Invariant properties in coevolutionary networks of plant–animal interactions

Abstract

Plant-animal mutualistic networks are interaction webs consisting of two sets of entities, plant and animal species, whose evolutionary dynamics are deeply influenced by the outcomes of the interactions, yielding a diverse array of coevolutionary processes. These networks are two-mode networks sharing many common properties with others such as food webs, social, and abiotic networks. Here we describe generalized patterns in the topology of 29 plant-pollinator and 24 plant-frugivore networks in natural communities. Scale-free properties have been described for a number of biological, social, and abiotic networks; in contrast, most of the plant-animal mutualistic networks (65.6%) show species connectivity distributions (number of links per species) with a power-law regime but decaying as a marked cut-off, i.e. truncated power-law or broad-scale networks and few (22.2%) show scale-invariance. We hypothesize that plant-animal mutualistic networks follow a build-up process similar to complex abiotic nets, based on the preferential attachment of species. However, constraints in the addition of links such as morphological mismatching or phenological uncoupling between mutualistic partners, restrict the number of interactions established, causing deviations from scale-invariance. This reveals generalized topological patterns characteristic of self-organized complex systems. Relative to scale-invariant networks, such constraints may confer higher robustness to the loss of keystone species that are the backbone of these webs.

Build-up mechanisms determining the topology of mutualistic networks

“…Thus, the proposed mechanisms cannot be interpreted as constraints acting on preferential attachment. This is an important difference in relation to previous mechanisms such as forbidden links or filtering information constraining the preferential attachment process (Amaral et al, 2000;Jordano et al, 2003;Mossa et al, 2002).…”

“…5A). The cut-off value, k x , was recorded from the literature (N ¼ 41 networks; Jordano et al, 2003) and /kS was estimated for each set separately.…”

“…In the network formalism, species are represented by nodes, and interactions between species are described by links (reviewed by Pimm, 2002). The network approach is helping to describe community-level patterns of interspecific interactions and understanding how interactions coevolve in species-rich assemblages Guimara˜es et al, 2006;Jordano et al, 2003;Lewinsohn et al, 2006;Montoya et al, 2006;Prado and Lewinsohn, 2004). Our major challenge, however, is to infer what are the ecological and evolutionary factors that generate the observed community-level structure of ecological networks (Fig.…”

“…For example, power-law distributions can arise when recently arrived species are likely to interact with the most generalist species . In contrast, exponential truncations have been associated with constraints limiting the existence of species with many interactions (Amaral et al, 2000;Jordano et al, 2003;Mossa et al, 2002) or with the random initial condition at the origin of network (Guimara˜es et al, 2005). However, few theoretical studies explore alternative explanations for exponential truncations that characterize typical features of plant-animal mutualisms (but see Vazquez, 2005).…”

“…However, few theoretical studies explore alternative explanations for exponential truncations that characterize typical features of plant-animal mutualisms (but see Vazquez, 2005). Plant-animal mutualisms are best described as bipartite networks, in which there are two disjoint sets of species (animals and plants) and there are no interactions between species within the same set (Harary, 1969;Jordano et al, 2003). The bipartite structure per se does not affect the degree distribution (Ergun, 2002;Liljeros et al, 2001).…”