author={Steven N. Evans and David Steinsaltz},
  journal={Annals of Applied Probability},
Kauffman and Levin introduced a class of models for the evolution of hereditary systems which they called NK fitness landscapes. Inspired by spinglasses, these models have the attractive feature of being tunable, with regard to both overall size (through the parameter N) and connectivity (through K). There are N genes, each of which exists in two possible alleles [leading to a system indexed by {0, 1} N ]; the fitness score of an allele at a given site is determined by the alleles of K… 

Universality Classes of Interaction Structures for NK Fitness Landscapes

A unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L is developed, and two different universality classes of interaction structures that display different asymptotics of this quantity for large k are identified.

Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

This paper studies the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined and finds that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern.

Evolutionary Accessibility of Modular Fitness Landscapes

The block model can be viewed as a special case of Kauffman’s NK-model, and it is shown that the number of accessible paths can be written as a product of the path numbers within the blocks, which provides a detailed analytic description of the paths statistics.

Evolutionary Accessibility in Tunably Rugged Fitness Landscapes

Some measures of accessibility behave non-monotonically as a function of K, indicating a special role of the most sparsely connected, non-trivial cases K=1 and 2, and the relation between models for fitness landscapes and spin glasses is addressed.

Properties of Random Fitness Landscapes and Their Influence on Evolutionary Dynamics. A Journey through the Hypercube

The individual-based Wright-Fisher model is used to study recombination of genotypes, interactions between individuals and the influence of the underlying fitness landscape on these mechanisms.

Adaptation in Tunably Rugged Fitness Landscapes: The Rough Mount Fuji Model

A simple fitness landscape model with tunable ruggedness based on the rough Mount Fuji (RMF) model originally introduced by Aita et al. in the context of protein evolution is proposed and compared to the known behavior in the MLM model.

Statistical topography of fitness landscapes

Fitness landscapes are generalized energy landscapes that play an important conceptual role in evolutionary biology. These landscapes provide a relation between the genetic configuration of an

Fitness Landscapes, Adaptation and Sex on the Hypercube

In this thesis, several models of fitness landscapes are analyzed with different analytical and numerical methods to identify characteristics in order to compare the model landscapes to experimental measurements.

Maximally rugged NK landscapes contain the highest peaks

It is shown that the global optimum behaves quite differently: the expected value of the global maximum is highest in the maximally rugged case, and it is demonstrated that this expected value increases with K, despite the fact that the average fitness of the local optima decreases.



Towards a general theory of adaptive walks on rugged landscapes.

Rigorous results for the N K model

Motivated by the problem of the evolution of DNA sequences, Kauffman and Levin introduced a model in which fitnesses were assigned to strings of 0's and 1's of length N based on the values observed


Motivated by the problem of the evolution of DNA sequences, Kauffman and Levin introduced a model in which fitnesses were assigned to strings of 0’s and 1’s of length N based on the values observed in

Size effects in Kauffman type evolution for rugged fitness landscapes.

Random noise (simulated annealing) is shown to increase appreciably the fitness in an NK fitness model of evolution and coevolution.

Understanding and attenuating the complexity catastrophe in Kauffman'sN K model of genome evolution

Analysis and simulations are used to establish the idea that relaxing any one of these assumptions results in a new model in which the complexity catastrophe is attenuated, and good performance from systems having high levels of interactions is possible.

Probability Measures on Semigroups: Convolution Products, Random Walks and Random Matrices

This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their

Some Random Series of Functions

1. A few tools from probability theory 2. Random series in a Banach space 3. Random series in a Hilbert space 4. Random Taylor series 5. Random Fourier series 6. A bound for random trigonometric

Ergodic Theory of Stochastic Petri Networks

This paper determines the conditions under which the existence of this regime is guaranteed and makes use of an associated stochastic recursive equation in order to construct its stationary and ergodic regime.

Local properties of Kauffman's N-k model: A tunably rugged energy landscape.

  • Weinberger
  • Physics, Medicine
    Physical review. A, Atomic, molecular, and optical physics
  • 1991