Related papers: Asymptotic behavior of Eigen's quasispecies model
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. We give several explicit formulas for the stationary solutions of the limiting system of…
We prove that a Moran model converges in probability to Eigen's quasispecies model in the infinite population limit.
Biological evolution in a sequence space with random fitnesses is studied within Eigen's quasispecies model. A strong selection limit is employed, in which the population resides at a single sequence at all times. Evolutionary trajectories…
In this paper, we study the equilibrium behavior of Eigen's quasispecies equations for an arbitrary gene network. We consider a genome consisting of $ N $ genes, so that each gene sequence $ \sigma $ may be written as $ \sigma = \sigma_1…
Evolutionary dynamics in an uncorrelated rugged fitness landscape is studied in the framework of Eigen's molecular quasispecies model. We consider the case of strong selection, which is analogous to the zero temperature limit in 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…
We reconsider the Eigen's quasi-species model for competing self-reproductive macromolecules in populations characterized by a single-peaked fitness landscape. The use of ideas and tools borrowed from polymers theory and statistical…
Eigen's quasispecies system with explicit space and global regulation is considered. Limit behavior and stability of the system in a functional space under perturbations of a diffusion matrix with nonnegative spectrum are investigated. It…
A population genetics formulation of Eigen's molecular quasispecies model is proposed and several simple replication landscapes are investigated analytically. Our results show a remarcable similarity to those obtained with the original…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of $C_0$-semigroups to obtain a…
A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called single or sharply peaked landscape. A general, non permutation…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic…
We introduce a toy model for interacting populations connected by mutations and limited by a shared resource. We study the presence of Eigen's error threshold and mutational meltdown. The phase diagram of the system shows that the…
Recombination is introduced into Eigen's theory of quasispecies evolution. Comparing numerical simulations of the rate equations in the non-recombining and recombining cases show that recombination has a strong effect on the error threshold…
We investigate Eigen's model for the evolution of the genetic code of microorganisms using a novel method based on population dynamics analysis. This model, for a given number of offspring, determines long-term survival as a function of the…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…
In this paper, we investigate the convergence of asymptotic systems in non-autonomous Cohen--Grossberg neural network models, which include both infinite discrete time-varying and distributed delays. We derive stability results under…
Using methods of statistical physics, we present rigorous theoretical calculations of Eigen's quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of a reproducing quasispecies.…