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Radial basis function regression methods for predicting quantitative traits using SNP markers

  • NANYE LONG (a1), DANIEL GIANOLA (a1) (a2), GUILHERME J. M. ROSA (a2), KENT A. WEIGEL (a2), ANDREAS KRANIS (a3) and OSCAR GONZÁLEZ-RECIO (a4)...

Summary

A challenge when predicting total genetic values for complex quantitative traits is that an unknown number of quantitative trait loci may affect phenotypes via cryptic interactions. If markers are available, assuming that their effects on phenotypes are additive may lead to poor predictive ability. Non-parametric radial basis function (RBF) regression, which does not assume a particular form of the genotype–phenotype relationship, was investigated here by simulation and analysis of body weight and food conversion rate data in broilers. The simulation included a toy example in which an arbitrary non-linear genotype–phenotype relationship was assumed, and five different scenarios representing different broad sense heritability levels (0·1, 0·25, 0·5, 0·75 and 0·9) were created. In addition, a whole genome simulation was carried out, in which three different gene action modes (pure additive, additive+dominance and pure epistasis) were considered. In all analyses, a training set was used to fit the model and a testing set was used to evaluate predictive performance. The latter was measured by correlation and predictive mean-squared error (PMSE) on the testing data. For comparison, a linear additive model known as Bayes A was used as benchmark. Two RBF models with single nucleotide polymorphism (SNP)-specific (RBF I) and common (RBF II) weights were examined. Results indicated that, in the presence of complex genotype–phenotype relationships (i.e. non-linearity and non-additivity), RBF outperformed Bayes A in predicting total genetic values using SNP markers. Extension of Bayes A to include all additive, dominance and epistatic effects could improve its prediction accuracy. RBF I was generally better than RBF II, and was able to identify relevant SNPs in the toy example.

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Corresponding author

*Corresponding author. Nanye Long, Department of Animal Sciences, University of Wisconsin, Madison, WI 53706, USA. e-mail: nlong@wisc.edu

References

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Bell, D. D. & Weaver, W. D. (ed.) (2002). Commercial Chicken Meat and Egg Production. New York, NY: Springer.
Bennewitz, J., Solberg, T. & Meuwissen, T. (2009). Genomic breeding value estimation using nonparametric additive regression models. Genetics Selection Evolution 41, 20.
Broomhead, D. & Lowe, D. (1988). Multivariable functional interpolation and adaptive networks. Complex Systems 2, 321355.
Cockerham, C. C. (1954). An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 39, 859882.
Cordell, H. J. (2002). Epistasis: what it means, what it doesn't mean, and statistical methods to detect it in humans. Human Molecular Genetics 11, 24632468.
de los Campos, G., Gianola, D. & Rosa, G. J. M. (2009 a). Reproducing kernel Hilbert spaces regression: a general framework for genetic evaluation. Journal of Animal Science 87, 18831887.
de los Campos, G., Naya, H., Gianola, D., Crossa, J., Legarra, A., Manfredi, E., Weigel, K. & Cotes, J. (2009 b). Predicting quantitative traits with regression models for dense molecular markers and pedigrees. Genetics 182, 375385.
Falconer, D. S. and Mackay, T. F. C. (1996). Introduction to Quantitative Genetics. 4th edn. Harlow, Essex, UK: Longmans Green.
Gianola, D. & de los Campos, G. (2008). Inferring genetic values for quantitative traits non-parametrically. Genetics Research 90, 525540.
Gianola, D., Fernando, R. & Stella, A. (2006). Genomic-assisted prediction of genetic value with semiparametric procedures. Genetics 173, 17611776.
Gianola, D. & van Kaam, J. (2008). Reproducing kernel Hilbert spaces regression methods for genomic assisted prediction of quantitative traits. Genetics 178, 22892303.
González-Recio, O., Gianola, D., Long, N., Weigel, K. A., Rosa, G. J. M. & Avendano, S. (2008). Nonparametric methods for incorporating genomic information into genetic evaluations: An application to mortality in broilers. Genetics 178, 23052313.
González-Recio, O., Gianola, D., Rosa, G., Weigel, K. & Kranis, A. (2009). Genome-assisted prediction of a quantitative trait measured in parents and progeny: application to food conversion rate in chickens. Genetics Selection Evolution 41, 3.
Haykin, S. (1999). Neural Networks: A Comprehensive Foundation. 2nd edn. Upper Saddle River, NJ: Prentice-Hall.
Hill, W. G., Goddard, M. E. & Visscher, P. M. (2008). Data and theory point to mainly additive genetic variance for complex traits. PLoS Genetics 4, e1000008.
Hu, Y. H. & Hwang, J.-N. (ed.) (2001). Handbook of Neural Network Signal Processing. Boca Raton, FL: CRC Press.
Kaufman, L. & Rousseeuw, P. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. New York, NY: Wiley.
Mackay, T. F. C. (2009). The genetic architecture of complex behaviors: lessons from Drosophila. Genetica 136, 295302.
Manly, B. F. J. (2005). Multivariate Statistical Methods: A Primer. 3rd edn. Boca Raton, FL: Chapman and Hall/CRC.
McVean, G. (2009). A genealogical interpretation of principal components analysis. PLoS Genetics 5, e1000686.
Meuwissen, T. H., Hayes, B. J. & Goddard, M. E. (2001). Prediction of total genetic value using genome-wide dense marker maps. Genetics 157, 18191829.
Moody, J. & Darken, C. J. (1989). Fast learning in networks of locally-tuned processing units. Neural Computation 1, 281294.
Park, T. & Casella, G. (2008). The Bayesian lasso. Journal of the American Statistical Association 103, 681686.
Poggio, T. & Girosi, F. (1990). Regularization algorithms for learning that are equivalent to multilayer networks. Science 247, 978982.
Powell, M. J. D. (1987). Radial basis functions for multivariable interpolation: a review. In Algorithms for Approximation, pp. 143167. New York, NY: Clarendon Press.
Price, A. L., Patterson, N. J., Plenge, R. M., Weinblatt, M. E., Shadick, N. A. & Reich, D. (2006). Principal components analysis corrects for stratification in genome-wide association studies. Nature Genetics 38, 904909.
Ripley, B. D. (1996). Pattern Recognition and Neural Networks. New York, NY: Cambridge University Press.
Risch, N. J. (2000). Searching for genetic determinants in the new millennium. Nature 405, 847856.
Solberg, T. R., Sonesson, A. K., Woolliams, J. A. & Meuwissen, T. H. E. (2008). Genomic selection using different marker types and densities. Journal of Animal Science 86, 24472454.
Sturtz, S., Ligges, U. & Gelman, A. (2005). R2WinBUGS: a package for running WinBUGS from R. Journal of Statistical Software 12, 116.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society B 58, 267288.
Varmuza, K. & Filzmoser, P. (2009). Introduction to Multivariate Statistical Analysis in Chemometrics. Boca Raton, FL: CRC Press.
Wahba, G. (2002). Soft and hard classification by reproducing kernel Hilbert space methods. Proceedings of the National Academy of Sciences of the USA 99, 1652416530.
Xu, S. & Jia, Z. (2007). Genome-wide analysis of epistatic effects for quantitative traits in barley. Genetics 175, 19551963.
Yamamoto, A., Zwarts, L., Callaerts, P., Norga, K., Mackay, T. F. C. & Anholt, R. R. H. (2008). Neurogenetic networks for startle-induced locomotion in Drosophila melanogaster. Proceedings of the National Academy of Sciences of the USA 105, 1239312398.

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