Accounting for variation in designing greenhouse experiments Chris Brien 1, Bettina Berger 2, Huwaida Rabie 1, Mark Tester 2 1 Phenomics & Bioinformatics

Accounting for variation in designing greenhouse experiments

Chris Brien1, Bettina Berger2, Huwaida Rabie1, Mark Tester2

1Phenomics & Bioinformatics Research Centre, University of South Australia; 2Australian Centre for Plant Functional Genomics, Adelaide.

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Outline

1. The issues.

2. The PA experiment.

3. Results of the experiment.

4. Uniformity trials to compare designs.

5. Current designs.

6. Conclusions.

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1. The issues The Plant accelerator ®

Latest technology in high throughput plant imaging Plants are first grown in a Greenhouse then moved to the

imaging room (Smarthouse) Automatic, non-destructive, repeated measurements of

the physical attributes (phenotype) of plants in Smarthouse.

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Issues in designing PA experiments At least two phases: Greenhouse and Smarthouse

phases. Should one worry about design at all?

o Perhaps better to rearrange location of plants during the experiment to average out microclimate effects.

Even if design Smarthouse phase, do we need to worry about design in the Greenhouse phase?

If do use designs, what design to use in a phase? What N-S or E-W trends should be accounted for? Is there spatial correlation?

Does movement in PA have a thigmomorphogenic or other effect of movement? Other possible effects of movement are soil compaction

and or root damage due to soil movement.

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2. The PA experiment Ran a two-phase wheat experiment in PA.

Brien & Bailey (2006) and Brien et al (2011) discuss such experiments;

They generally involve multiple allocations and/or randomizations.

In this case, a Greenhouse and a Smarthouse phase.

All plants are Gladius. Specifically designed soil substrate to circumvent

soil movement effects.

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Greenhouse phaseEast

Western door

North South

Air con

288 pots

2 Sides2 Blocks3 Rows in S24Columns in B

The 2 Sides by 2 Blocks correspond to 4 Locations in the Greenhouse.

No allocations

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Smarthouse phase: allocation of pots to carts

North

West

SouthZone 1

Zone 2Zone 3Zone 4

288 carts

4 Zones3 Lanes in Z24Positions

Smarthouse

288 pots


Greenhouse

EastNorth

SouthAir con

Zone 1Zone 2

Zone 3Zone 4

Solid lines indicate randomization while dashed lines indicate systematic assignment.

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Smarthouse tactics

Four tactics, each of 3 rows of 24 carts, were applied in the Smarthouse:1. Bench: Plants placed on benches at the end of the

conveyer system and not moved – no relocation;2. Same lane: always return to the same position after

watering or imaging – standard practice;3. Half lane: After watering or imaging, move pots forward

half a lane, which will result in pots changing sides from East to West and vice-a-versa with each move – restricted relocation;

4. Next lane: After watering or imaging, move the whole lane forward to the next lane in the Smarthouse – restricted relocation.

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Allocation of Smarthouse tactics Pots have been allocated to carts . Four tactics are systematically allocated to zones.

288 carts

4 Zones3 Lanes in Z24Positions

Smarthouse

288 pots


Greenhouse

4 treatments

4 Tactics

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Smarthouse phase

North

West

South

Air con

Imaging

Bench

SameHalfNext

North

Zone 4 – Next lane

West

Air con

Zone 3 – Half lane

East

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3. Results: data obtained Fresh weight at the end of the trial Total area (pixels) on Mon, Wed & Fri from day 21

to day 51. Height (cm) on day 51, from which derived a

Density index ( = Total area / height).

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Profile plots of the longitudinal data

Next lane has slower

growth is more

variable.

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Predicted growth curves using splines

Next lane has slowest growth

Half-lane has fastest growth

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Total area measurements for Days 21 and 51 Focus on these:

Day 21 represents the effect of the Greenhouse; Day 51 represents the combined effect of the

Greenhouse and Smarthouse. Mixed models:

Tactics + Tactics Lanes + ∧ td(Positions) + td(Positions) Tactics ∧| idh(Tactics) Lanes∧ ∧ar1(Positions)o td means investigate trend over this factor;o idh mean investigate unequal variances between levels;o ar1 mean investigate autocorrelation between levels.

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Results of mixed model analyses

Similar models for Day 21 and Day 51. Differences in means and variances between the

Tactics. However, no differences between bench and same lane

for any responses (including density index). No evidence of spatial correlation. No differences between the three Lanes within

each Tactic. Trends over Columns in the greenhouse and

Positions in the Smarthouse that differ between Tactics.

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Column/Position trends in Total areaDay 21 Day 51

Area increases eastwards in the Greenhouse, mainly in south (light?). Increasing slope for all on Day 51, except for half-lane.

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Position trends for Day 51 adjusted for Day 21

For same lane (and probably bench) there is a trend in the Smarthouse that increases from West to East (air in W).

The Position trend in next lane parallels Column trend in Day 21 total areas — greenhouse or Smarthouse?

For half lane, no Smarthouse Position trend — little Column trend in north-east and no Smarthouse contribution.

Day 51

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Lane trend

Three split plots Exp. 1 – 22 lines and 3 conditions in 8 blocks; conditions

in 3 vertical subplots. Exp. 2 – 153 lines and 2 conditions in 3 blocks; lines

partially replicated; conditions in 2 horizontal subplots. Exp. 3 – 214 lines and 2 conditions in 8 blocks; lines

partially replicated; conditions in 2 vertical subplots.

Jo Tillbrooks’ 2011 experiments – fill Smarthouse

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Estimated lane trend

Plants in Lanes towards north grow less no. lanes with lower area depends on time of the year.

Seems about 4 lanes are homogeneous. It would appear that the lower total area for next-

lane tactic is due to shading in the northern zone.

Ribbons are CIs

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Relative efficiencies from taking lane & position into account

Experiment1 2 3

No trend 100.0 100.0 100.0Lane trend 139.9 236.07 146.8

Position trend 102.8 95.9 98.0Lane + Position trend 148.8 230.1 147.7

The efficiencies are relative to the no-tend analysis.

Gains vary. Gains in efficiency of 40% or more can be

expected from allowing for lane trends. A 10% gain in efficiency can be expected from

allowing for position trends in Experiment 1 only, and provided that lane trends allowed for.

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Relocation during the PA experiment In half-lane tactic:

Plants spend half time in eastern half and western half; Plants not equal in exposure to trend: when carts 13–24

moved to positions 1–12, relative east west positions maintained;

Result is unable to detect trend, but greater individual plant variability (30% less precision).

In next-lane tactic: Plants spend equal amount of time in shaded lanes; 5 or less days difference in entry of 1st and exit of 3rd

lanes; No difference between lanes of next-lane tactic supports

uniform exposure of plants to lane trend.

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4. Uniformity trials to compare designs

Each tactic, 3 Lanes 24 Positions, is essentially a uniformity trial (all Gladius, all treated equally).

Perfect for comparing different designs to deal with position trends: Superimpose treatments (lines) on a zone using different

designs; Analyse the total area according to the design; Compute the relative efficiencies (%) of designs: Repeat for a random sample of possible randomizations

of the designs.

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Relative efficiency (relative to a CRD) For a Proposed Design or Analysis (PDA):

CRDPDA

PDA

100AP

REAP

where each 21, ,1 .d diffAP F

It is a modified A-optimality criterion, the F taking into account any differences in denominator df.

It compares the average sizes of the confidence intervals for pairwise differences between predictions for treatments.

PDA with REPDA > 100 is more efficient than a CRD: it has smaller s.e.d.s and so better able to detect

treatment (line) differences.

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Equally-replicated lines Consider the following designs & analyses with 36

(24) lines:1) A CRD, without and with adjustment for Position trend;

2) An RCBD with two 3 12 (three 3 8 & 1 24) blocks, without and with adjustment for Position trend;

3) (Nearly) Trend-free designs for CRD & RCBD (DiGGer);

4) Resolved IBDs with blocks 3 1, 1 4 & 3 6 (3 1, 1 4 & 3 4) (CycDesigN);

5) Resolved row-col designs with two 3 12 (three 3 8) rectangles.

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2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

3

2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

3

2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

3

2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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Equally-replicated lines

Look for designs which give > 10% increase for all tactics. For 36 lines: small blocks,

CRD + Adj, or TFD; but, TFCBD312EqLin best for same & next.

For 24 lines: small blocks, CRD + Adj, RCBD 38 ( RRCD 38); TF or NTF no advantage.

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Partially-replicated lines, with 2 conditions (an initial investigation) A split-plot design for 72 carts with:

1) 6 (or 8) duplicated lines, 20 (or 16) unreplicated lines and 2 control lines replicated twice;

2) Lines applied to 36 main plots, of 2 consecutive carts in the same lane, using an augmented block design;

3) 2 conditions randomized to the 2 subplots (carts) of a main plot.

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2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

3

2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Again, looked at designs with varying block sizes.

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2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

3

2

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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Partially-replicated lines, with two conditions Look for designs which

give > 10% increase for all tactics. Line comparisons: best is

main plots (2 carts) of 33 (= 3 Lanes 6 Positions) for t6 & t8, and 32 (= 3 Lanes 4 Positions) for t6.

Conditions comparisons: little affected (as assigned to carts), but same designs best.

t6 t6t8 t8

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5. Current designs Smarthouse experiments run with 24 lanes x 22 positions

528 carts. Maximum of 23 carts per row because of weight limitations of

conveyor system. Smarthouse divided into:

(6 zones of 4 lanes) x (2 halves of 10 & 12 positions). Block designs for 12 blocks.

Nearly trend-free designs: Lines are balanced across positions so that they are unaffected by a

linear trend across positions in the Smarthouse. Often partially replicated designs:

Parents/controls several replicates, 20% replicated twice, rest unreplicated.

Generated using DiGGer software, an add-in to the statistical programming language R. (free)

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Fleet x Commander mapping popn

Germination and initial growth of 528 single-plant pots on 10 tables in southern space in Smarthouse.

Smarthouse Table 1 Table 3 Table 5 Table 7 Table 9

Position 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4

2 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24












Table 2 Table 4 Table 6 Table 8Table

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Colours represent 6 Zones of 4 Lanes on the conveyor system.

Within a lane, 22 pots arranged in same order as will be placed on conveyor system.

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Fleet x Commander mapping popn

6 Zones each of 2 blocks of 4 lanes x 10 & 12 Positions.

2 parents replicated 6 times (blue), 36 lines replicated twice (grey), 180 lines unreplicated (green). 16.7% replicated.

2 consecutive carts have 2 conditions (no & added salt) randomized to them.

Asymmetrical in 26–1 to distance from air con.

A partially-replicated, nearly-trend-free, block design with split plots.

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Barley GWAS experiment 168 lines from a barley diversity panel from James

Hutton Institute, each replicated thrice. 3 Australian varieties as controls, each replicated 8

times. 2 watering conditions to study drought tolerance. A total of 1024 pots requiring 2 Smarthouses.

In one Smarthouse, controls have 4 replicates, 84 lines replicated twice and 84 occur only once.

A partially-replicated, nearly-trend-free, block design with split plots used in each Smarthouse.

Initial growth on tables with lanes kept in blocks.

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Barley GWAS experiment

Controls (blue), replicated twice (grey), unreplicated (green).

NW Smarthouse NE Smarthouse

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6. Specific conclusions Not much Greenhouse column trend, except in south-east. There are substantial lane and, to a lesser extent, position

trends in the Smarthouse. Designs in the Smarthouse should be block or trend-free

designs, not row-and-column designs, nor spatial designs. The blocks in such design should be no larger than 4 Lanes by 12

Positions and smaller would be better. These conclusions need to be re-evaluated in other

situations.

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General conclusions No evidence of a thigmomorphogenic or other movement

effect in the Smarthouse. (Bench & Same Lane tactics do not differ.)

Rearranging carts only minimizes plant variability where exposure of the plants to microclimates is equalized.

Designed experiments and statistical analysis can more easily and reliably achieve same as rearranging carts.

Have aligned Greenhouse and Smarthouse features, e.g. blocks and trends, so both dealt with simultaneously.

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Acknowledgements The work was supported by:

Documents

Accounting for variation in designing greenhouse experiments Chris Brien 1, Bettina Berger 2, Huwaida Rabie 1, Mark Tester 2 1 Phenomics & Bioinformatics