Stochastic Dynamics of a Harvested Two-Species Fishery Model with Random Birth and Death Effects

Fish populations in natural ecosystems are influenced not only by biological interactions and fishing activities, but also by random fluctuations in the environment and natural populations. Deterministic models, though useful for modelling, sometimes fail to capture the complexity of uncertainty in fish populations. Motivated by this limitation, this study introduces and examines a stochastic model of the interaction between two competing fish species with random birth and death rates. Within the proposed framework, the classical model of a two-species competing population is extended to include a harvesting term and stochastic fluctuations in the reproduction and death rates. This is achieved by formulating continuous-time stochastic differential equations in which the intensities of the stochastic fluctuations depend on population densities in a biologically realistic manner. Analytical techniques have been employed to investigate the equilibria of stochastic populations, as well as the conditions for their persistence and extinction. The impacts of harvesting and stochasticity on system dynamics are investigated numerically using the Euler–Maruyama method. In contrast to the deterministic situation, stochastic impacts can significantly change the system's behavior. In particular, random perturbations may increase the risk of extinction even at harvesting levels considered sustainable in a deterministic framework. We observed that stochasticity, together with suitably designed harvesting strategies, affects the two competing fish species. Overall, the results of this study demonstrate the significance of random births and deaths in fishery models and provide insights for developing harvesting policies that ensure sustainability even with uncertainty, emphasising the importance of stochastic approaches for interacting species, specifically competitive fish populations, in fluctuating environments.