The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole. In order to understand the mechanism driving the complexity and stability of such food webs, we developed an eco-evolutionary model in which new species emerge as modifications of existing ones and dynamic ecological interactions determine which species are viable. The food-web structure thereby emerges from the dynamical interplay between speciation and trophic interactions. The proposed model is less abstract than earlier evolutionary food web models in the sense that all three evolving traits have a clear biological meaning, namely the average body mass of the individuals, the preferred prey body mass, and the width of their potential prey body mass spectrum. We observed networks with a wide range of sizes and structures and high similarity to natural food webs. The model networks exhibit a continuous species turnover, but massive extinction waves that affect more than 50% of the network are not observed.

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

Supply networks need to exhibit stability in order to remain functional. Here, we apply a generalized modeling (GM) approach, which has a strong pedigree in the analysis of dynamical systems, to study the stability of real‐world supply networks. It goes beyond purely structural network analysis approaches by incorporating material flows, which are defining characteristics of supply networks. The analysis focuses on the network of interactions between material flows, providing new conceptualizations to capture key aspects of production and inventory policies. We provide stability analyses of two contrasting real‐world networks—that of an industrial engine manufacturer and an industry‐level network in the luxury goods sector. We highlight the criticality of links with suppliers that involve the dispatch, processing, and return of parts or sub‐assemblies, cyclic motifs that involve separate paths from a common supplier to a common firm downstream, and competing demands of different end products at specific nodes. Based on a critical discussion of our findings in the context of the supply chain management literature, we generate five propositions to advance knowledge and understanding of supply network stability. We discuss the implications of the propositions for the effective management, control, and development of supply networks. The GM approach enables fast screening to identify hidden vulnerabilities in extensive supply networks.

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