Relationships among generalized positive feedback loops determine possible community outcomes in plant-pollinator...

Attractors in Boolean network models representing complex systems such as ecological communities correspond to long-term outcomes (e.g., stable communities) in such systems. As a result, identifying efficient methods to find and characterize these attractors allows for a better understanding of the diversity of possible outcomes. Here we analyze networks that model mutualistic communities of plant and pollinator species governed by Boolean threshold functions. We propose a novel attractor identification method based on generalized positive feedback loops and their functional relationships in such networks. We show that these relationships determine the mechanisms by which groups of stable positive feedback loops collectively trap the system in specific regions of the state space and lead to attractors. Put into the ecological context, we show how survival units-small groups of species in which species can maintain a specific survival state-and their relationships determine the final community outcomes in plant-pollinator networks. We find a remarkable diversity of community outcomes: up to an average of 43 attractors possible for networks with 100 species. This diversity is due to the multiplicity of survival units (up to 34) and stable subcommunities (up to 14). The timing of species influx or outflux does not affect the number of attractors, but it may influence their basins of attraction.