Indirect connectance and scaling relations in food webs.
Allesina, Stefano *,1, Bodini, Antonio2, 1 Michigan State University, East Lansing, MI, USA2 Università di Parma, Parma, Italy
ABSTRACT- Research on food webs has focused primarily on direct species interactions in order to identify and understand features and properties common (and distinct) to all ecosystems. Direct interactions between species, however, combine to give rise to a huge number of indirect relationships. Nevertheless, indices based on indirect interactions are scarcely represented in the food web literature. New patterns emerge if one traces in a matrix "who interacts with whom" more broadly (i.e. direct and indirect interactions as opposed to just direct). We examined a food web by tracing its indirect connectance and the one of all the possible source webs included in the food web, that is to say all the sub-food webs contained in the original one. The distribution of the number of connections of the sub-webs is related to the number of species in the sub-web with a power law. Patterns of indirect connectance in food webs and in sub-food webs are therefore self-similar. This fractal feature holds for the 16 published and well-resolved food webs we analyzed. The goodness of fit of the power law and a constant shape shown by all systems cast new significance to previous studies in self-similarity in food webs. Moreover, the technique presented does not require the simplification of systems to spanning trees, retaining more of the realism of food webs Analyzing food webs' indirect connectance illuminates common organization structure of natural communities, allowing further insight and suggesting new lines of research.
Key words: food web, allometry, power law, indirect connectance
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