Related papers: Random matrices and localization in the quasispeci…
We study a continuous-time nearest-neighbor branching random walk on the $d$-dimensional $b$-ary hypercube $\{0,1,\dots,b-1\}^d$ as a model for viral quasispecies evolution under mutation and replication. Motivated by mutagenic antiviral…
Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic…
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…
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 will study the relationship between two well-known theories, genetic evolution and random matrix theory in the context of many-body systems. It is suggested that genetic evolution can be described by a random matrix theory with…
The coexistence of different viral strains (quasispecies) within the same host are nowadays observed for a growing number of viruses, most notably HIV, Marburg and Ebola, but the conditions for the formation and survival of new strains have…
A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity. It is shown that the system is organized close to a boundary of marginal stability in…
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…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
The quasispecies model was introduced in 1971 by Manfred Eigen to discuss the first stages of life on Earth. It provides an appealing mathematical framework to study the evolution of populations in biology, for instance viruses. We present…
For taxonomic levels higher than species, the abundance distributions of number of subtaxa per taxon tend to approximate power laws, but often show strong deviationns from such a law. Previously, these deviations were attributed to…
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…
We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…
We consider the general properties of the quasispecies dynamical system from the standpoint of its evolution and stability. Vector field analysis as well as spectral properties of such system has been studied. Mathematical modelling of 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…
When mutations are rampant, quasispecies theory or Eigen's model predicts that the fittest type in a population may not dominate. Beyond a critical mutation rate, the population may even be delocalized completely from the peak of the…
Subcritical population processes are attracted to extinction and do not have non-trivial stationary distributions, which prompts the study of quasi-stationary distributions (QSDs) instead. In contrast to what generally happens for…
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,…
RNA viruses form genetically diverse populations structured as mutant spectra, or quasispecies, whose internal organization influences their evolutionary and adaptive dynamics. While genetic diversity has been extensively characterized, the…
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…