{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T02:51:14Z","timestamp":1780109474870,"version":"3.54.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012008","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,4,10]],"date-time":"2024-04-10T00:00:00Z","timestamp":1712707200000}}],"reference-count":42,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T00:00:00Z","timestamp":1711670400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["CoG 863818 (ForM-SMArt)."],"award-info":[{"award-number":["CoG 863818 (ForM-SMArt)."]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["CoG 863818 (ForM-SMArt)."],"award-info":[{"award-number":["CoG 863818 (ForM-SMArt)."]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["CoG 863818 (ForM-SMArt)."],"award-info":[{"award-number":["CoG 863818 (ForM-SMArt)."]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007397","name":"Univerzita Karlova v Praze","doi-asserted-by":"publisher","award":["UNCE\/SCI\/004"],"award-info":[{"award-number":["UNCE\/SCI\/004"]}],"id":[{"id":"10.13039\/100007397","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007397","name":"Univerzita Karlova v Praze","doi-asserted-by":"publisher","award":["PRIMUS\/24\/SCI\/012"],"award-info":[{"award-number":["PRIMUS\/24\/SCI\/012"]}],"id":[{"id":"10.13039\/100007397","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate. Amplifiers of selection are networks that increase the fixation probability of advantageous mutants, as compared to the unstructured fully-connected network. Whether or not a network is an amplifier depends on the choice of the random process that governs the evolutionary dynamics. Two popular choices are Moran process with Birth-death updating and Moran process with death-Birth updating. Interestingly, while some networks are amplifiers under Birth-death updating and other networks are amplifiers under death-Birth updating, so far no spatial structures have been found that function as an amplifier under both types of updating simultaneously. In this work, we identify networks that act as amplifiers of selection under both versions of the Moran process. The amplifiers are robust, modular, and increase fixation probability for any mutant fitness advantage in a range <jats:italic>r<\/jats:italic> \u2208 (1, 1.2). To complement this positive result, we also prove that for certain quantities closely related to fixation probability, it is impossible to improve them simultaneously for both versions of the Moran process. Together, our results highlight how the two versions of the Moran process differ and what they have in common.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012008","type":"journal-article","created":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T17:36:54Z","timestamp":1711733814000},"page":"e1012008","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":7,"title":["Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1419-3267","authenticated-orcid":true,"given":"Jakub","family":"Svoboda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-9987-8106","authenticated-orcid":true,"given":"Soham","family":"Joshi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1097-9684","authenticated-orcid":true,"given":"Josef","family":"Tkadlec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4561-241X","authenticated-orcid":true,"given":"Krishnendu","family":"Chatterjee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,3,29]]},"reference":[{"key":"pcbi.1012008.ref001","doi-asserted-by":"crossref","unstructured":"Moran PAP. Random processes in genetics. In: Mathematical proceedings of the cambridge philosophical society. vol. 54. Cambridge University Press; 1958. p. 60\u201371.","DOI":"10.1017\/S0305004100033193"},{"key":"pcbi.1012008.ref002","doi-asserted-by":"crossref","unstructured":"Ewens WJ. Mathematical population genetics: theoretical introduction. vol. 27. Springer; 2004.","DOI":"10.1007\/978-0-387-21822-9"},{"issue":"7023","key":"pcbi.1012008.ref003","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1038\/nature03204","article-title":"Evolutionary dynamics on graphs","volume":"433","author":"E Lieberman","year":"2005","journal-title":"Nature"},{"key":"pcbi.1012008.ref004","doi-asserted-by":"crossref","unstructured":"Nowak MA. Evolutionary dynamics: exploring the equations of life. Harvard University Press; 2006.","DOI":"10.2307\/j.ctvjghw98"},{"issue":"1","key":"pcbi.1012008.ref005","doi-asserted-by":"crossref","first-page":"17979","DOI":"10.1038\/s41598-021-97187-6","article-title":"Fixation probabilities in network structured meta-populations","volume":"11","author":"S Yagoobi","year":"2021","journal-title":"Scientific Reports"},{"issue":"21","key":"pcbi.1012008.ref006","doi-asserted-by":"crossref","first-page":"218102","DOI":"10.1103\/PhysRevLett.127.218102","article-title":"Toward a universal model for spatially structured populations","volume":"127","author":"L Marrec","year":"2021","journal-title":"Physical review letters"},{"issue":"2271","key":"pcbi.1012008.ref007","doi-asserted-by":"crossref","first-page":"20220685","DOI":"10.1098\/rspa.2022.0685","article-title":"Coexistence times in the Moran process with environmental heterogeneity","volume":"479","author":"J Svoboda","year":"2023","journal-title":"Proceedings of the Royal Society A"},{"issue":"200","key":"pcbi.1012008.ref008","doi-asserted-by":"crossref","first-page":"20220769","DOI":"10.1098\/rsif.2022.0769","article-title":"Categorizing update mechanisms for graph-structured metapopulations","volume":"20","author":"S Yagoobi","year":"2023","journal-title":"Journal of the Royal Society Interface"},{"issue":"208","key":"pcbi.1012008.ref009","doi-asserted-by":"crossref","first-page":"20230355","DOI":"10.1098\/rsif.2023.0355","article-title":"Evolutionary dynamics of mutants that modify population structure","volume":"20","author":"J Tkadlec","year":"2023","journal-title":"Journal of the Royal Society Interface"},{"issue":"2181","key":"pcbi.1012008.ref010","doi-asserted-by":"crossref","first-page":"20150114","DOI":"10.1098\/rspa.2015.0114","article-title":"Amplifiers of selection","volume":"471","author":"B Adlam","year":"2015","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"issue":"1762","key":"pcbi.1012008.ref011","doi-asserted-by":"crossref","first-page":"20130211","DOI":"10.1098\/rspb.2013.0211","article-title":"The effect of population structure on the rate of evolution","volume":"280","author":"M Frean","year":"2013","journal-title":"Proceedings of the Royal Society B: Biological Sciences"},{"issue":"1","key":"pcbi.1012008.ref012","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1038\/s42003-019-0373-y","article-title":"Population structure determines the tradeoff between fixation probability and fixation time","volume":"2","author":"J Tkadlec","year":"2019","journal-title":"Communications biology"},{"key":"pcbi.1012008.ref013","doi-asserted-by":"crossref","unstructured":"Brendborg J, Karras P, Pavlogiannis A, Rasmussen AU, Tkadlec J. Fixation maximization in the positional moran process. In: Proceedings of the AAAI Conference on Artificial Intelligence. vol. 36; 2022. p. 9304\u20139312.","DOI":"10.1609\/aaai.v36i9.21160"},{"issue":"3","key":"pcbi.1012008.ref014","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1093\/biomet\/60.3.581","article-title":"A model for spatial conflict","volume":"60","author":"P Clifford","year":"1973","journal-title":"Biometrika"},{"key":"pcbi.1012008.ref015","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1007\/s11538-005-9046-8","article-title":"Spatial stochastic models for cancer initiation and progression","volume":"68","author":"NL Komarova","year":"2006","journal-title":"Bulletin of mathematical biology"},{"issue":"7649","key":"pcbi.1012008.ref016","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1038\/nature21723","article-title":"Evolutionary dynamics on any population structure","volume":"544","author":"B Allen","year":"2017","journal-title":"Nature"},{"issue":"7","key":"pcbi.1012008.ref017","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s00285-021-01609-y","article-title":"Spectral analysis of transient amplifiers for death\u2013birth updating constructed from regular graphs","volume":"82","author":"H Richter","year":"2021","journal-title":"Journal of Mathematical Biology"},{"issue":"18","key":"pcbi.1012008.ref018","doi-asserted-by":"crossref","first-page":"188104","DOI":"10.1103\/PhysRevLett.96.188104","article-title":"Evolutionary dynamics on degree-heterogeneous graphs","volume":"96","author":"T Antal","year":"2006","journal-title":"Physical review letters"},{"issue":"2098","key":"pcbi.1012008.ref019","doi-asserted-by":"crossref","first-page":"2609","DOI":"10.1098\/rspa.2008.0058","article-title":"An analysis of the fixation probability of a mutant on special classes of non-directed graphs","volume":"464","author":"M Broom","year":"2008","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"issue":"4","key":"pcbi.1012008.ref020","doi-asserted-by":"crossref","first-page":"140465","DOI":"10.1098\/rsos.140465","article-title":"The duality of spatial death\u2013birth and birth\u2013death processes and limitations of the isothermal theorem","volume":"2","author":"K Kaveh","year":"2015","journal-title":"Royal Society open science"},{"issue":"11","key":"pcbi.1012008.ref021","doi-asserted-by":"crossref","first-page":"e1004437","DOI":"10.1371\/journal.pcbi.1004437","article-title":"Most undirected random graphs are amplifiers of selection for birth-death dynamics, but suppressors of selection for death-birth dynamics","volume":"11","author":"L Hindersin","year":"2015","journal-title":"PLoS computational biology"},{"issue":"1","key":"pcbi.1012008.ref022","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1038\/s42003-018-0078-7","article-title":"Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory","volume":"1","author":"A Pavlogiannis","year":"2018","journal-title":"Communications biology"},{"issue":"1","key":"pcbi.1012008.ref023","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1038\/s42003-019-0374-x","article-title":"Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time","volume":"2","author":"M M\u00f6ller","year":"2019","journal-title":"Communications biology"},{"issue":"1","key":"pcbi.1012008.ref024","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1038\/s41598-017-00107-w","article-title":"Amplification on undirected population structures: comets beat stars","volume":"7","author":"A Pavlogiannis","year":"2017","journal-title":"Scientific reports"},{"issue":"3","key":"pcbi.1012008.ref025","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1007\/s13235-011-0022-7","article-title":"Evolutionary games on star graphs under various updating rules","volume":"1","author":"C Hadjichrysanthou","year":"2011","journal-title":"Dynamic Games and Applications"},{"issue":"2165","key":"pcbi.1012008.ref026","doi-asserted-by":"crossref","first-page":"20130730","DOI":"10.1098\/rspa.2013.0730","article-title":"Martingales and fixation probabilities of evolutionary graphs","volume":"470","author":"T Monk","year":"2014","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"pcbi.1012008.ref027","unstructured":"Chalub FA. Asymptotic expression for the fixation probability of a mutant in star graphs. arXiv preprint arXiv:14043944. 2014;."},{"issue":"1","key":"pcbi.1012008.ref028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3019609","article-title":"Amplifiers for the Moran process","volume":"64","author":"A Galanis","year":"2017","journal-title":"Journal of the ACM (JACM)"},{"key":"pcbi.1012008.ref029","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.tcs.2018.08.005","article-title":"Asymptotically optimal amplifiers for the Moran process","volume":"758","author":"LA Goldberg","year":"2019","journal-title":"Theoretical Computer Science"},{"issue":"1","key":"pcbi.1012008.ref030","doi-asserted-by":"crossref","first-page":"4009","DOI":"10.1038\/s41467-021-24271-w","article-title":"Fast and strong amplifiers of natural selection","volume":"12","author":"J Tkadlec","year":"2021","journal-title":"Nature Communications"},{"issue":"1","key":"pcbi.1012008.ref031","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s00285-023-01937-1","article-title":"Spectral dynamics of guided edge removals and identifying transient amplifiers for death\u2013Birth updating","volume":"87","author":"H Richter","year":"2023","journal-title":"Journal of Mathematical Biology"},{"issue":"1","key":"pcbi.1012008.ref032","doi-asserted-by":"crossref","first-page":"e1007529","DOI":"10.1371\/journal.pcbi.1007529","article-title":"Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs","volume":"16","author":"B Allen","year":"2020","journal-title":"PLoS computational biology"},{"issue":"1","key":"pcbi.1012008.ref033","doi-asserted-by":"crossref","first-page":"e1007494","DOI":"10.1371\/journal.pcbi.1007494","article-title":"Limits on amplifiers of natural selection under death-Birth updating","volume":"16","author":"J Tkadlec","year":"2020","journal-title":"PLoS computational biology"},{"issue":"2121","key":"pcbi.1012008.ref034","doi-asserted-by":"crossref","first-page":"2795","DOI":"10.1098\/rspa.2010.0067","article-title":"Two results on evolutionary processes on general non-directed graphs","volume":"466","author":"M Broom","year":"2010","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"pcbi.1012008.ref035","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.jtbi.2013.09.032","article-title":"Reproductive value in graph-structured populations","volume":"340","author":"W Maciejewski","year":"2014","journal-title":"Journal of Theoretical Biology"},{"issue":"3","key":"pcbi.1012008.ref036","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1006\/tpbi.1994.1032","article-title":"The importance of being discrete (and spatial)","volume":"46","author":"R Durrett","year":"1994","journal-title":"Theoretical population biology"},{"issue":"1","key":"pcbi.1012008.ref037","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1002\/rsa.20617","article-title":"Absorption time of the Moran process","volume":"49","author":"J D\u00edaz","year":"2016","journal-title":"Random Structures & Algorithms"},{"issue":"2241","key":"pcbi.1012008.ref038","doi-asserted-by":"crossref","first-page":"20200135","DOI":"10.1098\/rspa.2020.0135","article-title":"Wald\u2019s martingale and the conditional distributions of absorption time in the Moran process","volume":"476","author":"T Monk","year":"2020","journal-title":"Proceedings of the Royal Society A"},{"issue":"10","key":"pcbi.1012008.ref039","doi-asserted-by":"crossref","first-page":"210657","DOI":"10.1098\/rsos.210657","article-title":"Martingales and the characteristic functions of absorption time on bipartite graphs","volume":"8","author":"T Monk","year":"2021","journal-title":"Royal Society Open Science"},{"key":"pcbi.1012008.ref040","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/s00453-012-9722-7","article-title":"Approximating fixation probabilities in the generalized moran process","volume":"69","author":"J D\u00edaz","year":"2014","journal-title":"Algorithmica"},{"key":"pcbi.1012008.ref041","doi-asserted-by":"crossref","unstructured":"Durocher L, Karras P, Pavlogiannis A, Tkadlec J. Invasion dynamics in the biased voter process. In: Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence; 2022. p. 265\u2013271.","DOI":"10.24963\/ijcai.2022\/38"},{"issue":"37","key":"pcbi.1012008.ref042","doi-asserted-by":"crossref","first-page":"e2205424119","DOI":"10.1073\/pnas.2205424119","article-title":"Suppressors of fixation can increase average fitness beyond amplifiers of selection","volume":"119","author":"N Sharma","year":"2022","journal-title":"Proceedings of the National Academy of Sciences"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1012008","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,4,10]],"date-time":"2024-04-10T00:00:00Z","timestamp":1712707200000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,10]],"date-time":"2024-04-10T17:48:27Z","timestamp":1712771307000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012008"}},"subtitle":[],"editor":[{"given":"Roger Dimitri","family":"Kouyos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2024,3,29]]},"references-count":42,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3,29]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1012008","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1012008","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,29]]}}}