accounting for variation in designing greenhouse experiments chris brien 1, bettina berger 2,...
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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
2 Sides2 Blocks3 Rows in S24Columns in B
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
2 Sides2 Blocks3 Rows in S24Columns in B
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
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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
3 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
4 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
5 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
6 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
7 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
8 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
9 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
10 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
11 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
12 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
13 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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14 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
15 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
16 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
17 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
18 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
19 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
20 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
21 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
22 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
23 Lane1 Lane2 Lane3 Lane4 Lane5 Lane6 Lane7 Lane8 Lane9 Lane10 Lane11 Lane12 Lane13 Lane14 Lane15 Lane16 Lane17 Lane18 Lane19 Lane20 Lane21 Lane22 Lane23 Lane24
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: