The structure of genotype-phenotype maps makes fitness landscapes navigable

ABSTRACT Fitness landscapes are often described in terms of ‘peaks’ and ‘valleys’, indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space

of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the

presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models—RNA secondary structure, protein tertiary structure

and protein complexes—we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn

indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also

likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution. Access through your

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EVOLVABILITY-ENHANCING MUTATIONS IN THE FITNESS LANDSCAPES OF AN RNA AND A PROTEIN Article Open access 19 June 2023 ROBUSTNESS AND INNOVATION IN SYNTHETIC GENOTYPE NETWORKS Article Open

access 28 April 2023 ENVIRONMENTAL SELECTION AND EPISTASIS IN AN EMPIRICAL PHENOTYPE–ENVIRONMENT–FITNESS LANDSCAPE Article 24 February 2022 DATA AVAILABILITY The dataset containing fRNA

(fRNAdb) used in this paper is available at: https://doi.org/10.18908/lsdba.nbdc00452-001. The GP maps analysed are available in the Code availability section. CODE AVAILABILITY The

ViennaRNA package (v.1.8.5), RNAshape package https://anaconda.org/bioconda/rnashapes and custom C++ and Python source code was used to construct GP maps and perform computational

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Central  Google Scholar  Download references ACKNOWLEDGEMENTS S.E.A. was supported by the Royal Society and the Gatsby Foundation. S.F.G. was supported by the Engineering and Physical

Sciences Research Council. We thank M. Weiß for helpful discussions and insights. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Theory of Condensed Matter Group, Cavendish Laboratory,

University of Cambridge, Cambridge, UK Sam F. Greenbury * The Alan Turing Institute, British Library, London, UK Sam F. Greenbury & Sebastian E. Ahnert * Rudolf Peierls Centre for

Theoretical Physics, University of Oxford, Oxford, UK Ard A. Louis * Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, UK Sebastian E. Ahnert Authors

* Sam F. Greenbury View author publications You can also search for this author inPubMed Google Scholar * Ard A. Louis View author publications You can also search for this author inPubMed 

Google Scholar * Sebastian E. Ahnert View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS S.F.G., A.A.L. and S.E.A. conceived and designed the

experiments. S.F.G. performed the experiments. S.F.G., A.A.L. and S.E.A. analysed the data. S.E.A. supervised the work. S.F.G., A.A.L. and S.E.A. wrote the paper. CORRESPONDING AUTHORS

Correspondence to Sam F. Greenbury, Ard A. Louis or Sebastian E. Ahnert. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. PEER REVIEW PEER REVIEW

INFORMATION _Nature Ecology & Evolution_ thanks Jacobo Aguirre and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. ADDITIONAL INFORMATION

PUBLISHER’S NOTE Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. EXTENDED DATA EXTENDED DATA FIG. 1 DEPICTION OF THE

DIFFERENT BIOLOGICAL SYSTEMS, SPECIFIC GP MAPS CONSIDERED AND EXAMPLE GENOTYPE, PHENOTYPE AND ENCODING OF PHENOTYPE. Each row is a specific GP map included in this work and is situated

within one of the four categories of system: RNA, Polyomino, HP (compact), and HP (non-compact). RNA and HP genotypes are depicted with distinct colours for their constituent bases.

Polyomino genotypes are shown as numerical sequences that map to the edges of distinctly coloured tiles with arrows used to indicate the tile orientation. The corresponding phenotype (the

structure that is formed following the self-assembly process on the example genotype) is shown with the colours and arrows used in the genotype depiction highlighting the mechanism by which

bonds are formed. The encoding of the example phenotypes are shown in the final column: dot-bracket and shape notation for RNA, grid coordinates for tile placements of polyominoes, and the

lattice directions for the HP lattice fold. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION. REPORTING SUMMARY. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE

THIS ARTICLE Greenbury, S.F., Louis, A.A. & Ahnert, S.E. The structure of genotype-phenotype maps makes fitness landscapes navigable. _Nat Ecol Evol_ 6, 1742–1752 (2022).

https://doi.org/10.1038/s41559-022-01867-z Download citation * Received: 21 September 2021 * Accepted: 01 August 2022 * Published: 29 September 2022 * Issue Date: November 2022 * DOI:

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