--- _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. Bulletin of Mathematical Biology. 2022;84(8). doi:10.1007/s11538-022-01029-z apa: Saona Urmeneta, R. J., Kondrashov, F., & Khudiakova, K. (2022). Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. Springer Nature. https://doi.org/10.1007/s11538-022-01029-z chicago: Saona Urmeneta, Raimundo J, Fyodor Kondrashov, and Kseniia Khudiakova. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical Biology. Springer Nature, 2022. https://doi.org/10.1007/s11538-022-01029-z. ieee: R. J. Saona Urmeneta, F. Kondrashov, and K. Khudiakova, “Relation between the number of peaks and the number of reciprocal sign epistatic interactions,” Bulletin of Mathematical Biology, 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.” Bulletin of Mathematical Biology, vol. 84, no. 8, 74, Springer Nature, 2022, doi:10.1007/s11538-022-01029-z. 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 checksum: 05a1fe7d10914a00c2bca9b447993a65 content_type: application/pdf creator: dernst date_created: 2022-06-20T07:51:32Z date_updated: 2022-06-20T07:51:32Z file_id: '11455' file_name: 2022_BulletinMathBiology_Saona.pdf file_size: 463025 relation: main_file success: 1 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' ...