Phase Transitions in Mutualistic Communities under Invasion

Abstract

Predicting the outcome of species invasion in ecosystems is a challenge of both theoretical and practical significance. Progress so far has been limited by the intractability of the far-fromequilibrium nature of the transitions that occur during invasion events. 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 species invasion induces discontinuous transitions in the community composition, resembling phase transitions in physical systems. These sharp transitions are emergent properties of speciesresource interactions and relate directly to the extent of niche overlap between invasive and native species. The high susceptibility of community structure to small variations in species phenotype and resource conditions near the phase boundaries can explain empirically observed stochasticity and the emergence of tipping points in ecosystems. Moreover, we demonstrate that these phase transitions can be modulated by environmental variations to construct nonlinear organization of species both in space and time.3