Persistence analysis of the age-structured population model on several patches

TL;DR

This paper analyzes a complex age-structured population model across multiple patches, proving conditions for persistence or extinction based on spectral properties of the reproductive operator.

Contribution

It establishes existence, uniqueness, and long-term behavior of solutions for a nonlinear PDE system modeling populations in variable environments across multiple patches.

Findings

Population persists if spectral radius > 1

Extinction occurs if spectral radius ≤ 1

Results hold for various environmental change patterns

Abstract

We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the system in time-independent case, for periodically changing and for irregularly varying environment. Under the assumption that every patch can be reached from every other patch, directly or through several intermediary patches, and that net reproductive operator has spectral radius larger than one, we prove that population is persistent on all patches. If the spectral radius is less or equal one, extinction on all patches is imminent.