Category: Pop. Genetics

Summary: Testing whether a smooth compartment-capacity gradient can restore exchange tolerance in a compartmentalized hypercycle after plain exchange already causes delocalization.

Hypercycle models are a standard framework for studying cooperative replication and its vulnerability to mixing and parasites. This experiment asks whether a smooth gradient in compartment capacity can rescue the system once ordinary exchange has already become strong enough to delocalize the cooperative state.

The model builds dense modular hypercycle operators and uses GPU iterative deepening to locate the threshold where a fixed capacity gradient restores a nonzero tolerance to exchange. In practice, that means finding whether a spatially organized asymmetry can keep cooperative activity localized even after unstructured exchange would wash it out.

That is a structural rescue question rather than a baseline survival calculation. The value is in isolating capacity gradients as a potential stabilizing design principle for compartmentalized prebiotic systems, beyond the classic emphasis on compartmentalization alone.

Method: GPU dense eigensolves with iterative deepening and bisection on exchange tolerance in a compartmentalized hypercycle operator with a fixed capacity gradient.

What is measured: Critical rescued exchange threshold, localization or delocalization of the cooperative mode, finite-size bracket width, and gradient-induced rescue behavior.