Evolution in random fitness landscapes: the infinite sites model

@article{Park2008EvolutionIR,
  title={Evolution in random fitness landscapes: the infinite sites model},
  author={Su-Chan Park and Joachim H A Krug},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2008},
  volume={2008},
  pages={P04014}
}
  • Su-Chan Park, J. Krug
  • Published 13 November 2007
  • Mathematics
  • Journal of Statistical Mechanics: Theory and Experiment
We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability distribution g(w). This is the finite population version of Kingman’s house of cards model (Kingman 1978 J. Appl. Probab. 15 1). In contrast to Kingman’s work, the focus here is on unbounded distributions g(w) which lead to an indefinite growth of the population… 
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References

SHOWING 1-10 OF 62 REFERENCES
Evolutionary dynamics of the most populated genotype on rugged fitness landscapes.
  • K. Jain
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
TLDR
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
TLDR
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.
Breaking records in the evolutionary race
A study on a nearly neutral mutation model in finite populations.
TLDR
As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations and it is found that deviation from the neutral expectation becomes apparent only when 4N sigma is more than two.
EVOLUTION AND EXTINCTION DYNAMICS IN RUGGED FITNESS LANDSCAPES
TLDR
The "reset" model and its (in part analytically soluble) mean field version are described and the predictions for various quantities of paleontological interest are robust and in good agreement with available data.
Adaptation in simple and complex fitness landscapes
TLDR
The stationary population distribution in simple, single peak fitness landscapes is discussed at length, with particular emphasis on the error threshold phenomenon.
Clonal interference in large populations
TLDR
It is shown that the nature of the substitution process changes qualitatively when multiple mutations are allowed for, because several mutations can be fixed in a single fixation event, and the index of dispersion for counts of the fixation process displays a minimum as a function of population size.
Towards a general theory of adaptive walks on rugged landscapes.
Punctuated evolution for the quasispecies model
Substitution processes in molecular evolution. III. Deleterious alleles.
TLDR
It is argued that there are no biologically reasonable models of molecular evolution where the vast majority of all substitutions are deleterious, and only the optimum and HDD models appear to be reasonable candidates for silent evolution.
...
...