The role of harvesting and growth rate for spatially heterogeneous populations

TL;DR

This paper explores how harvesting and growth rates influence the competition dynamics of two species in a spatially heterogeneous environment, providing theoretical analysis and numerical validation of coexistence and extinction scenarios.

Contribution

It introduces a model incorporating realistic harvesting linked to intrinsic growth rates and proves existence, uniqueness, and long-term outcomes of solutions.

Findings

Coexistence can lead to one species driving the other to extinction.

Both species can also become extinct under certain parameter conditions.

Numerical simulations align with theoretical predictions.

Abstract

This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are developed based on this clause instead of random choice. We prove the existence and uniqueness of the solution to the model we consider. Theoretically, we state that when species coexist, one may drive the other to die out, and both species extinct, considering all possible rational values of parameters. These results highlight a comparative study between two harvesting coefficients. Finally, we solve the model using a backward-Euler, decoupled, and linearized time-stepping fully discrete algorithm and observe a match between the theoretical and numerical findings.