Related papers: Mutation frequencies in a birth-death branching pr…
An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during…
The classical Luria-Delbr\"uck model for fluctuation analysis is extended to the case where cells can either divide or die at the end of their generation time. This leads to a family of probability distributions generalizing the…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
Originally developed to elucidate the mechanisms of natural selection in bacteria, the Luria-Delbr\"uck model assumed that cells are intrinsically capable of dividing an unlimited number of times. This assumption however, is not true for…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
The Luria-Delbr\"uck distribution is a classical model of mutations in cell kinetics. It is obtained as a limit when the probability of mutation tends to zero and the number of divisions to infinity. It can be interpreted as a compound…
Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to…
Microbial populations adapt to their environment by acquiring advantageous mutations, but in the early twentieth century, questions about how these organisms acquire mutations arose. The experiment of Salvador Luria and Max Delbr\"uck that…
Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
The Luria-Delbr{\"u}ck experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense…
The estimation of mutation probabilities and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbr\"{u}ck…
The Luria--Delbr\"uck mutation model is a cornerstone of evolution theory and has been mathematically formulated in a number of ways. In this paper we illustrate how this model of mutation rates can be derived by means of classical…
Genomic evolution can be viewed as string-editing processes driven by mutations. An understanding of the statistical properties resulting from these mutation processes is of value in a variety of tasks related to biological sequence data,…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is…
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 to a branching process. Following typical parameter values…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…