Related papers: Open Quasispecies Models: Stability, Optimization,…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…
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…
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…
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…
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 show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold,…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…
We consider an asexual population evolving on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local optima. We track the most populated genotype as it changes when the population jumps from…
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…
A quasispecies evolving on a fitness landscape with a single peak of fluctuating height is studied. In the approximation that back mutations can be ignored, the rate equations can be solved analytically. It is shown that the error threshold…
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…
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. We give several explicit formulas for the stationary solutions of the limiting system of…
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…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
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…
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…
We investigate the evolutionary dynamics of a finite population of RNA sequences adapting to a neutral fitness landscape. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive…