Category: Ecology

Summary: Testing whether delayed recycling through a detrital buffer can restabilize mismatched consumer-resource communities, and locating the delay threshold where that rescue appears.

Consumer-resource communities are shaped by nutrient recycling, stoichiometric mismatch, and stability constraints, but those ingredients are usually analyzed separately. This experiment asks whether introducing a recycling delay through a detrital buffer can actually rescue stability in a random community matrix that would otherwise be destabilized by mismatch.

The script constructs dense non-symmetric Jacobians for layered consumer-resource systems with consumers, resources, and detritus. It then uses iterative deepening and bisection on the recycling delay to find the point where a target fraction of disorder realizations becomes stable, while also tracking whether the delayed component carries the dominant response.

That focus turns delay into a possible stabilizing mechanism rather than only a source of oscillation or instability. The result is a threshold map for when delayed recycling can offset mismatch strongly enough to restore stable dynamics in finite random ecosystems.

Method: Dense non-symmetric eigensolve with iterative deepening and bisection on recycling delay in stoichiometrically mismatched consumer-resource Jacobians.

What is measured: Critical recycling-delay estimate, bracket width, stable fraction, maximum real part of the spectrum, delay-localization score, detritus mass, and consumer-resource asymmetry.