Related papers: Common ancestor type distribution: a Moran model a…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…
Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population…
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…
We interpret the Moran model of natural selection and drift as an algorithm for learning features of a simplified fitness landscape, specifically genotype superiority. This algorithm's efficiency in extracting these characteristics is…
We consider the classic Moran process modeling the spread of genetic mutations, as extended to structured populations by Lieberman et al.\ (Nature, 2005). In this process, individuals are the vertices of a connected graph $G$. Initially,…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
We consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312--316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised…
This paper gives a new flavor of what Peter Jagers and his co-authors call `the path to extinction'. In a neutral population with constant size $N$, we assume that each individual at time $0$ carries a distinct type, or allele. We consider…
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
We build a general framework which establishes a one-to-one correspondence between species abundance distribution (SAD) and species accumulation curve (SAC). The appearance rates of the species and the appearance times of individuals of…
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…
For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as…
We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type…
We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal…
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…