Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy

Thesis Advisor: Gilmer L. Blankenship

Department of Systems and Control Engineering, Case Western Reserve University

January 1979



Michael Gene Waldon


Abstract - Theories of competitive interaction between species have served as central organizing concepts in ecology. Many significant factors, however, have not yet been considered as extensions of these theories. One of the most unrealistic assumptions of most contemporary theories requires that the model parameters remain constant. This assumption excludes consideration of seasonal or random environmental disturbance. Here, I present some extensions of the theories of competitive interactions, and test hypotheses suggested by these extensions using natural associations of phytoplankton in semi-continuous culture.


A purely competitive species assemblage may be viewed as a feedback control system, with feedback through the resource dynamics providing the stabilizing negative feedback path. It is shown that a necessary condition for coexistence is the controllability of the populations through the resource, and the observability of the populations through the exploitation of the resources. These conditions unify and extend most contemporary statements of the competitive exclusion principle. It is shown that, if the parameters describing the growth of the populations are piecewise constant over m intervals throughout one period, the upper bound on the number of species that may coexist is increased by a factor of m above the bound for constant parameters. Thus, the competitive exclusion principle is less restrictive in a variable environment.


Necessary and sufficient conditions for coexistence of two competitors are next calculated, based on the conditions that each species can successfully invade the other. This results in conditions which relate magnitude and frequency of disturbance of parameters, to coexistence. From these calculations, it appears that small disturbances will have no effect on coexistence, and that, for disturbances with long periods, the conditions for coexistence are independent of that period.


Conditions for coexistence do not give any information about the magnitude of the variations in the populations, or the relative proportions of each species. By assuming that the parameters for the growth of the two species differ only slightly, a seperation of time scales allows the approximate solution of the model in terms of a quickly changing biomass component, and a slowly changing variable, the logarithm of the ratio of the populations. This assumption, that the parameters of the two species differ only slightly, corresponds to the common choice of closely related species for experimental observation of the effects of competition.


The theoretical analyses presented here suggest the hypothesis that species diversity may be higher in time-varying environments. In order to test this hypothesis, semi-continuous cultures of natural associations of phytoplankton were maintained for eight weeks under conditions of temperature variation, light variation, light and temperature variation, and under constant light and temperature. New cultures were inoculated each week by sterile transfer of one ml into 14 ml of sterile medium. Application of the Mann Whitney U-test reveals that both Simpsonís index of diversity and the Shannon-Weiner index of diversity were significantly (p < .05) higher in the time-varying cultures. This demonstrates that temporal variations in the environment can result in increased species diversity.


In the future, the importance of the application of systems theory in ecology will continue to increase. Possible areas for the extension of the theories developed here are described in the final chapter. Other productive applications are also discussed. The development of these unique and exciting applications of systems theory may not only aid in the development of ecology, but also provides new insights and promotes extensions of our present understanding of modern control theory.



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