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arXiv · 2312.12179

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

Toni Gui
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Abstract

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 $\mu_c^*$.

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Toni Gui. 2023-12-19. The Yule-Kingman Nested Coalescent: Distribution of the Number of Lineages. https://arxiv.org/abs/2312.12179

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