Mathematical and statistical formulation of an ecological model with applications

In many cases, modelling of ecosystems results from the setting up of a system of ordinary, non-linear differential equations whose flow variables are functions obtained from experimental data. In this paper we develop a new methodology based on choosing a set of functions so that we are able to adjust their linear combination using multiple linear regression. Choosing these functions, however, implies the prior consideration of a finite set of analytical functions of ‘elementary type’ and then analyse their compositions up to an order n, which will be called ‘n-transformed’. These transformed functions are the ones which will then be adjusted. As an application of this new methodology the Mariola model is considered.