Related papers: Invasion by rare mutants in a spatial two-type Fis…
In this article, we investigate the long-term dynamics of a class of two- and three-dimensional non-Newtonian fluids of differential type, known as third-grade fluids. We first show that when the external forcing is sufficiently small, the…
Evolutionary game theory has proved to be a powerful tool to probe the self-organisation of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not…
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just…
The Fleming-Viot process with parent-independent mutation process is one particular neutral population genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high,…
Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying…
We study the ABC model in the cyclic competition and neutral drift versions, with mutations and migrations introduced into the model. When stochastic phenomena are taken into account, there are three distinct regimes in the model. (i) In…
Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in $\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either a standard Poisson…
We study the low-energy physics of a broad class of time-reversal invariant and SU(2)-symmetric one-dimensional spin-S systems in the presence of quenched disorder via a strong-disorder renormalization-group technique. We show that, in…
We examine a two-dimensional system of sterically repulsive interacting disks where each particle runs in a random direction. This system is equivalent to a run-and-tumble dynamics system in the limit where the run time is infinite. At low…
We study the evolution of gene frequencies in a population living in $\mathbb{R}^d$, modelled by the spatial Lambda Fleming-Viot process with natural selection (Barton, Etheridge and Veber, 2010 and Etheridge, Veber and Yu, 2014). We…
Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified…
The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation…
A collection of $N$-diffusing interacting particles where each particle belongs to one of $K$ different populations is considered. Evolution equation for a particle from population $k$ depends on the $K$ empirical measures of particle…
We prove exponential concentration estimates and a strong law of large numbers for a particle system that is the simplest representative of a general class of models for 2D grain boundary coarsening. The system consists of $n$ particles in…
We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…
We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
The competition between scrambling and projective measurements can lead to measurement-induced entanglement phase transitions (MIPT). In this work, we show that the universality class of the MIPT is drastically altered when the system is…
We investigate the evolution of a system of two super-Earths with masses < 4 Earth masses embedded in a turbulent protoplanetary disk. The aim is to examine whether or not resonant trapping can occur and be maintained in presence of…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…