title: Likelihood-free inference of population structure and local adaptation in a Bayesian hierarchical model.
abstract: We address the problem of finding evidence of natural selection from genetic data, accounting for the confounding effects of demographic history. In the absence of natural selection, gene genealogies should all be sampled from the same underlying distribution, often approximated by a coalescent model. Selection at a particular locus will lead to a modified genealogy, and this motivates a number of recent approaches for detecting the effects of natural selection in the genome as "outliers" under some models. The demographic history of a population affects the sampling distribution of genealogies, and therefore the observed genotypes and the classification of outliers. Since we cannot see genealogies directly, we have to infer them from the observed data under some model of mutation and demography. Thus the accuracy of an outlier-based approach depends to a greater or a lesser extent on the uncertainty about the demographic and mutational model. A natural modeling framework for this type of problem is provided by Bayesian hierarchical models, in which parameters, such as mutation rates and selection coefficients, are allowed to vary across loci. It has proved quite difficult computationally to implement fully probabilistic genealogical models with complex demographies, and this has motivated the development of approximations such as approximate Bayesian computation (ABC). In ABC the data are compressed into summary statistics, and computation of the likelihood function is replaced by simulation of data under the model. In a hierarchical setting one may be interested both in hyperparameters and parameters, and there may be very many of the latter--for example, in a genetic model, these may be parameters describing each of many loci or populations. This poses a problem for ABC in that one then requires summary statistics for each locus, which, if used naively, leads to a consequent difficulty in conditional density estimation. We develop a general method for applying ABC to Bayesian hierarchical models, and we apply it to detect microsatellite loci influenced by local selection. We demonstrate using receiver operating characteristic (ROC) analysis that this approach has comparable performance to a full-likelihood method and outperforms it when mutation rates are variable across loci.
authors.affiliation: School of Biological Sciences, University of Reading, Whiteknights, Reading RG6 6BX, United Kingdom.
authors.forename: Eric
authors.initials: E
authors.lastname: Bazin
authors.forename: Kevin J
authors.initials: KJ
authors.lastname: Dawson
authors.forename: Mark A
authors.initials: MA
authors.lastname: Beaumont
mesh_terms: D001699:Biometry; D003710:Demography; D016678:Genome; D006801:Humans; D016013:Likelihood Functions; D018895:Microsatellite Repeats; D008954:Models, Biological; D015233:Models, Statistical; D044382:Population Groups; D011336:Probability; D012372:ROC Curve; D012641:Selection, Genetic
references.citation: Heredity (Edinb). 1986 Dec;57 ( Pt 3):357-76
references.pmid: 3804765
references.citation: J R Soc Interface. 2009 Feb 6;6(31):187-202
references.pmid: 19205079
references.citation: Mol Ecol. 2004 Apr;13(4):969-80
references.pmid: 15012769
references.citation: Proc Natl Acad Sci U S A. 2003 Dec 23;100(26):15324-8
references.pmid: 14663152
references.citation: Genetics. 2008 Mar;178(3):1817-29
references.pmid: 18245358
references.citation: Stat Appl Genet Mol Biol. 2008;7(1):Article26
references.pmid: 18764775
references.citation: Genetics. 2009 Aug;182(4):1207-18
references.pmid: 19506307
references.citation: Proc Natl Acad Sci U S A. 2007 Nov 6;104(45):17614-9
references.pmid: 17978179
references.citation: J Am Stat Assoc. 2009 Mar 1;104(485):142-154
references.pmid: 19623271
references.citation: Genetics. 1973 May;74(1):175-95
references.pmid: 4711903
references.citation: PLoS Genet. 2007 Apr 20;3(4):e66
references.pmid: 17447846
references.citation: Genetics. 1931 Mar;16(2):97-159
references.pmid: 17246615
references.citation: Forensic Sci Int. 1994 Feb;64(2-3):125-40
references.pmid: 8175083
references.citation: Bioinformatics. 2004 Dec 12;20(18):3673-5
references.pmid: 15271777
references.citation: Mol Biol Evol. 1999 Dec;16(12):1791-8
references.pmid: 10605120
references.citation: Curr Biol. 2005 Mar 8;15(5):R159-60
references.pmid: 15753023
references.citation: Proc Natl Acad Sci U S A. 2009 Jun 30;106(26):10576-81
references.pmid: 19525398
references.citation: Bioinformatics. 2004 Oct 12;20(15):2485-7
references.pmid: 15117750
references.citation: Nature. 2007 Oct 18;449(7164):913-8
references.pmid: 17943131
references.citation: Genet Res. 1996 Apr;67(2):147-58
references.pmid: 8801187
references.citation: Genetics. 2001 Aug;158(4):1811-23
references.pmid: 11514464
references.citation: Curr Opin Genet Dev. 2006 Dec;16(6):624-9
references.pmid: 17008091
references.citation: Genetics. 2009 Apr;181(4):1507-19
references.pmid: 19189952
references.citation: Proc R Soc Lond B Biol Sci. 1966 Mar 22;164(995):362-79
references.pmid: 4379525
references.citation: Genetics. 2002 Dec;162(4):2025-35
references.pmid: 12524368
references.citation: Bioinformatics. 2005 Oct 15;21(20):3940-1
references.pmid: 16096348
references.citation: Genome Res. 2007 Oct;17(10):1505-19
references.pmid: 17712021
references.citation: Mol Ecol. 2008 Aug;17(15):3425-7
references.pmid: 19160473
references.citation: BMC Evol Biol. 2008 Nov 27;8:322
references.pmid: 19038027
references.citation: Evolution. 2002 Jan;56(1):154-66
references.pmid: 11913661
references.citation: Mol Ecol. 2006 Jan;15(1):209-23
references.pmid: 16367841
references.citation: Genet Res. 1997 Oct;70(2):155-74
references.pmid: 9449192
references.citation: Annu Rev Genet. 2002;36:721-50
references.pmid: 12359738
references.citation: Theor Popul Biol. 2003 May;63(3):221-30
references.pmid: 12689793
references.citation: Bioinformatics. 2002 Feb;18(2):337-8
references.pmid: 11847089
references.citation: Genetics. 1995 Jan;139(1):457-62
references.pmid: 7705646
references.citation: Genetics. 1989 Dec;123(4):887-99
references.pmid: 2612899
references.citation: Genome Res. 2006 Jun;16(6):702-12
references.pmid: 16687733
references.citation: Genome Res. 2005 Nov;15(11):1468-76
references.pmid: 16251456
references.citation: Genetics. 1996 Apr;142(4):1357-62
references.pmid: 8846911
references.citation: Comput Appl Biosci. 1997 Jun;13(3):235-8
references.pmid: 9183526
references.citation: Evolution. 1984 Nov;38(6):1358-1370
references.pmid: 28563791
references.citation: Theor Popul Biol. 1998 Apr;53(2):166-74
references.pmid: 9615475
references.citation: Proc Natl Acad Sci U S A. 2007 Feb 6;104(6):1760-5
references.pmid: 17264216
references.citation: Genetics. 2005 May;170(1):409-17
references.pmid: 15716508
references.citation: Genetics. 2008 Oct;180(2):977-93
references.pmid: 18780740
references.citation: Heredity (Edinb). 2009 Oct;103(4):285-98
references.pmid: 19623208
references.citation: Theor Popul Biol. 1983 Jun;23(3):300-13
references.pmid: 6623407