  We study a model of a population with individuals sampled from different
species. The Yule-$\Lambda$ nested coalescent describes the genealogy of the
sample when each species merges with another randomly chosen species with a
constant rate $c$ and the mergers of individuals in each species follow the
$\Lambda$-coalescent. For the Yule-$\Lambda$ nested coalescent with
$c<\int_0^1x^{-1}\Lambda(dx)<\infty$, where $\Lambda$ is the measure that
characterizes the $\Lambda$-coalescent, we show that under some initial
conditions, the distribution of the number of individual lineages belonging to
one species converges weakly to the distribution $\nu_c^*$, which is the
solution to some recursive distributional equation (RDE) with finite mean. In
addition, we show that for some values of $c$, the RDE has another solution
with infinite mean.
