Before revision:  Our approach is based is on a nonlinear least squares optimization procedure which takes into account both the first and the  second mutation events. The methodology developed in this paper is confirmed with numerical simulations with realistic parameter values .
After revision:  Our approach is based is on a nonlinear least squares optimization procedure which takes into account both the first and the second mutation event. The basic principle applied here is to minimize (for each trajectory) the mean squared errors of prediction w(t) - W(t) where the observed white cell frequencies w(t) are predicted by W(t), which is computed as the conditional expectation of w(t) given the available information at time (t-1). The pooling of all selective advantages estimates across all trajectories provides histograms on which we perform a precise peak analysis to compute final estimates of selective advantages. We validate our approach using ensembles of simulated trajectories .