Summary
A basic structure [Eqs. (5), (6), (3), (12), (30)] for mathematical models of resource-population systems is presented. This basic structure may be specified in order to include different alternative hypotheses and it represents, therefore, a family of particular models. The study of one of its particular realizations [Eqs. (31) and (39)] shows that its behavior agrees qualitatively with what should be expected from biological considerations.
Even when the system of nonlinear differential equations could not be solved explicitly, important information has been obtained, by studying its properties in the limiting cases, its sensitivity to changes in the parameters, and the results of computer simulation.
The proposed model, duplicating some of the basic features of a population living under resource limitation, and allowing a coupling with a predator population, is intended to be used as an elementary component in food web or ecosystem theoretical studies. The studies need not include detailed descriptions of the population variables, but rather only its essential, gross features, in order to explore the properties that characterize the complete systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Bertalanffy, L. von: General system theory. New York: George Braziller, Inc. 1968.
Gallopín, G. C.: A generalized model of a resource-population system. Ph. D. Thesis, Cornell University, New York (1969).
Hairston, N. G., Smith, F. E., Slobodkin, L. B.: Community structure, population control, and competition. Amer. Naturalist, 94, 412–425 (1960).
Herbert, D. 1958: In: Tsuchiya et al., 1966.
Ivlev, V. S.: Density and distribution of food as factors in determining the rations of fishes [Russian]. Zool. Zh. 24, 112–125 (1945).
—: Experimental ecology of the feeding of fishes. New Haven: Yale Univ. Press. 1961.
Kostitzin, V. A.: Mathematical biology. London: G. G. Harrap and Co. 1939.
Lotka, A. J.: Elements of physical biology. Baltimore: Williams & Wilkins 1925.
M'Kendrick, A. G., Pai, M. K.: Proc. roy. Soc. Edinb. B 31, 649–655 (1911). In: Tsuchiya et al., 1966.
Monod, J.: Recherches sur la croissance des cultures bacteriennes. Paris: Hermann et Cie. 1942. In: Tsuchiya et al., 1966.
Morin, F., Monod, J.: Sur l'expression analytique de la croissance des populations bacteriennes. Rev. Scient. No 3208, 227–229 (1942).
Pearl, R., Reed, L. J.: On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. nat. Acad. Sci. (Wash.) 6, 275–288 (1920).
Reddingius, J.: A mathematical note on a model of a consumer-food relation in which the food is continually replaced. Acta biother. (Leiden) 16, 133–198 (1963).
Smith, F. E.: Experimental methods in population dynamics: a critique. Ecology 33, 441–450 (1952).
—: Quantitative aspects of population growth. In: E. J. Boell (ed.), Dynamics of growth processes. Princeton, New Jersey: Princeton Univ. Press 1954.
—: Population dynamics in Daphnia magna and a new model for population growth. Ecology 44, 651–663 (1963).
Teissier, G.: Croissance des populations bacteriennes et quantite d'aliment disponsible. Rev. Scient. No 3208, 209–214 (1942).
Tsuchiya, H. M., Fredrickson, A. G., Arias, R.: Dynamics of microbial cell populations. Advanc. Chem. Engng. 6, 125–206 (1966).
Verhulst, P. F.: Notice sur la loi que la population suit dans son acroissement. Corr. Math. et Phys. 10, 113–121 (1938).
Volterra, V.: Variazioni e fluctuazioni del numero d'individui in specie animali conviventi. Mem. Acad. Siencie Roma 2, 31–113 (1926).
—: Leçons sur la theorie mathematique de la lutte pour la vie. Cahiers Scient. 7, 1–214. Paris: Gauthiers-Villard 1931.
Watt, K. E. F.: A mathematical model for the effect of densities of attacked and attacking species on the number attacked. Canad. Entomol. 91, 129–144 (1959).
—: Ecology and resource management. New York: McGraw Hill 1968.
Author information
Authors and Affiliations
Additional information
This work was partially supported by a Ford Foundation fellowship and various Cornell University fellowships.
Rights and permissions
About this article
Cite this article
Gallopín, G.C. A generalized model of a resource-population system. Oecologia 7, 382–413 (1971). https://doi.org/10.1007/BF00345861
Received:
Issue date:
DOI: https://doi.org/10.1007/BF00345861