Bayesian shrinkage mapping for multiple QTL in half-sib families

Heredity (2009) 103, 368–376 & 2009 Macmillan Publishers Limited All rights reserved 0018-067X/09 $32.00 ORIGINAL ARTICLE www.nature.com/hdy Bayesian shrinkage mapping for multiple QTL in half-sib families H Gao1,2, M Fang1,3, J Liu1 and Q Zhang1 State Key Laboratory of AgroBiotechnology, Key Laboratory of Animal Genetics and Breeding of the Ministry of Agriculture, College of Animal Science and Technology, China Agricultural University, Beijing, China; 2College of Animal Science and Technology, North-East Agricultural University, Harbin, China and 3Life Science College, Heilongjiang August First Land Reclamation University, Daqing, China 1 Recently, an effective Bayesian shrinkage estimation method has been proposed for mapping QTL in inbred line crosses. However, with regard to outbred populations, such as half-sib populations with maternal information unavailable, it is not straightforward to utilize such a shrinkage estimation for QTL mapping. The reasons are: (1) the linkage phase of markers in the outbred population is usually unknown; and (2) only paternal genotypes can be used for inferring QTL genotypes of offspring. In this article, a novel Bayesian shrinkage method was proposed for mapping QTL under the half-sib design using a mixed model. A simulation study clearly demonstrated that the proposed method was powerful for detecting multiple QTL. In addition, we applied the proposed method to map QTL for economic traits in the Chinese dairy cattle population. Two or more novel QTL harbored in the chromosomal region were detected for each trait of interest, whereas only one QTL was found using traditional maximum likelihood analyses in our earlier studies. This further validated that our shrinkage estimation method could perform well in empirical data analyses and had practical significance in the field of linkage studies for outbred populations. Heredity (2009) 103, 368–376; doi:10.1038/hdy.2009.71; published online 15 July 2009 Keywords: Bayesian shrinkage analysis; outbred population; multiple QTL Introduction Many economically important traits and disease-resistant traits in animals are controlled by multiple genes, and the locations of these genes on the chromosomes are called quantitative-trait loci (QTL). With the development of molecular technology, these QTL can be localized and eventually the actual genes within these QTL can be cloned. Outbred populations are very ubiquitous in domestic animals; moreover, paternal half-sib families are quite often used for mapping QTL in such populations, in which the phenotypes of the offspring and genotypes of paternal parents and offspring are used in the analysis. Numerous QTL mapping methods for half-sib design have been proposed. Georges et al. (1995) developed a maximum likelihood method for single-family analysis and implemented it to map QTL of milk production traits in the US Holstein population. The regression method of interval mapping proposed by Knott et al. (1996) is a common method used to map QTL in half-sib families, particularly in dairy cattle (Fulker and Cardon, 1994; Spelman et al., 1996; Zhang et al., 1998; Velmala et al., 1999; Heyen et al., 1999; de Koning et al., 2001; Nadesalingam et al., 2001; Ron et al., 2001; Plante et al., Correspondence: Professor Q Zhang, College of Animal Science and Technology, China Agricultural University, Beijing, 100094, People0 s Republic of China. E-mail: qzhang @ cau.edu.cn Received 1 December 2008; revised 11 May 2009; accepted 15 May 2009; published online 15 July 2009 2001; Freyer et al., 2002; Rodriguez-Zas et al., 2002; Viitala et al., 2003). Grignola et al. (1996a, b) proposed a restricted maximum likelihood method and it was used by Zhang et al. (1998); Freyer et al. (2002) and Liu et al. (2004) to map QTL in Holstein populations in America, Germany and Canada, respectively. All these methods are based on models of a single QTL, and are hard to be extended to handle multiple QTL. If the trait is controlled by multiple QTL, the single QTL model-based estimation of QTL position and effect may be biased because of the presence of multiple linked QTL on the same chromosome. In the situation where the effects of two-linked QTL are in the opposite direction, the QTL effects may cancel out each other and none of them can be detected. On the other hand, if their effects are in the same direction, a ‘ghost’ QTL may be mapped between the two real QTLs. To overcome the above problems, Jansen (1993) and Zeng (1994) independently proposed a composite interval mapping (CIM) method. The major problem in the CIM method is that it is difficult to determine the number of markers as cofactors, because too many nuisance markers will decrease the detection power and too few markers cannot control the genetic background. Kao et al. (1999) proposed a multiple interval mapping (MIM) approach that took multiple QTL simultaneously into consideration. However, MIM only detects epistasis between main-effect QTL and cannot identify QTL with small effects. Furthermore, the CIM and MIM methods were originally developed for QTL mapping in inbred populations rather than outbred populations. Recently, Bayesian approach has been developed for mapping multiple QTLs, in which the number of QTL is Bayesian shrinkage mapping H Gao et al 369 considered as a parameter to be estimated. Within the Bayesian multiple QTL mapping framework, several algorithms have been proposed, such as the reversible jump Markov chain Monte Carlo (RJMCMC) (Sillanpää and Arjas, 1998; Stephens and Fisch, 1998), the stochastic search variable selection (SSVS) (Yi, 2004) and the Bayesian shrinkage method (Xu, 2003; Wang et al., 2005; Xu, 2007). The key feature of the RJMCMC algorithm is that the number of QTL is treated as an unknown model parameter and is estimated through Bayesian model selection. A shortcoming of RJMCMC is that the Markov chain may converge slowly and have a poor mixing character due to model dimension changing with the number of QTL (Satagopan and Yandell, 1996; Yi and Xu, 2002; Liu et al., 2007; Yi et al., 2007). Compared with RJMCMC, SSVS and the Bayesian shrinkage estimation can overcome this issue to some extent. In SSVS, a previous mixture is adopted to explicitly make a probabilistic statement about the inclusion of a QTL, and the markers with significant effects can be identified as those with higher posterior probabilities involved in the model (Yi, 2004). In the Bayesian shrinkage analysis, each marker or marker interval is assumed to be associated with one QTL. If a marker or a marker interval is not associated with any QTL, the corresponding QTL effect will be shrunk toward zero. Accordingly, both SSVS and the Bayesian shrinkage estimation can largely avoid the problems existing in RJMCMC (Xu et al., 2005; Yang et al., 2006, 2007). A specific advantage of the Bayesian shrinkage estimation is that it can handle the situation where the number of unknown parameters is more t (...truncated)