Early appraisal of the fixation probability in directed networks
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/101906 |
Resumo: | In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen from a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant’s fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only.We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value and counting that event as having led to a total spread of the mutation. For advantageous mutations in large populations and regardless of the network’s topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about N/ r−1 1/4 mutants, where N is the number of simulation events and r is the ratio of the mutants’ fitness to that of the remainder of the population, leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10 000 nodes. |
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Barbosa, Valmir CarneiroDonangelo, Raul JoséSouza, Sergio Ricardo de Azevedo2014-08-26T09:26:51Z20101539-3755http://hdl.handle.net/10183/101906000762084In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen from a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant’s fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only.We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value and counting that event as having led to a total spread of the mutation. For advantageous mutations in large populations and regardless of the network’s topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about N/ r−1 1/4 mutants, where N is the number of simulation events and r is the ratio of the mutants’ fitness to that of the remainder of the population, leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10 000 nodes.application/pdfengPhysical review. E, Statistical, nonlinear and soft matter physics. Vol. 82, no. 4 (Oct. 2010), 046114, 9 p.Física matemáticaSistemas complexosMetodos matematicos em fisicaProbabilidadeEarly appraisal of the fixation probability in directed networksEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000762084.pdf000762084.pdfTexto completo (inglês)application/pdf743134http://www.lume.ufrgs.br/bitstream/10183/101906/1/000762084.pdffa776e1069cd7fb7e25711f1cdcc5002MD51TEXT000762084.pdf.txt000762084.pdf.txtExtracted Texttext/plain50009http://www.lume.ufrgs.br/bitstream/10183/101906/2/000762084.pdf.txtc0b08f517716a977c33574364c945229MD52THUMBNAIL000762084.pdf.jpg000762084.pdf.jpgGenerated Thumbnailimage/jpeg2015http://www.lume.ufrgs.br/bitstream/10183/101906/3/000762084.pdf.jpg0108ce19c67605a9d70da11002fe64a6MD5310183/1019062018-10-22 09:30:40.64oai:www.lume.ufrgs.br:10183/101906Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2018-10-22T12:30:40Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Early appraisal of the fixation probability in directed networks |
title |
Early appraisal of the fixation probability in directed networks |
spellingShingle |
Early appraisal of the fixation probability in directed networks Barbosa, Valmir Carneiro Física matemática Sistemas complexos Metodos matematicos em fisica Probabilidade |
title_short |
Early appraisal of the fixation probability in directed networks |
title_full |
Early appraisal of the fixation probability in directed networks |
title_fullStr |
Early appraisal of the fixation probability in directed networks |
title_full_unstemmed |
Early appraisal of the fixation probability in directed networks |
title_sort |
Early appraisal of the fixation probability in directed networks |
author |
Barbosa, Valmir Carneiro |
author_facet |
Barbosa, Valmir Carneiro Donangelo, Raul José Souza, Sergio Ricardo de Azevedo |
author_role |
author |
author2 |
Donangelo, Raul José Souza, Sergio Ricardo de Azevedo |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Barbosa, Valmir Carneiro Donangelo, Raul José Souza, Sergio Ricardo de Azevedo |
dc.subject.por.fl_str_mv |
Física matemática Sistemas complexos Metodos matematicos em fisica Probabilidade |
topic |
Física matemática Sistemas complexos Metodos matematicos em fisica Probabilidade |
description |
In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen from a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant’s fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only.We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value and counting that event as having led to a total spread of the mutation. For advantageous mutations in large populations and regardless of the network’s topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about N/ r−1 1/4 mutants, where N is the number of simulation events and r is the ratio of the mutants’ fitness to that of the remainder of the population, leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10 000 nodes. |
publishDate |
2010 |
dc.date.issued.fl_str_mv |
2010 |
dc.date.accessioned.fl_str_mv |
2014-08-26T09:26:51Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
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1539-3755 |
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000762084 |
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http://hdl.handle.net/10183/101906 |
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eng |
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eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. E, Statistical, nonlinear and soft matter physics. Vol. 82, no. 4 (Oct. 2010), 046114, 9 p. |
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openAccess |
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