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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35 Citations
Highly Influential Citations
1
Background Citations
18
Methods Citations
2
Results Citations
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35 Citations

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An exact solution of the infinite population size limit is presented and an estimate of the population size beyond which it is valid is provided.
The dynamics of adaptation on correlated fitness landscapes
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A theory that predicts how a population's mean fitness and the number of accumulated substitutions are expected to increase over time, depending on the underlying fitness landscape is developed and it is shown that linear substitution trajectories, long considered the hallmark of neutral evolution, can arise even when mutations are strongly selected.
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TLDR
This study indicates that an advantage for small populations is likely whenever the fitness landscape contains local maxima, which appears at intermediate time scales, which are long enough for trapping at local fitness maxima to have occurred but too short for peak escape by the creation of multiple mutants.
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TLDR
This work performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects.
The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis
TLDR
This work finds that the change in the form of fitness trajectory arises only through changes in the supply of beneficial mutations, and suggests that by carrying out evolution experiments in both regimes, one could potentially distinguish the different sources of macroscopic epistasis.
Speed of evolution in large asexual populations with diminishing returns.
Mathematical Models of Evolution for Replicator Systems: Fitness Landscape Adaptation
TLDR
The adaptive landscape metaphor by S. Wright and Fisher's fundamental theorem of natural selection is expanded, combining it with Kimura’s maximal principals to the case of dynamical fitness landscape and is reduced to a series mathematical programming problems or to a first eigenvalue maximization problem.
Inferring fitness landscapes by regression produces biased estimates of epistasis
TLDR
This work critically examine regression techniques used to approximate fitness landscapes from data, finding that such regressions are subject to two inherent biases that distort the biological quantities of greatest interest, often making evolution seem less predictable than it actually is.
Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect
TLDR
A detailed analysis of the Fisher–Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative fitness effects shows that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals.
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