Bifurcations and multistability in empirical mutualistic networks

TL;DR

This paper develops a theoretical framework using bifurcation analysis to understand species persistence and extinction in empirical mutualistic networks, revealing how interaction strengths influence multistability and community outcomes.

Contribution

It introduces a bifurcation-based approach to analyze species-level dynamics in empirical mutualistic networks, highlighting mechanisms of multistability and extinction scenarios.

Findings

Identification of transcritical bifurcations leading to species extinction

Demonstration of Hopf bifurcations causing multistability

Partitioning of parameter space into regimes with different extinction outcomes

Abstract

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.