Bayesian shrinkage analysis is the state-of-the-art method for whole genome analysis of quantitative traits. It can estimate the genetic effects for the entire genome using a dense marker map. The technique is now called genome selection. A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size of 300–500 individuals. In most cases, QTL can be detected with simple visual inspection of the entire genome for the effect because the false positive rate is low. As a Bayesian method, no significance test is needed. However, it is still desirable to put some confidences on the estimated QTL effects. We proposed to use the permutation test to draw empirical thresholds to declare significance of QTL under a predetermined genome wide type I error. With the permutation test, Bayesian shrinkage analysis can be routinely used for QTL detection. 1. Introduction Interval mapping [1] and multiple interval mapping [2] are the most commonly used methods for QTL mapping. These methods are developed in the maximum likelihood framework, which has limitation in terms of handling large saturated models. Bayesian mapping [3–7] deals with large models more efficiently through the reversible jump Markov chain Monte Carlo (RJMCMC) [4], the shrinkage analysis [8, 9], or the stochastic search variable selection (SSVS) [10]. Shrinkage mapping and SSVS are more efficient in terms of whole genome evaluation because they are statistically easy to understand and also provide better chance to evaluate the entire genome. These two methods are related to the Lasso method for regression analysis [11]. Rather than deleting nonsignificant QTL explicitly from the model, these methods use a special algorithm to shrink estimated QTL effects to zero or close to zero. A QTL with zero estimated effect is treated the same as being excluded from the model. No statistical test is required because genome regions bearing no QTL often show no bumps (QTL effects) in the QTL effect profile (plot of QTL effects against genome location). The visual inspection on the QTL effect profile is not optimal because small QTL may come and go during the MCMC sampling process. It is desirable to provide some kind of statistical confidence on these small QTL. Permutation test [12] itself is not a method of QTL mapping; rather, it is a method to find the critical value used to declare the significance of QTL for any method of QTL mapping. It is very efficient in interval mapping under the maximum likelihood framework. A
References
[1]
E. S. Lander and S. Botstein, “Mapping mendelian factors underlying quantitative traits using RFLP linkage maps,” Genetics, vol. 121, no. 1, pp. 185–199, 1989.
[2]
C. H. Kao, Z. B. Zeng, and R. D. Teasdale, “Multiple interval mapping for quantitative trait loci,” Genetics, vol. 152, no. 3, pp. 1203–1216, 1999.
[3]
J. M. Satagopan, B. S. Yandell, M. A. Newton, and T. C. Osborn, “A Bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo,” Genetics, vol. 144, no. 2, pp. 805–816, 1996.
[4]
M. J. Sillanpaa and E. Arjas, “Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data,” Genetics, vol. 148, no. 3, pp. 1373–1388, 1998.
[5]
N. Yi and S. Xu, “Bayesian mapping of quantitative trait loci under the identity-by-descent-based variance component model,” Genetics, vol. 156, no. 1, pp. 411–422, 2000.
[6]
N. Yi and S. Xu, “Bayesian mapping of quantitative trait loci for complex binary traits,” Genetics, vol. 155, no. 3, pp. 1391–1403, 2000.
[7]
N. Yi and S. Xu, “Bayesian mapping of quantitative trait loci under complicated mating designs,” Genetics, vol. 157, no. 4, pp. 1759–1771, 2001.
[8]
H. Wang, Y.-M. Zhang, X. Li, et al., “Bayesian shrinkage estimation of quantitative trait loci parameters,” Genetics, vol. 170, no. 1, pp. 465–480, 2005.
[9]
S. Xu, “Estimating polygenic effects using markers of the entire genome,” Genetics, vol. 163, no. 2, pp. 789–801, 2003.
[10]
N. Yi, B. S. Yandell, G. A. Churchill, D. B. Allison, E. J. Eisen, and D. Pomp, “Bayesian model selection for genome-wide epistatic quantitative trait loci analysis,” Genetics, vol. 170, no. 3, pp. 1333–1344, 2005.
[11]
R. Tibshirani, “Regression shrinkage and selection via the Lasso,” Journal of the Royal Statistical Society, Series B, vol. 58, pp. 267–288, 1996.
[12]
G. A. Churchill and R. W. Doerge, “Empirical threshold values for quantitative trait mapping,” Genetics, vol. 138, no. 3, pp. 963–971, 1994.
[13]
F. Zou, J. P. Fine, J. Hu, and D. Y. Lin, “An efficient resampling method for assessing genome-wide statistical significance in mapping quantitative trait loci,” Genetics, vol. 168, no. 4, pp. 2307–2316, 2004.
[14]
A. Kopp, R. M. Graze, S. Xu, S. B. Carroll, and S. V. Nuzhdin, “Quantitative trait loci responsible for variation in sexually dimorphic traits in Drosophila melanogaster,” Genetics, vol. 163, no. 2, pp. 771–787, 2003.
[15]
K. W. Broman and T. P. Speed, “A model selection approach for the identification of quantitative trait loci in experimental crosses,” Journal of the Royal Statistical Society. Series B, vol. 64, no. 4, pp. 641–656, 2002.
[16]
A. Manichaikul, J. Y. Moon, S. Sen, B. S. Yandell, and K. W. Broman, “A model selection approach for the identification of quantitative trait loci in experimental crosses, allowing epistasis,” Genetics, vol. 181, no. 3, pp. 1077–1086, 2009.
[17]
N. Yi, S. Xu, and D. B. Allison, “Bayesian model choice and search strategies for mapping interacting quantitative trait loci,” Genetics, vol. 165, no. 2, pp. 867–883, 2003.
[18]
T. H. E. Meuwissen, B. J. Hayes, and M. E. Goddard, “Prediction of total genetic value using genome-wide dense marker maps,” Genetics, vol. 157, no. 4, pp. 1819–1829, 2001.
[19]
T. H. Meuwissen, T. R. Solberg, R. Shepherd, and J. A. Woolliams, “A fast algorithm for BayesB type of prediction of genome-wide estimates of genetic value,” Genetics Selection Evolution, vol. 41, no. 1, p. 2, 2009.
[20]
A. Legarra, C. Robert-Granié, E. Manfredi, and J.-M. Elsen, “Performance of genomic selection in mice,” Genetics, vol. 180, no. 1, pp. 611–618, 2008.
[21]
S. H. Lee, J. H. J. Van Der Werf, B. J. Hayes, M. E. Goddard, and P. M. Visscher, “Predicting unobserved phenotypes for complex traits from whole-genome SNP data,” PLoS Genetics, vol. 4, no. 10, article e1000231, 2008.
[22]
C. J. F. Ter Braak, M. P. Boer, and M. C. A. M. Bink, “Extending Xu's Bayesian model for estimating polygenic effects using markers of the entire genome,” Genetics, vol. 170, no. 3, pp. 1435–1438, 2005.
[23]
O. Loudet, S. Chaillou, C. Camilleri, D. Bouchez, and F. Daniel-Vedele, “Bay-0 x Shahdara recombinant inbred line population: a powerful tool for the genetic dissection of complex traits in Arabidopsis,” Theoretical and Applied Genetics, vol. 104, no. 6-7, pp. 1173–1184, 2002.
[24]
Z. W. Luo, E. Potokina, A. Druka, R. Wise, R. Waugh, and M. J. Kearsey, “SFP genotyping from affymetrix arrays is robust but largely detects cis-acting expression regulators,” Genetics, vol. 176, no. 2, pp. 789–800, 2007.
[25]
C. Jiang and Z.-B. Zeng, “Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines,” Genetica, vol. 101, no. 1, pp. 47–58, 1997.
[26]
B. Dou, B. Hou, H. Xu, et al., “Efficient mapping of a female sterile gene in wheat (Triticum aestivum L.),” Genetics Research, vol. 91, no. 5, pp. 337–343, 2009.
