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

Lead Research Organisation: University of Bristol
Department Name: Engineering Mathematics

Abstract

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.

Planned Impact

This project will advance the state of the art of network science by developing new approaches and algorithms for dynamic multilayer networks. Moreover it will establish ecological meta-foodwebs as a paradigmatic class of real world systems that form dynamic multilayer networks. It will thus greatly enrich research in this field by providing a much-needed real world examples of dynamic multi-layer networks in the real world.

The project will create impact in ecology by advancing the understanding of the functioning of meta-foodwebs. In particular the project will deliver new insights into the formation of spatial, temporal and spatio-temporal patterns in these systems, which are essential for biodiversity maintenance. In particular we seek to reveal the impact of spatial habitat structure on the dynamics, which will be valuable for planning decisions and thus can have an impact on policy. Furthermore, we will develop an algorithms that can be used to provide early warning of impending critical transitions and thus aid in safeguarding endangered ecosystems.

The approaches and algorithms developed in this project will be applicable to the vast range of systems that can be described as dynamic multi-layer networks. In particular we see plentiful applications in the monitoring of technical systems, such as large IT systems.

Publications

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Barter E (2017) Spatial effects in meta-foodwebs. in Scientific reports

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Barter E (2019) Manifold cities: social variables of urban areas in the UK. in Proceedings. Mathematical, physical, and engineering sciences

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Yeakel JD (2018) Eco-evolutionary dynamics, density-dependent dispersal and collective behaviour: implications for salmon metapopulation robustness. in Philosophical transactions of the Royal Society of London. Series B, Biological sciences

 
Description We have uncovered the intriguing and complex way in which spatial structure of an ecosystem affects biodiversity in colonization-extinction meta-foodwebs (a class of ecological models)
Exploitation Route We have established a methodologies for assessing the impact of spatial structure for the conservation of biodiversity. This may feed into planning processes for conservation areas. The developed methods could also be applied more broadly to study the resilience of other systems that form networks in physical space.
Sectors Communities and Social Services/Policy,Environment,Financial Services, and Management Consultancy,Government, Democracy and Justice,Security and Diplomacy

URL http://www.for1748.de/
 
Title Master Stability Function Approach for Food Web Dynamics 
Description We developed a mathematical method that allows the highly efficient analysis of the onset of pattern formation in complex network of nonlinearly coupled dynamical units that are that are embedded in space. 
Type Of Material Improvements to research infrastructure 
Year Produced 2017 
Provided To Others? Yes  
Impact no Impact yet. Publication in press. 
URL https://journals.aps.org/pre/accepted/b907fK56Qed15b0fc10f4895c3d6537093f9ebc80
 
Title Generalized Meta-Foodweb model 
Description We have formulated a generalized model of meta-foodwebs. This is the first model of this kind. Publication is in Press. 
Type Of Material Computer model/algorithm 
Year Produced 2017 
Provided To Others? Yes  
Impact No impact yet. 
URL https://journals.aps.org/pre/accepted/b907fK56Qed15b0fc10f4895c3d6537093f9ebc80
 
Description FOR 1748 
Organisation Carl von Ossietzky University of Oldenburg
Country Germany 
Sector Academic/University 
PI Contribution The project is part of the German research Unit For 1748. We are in close contact with other members of this unit. We have contributed much of the theoretical groundwork the research unit is using, including mathematical approaches for the analysis of large ecological networks embedded in physical space.
Collaborator Contribution The partners have funded exchange visits of research assistants and investigators as well several mutli-day workshops. They have also contributed experimental data and numerical simulation results. For example we have one major paper that is presently in press where our lab formulated the theory, and then the Darmstadt lab implemented it an ran extensive tests. The published paper is a result of intense discussions with the Oldenburg group and also directly profited from interactions with external invitees at workshops.
Impact This is a multidisciplinary collaboration between the Bristol lab (Mathematics), Darmstadt (Physics), Oldenburg (Environmental Sciences), Jena (Experimental Ecology), and Potsdam (Theoretical Ecology). The first published output is Barter and Gross, Scientific Reports 7, 8890, 2017.
Start Year 2016
 
Description FOR 1748 
Organisation Darmstadt University of Applied Sciences
PI Contribution The project is part of the German research Unit For 1748. We are in close contact with other members of this unit. We have contributed much of the theoretical groundwork the research unit is using, including mathematical approaches for the analysis of large ecological networks embedded in physical space.
Collaborator Contribution The partners have funded exchange visits of research assistants and investigators as well several mutli-day workshops. They have also contributed experimental data and numerical simulation results. For example we have one major paper that is presently in press where our lab formulated the theory, and then the Darmstadt lab implemented it an ran extensive tests. The published paper is a result of intense discussions with the Oldenburg group and also directly profited from interactions with external invitees at workshops.
Impact This is a multidisciplinary collaboration between the Bristol lab (Mathematics), Darmstadt (Physics), Oldenburg (Environmental Sciences), Jena (Experimental Ecology), and Potsdam (Theoretical Ecology). The first published output is Barter and Gross, Scientific Reports 7, 8890, 2017.
Start Year 2016
 
Description FOR 1748 
Organisation Friedrich Schiller University Jena (FSU)
Country Germany 
Sector Academic/University 
PI Contribution The project is part of the German research Unit For 1748. We are in close contact with other members of this unit. We have contributed much of the theoretical groundwork the research unit is using, including mathematical approaches for the analysis of large ecological networks embedded in physical space.
Collaborator Contribution The partners have funded exchange visits of research assistants and investigators as well several mutli-day workshops. They have also contributed experimental data and numerical simulation results. For example we have one major paper that is presently in press where our lab formulated the theory, and then the Darmstadt lab implemented it an ran extensive tests. The published paper is a result of intense discussions with the Oldenburg group and also directly profited from interactions with external invitees at workshops.
Impact This is a multidisciplinary collaboration between the Bristol lab (Mathematics), Darmstadt (Physics), Oldenburg (Environmental Sciences), Jena (Experimental Ecology), and Potsdam (Theoretical Ecology). The first published output is Barter and Gross, Scientific Reports 7, 8890, 2017.
Start Year 2016
 
Description FOR 1748 
Organisation University of Leipzig
Country Germany 
Sector Academic/University 
PI Contribution The project is part of the German research Unit For 1748. We are in close contact with other members of this unit. We have contributed much of the theoretical groundwork the research unit is using, including mathematical approaches for the analysis of large ecological networks embedded in physical space.
Collaborator Contribution The partners have funded exchange visits of research assistants and investigators as well several mutli-day workshops. They have also contributed experimental data and numerical simulation results. For example we have one major paper that is presently in press where our lab formulated the theory, and then the Darmstadt lab implemented it an ran extensive tests. The published paper is a result of intense discussions with the Oldenburg group and also directly profited from interactions with external invitees at workshops.
Impact This is a multidisciplinary collaboration between the Bristol lab (Mathematics), Darmstadt (Physics), Oldenburg (Environmental Sciences), Jena (Experimental Ecology), and Potsdam (Theoretical Ecology). The first published output is Barter and Gross, Scientific Reports 7, 8890, 2017.
Start Year 2016
 
Description FOR 1748 
Organisation University of Potsdam
Country Germany 
Sector Academic/University 
PI Contribution The project is part of the German research Unit For 1748. We are in close contact with other members of this unit. We have contributed much of the theoretical groundwork the research unit is using, including mathematical approaches for the analysis of large ecological networks embedded in physical space.
Collaborator Contribution The partners have funded exchange visits of research assistants and investigators as well several mutli-day workshops. They have also contributed experimental data and numerical simulation results. For example we have one major paper that is presently in press where our lab formulated the theory, and then the Darmstadt lab implemented it an ran extensive tests. The published paper is a result of intense discussions with the Oldenburg group and also directly profited from interactions with external invitees at workshops.
Impact This is a multidisciplinary collaboration between the Bristol lab (Mathematics), Darmstadt (Physics), Oldenburg (Environmental Sciences), Jena (Experimental Ecology), and Potsdam (Theoretical Ecology). The first published output is Barter and Gross, Scientific Reports 7, 8890, 2017.
Start Year 2016