Estimation of the Parameters in Population Models

P.H. Kloppers and J.C. Greeff (S. Africa)


Systems modelling, Integral method, estimation of parameters


The purpose of mathematical models is, in principle, to assist management with decision-making processes in various fields of sciences, in this case applied to the field of environmental conservation. These models invariably include a number of parameters, of which the method of estimation has often been in question when the models as managerial tools are evaluated. Advanced software packages involving artificial intelligence are available to estimate these parameters, and have been proven to be extremely effective. However, they are expensive, require expert knowledge and often are not accessible to scientists. In this paper we discuss an elementary approach, referred to as the Integral method, to estimate the parameters of a nonlinear system. To illustrate the effectiveness of the proposed Integral method, a Lotka-Volterra model is used as vehicle: The results when estimating the model parameters using advanced methods are compared to the results when applying the Integral method. The different approaches result in completely different estimates of the parameters of the system, yet the solutions obtained by these two approaches fit the raw data equally well. The Integral method is accessible to researchers with little knowledge of mathematics or technology, and is applicable to a broad spectrum of sciences.

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