Markov Chain Monte Carlo Model Composition Search Strategy for Quantitative Trait Loci in a Bayesian Hierarchical Model

Quantitative trait loci (QTL) experiments have yielded important biological and biochemical information necessary for understanding the relationship between genetic markers and quantitative traits. For many years, most QTL algorithms only allowed one observation per genotype. Recently, there has been an increasing demand for QTL algorithms that can accommodate more than one observation per genotypic distribution. The Bayesian hierarchical model is very flexible and can easily incorporate this information into the model. Herein a methodology is presented that uses a Bayesian hierarchical model to capture the complexity of the data. Furthermore, the Markov chain Monte Carlo model composition (MC3) algorithm is used to search and identify important markers. An extensive simulation study illustrates that the method captures the true QTL, even under nonnormal noise and up to 6 QTL.




References:
[1] Lynch M., Walsh, B., Genetics and Analysis of Quantitative Traits,
Sinauer Associates Inc., Sunderland, MA, 1997.
[2] Jing-hu Z., Yuan-zhu X., Bo Z., Ming-gang L., Feng-e L., Jia-lian
L.,"Detection of Quantitative Trait Loci Associated with Live
Measurement Traits in Pigs", Agricultural Sciences in China 6 (7),
2007, pp. 863-868.
[3] Buitenhuis, A.J., Rodenburg, T.B., Siwek, M., Cornelissen, S.J.B.,
Nieuwland, M.G.B., Crooijmans, R.P., Groenen, M.A., Koene, P.
Bovenhuis, H., van der Poel, J.J., "Quantitative trait loci for behavioural
traits in chickens", Livestock Production Science 93 (1), 2005, pp. 95-
103.
[4] Séne, M., Causse, M., Damerval, C., Thévenot, C., Prioul, J.L.,
"Quantitative trait loci affecting amylose, amylopectin and starch
content in maize recombinant inbred lines", Plant Physiology and
Biochemistry 3 (6), 2000, pp. 459-472.
[5] Lander E.S,. Botstein D.., "Mapping Mendelian factors underlying
quantitative traits using RFLP linkage maps", Genetics 121, 1989, pp
185-199.
[6] Luo Z.W., Kearsey M.J., "Interval mapping of quantitative trait loci in
an F2 population", Heredity 69, 1992, pp 236¨C242.
[7] Jansen R.C.,"Interval mapping of multiple quantitative trait loci",
Genetics 135, 1993, pp. 205-211.
[8] Luo Z.W., Williams J.A. "Estimation of genetic parameters using
linkage between a marker gene and a locus underlying a quantitative
character in F2 populations", Heredity 70, 1993, pp. 245-253.
[9] Jansen R.C., Stam P., "High resolution of quantitative traits into multiple
loci via interval mapping", Genetics 136, 1994, pp. 1447-1455.
[10] Zeng Z.B., "Precision mapping of quantitative trait loci", Genetics 136,
1994, pp. 1457-1468.
[11] Jiang C., Zeng Z.B., "Mapping quantitative trait loci with dominant and
missing markers in various crosses from two inbred lines", Genetica
101, 1997, pp. 47-58.
[12] Gao H., Yang R., "Composite interval mapping of QTL for dynamic
traits", Chin Sci Bull 51, 2006, pp.: 1857-1862.
[13] Haley C., Knott S., "A simple regression method for mapping
quantitative trait loci in line crosses using flanking markers-, Heredity
69, 1992,:pp. 315-324.
[14] Jansen R.C. "A general Monte Carlo method for mapping multiple
quantitative trait loci", Genetics 142, 1996, pp. 305-311.
[15] Liu J., Mercer J.M., Stam L.F., Gibson G.C., Zeng Z.B., Laurie C.C.,
"Genetic analysis of a morphological shape difference in the male
genitalia of Drosophila simulans and D. mauritiana", Genetics 142,
1996, pp. 1129-1145.
[16] Kao C.H., Zeng Z.B. "General formulae for obtaining the MLEs and the
asymptotic variance-covariance matrix in mapping quantitative trait loci
when using the EM algorithm", Biometrics 53, 1997, pp. 653-665.
[17] Weber K., Eisman R., Higgins S., Kuhl L., Patty A., Sparks J., Zeng
Z.B. "An analysis of polygenes affecting wing shape on chromosome
three in Drosophila melanogaster", Genetics 153, 1999, pp. 773-786.
[18] Kao C.H., "On the differences between maximum likelihood and
regression interval mapping in the analysis of quantitative trait loci",
Genetics 156, 2000, pp. 855-865.
[19] Zeng Z.B., Liu J., Stam L.F., Kao C.H., Mercer J.M., Laurie C.C.,
"Genetic architecture of a morphological shape difference between two
drosophila species", Genetics 154, 2000, pp. 299-310.
[20] Zeng Z.B., Wang T., Zou W., "Modeling quantitative trait loci and
interpretation of models", Genetics 169, 2005, pp. 1711-1725.
[21] Satagopan J.M., Yandell B.S., Newton M.A., Osborn T.C., "Markov
chain Monte Carlo approach to detect polygene loci for complex traits",
Genetics 144, 1996, pp. 805-816.
[22] Sillanpaa M., Arjas E., (1998) "Bayesian mapping of multiple
quantitative trait loci from incomplete inbred line cross data", Genetics
148, 1998, pp. 1373-1388.
[23] Sen S., Churchill G.A.,"A statistical framework for quantitative trait
mapping", Genetics 159, 2001, pp. 371-387.
[24] Yandell B.S., Mehta T., Banerjee S., Shriner D., Venkataraman R.,
Moon J.Y., Neely W.W., Wu H., von Smith R., Yi N., "R/qtlbim: QTL
with Bayesian interval mapping in experimental crosses",
Bioinformatics 23, 2007, pp. 641-643.
[25] Ball R.D., "Bayesian methods for quantitative trait loci mapping based
on model selection: approximate analysis using the Bayesian
information criterion", Genetics 159, 2001, pp. 1351-1364.
[26] Broman, K. W., Speed, T. P., "A model selection approach for the
identification of quantitative trait loci in experimental crosses", Journal
of the Royal Statistical Society, Series B: Statistical Methodology 64,
2002, pp. 641-656
[27] Sillanpaa M.J., Corander J., "Model choice in gene mapping: what and
why", Trends in Genetics 18,2002, pp. 301-307.
[28] Boone, E.L., Simmons, S.J., Ye, K., Stapleton, A.E., "Analyzing
Quantitative Trait Loci for the Arabidopsis thaliana using Markov Chain
Monte Carlo Model Composition with restricted and unrestricted model
spaces", Statistical Methodology 3 (1), 2006, pp. 69-78.
[29] Loudet, Chaillou, Camilleri, Bouchez, Vedele, "Bay-0 x Shahdara
recombinant inbred lines population: a powerful tool for the genetic
dissection of complex traits in Arabidopsis", Theoretical and Applied
Genetics 104 (6-7), 2002, pp. 1173-1184.