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

多层网络是当前网络科学的一个研究热点。然而，对这些可以被认为是网络的网络的系统的研究仍然受到对具体应用数据的需求的阻碍。生态元食物网提供了一个有趣的网络上的网络的例子。生态食物网是生态学中谁吃谁的网络，已经被研究了很长时间。但是，经典的食物网模型没有考虑物种的空间分布。大多数自然环境远非同质，而是形成不同的斑块（例如城市中的岛屿、湖泊、公园系统，或农业景观中的森林斑块）。在这种斑块景观中，种群的传播被所谓的元种群模型所捕获。在过去的4年中，一些出版物已经开始出现，研究斑块景观中的食物网动态，所谓的元食物网。这就创造了一种可以利用强大协同作用的局面。一方面，生态学可以受益于新开发的数学工具，用于研究多层网络，这是目前出现在网络科学。另一方面，对于网络科学来说，元食物网提供了一个宝贵的现实世界的例子。该项目是一个更大的研究单元“1748：网络上的网络”的一部分，该单元侧重于从网络的角度研究元食物网。特别是，该研究单位将开发早期预警信号，可用于监测现实世界的元食物网，并警告即将崩溃。此外，研究将揭示这些网络的空间，时间和时空异质性的来源。从数学/物理的角度来看，这是有趣的，因为模式形成的中心驱动因素是诸如安德森局部化和图灵不稳定性等现象，这些现象尚未在动态多层网络中研究。这些调查的结果预计也将与生态学高度相关，因为空间和时间异质性被认为是生物多样性和生态系统功能的核心驱动因素。

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.