Harvesting in a stage-structured population with applications to red snapper in the Gulf of Mexico

We propose deterministic discrete-time, discrete stage-structured population models with harvesting to investigate population persistence and extinction. The mathematical analysis is centered around the inherent net reproductive number of the population. We apply data of the red snapper in the Gulf of Mexico to simulate the models. We use the models to test for a hypothesis proposed by marine biologists by adding a stochastic component to the deterministic systems that simulating pulses of early juveniles from other populations. We conclude that although pulses of early juveniles from other populations can contribute to the stock size of the early juveniles in the Gulf of Mexico, this contribution is insignificant for the adult population. Therefore, the population may still be in danger of extinction since the ocean environment is unpredictable. Other control strategies are needed in order for the population to be harvested annually.