A method for detecting modules in quantitative bipartite networks

Abstract

Summary1. Ecological networks are often composed of different subcommunities (often referred to as modules). Identifying such modules has the potential to develop a better understanding of the assembly of ecological communities and to investigate functional overlap or specialization. 2. The most informative form of networks are quantitative or weighted networks. Here, we introduce an algorithm to identify modules in quantitative bipartite (or two-mode) networks. It is based on the hierarchical random graphs concept of Clauset et al. (2008 Nature 453: 98-101) and is extended to include quantitative information and adapted to work with bipartite graphs. We define the algorithm, which we call QuanBiMo, sketch its performance on simulated data and illustrate its potential usefulness with a case study. 3. Modules are detected with a higher accuracy in simulated quantitative networks than in their binary counterparts. Even at high levels of noise, QuanBiMo still classifies 70% of links correctly as within-or betweenmodules. Recursively applying the algorithm results in additional information of within-module organization of the network. 4. The algorithm introduced here must be seen as a considerable improvement over the current standard of algorithms for binary networks. Due to its higher sensitivity, it is likely to lead to be useful for detecting modules in the typically noisy data of ecological networks.

Sampling completeness in seed dispersal networks: When enough is enough

“…We found both Qualitative and Quantitative Modularity to stabilize after 7 and 8 sampling days, respectively, and to encompass real ecological information as it cannot be explained by null models based solely on species abundances. However, it is important to note that wile Quantitative Modularity revealed a network more modular than expected by chance, the analyses based on binary matrices revealed the opposite pattern, reinforcing the value of weighted interaction networks in the capacity of this algorithm to detect modules (Dormann & Strauss 2014). Network Specialization H 2 stabilized around day 6 to 8 and was higher (i.e.…”

Vertical canopy gradient shaping the stratification of leaf‐chewer–parasitoid interactions in a temperate forest

“…Specifically, we used: (a) number of compartments (subsets of the web not connected to other compartments); (b) weighted nestedness based on overlap and decreasing fill (nestedness quantifies whether a given sequence of columns [rows] shows decreasing marginal totals, that is, incidences or richness); (c) weighted quantitative linkage density (linkage density is the weighted diversity of interactions per species); (d) weighted quantitative connectance (connectance is the weighted realized proportion of possible links, calculated as quantitative linkage density divided by the number of species in the network); (e) weighted quantitative interaction evenness (interaction evenness is a measure of the uniformity of energy flows along different pathways); (f) weighted quantitative network specialization index $H_2^{\prime }$ (degree of specialization among hosts and parasitoids across an entire network); (g) weighted quantitative generality (generality is the mean effective number of hosts per parasitoid weighted by their marginal totals); (h) weighted quantitative vulnerability (vulnerability is the mean effective number of parasitoids per host species, weighted by their marginal totals); and (i) weighted quantitative modularity (modularity is the degree to which a quantitative network can be divided into modules, within which within‐module interactions are more prevalent than between‐module interactions). Full formulae and software details are provided in Almeida‐Neto and Ulrich (2011), Dormann, Fründ, Blüthgen, and Gruber (2009), and Dormann and Strauss (2014). …”

Host–parasite network structure is associated with community-level immunogenetic diversity

“…We calculated nestedness using the NODF index 27 implemented in the software Aninhando 52 . We calculated modularity using the QuanBiMod algorithm for quantitative bipartite networks 53 as implemented in the package 'bipartite' (version 2.03; ref. 54) in R using default values.…”