in linkage or association mapping population, thereby allowing the researcher to interpret quantitative genetic variation in terms of biologically meaningful causal networks of correlated transcripts. In other words, it can be used to define biological networks and to predict molecular interactions by analyzing transcripts with expressions that co‐vary within genetic populations. The approach can be used to analyze effects of genome‐wide genetic variants on transcriptome‐wide variation in gene expression.
4.5 Predicting breeding value
Breeding value (or genetic merit) of an individual as a genetic parent is the sum of gene effects of the individual as measured by the performance of its progeny. Statistically, it is measured as twice the deviation of the offspring from the population mean (since the individual only contributes half of the alleles to its offspring). This estimate measures the ability of an individual to produce superior offspring. This is the part of an individual's genotypic value that is due to independent gene effects and hence can be transmitted. The mean breeding value becomes zero with random mating. This estimate is of importance to breeders because it assists them in selecting the best parents to use in their programs.
The Best Linear Unbiased Prediction(BLUP) is a common statistical method for estimating breeding values. It is unbiased because as more data are accumulated, the predicted breeding values approach the true values. BLUP is a method of estimating random effects. The context of this statistical method is the linear model
where y = is a vector of n observable random variables; B is vector of p unknown parameters with fixed value or effects; X and Z are known matrices; u and e are vectors of q and n, respectively, unobservable random variables (random effects).
To apply this technique, numerical scores are assigned to traits and compiled as predictions of the future. Simple traits can be most accurately and objectively measured and possibly predicted. Only one trait may be predicted in a model. This trait has to be objectively measurable with high accuracy. Further, it has to be heritable.
4.6 Genomic selection (genome‐wide selection)
Genomic selection and its application in plant breeding is the subject of Chapter 25. Selection in conventional plant breeding generally relies on breeding values estimated from pedigree‐based mixed models that cannot account for Mendelian segregation, and in the absence of inbreeding, can only explain one half of the genetic variability (individual contributes only half of its alleles to the next generation as previously stated). Molecular markers have the capacity to track mendelian segregation as several positions of the genome of the organism, thereby increasing the accuracy of estimates of genetic values (and the genetic progress achievable when the predictions are used for selection in breeding). Even though marker‐assisted selection (MAS) (see Chapter 24) has achieved some success, its application to improving quantitative traits is hampered by various factors. The biparental mating designs used for detection of loci affecting quantitative traits and statistical methods used are not well‐suited to traits that are under polygenic control (MAS uses molecular markers in linkage disequilibrium with QTL).
Genomic selection (or genome‐wide selection) is proposed as a more effective approach to improving quantitative traits. It uses all the available molecular markers across the entire genome (there are thousands of genome‐wide molecular markers) to estimate genetic or breeding values. Using high‐density marker scores in the prediction model and high throughput genotyping, genomic selection avoids biased marker effect estimates and captures more of the variation due to the small‐effect QTL. Genomic selection has advantages. It can accelerate the selection cycles and increase the selection gains per unit time.
4.7 Mapping quantitative traits
The subject of mapping is treated in detail in Chapter 22. Quantitative traits pose peculiar challenges to plant breeders compared to qualitative traits. They are difficult to map and breed. Over the years, researchers have developed new methodologies to address these challenges, thereby enabling breeders to achieve genetic gain more rapidly in their endeavors.
Key references and suggested reading
1 Ali, A. and Johnson, D.L. (2000). Heritability estimates for winter hardiness in lentil under natural and controlled conditions. Plant Breeding 119: 283–285.
2 Bernardo, R. (2002). Breeding for Quantitative Traits in Plants, 369. Stemma Press.
3 Bernardo, R. and Yu, J. (2007). Prospects for genome‐wide selection for quantitative traits in maize. Crop Science 47: 1082–1090.
4 Bhatnagar, S., Betran, F.J., and Rooney, L.W. (2004). Combining abilities of quality protein maize inbreds. Crop Science 44: 1997–2005.
5 Bohren, B.B., McKean, H.E., and Yamada, Y. (1961). Relative efficiencies of heritability estimates based on regression of offspring on parent. Biometrics 17: 481–491.
6 Cockerham, R.E., Robinson, H.F., and Harvey, P.H. (1949). A breeding procedure designed to make maximum use of both general and specific combining ability. Journal of American Society of Agronomy 41: 360–367.
7 Crossa, J., Perez, P., de los Campos, G. et al. (2010). Genomic selection and prediction in plant breeding. In: Quantitative Genetics, Genomics, and Plant Breeding, 2e (ed. M.S. Kang), 269–288.
8 Edwards, J.W. and Lamkey, K.R. (2002). Quantitative genetics of inbreeding in a synthetic maize population. Crop Science 42: 1094–1104.
9 Falconer, D.S. (1981). Introduction to Quantitative Genetics. New York: Longman Group, Ltd.
10 Falconer, D.S. and Mackay, T.F.C. (1996). Introduction to Quantitative Genetic, 4e. Harlow, UK: William Longman.
11 Gallais, A. (2003). Quantitative Genetics and Breeding Methods in Autopolyploid Plants. Paris: INRA 513p.
12 Gardner, C.O. (1977). Quantitative genetic studies and population improvement in maize and sorghum. In: Proc. Int. Conf. Quantitative Genetics (eds. E. Pollak, O. Kempthorne and T.B. Bailey), 475–489. Ames, Iowa: Iowa State University.
13 Glover, M.A., Willmot, D.B., Darrah, L.L. et al. (2005). Diallele analysis of agronomic traits using Chinese and US maize germplasm. Crop Science 45: 1096–1102.
14 Griffing, B. (1956). A generalized treatment of the use of diallele crosses in quantitative inheritance. Heredity 10: 31–50.
15 Griffing, B. (1956b). Concept of general and specific combining ability in relation to a diallele crossing system. Australian Journal of Biological Sciences 9: 463–493.
16 Heffner, E.L., Sorrells, M.E., and Jannink, J. (2009). Genomic selection for crop improvement. Crop Science 49 (1): 12.
17 Henderson, C.R. (1963). Selection index and expected genetic advance. In: Statistical Genetics and Plant Breeding (eds. W.D. Hanson and H.F. Robinson). Washington, D.C.: Nat. Acad. Sci. Nat. Res. Council Publ. No. 982.
18 Hill, W.G. (2010). Understanding and using quantitative genetic variation. Philosophical Transactions of The Royal Society B Biological Sciences 365 (1537): 73–85.
19 Hill, J., Becker,
