On an age-structured juvenile-adult model with harvesting pulse in moving and heterogeneous environment

TL;DR

This study analyzes an age-structured juvenile-adult model with harvesting pulses and moving boundaries in a heterogeneous environment, revealing how harvesting strategies and habitat expansion influence species survival or extinction.

Contribution

It introduces a novel model combining age structure, harvesting pulses, and moving boundaries, and provides criteria for species spread or extinction based on eigenvalue analysis.

Findings

Larger harvesting rates decrease species survival.

Shorter harvesting periods worsen species persistence.

Habitat expansion capacity influences spreading or vanishing outcomes.

Abstract

This paper concerns an age-structured juvenile-adult model with harvesting pulse and moving boundaries in a heterogeneous environment, in which the moving boundaries describe the natural expanding front of species and human periodic pulse intervention is carried on the adults. The principal eigenvalue is firstly defined and its properties involving the intensity of harvesting and length of habitat sizes are analysed. Then the criteria to determine whether the species spread or vanish is discussed, and some relevant sufficient conditions characterized by pulse are established. Our results reveal that the co-extinction or coexistence of species is influenced by internal expanding capacities from species itself and external harvesting pulse from human intervention, in which the intensity and timing of harvesting play key roles. The final numerical approximations indicate that the larger the harvesting rate and the shorter the harvesting period, the worse the survival of all individuals due to the cooperation among juveniles and adults, and such harvesting pulse can even alter the situation of species, from persistence to extinction. In addition, expanding capacities also affect or alter the outcomes of spreading-vanishing