Gaining insight into food webs reconstructed by the inverse method

The use of the inverse method to analyze flow patterns of organic components in ecological systems has had wide application in ecological modeling. Through this approach, an infinite number of food web flows describing the food web and satisfying biological constraints are generated, from which one (parsimonious) solution is drawn. Here we address two questions: (1) is there justification for the use of the parsimonious solution or is there a better alternative and (2) can we use the infinitely many solutions that describe the same food web to give more insight into the system? We reassess two published food webs, from the Gulf of Riga in the Baltic Sea and the Takapoto Atoll lagoon in the South Pacific. A finite number of random food web solutions is first generated using the Monte Carlo simulation technique. Using the Wilcoxon signed ranks test, we cannot find significant differences in the parsimonious solution and the average values of the finite random solutions generated. However, as the food web composed of the average flows has more attractive properties, the choice of the parsimonious solution to describe underdetermined food webs is challenged. We further demonstrate the use of the factor analysis technique to characterize flows that are closely related in the food web. Through this process sub-food webs are extracted within the plausible set of food webs, a property that can be utilized to gain insight into the sampling strategy for further constraining of the model. [KEYWORDS: Inverse method ; Carbon flow ; Food webs ; Parsimonious solution ; Mean solution ; Factor analysis (FA) ; Principal components (PC)