Global dynamics and regime shifts in a resource-consumer model with facilitation and habitat loss

TL;DR

This study models resource-consumer interactions with facilitation under habitat loss, revealing how habitat destruction influences stability, oscillations, and extinction risks through analytical and stochastic analyses.

Contribution

It provides a detailed analytical characterization of bifurcations and stability in a resource-consumer model with facilitation, incorporating habitat loss and stochastic effects.

Findings

Unique stable limit cycle identified in the model.

Heteroclinic bifurcation curve characterized analytically.

Stochasticity can lead to earlier co-extinctions.

Abstract

Modelling how populations respond to habitat loss is crucial for understanding ecosystem stability, especially when positive interactions among resource species, such as plant-plant facilitation, play a key role. Habitat loss not only reduces available organic nutrients and space for primary producers but also disrupts the positive feedbacks that sustain resource populations, thereby affecting consumer persistence and the overall system's stability. We analyse a cubic planar model describing resource-consumer dynamics with facilitation under progressive habitat loss. Our study characterizes the parameter space and enumerates all the phase portraits within the Poincar\'e disk under ecologically relevant conditions. We show that the system has a unique stable limit cycle and characterize analytically the heteroclinic bifurcation curve involving the collapse of the resource and the consumer, enabling us to determine how the parameter region sustaining coexistence oscillations narrows under habitat destruction. To further explore these dynamics, we construct a piecewise-linear (PWL) approximation that preserves the system's qualitative behaviour, allowing us to obtain an explicit expression for the heteroclinic bifurcation. Finally, we investigate how extrinsic noise affecting the resource species impacts the overall dynamics, showing that stochasticity can anticipate the onset of the heteroclinic bifurcation causing earlier co-extinctions.