{"doi":"10.1098/rspa.2022.0685","_id":"12787","type":"journal_article","volume":479,"title":"Coexistence times in the Moran process with environmental heterogeneity","quality_controlled":"1","date_published":"2023-03-29T00:00:00Z","article_processing_charge":"No","acknowledgement":"J.S. and K.C. acknowledge support from the ERC CoG 863818 (ForM-SMArt)","status":"public","isi":1,"article_number":"20220685","date_updated":"2023-08-01T13:58:34Z","ddc":["000"],"publication_status":"published","has_accepted_license":"1","scopus_import":"1","intvolume":"       479","related_material":{"link":[{"url":"https://doi.org/10.6084/m9.figshare.21261771.v1","relation":"research_data"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","abstract":[{"lang":"eng","text":"Populations evolve in spatially heterogeneous environments. While a certain trait might bring a fitness advantage in some patch of the environment, a different trait might be advantageous in another patch. Here, we study the Moran birth–death process with two types of individuals in a population stretched across two patches of size N, each patch favouring one of the two types. We show that the long-term fate of such populations crucially depends on the migration rate μ\r\n between the patches. To classify the possible fates, we use the distinction between polynomial (short) and exponential (long) timescales. We show that when μ is high then one of the two types fixates on the whole population after a number of steps that is only polynomial in N. By contrast, when μ is low then each type holds majority in the patch where it is favoured for a number of steps that is at least exponential in N. Moreover, we precisely identify the threshold migration rate μ⋆ that separates those two scenarios, thereby exactly delineating the situations that support long-term coexistence of the two types. We also discuss the case of various cycle graphs and we present computer simulations that perfectly match our analytical results."}],"oa_version":"Published Version","citation":{"ama":"Svoboda J, Tkadlec J, Kaveh K, Chatterjee K. Coexistence times in the Moran process with environmental heterogeneity. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2023;479(2271). doi:<a href=\"https://doi.org/10.1098/rspa.2022.0685\">10.1098/rspa.2022.0685</a>","ista":"Svoboda J, Tkadlec J, Kaveh K, Chatterjee K. 2023. Coexistence times in the Moran process with environmental heterogeneity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 479(2271), 20220685.","apa":"Svoboda, J., Tkadlec, J., Kaveh, K., &#38; Chatterjee, K. (2023). Coexistence times in the Moran process with environmental heterogeneity. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society. <a href=\"https://doi.org/10.1098/rspa.2022.0685\">https://doi.org/10.1098/rspa.2022.0685</a>","short":"J. Svoboda, J. Tkadlec, K. Kaveh, K. Chatterjee, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 479 (2023).","chicago":"Svoboda, Jakub, Josef Tkadlec, Kamran Kaveh, and Krishnendu Chatterjee. “Coexistence Times in the Moran Process with Environmental Heterogeneity.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society, 2023. <a href=\"https://doi.org/10.1098/rspa.2022.0685\">https://doi.org/10.1098/rspa.2022.0685</a>.","ieee":"J. Svoboda, J. Tkadlec, K. Kaveh, and K. Chatterjee, “Coexistence times in the Moran process with environmental heterogeneity,” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 479, no. 2271. The Royal Society, 2023.","mla":"Svoboda, Jakub, et al. “Coexistence Times in the Moran Process with Environmental Heterogeneity.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 479, no. 2271, 20220685, The Royal Society, 2023, doi:<a href=\"https://doi.org/10.1098/rspa.2022.0685\">10.1098/rspa.2022.0685</a>."},"publication_identifier":{"eissn":["1471-2946"],"issn":["1364-5021"]},"ec_funded":1,"project":[{"grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"department":[{"_id":"KrCh"}],"month":"03","article_type":"original","day":"29","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"issue":"2271","author":[{"id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","first_name":"Jakub","last_name":"Svoboda","full_name":"Svoboda, Jakub"},{"id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef","orcid":"0000-0002-1097-9684","last_name":"Tkadlec","full_name":"Tkadlec, Josef"},{"full_name":"Kaveh, Kamran","last_name":"Kaveh","first_name":"Kamran"},{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"}],"language":[{"iso":"eng"}],"year":"2023","publisher":"The Royal Society","external_id":{"isi":["000957125500002"]},"date_created":"2023-04-02T22:01:09Z","file":[{"checksum":"13953d349fbefcb5d21ccc6b303297eb","file_size":827784,"creator":"dernst","date_created":"2023-04-03T06:25:29Z","access_level":"open_access","file_id":"12796","success":1,"date_updated":"2023-04-03T06:25:29Z","relation":"main_file","file_name":"2023_ProceedingsRoyalSocietyA_Svoboda.pdf","content_type":"application/pdf"}],"oa":1,"file_date_updated":"2023-04-03T06:25:29Z"}