Theoretical and Applied Genetics

, Volume 128, Issue 11, pp 2189–2201 | Cite as

Forecasting the accuracy of genomic prediction with different selection targets in the training and prediction set as well as truncation selection

  • Pascal Schopp
  • Christian Riedelsheimer
  • H. Friedrich Utz
  • Chris-Carolin Schön
  • Albrecht E. Melchinger
Original Article

Abstract

Key message

Deterministic formulas accurately forecast the decline in predictive ability of genomic prediction with changing testers, target environments or traits and truncation selection.

Abstract

Genomic prediction of testcross performance (TP) was found to be a promising selection tool in hybrid breeding as long as the same tester and environments are used in the training and prediction set. In practice, however, selection targets often change in terms of testers, target environments or traits leading to a reduced predictive ability. Hence, it would be desirable to estimate for given training data the expected decline in the predictive ability of genomic prediction under such settings by deterministic formulas that require only quantitative genetic parameters available from the breeding program. Here, we derived formulas for forecasting the predictive ability under different selection targets in the training and prediction set and applied these to predict the TP of lines based on line per se or testcross evaluations. On the basis of two experiments with maize, we validated our approach in four scenarios characterized by different selection targets. Forecasted and empirically observed predictive abilities obtained by cross-validation generally agreed well, with deviations between −0.06 and 0.01 only. Applying the prediction model to a different tester and/or year reduced the predictive ability by not more than 18 %. Accounting additionally for truncation selection in our formulas indicated a substantial reduction in predictive ability in the prediction set, amounting, e.g., to 53 % for a selected fraction α = 10 %. In conclusion, our deterministic formulas enable forecasting the predictive abilities of new selection targets with sufficient precision and could be used to calculate parameters required for optimizing the allocation of resources in multi-stage genomic selection.

Supplementary material

122_2015_2577_MOESM1_ESM.docx (143 kb)
Supplementary material 1 (DOCX 143 kb)

References

  1. Albrecht T, Wimmer V, Auinger H et al (2011) Genome-based prediction of testcross values in maize. Theor Appl Genet 123:339–350CrossRefPubMedGoogle Scholar
  2. Albrecht T, Auinger H-J, Wimmer V et al (2014) Genome-based prediction of maize hybrid performance across genetic groups, testers, locations, and years. Theor Appl Genet 127:1375–1386CrossRefPubMedGoogle Scholar
  3. Astle W, Balding DJ (2009) Population structure and cryptic relatedness in genetic association studies. Stat Sci 24:451–471CrossRefGoogle Scholar
  4. Bastiaansen JWM, Coster A, Calus MPL et al (2012) Long-term response to genomic selection: effects of estimation method and reference population structure for different genetic architectures. Genet Sel Evol 44:3PubMedCentralCrossRefPubMedGoogle Scholar
  5. Bernardo R (2008) Molecular markers and selection for complex traits in plants: learning from the last 20 years. Crop Sci 48:1649–1664CrossRefGoogle Scholar
  6. Bernardo R, Yu J (2007) Prospects for genomewide selection for quantitative traits in maize. Crop Sci 47:1082–1090CrossRefGoogle Scholar
  7. Cochran WG (1950) Improvement by means of selection. In: Proceedings of second Berkeley symposium on mathematical statistics and probability, University of California Press, pp 449–470Google Scholar
  8. Dekkers JCM (2007) Prediction of response to marker-assisted and genomic selection using selection index theory. Genetics 124:331–341Google Scholar
  9. Eding H, Meuwissen T (2001) Marker-based estimates of between and within population kinships for the conservation of genetic diversity. J Anim Breed Genet 118:141–159CrossRefGoogle Scholar
  10. Endelman JB (2011) Ridge regression and other kernels for genomic selection with R package rrBLUP. Plant Genome 4:250–255CrossRefGoogle Scholar
  11. Falconer DS, Mackay TFC (1996) Introduction to quantitative genetics, 4th edn. Longmans Green, HarlowGoogle Scholar
  12. Foiada F, Westermeier P, Kessel B, Ouzunova M, Wimmer V, Mayerhofer W, Presterl T, Dilger M, Kreps R, Eder J, Schön CC (2015) Improving resistance to the European corn borer: a comprehensive study in elite maize using QTL mapping and genome-wide prediction. Theor Appl Genet 128:875–891CrossRefPubMedGoogle Scholar
  13. Ganal MW, Durstewitz G, Polley A et al (2011) A large maize (Zea mays L.) SNP genotyping array: development and germplasm genotyping, and genetic mapping to compare with the B73 reference genome. PLoS One 6:e28334PubMedCentralCrossRefPubMedGoogle Scholar
  14. Gilmour A, Gogel B, Cullis B, Thompson R (2009) ASReml user guide release 3.0. VSN International Ltd, Hemel HempsteadGoogle Scholar
  15. Grieder C, Dhillon BS, Schipprack W, Melchinger AE (2012a) Breeding maize as biogas substrate in Central Europe: I. Quantitative-genetic parameters for testcross performance. Theor Appl Genet 124:971–980CrossRefPubMedGoogle Scholar
  16. Grieder C, Dhillon BS, Schipprack W, Melchinger AE (2012b) Breeding maize as biogas substrate in Central Europe: II. Quantitative-genetic parameters for inbred lines and correlations with testcross performance. Theor Appl Genet 124:981–988CrossRefPubMedGoogle Scholar
  17. Habier D, Fernando RL, Dekkers JCM (2007) The impact of genetic relationship information on genome-assisted breeding values. Genetics 177:2389–2397PubMedCentralPubMedGoogle Scholar
  18. Habier D, Tetens J, Seefried F et al (2010) The impact of genetic relationship information on genomic breeding values in German Holstein cattle. Genet Sel Evol 42:5PubMedCentralCrossRefPubMedGoogle Scholar
  19. Habier D, Fernando RL, Garrick DJ (2013) Genomic BLUP decoded: a look into the black box of genomic prediction. Genetics 194:597–607PubMedCentralCrossRefPubMedGoogle Scholar
  20. Hallauer AR (1990) Methods used in developing maize inbreds. Maydica 35:1–16Google Scholar
  21. Heffner EL, Sorrells ME, Jannink J-L (2009) Genomic selection for crop improvement. Crop Sci 49:1–12CrossRefGoogle Scholar
  22. Hill WG, Robertson A (1968) Linkage disequilibrium in finite populations. Theor Appl Genet 38:226–231CrossRefPubMedGoogle Scholar
  23. Jannink J-L (2010) Dynamics of long-term genomic selection. Genet Sel Evol 42:35PubMedCentralCrossRefPubMedGoogle Scholar
  24. Jannink J-L, Lorenz AJ, Iwata H (2010) Genomic selection in plant breeding: from theory to practice. Brief Funct Genomics Proteomics 9:166–177CrossRefGoogle Scholar
  25. Jensen J, Su G, Madsen P (2012) Partitioning additive genetic variance into genomic and remaining polygenic components for complex traits in dairy cattle. BMC Genet 13:44PubMedCentralCrossRefPubMedGoogle Scholar
  26. Lamkey KR, Schnicker BJ, Melchinger AE (1995) Epistasis in an elite maize hybrid and choice of generation for inbred line development. Crop Sci 35:1272–1281CrossRefGoogle Scholar
  27. Lande R, Thompson R (1990) Efficiency of marker-assisted selection in the improvement of quantitative traits. Genetics 124:743–756PubMedCentralPubMedGoogle Scholar
  28. Lehermeier C, Krämer N, Bauer E et al (2014) Usefulness of multi-parental populations of maize (Zea mays L.) for genome-based prediction. Genetics 198:3–16PubMedCentralCrossRefPubMedGoogle Scholar
  29. Massman JM, Gordillo A, Lorenzana RE, Bernardo R (2013) Genomewide predictions from maize single-cross data. Theor Appl Genet 126:13–22CrossRefPubMedGoogle Scholar
  30. Melchinger AE, Utz H, Schön C-C (1998) Quantitative trait locus (QTL) mapping using different testers and independent population samples in maize reveals low power of QTL detection and large bias in. Genetics 149:383–403PubMedCentralPubMedGoogle Scholar
  31. Meuwissen THE, Hayes BJ, Goddard ME (2001) Prediction of total genetic value using genome-wide dense marker maps. Genetics 157:1819–1829PubMedCentralPubMedGoogle Scholar
  32. Mi X, Utz HF, Technow F, Melchinger AE (2014) Optimizing resource allocation for multistage selection in plant breeding with r package. Crop Sci 54:1413–1418CrossRefGoogle Scholar
  33. Mihaljevic R, Schön C-C, Utz HF, Melchinger AE (2005a) Correlations and QTL correspondence between line per se and testcross performance for agronomic traits in four populations of European maize. Crop Sci 45:114–122CrossRefGoogle Scholar
  34. Mihaljevic R, Utz HF, Melchinger AE (2005b) No evidence for epistasis in hybrid and per se performance of elite European flint maize inbreeds from generation means and QTL analyses. Crop Sci 45:2605–2613CrossRefGoogle Scholar
  35. Muir WM (2007) Comparison of genomic and traditional BLUP-estimated breeding value accuracy and selection response under alternative trait and genomic parameters. J Anim Breed Genet 124:342–355CrossRefPubMedGoogle Scholar
  36. Reif JC, Gumpert F-M, Fischer S, Melchinger AE (2007) Impact of interpopulation divergence on additive and dominance variance in hybrid populations. Genetics 176:1931–1934PubMedCentralCrossRefPubMedGoogle Scholar
  37. Riedelsheimer C, Melchinger AE (2013) Optimizing the allocation of resources for genomic selection in one breeding cycle. Theor Appl Genet 126:2835–2848CrossRefPubMedGoogle Scholar
  38. Riedelsheimer C, Czedik-Eysenberg A, Grieder C et al (2012) Genomic and metabolic prediction of complex heterotic traits in hybrid maize. Nat Genet 44:217–220CrossRefPubMedGoogle Scholar
  39. Riedelsheimer C, Endelman JB, Stange M et al (2013) Genomic predictability of interconnected bi-parental maize populations. Genetics 194:493–503PubMedCentralCrossRefPubMedGoogle Scholar
  40. Schön C-C, Utz H, Groh S et al (2004) Quantitative trait locus mapping based on resampling in a vast maize testcross experiment and its relevance to quantitative genetics for complex traits. Genetics 498:485–498CrossRefGoogle Scholar
  41. Smith O (1986) Covariance between line per se and testcross performance. Crop Sci 2:540–543CrossRefGoogle Scholar
  42. Technow F, Riedelsheimer C, Schrag T, Melchinger AE (2012) Genomic prediction of hybrid performance in maize with models incorporating dominance and population specific marker effects. Theor Appl Genet 125:1181–1194CrossRefPubMedGoogle Scholar
  43. Technow F, Bürger A, Melchinger AE (2013) Genomic prediction of northern corn leaf blight resistance in maize with combined or separated training sets for heterotic groups. G3 3:197–203PubMedCentralCrossRefPubMedGoogle Scholar
  44. Technow F, Schrag T, Schipprack W et al (2014) Genome properties and prospects of genomic prediction of hybrid performance in a breeding program of maize. Genetics. doi:10.1534/genetics.114.165860 PubMedCentralPubMedGoogle Scholar
  45. Utz H (1969) Mehrstufenselektion in der Pflanzenzüchtung. Dissertation Thesis, University of HohenheimGoogle Scholar
  46. Utz H (2005) PLABSTAT—a computer program for statistical analysis of plant breeding experiments. University of Hohenheim, StuttgartGoogle Scholar
  47. VanRaden PM (2008) Efficient methods to compute genomic predictions. J Dairy Sci 91:4414–4423CrossRefPubMedGoogle Scholar
  48. Windhausen VS, Atlin GN, Hickey JM et al (2012) Effectiveness of genomic prediction of maize hybrid performance in different breeding populations and environments. G3 2:1427–1436PubMedCentralCrossRefPubMedGoogle Scholar
  49. Wray NR, Yang J, Hayes BJ et al (2013) Pitfalls of predicting complex traits from SNPs. Nat Rev Genet 14:507–515PubMedCentralCrossRefPubMedGoogle Scholar
  50. Zhao Y, Gowda M, Liu W et al (2012) Accuracy of genomic selection in European maize elite breeding populations. Theor Appl Genet 124:769–776CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Pascal Schopp
    • 1
  • Christian Riedelsheimer
    • 1
  • H. Friedrich Utz
    • 1
  • Chris-Carolin Schön
    • 2
  • Albrecht E. Melchinger
    • 1
  1. 1.Department of Applied Genetics, Institute of Plant Breeding, Seed Science and Population GeneticsUniversity of HohenheimStuttgartGermany
  2. 2.Plant Breeding, Center of Life and Food Sciences WeihenstephanTechnische Universität MünchenFreisingGermany

Personalised recommendations