By formalizing the relationship between genotype or phenotype and fitness, fitness landscapes harbor information on molecular and evolutionary constraints. The shape of the fitness landscape determines the potential for adaptation and speciation, as well as our ability to predict evolution. Consequently, fitness landscape theory has been invoked across the natural sciences and across multiple levels of biological organization. We review here the existing literature on fitness landscape theory by describing the main types of fitness landscape models, and highlight how these are increasingly integrated into an applicable statistical framework for the study of evolution. Specifically, we demonstrate how the interpretation of experimental studies with respect to fitness landscape models enables a direct link between evolution, molecular biology, and systems biology.

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Population size changes and selection drive patterns of parallel evolution in a host–virus system.

Repeatability of adaptation in experimental populations of different sizes.

Evaluating the impact of population bottlenecks in experimental evolution.

Population size dependence of fitness effect distribution and substitution rate probed by biophysical model of protein thermostability.

The impact of population size on the evolution of asexual microbes on smooth versus rugged fitness landscapes.

Some problems of stochastic processes in genetics.

Evolutionary meandering of intermolecular interactions along the drift barrier.

The fitness landscape of the codon space across environments.

Beyond the hypercube: evolutionary accessibility of fitness landscapes with realistic mutational networks.

On the existence of accessible paths in various models of fitness landscapes.

The peaks and geometry of fitness landscapes.

Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes.

The population genetics of adaptation: the adaptation of DNA sequences.

Length of adaptive walk on uncorrelated and correlated fitness landscapes.

A minimum on the mean number of steps taken in adaptive walks.

Understanding the evolution and stability of the G-matrix.

Epistasis and natural selection shape the mutational architecture of complex traits.

Fisher's geometrical model and the mutational patterns of antibiotic resistance across dose gradients.

Coadapted genomes and selection on hybrids: Fisher's geometric model explains a variety of empirical patterns.

The genetics of speciation: insights from Fisher's geometric model.

The role of hybridization in evolution.

Evolution of evolvability and phenotypic plasticity in virtual cells.

Evolution of new regulatory functions on biophysically realistic fitness landscapes.

The space of genotypes is a network of networks: implications for evolutionary and extinction dynamics.

From systems to structure: bridging networks and mechanism.

Phenotypic effect of mutations in evolving populations of RNA molecules.

Bridging the physical scales in evolutionary biology: from protein sequence space to fitness of organisms and populations.

How good are statistical models at approximating complex fitness landscapes?.

The structure of the genotype–phenotype map strongly constrains the evolution of non-coding RNA.

A comparison of genotype–phenotype maps for RNA and proteins.

Genotype–phenotype mapping and the end of the ‘genes as blueprint’ metaphor.

The genotype–phenotype relationships in the light of natural selection.

The arrival of the frequent: how bias in genotype–phenotype maps can steer populations to local optima.

From fitness landscapes to seascapes: non-equilibrium dynamics of selection and adaptation.

The Adaptive Seascape: The Mechanism of Evolution.

Prevalence of epistasis in the evolution of influenza A surface proteins.

Epistasis increases the rate of conditionally neutral substitution in an adapting population.

The NK model of rugged fitness landscapes and its application to maturation of the immune response.

Parallel genetic changes and nonparallel gene–environment interactions characterize the evolution of drug resistance in yeast.

Widespread genetic incompatibilities between first-step mutations during parallel adaptation of Saccharomyces cerevisiae to a common environment.

Characterizing the roles of changing population size and selection on the evolution of flux control in metabolic pathways.

Epistasis between beneficial mutations and the phenotype-to-fitness map for a ssDNA virus.

Properties of selected mutations and genotypic landscapes under Fisher's geometric model.

The evolution of epistasis and its links with genetic robustness, complexity and drift in a phenotypic model of adaptation.

Distributions of epistasis in microbes fit predictions from a fitness landscape model.

Stability-mediated epistasis constrains the evolution of an influenza protein.

Compensatory mutations cause excess of antagonistic epistasis in RNA secondary structure folding.

In search of the Goldilocks zone for hybrid speciation.

The limits to parapatric speciation: Dobzhansky–Muller incompatibilities in a continent–island model.

A genome-wide analysis reveals no nuclear Dobzhansky–Muller pairs of determinants of speciation between S. cerevisiae and S. paradoxus, but suggests more complex incompatibilities.

Genomics and the origin of species.

What do we need to know about speciation?.

The population genetics of speciation: the evolution of hybrid incompatibilities.

Studies on hybrid sterility. II. Localization of sterility factors in Drosophila pseudoobscura hybrids.

Epistasis – the essential role of gene interactions in the structure and evolution of genetic systems.

Biophysical models of protein evolution: understanding the patterns of evolutionary sequence divergence.

Fitness Landscapes and the Origin of Species.

Measuring epistasis in fitness landscapes: the correlation of fitness effects of mutations.

Epistasis and the structure of fitness landscapes: are experimental fitness landscapes compatible with Fisher's geometric model?.

Adaptation in protein fitness landscapes is facilitated by indirect paths.

On the (un)predictability of a large intragenic fitness landscape.

Mapping the fitness landscape of gene expression uncovers the cause of antagonism and sign epistasis between adaptive mutations.

Negative epistasis between beneficial mutations in an evolving bacterial population.

Darwinian evolution can follow only very few mutational paths to fitter proteins.

The utility of Fisher's geometric model in evolutionary genetics.

The end of the adaptive landscape metaphor?.

Empirical fitness landscapes and the predictability of evolution.

The genetic theory of adaptation: a brief history.

Proceedings of the Sixth International Congress of Genetics.

The roles of mutation, inbreeding, crossbreeding and selection in evolution.

Glossary

The set of elements (e.g., genes) necessary for the realization of a biological or ecological function, and the various relationships (e.g., activation, inhibition) that exist between the elements of the set.

Genetic background-specific (fitness) effect of a mutation.

The hypothetical population size of a Wright–Fisher population (panmictic and of constant size) that best reproduces the observed population genetics statistics.

The ability of a biological system (a population, individual, network, or molecule) to have or produce variants that can be acted upon by selection.

A measure of the reproductive or replicative success of a biological entity (from molecules to individuals). Usually, fitness-related phenotypes (e.g., growth rate) are used as proxies for fitness.

Random change in allele frequencies over time in a population of finite size.

The genetic constitution of an organism.

A map from (usually) discrete genotypes to fitness. Genotypes tend to represent nucleotide, amino acid, or gene differences.

A position in the genome of an individual. Depending on the focus of the study, a locus can correspond to a single nucleotide or amino acid position, several base pairs of DNA sequence, or a gene.

A heritable change in the genetic sequence of an individual.

A property of a mutation which harbors no fitness effect for an individual, such that its frequency in the population depends only on extraneous factors, such as genetic drift. A mutation is conditionally neutral if its neutrality is genetic-background or environment-dependent.

Mathematical model that describes a genotype–fitness landscape with different degrees of epistasis. This model is defined by the parameters N, the number of loci in the landscape, and K, the degree of epistasis between loci.

A set or subset of observable traits of an individual that stems from the interactions between genotype and environment.

A map from (usually) continuous phenotypes to fitness. In a multidimensional phenotype space, each dimension is composed by a different one-dimensional trait.

The property of a gene to affect more than one independent phenotypic trait.

A model describing a genotype–fitness landscape that is composed of an additive component and an epistasic component. Ruggedness is then tuned by changing the relative proportions of the two components.