Category: Ecology

Summary: Finding the minimum layer-selective self-regulation needed to restabilize a trophically coherent food web after nonreciprocal interactions have pushed it into instability.

Self-regulation is often invoked as a stabilizing ingredient in ecological communities, but how much is actually needed can depend strongly on network structure. This experiment asks for the minimum targeted self-regulation required to rescue a trophically coherent food web that has already crossed into an unstable regime because of nonreciprocal interactions.

The script builds dense non-symmetric food-web Jacobians and then carries a rescue bracket across increasing community sizes. At each size it bisects the self-regulation parameter and solves the full spectrum to estimate where the leading eigenvalue returns to the stable side.

This turns a familiar ecological idea into a concrete threshold question. Rather than treating self-regulation as generically helpful, the experiment asks how strong and how selective that feedback must be before stability is restored in a structured finite system.

Method: Dense non-symmetric eigensolves with iterative deepening and bisection on layer-selective self-regulation in trophically coherent food-web Jacobians.

What is measured: Critical self-regulation rescue threshold, leading-eigenvalue stability boundary, system size reached, and bracket width.