Category: Ecology

Summary: Finding the bridge strength where a weak secondary refuge and corridor cause persistence to shift from a single protected patch to a genuinely dual-refuge mode.

Species can persist in hostile landscapes by concentrating activity inside refuge patches, but it is less clear when two refuges connected by a corridor begin to function as one jointly protected system rather than as one strong refuge with a weak satellite. This experiment asks for the finite-size threshold where the dominant persistence mode stops living mostly in the primary refuge and instead spreads across both refuges and the bridge between them.

The model builds dense symmetric persistence operators with two refuge regions, a corridor, and hostile background habitat. It then uses iterative deepening and bisection over bridge strength while increasing system size, tracking how much of the leading eigenmode sits on the bridge-and-secondary-refuge structure.

That makes the result a structural threshold, not just a yes-or-no survival test. The goal is to identify when connectivity reorganizes where persistence lives, which is relevant to rescue effects, corridor design, and spatial population management.

Method: Dense symmetric eigensolve with iterative deepening and bisection on bridge strength in a heterogeneous two-refuge persistence operator.

What is measured: Critical bridge strength, leading-mode mass on the bridge and secondary refuge, dominant eigenvalue behavior, and bracket width.