Category: Ecology

Summary: Finding when increasingly nonreciprocal predator-prey interactions destabilize trophically coherent heavy-tailed food-web Jacobians.

Food-web stability depends both on trophic structure and on asymmetry between paired gains and losses, but those ingredients are usually studied separately. This experiment asks when a trophically coherent ecological interaction matrix loses stability as predator-prey pairs become more nonreciprocal.

The script builds dense non-symmetric Jacobians for heavy-tailed, trophically coherent food webs and carries out iterative deepening across system sizes. It bisects a nonreciprocity parameter, evaluates stability through full eigenvalue computations, and propagates only the shrinking uncertainty bracket to larger systems.

The value of the experiment is that it turns a qualitative ecological idea into a finite-size threshold problem. Rather than asking only whether asymmetry matters, it estimates how much asymmetry a coherent food web can absorb before its stable regime breaks down.

Method: Dense non-symmetric eigensolves with iterative deepening and bisection on a stratified nonreciprocity parameter in coherent trophic Jacobians.

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