Skip to main content

Advertisement

SpringerLink
Log in

Identifying QTLs and Epistasis in Structured Plant Populations Using Adaptive Mixed LASSO

  • Published:
Journal of Agricultural, Biological, and Environmental Statistics Aims and scope Submit manuscript

Abstract

Association analysis in important crop species has generated heightened interest for its potential in dissecting complex traits by utilizing diverse mapping populations. However, the mixed linear model approach is currently limited to single marker analysis, which is not suitable for studying multiple QTL effects, epistasis and gene by environment interactions. In this paper, we propose the adaptive mixed LASSO method that can incorporate a large number of predictors (genetic markers, epistatic effects, environmental covariates, and gene by environment interactions) while simultaneously accounting for the population structure. We show that the adaptive mixed LASSO estimator possesses the oracle property of adaptive LASSO. Algorithms are developed to iteratively estimate the regression coefficients and variance components. Our results demonstrate that the adaptive mixed LASSO method is very promising in modeling multiple genetic effects when a large number of markers are available and the population structure cannot be ignored. It is expected to be a powerful tool for studying the architecture of complex traits in important plant species. Supplemental materials for this article are available from the journal website.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akbari, M., Wenzl, P., Caig, V., Carling, J., Xia, L., Yang, S., Uszynski, G., Mohler, V., Lehmensiek, A., Kuchel, H., Hayden, M. J., Howes, N., Sharp, P., Vaughan, P., Rathmell, B., Huttner, E., and Kilian, A. (2006), “Diversity Arrays Technology (DArT) for High-throughput Profiling of the Hexaploid Wheat Genome,” Theoretical and Applied Genetics, 113, 1409–1420.

    Article  Google Scholar 

  • Ball, R. D. (2001), “Bayesian Methods for Quantitative Trait Loci Mapping Based on Model Selection: Approximate Analysis Using the Bayesian Information Criterion,” Genetics, 159, 1351–1364.

    Google Scholar 

  • Bondell, H. D., Krishna, A., and Ghosh, S. K. (2010), “Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models,” Biometrics, doi:10.1111/j.1541-0420.2010.01391.x.

  • Broman, K. W., and Speed, T. P. (2002), “A Model Selection Approach for the Identification of Quantitative Trait Loci in Experimental Crosses,” Journal of the Royal Statistical Society Series B, 64, 641–656.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, J., and Chen, Z. (2008), “Extended Bayesian Information Criterion for Model Selection with Large Model Spaces,” Biometrika, 95, 759–771.

    Article  MathSciNet  MATH  Google Scholar 

  • Crossa, J., Burgueno, J., Dreisigacker, S., Vargas, M., Herrera-Foessel, S. A., Lillemo, M., Singh, R. P., Trethowan, R., Warburton, M., Franco, J., Reynolds, M., Crouch, J. H., and Ortiz, R. (2007), “Association Analysis of Historical Bread Wheat Germplasm Using Additive Genetic Covariance of Relatives and Population Structure,” Genetics, 177, 1889–1913.

    Article  Google Scholar 

  • de los Campos, G., Naya, H., Gianola, D., Crossa, J., Legarra, A., Manfredi, E., Weigel, K., and Cotes, J. M. (2009), “Predicting Quantitative Traits with Regression Models for Dense Molecular Markers and Pedigree,” Genetics, 182, 375–385.

    Article  Google Scholar 

  • Devlin, B., and Roeder, K. (1999), “Genomic Control for Association Studies,” Biometrics, 55, 997–1004.

    Article  MATH  Google Scholar 

  • Dudley, J. W. (2008), “Epistatic Interactions in Crosses of Illinois High Oil x Illinois Low Oil and of Illinois High Protein x Illinois Oil Protein Corn Strains,” Crop Science, 48, 59–68.

    Article  Google Scholar 

  • Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression,” Annals of Statistics, 32, 407–499.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultra-High Dimensional Feature Space” (with discussion), Journal of the Royal Statistical Society Series B, 70, 849–911.

    Article  MathSciNet  Google Scholar 

  • Foster, S. D., Verbyla, A. P., and Pitchford, W. S. (2007), “Incorporating LASSO Effects into a Mixed Model for Quantitative Trait Loci Detection,” Journal of Agricultural, Biological, and Environmental Statistics, 12, 300–314.

    Article  MathSciNet  Google Scholar 

  • Friedman, J., Hastie, T., Hoefling, H., and Tibshirani, R. (2007), “Pathwise Coordinate Optimization,” Annals of Applied Statistics, 1, 302–332.

    Article  MathSciNet  MATH  Google Scholar 

  • Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.), New York: Springer.

    MATH  Google Scholar 

  • Ibrahim, J. G., Zhu, H., Garcia, R. I., and Guo, R. (2010), “Fixed and Random Effects Selection in Mixed Effects Models,” Biometrics, doi:10.1111/j.1541-0420.2010.01463.x.

  • Jansen, R. C. (1993), “Interval Mapping of Multiple Quantitative Trait Loci,” Genetics, 135, 205–211.

    Google Scholar 

  • Jansen, R. C., and Stam, P. (1994), “High Resolution of Quantitative Traits into Multiple Loci via Interval Mapping,” Genetics, 136, 1447–1455.

    Google Scholar 

  • Kang, H. M., Zaitlen, N. A., Wade, C. M., Kirby, A., Heckerman, D., Daly, M. J., and Eskin, E. (2008), “Efficient Control of Population Structure in Model Organism Association Mapping,” Genetics, 178, 1709–1723.

    Article  Google Scholar 

  • Kao, C.-H., Zeng, Z.-B., and Teasdale, R. D. (1999), “Multiple Interval Mapping for Quantitative Trait Loci,” Genetics, 152, 1203–1216.

    Google Scholar 

  • Meuwissen, T. H. E., Hayes, B. J., and Goddard, M. E. (2001), “Prediction of Total Genetic Value Using Genome-Wide Dense Marker Maps,” Genetics, 157, 1819–1829.

    Google Scholar 

  • Park, T., and Casella, G. (2008), “The Bayesian LASSO,” Journal of the American Statistical Association, 103, 681–686.

    Article  MathSciNet  MATH  Google Scholar 

  • Price, A. L., Patterson, N. J., Plenge, R. M., Weinblatt, M. E., Shadick, N. A., and Reich, D. (2006), “Principal Components Analysis Corrects for Stratification in Genome-Wide Association Studies,” Nature Genetics, 38, 904–909.

    Article  Google Scholar 

  • Pritchard, J. K., Stephens, M., and Donnelly, P. (2000), “Inference of Population Structure Using Multilocus Genotype Data,” Genetics, 155, 945–959.

    Google Scholar 

  • Stich, B., Möhring, J., Piepho, H. P., Heckenberger, M., Buckler, E. S., and Melchinger, A. E. (2008), “Comparison of Mixed-Model Approaches for Association Mapping,” Genetics, 178, 1745–1754.

    Article  Google Scholar 

  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society Series B, 58, 267–288.

    MathSciNet  MATH  Google Scholar 

  • Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., and Knight, K. (2005), “Sparsity and Smoothness via the Fused Lasso,” Journal of the Royal Statistical Society Series B, 67, 91–108.

    Article  MathSciNet  MATH  Google Scholar 

  • Tibshirani, R., and Wang, P. (2008), “Spatial Smoothing and Hot Spot Detection for CGH Data Using the Fused Lasso,” Biostatistics, 9, 18–29.

    Article  MATH  Google Scholar 

  • Varshney, R. K., and Tuberosa, R. (2007), “Genomics-Assisted Crop Improvement: An Overview,” in Genomics-Assisted Crop Improvement, eds. R.K. Varshney and R. Ruberosa, Dordrecht, the Netherlands: Springer, pp. 1–12.

    Chapter  Google Scholar 

  • Wang, H., Zhang, Y.-M., Li, X., Masinde, G. L., Mohan, S., Baylink, D. J., and Xu, S. (2005), “Bayesian Shrinkage Estimation of Quantitative Trait Loci Parameters,” Genetics, 170, 465–480.

    Article  Google Scholar 

  • Wu, T. T., Chen, Y. F., Hastie, T., Sobel, E., and Lange, K. (2009), “Genome-Wide Association Analysis by Lasso Penalized Logistic Regression,” Bioinformatics, 25, 714–721.

    Article  Google Scholar 

  • Xu, S. (2003), “Estimating Polygenetic Effects Using Markers of the Entire Genome,” Genetics, 163, 789–801.

    Google Scholar 

  • — (2007), “An Empirical Bayes Method for Estimating Epistatic Effects of Quantitative Trait Loci,” Biometrics, 63, 513–521.

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, S., and Jia, Z. (2007), “Genomewide Analysis of Epistatic Effects for Quantitative Traits in Barley,” Genetics, 175, 1955–1963.

    Article  Google Scholar 

  • Xu, Y., and Crouch, J. H. (2008), “Marker-Assisted Selection in Plant Breeding: From Publications to Practice,” Crop Science, 48, 391–407.

    Article  Google Scholar 

  • Yi, N., and Xu, S. (2008), “Bayesian LASSO for Quantitative Trait Loci Mapping,” Genetics, 179, 1045–1055.

    Article  Google Scholar 

  • Yu, J., Pressoir, G., Briggs, W. H., Vroh Bi, I., Yamasaki, M., Doebley, J. F., McMullen, M. D., Gaut, B. S., Nielsen, D. M., Holland, J. B., Kresovich, S., and Buckler, E. S. (2006), “A Unified Mixed-Model Method for Association Mapping that Accounts for Multiple Levels of Relatedness,” Nature Genetics, 38, 203–208.

    Article  Google Scholar 

  • Zeng, Z.-B. (1994), “Precision Mapping of Quantitative Trait Loci,” Genetics, 136, 1457–1468.

    Google Scholar 

  • Zhang, H., and Lu, W. (2007), “Adaptive LASSO for Cox’s Proportional Hazards Model in Survival Analysis,” Statistics in Medicine, 11, 1871–1879.

    MathSciNet  Google Scholar 

  • Zhao, K., Aranzana, M. J., Kim, S., Lister, C., Shindo, C., Tang, C., Toomajian, C., Zheng, H., Dean, C., Marjoram, P., and Nordborg, M. (2007), “An Arabidopsis Example of Association Mapping in Structured Samples,” PLoS Genetics, 3, e4.

    Article  Google Scholar 

  • Zhu, C., and Yu, J. (2009), “Nonmetric Multidimensional Scaling Corrects for Population Structure in Association Mapping with Different Sample Types,” Genetics, 182, 875–888.

    Article  Google Scholar 

  • Zou, H. (2006), “The Adaptive LASSO and its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Nebraska, Lincoln, NE, 68583, USA

    Dong Wang & Kent M. Eskridge

  2. International Maize and Wheat Improvement Center, 06600, Mexico, DF Mexico

    Jose Crossa

Authors
  1. Dong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kent M. Eskridge
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jose Crossa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong Wang.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(PDF 199 KB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, D., Eskridge, K.M. & Crossa, J. Identifying QTLs and Epistasis in Structured Plant Populations Using Adaptive Mixed LASSO. JABES 16, 170–184 (2011). https://doi.org/10.1007/s13253-010-0046-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13253-010-0046-2

Key Words

Search

Navigation