Related papers: Understanding clustering in type space using field…
We consider a one-dimensional dyadic branching Brownian motion on $\mathbb{R}$ with positive drift $\beta \in (0,1)$, branching rate $1/2$, reflected at $0$ and killed at a boundary $L > 0$. The killing boundary $L$ is chosen so that the…
We introduce the following model for the evolution of a population. At every discrete time $j\geq 0$ exactly one individual is introduced in the population and is assigned a death probability $c_j$ sampled from $C$, a fixed probability…
We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits…
The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…
We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Prob. 39 (2002), 38-54) and Taylor…
A phylogenetic birth-and-death model is a probabilistic graphical model for a so-called phylogenetic profile, i.e., the size distribution for a homolog gene family at the terminal nodes of a phylogeny. Profile datasets are used in…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
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…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model…
The evolution of an infinite population of interacting point entities placed in $\mathbb{R}^d$ is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on $\mathbb{Z}$ with time varying and possible state-dependent…
Critical phase transitions have proven to be a powerful concept to capture the phenomenology of many systems, including deeply non-equilibrium ones like living systems. The study of these phase transitions has overwhelmingly relied on…
We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We mainly rely on two concepts, namely, the killed ancestral selection graph and the pruned…
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…