Detecting modules in quantitative bipartite networks: the QuaBiMo algorithm

Ecological networks are often composed of different sub-communities (often referred to as mod2 ules). Identifying such modules has the potential to develop a better understanding of the assem3 bly of ecological communities and to investigate functional overlap or specialisation. The most 4 informative form of networks are quantitative or weighted networks. Here we introduce an al5 gorithm to identify modules in quantitative bipartite (or two-mode) networks. It is based on the 6 hierarchical random graphs concept of Clauset et al. (2008 Nature 453: 98–101) and is extended 7 to include quantitative information and adapted to work with bipartite graphs. We define the al8 gorithm, which we call QuaBiMo, sketch its performance on simulated data and illustrate its 9 potential usefulness with a case study. 10

[1]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

[2]  J Memmott,et al.  The structure of a plant-pollinator food web. , 1999, Ecology letters.

[3]  Anders Nielsen,et al.  Conservation of species interaction networks , 2010 .

[4]  S. Allesina.  Cycling and Cycling Indices , 2008 .

[5]  Jari Saramäki,et al.  Characterizing the Community Structure of Complex Networks , 2010, PloS one.

[6]  J. Olesen,et al.  Biogeographical modules and island roles: a comparison of Wallacea and the West Indies , 2012 .

[7]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[8]  N. Blüthgen,et al.  Measuring specialization in species interaction networks , 2006, BMC Ecology.

[9]  Ricard V Solé,et al.  Reciprocal specialization in ecological networks. , 2009, Ecology letters.

[10]  L. Freitas,et al.  Do pollination syndromes cause modularity and predict interactions in a pollination network in tropical high‐altitude grasslands? , 2012 .

[11]  Carsten F. Dormann,et al.  Specialization of Mutualistic Interaction Networks Decreases toward Tropical Latitudes , 2012, Current Biology.

[12]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Carlos J. Melián,et al.  The nested assembly of plant–animal mutualistic networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Teja Tscharntke,et al.  Habitat modification alters the structure of tropical host–parasitoid food webs , 2007, Nature.

[15]  M. Newman,et al.  Hierarchical structure and the prediction of missing links in networks , 2008, Nature.

[16]  Stefano Allesina,et al.  Food web models: a plea for groups. , 2009, Ecology letters.

[17]  Carsten F. Dormann,et al.  Indices, Graphs and Null Models: Analyzing Bipartite Ecological Networks , 2009 .

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

[19]  R. May.  Food webs. , 1983, Science.

[20]  C. Elton,et al.  The Journal of Animal Ecology. , 1936 .

[21]  Amedeo Caflisch,et al.  Efficient modularity optimization by multistep greedy algorithm and vertex mover refinement. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Josep L. Garcia-Domingo,et al.  Effects of heterogeneous interaction strengths on food web complexity , 2008 .

[23]  Ina Ruck,et al.  USA , 1969, The Lancet.

[24]  Santo Fortunato,et al.  Limits of modularity maximization in community detection , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[26]  Roger Guimerà,et al.  Module identification in bipartite networks with applications to directed networks , 2007 .

[27]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[29]  Diego P. Vázquez,et al.  NULL MODEL ANALYSES OF SPECIALIZATION IN PLANT–POLLINATOR INTERACTIONS , 2003 .

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

[31]  Jens M. Olesen,et al.  Macroecology of pollination networks , 2013 .

[32]  J. Bascompte,et al.  Structure in plant–animal interaction assemblages , 2006 .

[33]  Timothée Poisot,et al.  A comparative study of ecological specialization estimators , 2012 .

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

[35]  Luciano Cagnolo,et al.  Uniting pattern and process in plant-animal mutualistic networks: a review. , 2009, Annals of botany.

[36]  M. N. Jacobi,et al.  Identification of subpopulations from connectivity matrices , 2012 .

[37]  R. Guimerà,et al.  The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Paulo Inácio Prado,et al.  Compartments in insect-plant associations and their consequences for community structure , 2004 .

[39]  Pedro Jordano,et al.  Evolution and Coevolution in Mutualistic Networks , 2022 .

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

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

[42]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Luciano Cagnolo,et al.  Network topology: patterns and mechanisms in plant-herbivore and host-parasitoid food webs. , 2011, The Journal of animal ecology.

[44]  J. Olesen,et al.  Ecological modules and roles of species in heathland plant-insect flower visitor networks. , 2009, The Journal of animal ecology.

[45]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Ferenc Jordán,et al.  Weighting, scale dependence and indirect effects in ecological networks: A comparative study , 2007 .

[47]  Lynn V. Dicks,et al.  Compartmentalization in plant–insect flower visitor webs , 2002 .

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

[49]  Jochen Fründ,et al.  What do interaction network metrics tell us about specialization and biological traits? , 2008, Ecology.

[50]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.

[51]  Stefano Allesina,et al.  Drivers of compartmentalization in a Mediterranean pollination network , 2012 .

[52]  Nico Blüthgen,et al.  Why network analysis is often disconnected from community ecology: A critique and an ecologist's guide , 2010 .

[53]  H. Charles J. Godfray,et al.  Experimental evidence for apparent competition in a tropical forest food web , 2004, Nature.

[54]  Stephen P. Borgatti,et al.  Identifying sets of key players in a social network , 2006, Comput. Math. Organ. Theory.