  We consider a model of a population with fixed size $N$, which is subjected
to an unlimited supply of beneficial mutations at a constant rate $\mu_N$.
Individuals with $k$ beneficial mutations have the fitness $(1+s_N)^k$. Each
individual dies at rate 1 and is replaced by a random individual chosen with
probability proportional to its fitness. We show that when $\mu_N \ll 1/(N \log
N)$ and $N^{-\eta} \ll s_N \ll 1$ for some $\eta < 1$, large numbers of
beneficial mutations are present in the population at the same time, competing
against each other, yet the fixation times of beneficial mutations, after a
time scaling, converge to the times of a Poisson process.
