Related papers: On mutations in the branching model for multitype …

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…

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,…

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…

We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…

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…

A multi-type neutral Cannings population model with mutation and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a…

Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…

We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give…

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…

The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…

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…

We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…

Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…

For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…

We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…

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…

We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…

We consider branching processes with interaction in continuous time, both with values in the integers and in the reals (in the second case we restrict ourselves to continuous processes), which model the evolution of the size of a…

A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…

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…