{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/exact-numerical-calculation-of-fixation","title":"Exact numerical calculation of fixation probability and time on graphs","arxiv_id":"1511.02696","date":"2016-11-11","proceeding":null,"authors":[],"abstract":"The Moran process on graphs is a popular model to study the dynamics of\nevolution in a spatially structured population. Exact analytical solutions for\nthe fixation probability and time of a new mutant have been found for only a\nfew classes of graphs so far. Simulations are time-expensive and many\nrealizations are necessary, as the variance of the fixation times is high. We\npresent an algorithm that numerically computes these quantities for arbitrary\nsmall graphs by an approach based on the transition matrix. The advantage over\nsimulations is that the calculation has to be executed only once. Building the\ntransition matrix is automated by our algorithm. This enables a fast and\ninteractive study of different graph structures and their effect on fixation\nprobability and time. We provide a fast implementation in C with this note\nhttps://github.com/hindersin/efficientFixation. Our code is very flexible, as\nit can handle two different update mechanisms (Birth-death or death-Birth), as\nwell as arbitrary directed or undirected graphs.","url_abs":"http://arxiv.org/abs/1511.02696v2","url_pdf":"http://arxiv.org/pdf/1511.02696v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"exact-numerical-calculation-of-fixation","repo_url":"https://github.com/hindersin/efficientFixation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}