The implications of this link diversity to the structure, stability and dynamics of networks are unknown. Melián et al. (2009), for example, found that strong links and a high ratio of mutualistic : consumer/resource links were important for the diversity of networks. In food webs, parasites are major determinants of stability (Lafferty et al. 2006), strongly affecting network features. Among network features recorded in mutualistic networks are nestedness, in which the links of specialists are subsets of the links of more generalized species (Bascompte et al. 2003), and modularity, in which species are organized into small, strongly linked groups or modules, which are loosely interlinked (Olesen et al. 2007).

The visitation matrix of Bignoniaceae had nine modules, each with 2–14 species. Most species were peripherals (N = 62%, figure 2), i.e. with only one to two links to other species, but three species were connectors between modules, viz. the nectar-robbing bees Xylocopa suspecta, Oxaea flavescens and Euglossa annectans. The plants Adenocalyma bracteatum and Anemopaegma chamberlaynii were module hubs, whereas Arrabidea triplinervia was a network hub (figure 2). Cheaters show much less co-occurrence among modules in the Bignoniaceae visitation matrix than expected by chance (C score = 0.86, P = 0.0002), indicating that cheaters were overdispersed among modules. However, one module was composed exclusively of cheaters and Lundia obliqua. The plant–cheater matrix of Bignoniaceae had seven non-connected modules with 3–12 peripheral species. Here, the same bee species as in the visitation matrix were classified as connectors, whereas A. bracteatum and A. triplinervia were module hubs. The pollen robbery matrix had five modules with two to six species, and all animals were peripherals (L_m = 1.0, table 1).

The Bignoniaceae networks had a completely different topology from our Malpighiaceae networks. In the Bignoniaceae networks, connectance is only half of that in the Malpighiaceae networks, indicating that the Bignoniaceae networks are more specialized. In addition, the Bignoniaceae visitation network was non-nested, but modular. The reason for this was the many specialized links (i.e. one or two animals visiting one plant species only) between pollen robbers and their plants. Pollen robbery is similar to herbivory, and herbivory networks are strongly modular (Lewinsohn et al. 2006). An increase in cheating in visitation networks may decrease nestedness, but increase modularity. Large pollination networks are modular (Olesen et al. 2007). However, this assumes that all links are pollinatory. We show that, besides phylogenetic clustering and trait convergence (Olesen et al. 2007), consumer/resource links, such as cheating links, also contribute to modularity.

Malpighiaceae is pan(sub)tropical with ca 1250 species, with oil flower species restricted to the neotropics. Female bees collect pollen and oil, which is used as larval provision and for nest cell walls (Sigrist & Sazima 2004). In this study, 26 of the 29 bee visitor species were known oil collectors (Vogel 1974). The oil-collecting species made 93–96% of all links in the matrices. Thus, the Malpighiaceae visitation and pollination networks are bee pollination–floral-oil systems, and the small cheating networks are a floral-oil harvesting system. However, floral resources in Malpighiaceae species seem difficult to exploit by visiting animals without pollinating. As Bezerra et al. (2009) indicated, the phylogenetic and ecological similarity among partners results in a high nested pattern in this flower-oil system.

Bignoniaceae is a predominantly neotropical family with ca 800 species pollinated by insects, birds and bats (Gentry 1980). Bignoniaceae flowers are much more diverse than Malpiguiaceae, allowing a much larger array of flower visitors the access to their flower rewards. In the network, 54 per cent, 23 per cent and 23 per cent of the animals were bees, butterflies and others (Diptera, Coleoptera and hummingbirds), respectively. Bees were mainly pollinators or nectar robbers; butterflies and hummingbirds were mainly nectar robbers, and most of the ‘others’ were pollen robbers. Nectar robbers act as the glue of the Bignoniaceae network, connecting the modules and increasing the cohesiveness of the network, while pollen robbers show more specialized links. The distribution of cheaters among modules might imply that robbers are overdispersed in niche space leading to the observed modular pattern, and/or may be a result of flower features such as calyx thickness and pubescence and corolla shape, which constrains the foraging of bees. Finally, the proportion of cheaters was three times higher in Bignoniaceae networks than in Malpighiaceae networks. The reasons might be that (i) the adaptations of the morphology and behaviour of visitors to flowers of the Malpighiaceae are much tighter, making it more difficult to harvest rewards without pollinating, and (ii) the oil resource is more costly than nectar to produce, resulting in a more specialized, conservative flower-pollination system, and the adapted visitors morphology and behaviour on Malpighiaceae flowers.