Lotka–Volterra model parameter estimation using experiential data

The purpose of mathematical models is, in principle, to assist management with decision-making processes in various fields of science. These models invariably include a number of parameters, of which the method of estimation is often 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, these techniques are expensive, require expert knowledge and often are not accessible to scientists. In this paper we discuss two alternative methods to estimate the parameters, using basic mathematical and statistical principles and a standard linear regression software package. The first method is referred to as the Integral method and the second as the Log Integral method. As an example, both these techniques are applied to determine the unknown parameters in a system of non-linear differential equations that describe an available set of data.To illustrate the effectiveness of these simplistic methods, a three competing species Lotka–Volterra model is used as vehicle: For a given data set the model parameters obtained by an advanced artificial intelligence method are compared to the parameter values obtained when applying the proposed methods. The different approaches result in completely different estimates of the parameter values for the system, yet the solutions, using these different sets of parameters values, fit the raw data equally well. The Integral and Log Integral methods are accessible to researchers with little knowledge of mathematics, statistics or technology, and are not restricted by the nature of the problem, the number of equations or number of parameters involved. These methods are applicable to a broad spectrum of dynamical systems originating in the fields of environmental, physical, biological and social sciences.