Phase-type distributions in population genetics
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent models for coalescence (with or without recombination)can be...
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ftuniaarhuspubl:oai:pure.atira.dk:publications/b01877a2-1736-455b-84a3-1f667dcbc5d0 2024-06-23T07:51:06+00:00 Phase-type distributions in population genetics Hobolth, Asger Siri-Jegousse, Arno Bladt, Mogens 2019 https://pure.au.dk/portal/en/publications/b01877a2-1736-455b-84a3-1f667dcbc5d0 https://doi.org/10.1016/j.tpb.2019.02.001 https://arxiv.org/pdf/1806.01416.pdf eng eng https://pure.au.dk/portal/en/publications/b01877a2-1736-455b-84a3-1f667dcbc5d0 info:eu-repo/semantics/restrictedAccess Hobolth , A , Siri-Jegousse , A & Bladt , M 2019 , ' Phase-type distributions in population genetics ' , Theoretical Population Biology , vol. 127 , pp. 16-32 . https://doi.org/10.1016/j.tpb.2019.02.001 Coalescent theory Multiple merger Phase-type theory Recombination Segregating sites Site frequency spectrum article 2019 ftuniaarhuspubl https://doi.org/10.1016/j.tpb.2019.02.001 2024-06-11T14:19:17Z Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent models for coalescence (with or without recombination)can be described in terms of the so-called phase-type theory, where complicated and tedious calculations are circumvented by the use of matrix manipulations. The application of phase-type theory in population genetics consists of describing the biological system as a Markov model by appropriately setting up a state space and calculating the corresponding intensity and reward matrices. Formulae of interest are then expressed in terms of these aforementioned matrices. We illustrate this procedure by a number of examples: (a)Calculating the mean, (co)variance and even higher order moments of the site frequency spectrum in multiple merger coalescent models, (b)Analysing a sample of DNA sequences from the Atlantic Cod using the Beta-coalescent, and (c)Determining the correlation of the number of segregating sites for multiple samples in the two-locus ancestral recombination graph. We believe that phase-type theory has great potential as a tool for analysing probability models in population genetics. The compact matrix notation is useful for clarification of current models, and in particular their formal manipulation and calculations, but also for further development or extensions. Article in Journal/Newspaper atlantic cod Aarhus University: Research Theoretical Population Biology 127 16 32 |
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Open Polar |
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Aarhus University: Research |
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ftuniaarhuspubl |
language |
English |
topic |
Coalescent theory Multiple merger Phase-type theory Recombination Segregating sites Site frequency spectrum |
spellingShingle |
Coalescent theory Multiple merger Phase-type theory Recombination Segregating sites Site frequency spectrum Hobolth, Asger Siri-Jegousse, Arno Bladt, Mogens Phase-type distributions in population genetics |
topic_facet |
Coalescent theory Multiple merger Phase-type theory Recombination Segregating sites Site frequency spectrum |
description |
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent models for coalescence (with or without recombination)can be described in terms of the so-called phase-type theory, where complicated and tedious calculations are circumvented by the use of matrix manipulations. The application of phase-type theory in population genetics consists of describing the biological system as a Markov model by appropriately setting up a state space and calculating the corresponding intensity and reward matrices. Formulae of interest are then expressed in terms of these aforementioned matrices. We illustrate this procedure by a number of examples: (a)Calculating the mean, (co)variance and even higher order moments of the site frequency spectrum in multiple merger coalescent models, (b)Analysing a sample of DNA sequences from the Atlantic Cod using the Beta-coalescent, and (c)Determining the correlation of the number of segregating sites for multiple samples in the two-locus ancestral recombination graph. We believe that phase-type theory has great potential as a tool for analysing probability models in population genetics. The compact matrix notation is useful for clarification of current models, and in particular their formal manipulation and calculations, but also for further development or extensions. |
format |
Article in Journal/Newspaper |
author |
Hobolth, Asger Siri-Jegousse, Arno Bladt, Mogens |
author_facet |
Hobolth, Asger Siri-Jegousse, Arno Bladt, Mogens |
author_sort |
Hobolth, Asger |
title |
Phase-type distributions in population genetics |
title_short |
Phase-type distributions in population genetics |
title_full |
Phase-type distributions in population genetics |
title_fullStr |
Phase-type distributions in population genetics |
title_full_unstemmed |
Phase-type distributions in population genetics |
title_sort |
phase-type distributions in population genetics |
publishDate |
2019 |
url |
https://pure.au.dk/portal/en/publications/b01877a2-1736-455b-84a3-1f667dcbc5d0 https://doi.org/10.1016/j.tpb.2019.02.001 https://arxiv.org/pdf/1806.01416.pdf |
genre |
atlantic cod |
genre_facet |
atlantic cod |
op_source |
Hobolth , A , Siri-Jegousse , A & Bladt , M 2019 , ' Phase-type distributions in population genetics ' , Theoretical Population Biology , vol. 127 , pp. 16-32 . https://doi.org/10.1016/j.tpb.2019.02.001 |
op_relation |
https://pure.au.dk/portal/en/publications/b01877a2-1736-455b-84a3-1f667dcbc5d0 |
op_rights |
info:eu-repo/semantics/restrictedAccess |
op_doi |
https://doi.org/10.1016/j.tpb.2019.02.001 |
container_title |
Theoretical Population Biology |
container_volume |
127 |
container_start_page |
16 |
op_container_end_page |
32 |
_version_ |
1802642093758218240 |