相关论文: Error threshold in simple landscapes

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…

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…

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…

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 introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic…

We study the simple genetic algorithm with a ranking selection mechanism (linear ranking or tournament). We denote by $\ell$ the length of the chromosomes, by $m$ the population size, by $p_C$ the crossover probability and by $p_M$ the…

We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories…

RNA viruses are known to replicate with extremely high mutation rates. These rates are actually close to the so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a…

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…

We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…

We study sharp peak landscapes (SPL) of Eigen model from a new perspective about how the quasispecies distribute in the sequence space. To analyze the distribution more carefully, we bring forth two tools. One tool is the variance of…

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 Letter, we extend the semiconservative quasispecies equations to incorporate imperfect DNA lesion repair. We study the equilibrium behavior of this model in the limit of infinite sequence length and population size, using a…

In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other…

This paper extends Eigen's quasispecies equations to account for the semiconservative nature of DNA replication. We solve the equations in the limit of infinite sequence length for the simplest case of a static, sharply peaked fitness…

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…

We introduce a model of molecular evolution in which the fitness of an individual depends both on its own and on the parent's genotype. The model can be solved by means of a nonlinear mapping onto the standard quasispecies model. The…

We discuss the zero-temperature susceptibility of elastic manifolds with quenched randomness. It diverges with system size due to low-lying local minima. The distribution of energy gaps is deduced to be constant in the limit of vanishing…

Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…

In this note we formulate a finite dimensional generalization of the Random Energy Model (REM) where we introduce a geometry and spatial correlations between energies. We study the model in dimension one by transfer matrix techniques and we…