# The Wright–Fisher model for class–dependent fitness landscapes

@article{Dalmau2017TheWM, title={The Wright–Fisher model for class–dependent fitness landscapes}, author={Joseba Dalmau}, journal={Electronic Journal of Probability}, year={2017} }

We consider a population evolving under mutation and selection. The genotype of an individual is a word of length $\ell$ over a finite alphabet. Mutations occur during reproduction, independently on each locus; the fitness depends on the Hamming class (the distance to a reference sequence $w^*$). Evolution is driven according to the classical Wright--Fisher process. We focus on the proportion of the different classes under the invariant measure of the process. We consider the regime where the…

## References

SHOWING 1-10 OF 13 REFERENCES

### Critical population and error threshold on the sharp peak landscape for a Moran model

- Computer Science
- 2012

A finite population counterpart to Eigen's model, which incorporates stochastic effects, is proposed and the existence of a critical population size necessary for a quasispecies to emerge is observed.

### Critical population and error threshold on the sharp peak landscape for the Wright–Fisher model

- Computer Science
- 2015

The result is the twin brother of the corresponding result for the Moran model, and it relies on the Freidlin-Wentzell theory of random perturbations of dynamical systems.

### The distribution of the quasispecies for the Wright–Fisher model on the sharp peak landscape

- Environmental Science
- 2014

### Quasispecies on Class-Dependent Fitness Landscapes

- MathematicsBulletin of mathematical biology
- 2016

Eigen’s quasispecies model in the asymptotic regime where the length of the genotypes goes to ∞ and the mutation probability goes to 0 is studied.

### Asymptotic Behavior of Eigen’s Quasispecies Model

- MathematicsBulletin of mathematical biology
- 2018

It is proved convergence of trajectories, as well as convergence of the equilibrium solutions, for a discrete-time version of Eigen’s model, which coincides with a model proposed by Moran.

### Selforganization of matter and the evolution of biological macromolecules

- BiologyNaturwissenschaften
- 2004

The causes and effect of cause and effect, and the prerequisites of Selforganization, are explained in more detail in the I.IA.

### Random Perturbations of Dynamical Systems

- Mathematics, Physics
- 1984

1.Random Perturbations.- 2.Small Random Perturbations on a Finite Time Interval.- 3.Action Functional.- 4.Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point.-…

### The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle.

- BiologyDie Naturwissenschaften
- 1977

An analysis of experimental data regarding RNA and D N A replication reveals that a sufficient amount of information for the build up of a translation machinery can be gained only via integration of several different replicative units (or reproductive cycles) throughfimctional linkages.

### Extremely High Mutation Rate of a Hammerhead Viroid

- BiologyScience
- 2009

The results suggest that the emergence of replication fidelity was critical for the evolution of complexity in the early history of life, and the highest mutation rate reported for any biological entity is suggested.