Phase transitions in mutualistic communities under invasion.

Predicting the outcome of species invasion in ecosystems is challenging due to the non-equilibrium nature of the transitions that occur during invasion events. This limits the accuracy of classical ecological models that are typically fit to equilibrium conditions. Here, we address this limitation by solving for the transition dynamics of a cross-feeding community along an analytically tractable manifold defined by the system carrying capacity. We find that continuous changes in invader characteristics and environmental conditions induce discontinuous transitions in the invasion outcomes, resembling phase transitions in physical systems. These sharp transitions are emergent properties of species-resource interactions and relate directly to the extent of overlap in the growth strategy of competing species, with first and second order transitions resulting from complete and partial overlap, respectively. Moreover, we demonstrate that these phase transitions can be modulated by environmental variations to organize species in space.