Applications of Discrete and Continuous Network Theory to Linear Population Models

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Abstract
The well—established methods of network construction and analysis are adapted to the problem of modeling single populations. A major advantage of the resulting approach is that it allows explicit incorporation of key processes in the life cycle of the organism being modeled, with feedback loops providing economy of representation where they are allowed. Thus, network structures provide heuristic vehicles by which population models can be developed and modified. When a model is linear and has parameters that do not vary with time, a characteristic dynamic function can be derived by inspection from a simple transform of the network representation. The zeros of the function can be found (analytically or by commonly available numerical methods) and used directly to deduce the modeled population's dominant growth pattern and its propensity to sustain oscillations. In addition, under certain conditions (i.e., that the network model not contain both time delays and integrators), a straightforward mathod (partial fraction expansion) is available for deduction of the modeled population's specific responses to a variety of perturbations.

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