Related papers: A Multivariate Moran Process with Lotka-Volterra P…
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
Evolutionary game dynamics in finite populations provides a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call {\sigma} law,…
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,…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…
The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species towards rarity or abundance is crucial to assessing ecosystem resilience and…
Mutation and drift play opposite roles in genetics. While mutation creates diversity, drift can cause gene variants to disappear, especially when they are rare. In the absence of natural selection and migration, the balance between the…
A model of population genetics of the Lotka-Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace-Beltrami…
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into 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…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benam and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to…
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 study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
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 explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…
In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash…
Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…