Multilayer diffusion networks as a tool to assess the structure and functioning of fine grain sub-specific plant-pollinator networks

Interaction networks are a widely used tool to understand the dynamics of plant-pollinator ecological communities. However, while most mutualistic networks have been defined at the species level, ecological processes such as pollination take place at different scales, including the individual or patch levels. Yet, current approaches studying fine-grain sub-specific plant-pollinator networks only account for interactions among nodes belonging to a single plant species due to the conceptual and mathematical limitations of modeling simultaneously several plant species each composed of several nodes. Here, we introduce a multilayer diffusion network framework that allows modeling simple diffusion processes between nodes pertaining to the same or different layers (i.e. species). It is designed to depict from the network structure the potential conspecific and heterospecific pollen flows among plant individuals or patches. This potential pollen flow is modeled as a transport-like system, in which pollen grain movements are represented as random-walkers that diffuse on an ensemble of bipartite layers of conspecific plants and their shared pollinators. We exemplify this physical conceptualization using a dataset of nine fine-grain sub-specific plant-pollinator networks from a Mediterranean grassland of annual plants, where plant nodes represent groups of conspecifics within patches of 1 m2. The diffusion networks show pollinators effectively connecting sets of patches of the same and different plant species, forming a modular structure. Interestingly, different properties of the network structure, such as the conspecific pollen arrival probability and the number of conspecific subgraphs in which plants are embedded, are critical for the seed production of different plant species. We provide a simple but robust set of metrics to calculate potential pollen flow and scale down network ecology to functioning properties at the individual or patch level, where most ecological processes take place, hence moving forward the description and interpretation of species-rich communities across scales.