2. Past and Present Issues in the Design of Variety Trials
IAMFE, Denmark 2008
Johannes Forkman
Swedish University of Agricultural Sciences

3. Outline
Breeding Trials
Interference and Competition
Spatial Design

4. Breeding Trials
Large number of entries
Objective: Selection
The entries could be modeled as random
Correlated by pedigree

5. Multiple Lattice Design
Replicate I Replicate II 5 14 17 4 13 6 C1 2 3 9 C4 8 20 18 C5 10 7 C3 19 16 C2 11 15 12 1

6. Multiple Lattice Design
Replicate I Replicate II C3 29 C2 26 21 24 C1 32 C4 38 23 C5 37 22 35 27 30 34 40 31 28 25 33 39 36

7. Alpha Design
A family of resolvable incomplete block designs introduced by Patterson and Williams (1976)
Requires less plots than multiple lattice designs
More efficient than multiple lattice designs (Piepho, Büchse and Truberg, 2006)

8. Related entries Split-plot design with related entries on whole plots?
Maximize the number of groups per whole plot?
Alpha design?

9. Related entries
Alpha Design
More correct ranking of the entries

10. Interference and Competition

11. Interference Groups
Short varieties: A, B
2. Medium sized varieties: C, D, E, F, G
3. Tall varieties: H, I

12. A C D E H I F G B 1 2 3 Initial design Circular permutation Reversion
Randomization
within groups

13. Interference Groups David and Kempton (1996)
Similar varieties are kept together
Weakly valid randomization
Strong validity requires use of subblocks

14. Covariance Analysis

15. Covariance Analysis
Use average difference in height as a covariate
Guard plots at the ends of the blocks

16. Covariance Analysis 65 spring wheat trials: 4% per decimeter
5 triticale trials: 2% per decimeter
17 barley trials: 3.5% per decimeter

17. Neighbour-Balanced DesignII
III IV

18. Inter-Block RandomizationII
III IV

19. Neighbour-Balanced DesignII
III IV

20. Circular Permutation I A B C D E II
III IV

21. Neighbour-Balanced DesignII
III IV

22. Border Plots I B C D E A II
III IV

23. Neighbour-Balanced Design
Strongly valid randomization

24. Partially Neighbour-Balanced DesignJ H L D C E B F K A II
III

25. Spatial Design
Classical analysis Spatial analysis I II
III I II
III

26. Spatial Design
Blocks, rows and columns are not needed?

27. Spatial Design Blocks reduce the variance
Restrictions should be taken into account in the analysis
Restricted randomization within blocks

28. 2-Latinized Row-Column DesignIV
III II I

29. Spatial Design
Design Analysis

30. Thank you
for your attention!

31. References
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Clarke, F. R., Baker, R. J. and DePauw, R. M Using height to adjust for interplot interference in spring wheat yield trials. Canadian Journal of Plant Science 79 (2),
David, O. and Kempton, R. A Designs for interference. Biometrics 52,
John, J. A. and Williams, E. R t-Latinized designs. Australian and New Zealand Journal of Statistics 40,
Kempton, R. A., Gregory, R. S., Hughes, W. G. and Stoehr, P. J The effect of interplot competition on yield assessment in triticale trials. Euphytica 35,
Patterson, H. D. and Williams E. R A new class of resolvable block designs. Biometrika 63,
Piepho, H. P., Büchse, A. and Truberg B On the use of multiple designs and a-designs in plant breeding trials. Plant Breeding 125,
Piepho, H. P. and Williams, E. R A comparison of experimental designs for selection in breeding trials with nested treatment structure. Theoretical and Applied Genetics 113,
Williams, E. R: A criterion for the construction of optimal neighbour designs. Journal of the Royal Statistical Society B 47,
Williams, E. R., John, J. A. and Whitaker D Construction of resolvable spatial row-column designs. Biometrics 62,