Stability of modular structure in temporal cumulative plant–flower-visitor networks

Abstract

Modularity is a structural property of ecological networks, which has received much interest, but has been poorly explored. Modules are distinct subsets of species interacting strongly with each other, but sparsely with species outside the subset. Using a series of temporal cumulative networks, we investigated the stability of modular organization of pollination networks to temporal scaling. To test for modularity, we used the method ‘functional cartography by simulated annealing’ (Guimerà and Amaral, 2005a,b), a stochastic optimization technique. Modules are detected, and species classified into three types of topological roles in a network, based on patterns of within and between-module links: Hubs are highly connected species; peripherals interact with few species, mainly within their own module; and connectors have few interactions, too, but link across modules. We observed interactions between all flowering plants and flower-visiting insect species throughout the flowering season at three dry heathland sites in Denmark. For each site, we constructed cumulative networks every 0.5 months, resulting in series of 10–12 networks per site. Numbers of interactions, and plant and insect species accumulated throughout the period, while level of modularity (M) and number of modules (NM) was largely invariant to temporal scaling. The proportions of hub, peripheral and connector species were unaffected by scaling of the network. The networks had a multi-star structure, consisting of modules each formed around one or two hubs. These hub species encompassed a small number of plant species, many of which acted as hubs at several study sites and throughout most of their flowering season. Thus, these plants become of key importance in maintaining the structure of their pollination network. We conclude that the modular structure of heathland pollination networks is stable to temporal scaling, a pattern repeatedly found at three sites of similar habitat.