Category: Ecology

Summary: Finding how strongly recycled biomass must be routed one trophic step downward to restabilize a mismatched consumer-resource community.

Nutrient recycling can either stabilize a food web or spread perturbations in unhelpful ways, depending on how recycled material is routed. This experiment asks whether a consumer-resource community destabilized by stoichiometric mismatch can be rescued only when recycling is sufficiently directional toward the next lower trophic layer.

The script constructs dense trophically coherent Jacobians, fixes mismatch and recycling dispersion, and then bisects a directionality parameter while carrying the threshold bracket across larger system sizes. Stability is read from the leading eigenvalue, so the output is a direct finite-size estimate of when directional routing becomes strong enough to restore stability.

That isolates architecture from quantity. Ecological stoichiometry, recycling, and food-web stability are all established topics, but this experiment focuses on whether the direction of recycling itself is a distinct stabilizing control knob.

Method: Dense non-symmetric Jacobian eigensolve with iterative deepening and bisection on trophic recycling directionality at fixed mismatch and recycling dispersion.

What is measured: Critical recycling-directionality threshold, stability fraction, leading-eigenvalue boundary, and threshold bracket width.