The nested Kingman coalescent describes the ancestral tree of a population
undergoing neutral evolution at the level of individuals and at the level of
species, simultaneously. We study the speed at which the number of lineages
descends from infinity in this hierarchical coalescent process and prove the
existence of an early-time phase during which the number of lineages at time
$t$ decays as $ 2\gamma/ct^2$, where $c$ is the ratio of the coalescence rates
at the individual and species levels, and the constant $\gamma\approx 3.45$ is
derived from a recursive distributional equation for the number of lineages
contained within a species at a typical time.