Abstract
A Bayesian method for determining if there are large departures from independence between pairs of alleles at a locus, Hardy-Weinberg equilibrium (HWE), is presented. We endorse the view that a population will never be exactly in HWE and that there will be occasions when there is a need for an alternative to the usual hypothesis-testing setting. Bayesian methods provide such an alternative, and our approach differs from previous Bayesian treatments in using the disequilibrium and inbreeding coefficient parameterizations. These are easily interpretable but may be less mathematically tractable than other parameterizations. We examined the posterior distributions of our parameters for evidence that departures from HWE were large. For either parameterization, when a conjugate prior was used, the prior probability for small departures was itself small, i.e., the prior was weighted against small departures from independence. We could avoid this uneven weighting by using a step prior which gave equal weighting to both small and large departures from HWE. In most cases, the Bayesian methodology makes it clear that there are not enough data to draw a conclusion.
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- Allard R. W., Kahler A. L., Weir B. S. The effect of selection on esterase allozymes in a barley population. Genetics. 1972 Nov;72(3):489–503. doi: 10.1093/genetics/72.3.489. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Ayres K. L., Balding D. J. Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient. Heredity (Edinb) 1998 Jun;80(Pt 6):769–777. doi: 10.1046/j.1365-2540.1998.00360.x. [DOI] [PubMed] [Google Scholar]
- Budowle B., Lindsey J. A., DeCou J. A., Koons B. W., Giusti A. M., Comey C. T. Validation and population studies of the loci LDLR, GYPA, HBGG, D7S8, and Gc (PM loci), and HLA-DQ alpha using a multiplex amplification and typing procedure. J Forensic Sci. 1995 Jan;40(1):45–54. [PubMed] [Google Scholar]
- Clegg M. T., Allard R. W., Kahler A. L. Is the gene the unit of selection? Evidence from two experimental plant populations. Proc Natl Acad Sci U S A. 1972 Sep;69(9):2474–2478. doi: 10.1073/pnas.69.9.2474. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Gianola D., Fernando R. L. Random-effects models for binary responses. Biometrics. 1986 Mar;42(1):217–218. [PubMed] [Google Scholar]
- Gyllensten U. B., Erlich H. A. Generation of single-stranded DNA by the polymerase chain reaction and its application to direct sequencing of the HLA-DQA locus. Proc Natl Acad Sci U S A. 1988 Oct;85(20):7652–7656. doi: 10.1073/pnas.85.20.7652. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hardy G. H. MENDELIAN PROPORTIONS IN A MIXED POPULATION. Science. 1908 Jul 10;28(706):49–50. doi: 10.1126/science.28.706.49. [DOI] [PubMed] [Google Scholar]
- Hernández J. L., Weir B. S. A disequilibrium coefficient approach to Hardy-Weinberg testing. Biometrics. 1989 Mar;45(1):53–70. [PubMed] [Google Scholar]
- Olson M. S. Bayesian procedures for discriminating among hypotheses with discrete distributions: inheritance in the tetraploid Astilbe biternata. Genetics. 1997 Dec;147(4):1933–1942. doi: 10.1093/genetics/147.4.1933. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Rogatko A., Rebbeck T., Zacks S. Risk prediction with linked markers: pedigree analysis. Am J Med Genet. 1995 Oct 23;59(1):24–32. doi: 10.1002/ajmg.1320590106. [DOI] [PubMed] [Google Scholar]
- Silver J., Buckler C. E. Statistical considerations for linkage analysis using recombinant inbred strains and backcrosses. Proc Natl Acad Sci U S A. 1986 Mar;83(5):1423–1427. doi: 10.1073/pnas.83.5.1423. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Uimari P., Thaller G., Hoeschele I. The use of multiple markers in a Bayesian method for mapping quantitative trait loci. Genetics. 1996 Aug;143(4):1831–1842. doi: 10.1093/genetics/143.4.1831. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Yamamoto T., Davis C. G., Brown M. S., Schneider W. J., Casey M. L., Goldstein J. L., Russell D. W. The human LDL receptor: a cysteine-rich protein with multiple Alu sequences in its mRNA. Cell. 1984 Nov;39(1):27–38. doi: 10.1016/0092-8674(84)90188-0. [DOI] [PubMed] [Google Scholar]
- Yang Z., Rannala B. Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method. Mol Biol Evol. 1997 Jul;14(7):717–724. doi: 10.1093/oxfordjournals.molbev.a025811. [DOI] [PubMed] [Google Scholar]
- Zaykin D., Zhivotovsky L., Weir B. S. Exact tests for association between alleles at arbitrary numbers of loci. Genetica. 1995;96(1-2):169–178. doi: 10.1007/BF01441162. [DOI] [PubMed] [Google Scholar]