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Inferring genetic values for quantitative traits non-parametrically

  • DANIEL GIANOLA (a1) (a2) (a3) (a4) and GUSTAVO de los CAMPOS (a1)

Inferences about genetic values and prediction of phenotypes for a quantitative trait in the presence of complex forms of gene action, issues of importance in animal and plant breeding, and in evolutionary quantitative genetics, are discussed. Current methods for dealing with epistatic variability via variance component models are reviewed. Problems posed by cryptic, non-linear, forms of epistasis are identified and discussed. Alternative statistical procedures are suggested. Non-parametric definitions of additive effects (breeding values), with and without employing molecular information, are proposed, and it is shown how these can be inferred using reproducing kernel Hilbert spaces regression. Two stylized examples are presented to demonstrate the methods numerically. The first example falls in the domain of the infinitesimal model of quantitative genetics, with additive and dominance effects inferred both parametrically and non-parametrically. The second example tackles a non-linear genetic system with two loci, and the predictive ability of several models is evaluated.

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P. Craven & G. Wahba (1979). Smoothing noisy data with spline functions. Numerische Mathematik 31, 377403.

M. W. Feldman & R. C. Lewontin (1975). The heritability hang-up. Science 190, 11631168.

A. Gallais (1974). Covariances between arbitrary relatives with linkage and epistasis in the case of linkage disequilibrium. Biometrics 30, 429446.

D. Gianola , R. L. Fernando & A. Stella (2006). Genomic assisted prediction of genetic value with semi-parametric procedures. Genetics 173, 17611776.

D. Gianola & J. B. C. H. M. van Kaam (2008). Reproducing kernel Hilbert spaces methods for genomic assisted prediction of quantitative traits. Genetics 178, 22892303.

O. González-Recio , D. Gianola , N. Long , K. A. Weigel , G. J. M. Rosa & S. Avendaño (2008 a). Nonparametric methods for incorporating genomic information into genetic evaluations: an application to mortality in broilers. Genetics 178, 23052313.

W. G. Hill , M. E. Goddard & P. M. Visscher (2008). Data and theory point to mainly additive genetic variance for complex traits. PLOS Genetics 4, el000008.

O. Kempthorne (1954). The correlation between relatives in a random mating population. Proceedings of the Royal Society of London, Series B 143, 103113.

O. Kempthorne (1978). Logical, epistemological and statistical aspects of nature-nurture data interpretation. Biometrics 34, 123.

K. I. Kojima (1959). Role of epistasis and overdominance in stability of equilibria with selection. Proceedings of the National Academy of Sciences of the USA 45, 984989.

H. K. H. Lee (2004). Bayesian Nonparametrics Via Neural Networks. Philadelphia, PA: ASA-SIAM.

N. Long , D. Gianola , G. J. M. Rosa , K. Weigel & S. Avendaño (2007). Machine learning classification procedure for selecting SNPs in genomic selection: application to early mortality in broilers. Journal of Animal Breeding and Genetics 124, 377389.

N. Long , D. Gianola , G. J. M. Rosa , K. A. Weigel & S. Avendaño (2008). Marker-assisted assessment of genotype by environment interaction: a case study of SNP–mortality association in broilers in two hygiene environments. Journal of Animal Science (in press).

A. A. Motsinger-Reif , S. M. Dudek , L. W. Hahn & M. D. Ritchie (2008). Comparison of approaches for machine learning optimization of neural networks for detecting gene–gene interactions in genetic epidemiology. Genetic Epidemiology 32, 325340.

D. Sorensen & D. Gianola (2002). Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics. New York: Springer.

G. Wahba (1990). Spline Models for Observational Data. Philadelphia, PA: Society for Industrial and Applied Mathematics.

C. S. Wang , J. J. Rutledge & D. Gianola (1993). Marginal inferences about variance components in a mixed linear model using Gibbs sampling. Genetics Selection Evolution 25, 4162.

C. S. Wang , J. J. Rutledge & D. Gianola (1994). Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs. Genetics Selection Evolution 26, 91115.

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Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
  • URL: /core/journals/genetics-research
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