Related papers: Mutation, selection, and ancestry in branching mod…
We consider a multi-type Moran model (in continuous time) with selection and type-dependent mutation. This paper is concerned with the evolution of genealogical information forward in time. For this purpose we define and analytically…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral…
We model evolution according to an asymmetric game as occurring in multiple finite populations, one for each role in the game, and study the effect of subjecting individuals to stochastic strategy mutations. We show that, when these…
A stochastic model for the evolution of a growing population is proposed, in order to explain empirical power-law distributions in the frequency of family names as a function of the family size. Preliminary results show that the predicted…
One of the fundamental questions in population dynamics is how biological populations respond to environmental perturbations. In population dynamics, the mean fitness and the fraction of a trait in the steady state are important because…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of 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…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…