Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions

TL;DR

This paper demonstrates that increasing non-reciprocal interactions in a generalized ecological model causes a phase transition to chaos, with the chaos emergence governed by the ratio of surviving species to resources.

Contribution

It analytically and numerically shows how non-reciprocity induces chaos in ecological models, providing a phase diagram and understanding of the transition mechanism.

Findings

Ecosystems undergo a chaos transition with increased non-reciprocity.

The chaos emergence is controlled by the ratio of surviving species to resources.

Lyapunov exponents confirm chaotic dynamics in the model.

Abstract

Non-reciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of non-reciprocity in the context of theoretical ecology by analyzing a generalization of MacArthur's consumer-resource model with asymmetric interactions between species and resources. Using a mixture of analytic cavity calculations and numerical simulations, we show that such ecosystems generically undergo a phase transition to chaotic dynamics as the amount of non-reciprocity is increased. We analytically construct the phase diagram for this model and show that the emergence of chaos is controlled by a single quantity: the ratio of surviving species to surviving resources. We also numerically calculate the Lyapunov exponents in the chaotic phase and carefully analyze finite-size effects. Our findings show how non-reciprocal interactions can give rise to complex and unpredictable dynamical behaviors even in the simplest ecological consumer-resource models.