Dynamical systems on hypergraphs

Carletti, Timotéo; Fanelli, Duccio; Nicoletti, Sara

doi:10.1088/2632-072x/aba8e1

Cited by 70 publications

(69 citation statements)

References 67 publications

(55 reference statements)

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“…Indirect interactions-either higher-order interactions between species, or interaction strengths that themselves interact-have gained interest in recent years [172,173]. One mathematical tool to describe these situations is hypergraphs: hypergraphs are the generalization of a graph, allowing a broad yet manageable approach to complex interactions [174], by allowing for particular interactions to occur beyond a pair of nodes. An additional degree of complexity is introduced by multilayer networks [175].…”

Section: (V) How Do We Determine What Interaction Networkmentioning

confidence: 99%

A roadmap towards predicting species interaction networks (across space and time)

Strydom

Catchen

Banville

et al. 2021

Phil. Trans. R. Soc. B

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Networks of species interactions underpin numerous ecosystem processes, but comprehensively sampling these interactions is difficult. Interactions intrinsically vary across space and time, and given the number of species that compose ecological communities, it can be tough to distinguish between a true negative (where two species never interact) from a false negative (where two species have not been observed interacting even though they actually do). Assessing the likelihood of interactions between species is an imperative for several fields of ecology. This means that to predict interactions between species—and to describe the structure, variation, and change of the ecological networks they form—we need to rely on modelling tools. Here, we provide a proof-of-concept, where we show how a simple neural network model makes accurate predictions about species interactions given limited data. We then assess the challenges and opportunities associated with improving interaction predictions, and provide a conceptual roadmap forward towards predictive models of ecological networks that is explicitly spatial and temporal. We conclude with a brief primer on the relevant methods and tools needed to start building these models, which we hope will guide this research programme forward. This article is part of the theme issue ‘Infectious disease macroecology: parasite diversity and dynamics across the globe’.

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Section: (V) How Do We Determine What Interaction Networkmentioning

confidence: 99%

A roadmap towards predicting species interaction networks (across space and time)

Strydom

Catchen

Banville

et al. 2021

Phil. Trans. R. Soc. B

View full text Add to dashboard Cite

show abstract

“…Indirect interactions-either higher-order interactions between species, or interaction strengths that themselves interact -have gained interest in recent years (Golubski et al 2016;Golubski and Abrams 2011). One mathematical tool to describe these situations is hypergraphs: hypergraphs are the generalization of a graph, allowing a broad yet manageable approach to complex interactions (Carletti, Fanelli, and Nicoletti 2020), allowing for particular interactions to occur beyond a pair of nodes. An additional degree of complexity is introduced by multi-layer networks (Hutchinson et al 2019).…”

Section: What About Indirect and Higher-order Interactions?mentioning

confidence: 99%

A Roadmap Toward Predicting Species Interaction Networks (Across Space and Time)

Strydom¹,

Catchen²,

Banville³

et al. 2021

Preprint

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Networks of species interactions can capture meaningful information on the structure and functioning of ecosystems. Yet the scarcity of existing data, and the difficulty associated with comprehensively sampling interactions between species, means that to describe the structure, variation, and change of ecological networks over time and space, we need to rely on modeling tools with the capacity to make accurate predictions about how species interact. Here we provide a proof-of-concept, where we show a simple neural-network model makes accurate predictions about species interactions, and use this model to reconstruct a metaweb of host-parasite interactions across space, and assess the challenges and opportunities associated with improving interaction predictions. We then provide a primer on the relevant method and tools that will guide the development and integration of these tools, and provide a road map forward toward integration of multiple sources of data and methodlogical approaches (including statistical, dynamical, and inferential models) to sketch the path forward for this research program.

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“…Recent works have focused on investigating dynamics on higher-order topologies [4], and a variety of dynamical processes such as diffusion [3,24], synchronization [27] or social and opinion dynamics [7,16,23] have been extended to multi-body frameworks. As a result, it was shown that higher-order interactions can significantly modify the dynamical process in comparison to the dynamical process on the underlying reduced network.…”

Section: Dynamics On Hypergraphsmentioning

confidence: 99%

Consensus dynamics on temporal hypergraphs

Neuhäuser,

Lambiotte,

Schaub

2021

Preprint

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We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multi-way interactions. We compare this dynamics with that on appropriate projections of this higher-order network representation that flatten the temporal, the multi-way component, or both. For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multi-way interactions is slower than the convergence of the corresponding system with pairwise interactions, which in turn exhibits a slower convergence rate than a consensus dynamics on the corresponding static network. We then consider a nonlinear consensus dynamics model in the temporal setting. Here we find that in addition to an effect on the convergence speed, the final consensus value of the temporal system can differ strongly from the consensus on the aggregated, static hypergraph. In particular we observe a first-mover advantage in the consensus formation process: If there is a local majority opinion in the hyperedges that are active early on, the majority in these first-mover groups has a higher influence on the final consensus value -a behaviour that is not observable in this form in projections of the temporal hypergraph.

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Dynamical systems on hypergraphs

Cited by 70 publications

References 67 publications

A roadmap towards predicting species interaction networks (across space and time)

A roadmap towards predicting species interaction networks (across space and time)

A Roadmap Toward Predicting Species Interaction Networks (Across Space and Time)

Consensus dynamics on temporal hypergraphs

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