We start from a  family of continuous approximations to frequency dependtent Moran and Wright-Fisher studied in [1] and [2].  The approximations depend on scaling assumptions, and can be of diffusive or non-diffusive type---the later being equivalent to the Replicator Dynamics. In the large intenstity fo selection limit, we show how the Replicator Dynamics can be consistenly fitted in a diffusive approximation. Time allowing, we will also show  results about fixation probabilities in very general scaling settings. This is joint work with Fabio Chalub.

References

[1] FACC Chalub & MO Souza, From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics. Theor. Pop. Biol., 76 (4), 268--277 (2009)

[2] The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations. Forthcoming  in J. Math. Biol (2014)