  In this paper, we develop a computational approach for computing most likely
trajectories describing rare events that correspond to the emergence of
non-dominant genotypes. This work is based on the large deviations approach for
discrete Markov chains describing the genetic evolution of large bacterial
populations. We demonstrate that a gradient descent algorithm developed in this
paper results in the fast and accurate computation of most-likely trajectories
for a large number of bacterial genotypes. We supplement our analysis with
extensive numerical simulations demonstrating the computational advantage of
the designed gradient descent algorithm over other, more simplified,
approaches.
