Bayesian analysis of mixed linear models  via Gibbs sampling with an application  to litter size in Iberian pigs

Cs, Wang; Rutledge, J.J.; Gianola, D.

doi:10.1051/gse:19940202

Cited by 90 publications

(114 citation statements)

References 20 publications

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“…In each of the mapping procedures, permutation test was exploited to control genome-wide false positive rate. Parameters of the full-QTL model were estimated using a Bayesian method via Gibbs sampling (Wang et al 1994). A relative contribution was calculated as the proportion of variance caused by a specific genetic source in the total phenotypic variance, and the general contribution for each genetic source was calculated from the relative contributions of all the putative QTL involved.…”

Section: Discussionmentioning

confidence: 99%

QTL mapping for test weight by using F 2:3 population in maize

Ding

Zhang

et al. 2011

J Genet

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Test weight is an important trait in maize breeding. Understanding the genetic mechanism of test weight is important for effective selection of maize test weight improvement. In this study, quantitative trait loci (QTL) for maize test weight were identified. In the years 2007 and 2008, a F(2:3) population along with the parents Chang7-2 and Zheng58 were planted in Zhengzhou, People's Republic of China. Significant genotypic variation for maize test weight was observed in both years. Based on the genetic map containing 180 polymorphic SSR markers with an average linkage distance of 11.0 cM, QTL for maize test weight were analysed by mixed-model composite interval mapping. Five QTL, including four QTL with only additive effects, were identified on chromosomes 1, 2, 3, 4 and 5, and together explained 25.2% of the phenotypic variation. Seven pairs of epistatic interactions were also detected, involving 11 loci distributed on chromosomes 1, 2, 3, 4, 5 and 7, respectively, which totally contributed 18.2% of the phenotypic variation. However, no significant QTL x environment (QxE) interaction and epistasis x environment interaction effects were detected. The results showed that besides the additive QTL, epistatic interactions also formed an important genetic basis for test weight in maize.

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Section: Discussionmentioning

confidence: 99%

QTL mapping for test weight by using F 2:3 population in maize

Ding

Zhang

et al. 2011

J Genet

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“…An F test was executed at all stepwise model selection procedures. The Bayesian method using Gibbs sampling (Wang 1994) as a type of Markov Chain Monte Carlo (MCMC) was used to estimate parameters in the model without the consideration for the distribution of canopy wilting. For each sequential model in one-and two-genome scans, a permutation test (1000 times) (Churchill and Doerge 1994) was applied for new coefficient terms in the model (Yang et al 2007) to determine the empirical experiment-wise false-positive rate.…”

Section: Qtl Analysis and Mappingmentioning

confidence: 99%

Confirmation of delayed canopy wilting QTLs from multiple soybean mapping populations

et al. 2015

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QTLs for delayed canopy wilting from five soybean populations were projected onto the consensus map to identify eight QTL clusters that had QTLs from at least two independent populations. Quantitative trait loci (QTLs) for canopy wilting were identified in five recombinant inbred line (RIL) populations, 93705 KS4895 × Jackson, 08705 KS4895 × Jackson, KS4895 × PI 424140, A5959 × PI 416937, and Benning × PI 416937 in a total of 15 site-years. For most environments, heritability of canopy wilting ranged from 0.65 to 0.85 but was somewhat lower when averaged over environments. Putative QTLs were identified with composite interval mapping and/or multiple interval mapping methods in each population and positioned on the consensus map along with their 95% confidence intervals (CIs). We initially found nine QTL clusters with overlapping CIs on Gm02, Gm05, Gm11, Gm14, Gm17, and Gm19 identified from at least two different populations, but a simulation study indicated that the QTLs on Gm14 could be false positives. A QTL on Gm08 in the 93705 KS4895 × Jackson population co-segregated with a QTL for wilting published previously in a Kefeng1 × Nannong 1138-2 population, indicating that this may be an additional QTL cluster. Excluding the QTL cluster on Gm14, results of the simulation study indicated that the eight remaining QTL clusters and the QTL on Gm08 appeared to be authentic QTLs. QTL × year interactions indicated that QTLs were stable over years except for major QTLs on Gm11 and Gm19. The stability of QTLs located on seven clusters indicates that they are possible candidates for use in marker-assisted selection.

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“…Using well known results (e.g., Wang et al 1993Wang et al , 1994Sorensen and Gianola 2002) it can be shown that…”

Section: Conditional Posterior Distribution Of Genomic Effectsmentioning

confidence: 96%

“…As shown by Wang et al (1993Wang et al ( , 1994) the conditional posterior distribution of b given everything else is the multivariate normal process…”

Section: Conditional Posterior Distributions Of Other Location and DImentioning

confidence: 98%

A non-parametric mixture model for genome-enabled prediction of genetic value for a quantitative trait

Gianola

Manfredi³

et al. 2010

Genetica

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A Bayesian nonparametric form of regression based on Dirichlet process priors is adapted to the analysis of quantitative traits possibly affected by cryptic forms of gene action, and to the context of SNP-assisted genomic selection, where the main objective is to predict a genomic signal on phenotype. The procedure clusters unknown genotypes into groups with distinct genetic values, but in a setting in which the number of clusters is unknown a priori, so that standard methods for finite mixture analysis do not work. The central assumption is that genetic effects follow an unknown distribution with some "baseline" family, which is a normal process in the cases considered here. A Bayesian analysis based on the Gibbs sampler produces estimates of the number of clusters, posterior means of genetic effects, a measure of credibility in the baseline distribution, as well as estimates of parameters of the latter. The procedure is illustrated with a simulation representing two populations. In the first one, there are 3 unknown QTL, with additive, dominance and epistatic effects; in the second, there are 10 QTL with additive, dominance and additive × additive epistatic effects. In the two populations, baseline parameters are inferred correctly. The Dirichlet process model infers the number of unique genetic values correctly in the first population, but it produces an understatement in the second one; here, the true number of clusters is over 900, and the model gives a posterior mean estimate of about 140, probably because more replication of genotypes is needed for correct inference. The impact on inferences of the prior distribution of a key parameter (M), and of the extent of replication, was examined via an analysis of mean body weight in 192 paternal half-sib families of broiler chickens, where each sire was genotyped for nearly 7,000 SNPs. In this small sample, it was found that inference about the number of clusters was affected by the prior distribution of M. For a set of combinations of parameters of a given prior distribution, the effects of the prior dissipated when the number of replicate samples per genotype was increased. Thus, the Dirichlet process model seems to be useful for gauging the number of QTLs affecting the trait: if the number of clusters inferred is small, probably just a few QTLs code for the trait. If the number of clusters inferred is large, this may imply that standard parametric models based on the baseline distribution may suffice. However, priors may be influential, especially if sample size is not large and if only a few genotypic configurations have replicate phenotypes in the sample.

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Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs

Cited by 90 publications

References 20 publications

QTL mapping for test weight by using F 2:3 population in maize

QTL mapping for test weight by using F 2:3 population in maize

Confirmation of delayed canopy wilting QTLs from multiple soybean mapping populations

A non-parametric mixture model for genome-enabled prediction of genetic value for a quantitative trait

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