Animal and Plant Species in Antagonistic and Mutualistic Networks, a Multispecies Mean Field Model

We construct a dynamic system model of a web of NA?animal species interacting with NP plant species using a system of coupled differential equations. The model has a parameter which represents the effect of animal on plant species that can be positive (mutualistic interaction) or negative (antagonistic interaction). We work a Multispecies Mean Field Model MMFM in which the full set of NA and NP variables are reduced to a couple of an average animal and plant species. We study the conditions for existence of the MMFM and relate the result to the difference between animal and plant species in the network. We compare our results with empirical data from pollinators (mutualistic) and herbivorous insect (antagonistic) networks. We conclude by combining analytical and empirical work that antagonistic networks present fewer animal species in relation to plant species than mutualistic ones.

Comparisons and Contrasts between Asymmetry and Nestedness in Interacting Ecological Networks

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.