The design and analysis of multi-phase variety trials using both ... · The design and analysis of multi-phase variety trials using both composite and individual replicate samples

The design and analysis of multi-phasevariety trials using both composite and

individual replicate samples.

Alison Smith1 David Butler2 & Brian Cullis13

1 School of Mathematics & Applied Statistics, University of Wollongong, Australia2 Department of Agriculture, Fisheries & Forestry, Qld, Australia

3 Mathematics, Informatics & Statistics, CSIRO, Australia

XVth Eucarpia Biometrics in plant breeding

Brian Cullis Multi-phase variety trials with partial compositing

Collaborations and Acknowledgements

• This presentation is joint work through the Statistics for theAustralian Grains Industry project funded by GrainsResearch and Development Corporation (GRDC).

• Thanks to Robin Thompson (Rothamsted Research, UK)for unstinting support and inspiration

• Colin Cavanagh and Marcus Newberry (Plant Industries)for helpful discussions and stimulating some of the ideas.


MotivationTraditional applications

• Phenotyping remains one of the major costs andchallenges in plant improvement programs

• Genetic gain using traditional selection approachesdepends on the accuracy of the predictions of eitheradditive and/or total genetic effects

• Example 1 - Protocols for wheat variety classification• Phenotyping for quality traits in wheat involves use of multi-phase

experiments but due to the cost (A$1000 per sample for allclassification traits) most common approach uses no design withcomposite samples.

• Accurate classification of wheat varieties for end-use capabilitiesis crucial since growers are paid differentially on this basis.

• Traits including flour yield and dough and baking characteristics;current phenotyping protocols lack statistical rigour


MotivationExample 2: Marker-trait association and genomic selection for complex traits

• Meuwissen (this meeting) listed the factors that underlieand determine the accuracy of genomic selection. Twoinvolve phenotypic information and are

• size of the training population and• trait heritability (narrow sense).

• Phenotyping either large training populations or mappingpopulations is both challenging and costly

• Use of inappropriate, inefficient experimental design andanalysis will lead to reduced accuracy (through lowerheritability)

• Use of appropriate, efficient experimental design andanalysis can lead to SUBSTANTIAL improvements inaccuracy (through higher heritability)


Designs for variety trialsm varieties, r replicates

• Traditional experiment designs were about low m < 20large r > 3

• With large m > 50 (often more than 1000) resources, costsand seed supply usually results in low r < 3 (often 1).

• Costs, high throughput and lack of awareness have allhave led to widespread use of inefficient phenotypingprotocols with use of poor experimental design andinefficient methods of analysis in many plant improvementprograms and genomic and marker-trait associationstudies


High m, low r < 2 design solutionsBrief review

• p-rep designs (Cullis et al., 2006) replacement forcheck-plot designs, used for phenotyping field traits

• p/q-rep designs (Smith et al., 2006) replacement for nodesigns for phenotyping traits in laboratory (ie multi-phasefield-lab designs)

• Partial compositing and embedded designs (Smith et al.,2011) replacement for fully composited or single replicatephenotyping of expensive (eg physical grain traits, oil %,protein %) field traits

• Designs for correlated variety effects using marker orpedigree based information (Butler et al., 2012)

• multi-phase designs with mixture of individual andcomposite samples: today’s presentation


Example 1Wheat variety classification project

• Aim of this project is to enable estimation of all sources ofvariation for traits relevant for wheat variety classification.

• Full project spans 3 years with 24 field trials grown inlocations across Australia each year.

• Here consider the experimental design for themeasurement of flour yield for one of these field trials.

• Field trial comprised 54 plots arranged in a rectangulararray of 6 columns by 9 rows.

• r = 3 replicates, m = 18 varieties, replicate blocks alignedwith pairs of columns.


Example 1: Milling designsPractical constraints

• Grain samples will be taken from each plot and, providedthe trial meets certain protein specifications, all 18 varietieswill be milled to obtain flour yield.

• We present various approaches for designing the millingphase of this trial, noting that budgetary constraintsrestricts 40 samples for milling.

• Further practical constraints for quality testing usuallyrequire a minimum amount of grain. Here we need aminimum of 2kg of grain to allow measurement of all traits

• For illustrative purposes and to keep things simpler weignore this constraint for the moment

• Example 2 accounts for this additional constraint


Example 1p/q-rep approach

• Fully replicated design with 18 varieties, 3 field replicatesand two laboratory replicates would require 180 samples!

• Constraint of 40 milling samples can be achieved using ap/q-rep design with p = q = 1/3.

• Choose 6 varieties with 3 field replicates, 12 varieties withone field replicate and of these choose 10 to be replicatedin the laboratory (ie milling) phase.

• That is, there are 30 so-called field samples, and 10 arereplicated in the laboratory to produce 40 milling samples

• Plots chosen to be replicated in the laboratory providereasonable spatial coverage


Example 1: p/q-rep approachField layout showing plots milled

• Grey and white plots milled as individual replicates(varieties in grey single replicate only; varieties in white all3 replicates; 30 of these).

• Blue plots will not be milled (24 of these - see later).• Plots replicated in the milling phase are circled (10 of

these).

Column

Row

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6

Derrimut

Emu Rock

Janz

Crusader

Gregory

Katana

Lincoln

Kennedy

Cunningham

Yitpi

Wallup

GBA Sapphire

Elmore Cl Plus

Bonnie Rock

Annuello

Mace

Longreach Cobra

King Rock

GBA Sapphire

Derrimut

Crusader

Bonnie Rock

Wallup

Lincoln

Gregory

Annuello

Longreach Cobra

Emu Rock

Mace

Cunningham

Janz

Elmore Cl Plus

Yitpi

Kennedy

King Rock

Katana

Yitpi

Crusader

Longreach Cobra

Wallup

Janz

King Rock

Elmore Cl Plus

Gregory

Emu Rock

Mace

Kennedy

Derrimut

Cunningham

Lincoln

Bonnie Rock

Katana

GBA Sapphire

Annuello


Example 1: p/q-rep approachGenerating the milling design using od

• Given a valid design for the first phase we seek a secondphase design using the model-based techniques of Butleret al. (2013b).

• Uses extended A-optimality criteria for random effects (seeBueno Filho and Gilmour, 2007)

• od package in R produces designs given a specified model(and associated variance parameter values) and startingdesign. (od stands for “optimal design” but more like“over-done”!)

• The starting design is created and then od undertakes asupervised search of design space via permutation of the40 mill samples (formed from the 30 field samples: in thiscase field plots) subject to resolvability constraints


Example 1: p/q-rep approachFinal milling design

Final p/q-rep mill design:• 8 samples per day, each day is split into 2 half days, so

total of 10 milling “sessions” (factor MBlk)• Enforce resolvability for MRep sessions 1 to 4 and 5 to 8

respectively with respect to the 10 field samples which arereplicated in the laboratory

pq.init <- od.init(Geno=1.0,Frep=0.1,Column=0.1,FRow=0.1,FPlot=0.2,MRep=0.3,MBlk=0.2)pq.od <- od(fixed=∼1,random = ∼Geno + FRep + FRow +Fcol + FPlot + MRep + MBlk, permute= ∼Geno|FRep +FCol + FRow + FPlot, swap= ∼MRep,Gstart=milldes.G,data=pqinit.df, . . . )


Example 1: p/q-rep approachMilling layout

• 40 samples 4 per session with 2 sessions per day (orders1-4 and 5-8) and for 5 days.

• Samples labelled by variety and FRep.• 30 field samples; replicated samples coloured grey (10).• MRep 1 = days 1,2 and session 2 day 3; MRep 2 = session

1 day 3 and days 4 and 5).

Milling day

Ord

er w

ithin

day

1

2

3

4

5

6

7

8

1 2 3 4 5

Longreach Cobra:1

GBA Sapphire:3

Emu Rock:2

Bonnie Rock:3

Derrimut:2

Cunningham:2

Annuello:2

Gregory:2

Lincoln:1

Kennedy:1

Katana:1

Janz:1

Yitpi:1

Mace:2

Elmore Cl Plus:1

King Rock:1

Wallup:3

Longreach Cobra:3

Crusader:3

Gregory:3

Yitpi:2

Cunningham:2

Emu Rock:2

Kennedy:2

Annuello:2

Mace:1

Lincoln:3

GBA Sapphire:3

Mace:3

Crusader:3

Bonnie Rock:3

Kennedy:3

Yitpi:3

Lincoln:2

Derrimut:2

Longreach Cobra:2

Gregory:1

Katana:1

Elmore Cl Plus:1

Janz:1


Example 1Partial compositing

• p/q-rep design produces milling design with 40 samplesbut,

• wasteful of information using only 30/54 field plots.• Smith et al. (2011) suggested the use of mixture of

individual replicates for a proportion of varieties andcomposite samples for the remainder.

• For the latter a single sample is used for each variety but itrepresents a composite sample from all replicate plots forthat variety rather than just a sample from a singlereplicate.

• Analysis proceeds as “usual” without much loss ofaccuracy compared to analysis based on analysis usingindividual replicates


Example 1: Partial compositingTwo strategies ignoring grain amount constraints

• Strategy A:• C3: 12 field samples created for 12 varieties by compositing all 3

field reps for each variety• IR: 18 field samples created for each of 6 varieties × 3 field reps

• Strategy B:• C3: 10 field samples created for each of 10 varieties by

compositing all 3 field reps• C2: 8 field samples created for each of 4 varieties by compositing

2 field reps and separate sample for remaining field rep• IR: 12 field samples created for each of 4 varieties × 3 field reps


Example 1: Partial compositingField layout for strategy B

• Grey plots milled as composites of all 3 freps/variety (30 ofthese);

• Pink plots milled as composites of 2 freps/variety (8 ofthese);

• White plots milled as individual freps/variety (16 of these).• Plots replicated in the milling phase are circled (10).

Column

Row

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6

Derrimut

Emu Rock

Janz

Crusader

Gregory

Katana

Lincoln

Kennedy

Cunningham

Yitpi

Wallup

GBA Sapphire

Elmore Cl Plus

Bonnie Rock

Annuello

Mace

Longreach Cobra

King Rock

GBA Sapphire

Derrimut

Crusader

Bonnie Rock

Wallup

Lincoln

Gregory

Annuello

Longreach Cobra

Emu Rock

Mace

Cunningham

Janz

Elmore Cl Plus

Yitpi

Kennedy

King Rock

Katana

Yitpi

Crusader

Longreach Cobra

Wallup

Janz

King Rock

Elmore Cl Plus

Gregory

Emu Rock

Mace

Kennedy

Derrimut

Cunningham

Lincoln

Bonnie Rock

Katana

GBA Sapphire

Annuello


Example 1: Partial compositingMilling layout for strategy B: better than A

• Laboratory phase as for p/q-rep approach• Samples labelled by variety and field replicate status.• A total of 30 field samples milled (representing 54 field

plots)• 10 field samples replicated in the milling process (samples

coloured grey).

Milling day

Ord

er w

ithin

day

1

2

3

4

5

6

7

8

1 2 3 4 5

Mace:CR23

Gregory:IR2

Derrimut:CR13

Yitpi:IR1

Gregory:IR1

Katana:CR12

Yitpi:IR2

Janz:CR123

Crusader:CR123

Wallup:CR123

Kennedy:IR1

Lincoln:IR3

King Rock:CR123

Gregory:IR3

Emu Rock:CR123

Kennedy:IR2

Annuello:CR123

Lincoln:IR2

Kennedy:IR3

Longreach Cobra:CR12

Gregory:IR3

Longreach Cobra:IR3

Yitpi:IR3

Kennedy:IR1

Lincoln:IR3

Yitpi:IR2

Gregory:IR2

Cunningham:CR123

Katana:IR3

Kennedy:IR3

Derrimut:IR2

Lincoln:IR1

Bonnie Rock:CR123

Lincoln:IR2

GBA Sapphire:CR123

Yitpi:IR1

Mace:IR1

Elmore Cl Plus:CR123

Kennedy:IR2

Gregory:IR1


Example 1: Partial compositingWRAP UP

• EXIT stage right!• This approach is good but ignores grain amount

constraints, and• perhaps not the best approach as we should also relax

constraint to replicate IR samples in milling proces: givesbetter balance with replication across varieties

• Issue of BIG with BIG (Chris Brien and Rosemary Bailey)and many more . . .


Example 2: Genomic selection in wheatField trial and summary of milling entries/plots

• 1000 field plots arranged as 50 rows × 20 columns• 773 entries (760 lines, 13 varieties); 544 single plot, 213

two plots and 6 more than 2 plots, p-rep design• 480 entries (471 lines, 9 varieties) chosen on genetic

diversity and amount of grain

All entries Entries for millingPlots/entry Entries Plots Entries Plots

1 554 554 330 3302 213 426 145 2883 4 12 3 34 2 8 2 2

Total 773 1000 480 623


Example 2: Genomic selection in wheatSummary of milling and compositing approach

• I1 entries: tested as single field replicate• I2 entries: tested as two field replicates• C2 entries: tested as composite of two field replicates• 78 milling days, 7 samples per days with resolvable milling

replicates (MRep 1: 1 to 39, MRrep 2: 40 to 78)

Testing Field Field MillingRegime Entries Plots Samples SamplesI1 337 337 337 349I2 29 58 58 58C2 114 228 114 139Total 480 623 509 546


Example 2: Genomic selection in wheatWhich entries composited? Which field samples replicated?

• A very low yielding trial so many individual field plots withinsufficient grain for milling. Thus

• Most of entries composited were done this way otherwise notpossible to mill at all (insufficient grain for a single milling samplefrom individual plots)

• Most of field samples replicated in lab were composite samplesotherwise very few lab replicates possible (insufficient grain fortwo milling samples from individual plots)

• Final milling design again generated using od based on themodel we will most likely use for analysis (details notpresented)


Example 2: Genomic selection in wheatLaboratory replication of composite samples

• Concept of splitting composite field samples to makereplicates for lab is radical!

• Not recommended unless necessary (as was case here)• Simulation study showed negligible bias in REML estimate

of genetic variance (but small bias for field plot errorvariance)

• Implementation needs care and use of novel designapproaches, BUT . . .


Example 2: Genomic selection in wheatWRAP UP

• Approach uses maximum number of field plots and fitswithin the budgetary constraint of less than 550 millingsamples

• Phenotyping protocols use an efficient and statisticallyvalid experimental design and analysis

• Have used these ideas on many two and three phaseexperiments and these designs and subsequent analyseshave accounted for numerous sources of non-geneticvariation and

• hence results in significant improvements in accuracy!


For Further Reading I

B. R. Cullis, A. B. Smith, N. E. Coombes.On the design of early generation variety trials.Journal of Agricultural, Biologicaland EnvironmentalStatistics, 2(1):50–100, 2006.

A. B. Smith, P. Lim, B. R. Cullis.The design and analysis of multi-phase plant breedingexperiments.Journal of Agricultural Science, 144:393-409, 2006.

D. G. Butler, J. A. Eccleston, and B. R. Cullis.On an approximate optimality criterion for the design of fieldexperiments under spatial dependence.Australian and New Zealand Journal of Statistics,50:295–307, 2008.


For Further Reading II

A. B. Smith, R. Thompson, D. G. Butler, and B. R. Cullis.The analysis of variety trials using mixtures of compositeand individual plot samples.Journal of the Royal Statistical Society, Series C,60:437–455, 2011.

D. G. Butler, A. B. Smith and B. R. Cullis.On the design of experiments where treatment effects arecorrelated.submitted.

D. G. Butler, A. B. Smith and B. R. Cullis.On model based design of comparative experiments.submitted.


For Further Reading III

A. B. Smith, D. G. Butler, C. Cavanagh and B. R. Cullis.The design and analysis of multi-phase variety trials usingboth composite and individual replicate samples.submitted.


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The design and analysis of multi-phase variety trials using both ... · The design and analysis of multi-phase variety trials using both composite and individual replicate samples