Networks on Networks: Self-organized patterns in meta food webs

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A current hot topic of research in network science are multi-layer networks. However, research on these systems, which can be thought of as networks of networks, is still held back by the need for data on concrete applications. An interesting example of networks on networks is provided by ecological meta-foodwebs. Ecological foodwebs, the networks of who eats who in ecology, have been studied for a long time. But, classical food web models do not consider the spatial distribution of species. Most natural environments are far from homogeneous but form distinct patches (e.g. systems of islands, lakes, parks in a city, or patches of forest in an agricultural landscape). The spread of a population in such patchy landscapes is captured by so-called meta-population models. In the past 4 years a number of publications have begun to appear which study the dynamics of foodwebs in patchy landscapes, so-called meta-foodwebs. This has created a situation where strong synergies can be exploited. On the one hand, ecology can profit from newly-developed mathematical tools for the study of multilayer networks, which are currently emerging in network science. On the other hand, for network science meta-foodwebs provide an invaluable real-world example. This project is part of a larger research unit "For 1748: Networks on Networks", which focuses on the study of meta-foodwebs from a networks perspective. In particular the research unit will develop early warning signals that can be used to monitor real-world meta-foodwebs and warn of impending collapse. Furthermore research will reveal sources of spatial, temporal, and spatiotemporal heterogeneity in these networks. This is interesting from a mathematical/physical perspective, as the central drivers of pattern formation are phenomena such as Anderson Localization and Turing instabilities, which have not been studied in dynamic multi-layer networks. The result of these investiagtions is also expected to be highly relevant for ecology as spacial and temporal heterogeneities are thought to be central drivers for biodiversity and ecosystem functioning.