Tractable models of ecological assembly

Ecological assembly, the way natural communities form under ecological time-scales, is a fundamental and yet poorly understood process. Recent theoretical and empirical approaches to assembly consider systems in which a group of species is introduced in a new environment, and dynamics prune the system down to a sub-community of coexisting species. This "top-down" assembly approach contrasts with the well-studied "bottom-up", or sequential, assembly, in which species from a pool enter the system one at a time, giving rise to priority effects and complex dynamics. Here we determine under which conditions the two approaches are equivalent, i.e., lead asymptotically to the same exact set of coexisting species. To achieve this result, we represent the assembly process as a network in which nodes are sub-communities and edges stand for invasions shifting the composition of the ecological community from a stable configuration to another. This abstraction makes it easy to determine which states the community can occupy, as well as highlight the potential for priority effects or cyclic species composition. We discuss how the equivalence between bottom-up and top-down assembly can advance our understanding of this challenging process from an empirical and theoretical point of view, informing the study of ecological restoration and the design and control of ecological communities.