Based on the fact that, a standard prey-predator model (SPPM), exhibits irreversible phase transitions, belonging to the universality class of directed percolation (DP), between prey-predator coexistence and predator extinction [Phys. Lett. A 280 (2001) 45], a self-organized prey-predator model (SOPPM) is formulated and studied by means of extensive Monte Carlo simulations. The SOPPM is achieved defining the parameters of the SPPM as functions of the density of species. It is shown that the SOPPM self-organizes into an active state close the absorbing phase of the SPPM, and consequently their avalanche exponents also belong the the universality class of DP.