Related papers: Punctuated evolution for the quasispecies model
Eigen's quasi-species model describes viruses as ensembles of different mutants of a high fitness "master" genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When…
The quasispecies model of biological evolution for asexual organisms such as bacteria and viruses has attracted considerable attention of biological physicists. Many variants of the model have been proposed and subsequently solved using the…
We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution…
We study Eigen's model of quasi-species, characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum…
We present stochastic, finite-population formulations of the Crow-Kimura and Eigen models of quasispecies theory, for fitness functions that depend in an arbitrary way on the number of mutations from the wild type. We include back mutations…
The quasispecies theory is studied for dynamic replication landscapes. A meaningful asymptotic quasispecies is defined for periodic time dependencies. The quasispecies' composition is constantly changing over the oscillation period. The…
In this research, we present a generalized quasispecies model in which population growth is governed by an arbitrary nonlinear function incorporating time delays. We begin by demonstrating that, under the constant population constraint, the…
We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to infinity and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove the…
The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generalizing this observation we introduce an abstract quasispecies…
A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The…
The quasi-species equation describes the evolution of the probability that a random individual in a population carries a given genome. Here we map the quasi-species equation for individuals of a self-reproducing population to an ensemble of…
We examine a model of biological evolution of Eigen's quasispecies in a holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). So, the evolution dynamics is determined by…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
We review the major progress in the rigorous analysis of the classical quasispecies model that usually comes in two related but different forms: the Eigen model and the Crow--Kimura model. The model itself was formulated almost 50 years…
Several pathogens use evolvability as a survival strategy against acquired immunity of the host. Despite their high variability in time, some of them exhibit quite low variability within the population at any given time, a somehow…
We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are…
A quasispecies is a set of interrelated genotypes that have reached a situation of equilibrium while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to…