Before revision:  In particular, we develop a numerical approach for estimating genotypes' fitnesses in locked-box  models describing bacterial evolution in experimental setups similar to the celebrated Lenski experiment . Our approach is based is on a nonlinear least squares optimization procedure which takes into account both the first and the  second mutation events.
After revision:  In particular, we develop a numerical approach for estimating genotypes' fitnesses in locked-box models describing bacterial evolution in experimental setups similar to the celebrated Lenski experiment on Escherichia Coli. Our algorithm first analyses emergence of new mutant strains for each individual trajectory. For each trajectory our analysis is progressive in time, and successively focuses on the second mutation events.