Hardy-Weinberg Equilibrium: A Nonparametric Compositional Approach

Compositional Data Analysis: Theory and Applications

Volumn , Issue , 2011, Pages 208-217

  Graffelman, Jan ^a   Egozcue, Juan José ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Bootstrap test, to empirical data set result compared with those obtained by classical tests; Classical tests for HWE most important statistical tests for HWE; Compositional approach Bruno de Finetti, that genotype frequencies for bi allelic locus, being represented in ternary plot; Compositional considerations based on Aitchison's geometry different equilibrium composition, affecting the inference made; Euclidean distance in ilr coordinates corresponding to the Aitchison distance; Genetic data sets most SNPs, being bi allelic markers; Hardy and Weinberg (1908), independently formulated principle, that the genotypes at a bi allelic locus, in proportions p2, 2pq and q2; Hardy Weinberg equilibrium nonparametric compositional approach; Modern genetic studies using single nucleotide polymorphisms (SNPs); SNPs, grouped as per particular position within gene

Indexed keywords

EID: 84885529408     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781119976462.ch15     Document Type: Chapter

References (35)

1. Aitchison J 2003 The Statistical Analysis of Compositional Data. The Blackburn Press, Caldwell, NJ (USA). 435 p.
2. Ayres KL and Balding DJ 1998 Measuring departures from Hardy-Weinberg: a Markov-chain-Monte Carlo method for estimating the inbreeding coefficient. Heredity 80, 769-777.
3. Cannings C and Edwards AWF 1968 Natural selection and the de Finetti diagram. Annals of Human Genetics 31, 421-428.
4. Cleghorn 1960 MNSs gene frequencies in english blood donors. Nature 187(4738), 701.
5. Crow JF 1988 Eighty years ago: the beginnings of population genetics. Genetics 119, 473-476.
6. de Finetti B 1926 Considerazioni matematiche sull'ereditarieta mendeliana. Metron 6(3), 3-41.
7. Edwards AWF 2008 G. H. Hardy (1908) and Hardy-Weinberg Equilibrium. Genetics 179, 1143-1150.
8. Efron B and Tibshirani RJ 1993 An Introduction to the Bootstrap. Chapman & Hall, New York, NY (USA). pp. 124-133, 224-227.
9. Egozcue JJ, Pawlowsky-Glahn V, Mateu-Figueras G and Barceló-Vidal C 2003 Isometric logratio transformations for compositional data analysis. Mathematical Geology 35(3), 279-300.
10. Elston RC and Forthofer R 1977 Testing for Hardy-Weinberg equilibrium in small samples. Biometrics 33(3), 536-542.
11. Emigh TH 1980 A comparison of tests for Hardy-Weinberg equilibrium. Biometrics 36, 627-642.
12. Fry JM, Fry TRL and McLaren KR 2000 Compositional data analysis and zeros in micro data. Applied Economics 32(8), 953-959.
13. Graffelman J 2010 The number of markers in the hapmap project: some notes on chi-square and exact tests for Hardy-Weinberg equilibrium. The American Journal of Human Genetics 86, 813-818.
14. Graffelman J and Morales-Camarena J 2008 Graphical tests for Hardy-Weinberg equilibrium based on the ternary plot. Human Heredity 65(2), 77-84. DOI: 10.1159/000108939.
15. Haber M 1981 Exact significance levels of goodness-of-fit tests for the Hardy-Weinberg equilibrium. Human Heredity 31, 161-166.
16. Haldane JBS 1954 An exact test for randomness of mating. Journal of Genetics 52, 631-635.
17. Hardy GH 1908 Mendelian proportions in a mixed population. Science 28, 49-50.
18. Hedrick PW 2005 Genetics of Populations, 3rd edition. Jones and Bartlett, Sudbury, MA (USA). 69 p.
19. Hernández JL and Weir BS 1989 A disequilibrium coefficient approach to Hardy-Weinberg testing. Biometrics 45(1), 53-70.
20. Jeffreys H 1946 An invariant form for the prior probability in estimation problems. Royal Society of London Proceedings Series A 186, 453-461.
21. Levene H 1949 On a matching problem arising in genetics. Annals of Mathematical Statistics 20, 91-94.
22. Li CC 1976 First Course in Population Genetics. Boxwood Press, Pacific Grove, CA (USA).
23. Lindley DV 1988 Statistical inference concerning hardy-weinberg equilibrium. In Bayesian Statistics 3 (ed. Bernardo JM, DeGroot MH, Lindley DV and Smith AFM), Oxford University Press, New York, NY (USA), pp. 307-326.
24. Mackenzie JR, Egozcue JJ, HeilbronnerR,Hielscher R,MüllerAand SchaebenH2008 Quantifying rock fabricks-a test of independence of the spatial distribution of crystals. In Proceedings ofCoDaWork'08, The 3rd Compositional Data Analysis Workshop (ed. Daunis-i Estadella J and Martín-Fernández J). http://hdl.handle.net/10256/723. University of Girona, Girona (Spain). CD-ROM.
25. Martín-Fernández JA and Thió-Henestrosa S 2006 Rounded zeros: some practical aspects for compositional data. In Compositional Data Analysis in the Geosciences: From Theory to Practice (ed. Buccianti A, Mateu-Figueras G and Pawlowsky-Glahn V). Geological Society, London (UK). pp. 191-201.
26. Noreen EW 1989 Computer Intensive Methods for Testing Hypotheses. An Introduction. John Wiley & Sons, Ltd, New York, NY (USA). pp. 66-69.
27. Pawlowsky-Glahn V and Egozcue JJ 2001 Geometric approach to statistical analysis on the simplex. Stochastic Environmental Research and Risk Assessment (SERRA) 15(5), 384-398.
28. Shoemaker J, Painter I and Weir BS 1998 A bayesian characterization of Hardy-Weinberg disequilibrium. Genetics 149, 2079-2088.
29. Teo YY, Fry AE, Clark TG, Tai ES and Seielstad M 2007 On the usage of HWE for identifying genotyping errors. Annals of Human Genetics 71(5), 701-703.
30. The International HapMap Consortium 2007 A second generation human haplotype map of over 3.1 million SNPs. Nature 449, 851-861.
31. Wakefield J 2010 Bayesian methods for examining Hardy-Weinberg equilibrium. Biometrics 66, 257-265.
32. Weinberg W 1908 Ü ber den Nachweis der Vererbung beim Menschen. Jahreshefte des Vereins für Vaterländische. Naturkunde in Württemberg, Stuttgart 64, 369-382.
33. Weir BS. 1996, Genetic Data Analysis II. Sinauer Associates, Sunderland, MA (USA). pp. 92-102.
34. Wigginton JE, Cutler DJ and Abecasis GR 2005 A note on exact tests of Hardy-Weinberg equilibrium. American Journal of Human Genetics 76, 887-893.
35. Wittke-Thompson JK, Pluzhnikov A and Cox NJ 2005 Rational inferences about departures from Hardy-Weinberg equilibrium. American Journal of Human Genetics 76, 967-986.