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

The Yule-Kingman Nested Coalescent: Distribution of the Number of Lineages