Modularity and the spread of perturbations in complex dynamical systems

Modularity buffers the spread of spatial perturbations in macroalgal networks

Theory predicts that spatial modular networks contain the propagation of local disturbances, but field experimental tests of this hypothesis are lacking. We combined a field experiment with a metacommunity model to assess the role of modularity in buffering the spatial spread of algal turfs in three replicated canopy-dominated macroalgal networks. Experimental networks included three modules where plots with intact canopy cover (nodes) were connected through canopy-thinned corridors. The local perturbation consisted of removal of the canopy and understory species from four nodes within a single module to enable the establishment of algal turfs, which could then spread vegetatively to other untouched nodes through the canopy-thinned links. Results show that algal turfs invade mainly untouched nodes in the perturbed module, in agreement with the hypothesis that modularity can effectively constrain the spread of a spatial perturbation. The metacommunity model supports the empirical findings, illustrating greater resistance to perturbations of modular than random macroalgal canopy networks and making alternative explanations for the observed results unlikely. Evidence that the buffering effect of modularity can operate in natural environmental conditions has important implications for designing more robust networks of protected areas and less-fragile human-dominated fragmented landscapes.

Accelerating network layouts using graph neural networks

Graph layout algorithms used in network visualization represent the first and the most widely used tool to unveil the inner structure and the behavior of complex networks. Current network visualization software relies on the force-directed layout (FDL) algorithm, whose high computational complexity makes the visualization of large real networks computationally prohibitive and traps large graphs into high energy configurations, resulting in hard-to-interpret "hairball" layouts. Here we use Graph Neural Networks (GNN) to accelerate FDL, showing that deep learning can address both limitations of FDL: it offers a 10 to 100 fold improvement in speed while also yielding layouts which are more informative. We analytically derive the speedup offered by GNN, relating it to the number of outliers in the eigenspectrum of the adjacency matrix, predicting that GNNs are particularly effective for networks with communities and local regularities. Finally, we use GNN to generate a three-dimensional layout of the Internet, and introduce additional measures to assess the layout quality and its interpretability, exploring the algorithm's ability to separate communities and the link-length distribution. The novel use of deep neural networks can help accelerate other network-based optimization problems as well, with applications from reaction-diffusion systems to epidemics.

The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling

The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization-the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular.

Small vertebrates are key elements in the frugivory networks of a hyperdiverse tropical forest

The local, global or functional extinction of species or populations of animals, known as defaunation, can erode important ecological services in tropical forests. Many mutualistic interactions, such as seed dispersal of large seeded plants, can be lost in large continuous forests due to the rarity of large-bodied mammalian frugivores. Most of studies that try to elucidate the effects of defaunation on seed dispersal focused on primates or birds, and we lack a detailed understanding on the interactions between ground-dwelling fauna and fleshy fruits. Using camera traps in forest areas with different degrees of defaunation, we described the organization of frugivory networks involving birds, mammals and plants. We recorded 375 frugivory interactions between 21 frugivores and 150 fruiting trees of 30 species of fleshy fruit plants in six sites in continuous Atlantic forest of Brazil. We found that small frugivores-particularly small rodents and birds-were responsible for 72% of the events of frugivory. Large frugivores, such as tapirs and peccaries, were responsible for less than 21% of frugivory events. Our results indicate that the interactions between flesh fruiting plants and frugivores are dominated by small frugivores, an indication of a functional loss of large frugivores in this endangered biome.

Multiscale dynamical embeddings of complex networks

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.