Quantifying the interaction structure and the topological importance of species in food webs: a signed digraph approach.

Due to the structural complexity of nature, it is not always easy to identify topologically importance species in an ecosystem. In the past decade, several studies in ecology have developed methods for measuring species importance basing on direct and indirect inter-specific interactions. Here, by extending a previously developed methodology, we present an approach that can quantify the interaction structure of a food web and consequently the topological importance of species when the food web is viewed as a signed digraph. The basic principle behind our approach is to determine the sign and strength of direct and indirect interactions for all pathways up to a predefined number of steps. Our approach mainly differs from the previous methodology in that we are able to quantify the strength of inter-specific interaction as well as in what way species interact with each other, as it can explicitly quantify a wide range of ecological interactions such as cascading effect, indirect food supply effect, apparent and exploitive competitions in the same framework. This then allows us to quantify the topological importance of a species and examine whether it is a predominately positive or negative interactor in a food web. Furthermore, our analysis reveals that positive and negative effects from one species on others eventually cancel each other out for longer pathways resulting in stable interaction structure. Applications of our methodology include providing a more informative index for conservation biologists, and the potential use of interaction structure derived from our approach in food web robustness studies is also discussed.