Category: Ecology

Summary: Testing when trophically stratified nonreciprocity pushes a coherent food-web community from passive stability into transiently amplifying reactivity.

A community can be linearly stable and still show strong short-term amplification if its interaction matrix is sufficiently non-normal. This experiment asks when trophically organized predator-prey nonreciprocity becomes strong enough to make a coherent food-web operator reactive, meaning perturbations can initially grow even before long-run stability is considered.

The script constructs dense heavy-tailed community matrices, symmetrizes the reactivity operator, and uses GPU eigensolves with iterative deepening to find the threshold where the top reactive mode crosses zero. By carrying the bracket to larger matrix sizes, it maps a finite-size onset for transient amplification rather than only checking a few parameter samples.

That is important because ecological instability is not only about asymptotic eigenvalues. Transient bursts can matter ecologically even in systems that are formally stable, so locating the onset of reactivity gives a complementary measure of systemic fragility.

Method: GPU dense symmetric eigensolves on reactivity operators derived from nonreciprocal trophically coherent food-web Jacobians, with iterative deepening and bisection.

What is measured: Critical nonreciprocity threshold for reactivity onset, top reactive eigenvalue, transient-amplification boundary, system size reached, and bracket width.