Many ecological community dynamics display some degree of directionality, known as succession patterns. But complex interaction networks frequently tend to non-directional dynamics such as chaos, unless additional structures or mechanisms impose some form of, often fragile or shot-lived, directionality. We exhibit here a novel property of emergent long-lasting directionality in competitive communities, which relies on very minimal assumptions. We model communities where each species has a few strong competitive interactions, and many weak ones. We find that, at high enough diversity, the dynamics become directional, meaning that the community state can be characterized by a function that increases in time, which we call "maturity". In the presence of noise, the community composition changes toward increasingly stable and productive states. This scenario occupies a middle ground between deterministic succession and purely random species associations: there are many overlapping stable states, with stochastic transitions, that are nevertheless biased in a particular direction. When a spatial dimension is added in the form of a meta-community, higher-maturity community states are able to expand in space, replacing others by (exact or approximate) copies of themselves. This leads to community-level selection, with the same maturity function acting as fitness. Classic concepts from evolutionary dynamics provide a powerful analogy to understand this strictly ecological, community-level phenomenon of emergent directionality.
Graph theory and stability analysis of protein complex interaction networks
