1 / 22

PBG 650 Advanced Plant Breeding

PBG 650 Advanced Plant Breeding. Module 9: Best Linear Unbiased Prediction – Purelines – Single-crosses. Best Linear Unbiased Prediction (BLUP). Allows comparison of material from different populations evaluated in different environments

jayden
Download Presentation

PBG 650 Advanced Plant Breeding

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PBG 650 Advanced Plant Breeding Module 9: Best Linear Unbiased Prediction –Purelines – Single-crosses

  2. Best Linear Unbiased Prediction (BLUP) • Allows comparison of material from different populations evaluated in different environments • Makes use of all performance data available for each genotype, and accounts for the fact that some genotypes have been more extensively tested than others • Makes use of information about relatives in pedigree breeding systems • Provides estimates of genetic variances from existing data in a breeding program without the use of mating designs Bernardo, Chapt. 11

  3. BLUP History • Initially developed by C.R. Henderson in the 1940’s • Most extensively used in animal breeding • Used in crop improvement since the 1990’s, particularly in forestry • BLUP is a general term that refers to two procedures • true BLUP – the ‘P’ refers to prediction in random effects models (where there is a covariance structure) • BLUE – the ‘E’ refers to estimationin fixed effect models (no covariance structure)

  4. B-L-U • “Best” means having minimum variance • “Linear” means that the predictions or estimates are linear functions of the observations • Unbiased • expected value of estimates = their true value • predictions have an expected value of zero (because genetic effects have a mean of zero)

  5. Regression in matrix notation Linear model Y = X + ε Parameter estimates b = (X’X)-1X’Y

  6. BLUP Mixed Model in Matrix Notation • Fixed effects are constants • overall mean • environmental effects (mean across trials) • Random effects have a covariance structure • breeding values • dominance deviations • testcross effects • general and specific combining ability effects Design matrices Y = X + Zu + e Fixed effects Random effects Classification for the purposes of BLUP

  7. BLUP for purelines – barley example Parameters to be estimated • means for two sets of environments – fixed effects • we are interested in knowing effects of these particular sets of environments • breeding values of four cultivars – random effects • from the same breeding population • there is a covariance structure (cultivars are related) Bernardo, pg 269

  8. Linear model for barley example Yij =  + ti + uj + eij ti = effect of ith set of environments uj = effect of jth cultivar Y = X + Zu + e In matrix notation:

  9. Weighted regression Y = X + ε Where εij ~N (0, σ2) b = (X’X)-1X’Y For the barley example When εij ~N (0, Rσ2) Then b = (X’R-1X)-1X’R-1Y

  10. r = 2XY Remember Covariance structure of random effects XY

  11. Mixed Model Equations • each matrix is composed of submatrices • the algebra is the same -1 = Rσ2 Calculations in Excel

  12. Results from BLUP Original data BLUP estimates For fixed effects b1 =  + t1 b2 =  + t2

  13. Interpretation from BLUP BLUP estimates For a set of recombinant inbred linesfrom an F2 cross of Excel x Stander Predicted mean breeding value = ½(0.18+0.36) = 0.27

  14. Shrinkage estimators • In the simplest case (all data balanced, the only fixed effect is the overall mean, inbreds unrelated) • If h2 is high, BLUP values are close to the phenotypic values • If h2 is low, BLUP values shrink towards the overall mean • For unrelated inbreds or families, ranking of genotypes is the same whether one uses BLUP or phenotypic values

  15. Sampling error of BLUP • Diagonal elements of the inverse of the coefficient matrix can be used to estimate sampling error of fixed and random effects -1 = invert the matrix Rσ2 each element of the matrix is a matrix coefficient matrix

  16. Sampling error of BLUP fixed effects random effects

  17. Estimation of Variance Components (would really need a larger data set) • Use your best guess for an initial value ofσε2/σA2 • Solve for  and û • Use current solutions to solve for σε2and then forσA2 • Calculate a newσε2/σA2 • Repeat the process until estimates converge ˆ

  18. BLUP for single-crosses Performance of a single cross: BLUP Model • Sets of environments are fixed effects • GCA and SCA are considered to be random effects GB73,Mo17 = GCAB73 + GCAMo17 + SCAB73,Mo17 Y = X + Ug1 + Wg2 + Ss + e Example in Bernardo, pg 277 from Hallauer et al., 1996

  19. Performance of maize single crosses Iowa Stiff Stalk x Lancaster Sure Crop

  20. Covariance of single crosses SC-X is jxkSC-Yis j’xk’ B73, B84, H123 MO17, N197 assuming no epistasis

  21. Covariance of single crosses SC-X is jxkSC-Yis j’xk’ SC-1=B73xMO17 SC-2=H123xMO17 SC-3=B84xN197

  22. Solutions -1 X

More Related