Skip to main content Accessibility help
×
Home

Bayesian B-spline mapping for dynamic quantitative traits

  • JUN XING (a1), JIAHAN LI (a2), RUNQING YANG (a3) (a4), XIAOJING ZHOU (a5) and SHIZHONG XU (a6)...

Summary

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Bayesian B-spline mapping for dynamic quantitative traits
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Bayesian B-spline mapping for dynamic quantitative traits
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Bayesian B-spline mapping for dynamic quantitative traits
      Available formats
      ×

Copyright

Corresponding author

*Corresponding author: School of Agriculture and Biology, Shanghai Jiaotong University, Shanghai 200240, People's Republic of China. Tel: (8621) 34206146. Fax: (8621) 34206146. E-mail: runqingyang@sjtu.edu.cn

References

Hide All
de Boor, C. (2001). A Practical Guide to Splines, Vol. 27, 2nd edn. New York: Springer-Verlag.
Friedman, J. H. & Silverman, B. W. (1989). Flexible parsimonious smoothing and additive modeling. Technometrics 31, 3–21.
Gelman, A., Carlin, J. B., Stern, H. S. & Rubin, D. B. (1995). Bayesian Data Analysis. New York: Chapman & Hall.
Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109.
Henderson, C. R. (1982). Analysis of covariance in the mixed model: higher-level, nonhomogeneous, and random regressions. Biometrics 38, 623640.
Jamrozik, J., Schaeffer, L. R. & Dekkers, J. C. M. (1997). Genetic evaluation of dairy cattle using test day yields and random regression model. Journal of Dairy Science 80, 12171226.
Jin, T., Li, J., Guo, Y., Zhou, X., Yang, R. & Wu, R. (2010). An optimal strategy for functional mapping of dynamic trait loci. Genetical Research 3, 18.
Kooperberg, C. & Stone, C. J. (1991). A study of logspline density estimation. Computational Statistics and Data Analysis 12, 327348.
Kooperberg, C. & Stone, C. J. (1992). Logspline density estimation for censored data. Journal of Computational and Graphical Statistics 1, 301328.
Ma, C. X., Casella, G. & Wu, R. (2002). Functional mapping of quantitative trait loci underlying the character process: a theoretical framework. Genetics 161, 17511762.
Macgregor, S., Knott, S. A., White, I. & Visscher, P. M. (2005). Quantitative trait locus analysis of longitudinal quantitative trait data in complex pedigrees. Genetics 171, 13651376.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 10871092.
Min, A. & Czado, C. (2011). Bayesian model selection for D-vine pair-copula constructions. Canadian Journal of Statistics 2, 239258.
Ruppert, D., Wand, M. P. & Carroll, R. J. (2003). Semiparametric Regression. New York: Cambridge University Press.
Schaeffer, L. R. (2004). Application of random regression models in animal breeding. Livestock Production Science 86, 3545.
Sen, Ś. & Churchill, G. A. (2001). A statistical framework for quantitative trait mapping. Genetics 159, 371387.
Sillanpää, M. J. & Arjas, E. (1998). Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data. Genetics 148, 13731388.
Sillanpää, M. J. & Arjas, E. (1999). Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics 151, 16051619.
Wang, H., Zhang, Y. M., Li, X., Masinde, G. L., Mohan, S., Baylink, D. J. & Xu, S. (2005). Bayesian shrinkage estimation of quantitative trait loci parameters. Genetics 170, 465480.
Wahba, G. (1990). Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics 59. Philadelphia, PA: SIAM.
Wu, R., Ma, C. X., Littell, R. C., Wu, S. S., Yin, T., Huang, M., Wang, M. & Casella, G. (2002). A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories. Genetical Research 79, 235245.
Wu, R. L., Ma, C. X., Lin, M., Wang, Z. H. & George, C. (2004). Functional mapping of quantitative trait loci underlying growth trajectories using a transform-both-sides logistic model. Biometrics 60, 729738.
Wu, R., Ma, C. X., Zhao, W. & Casella, G. (2003). Functional mapping for quantitative trait loci governing growth rates: a parametric model. Physiological Genomics 14, 241249.
Yang, J., Wu, R. & Casella, G. (2009). Nonparametric functional mapping of quantitative trait loci. Biometrics 65, 3039.
Yang, R., Gao, H., Wang, X., Zhang, J., Zeng, Z. B. & Wu, R. (2007). A semiparametric approach for composite functional mapping of dynamic quantitative traits. Genetics 177, 18591870.
Yang, R., Tian, Q. & Xu, S. (2006). Mapping quantitative trait loci for longitudinal traits in line crosses. Genetics 173, 23392356.
Yang, R. & Xu, S. (2007). Bayesian shrinkage analysis of quantitative trait loci for dynamic traits. Genetics 176, 11691185.
Yi, N. & Xu, S. (2000 a). Bayesian mapping of quantitative trait loci for complex binary traits. Genetics 155, 13911403.
Yi, N. & Xu, S. (2000 b). Bayesian mapping of quantitative trait loci under the identity-by-descent-based variance component model. Genetics 156, 411422.
Yi, N., Yandell, B. S., Churchill, G. A., Allison, D. B., Eisen, E. J. & Pomp, D. (2005). Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics 170, 13331344.
Zhang, Y. M. & Xu, S. (2005). Advanced statistical methods for detecting multiple quantitative trait loci. Recent Research Developments in Genetics and Breeding 2, 123.

Bayesian B-spline mapping for dynamic quantitative traits

  • JUN XING (a1), JIAHAN LI (a2), RUNQING YANG (a3) (a4), XIAOJING ZHOU (a5) and SHIZHONG XU (a6)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed