Bayesian Model Selection for Genome-Wide Epistatic Quantitative Trait Loci Analysis

Yi, Nengjun; Yandell, Brian S.; Churchill, Gary A.; Allison, David B.; Eisen, E. J.; Pomp, Daniel

doi:10.1534/genetics.104.040386

Cited by 125 publications

(251 citation statements)

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“…Extending R LR 2 to the REML approach needs further study because comparing models with different fixed or random terms is only valid under the ML framework (Littell et al, 2006). The relationship between model fit and model selection, particularly in genomic mapping, is beyond the scope of this study (Broman and Speed, 2002;Sillanpaa and Corander, 2002;Yi et al, 2005). We have no intention of using R LR 2 to conduct model selection because the monotonic nondecreasing property of R LR 2 does not indicate a better model as additional fixed or random effects are added.…”

Section: Discussionmentioning

confidence: 99%

Variation explained in mixed-model association mapping

et al. 2010

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Genomic mapping of complex traits across species demands integrating genetics and statistics. In particular, because it is easily interpreted, the R 2 statistic is commonly used in quantitative trait locus (QTL) mapping studies to measure the proportion of phenotypic variation explained by molecular markers. Mixed models with random polygenic effects have been used in complex trait dissection in different species. However, unlike fixed linear regression models, linear mixed models have no well-established R 2 statistic for assessing goodness-of-fit and prediction power. Our objectives were to assess the performance of several R 2 -like statistics for a linear mixed model in association mapping and to identify any such statistic that measures model-data agreement and provides an intuitive indication of QTL effect. Our results showed that the likelihood-ratio-based R 2 (R LR 2 ) satisfies several critical requirements proposed for the R 2 -like statistic. As R LR 2 reduces to the regular R 2 for fixed models without random effects other than residual, it provides a general measure for the effect of QTL in mixed-model association mapping. Moreover, we found that R LR 2 can help explain the overlap between overall population structure modeled as fixed effects and relative kinship modeled though random effects. As both approaches are derived from molecular marker information and are not mutually exclusive, comparing R LR Researchers in many disciplines use linear regression models widely. The R 2 statistic, the coefficient of determination, is one of the most frequently used measures of prediction power and goodness-of-fit for simple linear regression models (Draper and Smith, 1981;Everitt, 2002). In the literature on genetics, researchers often report R 2 values of newly identified genetic loci in addition to effect sizes and P-values (Lettre et al., 2008;Weedon et al., 2008). For nonstandard linear regression models, however, several competing R 2 -like statistics have been proposed to measure prediction power and goodness-of-fit (Buse, 1973;Magee, 1990;Xu, 2003;Kramer, 2005) but have not been used in genetics. Indeed, it is desirable to have a measure for general linear mixed models analogous in some ways to the R 2 of the linear regression model, which has a 'variation explained' interpretation.Association mapping searches the association between genetic markers and complex traits (for example disease susceptibility) based on populations (Hirschhorn and Daly, 2005). It complements linkage analysis in mapping the genetic basis of complex traits. Mixed models have long been used in genetic research (Henderson, 1984;Lynch and Walsh, 1998), and the mixed-model association mapping methods were developed to account for complex population structure (Meuwissen et al., 2002;Yu et al., 2006;Malosetti et al., 2007). Although statistics like deviance and the Bayesian Information Criterion (BIC) (Schwarz, 1978) can be used to select models (Broman and Speed, 2002;Littell et al., 2006), many researchers desire a R 2 -like stat...

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Section: Discussionmentioning

confidence: 99%

Variation explained in mixed-model association mapping

et al. 2010

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“…By assigning a maximum number of detectable QTLs and using latent binary variables to indicate which main and epistatic effects of putative QTLs are included in or excluded from the model, Yi et al (2005) first applied a (Yi et al, 2007b), the Bayesian mapping method can fairly quickly identify interacting QTLs for dynamic traits in models with large numbers of genetic effects. Generally, there are three types of epistatic interaction between QTLs: (1) where both QTLs are the main effect; (2) where both QTLs are not the main effect and (3) where only one QTL is the main effect.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, in Bayesian mapping for dynamic traits, choices of the upper bound L and specification of the prior on g and l should be the same as those for regular quantitative traits. As described by Yi et al (2005), we take L as l 0 þ 3Ol 0 , where l 0 is the prior expected number of QTLs and is determined according to initial investigations with traditional methods. The binary indicator g is assumed to have an independent prior pðgÞ ¼ Q w g ð1 À w Þ ð1Àg Þ , where w is the prior inclusion probability for a certain QTL effect and equals the predetermined hyperparameter w m for main effects or w e for epistatic effects, respectively.…”

Section: Genetic Modelmentioning

confidence: 99%

“…In fact, the unknown number of QTLs and the possibly huge number of epistatic effects make the issue extremely complex. A promising approach for solving the issue is the Bayesian model selection framework, which has been developed to identify epistatic QTL for regular quantitative traits (Yi et al, 2005(Yi et al, , 2007b and for ordinal traits (Yi et al, 2007a), but not for dynamic traits.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we will extend the Bayesian model selection for mapping interacting QTLs developed by Yi et al (2005Yi et al ( , 2007b to dynamic traits in experimental crosses. The extension is realized by embedding the Legendre polynomials in QTL effects and taking into account the individual-specific time-dependent random environmental effects in the genetic model.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian analysis for genetic architecture of dynamic traits

et al. 2010

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The dissection of the genetic architecture of quantitative traits, including the number and locations of quantitative trait loci (QTL) and their main and epistatic effects, has been an important topic in current QTL mapping. We extend the Bayesian model selection framework for mapping multiple epistatic QTL affecting continuous traits to dynamic traits in experimental crosses. The extension inherits the efficiency of Bayesian model selection and the flexibility of the Legendre polynomial model fitting to the change in genetic and environmental effects with time. We illustrate the proposed method by simultaneously detecting the main and epistatic QTLs for the growth of leaf age in a doubled-haploid population of rice. The behavior and performance of the method are also shown by computer simulation experiments. The results show that our method can more quickly identify interacting QTLs for dynamic traits in the models with many numbers of genetic effects, enhancing our understanding of genetic architecture for dynamic traits. Our proposed method can be treated as a general form of mapping QTL for continuous quantitative traits, being easier to extend to multiple traits and to a single trait with repeat records.

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Mapping Quantitative Trait Loci in Outbred Pedigrees

Höschele¹

2007

Handbook of Statistical Genetics

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In this chapter, we present statistical methods for mapping quantitative-trait loci (QTLs) in outbred or complex pedigrees. Such pedigrees exist primarily in livestock populations, also in human populations, and occasionally in experimental animal or plant populations. The main focus of this chapter is on linkage mapping, but methods for linkage disequilibrium (LD) and combined linkage/LD mapping are also discussed. We describe least-squares and maximum likelihood (ML) methods for estimating QTL effects, and variance-components analysis by approximate (residual) ML for estimating QTL variance contributions. We describe Bayesian QTL mapping, its prior distributions and other distributional assumptions, its implementation via Markov chain Monte Carlo (MCMC) algorithms, its inferences, and contrast it with frequentist methodology. Genotype sampling algorithms using genotypic peeling, allelic peeling or descent graphs are described. Genotype samplers are a critical component of MCMC algorithms implementing ML and Bayesian analyses for complex pedigrees. Lastly, fine-mapping methods including chromosome dissection and LD mapping using current and historical recombinations, respectively, are outlined, and recently developed methods for joint LD and linkage mapping of disease genes and QTL are discussed. INTRODUCTIONIn this chapter, the focus is on statistical methods for mapping of quantitative-trait loci (QTLs) in populations which have not been formed recently by line crossing, and which have pedigree information available over multiple generations. Methods suitable for QTL mapping in (inbred) line crosses are described in Chapter 18. Pedigrees are used for QTL mapping in livestock and human populations, where the development and crossing of inbred lines is not feasible. Therefore, the methods discussed here have applications primarily in mapping genes for quantitative traits of economic importance in livestock and complex disease risk factors in humans. Examples include milk production in dairy 623 Handbook of Statistical Genetics, Third Edition . E dited by D . J. Balding, M . Bishop and C. Cannings.

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Bayesian Model Selection for Genome-Wide Epistatic Quantitative Trait Loci Analysis

Cited by 125 publications

References 45 publications

Variation explained in mixed-model association mapping

Variation explained in mixed-model association mapping

Bayesian analysis for genetic architecture of dynamic traits

Mapping Quantitative Trait Loci in Outbred Pedigrees

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