On an age-structured model in moving boundaries: The effects of nonlocal diffusion and harvesting pulse

TL;DR

This paper analyzes an age-structured nonlocal diffusion model with moving boundaries and harvesting pulses, revealing how dispersal, habitat, and human intervention influence species survival or extinction.

Contribution

It introduces a generalized principal eigenvalue framework to determine spreading or vanishing outcomes in a complex, nonlocal, age-structured ecological model.

Findings

Harvesting rate and habitat size critically affect species survival.

Long-range dispersal can induce complex population dynamics.

Proper management can shift outcomes from coexistence to extinction.

Abstract

In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long range dispersal of species itself and time-periodic harvesting pulse exacting on the adult reflects human intervention. A generalized principal eigenvalue involving harvesting rate used to identify the spreading and vanishing outcomes is firstly defined and the existence of the principal eigenvalue is given under some conditions. Subsequently, properties of the generalized principal eigenvalue and the principal eigenvalue related to harvesting rate and length of habitat interval are analyzed, respectively. The criteria to governing spreading or vanishing of the species are finally investigated, with sufficient conditions for spreading-vanishing established. Our results indicate that complexities can be induced by the internal long rang dispersal and expanding capacities of species, as well as external harvesting intervention of human. Specifically, appropriate harvesting rate and expanding capacities can even change the reciprocal outcomes of species from co-existence to co-extinction.