A continuous time version and a generalization of a Markovrecapture model for trapping experiments
Autor(a) principal: | |
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Data de Publicação: | 2008 |
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Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/6632 https://doi.org/10.1016/j.mbs.2008.01.004 |
Resumo: | Wileyto et al. [E.P. Wileyto, W.J. Ewens, M.A. Mullen, Markov-recapture population estimates: a tool for improving interpretation of trapping experiments, Ecology 75 (1994) 1109] propose a four-state discrete time Markov process, which describes the structure of a marking-capture experiment as a method of population estimation. They propose this method primarily for estimation of closed insect populations. Their method provides a mark-recapture estimate from a single trap observation by allowing subjects to mark themselves. The estimate of the unknown population size is based on the assumption of a closed population and a simple Markov model in which the rates of marking, capture, and recapture are assumed to be equal. Using the one step transition probability matrix of their model, we illustrate how to go from an embedded discrete time Markov process to a continuous time Markov process assuming exponentially distributed holding times. We also compute the transition probabilities after time t for the continuous time case and compare the limiting behavior of the continuous and discrete time processes. Finally, we generalize their model by relaxing the assumption of equal per capita rates for marking, capture, and recapture. Other questions about how their results change when using a continuous time Markov process are examined. © 2008 Elsevier Inc. All rights reserved. |
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A continuous time version and a generalization of a Markovrecapture model for trapping experimentsContinuous time systemsmark-recaptureMarkov chainWileyto et al. [E.P. Wileyto, W.J. Ewens, M.A. Mullen, Markov-recapture population estimates: a tool for improving interpretation of trapping experiments, Ecology 75 (1994) 1109] propose a four-state discrete time Markov process, which describes the structure of a marking-capture experiment as a method of population estimation. They propose this method primarily for estimation of closed insect populations. Their method provides a mark-recapture estimate from a single trap observation by allowing subjects to mark themselves. The estimate of the unknown population size is based on the assumption of a closed population and a simple Markov model in which the rates of marking, capture, and recapture are assumed to be equal. Using the one step transition probability matrix of their model, we illustrate how to go from an embedded discrete time Markov process to a continuous time Markov process assuming exponentially distributed holding times. We also compute the transition probabilities after time t for the continuous time case and compare the limiting behavior of the continuous and discrete time processes. Finally, we generalize their model by relaxing the assumption of equal per capita rates for marking, capture, and recapture. Other questions about how their results change when using a continuous time Markov process are examined. © 2008 Elsevier Inc. All rights reserved.Elsevier2012-12-07T15:43:17Z2012-12-072008-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/6632http://hdl.handle.net/10174/6632https://doi.org/10.1016/j.mbs.2008.01.004engAlpizar-Jara, R. & C.E. Smith. (2008). A continuous-time version and a generalization of a Markov-recapture model for trapping experiments. Mathematical Biosciences, 214(1-2):11-19.0025-5564http://www.scopus.com/record/display.url?eid=2-s2.0-47549110736&origin=inward&txGid=A088AB9FCD371FCA1B37DA28FBB5753E.CnvicAmOODVwpVrjSeqQ%3a2214Mathematical Biosciencesalpizar@uevora.ptnd336Alpizar-Jara, R.Smith, C.E.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-08T03:55:45ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments |
title |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments |
spellingShingle |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments Alpizar-Jara, R. Continuous time systems mark-recapture Markov chain |
title_short |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments |
title_full |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments |
title_fullStr |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments |
title_full_unstemmed |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments |
title_sort |
A continuous time version and a generalization of a Markovrecapture model for trapping experiments |
author |
Alpizar-Jara, R. |
author_facet |
Alpizar-Jara, R. Smith, C.E. |
author_role |
author |
author2 |
Smith, C.E. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Alpizar-Jara, R. Smith, C.E. |
dc.subject.por.fl_str_mv |
Continuous time systems mark-recapture Markov chain |
topic |
Continuous time systems mark-recapture Markov chain |
description |
Wileyto et al. [E.P. Wileyto, W.J. Ewens, M.A. Mullen, Markov-recapture population estimates: a tool for improving interpretation of trapping experiments, Ecology 75 (1994) 1109] propose a four-state discrete time Markov process, which describes the structure of a marking-capture experiment as a method of population estimation. They propose this method primarily for estimation of closed insect populations. Their method provides a mark-recapture estimate from a single trap observation by allowing subjects to mark themselves. The estimate of the unknown population size is based on the assumption of a closed population and a simple Markov model in which the rates of marking, capture, and recapture are assumed to be equal. Using the one step transition probability matrix of their model, we illustrate how to go from an embedded discrete time Markov process to a continuous time Markov process assuming exponentially distributed holding times. We also compute the transition probabilities after time t for the continuous time case and compare the limiting behavior of the continuous and discrete time processes. Finally, we generalize their model by relaxing the assumption of equal per capita rates for marking, capture, and recapture. Other questions about how their results change when using a continuous time Markov process are examined. © 2008 Elsevier Inc. All rights reserved. |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008-07-01T00:00:00Z 2012-12-07T15:43:17Z 2012-12-07 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/6632 http://hdl.handle.net/10174/6632 https://doi.org/10.1016/j.mbs.2008.01.004 |
url |
http://hdl.handle.net/10174/6632 https://doi.org/10.1016/j.mbs.2008.01.004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Alpizar-Jara, R. & C.E. Smith. (2008). A continuous-time version and a generalization of a Markov-recapture model for trapping experiments. Mathematical Biosciences, 214(1-2):11-19. 0025-5564 http://www.scopus.com/record/display.url?eid=2-s2.0-47549110736&origin=inward&txGid=A088AB9FCD371FCA1B37DA28FBB5753E.CnvicAmOODVwpVrjSeqQ%3a2 214 Mathematical Biosciences alpizar@uevora.pt nd 336 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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1777304581929172992 |