Past and Present Issues in the Design of Variety Trials

IAMFE, Denmark 2008

Johannes Forkman

Swedish University of Agricultural Sciences

Swedish University of Agricultural Scienceswww.slu.se

Outline

1. Breeding Trials

2. Interference and Competition

3. Spatial Design

Swedish University of Agricultural Scienceswww.slu.se

Breeding Trials

• Large number of entries

• Objective: Selection

• The entries could be modeled as random

• Correlated by pedigree

Swedish University of Agricultural Scienceswww.slu.se

Multiple Lattice Design

5 14 17 4 13 6 C1 2 3 9

C4 8 9 20 18 C5 10 7 C3 19

16 2 C2 10 11 15 13 16 11 12

6 19 15 C3 C5 4 17 20 1 18

3 C1 1 12 7 14 5 C2 8 C4

Replicate I Replicate II

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Multiple Lattice Design

C3 29 C2 26 21 24 C3 C1 32 C4

38 C1 23 32 C5 37 22 26 35 38

27 37 30 24 34 C5 40 27 C2 31

28 25 31 40 33 39 30 23 21 33

35 36 39 C4 32 28 25 34 29 36

Replicate I Replicate II

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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)

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Related entries

• Split-plot design with related entries on whole plots?

• Maximize the number of groups per whole plot?

• Alpha design?

Swedish University of Agricultural Scienceswww.slu.se

Related entries

Alpha Design

More correct ranking of the entries

Swedish University of Agricultural Scienceswww.slu.se

Interference and Competition

Swedish University of Agricultural Scienceswww.slu.se

Interference Groups

1. Short varieties: A, B

2. Medium sized varieties: C, D, E, F, G

3. Tall varieties: H, I

Swedish University of Agricultural Scienceswww.slu.se

A C D E H I F G B

1 2 2 2 3 3 2 2 1

F G B A C D E H I

2 2 1 1 2 2 2 3 3

I H E D C A B G F

3 3 2 2 2 1 1 2 2

H I F E G B A D C

3 3 2 2 2 1 1 2 2

Initial design

Circularpermutation

Reversion

Randomizationwithin groups

Swedish University of Agricultural Scienceswww.slu.se

Interference Groups

• David and Kempton (1996)

• Similar varieties are kept together

• Weakly valid randomization

• Strong validity requires use of subblocks

Swedish University of Agricultural Scienceswww.slu.se

Covariance Analysis

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Covariance Analysis

• Use average difference in height as a covariate

• Guard plots at the ends of the blocks

Swedish University of Agricultural Scienceswww.slu.se

Covariance Analysis

• 65 spring wheat trials: 4% per decimeter

• 5 triticale trials: 2% per decimeter

• 17 barley trials: 3.5% per decimeter

Swedish University of Agricultural Scienceswww.slu.se

Neighbour-Balanced Design

I A B C D E

II A C E B D

III A D B E C

IV A E D C B

Swedish University of Agricultural Scienceswww.slu.se

Inter-Block Randomization

I A B C D E

II A C E B D

III A D B E C

IV A E D C B

Swedish University of Agricultural Scienceswww.slu.se

Neighbour-Balanced Design

I A B C D E

II A E D C B

III A C E B D

IV A D B E C

Swedish University of Agricultural Scienceswww.slu.se

Circular Permutation

I A B C D E

II A E D C B

III A C E B D

IV A D B E C

Swedish University of Agricultural Scienceswww.slu.se

Neighbour-Balanced Design

I C D E A B

II D C B A E

III C E B D A

IV B E C A D

Swedish University of Agricultural Scienceswww.slu.se

Border Plots

I B C D E A B C

   

II E D C B A E D

   

III A C E B D A C

   

IV D B E C A D B

Swedish University of Agricultural Scienceswww.slu.se

Neighbour-Balanced Design

• Strongly valid randomization

Swedish University of Agricultural Scienceswww.slu.se

Partially Neighbour-Balanced Design

I G J H I L D C E B F K A G J

   

II I K D J C A B L G F H E I K

   

III J I A H B K G C F D E L J I

Swedish University of Agricultural Scienceswww.slu.se

Spatial Design

I

II

III

Classical analysis Spatial analysis

I

II

III

Swedish University of Agricultural Scienceswww.slu.se

Spatial Design

Blocks, rows and columns are not needed?

Swedish University of Agricultural Scienceswww.slu.se

Spatial Design

• Blocks reduce the variance

• Restrictions should be taken into account in the analysis

• Restricted randomization within blocks

Swedish University of Agricultural Scienceswww.slu.se

R Q b Z V I f cU T J P X M e LE G O N K F D Bd W a C S H Y A

H S V I T D U Je L M Y b R Z KN O A X d W F Qc f G E B P a C

X Y f S G Q b PZ J H F L E W VD M K c U a N dA B T R C e I O

I F d e J Z G SP b Q U A O H Ea V L B N Y R TK C D W f c X M

IV

III

II

I

2-Latinized Row-Column Design

Swedish University of Agricultural Scienceswww.slu.se

Spatial Design

Design Analysis

Swedish University of Agricultural Scienceswww.slu.se

Thank you

for your attention!

Swedish University of Agricultural Scienceswww.slu.se

References

Åssveen, M. 1991. Konkurranseeffekter i bygg (Hordeum vulgare L.) Doctor Scientiarum Theses 1991:20. Agricultural University of Norway.

Azaїs, J.-M., Bailey, R. A. and Monod H. 1993. A catalogue of efficient neighbour-designs with border plots. Biometrics 49, 1252-1261.

Clarke, F. R., Baker, R. J. and DePauw, R. M. 1999. Using height to adjust for interplot interference in spring wheat yield trials. Canadian Journal of Plant Science 79 (2), 169-174.

David, O. and Kempton, R. A. 1996. Designs for interference. Biometrics 52, 597-606.John, J. A. and Williams, E. R. 1998. t-Latinized designs. Australian and New Zealand

Journal of Statistics 40, 111-118.Kempton, R. A., Gregory, R. S., Hughes, W. G. and Stoehr, P. J. 1986. The effect of

interplot competition on yield assessment in triticale trials. Euphytica 35, 257-265.Patterson, H. D. and Williams E. R. 1976. A new class of resolvable block designs.

Biometrika 63, 83-92.Piepho, H. P., Büchse, A. and Truberg B. 2006. On the use of multiple designs and a-

designs in plant breeding trials. Plant Breeding 125, 523-528.Piepho, H. P. and Williams, E. R. 2006. A comparison of experimental designs for

selection in breeding trials with nested treatment structure. Theoretical and Applied Genetics 113, 1505-1513.

Williams, E. R: 1985. A criterion for the construction of optimal neighbour designs. Journal of the Royal Statistical Society B 47, 489-497.

Williams, E. R., John, J. A. and Whitaker D. 2006. Construction of resolvable spatial row-column designs. Biometrics 62, 103-108.