5 citations · 5 across the 4 of their papers we have counts for
6 papers
Sequential mutations in exponentially growing populations
Michael D. Nicholson, David Cheek, Tibor Antal
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how ma…
Ancestral reproductive bias in branching processes
David Cheek, Samuel G. G. Johnston
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time and looking along the sampled cell's ancest…
The coalescent tree of a Markov branching process with generalised logistic growth
David Cheek
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows expone…
The empirical mean position of a branching Lévy process
David Cheek, Seva Shneer
We consider a supercritical branching Lévy process on the real line. Under mild moment assumptions on the number of offspring and their displacements, we prove a second-order limit…
Genetic composition of an exponentially growing cell population
David Cheek, Tibor Antal
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according…
Mutation frequencies in a birth-death branching process
David Cheek, Tibor Antal
First, we revisit the stochastic Luria-Delbrück model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact resul…