Category: Ecology

Summary: Finding how much exchange a compartment-protected hypercycle can tolerate before its growth mode delocalizes.

Compartmentalization is a classic proposed defense against parasites in origin-of-life hypercycle models, because it can keep successful replicators concentrated within protected protocell-like regions. This experiment asks how much exchange between compartments can occur before that protection fails and the leading growth mode spreads out instead of remaining compartment-confined.

The script builds dense non-symmetric Jacobians for modular hypercycle systems with fixed parasite pressure and heterogeneity, then bisects the exchange rate until localization breaks down. Iterative deepening pushes the threshold search to larger state counts while preserving a narrow bracket.

That creates a direct finite-size map of exchange tolerance in compartmentalized hypercycles. The result is useful because it quantifies when migration changes from helpful communication to destructive leakage in a setting central to prebiotic evolution discussions.

Method: Dense Jacobian eigensolve with iterative deepening and bisection on inter-compartment exchange strength.

What is measured: Critical exchange threshold, localization score, leading-compartment mass, leading eigenvalue real part, parasite pressure, and bracket width.