---
_id: '11447'
abstract:
- lang: eng
  text: Empirical essays of fitness landscapes suggest that they may be rugged, that
    is having multiple fitness peaks. Such fitness landscapes, those that have multiple
    peaks, necessarily have special local structures, called reciprocal sign epistasis
    (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the
    quantitative relationship between the number of fitness peaks and the number of
    reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk
    et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis
    is a necessary but not sufficient condition for the existence of multiple peaks.
    Applying discrete Morse theory, which to our knowledge has never been used in
    this context, we extend this result by giving the minimal number of reciprocal
    sign epistatic interactions required to create a given number of peaks.
acknowledgement: We are grateful to Herbert Edelsbrunner and Jeferson Zapata for helpful
  discussions. Open access funding provided by Austrian Science Fund (FWF). Partially
  supported by the ERC Consolidator (771209–CharFL) and the FWF Austrian Science Fund
  (I5127-B) grants to FAK.
article_number: '74'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Raimundo J
  full_name: Saona Urmeneta, Raimundo J
  id: BD1DF4C4-D767-11E9-B658-BC13E6697425
  last_name: Saona Urmeneta
  orcid: 0000-0001-5103-038X
- first_name: Fyodor
  full_name: Kondrashov, Fyodor
  id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
  last_name: Kondrashov
  orcid: 0000-0001-8243-4694
- first_name: Kseniia
  full_name: Khudiakova, Kseniia
  id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
  last_name: Khudiakova
  orcid: 0000-0002-6246-1465
citation:
  ama: Saona Urmeneta RJ, Kondrashov F, Khudiakova K. Relation between the number
    of peaks and the number of reciprocal sign epistatic interactions. <i>Bulletin
    of Mathematical Biology</i>. 2022;84(8). doi:<a href="https://doi.org/10.1007/s11538-022-01029-z">10.1007/s11538-022-01029-z</a>
  apa: Saona Urmeneta, R. J., Kondrashov, F., &#38; Khudiakova, K. (2022). Relation
    between the number of peaks and the number of reciprocal sign epistatic interactions.
    <i>Bulletin of Mathematical Biology</i>. Springer Nature. <a href="https://doi.org/10.1007/s11538-022-01029-z">https://doi.org/10.1007/s11538-022-01029-z</a>
  chicago: Saona Urmeneta, Raimundo J, Fyodor Kondrashov, and Kseniia Khudiakova.
    “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic
    Interactions.” <i>Bulletin of Mathematical Biology</i>. Springer Nature, 2022.
    <a href="https://doi.org/10.1007/s11538-022-01029-z">https://doi.org/10.1007/s11538-022-01029-z</a>.
  ieee: R. J. Saona Urmeneta, F. Kondrashov, and K. Khudiakova, “Relation between
    the number of peaks and the number of reciprocal sign epistatic interactions,”
    <i>Bulletin of Mathematical Biology</i>, vol. 84, no. 8. Springer Nature, 2022.
  ista: Saona Urmeneta RJ, Kondrashov F, Khudiakova K. 2022. Relation between the
    number of peaks and the number of reciprocal sign epistatic interactions. Bulletin
    of Mathematical Biology. 84(8), 74.
  mla: Saona Urmeneta, Raimundo J., et al. “Relation between the Number of Peaks and
    the Number of Reciprocal Sign Epistatic Interactions.” <i>Bulletin of Mathematical
    Biology</i>, vol. 84, no. 8, 74, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s11538-022-01029-z">10.1007/s11538-022-01029-z</a>.
  short: R.J. Saona Urmeneta, F. Kondrashov, K. Khudiakova, Bulletin of Mathematical
    Biology 84 (2022).
date_created: 2022-06-17T16:16:15Z
date_published: 2022-06-17T00:00:00Z
date_updated: 2023-08-03T07:20:53Z
day: '17'
ddc:
- '510'
- '570'
department:
- _id: GradSch
- _id: NiBa
- _id: JaMa
doi: 10.1007/s11538-022-01029-z
ec_funded: 1
external_id:
  isi:
  - '000812509800001'
file:
- access_level: open_access
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  creator: dernst
  date_created: 2022-06-20T07:51:32Z
  date_updated: 2022-06-20T07:51:32Z
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file_date_updated: 2022-06-20T07:51:32Z
has_accepted_license: '1'
intvolume: '        84'
isi: 1
issue: '8'
keyword:
- Computational Theory and Mathematics
- General Agricultural and Biological Sciences
- Pharmacology
- General Environmental Science
- General Biochemistry
- Genetics and Molecular Biology
- General Mathematics
- Immunology
- General Neuroscience
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 26580278-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '771209'
  name: Characterizing the fitness landscape on population and global scales
- _id: c098eddd-5a5b-11eb-8a69-abe27170a68f
  grant_number: I05127
  name: Evolutionary analysis of gene regulation
publication: Bulletin of Mathematical Biology
publication_identifier:
  eissn:
  - 1522-9602
  issn:
  - 0092-8240
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  link:
  - relation: erratum
    url: https://doi.org/10.1007/s11538-022-01118-z
scopus_import: '1'
status: public
title: Relation between the number of peaks and the number of reciprocal sign epistatic
  interactions
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 84
year: '2022'
...