Category: Ecology

Summary: Estimating how strong a decomposer-detritus recycling loop must become before it restores linear stability and shifts the dominant mode away from a stoichiometrically stressed consumer chain.

Food webs do not just pass biomass upward from resources to consumers. They also recycle material through detritus and decomposers, and that recycling may buffer systems that would otherwise be destabilized by strong nutrient mismatch between trophic levels. This experiment asks for the threshold at which a detrital loop stops being a minor side pathway and instead becomes strong enough to rescue stability in a mismatched consumer-resource community.

The script builds dense non-symmetric Jacobians for trophically coherent consumer-resource systems with a fixed high mismatch, then increases detrital-loop strength while tracking the leading eigenmode. Iterative deepening and repeated eigendecompositions are used to bisect the critical recycling strength across larger system sizes, with special attention to whether the dominant mode relocalizes onto basal and detrital components rather than remaining concentrated in the consumer chain.

That makes the project a structural stability-threshold study rather than a generic food-web simulation. The aim is to locate the rescue point directly and show when detrital recycling changes the geometry of instability, not just whether overall growth rates happen to improve.

Method: Dense non-symmetric Jacobian eigendecompositions with iterative deepening and bisection on detrital-loop strength omega across N=64 to 2048.

What is measured: Critical detrital-loop threshold, leading-mode real part, detrital rescue metric, detrital-to-chain mass ratio, basal mass, detrital mass, chain mass, and bracket width.