---
_id: '1167'
abstract:
- lang: eng
  text: Evolutionary pathways describe trajectories of biological evolution in the
    space of different variants of organisms (genotypes). The probability of existence
    and the number of evolutionary pathways that lead from a given genotype to a better-adapted
    genotype are important measures of accessibility of local fitness optima and the
    reproducibility of evolution. Both quantities have been studied in simple mathematical
    models where genotypes are represented as binary sequences of two types of basic
    units, and the network of permitted mutations between the genotypes is a hypercube
    graph. However, it is unclear how these results translate to the biologically
    relevant case in which genotypes are represented by sequences of more than two
    units, for example four nucleotides (DNA) or 20 amino acids (proteins), and the
    mutational graph is not the hypercube. Here we investigate accessibility of the
    best-adapted genotype in the general case of K > 2 units. Using computer generated
    and experimental fitness landscapes we show that accessibility of the global fitness
    maximum increases with K and can be much higher than for binary sequences. The
    increase in accessibility comes from the increase in the number of indirect trajectories
    exploited by evolution for higher K. As one of the consequences, the fraction
    of genotypes that are accessible increases by three orders of magnitude when the
    number of units K increases from 2 to 16 for landscapes of size N ∼ 106genotypes.
    This suggests that evolution can follow many different trajectories on such landscapes
    and the reconstruction of evolutionary pathways from experimental data might be
    an extremely difficult task.
acknowledgement: MZ acknowledges the Polish National Science Centre grant no. DEC-2012/07/N/NZ2/00107.
  BW was supported by the Scottish Government/Royal Society of Edinburgh Personal
  Research Fellowship. We thank Marjon de Vos and Oliver Martin for critically reading
  the manuscript.
article_number: e1005218
article_processing_charge: No
author:
- first_name: Marcin P
  full_name: Zagórski, Marcin P
  id: 343DA0DC-F248-11E8-B48F-1D18A9856A87
  last_name: Zagórski
  orcid: 0000-0001-7896-7762
- first_name: Zdzisław
  full_name: Burda, Zdzisław
  last_name: Burda
- first_name: Bartłomiej
  full_name: Wacław, Bartłomiej
  last_name: Wacław
citation:
  ama: Zagórski MP, Burda Z, Wacław B. Beyond the hypercube evolutionary accessibility
    of fitness landscapes with realistic mutational networks. <i>PLoS Computational
    Biology</i>. 2016;12(12). doi:<a href="https://doi.org/10.1371/journal.pcbi.1005218">10.1371/journal.pcbi.1005218</a>
  apa: Zagórski, M. P., Burda, Z., &#38; Wacław, B. (2016). Beyond the hypercube evolutionary
    accessibility of fitness landscapes with realistic mutational networks. <i>PLoS
    Computational Biology</i>. Public Library of Science. <a href="https://doi.org/10.1371/journal.pcbi.1005218">https://doi.org/10.1371/journal.pcbi.1005218</a>
  chicago: Zagórski, Marcin P, Zdzisław Burda, and Bartłomiej Wacław. “Beyond the
    Hypercube Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational
    Networks.” <i>PLoS Computational Biology</i>. Public Library of Science, 2016.
    <a href="https://doi.org/10.1371/journal.pcbi.1005218">https://doi.org/10.1371/journal.pcbi.1005218</a>.
  ieee: M. P. Zagórski, Z. Burda, and B. Wacław, “Beyond the hypercube evolutionary
    accessibility of fitness landscapes with realistic mutational networks,” <i>PLoS
    Computational Biology</i>, vol. 12, no. 12. Public Library of Science, 2016.
  ista: Zagórski MP, Burda Z, Wacław B. 2016. Beyond the hypercube evolutionary accessibility
    of fitness landscapes with realistic mutational networks. PLoS Computational Biology.
    12(12), e1005218.
  mla: Zagórski, Marcin P., et al. “Beyond the Hypercube Evolutionary Accessibility
    of Fitness Landscapes with Realistic Mutational Networks.” <i>PLoS Computational
    Biology</i>, vol. 12, no. 12, e1005218, Public Library of Science, 2016, doi:<a
    href="https://doi.org/10.1371/journal.pcbi.1005218">10.1371/journal.pcbi.1005218</a>.
  short: M.P. Zagórski, Z. Burda, B. Wacław, PLoS Computational Biology 12 (2016).
date_created: 2018-12-11T11:50:30Z
date_published: 2016-12-09T00:00:00Z
date_updated: 2025-09-22T09:53:16Z
day: '09'
ddc:
- '570'
department:
- _id: AnKi
doi: 10.1371/journal.pcbi.1005218
external_id:
  isi:
  - '000392126000015'
file:
- access_level: open_access
  checksum: 84f44ae92866c52ff1ca8a574558dca7
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:12:08Z
  date_updated: 2020-07-14T12:44:37Z
  file_id: '4926'
  file_name: IST-2017-740-v1+1_journal.pcbi.1005218.pdf
  file_size: 3822299
  relation: main_file
file_date_updated: 2020-07-14T12:44:37Z
has_accepted_license: '1'
intvolume: '        12'
isi: 1
issue: '12'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
publication: PLoS Computational Biology
publication_status: published
publisher: Public Library of Science
publist_id: '6190'
pubrep_id: '740'
quality_controlled: '1'
related_material:
  record:
  - id: '9866'
    relation: research_data
    status: public
scopus_import: '1'
status: public
title: Beyond the hypercube evolutionary accessibility of fitness landscapes with
  realistic mutational networks
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 12
year: '2016'
...