Bifurcations and multistability in empirical mutualistic networks

Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a theoretical framework still remains to be developed to understand species-level dynamical heterogeneity within a given community, hampering real-world ecosystems' theoretical assessment and management. Here, we consider empirical plant-pollinator mutualistic networks, additionally including all-to-all intragroup competition, where species abundance evolves under a Lotka-Volterra-type equation. Setting the strengths of competition and mutualism to be uniform, we investigate how individual species persist or go extinct under varying these interaction strengths. By taking a dynamical systems approach, we meticulously study how increments in these interactions create particular sequences of extinctions and find the interaction strengths threshold values in which multistability arises. Hence, we are able to elucidate interaction strength regimes where, depending on the initial abundances of the species, different extinction scenarios arise within an ecological network.