{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T10:22:31Z","timestamp":1770114151537,"version":"3.49.0"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T00:00:00Z","timestamp":1750723200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2025,12]]},"abstract":"Abstract<\/jats:title>\n \n We consider a stochastic model, called the\n replicator coalescent<\/jats:italic>\n , describing a system of blocks of\n k<\/jats:italic>\n different types that undergo pairwise mergers at rates depending on the block types: with rate\n \n \n \n $C_{ij}\\geq 0$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n blocks of type\n i<\/jats:italic>\n and\n j<\/jats:italic>\n merge, resulting in a single block of type\n i<\/jats:italic>\n . The replicator coalescent can be seen as a generalisation of Kingman\u2019s coalescent death chain in a multi-type setting, although without an underpinning exchangeable partition structure. The name is derived from a remarkable connection between the instantaneous dynamics of this multi-type coalescent when issued from an arbitrarily large number of blocks, and the so-called\n replicator equations<\/jats:italic>\n from evolutionary game theory. By dilating time arbitrarily close to zero, we see that initially, on coming down from infinity, the replicator coalescent behaves like the solution to a certain replicator equation. Thereafter, stochastic effects are felt and the process evolves more in the spirit of a multi-type death chain.\n <\/jats:p>","DOI":"10.1017\/jpr.2025.21","type":"journal-article","created":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T08:05:26Z","timestamp":1750752326000},"page":"1534-1548","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["The replicator coalescent"],"prefix":"10.1017","volume":"62","author":[{"given":"A. E.","family":"Kyprianou","sequence":"first","affiliation":[{"name":"University of Warwick"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Pe\u00f1aloza","sequence":"additional","affiliation":[{"name":"Universidad del Mar"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Rogers","sequence":"additional","affiliation":[{"name":"University of Bath"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,6,24]]},"reference":[{"key":"S002190022500021X_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1019737667"},{"key":"S002190022500021X_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10959-019-00921-0"},{"key":"S002190022500021X_ref4","first-page":"4210","article-title":"Multi-type","volume":"33","author":"Johnston","year":"2023","journal-title":"Ann. Appl. Prob."},{"key":"S002190022500021X_ref6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022294908268"},{"key":"S002190022500021X_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139173179"},{"key":"S002190022500021X_ref5","doi-asserted-by":"publisher","DOI":"10.1112\/S0024609399006098"},{"key":"S002190022500021X_ref8","volume-title":"Stochastic Integration and Differential Equations","author":"Protter","year":"2004"},{"key":"S002190022500021X_ref2","doi-asserted-by":"crossref","unstructured":"[2] Berestycki, N. (2009). Recent Progress in Coalescent Theory (Ensaios Matem\u00e1ticos [Mathematical Surveys] 16). Sociedade Brasileira de Matem\u00e1tica, Rio de Janeiro.","DOI":"10.21711\/217504322009\/em161"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002190022500021X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T00:25:40Z","timestamp":1770078340000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002190022500021X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,24]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["S002190022500021X"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.21","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,24]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}