BIOND LAB

Mutualistic networks provide essential contributions to long-term ecosystem functioning and food security, but Anthropocene stressors continue to alter their structure and size. Previous theoretical approaches produce conflicting predictions for how network features influence dynamical stability, which is the ability to return to the original state after a disturbance. The main methods, which are random matrix models and conventional differential equation models, face certain limitations, including difficulties in incorporating some biological details or explicit parameterization. An alternative approach is given by Generalized Modelling, which combines both high efficiency with high biological realism, but has not been applied to plant–animal mutualistic networks prior to this study. Here, we develop a Generalized Model for mutualism that allows the mathematically rigorous and highly efficient analysis of dynamical stability for many network replicates ( ∼105 per data point). The model incorporates important biological mechanisms that are known to influence stability behaviour, such as animal competition for limited plant resources and saturating mutualistic benefits, without the need for explicit parameterization. Using simulated network structures we find increasing dynamical stability with increasing complexity as measured by the product of species richness and connectance. We are able to explain this effect mechanistically: While mutualistic interactions do represent destabilizing positive feedbacks, the strengths of those feedbacks weaken with increasing complexity because mutualistic dependencies as given by the Jacobian matrix elements in the off-diagonal blocks decrease. We further show that the effect of nestedness on the dynamical stability of simulated networks is negligible compared to the effect of connectance and species richness. Additionally, we find similar relationships between network features and dynamical stability for 160 empirical networks as an input for our model, highlighting the robustness of our findings. As Anthropocene stressors lead to species and interaction loss, our model results predict a corresponding loss in dynamical stability if network complexity is decreased, highlighting the urgency of conservation strategies that preserve network complexity.

The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a network-based approach in which nodes represent communities of interacting agents holding one of two competing opinions, and links represent avenues of migration. Agents adapt to the dominant opinion within a community or migrate toward other communities. Using a master stability function approach, we analytically derive conditions for diffusion-driven pattern formation and identify structural features of the community network that sustain opinion diversity. Our model shows that even under minimal opinion rules, the interaction between local dynamics and community structure generates spatial patterns that allow minority opinions to persist by gaining local dominance.

The HAUSGARTEN Long-Term Ecological Research (LTER) observatory serves as a key information source on the processes occurring in the Fram Strait — a pivotal water exchange zone between the North Atlantic and the Arctic Ocean. This article presents an analysis of the frequencies of amplicon sequence variants (ASVs), derived from 18S rRNA gene metabarcoding profiles of 775 samples, collected in the photic zone during annual expeditions conducted between late May and early October from 2009 to 2021. We investigated spatial and temporal changes in the composition of eukaryotic plankton communities which are major contributors to primary production and fuel the food webs in Arctic marine environments. Our study reveals significant annual and inter-annual patterns in the eukaryotic community composition. Aggregating data by month shows distinct seasonal and spatial differences in the eukaryotic community composition, with biodiversity generally increasing with depth (in both regions) and from June to September. This increase is primarily driven by a rise in Syndiniales and Dinophyceae diversity at greater depths and towards autumn. Inter-annually, biodiversity notably declined, and the June–July community structure shifted significantly in the eastern part, influenced by warmer Atlantic waters, with increased copepod ASVs and reduced frequencies of Syndiniales, Dinophyceae, and various primary producer ASVs, whereas the western part, influenced by polar waters, remained relatively stable. Our findings suggest that ongoing environmental change is altering planktonic communities, potentially affecting carbon circulation pathways and carbon sequestration rates in Fram Strait, with its eastern part being stronger impacted, compared to the western part.

Bacterial cooperation involves the exchange of metabolites, which can range from costless byproducts of metabolism to intentionally produced and costly molecules. These interactions occur across spatial scales, from direct cell contact to the diffusion of metabolites in the environment. Due in part to this variety of interaction modes, the impacts of mutualism on bacterial community dynamics remain unclear. Using generalized models, we derive conditions for the onset of different dynamical behaviours in communities of interacting bacteria across these scenarios. These include exchanges of low-cost metabolites, costly cross-feeding and cases where bacteria produce either most or only a small fraction of available metabolites. Stability depends strongly on metabolite production costs and the balance between metabolite uptake and production. We further show that perturbations to bacteria have larger impacts than to metabolites. Finally, we demonstrate that spatial metabolite diffusion drives pattern formation, emphasizing the links between local stability and spatial structures in bacterial cooperation.

Counting the number of isomers of a chemical molecule is one of the formative problems of graph theory. However, recent progress has been slow, and the problem has largely been ignored in modern network science. Here we provide an introduction to the mathematics of counting network structures and then use it to derive results for two new classes of molecules. In contrast to previously studied examples, these classes take additional chemical complexity into account and thus require the use of multivariate generating functions. The results illustrate the elegance of counting theory, highlighting it as an important tool that should receive more attention in network science.

When studying a complex system, it is often useful to think of the system as a network of interacting units. One can then ask if some properties of the entire network are already explained by a small part of the network, a network motif. A famous example of an ecological motif is exploitative competition in food webs, where the presence of two species competing for a shared resource precludes the existence of a stable equilibrium for the whole system. However, other examples of motifs with such direct impacts on stability are not known. Here, we show why small motifs that allow conclusions on systemic stability are rare. More importantly, we show that another dynamical property, reactivity, is typically rooted in motifs. Computing the reactivity of motifs can reveal which parts of a network are prone to respond violently to perturbations. This highlights motif reactivity as a useful property to measure in real-world systems to understand likely modes of systemic failure in food webs or other networks in epidemics, supply chains, or power grids.

A key unresolved question in microbial ecology is how the extraordinary diversity of microbiomes emerges from the interactions among their many functionally distinct populations. This process is driven in part by the cross-feeding networks that help to structure these systems, in which consumers use resources to fuel their metabolism, creating by-products which can be used by others in the community. Understanding the effects of cross-feeding presents a major challenge, as it creates complex interdependencies between populations which can be hard to untangle. We address this problem using the tools of network science to develop a structural microbial community model. Using methods from percolation theory, we identify feasible community states for cross-feeding network structures in which the needs of consumers are met by metabolite production across the community. We identify tipping points at which small changes in structure can cause the catastrophic collapse of cross-feeding networks and abrupt declines in microbial community diversity. Our results are an example of a well-defined tipping point in a complex ecological system and provide insight into the fundamental processes shaping microbiomes and their robustness. We further demonstrate this by considering how network attacks affect community diversity and apply our results to show how the apparent difficulty in culturing the microbial diversity emerges as an inherent property of their cross-feeding networks.

Ships are technologies of maritime mobility. But sometimes ships are immobile—they stop and remain stationary for short or prolonged times. A degree of stasis inside and outside ports is both usual and essential for facilitating the movement of ships in global markets. This paper makes two important points: first, echoing existing literature, frequent stationarity (or waiting) is a normal occurrence in the industry. Second, it is not just mobilities that are disrupted via moments of stasis; immobilities themselves have distinct patterns that too can be disrupted. This nuance is vital: there is a need to understand the disruptions to immobilities rather than understanding immobilities as disruptions to the general condition of mobility, both within—and beyond—the shipping example. We argue that understanding disruptions to immobilities is vital to grasping the dynamics of shipping, alongside other (im)mobilites (car, train, plane), their conditions, and the politics that shape our world on the move. Using a data-driven approach, embracing AIS methods for exploring ship stationarity around US waters during the COVID-19 pandemic, this paper upends the assumptions of ship (im)mobilities through the example of wait times, calling for scholars to give space and time to everyday immobilities and their disruptions too.