EVOLUTIONARY RELATIONSHIP OF DNA SEQUENCES IN FINITE POPULATIONS

Fumio Tajima 1

1 Center for Demographic and Population Genetics, The University of Texas at Houston, Houston, Texas 77025

With the aim of analyzing and interpreting data on DNA polymorphism obtained by DNA sequencing or restriction enzyme technique, a mathematical theory on the expected evolutionary relationship among DNA sequences (nucleons) sampled is developed under the assumption that the evolutionary change of nucleons is determined solely by mutation and random genetic drift. The statistical property of the number of nucleotide differences between randomly chosen nucleons and that of heterozygosity or nucleon diversity is investigated using this theory. These studies indicate that the estimates of the average number of nucleotide differences and nucleon diversity have a large variance, and a large part of this variance is due to stochastic factors. Therefore, increasing sample size does not help reduce the variance significantly. The distribution of sample allele (nucleomorph) frequencies is also studied, and it is shown that a small number of samples are sufficient in order to know the distribution pattern.

Submitted on February 11, 1983
Accepted on June 22, 1983




This article has been cited by other articles:


Home page
 J HeredHome page
G. Tezanos-Pinto, C. S. Baker, K. Russell, K. Martien, R. W. Baird, A. Hutt, G. Stone, A. A. Mignucci-Giannoni, S. Caballero, T. Endo, et al.
A Worldwide Perspective on the Population Structure and Genetic Diversity of Bottlenose Dolphins (Tursiops truncatus) in New Zealand
J. Hered., January 1, 2009; 100(1): 11 - 24.
[Abstract] [Full Text] [PDF]

Home page
 J HeredHome page
H. Chen, P. L. Morrell, V. E. T. M. Ashworth, M. de la Cruz, and M. T. Clegg
Tracing the Geographic Origins of Major Avocado Cultivars
J. Hered., January 1, 2009; 100(1): 56 - 65.
[Abstract] [Full Text] [PDF]

Home page
 Genome ResHome page
G. K. Chen, P. Marjoram, and J. D. Wall
Fast and flexible simulation of DNA sequence data
Genome Res., January 1, 2009; 19(1): 136 - 142.
[Abstract] [Full Text] [PDF]

Home page
 BioinformaticsHome page
J. C. Oliver
AUGIST: inferring species trees while accommodating gene tree uncertainty
Bioinformatics, December 15, 2008; 24(24): 2932 - 2933.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
J. Wakeley
Conditional Gene Genealogies under Strong Purifying Selection
Mol. Biol. Evol., December 1, 2008; 25(12): 2615 - 2626.
[Abstract] [Full Text] [PDF]

Home page
 J HeredHome page
Z. Rongyan, L. Xianglong, L. Lanhui, L. Xiangyun, and F. Fujun
Evolution and Differentiation of the Prion Protein Gene (PRNP) among Species
J. Hered., November 1, 2008; 99(6): 647 - 652.
[Abstract] [Full Text] [PDF]

Home page
 The Plant GenomeHome page
E. Gaitan-Solis, I.-Y. Choi, C. Quigley, P. Cregan, and J. Tohme
Single Nucleotide Polymorphisms in Common Bean: Their Discovery and Genotyping Using a Multiplex Detection System
The Plant Genome, November 1, 2008; 1(2): 125 - 134.
[Abstract] [Full Text] [PDF]

Home page
 Plant CellHome page
Y. Yu, T. Tang, Q. Qian, Y. Wang, M. Yan, D. Zeng, B. Han, C.-I Wu, S. Shi, and J. Li
Independent Losses of Function in a Polyphenol Oxidase in Rice: Differentiation in Grain Discoloration between Subspecies and the Role of Positive Selection under Domestication
PLANT CELL, November 1, 2008; 20(11): 2946 - 2959.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
M. Lynch
Estimation of Nucleotide Diversity, Disequilibrium Coefficients, and Mutation Rates from High-Coverage Genome-Sequencing Projects
Mol. Biol. Evol., November 1, 2008; 25(11): 2409 - 2419.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
B. Joos, M. Fischer, H. Kuster, S. K. Pillai, J. K. Wong, J. Boni, B. Hirschel, R. Weber, A. Trkola, H. F. Gunthard, et al.
HIV rebounds from latently infected cells, rather than from continuing low-level replication
PNAS, October 28, 2008; 105(43): 16725 - 16730.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
A. R. Omilian, D. G. Scofield, and M. Lynch
Intron Presence-Absence Polymorphisms in Daphnia
Mol. Biol. Evol., October 1, 2008; 25(10): 2129 - 2139.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
M. Slatkin and J. L. Pollack
Subdivision in an Ancestral Species Creates Asymmetry in Gene Trees
Mol. Biol. Evol., October 1, 2008; 25(10): 2241 - 2246.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
T. J. Robinson, A. Ruiz-Herrera, and J. C. Avise
Hemiplasy and homoplasy in the karyotypic phylogenies of mammals
PNAS, September 23, 2008; 105(38): 14477 - 14481.
[Abstract] [Full Text] [PDF]

Home page
 J HeredHome page
C. L. Sole, A. D. S. Bastos, and C. H. Scholtz
Intraspecific Patterns of Mitochondrial Variation in Natural Population Fragments of a Localized Desert Dung Beetle Species, Pachysoma gariepinum (Coleoptera: Scarabaeidae)
J. Hered., September 1, 2008; 99(5): 464 - 475.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
L.-M. Chevin, S. Billiard, and F. Hospital
Hitchhiking Both Ways: Effect of Two Interfering Selective Sweeps on Linked Neutral Variation
Genetics, September 1, 2008; 180(1): 301 - 316.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
P. K. Ingvarsson
Multilocus Patterns of Nucleotide Polymorphism and the Demographic History of Populus tremula
Genetics, September 1, 2008; 180(1): 329 - 340.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
R. Burgess and Z. Yang
Estimation of Hominoid Ancestral Population Sizes under Bayesian Coalescent Models Incorporating Mutation Rate Variation and Sequencing Errors
Mol. Biol. Evol., September 1, 2008; 25(9): 1979 - 1994.
[Abstract] [Full Text] [PDF]

Home page
 Genome ResHome page
J. D. Wall, M. P. Cox, F. L. Mendez, A. Woerner, T. Severson, and M. F. Hammer
A novel DNA sequence database for analyzing human demographic history
Genome Res., August 1, 2008; 18(8): 1354 - 1361.
[Abstract] [Full Text] [PDF]

Home page
 The Plant GenomeHome page
M. Yamasaki, S. G. Schroeder, H. Sanchez-Villeda, B. S. Gaut, and M. D. McMullen
Empirical Analysis of Selection Screens for Domestication and Improvement Loci in Maize by Extended DNA Sequencing
The Plant Genome, July 1, 2008; 1(1): 33 - 43.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
G. Achaz
Testing for Neutrality in Samples With Sequencing Errors
Genetics, July 1, 2008; 179(3): 1409 - 1424.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
T. Slotte, H. Huang, M. Lascoux, and A. Ceplitis
Polyploid Speciation Did Not Confer Instant Reproductive Isolation in Capsella (Brassicaceae)
Mol. Biol. Evol., July 1, 2008; 25(7): 1472 - 1481.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
L. F. de Alencar Figueiredo, C. Calatayud, C. Dupuits, C. Billot, J.-F. Rami, D. Brunel, X. Perrier, B. Courtois, M. Deu, and J.-C. Glaszmann
Phylogeographic Evidence of Crop Neodiversity in Sorghum
Genetics, June 1, 2008; 179(2): 997 - 1008.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
D. A. Vasco
A Fast and Reliable Computational Method for Estimating Population Genetic Parameters
Genetics, June 1, 2008; 179(2): 951 - 963.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
J. M. Macpherson, J. Gonzalez, D. M. Witten, J. C. Davis, N. A. Rosenberg, A. E. Hirsh, and D. A. Petrov
Nonadaptive Explanations for Signatures of Partial Selective Sweeps in Drosophila
Mol. Biol. Evol., June 1, 2008; 25(6): 1025 - 1042.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
M. T. Levine and D. J. Begun
Evidence of Spatially Varying Selection Acting on Four Chromatin-Remodeling Loci in Drosophila melanogaster
Genetics, May 1, 2008; 179(1): 475 - 485.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
S. Beisswanger and W. Stephan
Evidence that strong positive selection drives neofunctionalization in the tandemly duplicated polyhomeotic genes in Drosophila
PNAS, April 8, 2008; 105(14): 5447 - 5452.
[Abstract] [Full Text] [PDF]

Home page
 Progress in Physical GeographyHome page
B. R. Riddle, M. N. Dawson, E. A. Hadly, D. J. Hafner, M. J. Hickerson, S. J. Mantooth, and A. D. Yoder
The role of molecular genetics in sculpting the future of integrative biogeography
Progress in Physical Geography, April 1, 2008; 32(2): 173 - 202.
[Abstract] [PDF]

Home page
 GeneticsHome page
Q. Zhao, A.-C. Thuillet, N. K. Uhlmann, A. Weber, J. A. Rafalski, S. M. Allen, S. Tingey, and J. Doebley
The Role of Regulatory Genes During Maize Domestication: Evidence From Nucleotide Polymorphism and Gene Expression
Genetics, April 1, 2008; 178(4): 2133 - 2143.
[Abstract] [Full Text] [PDF]

Home page
 Appl. Environ. Microbiol.Home page
W. Guo, T. Jiang, X. Zhang, G. Li, and X. Zhou
Molecular Variation of Satellite DNA{beta} Molecules Associated with Malvastrum yellow vein virus and Their Role in Pathogenicity
Appl. Envir. Microbiol., March 15, 2008; 74(6): 1909 - 1913.
[Abstract] [Full Text] [PDF]

Home page
 J HeredHome page
H. Chen, P. L. Morrell, M. de la Cruz, and M. T. Clegg
Nucleotide Diversity and Linkage Disequilibrium in Wild Avocado (Persea americana Mill.)
J. Hered., March 14, 2008; (2008) esn016v1.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Bot.Home page
G. E. McKinnon, R. E. Vaillancourt, D. A. Steane, and B. M. Potts
An AFLP marker approach to lower-level systematics in Eucalyptus (Myrtaceae)
Am. J. Botany, March 1, 2008; 95(3): 368 - 380.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
B. Eldon and J. Wakeley
Linkage Disequilibrium Under Skewed Offspring Distribution Among Individuals in a Population
Genetics, March 1, 2008; 178(3): 1517 - 1532.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
E. Eveno, C. Collada, M. A. Guevara, V. Leger, A. Soto, L. Diaz, P. Leger, S. C. Gonzalez-Martinez, M. T. Cervera, C. Plomion, et al.
"Contrasting Patterns of Selection at Pinus pinaster Ait. Drought Stress Candidate Genes as Revealed by Genetic Differentiation Analyses"
Mol. Biol. Evol., February 1, 2008; 25(2): 417 - 437.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
B. Nabholz, J.-F. Mauffrey, E. Bazin, N. Galtier, and S. Glemin
Determination of Mitochondrial Genetic Diversity in Mammals
Genetics, January 1, 2008; 178(1): 351 - 361.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
M. D. Carling and R. T. Brumfield
Integrating Phylogenetic and Population Genetic Analyses of Multiple Loci to Test Species Divergence Hypotheses in Passerina Buntings
Genetics, January 1, 2008; 178(1): 363 - 377.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
P. L. F. Johnson and M. Slatkin
Accounting for Bias from Sequencing Error in Population Genetic Estimates
Mol. Biol. Evol., January 1, 2008; 25(1): 199 - 206.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
D. Garrigan, S. B. Kingan, M. M. Pilkington, J. A. Wilder, M. P. Cox, H. Soodyall, B. Strassmann, G. Destro-Bisol, P. de Knijff, A. Novelletto, et al.
Inferring Human Population Sizes, Divergence Times and Rates of Gene Flow From Mitochondrial, X and Y Chromosome Resequencing Data
Genetics, December 1, 2007; 177(4): 2195 - 2207.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
T. Salcedo, A. Geraldes, and M. W. Nachman
Nucleotide Variation in Wild and Inbred Mice
Genetics, December 1, 2007; 177(4): 2277 - 2291.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
A. L. Evans, P. A. Mena, and B. F. McAllister
Positive Selection Near an Inversion Breakpoint on the Neo-X Chromosome of Drosophila americana
Genetics, November 1, 2007; 177(3): 1303 - 1319.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
S. Glemin
Mating Systems and the Efficacy of Selection at the Molecular Level
Genetics, October 1, 2007; 177(2): 905 - 916.
[Abstract] [Full Text] [PDF]

Home page
 ANN BOT (LOND)Home page
M. Yamasaki, S. I. Wright, and M. D. McMullen
Genomic Screening for Artificial Selection during Domestication and Improvement in Maize
Ann. Bot., October 1, 2007; 100(5): 967 - 973.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
K. R. Thornton
The Neutral Coalescent Process for Recent Gene Duplications and Copy-Number Variants
Genetics, October 1, 2007; 177(2): 987 - 1000.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
S. Hutter, H. Li, S. Beisswanger, D. De Lorenzo, and W. Stephan
Distinctly Different Sex Ratios in African and European Populations of Drosophila melanogaster Inferred From Chromosomewide Single Nucleotide Polymorphism Data
Genetics, September 1, 2007; 177(1): 469 - 480.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
T. L. Turner and M. W. Hahn
Locus- and Population-Specific Selection and Differentiation between Incipient Species of Anopheles gambiae
Mol. Biol. Evol., September 1, 2007; 24(9): 2132 - 2138.
[Abstract] [Full Text] [PDF]

Home page
 Am J Trop Med HygHome page
J. Jung, Y. Jung, G.-S. Min, and W. Kim
Analysis of the Population Genetic Structure of the Malaria Vector Anopheles sinensis in South Korea Based on Mitochondrial Sequences
Am J Trop Med Hyg, August 1, 2007; 77(2): 310 - 315.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
B. Zhang, M. Li, Z. Zhang, B. Goossens, L. Zhu, S. Zhang, J. Hu, M. W. Bruford, and F. Wei
Genetic Viability and Population History of the Giant Panda, Putting an End to the "Evolutionary Dead End"?
Mol. Biol. Evol., August 1, 2007; 24(8): 1801 - 1810.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
R. D. Hernandez, S. H. Williamson, and C. D. Bustamante
Context Dependence, Ancestral Misidentification, and Spurious Signatures of Natural Selection
Mol. Biol. Evol., August 1, 2007; 24(8): 1792 - 1800.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
K. Zeng, S. Shi, and C.-I Wu
Compound Tests for the Detection of Hitchhiking Under Positive Selection
Mol. Biol. Evol., August 1, 2007; 24(8): 1898 - 1908.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
J. O. Borevitz, S. P. Hazen, T. P. Michael, G. P. Morris, I. R. Baxter, T. T. Hu, H. Chen, J. D. Werner, M. Nordborg, D. E. Salt, et al.
Genome-wide patterns of single-feature polymorphism in Arabidopsis thaliana
PNAS, July 17, 2007; 104(29): 12057 - 12062.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
A Haudry, A Cenci, C Ravel, T Bataillon, D Brunel, C Poncet, I Hochu, S Poirier, S Santoni, S Glemin, et al.
Grinding up Wheat: A Massive Loss of Nucleotide Diversity Since Domestication
Mol. Biol. Evol., July 1, 2007; 24(7): 1506 - 1517.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
I. M. Ehrenreich, P. A. Stafford, and M. D. Purugganan
The Genetic Architecture of Shoot Branching in Arabidopsis thaliana: A Comparative Assessment of Candidate Gene Associations vs. Quantitative Trait Locus Mapping
Genetics, June 1, 2007; 176(2): 1223 - 1236.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
X. Liu and Y.-X. Fu
Test of Genetical Isochronism for Longitudinal Samples of DNA Sequences
Genetics, May 1, 2007; 176(1): 327 - 342.
[Abstract] [Full Text] [PDF]

Home page
 J HeredHome page
X.-L. Li, G.-R. Zheng, R.-Y. Zhou, and L.-H. Li
Evolution and Differentiation of MSHR Gene in Different Species
J. Hered., March 1, 2007; 98(2): 165 - 168.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
C. A. Machado, T. S. Haselkorn, and M. A. F. Noor
Evaluation of the Genomic Extent of Effects of Fixed Inversion Differences on Intraspecific Variation and Interspecific Gene Flow in Drosophila pseudoobscura and D. persimilis
Genetics, March 1, 2007; 175(3): 1289 - 1306.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
L. Gomez-Alpizar, I. Carbone, and J. B. Ristaino
An Andean origin of Phytophthora infestans inferred from mitochondrial and nuclear gene genealogies
PNAS, February 27, 2007; 104(9): 3306 - 3311.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
K. R. Thornton and J. D. Jensen
Controlling the False-Positive Rate in Multilocus Genome Scans for Selection
Genetics, February 1, 2007; 175(2): 737 - 750.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
K. A. Dyer, B. Charlesworth, and J. Jaenike
Chromosome-wide linkage disequilibrium as a consequence of meiotic drive
PNAS, January 30, 2007; 104(5): 1587 - 1592.
[Abstract] [Full Text] [PDF]

Home page
 Mol Biol EvolHome page
O Thalmann, A Fischer, F Lankester, S Paabo, and L Vigilant
The Complex Evolutionary History of Gorillas: Insights from Genomic Data
Mol. Biol. Evol., January 1, 2007; 24(1): 146 - 158.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
D. L. Hyten, Q. Song, Y. Zhu, I.-Y. Choi, R. L. Nelson, J. M. Costa, J. E. Specht, R. C. Shoemaker, and P. B. Cregan
Impacts of genetic bottlenecks on soybean genome diversity
PNAS, November 7, 2006; 103(45): 16666 - 16671.
[Abstract] [Full Text] [PDF]

Home page
 GeneticsHome page
K. Zeng, Y.-X. Fu, S. Shi, and C.-I Wu
Statistical Tests for Detecting Positive Selection by Utilizing High-Frequency Variants
Genetics, November 1, 2006; 174(3): 1431 - 1439.
[Abstract] [Full Text] [PDF]

Home page
 Proc. Natl. Acad. Sci. USAHome page
H. Fernandez, S. Hughes, J.-D. Vigne, D. Helmer, G. Hodgins, C. Miquel, C. Hanni, G. Luikart, and P. Taberlet
Divergent mtDNA lineages of goats in an Early Neolithic site, far from the initial domestication areas
PNAS, October 17, 2006; 103(42): 15375 - 15379.
[Abstract] [Full Text] [PDF]

Home page
 Hum Mol GenetHome page
B. McEvoy, S. Beleza, and M. D. Shriver
The genetic architecture of normal variation in human pigmentation: an evolutionary perspective and model
Hum. Mol. Genet., October 15, 2006; 15(suppl_2): R176 - R181.
[Abstract] [Full Text] [PDF]

Home page
 J. Gen. Virol.Home page
G. Hall
Selective constraint and genetic differentiation in geographically distant barley yellow dwarf virus populations.
J. Gen. Virol., October 1, 2006; 87(Pt 10): 3067 - 3075.
[Abstract]