Related papers: Error Thresholds in Presence of Epistatic Interact…
A deterministic mutation-selection model in the sequence space approach is investigated. Genotypes are identified with two-letter sequences. Mutation is modelled as a Markov process, fitness functions are of Hopfield type, where the fitness…
Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are classically governed by mutation rates and fitness landscapes,…
Muller's ratchet is a paradigmatic model for the accumulation of deleterious mutations in a population of finite size. A click of the ratchet occurs when all individuals with the least number of deleterious mutations are lost irreversibly…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
In this paper we investigate error-thresholds on dynamics fitness-landscapes. We show that there exists both lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed…
We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain…
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…
Motivated by present activities in (statistical) physics directed towards biological evolution, we review the interplay of three evolutionary forces: mutation, selection, and genetic drift. The review addresses itself to physicists and…
We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet of…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
This paper develops an analytically tractable model for determining the equilibrium distribution of mismatch repair deficient strains in unicellular populations. The approach is based on the single fitness peak (SFP) model, which has been…
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…
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,…
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 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…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…
In evolution, the effects of a single deleterious mutation can sometimes be compensated for by a second mutation which recovers the original phenotype. Such epistatic interactions have implications for the structure of genome space -…
Biochemical and regulatory interactions central to biological networks are expected to cause extensive genetic interactions or epistasis affecting the heritability of complex traits and the distribution of genotypes in populations. However,…
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…
A foundational assumption in complex-system collapse studies is that critical transitions are second-order, preceded by early-warning signals like rising autocorrelation, variance, and critical slowing down (Scheffer, 2009). We show this…