Related papers: $\Lambda$-Seed-Bank-Wright-Fisher process conditio…
We study the fixation and stationary behavior of the Lambda-Wright-Fisher process with parent-independent mutation and finitely many types, a jump-diffusion model for allele frequency dynamics in large populations with potentially large…
The purpose of this article is to study some asymptotic properties of the \Lambda-Wright-Fisher process with selection. This process represents the frequency of a disadvantaged allele. The resampling mechanism is governed by a finite…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
Our results characterize the long-term behavior for a broad class of $\Lambda$-Wright--Fisher processes with frequency-dependent and environmental selection. In particular, we reveal a rich variety of parameter-dependent behaviors and…
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…
We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample…
Seed banks are a common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the…
We construct extensions of the pure-jump $\Lambda$-Wright-Fisher processes with frequency-dependent selection ($\Lambda$-WF processes with selection) beyond their first passage time at the boundary $1$. We show that they satisfy some…
Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…
We identify a new natural coalescent structure, which we call the seed-bank coalescent, that describes the gene genealogy of populations under the influence of a strong seed-bank effect, where "dormant forms" of individuals (such as seeds…
We introduce a new Wright-Fisher type model for seed banks incorporating "simultaneous switching", which is motivated by recent work on microbial dormancy. We show that the simultaneous switching mechanism leads to a new jump-diffusion…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
We consider two population models subject to the evolutionary forces of selection and mutation, the Moran model and the $\Lambda$-Wright-Fisher model. In such models the block counting process traces back the number of potential ancestors…
When two (possibly different in distribution) continuous-state branching processes with immigration are present, we study the relative frequency of one of them when the total mass is forced to be constant at a dense set of times. This leads…
Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models; a well known example is the duality between the…
$\Lambda$-Wright--Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate…
This work is a systematic study of discrete Markov chains that are used to describe the evolution of a two-types population. Motivated by results valid for the well-known Moran (M) and Wright-Fisher (WF) processes, we define a general class…
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…