Skip to main content
Log in

Predicting genetic variance in bi-parental breeding populations is more accurate when explicitly modeling the segregation of informative genomewide markers

  • Published:
Molecular Breeding Aims and scope Submit manuscript

Abstract

Robust predictions of genetic variances for important traits would facilitate greater genetic gains in plant breeding. Previous attempts to predict the genetic variance (\(\sigma_{\text{G}}^{2}\)) of traits in bi-parental breeding populations were inconsistent and context specific. The weakness of methods that consider the phenotypic distance, genetic distance, and relationship-based distance of pairs of parents, which we collectively term historical methods, stems from the fact that they do not explicitly model the segregation of the underlying genetic effects for a trait within a population. To address this issue, we propose the use of three modern methods made possible by the commonplace use of genomewide molecular marker data and genomic selection in modern breeding programs. These modern methods utilize both phenotypic and genotypic records to, in varying degrees, explicitly model the segregation of informative genomewide markers to predict \(\sigma_{\text{G}}^{2}\) in bi-parental breeding populations. In this study, we evaluate the accuracy of historical and modern methods to predict \(\sigma_{\text{G}}^{2}\) using 40 field-tested bi-parental barley breeding populations evaluated during 2003–2010 for Fusarium head blight severity. In general, the modern methods predicted the field-based estimates of \(\sigma_{\text{G}}^{2}\) more accurately than the historical methods. Specifically, the modern method that most explicitly models the segregation of informative genomewide markers, called ‘PopVar,’ was the most accurate \(\sigma_{\text{G}}^{2}\) prediction method.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Bates D, Maechler M, Bolker B, Walker S (2014) lme4: Linear mixed-effects models using Eigen and S4. R package version 1.1-6. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Bernardo R (2013) Genomewide selection when major genes are known. Crop Sci 54(1):68–75

    Article  Google Scholar 

  • Bernardo R (2014) Genomewide selection of parental inbreds: classes of loci and virtual biparental populations. Crop Sci 54(6):2586–2595

    Article  Google Scholar 

  • Charcosset A, Lefort-Buson M, Gallais A (1991) Relationship between heterosis and heterozygosity at marker loci: a theoretical computation. Theor Appl Genet 81(5):571–575

    Article  CAS  PubMed  Google Scholar 

  • Cleveland WS (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 74(368):829–836

    Article  Google Scholar 

  • Close TJ, Prasanna BR et al (2009) Development and implementation of high-throughput SNP genotyping in barley. BMC Genom 10:582

    Article  Google Scholar 

  • Cohen J (1988) Statistical power analysis for the behavioral sciences, 2nd edn. Lawrence Erlbaum, Hillsdale

  • de los Campos G, Pérez P (2015) BGLR: Bayesian generalized linear regression. R package version 1.0.4. http://CRAN.R-project.org/package=BGLR

  • Durlak JA (2009) How to select, calculate, and interpret effect sizes. J Pediatr Psychol 34(9):917–928

    Article  PubMed  Google Scholar 

  • Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7(1):1–26

    Article  Google Scholar 

  • Endelman JB (2011) Ridge regression and other kernels for genomic selection with R package rrBLUP. Plant Genome 4:250–255

    Article  Google Scholar 

  • Falconer DS, Mackay TFC (1996) Introduction to quantitative genetics. Longman, England

    Google Scholar 

  • Goodman M, Lasker G (1974) Measurement of distance and propinquity in anthropological studies. In: Crow J, Denniston C (eds) Genetic distance. Plenum Press, New York

    Google Scholar 

  • Heffner EL, Jannink J-L, Sorrells ME (2011) Genomic selection accuracy using multifamily prediction models in a wheat breeding program. Plant Genome 4:65–75

    Article  Google Scholar 

  • Holland JB, Nyquist WE, Cervantes-Martińex CT (2003) Estimating and interpreting heritability for plant breeding: an update. In: Janick J (ed) Plant breeding reviews, vol 22. Wiley, New York, pp 9–112

    Google Scholar 

  • Hung HY, Browne C, Guill K, Coles N, Eller M, Garcia A, Lepak N, Melia-Hancock S, Oropeza-Rosas M, Salvo S, Upadyayula N, Buckler ES, Flint-Garcia S, McMullen MD, Rocheford TR, Holland JB (2012) The relationship between parental genetic or phenotypic divergence and progeny variation in the maize nested association mapping population. Heredity 108:490–499

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Jinks JL, Pooni HS (1976) Predicting the properties of recombinant inbred lines derived by single seed descent. Heredity 36:253–266

    Article  Google Scholar 

  • Lian L, Jacobson A, Zhong S, Bernardo R (2015) Prediction of genetic variance in biparental maize populations: genomewide marker effects versus mean genetic variance in prior populations. Crop Sci 55(3):1181–1188

    Article  Google Scholar 

  • Lorenz AJ, Smith KP (2015) Adding genetically distant individuals to training populations reduces genomic prediction accuracy in barley. Crop Sci 55(5). doi:10.2135/cropsci2015.02.0102

  • Lorenz AJ, Chao RE, Asoro F, Heffner EL, Hayashi T, Iwata H, Smith KP, Sorrels ME, Jannink J-L (2011) Genomic selection in plant breeding: knowledge and prospects. Adv Agron 110:77–123

    Article  Google Scholar 

  • Lorenzana RE, Bernardo R (2009) Accuracy of genotypic value predictions for marker-based selection in biparental plant populations. Theor Appl Genet 120:151–161

    Article  PubMed  Google Scholar 

  • Massman J, Cooper B, Horsley R, Neate S, Dill-Mackey R, Chao S, Dong Y, Schwarz P, Muehlbauer GJ, Smith KP (2011) Genome-wide association mapping of Fusarium head blight resistance in contemporary barley germplasm. Mol Breed 27(4):439–454

    Article  Google Scholar 

  • Mather K, Jinks J-L (1982) Biometrical genetics, 3rd edn. Chapman and Hall, London

    Book  Google Scholar 

  • McMullen MD, Kresovich S et al (2009) Genetic properties of the maize nested association mapping population. Science 325(5941):737–740

    Article  CAS  PubMed  Google Scholar 

  • Mohammadi M, Tiede T, Smith KP (2015) PopVar: a genome-wide procedure for predicting genetic variance and correlated response in bi-parental breeding populations. Crop Sci 55:2068–2077

    Article  Google Scholar 

  • Muñoz-Amatriaín M, Moscou MJ et al (2011) An improved consensus linkage map of barley based on flow-sorted chromosomes and single nucleotide polymorphism markers. Plant Gen. 4:238–249

    Article  Google Scholar 

  • Nei M (1974) A new measure of genetic distance. In: Crow JF, Denniston C (eds) Genetic distance. Plenum Press, New York, pp 63–76

    Chapter  Google Scholar 

  • Park T, Casella G (2008) The Bayesian lasso. J Am Stat Assoc 103(482):681–686

    Article  CAS  Google Scholar 

  • R Development Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www-R-project.org

  • Riedelsheimer CF, Technow F, Melchinger AE (2012) Comparison of whole-genome prediction models for traits with contrasting genetic architecture in a diversity panel of maize inbred lines. BMC Genom 13:452

    Article  CAS  Google Scholar 

  • Rincent R, Laloë D, Nicolas S et al (2012) Maximizing the reliability of genomic selection by optimizing the calibration set of reference individuals: comparison of methods in two diverse groups of maize inbreds (Zea mays L.). Genetics 192(2):715–728

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Sallam AH, Endelman JB, Jannink J-L, Smith KP (2015) Assessing genomic selection prediction accuracy in a dynamic barley breeding population. Plant Genome 8(1). doi:10.3835/plantgenome2014.05.0020

  • Souza E, Sorrels ME (1991) Prediction of progeny variation in oat from parental genetic relationships. Theor Appl Genet 82:233–241

    Article  CAS  PubMed  Google Scholar 

  • Szűcs P, Blake VC, Bhat VR, Close TJ, Cuesta-Marcos A, Muehlbauer GJ, Ramsay LV, Waugh R, Hayes PM (2009) An integrated resource for barley linkage map and malting quality QTL alignment. Plant Genome 2:123–140

    Google Scholar 

  • Technow F (2015) R package mvngGrAd: moving grid adjustment in plant breeding field trials. R package version 0.1.5

  • Tiede T, Mohammadi M, Smith KP (2015) PopVar: genomic breeding tools: genetic variance prediction and cross-validation. R package version 1.2.1

  • VanRaden PM (2008) Efficient methods to compute genomic predictions. J Dairy Sci 91:4414–4423

    Article  CAS  PubMed  Google Scholar 

  • Zhong S, Jannink J-L (2007) Using quantitative trait loci results to discriminate among crosses on the basis of their progeny mean and variance. Genetics 177:567–576

    Article  PubMed Central  PubMed  Google Scholar 

Download references

Acknowledgments

We thank Ed Schiefelbein, Karen Beaubien, Guillermo Velasquez, and members of Dr. Ruth Dill-Macky’s lab for collecting disease data used in this work. We also thank Dr. Shiaoman Chao for generating the marker genotype data. This research was supported by USDA NIFA 2006-55606-16722, USDA NIFA 2011-68002-30029, USDA-ARS U.S. Wheat and Barley Scab Initiative Grant No. 59-0790-4-120, and the Minnesota Agricultural Experiment Station Small Grains Initiative.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kevin P. Smith.

Electronic supplementary material

Below is the link to the electronic supplementary material.

11032_2015_390_MOESM1_ESM.tiff

Supplementary material 1 Fig. S1 Relationships between the \(\sigma_{\text{G}}^{2}\) predictor metric and \({\text{V}}_{{\widehat{\text{G}}}}\) for six prediction methods. The number of breeding populations (n) for PD is lower than the other five methods because only genotypes were available for some of the parents. As opposed to Figure 1, only breeding populations with a significant \({\text{V}}_{{\widehat{\text{G}}}}\) are considered (TIFF 60623 kb)

11032_2015_390_MOESM2_ESM.tiff

Supplementary material 2 Fig. S2 Relationship between μ sp and the number of progeny advanced across the 101 breeding populations whose parents were both included in the TP (TIFF 47822 kb)

11032_2015_390_MOESM3_ESM.tiff

Supplementary material 3 Fig. S3 Illustration of how to divide Figures 1 and S1 into quadrants for practical discussions (TIFF 48210 kb)

Supplementary material 4 (DOCX 37 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tiede, T., Kumar, L., Mohammadi, M. et al. Predicting genetic variance in bi-parental breeding populations is more accurate when explicitly modeling the segregation of informative genomewide markers. Mol Breeding 35, 199 (2015). https://doi.org/10.1007/s11032-015-0390-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11032-015-0390-6

Keywords

Navigation