  We consider a model of a population in which individuals are sampled from
different species. The Yule-Kingman nested coalescent describes the genealogy
of the sample when each species merges with another randomly chosen species
with a constant rate $c$ and each pair of lineages belonging to the same
species coalesces independently at rate 1. We study the distribution of the
number of individual lineages belonging to a given species and show that it
converges weakly to a distribution $\mu_c^*$, which is the unique solution to a
recursive distributional equation. Furthermore, the average number of
individual lineages belonging to each species converges in probability to the
mean of $\mu_c^*$.
