Statistical Properties of the Site-Frequency Spectrum Associated with Λ-Coalescents

Abstract

Abstract Statistical properties of the site-frequency spectrum associated with Λ-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Λ-coalescents for data sets too large for full-likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the parameter values that give the best fit to the observed frequency spectrum. The expected values are also used to approximate the probability a (derived) mutation arises on a branch subtending a given number of leaves (DNA sequences), allowing us to apply a pseudolikelihood inference to estimate coalescence parameters associated with certain subclasses of Λ-coalescents. The properties of the pseudolikelihood approach are investigated on simulated as well as real mtDNA data sets for the high-fecundity Atlantic cod (Gadus morhua). Our results for two subclasses of Λ-coalescents show that one can distinguish these subclasses from the Kingman coalescent, as well as between the Λ-subclasses, even for a moderate (maybe a few hundred) sample size.

Autoren

Matthias Birkner
Jochen Blath
Bjarki Eldon

DOI

10.1534/genetics.113.156612

eISSN

1943-2631

Ausgabe der Veröffentlichung

3

Zeitschrift

Genetics

Sprache

en

Online publication date

2013

Paginierung

1037 - 1053

Datum der Veröffentlichung

2013

Status

Published

Herausgeber

Oxford University Press (OUP)

Herausgeber URL

http://dx.doi.org/10.1534/genetics.113.156612

Datum der Datenerfassung

2022

Titel

Statistical Properties of the Site-Frequency Spectrum Associated with Λ-Coalescents

Ausgabe der Zeitschrift

195

Datenquelle: Crossref

Abstract

Statistical properties of the site-frequency spectrum associated with Λ-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Λ-coalescents for data sets too large for full-likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the parameter values that give the best fit to the observed frequency spectrum. The expected values are also used to approximate the probability a (derived) mutation arises on a branch subtending a given number of leaves (DNA sequences), allowing us to apply a pseudolikelihood inference to estimate coalescence parameters associated with certain subclasses of Λ-coalescents. The properties of the pseudolikelihood approach are investigated on simulated as well as real mtDNA data sets for the high-fecundity Atlantic cod (Gadus morhua). Our results for two subclasses of Λ-coalescents show that one can distinguish these subclasses from the Kingman coalescent, as well as between the Λ-subclasses, even for a moderate (maybe a few hundred) sample size.

Addresses

Institut für Mathematik, Johannes-Gutenberg-Universität, 55099 Mainz, Germany.

Autoren

Matthias Birkner
Jochen Blath
Bjarki Eldon

DOI

10.1534/genetics.113.156612

eISSN

1943-2631

Externe Identifier

PubMed Identifier: 24026094
PubMed Central ID: PMC3813835

Open access

false

ISSN

0016-6731

Ausgabe der Veröffentlichung

3

Zeitschrift

Genetics

Schlüsselwörter

Animals
Gadus morhua
DNA, Mitochondrial
Models, Statistical
Likelihood Functions
Genetics, Population
Population Density
Reproduction
Fertility
Mutation
Models, Genetic
Computer Simulation
Female
Male
Aquatic Organisms

Sprache

eng

Medium

Print-Electronic

Online publication date

2013

Paginierung

1037 - 1053

Datum der Veröffentlichung

2013

Status

Published

Datum der Datenerfassung

2013

Titel

Statistical properties of the site-frequency spectrum associated with lambda-coalescents.

Sub types

Research Support, Non-U.S. Gov't
research-article
Journal Article

Ausgabe der Zeitschrift

195

Files

https://www.genetics.org/content/genetics/195/3/1037.full.pdf https://europepmc.org/articles/PMC3813835?pdf=render

Datenquelle: Europe PubMed Central

Abstract

Statistical properties of the site-frequency spectrum associated with Λ-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Λ-coalescents for data sets too large for full-likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the parameter values that give the best fit to the observed frequency spectrum. The expected values are also used to approximate the probability a (derived) mutation arises on a branch subtending a given number of leaves (DNA sequences), allowing us to apply a pseudolikelihood inference to estimate coalescence parameters associated with certain subclasses of Λ-coalescents. The properties of the pseudolikelihood approach are investigated on simulated as well as real mtDNA data sets for the high-fecundity Atlantic cod (Gadus morhua). Our results for two subclasses of Λ-coalescents show that one can distinguish these subclasses from the Kingman coalescent, as well as between the Λ-subclasses, even for a moderate (maybe a few hundred) sample size.

Autoren

Matthias Birkner
Jochen Blath
Bjarki Eldon

Autoren-URL

https://www.ncbi.nlm.nih.gov/pubmed/24026094

DOI

10.1534/genetics.113.156612

eISSN

1943-2631

Externe Identifier

PubMed Central ID: PMC3813835

Ausgabe der Veröffentlichung

3

Zeitschrift

Genetics

Schlüsselwörter

Atlantic cod
covariance
pseudolikelihood
site-frequency spectrum
Λ-coalescents
Animals
Aquatic Organisms
Computer Simulation
DNA, Mitochondrial
Female
Fertility
Gadus morhua
Genetics, Population
Likelihood Functions
Male
Models, Genetic
Models, Statistical
Mutation
Population Density
Reproduction

Sprache

eng

Country

United States

Paginierung

1037 - 1053

PII

genetics.113.156612

Datum der Veröffentlichung

2013

Status

Published

Datum, an dem der Datensatz öffentlich gemacht wurde

2014

Titel

Statistical properties of the site-frequency spectrum associated with lambda-coalescents.

Sub types

Journal Article
Research Support, Non-U.S. Gov't

Ausgabe der Zeitschrift

195

Datenquelle: PubMed

Abstract

Statistical properties of the site frequency spectrum associated with Lambda-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Lambda-coalescents for datasets too large for full likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the parameter values which give the best fit to the observed frequency spectrum. The expected values are also used to approximate the probability a (derived) mutation arises on a branch subtending a given number of leaves (DNA sequences), allowing us to apply a pseudo-likelihood inference to estimate coalescence parameters associated with certain subclasses of Lambda coalescents. The properties of the pseudo-likelihood approach are investigated on simulated as well as real mtDNA datasets for the high fecundity Atlantic cod (\emph{Gadus morhua}). Our results for two subclasses of Lambda coalescents show that one can distinguish these subclasses from the Kingman coalescent, as well as between the Lambda-subclasses, even for moderate sample sizes.

Autoren

Matthias Birkner
Jochen Blath
Bjarki Eldon

Autoren-URL

http://arxiv.org/abs/1305.6043v2

Schlüsselwörter

q-bio.PE
q-bio.PE
92D15

Notes

45 pages, 14 figures, 4 tables, Appendix, supporting information

Datum der Veröffentlichung

2013

Datum der Datenerfassung

2013

Datum, an dem der Datensatz öffentlich gemacht wurde

2013

Titel

Statistical properties of the site-frequency spectrum associated with Lambda-coalescents

Files

1305.6043v2.pdf

Datenquelle: arXiv

Statistical Properties of the Site-Frequency Spectrum Associated with Λ-Coalescents

Files

Files

Werkzeuge