Effective trophic positions in ecologicalacyclic networks

In the tropho-dynamic analysis of ecosystems the heuristic, discrete concept of trophic level has been replaced by the more realistic, continuous definition of trophic position. In ecological network analysis (ENA) the suite of matrix manipulations called canonical trophic aggregation (CTA) apportions each species' feeding activity to a series of discrete trophic levels sensu Lindeman. The effective trophic position is computed as the sum of the fractions of trophic activity that each species performs at different trophic levels. In this paper we present an extension of the CTA that combines matrix manipulation and sensitivity analysis. Applying this "extended" CTA to an hypothetical network and to real ecosystems we show how trophic position can be computed taking into account the contribution of external inflows, making it scale-insensitive. Moreover "extended" CTA solves ambiguities related to trophic position in the presence of multiple non-living nodes, considering them as imports.