Flux-based estimation of parameters in S-systems

This paper proposes a technique for parameter estimation in S-systems which explicitly takes into account the structure of the S-system dynamic equations as the differences between two fluxes, each of which is a power-law function of state and external variables. If observed values of a flux are available for a number of sets of the variables which influence that flux, the technique of flux-based parameter estimation provides a simple method for estimating the parameters in the flux. Flux-based estimation applies multiple linear regression to the logarithms of the fluxes in terms of the logarithms of the variables and only requires that the number of sets of observations exceed the number of unknown parameters in the flux term. The technique is especially valuable for obtaining initial estimates for an application of a traditional nonlinear least-squares technique for fitting observed data to a dynamic model. Since the S-system fluxes are power-laws, the conclusions drawn here also apply to the estimation of power-laws. The straightforward application of flux-based estimation to data in which the state and external variables are subject to an allometric relationship can give estimates which are unrealistic. It is shown that under these conditions the estimated kinetic orders are linearly related to the logarithms of the rate constants, and that these relationships provide a powerful guide to selecting appropriate, meaningful estimates for the parameters. Different scenarios are illustrated with data obtained from an S-system model of forest growth. The effect of observational error is illustrated by using this model of forest growth to generate observations with varying amounts of observational error.