  Consider a birth and death process started from one individual in which each
individual gives birth at rate $\lambda$ and dies at rate $\mu$, so that the
population size grows at rate $r = \lambda - \mu$. Lambert and Harris,
Johnston, and Roberts came up with methods for constructing the exact genealogy
of a sample of size $n$ taken from this population at time $T$. We use the
construction of Lambert, which is based on the coalescent point process, to
obtain asymptotic results for the site frequency spectrum associated with this
sample. In the supercritical case $r > 0$, our results extend results of
Durrett for exponentially growing populations. In the critical case $r = 0$,
our results parallel those that Dahmer and Kersting obtained for Kingman's
coalescent.
