article published yes Raimundo J Saona Urmeneta author BD1DF4C4-D767-11E9-B658-BC13E66974250000-0001-5103-038X Fyodor Kondrashov author 44FDEF62-F248-11E8-B48F-1D18A9856A870000-0001-8243-4694 Kseniia Khudiakova author 4E6DC800-AE37-11E9-AC72-31CAE56974250000-0002-6246-1465 GradSch department NiBa department JaMa department Characterizing the fitness landscape on population and global scales project Evolutionary analysis of gene regulation project 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. https://research-explorer.ista.ac.at/download/11447/11455/2022_BulletinMathBiology_Saona.pdf application/pdfno Springer Nature2022 eng Computational Theory and MathematicsGeneral Agricultural and Biological SciencesPharmacologyGeneral Environmental ScienceGeneral BiochemistryGenetics and Molecular BiologyGeneral MathematicsImmunologyGeneral Neuroscience 0092-8240 1522-9602 35713756 00081250980000110.1007/s11538-022-01029-z 848 https://doi.org/10.1007/s11538-022-01118-z 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> 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. 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> 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. 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>. 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>. R.J. Saona Urmeneta, F. Kondrashov, K. Khudiakova, Bulletin of Mathematical Biology 84 (2022). 114472022-06-17T16:16:15Z2026-04-15T08:51:10Z