Category: Ecology

Summary: Finding the environmental-load level where a refuge-coupled trophic system loses its positive localized amplification mode.

Refuges can preserve localized activity in food webs, but external load can eventually overwhelm that protection. This experiment asks when a trophic response operator with reversible protected subcommunities stops supporting a positive mode concentrated in lower and middle layers.

The model builds dense symmetric block operators for refuge-coupled trophic systems and uses GPU eigensolves to bisect environmental load while increasing problem size. It tracks the point where the localized amplification mode disappears.

That matters because the system may lose organized trophic support before every form of response vanishes. The result is therefore a threshold for protected structure, not just for gross activity.

Method: GPU dense symmetric eigensolve with iterative deepening and bisection on environmental load in a refuge-coupled trophic operator.

What is measured: Critical load threshold, localization of the positive mode, lower-layer and mid-layer support, and bracket width.