Category: Ecology

Summary: Finding how local recycling loops must remain to restabilize a trophically coherent consumer-resource community under fixed mismatch and fixed recycling strength.

Nutrient recycling can stabilize ecological communities, but it is not just the amount of recycling that matters. This experiment asks whether recycling can rescue a stressed trophically coherent consumer-resource system only if those feedback loops stay sufficiently local instead of being spread broadly across the network.

The script constructs dense non-symmetric Jacobians for random consumer-resource communities with fixed mismatch and fixed recycling-buffer strength, then uses GPU-accelerated eigensolves, iterative deepening, and bisection to locate the locality threshold for renewed stability. In this setup, locality itself is the control knob while the major destabilizing and buffering ingredients are held constant.

That distinction is important because recycling strength and recycling architecture are often bundled together conceptually. The experiment isolates the geometry of recycling feedback and asks whether local routing is itself a necessary ingredient in ecological rescue.

Method: GPU dense non-symmetric Jacobian eigensolve with iterative deepening and bisection on recycling locality at fixed mismatch and rescue strength.

What is measured: Critical recycling-locality threshold, leading-eigenvalue stability boundary, localization statistics, and bracket width.