Species packing in open communities under continuous biological invasion

Abstract The problem of species packing, i.e. how many species a local community can sustain, has long been central to ecology. One approach, pioneered by Robert May and with many later updates, used random matrix theory to link complexity and stability in model communities, showing that beyond a critical threshold of species richness, linear stability is lost. A contrasting paradigm views local diversity as a dynamic equilibrium between colonisation and extinction, as in island biogeography theory and later neutral theory, with the latter assuming strict ecological equivalence among species. Yet many real communities are open, shaped by continuous invasions of ecologically distinct alien species, and thus remain in non-equilibrium states with ongoing turnover. We develop a model of such open communities, incorporating trait-mediated competition and growth, demographic stochasticity, and continuous invasions. Using this framework, we examine stationary states where species introductions are balanced by extinctions. We also derive a statistical formula to estimate species richness from key assembly parameters and invasion rates. Our results reveal a form of functional stasis: community functional profiles remain stable despite exponential declines in compositional similarity with increasing time lags. This reflects a dynamic equilibrium in both species richness and functional composition, maintained through the continuous introduction of new species. These findings clarify the assembly rules and dynamics of open communities under persistent biological invasion.