Adaptation in simple and complex fitness landscapes

  title={Adaptation in simple and complex fitness landscapes},
  author={Kavita Jain and Joachim H A Krug},
  journal={arXiv: Populations and Evolution},
  • K. Jain, J. Krug
  • Published 5 August 2005
  • Biology
  • arXiv: Populations and Evolution
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different types of mutation-selection dynamics are defined and their relation to problems of statistical physics are outlined. Then the stationary population distribution in simple, single peak fitness landscapes is discussed at length, with particular emphasis on the… 

Adaptation dynamics of the quasispecies model

This work focuses on the Eigen’s model that describes the deterministic dynamics of an infinite number of self-replicating molecules and calculates exactly several properties of this dynamical process within a simplified version of the quasispecies model.

Quasispecies on Fitness Landscapes.

  • P. Schuster
  • Environmental Science
    Current topics in microbiology and immunology
  • 2016
Selection-mutation dynamics is studied as adaptation and neutral drift on abstract fitness landscapes as well as the role of fitness neutral genotypes in quasispecies.

Deterministic and Stochastic Regimes of Asexual Evolution on Rugged Fitness Landscapes

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.

Evolutionary dynamics on strongly correlated fitness landscapes.

  • S. SeetharamanK. Jain
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
The dynamical properties such as the number of jumps in the most populated sequence and the temporal distribution of the last jump are calculated, which are shown to exhibit an inverse square dependence as in evolution on uncorrelated fitness landscapes.


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.

Robustness and epistasis in mutation-selection models.

In addition, the occurrence of an error threshold for a general class of epistatic landscapes is investigated and it is shown that diminishing epistasis is a necessary but not sufficient condition for error threshold behaviour.

Emergence of species in evolutionary “simulated annealing”

This study shows that the fitness landscape of a biophysically realistic system is extremely complex, with huge number of local peaks rendering adaptation dynamics to be a glass-like process.

Evolution in random fitness landscapes: the infinite sites model

The evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size is considered, which implies that each mutation generates a new fitness value drawn from a probability distribution g(w) which lead to an indefinite growth of the population fitness.

The Speed of Evolution in Large Asexual Populations

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.

Effects of recombination on the evolvability, genetic diversity and mutational robustness of neutrally evolving populations

This study focuses on finite populations evolving on neutral networks, and concludes that conflicting trends induced by recombination can be explained by an emerging trade-off between evolvability and genetic diversity on the one hand, and mutational robustness and fitness on the other.



Error Thresholds on Correlated Fitness Landscapes

Abstract The evolution of molecular quasispecies on two different complex fitness landscapes, the Sherrington Kirkpatrick spin glass and the Graph Bipartitioning landscape, is investigated in

Quasispecies evolution in general mean-field landscapes

It is shown that the stationary trait distribution in a class of fitness landscapes can be explicitly evaluated in a suitably defined “thermodynamic limit”, which is a combination of infinite-genome and strong selection limits.

Biological evolution and statistical physics

This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists, and includes Fisher's theorem, adaptive walks, quasispecies models, effects of finite population sizes, and neutral evolution.

Genealogical process on a correlated fitness landscape.

We study with extensive numerical simulation the genealogical process of 2N haploid genetic sequences. The sequences are under selective pressure, and fitness values are assigned at random, but with

Tempo and mode in quasispecies evolution

The case of strong selection is considered, which is analogous to the zero temperature limit in the equivalent problem of directed polymers in random media, and the statistical properties of the evolutionary trajectory which σ*(t) traces out in sequence space are studied.

Population evolution on a multiplicative single-peak fitness landscape.

An approximate theory for the way the evolution of population in a fitness landscape with a single fitness peak depends on N, L, s, and the mutation rate u is given, found to agree well with numerical simulation.

Evolutionary trajectories in rugged fitness landscapes

This work proposes a simple relation between the bypassing probability and the dynamic exponent which describes the scaling of the typical evolution time with genome size and finds that the fit genotypes that appear along a trajectory are a subset of suitably defined fitness records.