Spectral control for ecological stability

TL;DR

This paper introduces a spectral control method to stabilize complex ecological systems by minimally rewiring species interactions, highlighting the role of predator-prey dynamics in enhancing resilience.

Contribution

A novel mathematical approach for stabilizing ecosystems through spectral modifications of interaction networks, linking stability to specific interaction modalities.

Findings

Rewiring couplings can effectively stabilize ecosystems.

Predator-prey interactions increase resilience.

Minimal spectral modifications suffice for stability.

Abstract

A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered graph. A mathematical procedure is introduced and tested to stabilise the ecosystem via an {\it ad hoc} rewiring of the underlying couplings. The method implements minimal modifications to the spectrum of the Jacobian matrix which sets the stability of the fixed point and traces these changes back to species-species interactions. Resilience of the equilibrium state appear to be favoured by predator-prey interactions.