The aim of this work is to develop and analyze a mathematical model for a predator-2 preys system arising in marine environments. We are interested in the evolution of fish population depending of plankton. We first look at the model; this yields a singular system of ordinary differential equations having interesting dynamical futures, such as finite time extinction and persistence of populations. In addition, the mathematical analysis permits to isolate extinction conditions in finite or infinite time. Finally, the numerical simulations permits to establish the effect of the fishing on the evolution of fish population in spite of abundance resource and itís permit to know if area is severely exploited or not.