Comparisons and Contrasts between Asymmetry and Nestedness in Interacting Ecological Networks

Abstract

We compare and contrast asymmetry and nestedness, two concepts used in the characterisation of the specialist-generalist balance in bipartite ecological interaction networks. Our analysis is relevant to mutualistic networks such as those consisting of flowering plants and pollinators, or fruiting plants and frugivores, or antagonistic networks such as those consisting of plants and herbivores, in an ecological community. We shall refer to the two sets of species in the bipartite network as plants and animals, the usual but not the only ecological situation. By asymmetry we mean either connectivity asymmetry or dependence asymmetry, which are essentially equivalent. Asymmetry expresses two attributes: generalists interact preferentially with specialists, and specialists avoid interacting with each other. Nested patterns, in principle, should express these same two features and one more: the presence of a core of interactions among generalists. We compute the full set of perfectly nested patterns that are possible in an L × L matrix with N interactions representing an ecological network of L plants and L animals, and point out that the number of nested arrangements grows exponentially with N. In addition, we analyse asymmetry for the full set of perfectly nested patterns, and identify extremes of asymmetry inside the universe of nested patterns. The minimal asymmetry is marked by a modular core of interactions between species that are neither specialists nor generalists. On the other hand, the case of maximal asymmetry is formed by a set of few generalists and many specialists with equal connectivity. The stereotypic case of nestedness with a core of interactions among generalists has intermediate asymmetry.