The structure and robustness of ecological networks with two interaction types

Abstract

Until recently, most ecological network analyses investigating the effects of species' declines and extinctions have focused on a single type of interaction (e.g. feeding). In nature, however, diverse interactions co-occur, each of them forming a layer of a 'multilayer' network. Data including information on multiple interaction types has recently started to emerge, giving us the opportunity to have a first glance at possible commonalities in the structure of these networks. We studied the structural features of 44 tripartite ecological networks from the literature, each composed of two layers of interactions (e.g. herbivory and pollination), and investigated their robustness to species losses. Considering two interactions simultaneously, we found that the robustness of the whole community is a combination of the robustness of the two ecological networks composing it. The way in which the layers of interactions are connected to each other affects the interdependence of their robustness. In many networks, this interdependence is low, suggesting that restoration efforts would not automatically propagate through the whole community. Our results highlight the importance of considering multiple interactions simultaneously to better gauge the robustness of ecological communities to species loss and to more reliably identify key species that are important for the persistence of ecological communities.

Fig 1. Tripartite networks, robustness and interdependence.

A) An Herbivory(h)—Pollination(p) tripartite network, where plants (P) are the shared set of species. B) An Herbivory(h)—Parasitism(pa) tripartite network, where herbivores (H) are the shared set of species. Link colours represent the two interaction layers, and node colours the three sets of species. Connector nodes in the shared set of species are highlighted in black. C) Extinction curve showing the fraction of surviving animal species as a function of plant loss for a given plant extinction sequence in network A. The robustness to plant loss, R, is the area under the curve. Extinction protocol: plants (green nodes) are progressively removed from the community in the prescribed order, their corresponding links are erased (colored in red) and animal species are declared extinct (colored in red) whenever they lose all their feeding links. D) Pairwise correlation in the robustness of the two animal sets—interdependence, I—resulting from 3.000 simulations of random sequential loss of plant taxa in network A.

Fig 2. How does the shared set of nodes connect the network?

A) Proportion of connector nodes in the shared set, B) Proportion of shared set hubs that are connector nodes, C) Average participation coefficient of the connector nodes. Boxplots are color-coded by network type: AA: Antagonistic-Antagonistic, MA: Mutualistic-Antagonistic, and MM: Mutualistic-Mutualistic. Differences among categories are measured by independent t-tests (**** p<1e⁻⁴, *** p<1e⁻³, ns not significant).

Fig 3. Interdependence and robustness of tripartite networks.

A) Interdependence (I) of the tripartite networks in our data set. As I → 1 the importance of plants for the maintenance of the two animal species sets becomes more similar. B) Robustness of the tripartite networks in our data set (R) when plants are randomly driven to extinction. As R → 1, animal groups are increasingly robust to the simulated sequential loss of plant taxa. Grey points represent the values in each network. All boxplots are color-coded based on the type of tripartite network. Differences among the categories are measured by independent t-tests (**** p<1e⁻⁴, *** p<1e⁻³, * p<5e⁻², ns not significant). C) Robustness (R) vs Estimated Robustness (R_est) in the empirical MA and MM networks of our database. The text shows the best estimation of the robustness as a combination of the robustness of the larger (R_L) and smaller (R_S) bipartite networks that compose the tripartite network, and the correlation coefficient. Each point represents a network, color coded based on network type. AA: Antagonistic-Antagonistic in purple, MA: Mutualistic-Antagonistic in green, and MM: Mutualistic-Mutualistic in blue.

Fig 4. Plant importance rankings.

A-F: Scatter plot of the robustness of pollinators (R_P), of the tripartite network (R), and of herbivores (R_H) vs the order of two plants (plant 1 and plant 2, chosen as an illustrative example) in the extinction sequence. The correlation coefficients are used to determine the ranking of importance of plant species. G: Ranking of plant importance for pollinators (right), for the whole community (center) and for herbivores (left). Each plant is represented by a disk whose number reflects its order in the ranking of importance of the whole community (in the tripartite network). The height of the disk represents its order in each of the three different rankings (i.e. the higher the position, the more important). Lines between balls are a visual help to track changes in the rankings. H: Classification of the tripartite networks in our database according to S_set (similarity between the ranking of plant importance in the whole community and in the animal sets), illustrating if the ranking of plant importance in the whole community is mainly determined by only one animal set, is a mixture of the rankings of importance in the two animal sets (mixed), or does not resemble any of the rankings of importance in the two animal sets (emergent).

Fig 5. The 4 different null models used in this study.

Each figure represents what is kept fixed in each null model, going from the less restrictive on the left, to the more restrictive on the right. N_x is the number of nodes in the species set, L_x the number of links in the interaction layer, the color of the nodes represent the different species set, the colour of the link the two different ecological interactions, the size of the node is proportional to its degree (when kept), and connector nodes are highlighted in red.