The analysis of trophically complex mathematical ecosystem models is typically carried out using numerical techniques because it is considered that the number and nonlinear nature of the equations involved makes progress using analytic techniques virtually impossible. Exploiting the properties of systems that are written in Kolmogorov form, the conservative normal (CN) framework articulates a number of ecological axioms that govern ecosystems. Previous work has shown that trophically simple models developed within the CN framework are mathematically tractable, simplifying analysis. By exploiting the properties of Kolmogorov ecological systems it is possible to design particular properties, such as the property that all populations remain extant, into an ecological model. Here we demonstrate the usefulness of these results to construct a trophically complex ecosystem model. We also show that the properties of Kolmogorov ecological systems can be exploited to provide a computationally efficient method for the refinement of model parameters which can be used to precondition parameter values used in standard optimisation techniques, such as genetic algorithms, to significantly improve convergence towards a target equilibrium state.