Ecological Multilayer Networks: A New Frontier for Network Ecology

Networks provide a powerful approach to address myriad phenomena across ecology. Ecological systems are inherently 'multilayered'. For instance, species interact with one another in different ways and those interactions vary spatiotemporally. However, ecological networks are typically studied as ordinary (i.e., monolayer) networks. 'Multilayer networks' are currently at the forefront of network science, but ecological multilayer network studies have been sporadic and have not taken advantage of rapidly developing theory. Here we present the latest concepts and tools of multilayer network theory and discuss their application to ecology. This novel framework for the study of ecological multilayer networks encourages ecologists to move beyond monolayer network studies and facilitates ways for doing so. It thereby paves the way for novel, exciting research directions in network ecology.

[1]  Nicolas Loeuille,et al.  The ecological and evolutionary implications of merging different types of networks. , 2011, Ecology letters.

[2]  Vito Latora,et al.  Structural reducibility of multilayer networks , 2015, Nature Communications.

[3]  Philip H. Warren,et al.  Aquatic Food Webs: An Ecosystem Approach , 2008 .

[4]  Theodora Petanidou,et al.  Spatio‐temporal variation in the structure of pollination networks , 2009 .

[5]  Jordi Bascompte,et al.  Hot spots of mutualistic networks. , 2015, The Journal of animal ecology.

[6]  Mason A. Porter,et al.  Community Detection in Temporal Multilayer Networks, with an Application to Correlation Networks , 2014, Multiscale Model. Simul..

[7]  Jordi Bascompte,et al.  Networks of spatial genetic variation across species , 2009, Proceedings of the National Academy of Sciences.

[8]  Stephanie E. Chang,et al.  Estimation of the Economic Impact of Multiple Lifeline Disruption: Memphis Light, Gas and Water Division Case Study , 1996 .

[9]  R. Kitching,et al.  Spatial and temporal variation in food webs in water-filled treeholes , 1987 .

[10]  Joseph Tzanopoulos,et al.  Long-term observation of a pollination network: fluctuation in species and interactions, relative invariance of network structure and implications for estimates of specialization. , 2008, Ecology letters.

[11]  Philip H. Warren,et al.  Spatial and temporal variation in the structure of a freshwater food web , 1989 .

[12]  M. Barber.  Modularity and community detection in bipartite networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[14]  Jordi Bascompte,et al.  Disentangling the Web of Life , 2009, Science.

[15]  Patrick C Phillips,et al.  Network thinking in ecology and evolution. , 2005, Trends in ecology & evolution.

[16]  Jens M. Olesen,et al.  Strong Impact of Temporal Resolution on the Structure of an Ecological Network , 2013, PloS one.

[17]  David Lusseau,et al.  Taking sociality seriously: the structure of multi-dimensional social networks as a source of information for individuals , 2012, Philosophical Transactions of the Royal Society B: Biological Sciences.

[18]  P. Greig-Smith,et al.  Advances in Ecological Research. , 1964 .

[19]  Sonia Kéfi,et al.  More than a meal… integrating non-feeding interactions into food webs. , 2012, Ecology letters.

[20]  Shuang‐Quan Huang,et al.  Relative Stability of Core Groups in Pollination Networks in a Biodiversity Hotspot over Four Years , 2012, PloS one.

[21]  Joel E. Cohen,et al.  Temporal Variation in Food Web Structure: 16 Empirical Cases , 1991 .

[22]  Mason A. Porter,et al.  A local perspective on community structure in multilayer networks , 2015, Network Science.

[23]  Jane Memmott,et al.  The restoration of parasites, parasitoids, and pathogens to heathland communities. , 2009, Ecology.

[24]  Jordi Bascompte,et al.  Asymmetric Coevolutionary Networks Facilitate Biodiversity Maintenance , 2006, Science.

[25]  A. Arenas,et al.  Mathematical Formulation of Multilayer Networks , 2013, 1307.4977.

[26]  Kristian Trøjelsgaard,et al.  Beta Diversity of Plant-Pollinator Networks and the Spatial Turnover of Pairwise Interactions , 2014, PloS one.

[27]  K. Winemiller.  Spatial and Temporal Variation in Tropical Fish Trophic Networks , 1990 .

[28]  Linda A. Deegan,et al.  Evidence for spatial variability in estuarine food webs , 1997 .

[29]  Mason A. Porter,et al.  Multilayer Analysis and Visualization of Networks , 2014, J. Complex Networks.

[30]  Boris R. Krasnov,et al.  Co‐occurrence of ectoparasites on rodent hosts: null model analyses of data from three continents , 2010 .

[31]  Tiago P. Peixoto.  Hierarchical block structures and high-resolution model selection in large networks , 2013, ArXiv.

[32]  Paulo R. Guimarães,et al.  Spatial structure of ant–plant mutualistic networks , 2013 .

[33]  M. Pascual,et al.  Ecological networks : Linking structure to dynamics in food webs , 2006 .

[34]  S. Bauer,et al.  Migratory Animals Couple Biodiversity and Ecosystem Functioning Worldwide , 2014, Science.

[35]  Ferenc Jordán,et al.  Social and landscape effects on food webs: a multi-level network simulation model , 2013, J. Complex Networks.

[36]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[37]  Scott T. Grafton,et al.  Dynamic reconfiguration of human brain networks during learning , 2010, Proceedings of the National Academy of Sciences.

[38]  Jordi Bascompte,et al.  Temporal dynamics in a pollination network. , 2008, Ecology.

[39]  Colin R. Townsend,et al.  The Effect of Seasonal Variation on the Community Structure and Food-Web Attributes of Two Streams: Implications for Food-Web Science , 1999 .

[40]  V. Colizza,et al.  Analytical computation of the epidemic threshold on temporal networks , 2014, 1406.4815.

[41]  Mason A. Porter,et al.  Robust Detection of Dynamic Community Structure in Networks , 2012, Chaos.

[42]  Jens M. Olesen,et al.  Stability of modular structure in temporal cumulative plant–flower-visitor networks , 2012 .

[43]  J. Bascompte,et al.  The modularity of pollination networks , 2007, Proceedings of the National Academy of Sciences.

[44]  Mason A. Porter,et al.  Structure of triadic relations in multiplex networks , 2013, ArXiv.

[45]  M. Murakami,et al.  Reciprocal subsidies: dynamic interdependence between terrestrial and aquatic food webs. , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[46]  Serge Morand,et al.  Potential Parasite Transmission in Multi-Host Networks Based on Parasite Sharing , 2015, PloS one.

[47]  Matteo Magnani,et al.  Spreading Processes in Multilayer Networks , 2014, IEEE Transactions on Network Science and Engineering.

[48]  G. Closs,et al.  Spatial and Temporal Variation in the Structure of an Intermittent-Stream Food Web , 1994 .

[49]  Sonia Kéfi,et al.  Integrating non-feeding interactions into food webs , 2012 .

[50]  Richard James,et al.  Temporal dynamics and network analysis , 2012 .

[51]  Owen L. Petchey,et al.  Interaction strengths in food webs: issues and opportunities , 2004 .

[52]  Miguel A. Fortuna,et al.  Temporal dynamics of direct reciprocal and indirect effects in a host-parasite network. , 2013, The Journal of animal ecology.

[53]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[54]  Jens M. Olesen,et al.  Centrality measures and the importance of generalist species in pollination networks , 2010 .

[55]  Mason A. Porter,et al.  Communities in Networks , 2009, ArXiv.

[56]  Serguei Saavedra,et al.  Seasonal species interactions minimize the impact of species turnover on the likelihood of community persistence. , 2015, Ecology.

[57]  Kevin D Lafferty,et al.  Stage structure alters how complexity affects stability of ecological networks. , 2011, Ecology letters.

[58]  Stefano Allesina,et al.  Parasites in food webs: the ultimate missing links , 2008, Ecology letters.

[59]  S. Carpenter,et al.  Regulation of Lake Primary Productivity by Food Web Structure. , 1987, Ecology.

[60]  Jonathan M. Chase,et al.  The metacommunity concept: a framework for multi-scale community ecology , 2004 .

[61]  Werner Ulrich,et al.  A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement , 2008 .

[62]  Jens M. Olesen,et al.  Strong, Long-Term Temporal Dynamics of an Ecological Network , 2011, PloS one.

[63]  Judith L. Bronstein,et al.  Duality of interaction outcomes in a plant–frugivore multilayer network , 2017 .

[64]  Stuart R. Borrett,et al.  The rise of Network Ecology: Maps of the topic diversity and scientific collaboration , 2013, 1311.1785.

[65]  A. Dobson,et al.  Parasites dominate food web links. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[66]  Anna Traveset,et al.  Downscaling pollen-transport networks to the level of individuals. , 2014, The Journal of animal ecology.

[67]  Eran Segal,et al.  Host–parasite network structure is associated with community-level immunogenetic diversity , 2014, Nature Communications.

[68]  Jordi Bascompte,et al.  Diversity in a complex ecological network with two interaction types , 2009 .

[69]  Benjamin H. Good,et al.  Performance of modularity maximization in practical contexts. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  Santo Fortunato,et al.  Community detection in networks: A user guide , 2016, ArXiv.

[71]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[72]  Jane Memmott,et al.  Tolerance of pollination networks to species extinctions , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[73]  E. Wada,et al.  A Stable Isotope Study on Seasonal Food Web Dynamics in a Eutrophic Lake , 1994 .

[74]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[75]  J. Bascompte,et al.  Compartmentalization increases food-web persistence , 2011, Proceedings of the National Academy of Sciences.

[76]  Michel Loreau,et al.  Parallel ecological networks in ecosystems , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[77]  Colin Fontaine,et al.  Stability of Ecological Communities and the Architecture of Mutualistic and Trophic Networks , 2010, Science.

[78]  Daniel B. Stouffer,et al.  Origin of compartmentalization in food webs. , 2010, Ecology.

[79]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.

[80]  Mason A. Porter,et al.  Think Locally, Act Locally: The Detection of Small, Medium-Sized, and Large Communities in Large Networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[81]  David W. Willis,et al.  Temporal food web variability in an upper Missouri River backwater: energy origination points and transfer mechanisms , 2001 .

[82]  Vito Latora,et al.  Structural measures for multiplex networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[83]  Katherine Richardson,et al.  Spatial heterogeneity in the structure of the planktonic food web in the North Sea , 1998 .

[84]  P. Abell.  Social Networks in Urban Situations: Analyses of Personal Relationships in Central African Towns , 1971 .

[85]  D. Dudley Williams,et al.  The Importance of Temporal Resolution in Food Web Analysis: Evidence from a Detritus‐Based Stream , 1996 .

[86]  Ira R. Weiss,et al.  Issues and opportunities , 1988, DATB.

[87]  Jeff Ollerton,et al.  Year‐to‐year variation in the topology of a plant–pollinator interaction network , 2008 .

[88]  Rafael L. G. Raimundo,et al.  Long-term temporal variation in the organization of an ant-plant network. , 2013, Annals of botany.

[89]  Sonia Kéfi,et al.  How Structured Is the Entangled Bank? The Surprisingly Simple Organization of Multiplex Ecological Networks Leads to Increased Persistence and Resilience , 2016, PLoS biology.

[90]  Sergio Gómez,et al.  Ranking in interconnected multilayer networks reveals versatile nodes , 2015, Nature Communications.

[91]  G. Bianconi.  Statistical mechanics of multiplex networks: entropy and overlap. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[92]  Mason A. Porter,et al.  Generalized Master Equations for Non-Poisson Dynamics on Networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[93]  David B. Jepsen,et al.  Effects of seasonality and fish movement on tropical river food webs , 1998 .

[94]  J. Bascompte,et al.  Ecological networks : beyond food webs Ecological networks – beyond food webs , 2008 .

[95]  Elisa Thébault,et al.  Identifying compartments in presence–absence matrices and bipartite networks: insights into modularity measures , 2013 .

[96]  Michael J. O. Pocock,et al.  The robustness of a network of ecological networks to habitat loss. , 2013, Ecology letters.

[97]  Petter Holme,et al.  Modern temporal network theory: a colloquium , 2015, The European Physical Journal B.

[98]  Dominique Gravel,et al.  The dissimilarity of species interaction networks. , 2012, Ecology letters.

[99]  É. Thébault,et al.  Structure–stability relationships in networks combining mutualistic and antagonistic interactions , 2014 .

[100]  Mason A. Porter,et al.  Community detection in temporal multilayer networks, and its application to correlation networks , 2014, ArXiv.

[101]  Mason A. Porter,et al.  Eigenvector-Based Centrality Measures for Temporal Networks , 2015, Multiscale Model. Simul..

[102]  Peter C. de Ruiter,et al.  Temporal and spatial heterogeneity of trophic interactions within below-ground food webs , 1991 .

[103]  Tiago P. Peixoto.  Inferring the mesoscale structure of layered, edge-valued, and time-varying networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[104]  Daniel B. Stouffer,et al.  Nestedness versus modularity in ecological networks: two sides of the same coin? , 2010, The Journal of animal ecology.

[105]  Kwang-Il Goh,et al.  Towards real-world complexity: an introduction to multiplex networks , 2015, ArXiv.

[106]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[107]  Pedro Jordano,et al.  Geographical variation in mutualistic networks: similarity, turnover and partner fidelity , 2015, Proceedings of the Royal Society B: Biological Sciences.

[108]  Serhiy Morozov,et al.  A Distributed, Architecture-Centric Approach to Computing Accurate Recommendations from Very Large and Sparse Datasets , 2011 .

[109]  Gerardo Chowell,et al.  Null Models for Community Detection in Spatially-Embedded, Temporal Networks , 2014, bioRxiv.

[110]  Marc Barthelemy,et al.  Anatomy and efficiency of urban multimodal mobility , 2014, Scientific Reports.

[111]  Michael J. O. Pocock,et al.  The Robustness and Restoration of a Network of Ecological Networks , 2012, Science.

[112]  Jordi Bascompte,et al.  Plant-Animal Mutualistic Networks: The Architecture of Biodiversity , 2007 .

[113]  M. Craft,et al.  Network Models: An Underutilized Tool in Wildlife Epidemiology? , 2011, Interdisciplinary perspectives on infectious diseases.

[114]  Bland J. Finlay,et al.  Trophic coupling within the microbial food web: a study with fine temporal resolution in a eutrophic freshwater ecosystem , 1993 .

[115]  Thilo Gross,et al.  Meta-food-chains as a many-layer epidemic process on networks. , 2015, Physical review. E.

[116]  Lucas N Joppa,et al.  Network structure beyond food webs: mapping non-trophic and trophic interactions on Chilean rocky shores. , 2015, Ecology.

[117]  Jordi Bascompte,et al.  The architecture of mutualistic networks minimizes competition and increases biodiversity , 2009, Nature.

[118]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.