Coherent estimates of genetic effects with missing information

Affiliation(s)

Department of Information Technology, Box 337, Uppsala University, SE-75105, Uppsala, Sweden.

Linnaeus Centre for Bioinformatics, Box 598, Uppsala University, SE-75124, Uppsala, Sweden.

Department of Genetics, University of Santiago de Compostela, ES-27002, Lugo, Galiza, Spain.

Department of Information Technology, Box 337, Uppsala University, SE-75105, Uppsala, Sweden.

Linnaeus Centre for Bioinformatics, Box 598, Uppsala University, SE-75124, Uppsala, Sweden.

Department of Genetics, University of Santiago de Compostela, ES-27002, Lugo, Galiza, Spain.

ABSTRACT

Genetic effect estimates for loci detected in quantitative trait locus (QTL) mapping experiments depend upon two factors. First, they are parameterizations of the genotypic values determined by the model of genetic effects. Second, they are consequently also affected by the regression method used to estimate the genotypic values from the observed marker genotypes and phenotypes. There are two common causes for marker-genotype data to be incomplete in those experiments—missing marker-genotypes and within-interval mapping. Different regression methods tend to differ in how this missing information is represented and handled. In this communication we explain why the estimates of genetic effects of QTL obtained using standard regression methods are not coherent with the model of genetic effects and indeed show intrinsic inconsistencies when there is incomeplete genotype information. We then describe the interval mapping by imputations (IMI) regression method and prove that it overcomes those problems. A numerical example is used to illustrate the use of IMI and the consequences of using current methods of choice. IMI enables researchers to obtain estimates of genetic effects that are coherent with the model of genetic effects used, despite incomplete genotype information. Furthermore, because IMI allows orthogonal estimation of genetic effects, it shows potential performance advantages for being implemented in QTL mapping tools.

Genetic effect estimates for loci detected in quantitative trait locus (QTL) mapping experiments depend upon two factors. First, they are parameterizations of the genotypic values determined by the model of genetic effects. Second, they are consequently also affected by the regression method used to estimate the genotypic values from the observed marker genotypes and phenotypes. There are two common causes for marker-genotype data to be incomplete in those experiments—missing marker-genotypes and within-interval mapping. Different regression methods tend to differ in how this missing information is represented and handled. In this communication we explain why the estimates of genetic effects of QTL obtained using standard regression methods are not coherent with the model of genetic effects and indeed show intrinsic inconsistencies when there is incomeplete genotype information. We then describe the interval mapping by imputations (IMI) regression method and prove that it overcomes those problems. A numerical example is used to illustrate the use of IMI and the consequences of using current methods of choice. IMI enables researchers to obtain estimates of genetic effects that are coherent with the model of genetic effects used, despite incomplete genotype information. Furthermore, because IMI allows orthogonal estimation of genetic effects, it shows potential performance advantages for being implemented in QTL mapping tools.

Cite this paper

Nettelblad, C. , Carlobrg, Ö. , Pino-Querido, A. and M. Álvarez-Castro, J. (2012) Coherent estimates of genetic effects with missing information.*Open Journal of Genetics*, **2**, 31-38. doi: 10.4236/ojgen.2012.21003.

Nettelblad, C. , Carlobrg, Ö. , Pino-Querido, A. and M. Álvarez-Castro, J. (2012) Coherent estimates of genetic effects with missing information.

References

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[2] Lewontin, R.C. (1974) The genetic basis of evolutionary change. Columbia University Press, New York.

[3] álvarez-Castro, J.M. and Carlborg, ?. (2007) A unified model for functional and statistical epistasis and its application in quantitative trait loci analysis. Genetics, 176, 1151-1167. doi:10.1534/genetics.106.067348

[4] álvarez-Castro, J.M., Le Rouzic, A. and Carlborg, ?. (2008) How to perform meaningful estimates of genetic effects. PLoS Genetics, 4, e1000062. doi:10.1371/journal.pgen.1000062

[5] Besnier, F., Le Rouzic, A. and álvarez-Castro, J.M. (2010) Applying QTL analysis to conservation genetics. Conservation Genetics, 11, 399-408. doi:10.1007/s10592-009-0036-5

[6] Le Rouzic, A. andálvarez-Castro, J.M. (2008) Estimation of genetic ef-fects and genotype-phenotype maps. Evolutionary Bioinformatics, 4, 225-235.

[7] Le Rouzic, A., álvarez-Castro, J.M. and Carlborg, ?. (2008) Dissection of the genetic architecture of body weight in chicken reveals the impact of epistasis on domestication traits. Genetics, 179, 1591-1599. doi:10.1534/genetics.108.089300

[8] Lander, E.S. and Botstein, D. (1989) Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics, 121, 185-199.

[9] Haley, C.S. and Knott, S.A. (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity, 69, 315-324. doi:10.1038/hdy.1992.131

[10] Martínez, O. and Curnow, R.N. (1992) Estimating the locations and the sizes of the effects of quantitative trait loci using flanking markers. Theoretical and Applied Genetics, 85, 480-488.

[11] Tiwari, H.K. and Elston, R.C. (1997) Deriving components of genetic variance for multilocus models. Genetic Epidemiology, 14, 1131-1136. doi:10.1002/(SICI)1098-2272(1997)14:6<1131::AID-GEPI95>3.0.CO;2-H

[12] Fisher, R.A. (1918) The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edin-burgh, 52, 339-433.

[13] Mather, K. and Jinks, J.L. (1982) Introduction to biometrical genetics. Chapman and Hall, London.

[14] Zeng, Z.B., Wang, T. and Zou, W. (2005) Modeling quantitative trait Loci and interpretation of models. Genetics, 169, 1711-1725. doi:10.1534/genetics.104.035857

[15] Kao, C.H. and Zeng, Z.B. (2002) Modeling epistasis of quantitative trait loci using Cockerham’s model. Genetics, 160, 1243-1261.

[16] Yang, R.-C. (2004) Epistasis of quantitative trait loci under different gene action models. Genetics, 167, 1493- 1505. doi:10.1534/genetics.103.020016

[17] Jansen, R.C. (1993) Interval mapping of multiple quantitative trait loci. Genetics, 135, 205-211.

[18] Sen, S. and Churchill, G.A. (2001) A statistical framework for quantitative trait mapping. Genetics, 159, 371-387.

[19] Willett, J.B. and Singer, J.D. (1988) Another cautionary note about R2: Its use in least-squares regression analysis. The American Statistician, 42, 236-238. doi:10.2307/2685031

[20] Haley, C.S., Knott, S.A. and Elsen, J.M. (1994) Mapping quantitative trait loci in crosses between outbred lines using least squares. Genetics, 136, 1195-1207.

[21] Feenstra, B., Skovgaard, I.M. and Broman, K.W. (2006) Mapping quantitative trait loci by an extension of the Haley-Knott regression method using estimating equations. Genetics, 173, 2269-2282. doi:10.1534/genetics.106.058537

[22] Xu, S. (1995) A comment on the simple regression method for interval mapping. Genetics, 141, 1657-1659.

[23] Phillips, P.C. (2008) Epistasis—The essential role of gene interactions in the structure and evolution of genetic systems. Nature Reviews Genetics, 9, 855-867. doi:10.1038/nrg2452

[24] Yang, R.-C. and álva-rez-Castro, J.M. (2008) Functional and statistical genetic effects with miltiple alleles. Current Topics in Genetics, 3, 49-62.

[25] Amorim, A. and Pereira, M. (2005) Pros and cons in the use of SNPs in forensic kinship investigation: A comparative analysis with STRs. Forensic Science In-ternational, 150, 17-21. doi:10.1016/j.forsciint.2004.06.018

[1] Wu, R., Ma C.-X. and Casella, G.C. (2007) Statistical genetics of quantitative traits: Linkage, maps and QTL. In: Gail, M. et al. Eds. Statistics for Biology and Health, Springer, New York.

[2] Lewontin, R.C. (1974) The genetic basis of evolutionary change. Columbia University Press, New York.

[3] álvarez-Castro, J.M. and Carlborg, ?. (2007) A unified model for functional and statistical epistasis and its application in quantitative trait loci analysis. Genetics, 176, 1151-1167. doi:10.1534/genetics.106.067348

[4] álvarez-Castro, J.M., Le Rouzic, A. and Carlborg, ?. (2008) How to perform meaningful estimates of genetic effects. PLoS Genetics, 4, e1000062. doi:10.1371/journal.pgen.1000062

[5] Besnier, F., Le Rouzic, A. and álvarez-Castro, J.M. (2010) Applying QTL analysis to conservation genetics. Conservation Genetics, 11, 399-408. doi:10.1007/s10592-009-0036-5

[6] Le Rouzic, A. andálvarez-Castro, J.M. (2008) Estimation of genetic ef-fects and genotype-phenotype maps. Evolutionary Bioinformatics, 4, 225-235.

[7] Le Rouzic, A., álvarez-Castro, J.M. and Carlborg, ?. (2008) Dissection of the genetic architecture of body weight in chicken reveals the impact of epistasis on domestication traits. Genetics, 179, 1591-1599. doi:10.1534/genetics.108.089300

[8] Lander, E.S. and Botstein, D. (1989) Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics, 121, 185-199.

[9] Haley, C.S. and Knott, S.A. (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity, 69, 315-324. doi:10.1038/hdy.1992.131

[10] Martínez, O. and Curnow, R.N. (1992) Estimating the locations and the sizes of the effects of quantitative trait loci using flanking markers. Theoretical and Applied Genetics, 85, 480-488.

[11] Tiwari, H.K. and Elston, R.C. (1997) Deriving components of genetic variance for multilocus models. Genetic Epidemiology, 14, 1131-1136. doi:10.1002/(SICI)1098-2272(1997)14:6<1131::AID-GEPI95>3.0.CO;2-H

[12] Fisher, R.A. (1918) The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edin-burgh, 52, 339-433.

[13] Mather, K. and Jinks, J.L. (1982) Introduction to biometrical genetics. Chapman and Hall, London.

[14] Zeng, Z.B., Wang, T. and Zou, W. (2005) Modeling quantitative trait Loci and interpretation of models. Genetics, 169, 1711-1725. doi:10.1534/genetics.104.035857

[15] Kao, C.H. and Zeng, Z.B. (2002) Modeling epistasis of quantitative trait loci using Cockerham’s model. Genetics, 160, 1243-1261.

[16] Yang, R.-C. (2004) Epistasis of quantitative trait loci under different gene action models. Genetics, 167, 1493- 1505. doi:10.1534/genetics.103.020016

[17] Jansen, R.C. (1993) Interval mapping of multiple quantitative trait loci. Genetics, 135, 205-211.

[18] Sen, S. and Churchill, G.A. (2001) A statistical framework for quantitative trait mapping. Genetics, 159, 371-387.

[19] Willett, J.B. and Singer, J.D. (1988) Another cautionary note about R2: Its use in least-squares regression analysis. The American Statistician, 42, 236-238. doi:10.2307/2685031

[20] Haley, C.S., Knott, S.A. and Elsen, J.M. (1994) Mapping quantitative trait loci in crosses between outbred lines using least squares. Genetics, 136, 1195-1207.

[21] Feenstra, B., Skovgaard, I.M. and Broman, K.W. (2006) Mapping quantitative trait loci by an extension of the Haley-Knott regression method using estimating equations. Genetics, 173, 2269-2282. doi:10.1534/genetics.106.058537

[22] Xu, S. (1995) A comment on the simple regression method for interval mapping. Genetics, 141, 1657-1659.

[23] Phillips, P.C. (2008) Epistasis—The essential role of gene interactions in the structure and evolution of genetic systems. Nature Reviews Genetics, 9, 855-867. doi:10.1038/nrg2452

[24] Yang, R.-C. and álva-rez-Castro, J.M. (2008) Functional and statistical genetic effects with miltiple alleles. Current Topics in Genetics, 3, 49-62.

[25] Amorim, A. and Pereira, M. (2005) Pros and cons in the use of SNPs in forensic kinship investigation: A comparative analysis with STRs. Forensic Science In-ternational, 150, 17-21. doi:10.1016/j.forsciint.2004.06.018