Asymptotics for the site frequency spectrum associated with the genealogy of a birth and death process

2023/04/26 by Jason Schweinsberg, Schweinsberg, Jason, Yubo Shuai +1 · 2 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Random Matrices and Applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2304.13851

Abstract

Consider a birth and death process started from one individual in which each individual gives birth at rate λ and dies at rate μ, so that the population size grows at rate r = λ- μ. Lambert and Harris, Johnston, and Roberts came up with methods for constructing the exact genealogy of a sample of size n taken from this population at time T. We use the construction of Lambert, which is based on the coalescent point process, to obtain asymptotic results for the site frequency spectrum associated with this sample. In the supercritical case r > 0, our results extend results of Durrett for exponentially growing populations. In the critical case r = 0, our results parallel those that Dahmer and Kersting obtained for Kingman's coalescent.

Cited by

• Estimating the growth rate of a birth and death process using data from a small sample
• Site Frequency Spectrum in stationary branching populations

Related

• Transition in the ancestral reproduction rate and its implications for the site frequency spectrum
• The Site Frequency Spectrum in an Exponentially-Growing Population with Selection
• Asymptotic sampling formulae for Lambda-coalescents
• Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population
• Sampling through time and phylodynamic inference with coalescent and birth-death models