Transition in the ancestral reproduction rate and its implications for the site frequency spectrum

2024/02/26 by Shuai, Yubo
#FOS: Biological sciences #FOS: Mathematics #Probability (math.PR) #Quantitative Methods (q-bio.QM)

paper · doi:10.48550/arxiv.2402.16306

Abstract

Consider a supercritical birth and death process where the children acquire mutations. We study the mutation rates along the ancestral lineages in a sample of size n from the population at time T. The mutation rate is time-inhomogenous and has a natural probabilistic interpretation. We use these results to obtain asymptotic results for the site frequency spectrum associated with the sample.

Related

• Asymptotics for the site frequency spectrum associated with the genealogy of a birth and death process
• The Site Frequency Spectrum in an Exponentially-Growing Population with Selection
• Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population
• Mutation frequencies in a birth-death branching process
• Sample genealogy and mutational patterns for critical branching populations