Category: Ecology

Summary: Finding how unevenly recycling can be distributed before a recycling-stabilized consumer-resource community becomes unstable again.

A food web may be stabilized by nutrient recycling on average, yet still fail if that recycling is distributed too unevenly across trophic layers. This experiment asks where that failure point lies once mismatch, mean locality, and mean recycling strength are held fixed.

The script builds trophically coherent consumer-resource Jacobians, fixes the average recycling rescue conditions, and then bisects a dispersion parameter that makes recycling increasingly heterogeneous. Stability is tracked through the leading eigenvalue, while additional diagnostics measure whether localization or upper-lower layer asymmetry grows near the threshold.

This separates the benefit of having recycling from the benefit of distributing it well. The result is a finite-size map of how much heterogeneity the stabilizing feedback can tolerate.

Method: Dense non-symmetric Jacobian eigensolve with iterative deepening and bisection on recycling dispersion.

What is measured: Critical recycling-dispersion threshold, leading eigenvalue real part, midlayer localization score, upper-lower asymmetry, fixed mismatch, and bracket width.