Modeling Predator-Prey Interactions Barramundi in Dogamit Swamp Wasur National Park Merauke - Pratama, Rian Ade; Ruslau, Maria F V; Suryani, Dessy Rizki; Nurhayati, Nurhayati; Meirista, Etriana (JTAM (Jurnal Teori dan Aplikasi Matematika), 2024)
Dogamit, which serves as a habitat for fish species growth, has drawn attention due to its location within a national park and the practice of 'sasi' by the local community as a way to preserve the ecosystem and the species that interact within it. In this research, mathematical modeling variables are explained to describe species' life based on direct observation. As the ecosystem’s inhabitants, the dominant predator species in the ecosystem is the Barramundi fish. Historically, this predator species has migrated from the waters of Australia. The aim of this research is to determine the locally stable equilibrium point and analyze the growth trajectories of the species. The testing is conducted based on equilibrium point analysis. There are three equilibrium points, but only one is a non-negative and realistic point for stability testing. This equilibrium point is then tested using the Routh-Hurwitz criteria. Stability is analyzed using the Jacobian matrix to obtain the eigenvalues. All eigenvalues are negative, thus it can be concluded that the model tested is locally stable. A numerical simulation analysis is also provided, involving parameters that support the mathematical model. The parameters are derived from previous relevant studies and realistic assumptions. The numerical simulation analysis method is used to observe the population growth trajectories. The trajectories that appear show similar conditions for both populations. Both populations experience significant fluctuations with an average growth rate of 67%. It takes 3/5 of the species' lifespan for both populations to stabilize again within the ecosystem. The predator-prey populations also demonstrate resilience during fluctuations, indicating that both populations are highly robust in maintaining survival. The characteristics and findings of this research are commonly found only in endemic species populations. Endemic species tend to have long-term survival and endurance, allowing them to dominate their surrounding geographic habitat and maintain ecosystem balance.