  We consider a model of a population of fixed size $N$ undergoing selection.
Each individual acquires beneficial mutations at rate $\mu_N$, and each
beneficial mutation increases the individual's fitness by $s_N$. Each
individual dies at rate one, and when a death occurs, an individual is chosen
with probability proportional to the individual's fitness to give birth. Under
certain conditions on the parameters $\mu_N$ and $s_N$, we obtain rigorous
results for the rate at which mutations accumulate in the population and the
distribution of the fitnesses of individuals in the population at a given time.
Our results confirm predictions of Desai and Fisher (2007).
