A new measure of ecological network structure based on node overlap and segregation

Abstract

Summary1. Despite substantial recent progress, ecologists continue to search for methods of measuring the structure of ecological networks. Several studies have focused on nestedness, a pattern reflecting the tendency of network nodes to share interaction partners. Here, we introduce a new statistical procedure to measure both this kind of structure and the opposite one (i.e. species' tendency against sharing interacting partners) that we call 'node segregation'. In addition, our procedure provides also a straightforward measure of modularity, that is, the tendency of a network to be compartmented into separated clusters of interacting nodes. 2. This new analytical measure of network structure assesses the average deviation between the observed number of neighbours shared by any pair of nodes (species), and the expected number, that is computed using a probabilistic approach based on simple combinatorics. The measure can be applied to both bipartite networks (such as plant-pollinators) and unimode networks (such as food webs). We tested our approach on several sets of hypothetical and real-world networks. 3. We demonstrate that our approach makes it possible to identify different kinds of non-random network configurations (nestedness, node segregation and modularity). In addition, we show that nestedness in ecological networks is less common than previously thought, and that most ecological networks (including the majority of mutualistic ones) tend towards patterns of segregated associations. 4. Our analyses show that the new measure of node overlap and segregation can efficiently identify different structural patterns. The results of our analyses conducted on real networks highlight the need to carefully reconsider the assumption that ecological networks are stable due to their inherent nestedness.

NOS: a software suite to compute node overlap and segregation in ecological networks

“…A pattern where species tend to share more interacting partners than expected is commonly identified as nestedness (Ulrich et al 2009), and can be measured by different available metrics. As previously demonstrated (Strona and Veech 2015), Ɲ̅ is well correlated with popular nestedness metrics such as the NODF (AlmeidaNeto et al 2008), and the more recent spectral radius measure (Staniczenko et al 2013). The concept of nestedness became popular in the study of presence-absence species/ locality matrices before being used in ecological network analysis (Atmar andPatterson 1993, Brualdi andSanderson 1999).…”

“…Recently, Strona and Veech (2015) introduced a new measure (Ɲ̅ , pronounced 'nos') capable of quantifying the tendency of species to share (or not to share) interacting partners, a more detailed description of the unique features of Ɲ̅ are presented in Box 1. A pattern where species tend to share more interacting partners than expected is commonly identified as nestedness (Ulrich et al 2009), and can be measured by different available metrics.…”

“…species) in the network (cf. Almeida-Neto et al 2008, Strona andVeech 2015). The variability in the values of pairwise node overlap permits the discrimination between situations where all pairs of nodes show no tendency towards either more or less than expected overlap, from situations where a proportion of the node pairs show a tendency for high overlap, while the rest of the nodes show a tendency for segregation.…”

“…The most unique feature of Ɲ̅ is the way it is used to quantify pairwise node overlap/segregation as a standardized deviation from a probabilistic expectation. This allows for powerful significance testing, and for a direct comparison of Ɲ̅ values from different networks (Strona and Veech 2015). A second fundamental difference and advantage of Ɲ̅ compared to common overlap/segregation metrics is that Ɲ̅ can be applied to any kind of network Veech 2015, 2017), while most of the latter are designed for bipartite networks (but see, for example, Jonhson et al 2013, Cantor et al 2017.…”

“…Analyzing the distribution of Ɲ ij values provides an immediate visual way to distinguish between random and modular networks, with the latter showing a bimodal distribution of Ɲ ij values, with a negative peak arising from node segregation between different modules, and a positive one arising from node overlap within modules. As discussed in Strona and Veech (2015), a straightforward way to quantify this pattern is evaluating the statistical dispersion of Ɲ ij values around the mean. Thus, the standard deviation of the Ɲ ij values can serve as a simple measure of modularity (Mod).…”