models with very complicated dynamics. Nature 261: 459–467 (1976)
Namkoong, G., Selgrade, J.: Disruptions in density dependent succession (Preprint)
Selgrade, J., Namkoong, G.: Population interactions with growth rates dependent on weighted densities. Lect. Notes in Biomath. 92, Berlin Heidelberg New York: Springer 1990
Selgrade, J., Namkoong, G.: Stable periodic behavior in a pioneer-climax model. Nat. Res. Model. 4, 215–227 (1990)
Tilman, D.: Plant Strategies and Dynamics and Structure of Plant Communities. Princeton: Princeton University Press 1983
Waring, R., Schlesinger W.: Forest Ecosystems Concepts and Management. Orlando: Academic Press 1985
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Franke, J.E., Yakubu, AA. Pioneer exclusion in a one-hump discrete pioneer-climax competitive system. J. Math. Biol. 32, 771–787 (1994). https://doi.org/10.1007/BF00168797
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00168797