Phase-type distributions in population genetics
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Phase-type distributions in population genetics. / Hobolth, Asger; Siri-Jégousse, Arno; Bladt, Mogens.
I: Theoretical Population Biology, Bind 127, 2019, s. 16-32.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Phase-type distributions in population genetics
AU - Hobolth, Asger
AU - Siri-Jégousse, Arno
AU - Bladt, Mogens
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Coalescent theory
KW - Multiple merger
KW - Phase-type theory
KW - Recombination
KW - Segregating sites
KW - Site frequency spectrum
UR - http://www.scopus.com/inward/record.url?scp=85063079391&partnerID=8YFLogxK
U2 - 10.1016/j.tpb.2019.02.001
DO - 10.1016/j.tpb.2019.02.001
M3 - Journal article
C2 - 30822431
AN - SCOPUS:85063079391
VL - 127
SP - 16
EP - 32
JO - Theoretical Population Biology
JF - Theoretical Population Biology
SN - 0040-5809
ER -
ID: 222751916