Structural dynamics of plant-pollinator mutualistic networks

Abstract

The discourse surrounding the structural organization of mutualistic interactions mostly revolves around modularity and nestedness. The former is known to enhance the stability of communities, while the latter is related to their feasibility, albeit compromising the stability. However, it has recently been shown that the joint emergence of these structures poses challenges that can eventually lead to limitations in the dynamic properties of mutualistic communities. We hypothesize that considering compound arrangements-modules with internal nested organization-can offer valuable insights in this debate. We analyze the temporal structural dynamics of 20 plant-pollinator interaction networks and observe large structural variability throughout the year. Compound structures are particularly prevalent during the peak of the pollination season, often coexisting with nested and modular arrangements in varying degrees. Motivated by these empirical findings, we synthetically investigate the dynamics of the structural patterns across two control parameters-community size and connectance levels-mimicking the progression of the pollination season. Our analysis reveals contrasting impacts on the stability and feasibility of these mutualistic communities. We characterize the consistent relationship between network structure and stability, which follows a monotonic pattern. But, in terms of feasibility, we observe nonlinear relationships. Compound structures exhibit a favorable balance between stability and feasibility, particularly in mid-sized ecological communities, suggesting they may effectively navigate the simultaneous requirements of stability and feasibility. These findings may indicate that the assembly process of mutualistic communities is driven by a delicate balance among multiple properties, rather than the dominance of a single one.

Keywords: community ecology; feasibility; in-block nestedness; mutualistic networks; stability.

Fig. 1.

The figure illustrates the hypothesized impact of different pressures and parameter variations (network size and connectance) along the pollinator season on the structural arrangement of plant–pollinator networks. The upper part of the figure illustrates different structural transformations that one might find throughout the pollinator season: nested to modular, compound to nested, etc. The lower part of the figure shows a line plot with the average variation in size and connectance of the interaction networks observed in the empirical dataset used in this article.

Fig. 2.

Location of the plant–pollinator communities considered in our study. Inset provides information about the aggregated number of interactions captured over the years in the datasets.

Fig. 3.

A) Temporal evolution of the interaction networks’ structure in 20 plant–pollinator communities. Green, gray, and blue colors in the pie diagrams relate to the significant z-scores ($z-\text{score}>1.96$) obtained for modular, hybrid (in-block nested), and nested arrangements, respectively. Slices displaying a single color indicate that only one structure was found to be significant. In slices containing multiple colors, the area of each color represents the respective proportions of the different z-scores obtained. The area outlined with a thicker line indicates the structural descriptor that achieved the highest z-score. White circles indicate that no structure was found to be significant. Datasets are sorted in descending order by latitude, from North to South. The inset aggregates the results by month, highlighting the most predominant structure (indicated by the highest z-score) across the various temporal slices of the dataset. B) provides an intuitive hierarchy, matching each combination of significant z-scores to a prototypical structural pattern. Column 4 shows the expected structural configuration, while Column 5 relates the analysis to (A) of this figure. Lastly, Column 6 indicates the frequency of each structure detected in the dataset. Section S3 provides the raw values from the structural analysis. Also, it includes a scatter plot that illustrates the relationship between the z-scores obtained for Q and $\mathcal{I}$ arrangements.

Fig. 4.

Diagram illustrating the evolution of size and connectance in relation to the differences in statistical significance of the analyzed structural arrangements. Each point represents a snapshot of the interaction network from a specific dataset, with consecutive snapshots connected by lines. The color scale indicates the absolute difference between the z-scores obtained for nested-like and modular structures. The inset displays the average displacement of consecutive temporal snapshots over the size-connectance diagram with respect to the fraction of time a modular structure is found to be predominant in the plant–pollinator community. Each point corresponds to a dataset. See Section S3 for the raw values obtained in the analysis.

Fig. 5.

Stability and feasibility performance in nested, modular, and in-block structured networks. A) Stability vs. feasibility analysis for an ensemble of synthetic networks with varying levels of in-block nested ($B=2$, $p\in [0,0.06]$, $\mu \in [0,0.06]$, $\xi \in [1.2,1.5]$), nested ($B=1$, $p\in [0,0.1]$, $\mu =0$, $\xi \in [1.85,2.55]$), and modular ($B=2$, $p=1$, $\mu \in [0,0.1]$, $\xi \in [1.1,1.5]$) features, with $S=20$ species ($|A|=|P|=S$) and connectance $C=0.2$. Each point represents a network, with its color indicating the type of structural arrangement it contains: blue for nested networks, green for modular networks, and gray for in-block nested networks. Red crosses are located at the average values of stability and feasibility of the corresponding network clusters. B) Stability and feasibility dependence on connectance C) for nested, in-block and modular networks of size $S=20$ (left) and $S=60$ (right). For a fixed connectance, the average feasibility and stability on several network realizations are reported (shadowed areas represent the variance). All the experiments are performed with $\gamma =0.1$ and $\omega =0.01$ parameters of the Lotka–Volterra dynamics. C) Here, the stability–feasibility ordering across architectural patterns is portrayed for different values of connectance, varying in the range $[0.07,0.15]$ at fixed size. Dot-solid lines depict the average of the related network ensemble with size, while darker colors indicate increasing connectance. Deviation around central values arises because of the noise introduced in the interactions between species (see Materials and methods). D) Along the same line, the information of the previous plot is presented for different values of the size $[20,60]$ at fixed connectance.

Fig. 6.

Validity of the mediating role of IBN as a function of mutualism and competition strength. The green area depicts the parameter regime where Eq. 1 holds, i.e. the mediating role of IBN structures is present. Instead, the blue (grey) area indicates the parameter range where nested (modular) structures are best at balancing stability and feasibility. Experiments were conducted with networks of $S=20$ and $C=0.2$.

Fig. 7.

Description of the temporal slices used to construct the interaction network for each dataset in (19). Red dots indicate slices and datasets (dots near the name) we discard because lack of data to assemble the interaction network.

Fig. 8.

Examples of adjacency matrices of networks associated with nested A), modular B), and IBN C) structures. Rows represent species of group A and columns represent species of group P. Matrix entries portray the mutualistic interaction links between the two groups. In nested networks, the specialist species interact only with subsets of species interacting with the more generalists, and the related adjacency matrices manifest the traditional triangular structure. Modular networks are composed of weakly interlinked groups of species (modules) with strong internal connectivity, and this yields an adjacency matrix divided into blocks. IBN matrices are divided into blocks with an internal nested structure.