Tractable models of ecological assembly

Ecological assembly is a fundamental and yet poorly understood process. Three main obstacles hinder the development of a theory of assembly, and when these issues are sidestepped by making strong assumptions, one can build an assembly graph in which nodes are ecological communities and edges are invasions shifting their composition. The graph can then be analysed directly, without the need to consider dynamics. To showcase this framework, we build and analyse assembly graphs for the competitive Lotka-Volterra model, showing that in these cases sequential assembly (in which species invade a community one at a time) can reach the same configurations found when starting the system with all species present at different initial conditions. We discuss how our results can advance our understanding of assembly both from an empirical and a theoretical point of view, informing the study of ecological restoration and the design of ecological communities.