Category: Ecology

Summary: Finding how strong a compartment-capacity gradient must be to pull hypercycle growth into one favored compartment.

Compartmentalization is one of the main ideas proposed for protecting fragile hypercycles in origin-of-life models. This experiment asks when a smooth capacity gradient across compartments becomes strong enough to break a shared multi-compartment state and concentrate the dominant growth mode inside a single favored compartment.

The model builds dense growth operators for modular hypercycles and then bisects the strength of the imposed resource-capacity gradient. Iterative deepening carries the same narrowing threshold bracket to larger systems, so the result is a finite-size estimate of when localization into one compartment takes over.

This is scientifically useful because compartment protection is often discussed in qualitative terms, while resource asymmetry is treated separately. Here the interaction between the two becomes a measurable threshold problem.

Method: Dense symmetric eigensolve with iterative deepening and bisection on compartment-capacity gradient strength.

What is measured: Critical capacity-gradient threshold, localization of the Perron mode, favored-compartment mass, and bracket width.