The puzzling affinity between modularity and dependence asymmetry

• Modularity and dependence asymmetry (DA) are used to characterize interactions networks in ecology.
• DA suggests an interplay of generalists and specialist forming an entangled web of interconnected species while modularity evokes the idea of species interacting in isolated cliques.
• We construct an algorithm to compute maximal DA pattern and estimated also the DA of random matrices.
• We found that a modular pattern, depending on the difference between the sizes of the modules, can have an high DA compared with patterns of maximal and random DA.

We discuss the relationship between two patterns found in interaction networks (INs) of community ecology: modularity and asymmetric specialisation. These two patterns express two opposite features: asymmetric specialisation suggests an interplay of generalists and specialists forming an entangled web of interconnected species, while modularity brings the idea of groups of species interacting in isolated cliques. We perform the analysis using Dependence Asymmetry (DA), which is the simplest way to quantify asymmetric specialisation. We construct an algorithm that finds the pattern of maximal DA, and we estimate the upper bound of DA analytically. We study the symmetric modular structure that has zero DA, and then force an asymmetric mismatch in this pattern to generate high DA, allowing us to compare it with a random pattern and with the maximal possible value. We conclude that, despite the opposite notions suggested by the studied patterns, if a modular pattern has enough asymmetry it resembles a specialised asymmetric pattern.