Related papers: Fixation in Fluctuating Populations
The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
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 explore the voter model dynamics on a directed random graph model ensemble (digraphs), given by the Directed Configuration Model. The voter model captures the evolution of opinions over time on a graph where each vertex represents an…
We introduce the vacillating voter model in which each voter consults two neighbors to decide its state, and changes opinion if it disagrees with either neighbor. This irresolution leads to a global bias toward zero magnetization. In…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Inspired by the work of [Kempe, Kleinberg, Oren, Slivkins, EC13] we introduce and analyze a model on opinion formation; the update rule of our dynamics is a simplified version of that of Kempe et. al. We assume that the population is…
We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the…
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…
Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations and environmental variability therefore have a significant impact on the evolution of microbial populations. Here, we consider a class of…
In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexual adaptation such as the…
Recent experiments in adult mammalian tissues have found scaling relations of the voter model in the dynamics of the genetically labeled population of stem cells. Yet, the reason for this seemingly robust appearance of the voter model…
The spatial Lambda-Fleming-Viot (SLFV) process (Barton, Etheridge and V\'eber, 2010) can be seen as a generalised Voter Model with configuration space $M^{R^d}$, where M is the set of probability measures on some space K. Such processes are…
We investigate opinion dynamics in multi-agent networks when a bias toward one of two possible opinions exists; for example, reflecting a status quo vs a superior alternative. Starting with all agents sharing an initial opinion representing…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…
We study the performance of different methods for processing information, incorporating narrative selection within an evolutionary model. All agents update their beliefs according to Bayes' Rule, but some strategically choose the narrative…
Starting from the well-known field theory for directed percolation, we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…