The Genealogy of Samples in Models With Selection

INVESTIGATIONS

The Genealogy of Samples in Models With Selection

C. Neuhauser and S. M. Krone
School of Mathematics, University of Minnesota, Minneapolis, Minnesota

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman's well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman's coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models, DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case.

This article has been cited by other articles:

P. Fearnhead
Perfect Simulation From Nonneutral Population Genetic Models: Variable Population Size and Population Subdivision
Genetics, November 1, 2006; 174(3): 1397 - 1406.
[Abstract] [Full Text] [PDF]

A. Carvajal-Rodriguez, K. A. Crandall, and D. Posada
Recombination Estimation Under Complex Evolutionary Models with the Coalescent Composite-Likelihood Method
Mol. Biol. Evol., April 1, 2006; 23(4): 817 - 827.
[Abstract] [Full Text] [PDF]

L. Zhu and C. D. Bustamante
A Composite-Likelihood Approach for Detecting Directional Selection From DNA Sequence Data
Genetics, July 1, 2005; 170(3): 1411 - 1421.
[Abstract] [Full Text] [PDF]

S. Williamson, S. M. Perry, C. D. Bustamante, M. E. Orive, M. N. Stearns, and J. K. Kelly
A Statistical Characterization of Consistent Patterns of Human Immunodeficiency Virus Evolution Within Infected Patients
Mol. Biol. Evol., March 1, 2005; 22(3): 456 - 468.
[Abstract] [Full Text] [PDF]

P. F. Slade and J. Wakeley
The Structured Ancestral Selection Graph and the Many-Demes Limit
Genetics, February 1, 2005; 169(2): 1117 - 1131.
[Abstract] [Full Text] [PDF]

E. W. Price and I. Carbone
SNAP: workbench management tool for evolutionary population genetic analysis
Bioinformatics, February 1, 2005; 21(3): 402 - 404.
[Abstract] [Full Text] [PDF]

J. Wakeley
The Limits of Theoretical Population Genetics
Genetics, January 1, 2005; 169(1): 1 - 7.
[Full Text] [PDF]

J. Wakeley
Recent Trends in Population Genetics: More Data! More Math! Simple Models?
J. Hered., September 1, 2004; 95(5): 397 - 405.
[Abstract] [Full Text] [PDF]

N. Takebayashi, E. Newbigin, and M. K. Uyenoyama
Maximum-Likelihood Estimation of Rates of Recombination Within Mating-Type Regions
Genetics, August 1, 2004; 167(4): 2097 - 2109.
[Abstract] [Full Text] [PDF]

I. Carbone, Y.-C. Liu, B. I. Hillman, and M. G. Milgroom
Recombination and Migration of Cryphonectria hypovirus 1 as Inferred From Gene Genealogies and the Coalescent
Genetics, April 1, 2004; 166(4): 1611 - 1629.
[Abstract] [Full Text] [PDF]

N. H. Barton and A. M. Etheridge
The Effect of Selection on Genealogies
Genetics, February 1, 2004; 166(2): 1115 - 1131.
[Abstract] [Full Text] [PDF]

M. Nordborg and H. Innan
The Genealogy of Sequences Containing Multiple Sites Subject to Strong Selection in a Subdivided Population
Genetics, March 1, 2003; 163(3): 1201 - 1213.
[Abstract] [Full Text] [PDF]

J. Wakeley
Polymorphism and Divergence for Island-Model Species
Genetics, January 1, 2003; 163(1): 411 - 420.
[Abstract] [Full Text] [PDF]

S. Williamson and M. E. Orive
The Genealogy of a Sequence Subject to Purifying Selection at Multiple Sites
Mol. Biol. Evol., August 1, 2002; 19(8): 1376 - 1384.
[Abstract] [Full Text] [PDF]

A. Llopart, J. M. Comeron, F. G. Brunet, D. Lachaise, and M. Long
Intron presence-absence polymorphism in Drosophila driven by positive Darwinian selection
PNAS, June 11, 2002; 99(12): 8121 - 8126.
[Abstract] [Full Text] [PDF]

G. B. Golding
Reconstructing the Prior Probabilities of Allelic Phylogenies
Genetics, June 1, 2002; 161(2): 889 - 896.
[Abstract] [Full Text] [PDF]

J. M. Comeron and M. Kreitman
Population, Evolutionary and Genomic Consequences of Interference Selection
Genetics, May 1, 2002; 161(1): 389 - 410.
[Abstract] [Full Text] [PDF]

T.-K. Seo, J. L. Thorne, M. Hasegawa, and H. Kishino
Estimation of Effective Population Size of HIV-1 Within a Host: A Pseudomaximum-Likelihood Approach
Genetics, April 1, 2002; 160(4): 1283 - 1293.
[Abstract] [Full Text] [PDF]

P. Donnelly, M. Nordborg, and P. Joyce
Likelihoods and Simulation Methods for a Class of Nonneutral Population Genetics Models
Genetics, October 1, 2001; 159(2): 853 - 867.
[Abstract] [Full Text] [PDF]

J. Wakeley and N. Aliacar
Gene Genealogies in a Metapopulation
Genetics, October 1, 2001; 159(2): 893 - 905.
[Abstract] [Full Text] [PDF]

I. M. Rouzine, A. Rodrigo, and J. M. Coffin
Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology
Microbiol. Mol. Biol. Rev., March 1, 2001; 65(1): 151 - 185.
[Abstract] [Full Text] [PDF]

B. C. Verrelli and W. F. Eanes
Extensive Amino Acid Polymorphism at the Pgm Locus Is Consistent With Adaptive Protein Evolution in Drosophila melanogaster
Genetics, December 1, 2000; 156(4): 1737 - 1752.
[Abstract] [Full Text]

G. A. T. McVean and B. Charlesworth
The Effects of Hill-Robertson Interference Between Weakly Selected Mutations on Patterns of Molecular Evolution and Variation
Genetics, June 1, 2000; 155(2): 929 - 944.
[Abstract] [Full Text]

I. M. Rouzine and J. M. Coffin
Linkage disequilibrium test implies a large effective population number for HIV in vivo
PNAS, September 14, 1999; 96(19): 10758 - 10763.
[Abstract] [Full Text] [PDF]

R. Nielsen and D. M. Weinreich
The Age of Nonsynonymous and Synonymous Mutations in Animal mtDNA and Implications for the Mildly Deleterious Theory
Genetics, September 1, 1999; 153(1): 497 - 506.
[Abstract] [Full Text]

A. G. Rodrigo, E. G. Shpaer, E. L. Delwart, A. K. N. Iversen, M. V. Gallo, J. Brojatsch, M. S. Hirsch, B. D. Walker, and J. I. Mullins
Coalescent estimates of HIV-1 generation time in vivo
PNAS, March 2, 1999; 96(5): 2187 - 2191.
[Abstract] [Full Text] [PDF]

S. A. Tishkoff, R. Varkonyi, N. Cahinhinan, S. Abbes, G. Argyropoulos, G. Destro-Bisol, A. Drousiotou, B. Dangerfield, G. Lefranc, J. Loiselet, et al.
Haplotype Diversity and Linkage Disequilibrium at Human G6PD: Recent Origin of Alleles That Confer Malarial Resistance
Science, July 20, 2001; 293(5529): 455 - 462.
[Abstract] [Full Text] [PDF]

				A. Carvajal-Rodriguez, K. A. Crandall, and D. Posada Recombination Estimation Under Complex Evolutionary Models with the Coalescent Composite-Likelihood Method Mol. Biol. Evol., April 1, 2006; 23(4): 817 - 827. [Abstract] [Full Text] [PDF]

				L. Zhu and C. D. Bustamante A Composite-Likelihood Approach for Detecting Directional Selection From DNA Sequence Data Genetics, July 1, 2005; 170(3): 1411 - 1421. [Abstract] [Full Text] [PDF]

				S. Williamson, S. M. Perry, C. D. Bustamante, M. E. Orive, M. N. Stearns, and J. K. Kelly A Statistical Characterization of Consistent Patterns of Human Immunodeficiency Virus Evolution Within Infected Patients Mol. Biol. Evol., March 1, 2005; 22(3): 456 - 468. [Abstract] [Full Text] [PDF]

				P. F. Slade and J. Wakeley The Structured Ancestral Selection Graph and the Many-Demes Limit Genetics, February 1, 2005; 169(2): 1117 - 1131. [Abstract] [Full Text] [PDF]

				E. W. Price and I. Carbone SNAP: workbench management tool for evolutionary population genetic analysis Bioinformatics, February 1, 2005; 21(3): 402 - 404. [Abstract] [Full Text] [PDF]

				J. Wakeley The Limits of Theoretical Population Genetics Genetics, January 1, 2005; 169(1): 1 - 7. [Full Text] [PDF]

				J. Wakeley Recent Trends in Population Genetics: More Data! More Math! Simple Models? J. Hered., September 1, 2004; 95(5): 397 - 405. [Abstract] [Full Text] [PDF]

				N. Takebayashi, E. Newbigin, and M. K. Uyenoyama Maximum-Likelihood Estimation of Rates of Recombination Within Mating-Type Regions Genetics, August 1, 2004; 167(4): 2097 - 2109. [Abstract] [Full Text] [PDF]

				I. Carbone, Y.-C. Liu, B. I. Hillman, and M. G. Milgroom Recombination and Migration of Cryphonectria hypovirus 1 as Inferred From Gene Genealogies and the Coalescent Genetics, April 1, 2004; 166(4): 1611 - 1629. [Abstract] [Full Text] [PDF]

				N. H. Barton and A. M. Etheridge The Effect of Selection on Genealogies Genetics, February 1, 2004; 166(2): 1115 - 1131. [Abstract] [Full Text] [PDF]

				M. Nordborg and H. Innan The Genealogy of Sequences Containing Multiple Sites Subject to Strong Selection in a Subdivided Population Genetics, March 1, 2003; 163(3): 1201 - 1213. [Abstract] [Full Text] [PDF]

				J. Wakeley Polymorphism and Divergence for Island-Model Species Genetics, January 1, 2003; 163(1): 411 - 420. [Abstract] [Full Text] [PDF]

				S. Williamson and M. E. Orive The Genealogy of a Sequence Subject to Purifying Selection at Multiple Sites Mol. Biol. Evol., August 1, 2002; 19(8): 1376 - 1384. [Abstract] [Full Text] [PDF]

				A. Llopart, J. M. Comeron, F. G. Brunet, D. Lachaise, and M. Long Intron presence-absence polymorphism in Drosophila driven by positive Darwinian selection PNAS, June 11, 2002; 99(12): 8121 - 8126. [Abstract] [Full Text] [PDF]

				G. B. Golding Reconstructing the Prior Probabilities of Allelic Phylogenies Genetics, June 1, 2002; 161(2): 889 - 896. [Abstract] [Full Text] [PDF]

				J. M. Comeron and M. Kreitman Population, Evolutionary and Genomic Consequences of Interference Selection Genetics, May 1, 2002; 161(1): 389 - 410. [Abstract] [Full Text] [PDF]

				T.-K. Seo, J. L. Thorne, M. Hasegawa, and H. Kishino Estimation of Effective Population Size of HIV-1 Within a Host: A Pseudomaximum-Likelihood Approach Genetics, April 1, 2002; 160(4): 1283 - 1293. [Abstract] [Full Text] [PDF]

				P. Donnelly, M. Nordborg, and P. Joyce Likelihoods and Simulation Methods for a Class of Nonneutral Population Genetics Models Genetics, October 1, 2001; 159(2): 853 - 867. [Abstract] [Full Text] [PDF]

				J. Wakeley and N. Aliacar Gene Genealogies in a Metapopulation Genetics, October 1, 2001; 159(2): 893 - 905. [Abstract] [Full Text] [PDF]

				I. M. Rouzine, A. Rodrigo, and J. M. Coffin Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology Microbiol. Mol. Biol. Rev., March 1, 2001; 65(1): 151 - 185. [Abstract] [Full Text] [PDF]

				B. C. Verrelli and W. F. Eanes Extensive Amino Acid Polymorphism at the Pgm Locus Is Consistent With Adaptive Protein Evolution in Drosophila melanogaster Genetics, December 1, 2000; 156(4): 1737 - 1752. [Abstract] [Full Text]

				G. A. T. McVean and B. Charlesworth The Effects of Hill-Robertson Interference Between Weakly Selected Mutations on Patterns of Molecular Evolution and Variation Genetics, June 1, 2000; 155(2): 929 - 944. [Abstract] [Full Text]

				I. M. Rouzine and J. M. Coffin Linkage disequilibrium test implies a large effective population number for HIV in vivo PNAS, September 14, 1999; 96(19): 10758 - 10763. [Abstract] [Full Text] [PDF]

				R. Nielsen and D. M. Weinreich The Age of Nonsynonymous and Synonymous Mutations in Animal mtDNA and Implications for the Mildly Deleterious Theory Genetics, September 1, 1999; 153(1): 497 - 506. [Abstract] [Full Text]

				A. G. Rodrigo, E. G. Shpaer, E. L. Delwart, A. K. N. Iversen, M. V. Gallo, J. Brojatsch, M. S. Hirsch, B. D. Walker, and J. I. Mullins Coalescent estimates of HIV-1 generation time in vivo PNAS, March 2, 1999; 96(5): 2187 - 2191. [Abstract] [Full Text] [PDF]

				S. A. Tishkoff, R. Varkonyi, N. Cahinhinan, S. Abbes, G. Argyropoulos, G. Destro-Bisol, A. Drousiotou, B. Dangerfield, G. Lefranc, J. Loiselet, et al. Haplotype Diversity and Linkage Disequilibrium at Human G6PD: Recent Origin of Alleles That Confer Malarial Resistance Science, July 20, 2001; 293(5529): 455 - 462. [Abstract] [Full Text] [PDF]