  We consider population dynamics as implemented by the cloning algorithm for
analysis of large deviations of time-averaged quantities. Using the simple
symmetric exclusion process as a prototypical example, we investigate the
convergence of the results with respect to the algorithmic parameters,
focussing on the dynamical phase transition between homogeneous and
inhomogeneous states, where convergence is relatively difficult to achieve. We
discuss how the performance of the algorithm can be optimised, and how it can
be efficiently exploited on parallel computing platforms.
