Linear Inverse Modeling refers to a class of methods used in ecology for modeling trophic networks and estimating unknown flows therein. The model is constrained by both structural and empirical linear equations. The empirical ones come from measures with uncertainty. Here, we introduce a degradation methodology whose goal is to study the impact of this uncertainty on Ecological Network Analysis (ENA) indices. Two approaches are compared. The deterministic approach uses Sequential Quadratic Programming to find the optimum solution of a given ENA. The stochastic approach uses the distribution of a Markov Chain Monte Carlo sampling based on a reflective version of Hit-and-Run. The results of these two approaches are compared for three ENA: Quadratic Energy, McArthur Index and Overhead.The comparison is illustrated by one hundred and twenty-eight degradation scenarios of an aggregated model of the Sylt-Rømø Bight ecosystem.