Date of Award:

5-1978

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Plants, Soils, and Climate

Department name when degree awarded

Biology Ecology

Committee Chair(s)

David W. Goodall

Committee

David W. Goodall

Committee

Clayton S. Gist

Committee

Rex L. Hurst

Committee

James A. MacMahon

Committee

H. Charles Romesburg

Committee

Glen H. Smerage

Abstract

Recent attempts to apply frequency response analysis to compartmental models of ecosystems are flawed by the failure to define terms in an unambiguous and ecologically meaningful way, and by the failure to distinguish between information feedback and closed material loops. Analysis of the sensitivity of linear models to changes in the A matrix has shortcomings too: elements of the A matrix are often derived from more fundamental parameters and thus do not have a direct relationship to the parent model; only sensitivities to the fundamental parameters will be unconfounded and readily interpretable. A more serious problem with these techniques is that they apply to only linear models.

A general approach to the analysis of compartmental models of ecosystems should include an investigation of the model's sensitivity to changes in: (1) the particular assemblage of compartments, flows and exogenous inputs incorporated into the model; (2) forms of the equations describing the flows; (3) initial conditions of state variables, and values of parameters and exogenous variables. These test provide adequate information for a meaningful appraisal of a model's behavior, predictive potential, and scope of applicability-- precisely the things one must know before he can make rational use of the model as a predictor. Furthermore, these tests can be applied to nonlinear models.

This approach is employed here in an analysis of a model of desert ecosystems. The parameters in the model's feeding function are the only ones to which the model has an unreasonably high sensitivity. A new herbivory function, accounting for the effects of interference competition and exploitation competition, is suggested. The study illustrates the value of relatively high resolution in terms of the number of compartments included in a model, even when there is low resolution in terms of the complexity of the mathematical functions representing the flows between compartments.

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