Stability and selective extinction in complex mutualistic networks

TL;DR

This paper analyzes the stability of plant-pollinator mutualistic networks using Lotka-Volterra equations, revealing how species extinction patterns depend on network structure and interaction strengths, with theoretical predictions matching empirical data.

Contribution

It introduces a theoretical framework for understanding stability and selective extinction in mutualistic networks, linking network topology to species abundance and stability phases.

Findings

Small-degree species tend to go extinct in the selective extinction phase.

Theoretical predictions of species abundance match empirical data after rescaling.

Different stable fixed points depend on network parameters and interaction strengths.

Abstract

We study species abundance in the empirical plant-pollinator mutualistic networks exhibiting broad degree distributions, with uniform intra-group competition assumed, by the Lotka-Volterra equation. The stability of a fixed point is found to be identified by the signs of its non-zero components and those of its neighboring fixed points. Taking the annealed approximation, we derive the non-zero components to be formulated in terms of degrees and the rescaled interaction strengths, which lead us to find different stable fixed points depending on parameters, and we obtain the phase diagram. The selective extinction phase finds small-degree species extinct and effective interaction reduced, maintaining stability and hindering the onset of instability. The non-zero minimum species abundances from different empirical networks show data collapse when rescaled as predicted theoretically.