# Evolutionary trajectories in rugged fitness landscapes

@article{Jain2005EvolutionaryTI, title={Evolutionary trajectories in rugged fitness landscapes}, author={Kavita Jain and Joachim H A Krug}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2005}, volume={2005}, pages={P04008} }

We consider the evolutionary trajectories traced out by an infinite population undergoing mutation–selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the most populated genotype jumps from one local fitness maximum to another and eventually reaches the global maximum. We use a strong selection limit, which reduces the dynamics beyond the first time step to the competition between independent mutant…

## 38 Citations

Evolutionary dynamics of the most populated genotype on rugged fitness landscapes.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

It is shown that the population fraction of a genotype obtained within the quasispecies model and the shell model match for fit genotypes and at short times, but the dynamics of the two models are identical for questions related to the most populated genotype.

Deterministic and Stochastic Regimes of Asexual Evolution on Rugged Fitness Landscapes

- BiologyGenetics
- 2007

Whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance deff up to which the population can spread in genotype space, which is relevant to the interpretation of evolution experiments with microbial populations.

From adaptive dynamics to adaptive walks.

- MathematicsJournal of mathematical biology
- 2019

This work considers an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event, and modelled as a measure-valued Markov process.

A general multi-scale description of metastable adaptive motion across fitness valleys

- Mathematics
- 2021

This work develops the framework of a meta graph that is constituted of ESCs and possible metastable transitions between those, and proves the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

Adaptation in simple and complex fitness landscapes

- Biology
- 2005

The stationary population distribution in simple, single peak fitness landscapes is discussed at length, with particular emphasis on the error threshold phenomenon.

Adaptive walks and extreme value theory.

- BiologyPhysical review letters
- 2011

Assigning fitness randomly to genotypes, it is shown that the mean walk length is logarithmic in the number of initially available beneficial mutations, with a prefactor determined by the tail of the fitness distribution.

Predictability of evolution depends nonmonotonically on population size

- BiologyProceedings of the National Academy of Sciences
- 2012

An extensive computational study of evolutionary predictability based on an experimentally measured eight-locus fitness landscape for the filamentous fungus Aspergillus niger finds that these entropies display an initial decrease and a subsequent increase with population size N, governed by the scales Nμ and Nμ2.

Exact and limit distributions of the largest fitness on correlated fitness landscapes

- Mathematics
- 2009

Analytical calculations for the distribution of the maximum of a set of random fitnesses with a fixed number of mutations in a model of biological evolution find that the limit distribution for the maximum fitness is not of the standard Gumbel form.

Number of adaptive steps to a local fitness peak

- Biology
- 2011

A population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks is considered and it is found that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean.

Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape

- Mathematics
- 2006

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 behaviour can…

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