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Population dynamics provides a numerical tool allowing for the study of rare events by means of simulating a large number of copies of the system N, supplemented with a selection rule that favours the rare trajectories of interest. This method is known as the cloning algorithm which allows the estimation of a large deviation function (LDF) of additive observables in Markov processes. However, such kind of algorithms are plagued by finite simulation time (t) and finite population size (N) effects that can render their use delicate.  We first analyze the small-N effects in the initial transient regime of the evolution of a system. We show how to overcome these effects (which play an important role in the numerical determination of LDF) by introducing a time delay in the evolution of populations, additional to the discarding of the initial regime of the population growth where these discreteness effects are strong. Then, we study the finite-t and finite-N scalings in the LDF evaluation. Using a discrete-time and a continuous-time version of the algorithm, we show these scalings behave as 1/N and 1/t in the large-N and large-t asymptotics respectively. These scalings provide valuable information about the convergence of the LDF estimator in the infinite-t and infinite-N limits. Moreover, this convergence speed can be used in order to extract an asymptotic limit which rendered a better LDF estimation in comparison to the standard estimator. However, when this analysis is extended to a wider range of system sizes L, in the large-L limit these scalings are no longer valid. Moreover, as the convergence of the estimator relies on the positivity of these exponents, we show how for some cases can be negative implying that the estimation provided by the cloning algorithm is no longer reliable.