Related papers: Lookdown construction for a Moran seed-bank model
The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta…
We present an elementary model of random size varying population given by a stationary continuous state branching process. For this model we compute the joint distribution of: the time to the most recent common ancestor, the size of the…
Evolutionary dynamics on graphs can lead to many interesting and counterintuitive findings. We study the Moran process, a discrete time birth-death process, that describes the invasion of a mutant type into a population of wild-type…
The Moran process, as studied by [Lieberman, E., Hauert, C. and Nowak, M. Evolutionary dynamics on graphs. Nature 433, pp. 312-316 (2005)], is a stochastic process modeling the spread of genetic mutations in populations. In this process,…
We consider the spatially inhomogeneous Moran model with seed-banks introduced in den Hollander and Nandan (2021). Populations comprising $active$ and $dormant$ individuals are structured in colonies labelled by $\mathbb{Z}^d,~d\geq 1$. The…
We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations…
We consider a spatial version of the classical Moran model with seed-banks where the constituent populations have finite sizes. Individuals live in colonies labelled by $\mathbb{Z}^d$, $d\geq 1$, playing the role of a geographic space,…
In this paper we propose a Moran model that describes the population dynamics of two types: While the first type has a selective advantage during reproduction, the second type can avoid replacement during reproduction with some positive…
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of…
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age"…
We consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are $active$. Each colony has a seed-bank into which individuals can retreat to…
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…
We study the fixation probability for two versions of the Moran process on the random graph $G_{n,p}$ at the threshold for connectivity. The Moran process models the spread of a mutant population in a network. Throughtout the process there…
We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider…
The Moran process is a classic stochastic process that models the rise and takeover of novel traits in network-structured populations. In biological terms, a set of mutants, each with fitness $m\in(0,\infty)$ invade a population of…
Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random…
The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in…
The Moran process is a classic stochastic process that models invasion dynamics on graphs. A single "mutant" (e.g., a new opinion, strain, social trait etc.) invades a population of residents spread over the nodes of a graph. The mutant…
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…
Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birth and for death. If the same type is chosen for both steps,…