In this talk, we introduce a class of first order ergodic mean field games (MFG) arising from ecology, and a numerical method for the approximation of their solution. The algorithms we propose are inspired by best response dynamics in evolutionary game theory, the minimisation of the highest income of a game, and De Giorgi's minimising movement schemes. Unlike other non-standard schemes for MFG, this kind of approximation does not assume any variational structure of the system. To conclude, we present and compare various numerical simulations both in 1D and 2D domains. https://uniroma1.zoom.us/j/88301496298?pwd=mPe3ZTFDt7I5dSvorX7wZAfaD0Z0Wy.1