Temporal origin of nestedness in interaction networks

Abstract Nestedness is a common property of communication, finance, trade, and ecological networks. In networks with high levels of nestedness, the link positions of low-degree nodes (those with few links) form nested subsets of the link positions of high-degree nodes (those with many links), leading to matrix representations with characteristic upper-triangular or staircase patterns. Recent theoretical work has connected nestedness to the functionality of complex systems and has suggested it is a structural by-product of the skewed degree distributions often seen in empirical data. However, mechanisms for generating nestedness remain poorly understood, limiting the connections that can be made between system processes and observed network structures. Here, we show that a simple probabilistic model based on phenology — the timing of co-presences among interaction partners — can produce nested structures and correctly predict around two-thirds of interactions in two fish market networks and around one-third of interactions in 22 plant-pollinator networks. Notably, the links most readily explained by frequent actor co-presences appear to form a backbone of nested interactions, with the remaining interactions attributable to opportunistic interactions or preferences for particular interaction partners that are not routinely available. Significance statement Networks describe the relationships among actors in complex systems. In nested networks, actors involved in few interactions are connected to actors involved in many interactions, with those highly-connected actors also interacting with other highly-connected actors. This pattern is seen in a variety of empirical systems and influences the response to external perturbations, but little is known about the processes that give rise to nestedness. We show that phenology, the day-to-day timing of interaction partner availability, is a general mechanism that generates nested structures. We present a simple probabilistic model which accounts for actor overlap through time but assumes actors have no preference for specific interaction partners, thereby providing an instructive baseline for investigating higher-level selection processes in interaction networks.