Mutation frequencies in a birth-death branching process

Abstract

A growing population of cells accumulates genetic mutations. We study stochastic models of this process. Cells divide and die as a branching process, and a cell's genetic information is a sequence of nucleotides which mutates randomly at division. Motivated by biologically realistic parameters, we consider that few cells grow to many cells and mutation rates are small, proving approximations in this limit. In particular we are interested in mutation frequencies and their dependency structure along the genetic sequence; the relevance of the evolutionary tree and selection are discussed. Amongst other results, we recover a power-law distribution for mutation frequencies which is consistent with previously published cancer genetic data.