Related papers: Fixation and stationary times for the $\Lambda$-Wr…
We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…
In stochastic evolutionary dynamics, the replacement of an existing genotype or cultural trait by a newly introduced mutant is typically characterized by the quantities of fixation probability and fixation time. But in a structured…
In this thesis we study properties of open quantum dissipative evolutions of spin systems on lattices described by Lindblad generators, in a particular regime that we denote rapid mixing. We consider dissipative evolutions with a unique…
Consider a two-type Moran population of size $N$ with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to $N$,…
Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). However, these measures - corresponding to specific displacement…
We introduce a delay nonlinear differential equation model which describes how fish are harvested. In our previous studies we investigated the persistence of that equation and existence of a periodic solution for this equation. Here we…
Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding…
We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…
We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…
In this paper, we prove a fluctuation theorem for the occupation time of the multi-species stirring process on a lattice starting from a stationary distribution. Our result shows that the occupation times of different species interact with…
Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…
We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation…
We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the…
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…
Background: The accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist. Muller's ratchet provides a quantitative framework to study the effect of accumulation.…
We discuss properties of the $\epsilon$-expansion in $d=4-\epsilon$ dimensions. Using Lagrange inversion we write down an exact expression for the value of the Wilson-Fisher fixed point coupling order by order in $\epsilon$ in terms of the…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…