A novel approach for choosing summary statistics in approximate Bayesian computation

Genetics

Volumn 192, Issue 3, 2012, Pages 1027-1047

  Aeschbacher, Simon ^a,b   Beaumont, Mark A ^c   Futschik, Andreas ^d  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA   (Austria)

^c UNIVERSITY OF BRISTOL   (United Kingdom)

^d UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BAYESIAN LEARNING; BREEDING; EVOLUTION; GENE MUTATION; GENE POOL; ITALY; MACHINE LEARNING; MATING; MIGRATION; NONHUMAN; POPULATION GENETICS; PRIORITY JOURNAL; STATISTICAL PARAMETERS; STATISTICS; SWITZERLAND; ZOOLOGY;

ALGORITHMS; ANIMALS; BAYES THEOREM; BREEDING; COMPUTER SIMULATION; GENETICS, POPULATION; MALE; MODELS, GENETIC; MUTATION RATE; REPRODUCIBILITY OF RESULTS; SWITZERLAND;

CAPRA IBEX;

EID: 84869057921     PISSN: 00166731     EISSN: 19432631     Source Type: Journal    
DOI: 10.1534/genetics.112.143164     Document Type: Article

References (83)

1. Aeschbacher, A., 1978 Das Brunftverhalten des Alpensteinbocks. Eugen Rentsch Verlag, Erlenbach-Zürich, Switzerland.
2. Akaike, H., 1974 A new look at the statistical model identification. IEEE Trans. Automat. Contr. 19: 716-723.
3. Barton, N. H., 2000 Genetic hitchhiking. Philos. Trans. R. Soc. B 355: 1553-1562.
4. Beaumont, M. A., 2010 Approximate Bayesian computation in evolution and ecology. Annu. Rev. Ecol. Evol. Syst. 41: 379-406.
5. Beaumont, M. A., and B. Rannala, 2004 The Bayesian revolution in genetics. Nat. Rev. Genet. 5: 251-261.
6. Beaumont, M. A., W. Zhang, and D. J. Balding, 2002 Approximate Bayesian computation in population genetics. Genetics 162: 2025-2035.
7. Beaumont, M. A., J.-M. Cornuet, J.-M. Marin, and C. P. Robert, 2009 Adaptive approximate Bayesian computation. Biometrika 96: 983-990.
8. Beaumont, M. A., R. Nielsen, C. P. Robert, J. Hey, O. Gaggiotti et al., 2010 In defence of model-based inference in phylogeography-reply. Mol. Ecol. 19: 436-446.
9. Bertorelle, G., A. Benazzo, and S. Mona, 2010 ABC as a flexible framework to estimate demography over space and time: some cons, many pros. Mol. Ecol. 19: 2609-2625.
10. Biebach, I., and L. F. Keller, 2009 A strong genetic footprint of there-introduction history of Alpine ibex (Capra ibex ibex). Mol. Ecol. 18: 5046-5058.
11. Blum, M., and O. François, 2010 Non-linear regression models for approximate Bayesian computation. Stat. Comput. 20: 63-73.
12. Blum, M. G. B., and M. Jakobsson, 2011 Deep divergences of human gene trees and models of human origins. Mol. Biol. Evol. 28: 889-898.
13. Blum, M. G. B., M. A. Nunes, D. Prangle, and S. A. Sisson, 2012 A comparative review of dimension reduction methods in approximate Bayesian computation. Stat. Sci. (in press).
14. Bühlmann, P., and T. Hothorn, 2007 Boosting algorithms: regularization, prediction and model fitting. Stat. Sci. 22: 477-505.
15. Charlesworth, B., and D. Charlesworth, 2010 Elements of Evolutionary Genetics. Roberts & Company Publishers, Greenwood Village, Colorado.
16. Charlesworth, B., M. T. Morgan, and D. Charlesworth, 1993 The effect of deleterious mutations on neutral molecular variation. Genetics 134: 1289-1303.
17. Cook, S. R., A. Gelman, and D. B. Rubin, 2006 Validation of software for Bayesian models using posterior quantiles. J. Comput. Graph. Stat. 15: 675-692.
18. Couturier, M. A. J., 1962 Alpine Ibex. Chez l'auteur, Allier, France (in French).
19. Csilléry, K., M. G. B. Blum, O. E. Gaggiotti, and O. François, 2010 Approximate Bayesian computation (ABC) in practice. Trends Ecol. Evol. 25: 410-418.
20. Csilléry, K., O. François, and M. G. B. Blum, 2012 Abc: an R package for approximate Bayesian computation (ABC). Methods Ecol. Evol. 3: 475-479.
21. Didelot, X., R. G. Everitt, A. M. Johansen, and D. J. Lawson, 2011 Likelihood-free estimation of model evidence. Bayesian Anal. 6: 49-76.
22. Diggle, P. J., 1979 On parameter estimation and goodness-of-fit testing for spatial point patterns. Biometrics 35: 87-101.
23. Diggle, P. J., and R. J. Gratton, 1984 Monte Carlo methods of inference for implicit statistical models. J. R. Stat. Soc. B 46: 193-227.
24. Di Rienzo, A., P. Donnelly, C. Toomajian, B. Sisk, A. Hill et al., 1998 Heterogeneity of microsatellite mutations within and between loci, and implications for human demographic histories. Genetics 148: 1269-1284.
25. Estoup, A., and B. Angers, 1998 Microsatellites and minisatellites for molecular ecology: theoretical and empirical considerations, pp. 55-86 in Advances in Molecular Ecology, Vol. 306, edited by G. R. Carvalho. IOS Press, Amsterdam.
26. Estoup, A., and J.-M. Cornuet, 1999 Microsatellite evolution: inference from population data, pp. 49-65 in Microsatellites-Evolution and Application, edited by D. B. Goldstein and C. Schloetterer. Oxford University Press, London/New York/Oxford.
27. Fagundes, N. J. R., N. Ray, M. Beaumont, S. Neuenschwander, F. M. Salzano et al., 2007 Statistical evaluation of alternative models of human evolution. Proc. Natl. Acad. Sci. USA 104: 17614-17619.
28. Fearnhead, P., and D. Prangle, 2012 Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation. J. R. Stat. Soc. B 74: 419-474.
29. Fisher, R. A., 1922 On the mathematical foundations of theoretical statistics. Phil. Trans. R. Soc. A 222: 309-368.
30. Frazer, K. A., D. G. Ballinger, D. R. Cox, D. A. Hinds, and L. L. e. Stuve, 2007 A second generation human haplotype map of over 3.1 million SNPs. Nature 449: 851-861.
31. Freund, Y., 1995 Boosting a weak learning algorithm by majority. Inform. Comput. 121: 256-285.
32. Freund, Y., and R. E. Schapire, 1996 Experiments with a new boosting algorithm, pp. 148-156 in Machine Learning: Proceedings of the Thirteenth International Conference. Morgan Kaufmann Publishers, San Francisco.
33. Freund, Y., and R. E. Schapire, 1999 A short introduction to boosting. J. Jpn. Soc. Artif. Intell. 14: 771-780.
34. Friedman, J., T. Hastie, and R. Tibshirani, 2000 Special invited paper. additive logistic regression: a statistical view of boosting. Ann. Stat. 28: 337-374.
35. Friedman, J. H., 2001 Greedy function approximation: a gradient boosting machine. Ann. Stat. 29: 1189-1232.
36. Fu, Y. X., and W. H. Li, 1997 Estimating the age of the common ancestor of a sample of DNA sequences. Mol. Biol. Evol. 14: 195-199.
37. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin, 2004 Bayesian Data Analysis, Ed. 2. Chapman & Hall/CRC, Boca Raton, Florida.
38. Ghosh, M., N. Reid, and D. A. S. Fraser, 2010 Ancillary statistics: a review. Stat. Sin. 20: 1309-1332.
39. Haldane, J. B. S., 1932 The Causes of Evolution, Ed. 2. Princeton University Press, Princeton, NJ.
40. Hamilton, G., M. Currat, N. Ray, G. Heckel, M. Beaumont et al., 2005 Bayesian estimation of recent migration rates after a spatial expansion. Genetics 170: 409-417.
41. Hastie, T., R. Tibshirani, and J. Friedman, 2011 The Elements of Statistical Learning - Data Mining, Inference, and Prediction, Ed. 2. Springer-Verlag, Berlin/Heidelberg, Germany/New York.
42. Hothorn, T., P. Buehlmann, T. Kneib, M. Schmid, and B. Hofner, 2010 Model-based boosting 2.0. J. Mach. Learn. Res. 11: 2109-2113.
43. Joyce, P., and P. Marjoram, 2008 Approximately sufficient statistics and Bayesian computation. Stat. Appl. Genet. Mol. Biol. 7: 26.
44. Jung, H., and P. Marjoram, 2011 Choice of summary statistic weights in approximate Bayesian computation. Stat. Appl. Genet. Mol. Biol. 10: DOI:10.2202/1544-6115.1586.
45. Kuhner, M. K., 2009 Coalescent genealogy samplers: windows into population history. Trends Ecol. Evol. 24: 86-93.
46. Le Cam, L., 1964 Sufficiency and approximate sufficiency. Ann. Math. Stat. 35: 1419-1455.
47. Leuenberger, C., and D. Wegmann, 2010 Bayesian computation and model selection without likelihoods. Genetics 184: 243-252.
48. Lin, K., H. Li, C. Schlötterer, and A. Futschik, 2011 Distinguishing positive selection from neutral evolution: boosting the performance of summary statistics. Genetics 187: 229-244.
49. Mahalanobis, P. C., 1936 On the generalized distance in statistics. Proc. Natl. Inst. Sci. India 2: 49-55.
50. Marjoram, P., and S. Tavaré, 2006 Modern computational approaches for analysing molecular genetic variation data. Nat. Rev. Genet. 7: 759-770.
51. Marjoram, P., J. Molitor, V. Plagnol, and S. Tavaré, 2003 Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 100: 15324-15328.
52. Maudet, C., C. Miller, B. Bassano, C. Breitenmoser-Wursten, D. Gauthier et al., 2002 Microsatellite DNA and recent statistical methods in wildlife conservation management: applications in Alpine ibex [Capra ibex (ibex)]. Mol. Ecol. 11: 421-436.
53. Maynard Smith, J., and J. Haigh, 1974 Hitch-hiking effect of a favorable gene. Genet. Res. 23: 23-35.
54. Mevik, B.-H., and R. Wehrens, 2007 The pls package: principal component and partial least squares regression in R. J. Stat. Softw. 18: 1-24.
55. Nei, M., and R. K. Chesser, 1983 Estimation of fixation indexes and gene diversities. Ann. Hum. Genet. 47: 253-259.
56. Nunes, M. A., and D. J. Balding, 2010 On optimal selection of summary statistics for approximate Bayesian computation. Stat. Appl. Genet. Mol. Biol. 9: 34.
57. Ohta, T., and M. Kimura, 1973 Model of mutation appropriate to estimate number of electrophoretically detectable alleles in a finite population. Genet. Res. 22: 201-204.
58. Pritchard, J., M. Seielstad, A. Perez-Lezaun, and M. Feldman, 1999 Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol. 16: 1791-1798.
59. Raiffa, H., and R. Schlaifer, 1968 Applied Statistical Decision Theory. John Wiley & Sons, New York.
60. R Development Core Team, 2011 R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna.
61. Robert, C. P., J.-M. Cornuet, J.-M. Marin, and N. S. Pillai, 2011 Lack of confidence in approximate Bayesian computation model choice. Proc. Natl. Acad. Sci. USA 108: 15112-15117.
62. Rosenberg, N. A., J. K. Pritchard, J. L. Weber, H. M. Cann, K. K. Kidd et al., 2002 Genetic structure of human populations. Science 298: 2381-2385.
63. Rubin, D. B., 1984 Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Stat. 12: 1151-1172.
64. Schapire, R. E., 1990 The strength of weak learnability. Mach. Learn. 5: 197-227.
65. Scribner, K. T., and M. Stuwe, 1994 Genetic relationships among Alpine ibex Capra ibex populations reestablished from a common ancestral source. Biol. Conserv. 69: 137-143.
66. Shao, J., 2003 Mathematical Statistics, Ed. 2. Springer-Verlag, New York.
67. Sisson, S. A., Y. Fan, and M. M. Tanaka, 2007 Sequential Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 104: 1760-1765.
68. Sisson, S. A., Y. Fan, and M. M. Tanaka, 2009 Correction for Sisson et al., Sequential Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 106: 16889.
69. Slatkin, M., 1995 A measure of population subdivision based on microsatellite allele frequencies. Genetics 139: 457-462.
70. Sokal, R. R., and J. F. Rohlf, 1981 Biometry - The Principles and Practice of Statistics in Biological Research, Ed. 2. W. H. Freeman, New York.
71. Stuwe, M., and C. Grodinsky, 1987 Reproductive biology of captive Alpine ibex (Capra i. ibex). Zoo Biol. 6: 331-339.
72. Stuwe, M., and B. Nievergelt, 1991 Recovery of Alpine ibex from near extinction-the result of effective protection, captive breeding, and reintroduction. Appl. Anim. Behav. Sci. 29: 379-387.
73. Stuwe, M., and K. T. Scribner, 1989 Low genetic variablility in reintroduced Alpine ibex (Capra ibex ibex) populations. J. Mammal. 70: 370-373.
74. Tavaré, S., D. J. Balding, R. C. Griffiths, and P. Donnelly, 1997 Inferring coalescence times from DNA sequence data. Genetics 145: 505-518.
75. Toni, T., D. Welch, N. Strelkowa, A. Ipsen, and M. P. H. Stumpf, 2009 Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6: 187-202.
76. Wegmann, D., C. Leuenberger, and L. Excoffier, 2009 Efficient approximate Bayesian computation coupled with Markov chain Monte Carlo without likelihood. Genetics 182: 1207-1218.
77. Wegmann, D., C. Leuenberger, S. Neuenschwander, and L. Excoffier, 2010 ABCtoolbox: a versatile toolkit for approximate Bayesian computations. BMC Bioinformatics 11: 116.
78. Weiss, G., and A. von Haeseler, 1998 Inference of population history using a likelihood approach. Genetics 149: 1539-1546.
79. Wilkinson, R. D., 2008 Approximate Bayesian computation (ABC) gives exact results under the assumption of model error. arXiv:0811.3355v1.
80. Williamson, S. H., R. Hernandez, A. Fledel-Alon, L. Zhu, R. Nielsen et al., 2005 Simultaneous inference of selection and population growth from patterns of variation in the human genome. Proc. Natl. Acad. Sci. USA 102: 7882-7887.
81. Willisch, C. S., and P. Neuhaus, 2009 Alternative mating tactics and their impact on survival in adult male Alpine ibex (Capra ibex ibex). J. Mammal. 90: 1421-1430.
82. Willisch, C., I. Biebach, U. Koller, T. Bucher, N. Marreros et al., 2012 Male reproductive pattern in a polygynous ungulate with a slow life-history: the role of age, social status and alternative mating tactics. Evol. Ecol. 26: 187-206.
83. Wright, S., 1951 The genetical structure of populations. Ann. Eugen. 15: 323-354.