Related papers: Error-induced extinction in a multi-type critical …
We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
We consider a discrete-time host-parasite model for a population of cells which are colonized by proliferating parasites. The cell population grows like an ordinary Galton-Watson process, but in reflection of real biological settings the…
A cell-molecular based evolutionary model of tumor development driven by a stochastic Moran birth-death process is developed, where each cell carries molecular information represented by a four-digit binary string, used to differentiate…
In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov processes including diffusion and jumps. We consider the three…
Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by…
We consider a continuous time Markov process on $\mathbb{N}_0$ which can be interpreted as generalized alternating birth-death process in a non-autonomous random environment. Depending on the status of the environment the process either…
We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…
An agent-based computer simulation of death by inheritable mutations in a changing environment shows a maximal population, or avoids extinction, at so intermediate mutation rate of the individuals. Thus death seems needed to al for…
We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an…
An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the…
The asymptotic behavior, as $n\rightarrow \infty $ of the conditional distribution of the number of particles in a decomposable critical branching process $\mathbf{Z}% (m)=(Z_{1}(m),...,Z_{N}(m)),$ with $N$ types of particles at moment…
Quantitative assessment of extinction risk requires confidence intervals (CIs) that remain informative with limited data. Their usefulness has long been debated because short observation spans can make uncertainty so large that population…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We consider a stochastic model for an evolving population. We show that in the presence of genotype extinctions the population dies out for a low mutation probability but may survive for a high mutation probability. This turns upside down…
We develop a stochastic framework for viral population dynamics at the cellular level that explicitly incorporates the replication cycle with random stage durations. The model is formulated as a structured birth-death process coupled with a…
Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,\infty)$.…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the…