  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 the interaction strengths. By employing bifurcation
theory in tandem with numerical continuation, we elucidate transcritical
bifurcations underlying species extinction and demonstrate that the Hopf
bifurcation of unfeasible equilibria and degenerate transcritical bifurcations
give rise to multistability, i.e., the coexistence of multiple attracting
feasible equilibria. These bifurcations allow us to partition the parameter
space into different regimes, each with distinct sets of extinct species,
offering insights into how interspecific interactions generate one or multiple
extinction scenarios within an ecological network.
