Theory and applications of a deterministic approximation to the coalescent model

Theoretical Population Biology

Volumn 93, Issue , 2014, Pages 14-29

  Jewett, Ethan M ^a   Rosenberg, Noah A ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Approximation; Coalescent; Computational complexity

Indexed keywords

ACCURACY ASSESSMENT; ALLELE; COALESCENCE; DEMOGRAPHIC METHOD; ESTIMATION METHOD; GENETIC VARIATION; NUMERICAL METHOD; NUMERICAL MODEL; SAMPLING;

APPROXIMATION; ARTICLE; COALESCENT; COMPUTATIONAL COMPLEXITY; GAME; THEORETICAL MODEL;

APPROXIMATION; COALESCENT; COMPUTATIONAL COMPLEXITY;

GAME THEORY; MODELS, THEORETICAL;

EID: 84896541526     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2013.12.007     Document Type: Article

References (61)

1. Ariani C.V., Pickles R.S.A., Jordan W.C., Lobo-Hajdu G., Rocha C.F.D. Mitochondrial DNA and microsatellite loci data supporting a management plan for a critically endangered lizard from Brazil. Conserv. Genet. 2013, 14:943-951.
2. Atkinson K.E., Han W. Theoretical Numerical Analysis: a Functional Analysis Framework 2009, Springer-Verlag, New York.
3. Bryant D., Bouckaert R., Felsenstein J., Rosenberg N.A., RoyChoudhury A. Inferring species trees directly from biallelic genetic markers: bypassing gene trees in a full coalescent analysis. Mol. Biol. Evol. 2012, 29:1917-1932.
4. Casella G., Berger R.L. Statistical Inference 2002, Duxbury Press, Pacific Grove, CA. second ed.
5. Chen H., Chen K. Asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. Genetics 2013, 194:721-736.
6. Davison D., Pritchard J.K., Coop G. An approximate likelihood for genetic data under a model with recombination and population splitting. Theor. Popul. Biol. 2009, 75:331-345.
7. Degnan J.H. Probabilities of gene trees with intraspecific sampling given a species tree. Estimating Species Trees: Practical and Theoretical Aspects 2010, 53-78. Wiley-Blackwell, Hoboken, NJ. L.L. Knowles, L.S. Kubatko (Eds.).
8. Degnan J.H., Salter L.A. Gene tree distributions under the coalescent process. Evolution 2005, 59:24-37.
9. DiBenedetto E. Real Analysis 2002, Birkhauser, Boston.
10. Donnelly P. The transient behaviour of the Moran model in population genetics. Math. Proc. Cambridge Philos. Soc. 1984, 95:349-358.
11. Efromovich S., Kubatko L. Coalescent time distributions in trees of arbitrary size. Stat. Appl. Genet. Mol. Biol. 2008, 7. Article 2.
12. Franks J.M. A (Terse) Introduction to Lebesgue Integration 2009, American Mathematical Society, Providence, RI.
13. Frost S.D.W., Volz E.M. Viral phylodynamics and the search for an effective number of infections. Philos. Trans. R. Soc. Lond. B 2010, 365:1879-1890.
14. Griffiths R.C. Lines of descent in the diffusion approximation of neutral Wright-Fisher models. Theor. Popul. Biol. 1980, 17:37-50.
15. Griffiths R.C. Asymptotic line-of-descent distributions. J. Math. Biol. 1984, 21:67-75.
16. Griffiths R.C. Coalescent lineage distributions. Adv. Appl. Probab. 2006, 38:405-429.
17. Griffiths R.C., Tavaré S. Sampling theory for neutral alleles in a varying environment. Philos. Trans. R. Soc. Lond. B 1994, 29:403-410.
18. Griffiths R.C., Tavaré S. The age of a mutation in a general coalescent tree. Stoch. Models 1998, 14:273-295.
19. Gutenkunst R.N., Hernandez R.D., Williamson S.H., Bustamante C.D. Inferring the joint demographic history of multiple populations from multidimensional SNP frequency data. PLoS Genet. 2009, 5:e1000695.
20. Helmkamp L.J., Jewett E.M., Rosenberg N.A. Improvements to a class of distance matrix methods for inferring species trees from gene trees. J. Comput. Biol. 2012, 19:632-649.
21. Hendrix E.M.T., Tóth B.G. Introduction to Nonlinear and Global Optimization 2010, Springer, New York.
22. Huang L., Buzbas E.O., Rosenberg N.A. Genotype imputation in a coalescent model with infinitely-many-sites mutation. Theor. Popul. Biol. 2013, 87:62-74.
23. Hudson R.R., Coyne J.A. Mathematical consequences of the genealogical species concept. Evolution 2002, 56:1557-1565.
24. Jewett E.M., Rosenberg N.A. iGLASS: an improvement to the GLASS method for estimating species trees from gene trees. J. Comput. Biol. 2012, 19:293-315.
25. Jewett E.M., Zawistowski M., Rosenberg N.A., Zöllner S. A coalescent model for genotype imputation. Genetics 2012, 191:1239-1255.
26. Kalinowski S.T. Counting alleles with rarefaction: private alleles and hierarchical sampling designs. Conserv. Genet. 2004, 5:539-543.
27. Li H., Durbin R. Inference of human population history from individual whole-genome sequences. Nature 2011, 475:493-496.
28. Li N., Stephens M. Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics 2003, 165:2213-2233.
29. Liu L., Yu L., Pearl D.K. Maximum tree: a consistent estimator of the species tree. J. Math. Biol. 2010, 60:95-106.
30. Marjoram P., Wall J.D. Fast "coalescent" simulation. BMC Genet. 2006, 7:16.
31. Maruvka Y.E., Shnerb N.M., Bar-Yam Y., Wakeley J. Recovering population parameters from a single gene genealogy: an unbiased estimator of the growth rate. Mol. Biol. Evol. 2011, 28:1617-1631.
32. Mas-Colell A. The Theory of General Economic Equilibrium: a Differentiable Approach 1989, Cambridge University Press, New York.
33. McVean G.A.T., Cardin N.J. Approximating the coalescent with recombination. Philos. Trans. R. Soc. Lond. B 2005, 360:1387-1393.
34. Miller P.D. Applied Asymptotic Analysis 2006, American Mathematical Society, Providence, RI.
35. Mossel E., Roch S. Incomplete lineage sorting: consistent phylogeny estimation from multiple loci. IEEE/ACM Trans. Comput. Biol. Bioinform. 2010, 7:166-171.
36. Nielsen R., Hubisz M.J., Hellmann I., Torgerson D., Andrés A.M., Albrechtsen A., Gutenkunst R., Adams M.D., Cargill M., Boyko A., Indap A., Bustamante C.D., Clark A.G. Darwinian and demographic forces affecting human protein coding genes. Genome Res. 2009, 19:838-849.
37. Paul J.S., Song Y.S. A principled approach to deriving approximate conditional sampling distributions in population genetics models with recombination. Genetics 2010, 186:321-338.
38. Rauch E.M., Bar-Yam Y. Estimating the total genetic diversity of a spatial field population from a sample and implications of its dependence on habitat area. Proc. Natl. Acad. Sci. USA 2005, 102:9826-9829.
39. Reppell M., Boehnke M., Zöllner S. FTEC: a coalescent simulator for modeling faster than exponential growth. Bioinformatics 2012, 28:1282-1283.
40. Rosenberg N.A. The probability of topological concordance of gene trees and species trees. Theor. Popul. Biol. 2002, 61:225-247.
41. Rosenberg N.A. The shapes of neutral gene genealogies in two species: probabilities of monophyly, paraphyly, and polyphyly in a coalescent model. Evolution 2003, 57:1465-1477.
42. Rosenberg N.A., Feldman M.W. The relationship between coalescence times and population divergence times. Modern Developments in Theoretical Population Genetics 2002, 130-164. Oxford University Press, Oxford. M. Slatkin, D. Veuille (Eds.).
43. Ross S. Introduction to Probability Models 2007, Academic Press, New York. ninth ed.
44. RoyChoudhury A. Composite likelihood-based inferences on genetic data from dependent loci. J. Math. Biol. 2011, 62:65-80.
45. Rudin W. Real and Complex Analysis 1975, McGraw Hill, New York.
46. Sheehan S., Harris K., Song Y.S. Estimating variable effective population sizes from multiple genomes: a sequentially Markov conditional sampling distribution approach. Genetics 2013, 194:647-662.
47. Slatkin M. Allele age and a test for selection on rare alleles. Philos. Trans. R. Soc. Lond. B 2000, 355:1663-1668.
48. Slatkin M., Rannala B. Estimating the age of alleles by use of intraallelic variability. Am. J. Hum. Genet. 1997, 60:447-458.
49. Szpiech Z.A., Jakobsson M., Rosenberg N.A. ADZE: a rarefaction approach for counting alleles private to combinations of populations. Bioinformatics 2008, 24:2498-2504.
50. Takahata N. Gene genealogy in three related populations: consistency probability between gene and population trees. Genetics 1989, 122:957-966.
51. Takahata N., Nei M. Gene genealogy and variance of interpopulational nucleotide differences. Genetics 1985, 110:325-344.
52. Takahata N., Slatkin M. Genealogy of neutral genes in two partially isolated populations. Theor. Popul. Biol. 1990, 38:331-350.
53. Tao T. An Introduction to Measure Theory 2011, Amerian Mathematical Society, Providence, RI.
54. Tavaré S. Line-of-descent and genealogical processes, and their applications in population genetics models. Theor. Popul. Biol. 1984, 26:119-164.
55. Tishkoff S.A., Kidd K.K. Implications of biogeography of human populations for 'race' and medicine. Nat. Genet. 2004, 36:S21-S27.
56. Van der Vaart A.W. Asymptotic Statistics 2000, Cambridge University Press.
57. Volz E.M., Kosakovsky Pond S.L., Ward M.J., Leigh Brown A.J., Frost S.D.W. Phylodynamics of infectious disease epidemics. Genetics 2009, 183:1421-1430.
58. Wakeley J., Hey J. Estimating ancestral population parameters. Genetics 1997, 145:847-855.
59. Watterson G.A. On the number of segregating sites in genetical models without recombination. Theor. Popul. Biol. 1975, 7:256-276.
60. Wilson A.S., Marra P.P., Fleischer R.C. Temporal patterns of genetic diversity in Kirtlands warblers (Dendroica kirtlandii), the rarest songbird in North America. BMC Ecol. 2012, 12:8.
61. Wu Y. Coalescent-based species tree inference from gene tree topologies under incomplete lineage sorting by maximum likelihood. Evolution 2012, 66:763-775.