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Bayesian functional mapping of dynamic quantitative traits

Abstract

Without consideration of other linked QTLs responsible for dynamic trait, original functional mapping based on a single QTL model is not optimal for analyzing multiple dynamic trait loci. Despite that composite functional mapping incorporates the effects of genetic background outside the tested QTL in mapping model, the arbitrary choice of background markers also impact on the power of QTL detection. In this study, we proposed Bayesian functional mapping strategy that can simultaneously identify multiple QTL controlling developmental patterns of dynamic traits over the genome. Our proposed method fits the change of each QTL effect with the time by Legendre polynomial and takes the residual covariance structure into account using the first autoregressive equation. Also, Bayesian shrinkage estimation was employed to estimate the model parameters. Especially, we specify the gamma distribution as the prior for the first-order auto-regressive coefficient, which will guarantee the convergence of Bayesian sampling. Simulations showed that the proposed method could accurately estimate the QTL parameters and had a greater statistical power of QTL detection than the composite functional mapping. A real data analysis of leaf age growth in rice is used for the demonstration of our method. It shows that our Bayesian functional mapping can detect more QTLs as compared to composite functional mapping.

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References

  1. Gao HJ, Yang RQ (2006) Composite interval mapping of QTL for dynamic traits. Chin Sci Bull 51(15):1857–1862

  2. Gianola D, Perez-Enciso M, Toro MA (2003) On marker-assisted prediction of genetic value: beyond the ridge. Genetics 163(1):347–365

  3. Giraldo J (2003) Empirical models and Hill coefficients. Trends Pharmacol Sci 24(2):63–65

  4. Henderson CR Jr (1982) Analysis of covariance in the mixed model: higher-level, nonhomogeneous, and random regressions. Biometrics 38(3):623–640

  5. Jansen RC, Stam P (1994) High resolution of quantitative traits into multiple loci via interval mapping. Genetics 136(4):1447–1455

  6. Kirkpatrick M, Heckman N (1989) A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J Math Biol 27(4):429–450

  7. Kirkpatrick M, Lofsvold D, Bulmer M (1990) Analysis of the inheritance, selection and evolution of growth trajectories. Genetics 124(4):979–993

  8. Lander ES, Botstein D (1989) Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121(1):185–199

  9. Ma CX, Casella G, Wu R (2002) Functional mapping of quantitative trait loci underlying the character process: a theoretical framework. Genetics 161(4):1751–1762

  10. Macgregor S, Knott SA, White I, Visscher PM (2005) Quantitative trait locus analysis of longitudinal quantitative trait data in complex pedigrees. Genetics 171(3):1365–1376

  11. Perelson AS, Neumann AU, Markowitz M, Leonard JM, Ho DD (1996) HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science 271(5255):1582–1586

  12. Schaeffer LR (2004) Application of random regression models in animal breeding. Livest Prod Sci 86(3):35–45

  13. Sen S, Churchill GA (2001) A statistical framework for quantitative trait mapping. Genetics 159(1):371–387

  14. Sillanpää MJ, Arjas E (1998) Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data. Genetics 148(3):1373–1388

  15. Sillanpää MJ, Arjas E (1999) Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. Genetics 151(4):1605–1619

  16. Tobalske BW, Hedrick TL, Dial KP, Biewener AA (2003) Comparative power curves in bird flight. Nature 421(6921):363–366

  17. Wang H, Zhang YM, Li X, Masinde GL, Mohan S, Baylink DJ, Xu S (2005) Bayesian shrinkage estimation of quantitative trait loci parameters. Genetics 170(1):465–480

  18. Weng QM, Wu WR, Li WM, Liu HQ, Tang DZ, Zhou YC, Zhang QF (2000) Construction of an RFLP linkage map of rice using DNA probes from two different sources. J Fujian Agric Univ 29(2):129–133

  19. Wu R, Ma CX, Littell RC, Wu SS, Yin T, Huang M, Wang M, Casella G (2002) A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories. Genet Res 79(3):235–245

  20. Wu R, Ma CX, Zhao W, Casella G (2003) Functional mapping for quantitative trait loci governing growth rates: a parametric model. Physiol Genomics 14(3):241–249

  21. Wu R, Ma CX, Lin M, Casella G (2004a) A general framework for analyzing the genetic architecture of developmental characteristics. Genetics 166(3):1541–1551

  22. Wu RL, Ma CX, Lin M, Wang ZH, George C (2004b) Functional mapping of quantitative trait loci underlying growth trajectories using a transform-both-sides logistic model. Biometrics 60(4):729–738

  23. Xu S (2007) Derivation of the shrinkage estimates of quantitative trait locus effects. Genetics 177(2):1255–1258

  24. Yang R, Xu S (2007) Bayesian shrinkage analysis of quantitative trait loci for dynamic traits. Genetics 176(2):1169–1185

  25. Yang R, Tian Q, Xu S (2006) Mapping quantitative trait loci for longitudinal traits in line crosses. Genetics 173(4):2339–2356

  26. Yang R, Gao H, Wang X, Zhang J, Zeng ZB, Wu R (2007) A semiparametric approach for composite functional mapping of dynamic quantitative traits. Genetics 177(3):1859–1870

  27. Yi N, Xu S (2000a) Bayesian mapping of quantitative trait loci for complex binary traits. Genetics 155(3):1391–1403

  28. Yi N, Xu S (2000b) Bayesian mapping of quantitative trait loci under the identity-by-descent-based variance component model. Genetics 156(1):411–422

  29. Yi N, George V, Allison DB (2003a) Stochastic search variable selection for identifying multiple quantitative trait loci. Genetics 164(3):1129–1138

  30. Yi N, Xu S, Allison DB (2003b) Bayesian model choice and search strategies for mapping interacting quantitative trait loci. Genetics 165(2):867–883

  31. Yi N, Yandell BS, Churchill GA, Allison DB, Eisen EJ, Pomp D (2005) Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics 170(3):1333–1344

  32. Zeng ZB (1994) Precision mapping of quantitative trait loci. Genetics 136(4):1457–1468

  33. Zhang YM, Xu S (2005) Advanced statistical methods for detecting multiple quantitative trait loci. Recent Res Devel Genet Breed 2(1):1–23

  34. Zhao W, Chen YQ, Casella G, Cheverud JM, Wu R (2005) A non-stationary model for functional mapping of complex traits. Bioinformatics 21(10):2469–2477

  35. Zhou Y, Li W, Wu W, Chen Q, Mao D, Worland J (2001) Genetic dissection of heading time and its components in rice. Theor Appl Genet 102(8):1236–1242

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Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (30972077).

Author information

Correspondence to Runqing Yang.

Additional information

Communicated by F. van Eeuwijk.

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Cite this article

Yang, R., Li, J., Wang, X. et al. Bayesian functional mapping of dynamic quantitative traits. Theor Appl Genet 123, 483–492 (2011). https://doi.org/10.1007/s00122-011-1601-0

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Keywords

  • Markov Chain Monte Carlo
  • Legendre Polynomial
  • Functional Mapping
  • Autoregressive Coefficient
  • Conditional Posterior Distribution