Evidence of structural balance in spatial ecological networks

Abstract

International audienceDespite recent advances in applying networks to study ecological systems, most of the network datasets are built attending only to a single type of interaction between nodes, which can be an oversimplification. In the present work, we built ecological networks that had positive and negative links for multiple plant communities based on the local spatial association between species. Then, we evaluated whether those networks were in balance, a hypothesis commonly formulated for real signed graphs but never tested in systems other than social networks. Specifically, we quantified the global and the local structural balance in the networks. We found that plant community networks were more balanced than expected by chance, and that this pattern was due to a large number of balanced triads to the detriment of unbalanced ones. Furthermore, this pattern was consistent among all of the types of the plant communities examined, which suggests that configurations that promote structural balance might be common in ecological signed networks. We also found that almost all networks had some unbalanced components, which might be responsible for the adaptation of the system. Mechanisms behind these structure and possible applications for community ecology are discussed. Our results encourage testing structural balance in other ecological networks to confirm if it is a widespread architecture of natural systems

The structure of plant spatial association networks is linked to plant diversity in global drylands

“…High values of K indicate that the network presents a “balanced” structure (with K = 1 indicating a perfect balance), while low values indicate that several links do not fulfil this criterion and network is “unbalanced” (“frustrated,” sensu Doreian & Mrvar, ). In our case, high K indicates the presence of different types of vegetation patches in the community, where species from the same block conform a particular type of patch and present the same spatial pattern respect to the species present in another patch (Saiz et al., ). In summary, these indices allow us to cover different components of the spatial structure of the plant community: the importance ( D ) and variety ( H ) of spatial patterns, the dominant type of association (i.e.…”

“…For each of the sites studied, we built a plant–plant spatial association network (Saiz et al., , ) using the cover data of all the perennial species ( S ) surveyed. These networks are characterized by the adjacency graph A SxS (hereafter A ), where the nodes ( i , j ) are the plant species and the links ( l ij ) are the spatial association between each pair of species.…”

“…However, and regardless of the dominant spatial pattern found at each site, vegetation patches seem to be organized according to the structural balance criteria in drylands. Thus, within a given plant community, there are different types of patches, and plant species that conform the same type of patch do not appear in patches formed by other species (Saiz et al, 2017). In drylands, usually species responsible of patch formation are well adapted to local conditions and facilitate the establishment of seedlings of less adapted species under their canopies (Valiente-Banuet, Rumebe, Verdú, & Callaway, 2006 scarce resources present in the environment, and facilitated species compete among them for the space and resources below the canopy of the nurses (Soliveres et al, 2011).…”

“…Plant communities are the bottom of the trophic web, play a major role in ecosystem nutrient cycling and are responsible of community physiognomy (Barbour, ). Despite their critical ecological role, plant–plant interactions have been largely unnoticed by network studies until very recently (Saiz et al., ; Verdú & Valiente‐Banuet, ). The efforts required for obtaining data on plant–plant interactions at the community level over a large number of sites (Soliveres & Maestre, ), and the different type of interactions that can be established between plants (Brooker et al., ), have traditionally hampered the use of network analyses to study the structure of plant communities.…”

The structure of plant spatial association networks increases plant diversity in global drylands

“…Plant communities are the bottom of the trophic web, play a major role in ecosystem 54 nutrient cycling and are responsible of community physiognomy (Barbour, 1987). Despite their 55 critical ecological role, and the long tradition of ecological studies with plants, they have been 56 largely unnoticed by network studies until very recently (Verdú et al, 2008;Saiz et al, 2016). 57…”