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

2023/12/19 by Toni Gui, Gui, Toni
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #60J90 60J95 #Bayesian Methods and Mixture Models #Evolution and Genetic Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2312.12179

openalex publication_date 2023/12/19 · openalex created_date 2023/12/22 · openalex updated_date 2026/07/28

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 μ_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 μ_c^*.

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