Category: Ecology

Summary: Finding the elemental-mismatch level where trophically coherent consumer-resource communities lose linear stability despite fixed recycling.

Ecological communities can be stable on average yet fail when consumers and resources are mismatched in elemental composition. This experiment asks how much stoichiometric mismatch a trophically coherent consumer-resource community can tolerate before its linearized dynamics become unstable, even when recycling remains fixed.

The script builds dense non-symmetric Jacobians for random layered consumer-resource systems with trophic coherence and recycling. It then bisects the mismatch parameter across increasing system sizes and records the point where the leading eigenvalue crosses the stability boundary.

This separates the effect of mismatch from the effect of recycling rescue. The result is a direct threshold map for when coherent structure is no longer enough to offset stoichiometric stress.

Method: Dense non-symmetric Jacobian eigensolve with iterative deepening and bisection on stoichiometric mismatch at fixed recycling strength.

What is measured: Critical mismatch threshold, leading-eigenvalue stability boundary, stability fraction across disorder samples, and bracket width.