  We study the dynamics of a population subject to selective pressures,
evolving either on RNA neutral networks or in toy fitness landscapes. We
discuss the spread and the neutrality of the population in the steady state.
Different limits arise depending on whether selection or random drift are
dominant. In the presence of strong drift we show that observables depend
mainly on $M \mu$, $M$ being the population size and $\mu$ the mutation rate,
while corrections to this scaling go as 1/M: such corrections can be quite
large in the presence of selection if there are barriers in the fitness
landscape. Also we find that the convergence to the large $M \mu$ limit is
linear in $1/M \mu$. Finally we introduce a protocol that minimizes drift; then
observables scale like 1/M rather than $1/(M\mu)$, allowing one to determine
the large $M$ limit faster when $\mu$ is small; furthermore the genotypic
diversity increases from $O(\ln M)$ to $O(M)$.

Populations and Evolution;Statistical Mechanics