Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population

TL;DR

This paper analyzes the site frequency spectrum of neutral mutations in exponentially growing populations, providing theoretical results and estimators relevant for understanding neutral evolution in contexts like cancer.

Contribution

It establishes first-order almost sure convergence results for the SFS in branching processes and constructs consistent estimators for key parameters.

Findings

Convergence results for the SFS in Galton-Watson processes

Estimators for extinction probability and mutation rate

Application to neutral evolution in cancer

Abstract

The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing population. Using branching process techniques, we establish (first-order) almost sure convergence results for the SFS of a Galton-Watson process, evaluated either at a fixed time or at the stochastic time at which the population first reaches a certain size. We finally use our results to construct consistent estimators for the extinction probability and the effective mutation rate of a birth-death process.