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

2024/01/04 by Toni Gui, Gui, Toni
Computer Science · Mathematics · Medicine · #60J90 60J95 #Bayesian Methods and Mixture Models #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2401.02233

openalex publication_date 2024/01/04 · openalex created_date 2024/01/07 · openalex updated_date 2026/07/28

Abstract

We study a model of a population with individuals sampled from different species. The Yule-Λ 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 Λ-coalescent. For the Yule-Λ nested coalescent with c<∫₀¹x^-1Λ(dx)<∞, where Λ is the measure that characterizes the Λ-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 ν_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.

Related

• The Yule-Kingman Nested Coalescent: Distribution of the Number of Lineages
• Coalescent processes emerging from large deviations
• The Nested Kingman Coalescent: Speed of Coming Down from Infinity
• Cannings models, population size changes and multiple-merger coalescents
• The coalescent and its descendants