# Correlated and uncorrelated fitness landscapes and how to tell the difference

@article{Weinberger2004CorrelatedAU, title={Correlated and uncorrelated fitness landscapes and how to tell the difference}, author={Edward D. Weinberger}, journal={Biological Cybernetics}, year={2004}, volume={63}, pages={325-336} }

The properties of multi-peaked “fitness landscapes” have attracted attention in a wide variety of fields, including evolutionary biology. However, relaively little attention has been paid to the properties of the landscapes themselves. Herein, we suggest a framework for the mathematical treatment of such landscapes, including an explicit mathematical model. A central role in this discussion is played by the autocorrelation of fitnesses obtained from a random walk on the landscape. Our ideas… Expand

#### 484 Citations

Statistical topography of fitness landscapes

- Geography
- 2011

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… Expand

Fourier and Taylor series on fitness landscapes

- Mathematics, Computer Science
- Biological Cybernetics
- 2004

It is shown that an analogue of the KarhunenLoève expansion can be used to prove that the Fourier coefficients of landscapes on commutative groups are uncorrelated and to infer their variance from the autocorrelation function of a random walk on the landscape. Expand

Long-term evolution on complex fitness landscapes when mutation is weak

- Biology, Medicine
- Heredity
- 2018

An integrated suite of mathematical tools for understanding evolution on time-invariant fitness landscapes when mutations occur sufficiently rarely that the population is typically monomorphic and evolution can be modeled as a sequence of well-separated fixation events are presented. Expand

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

- Biology, Medicine
- Genetics
- 2014

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. Expand

Smoothness, ruggedness and neutrality of fitness landscapes: from theory to application

- Mathematics
- 2003

The theory of fitness landscapes has been developed to provide a suitable mathematical framework for studying the evolvability of a variety of complex systems. In evolutionary computation the notion… Expand

Evolutionary Accessibility in Tunably Rugged Fitness Landscapes

- Mathematics, Biology
- 2012

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. Expand

A gaussian random field model of smooth fitness landscapes

- Mathematics, Computer Science
- FOGA '09
- 2009

It is shown experimentally that traditional search algorithms with search operators based on this space reach better performance on smoother fitness landscapes, showing that the formalized notion of smoothness captures the important heuristic property of its informal counterpart. Expand

The effect of phenotypic plasticity on evolution in multipeaked fitness landscapes

- Biology, Medicine
- Journal of evolutionary biology
- 2006

It is shown that the convergence rate of the evolutionary process in a given arbitrary one‐dimensional fitness landscape is dominated by the largest descent (drawdown) in the landscape and numerical evidence is provided to support an analogous dominance also in multidimensional landscapes. Expand

Where are bottlenecks in NK fitness landscapes?

- Computer Science
- The 2003 Congress on Evolutionary Computation, 2003. CEC '03.
- 2003

This paper uses the bottleneck metaphor to emphasis fitness levels in landscape that cause local search process to slow down, and shows where the bottlenecks are in the well-known NK fitness landscape. Expand

Artificial Evolution

- Computer Science
- Lecture Notes in Computer Science
- 2003

This work proposes a family of tunable fitness landscapes based on VLR of genotypes that possess a tunable degree of both neutrality and epistasis, and evaluates the performances of evolutionary algorithms on these landscapes for various values of the neutral and the epistatic parameters. Expand

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