Causes of spatial variation
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- Alyson Gilmore
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1
2 Field Trials Plant breeding trials Laid out in a grid (rows and columns) From few entries (3-5) to many entries (100s) Plots close together are more similar than those far away.
3 Causes of spatial variation Topography Soil type & depth, cultivation Irrigation/rainfall Shelter/shading Insects/pests/diseases Sowing/harvesting Management (sprays/fertiliser) Previous management/history
4 Grass Trial
5 Plots various sizes & shapes
6 Wheat Trial at Rothamsted
7 Fisher at Rothamsted 1920s Replication (estimation of variability) Randomization (unbiasedness) Blocking (reduction of variability) Resolvable design each treatment occurs once in each block Treat each block together (maximise between block differences to minimize within block differences)
8 Randomized Block Design
9 Latin Square Design
10 Knight s move Latin Square Design
11 Fisher Student argument Analysis of variance table Source SS DF MS F Ratio Rows BSS 4 Columns CSS 4 Entries ESS 4 ESS/4 4 ESS/RSS Residual RSS 12 RSS/12 Total TSS 24 ESS + RSS = TSS-BSS-CSS (constant) i.e. if ESS goes down RSS goes up The more precise the experiment, the less the evidence of Entry effects
12 Incomplete Block Design Balanced single SED for treatments 96% efficient Co-occurrences in blocks
13 Row-Column design Remove row and columns effects Not balanced but optimal
14 Resolvable Incomplete Block Design Not balanced, but optimal Co-occurrences in blocks
15 Doubly Resolvable Designs Columns are replicates. Plots numbered in a serpentine order (sowing order) form replicates Rows form a balanced incomplete block design (co-occurrences = 3)
16 Doubly Resolvable Designs Pairs of columns make a replicate. Plots in a serpentine order form reps. Rows and columns optimized incomplete block designs.
17 DRD Algorithm 1. Start with random RB in columns 2. Exchange treatments in columns to get replicates in rows (if not found go to 1) 3. Randomize within row & column blocks to improve row & column efficiencies (n times) 4. Look for exchanges to improve efficiency (swaps and double swaps) 5. Repeat, keeping most efficient design Occurrence matrix of treatments in row reps
18 DRD Algorithm 1. Start with random RB in columns 2. Exchange treatments in columns to get replicates in rows (if not found go to 1) 3. Randomize within row & column blocks to improve row & column efficiencies (n times) 4. Look for exchanges to improve efficiency (swaps and double swaps) 5. Repeat, keeping most efficient design
19 DRD Algorithm 1. Start with random RB in columns 2. Exchange treatments in columns to get replicates in rows (if not found go to 1) 3. Randomize within row & column blocks to improve row & column efficiencies (n times) 4. Look for exchanges to improve efficiency (swaps and double swaps) 5. Repeat, keeping most efficient design
20 DRD Algorithm 1. Start with random RB in columns 2. Exchange treatments in columns to get replicates in rows (if not found go to 1) 3. Randomize within row & column blocks to improve row & column efficiencies (n times) 4. Look for exchanges to improve efficiency (swaps and double swaps) 5. Repeat, keeping most efficient design
21 DRD Algorithm 1. Start with random RB in columns 2. Exchange treatments in columns to get replicates in rows (if not found go to 1) 3. Randomize within row & column blocks to improve row & column efficiencies (n times) 4. Look for exchanges to improve efficiency (swaps and double swaps) 5. Repeat, keeping most efficient design
22 Extensions Triply Resolvable Designs
23 GPU/multi-threaded optimizations 6 cores in my CPU 1594 cores in my GPU CUDA interface to GPU Intel Fortran multi-threaded maths kernel library (mkl)
24 Open Multi-processor Code Start 4 parallel searches for an optimal design:!$omp PARALLEL SECTIONS!$OMP SECTION call optimize_dogleg(nr,nc,nt,r,ncr,des1,eff1)!$omp SECTION call optimize_dogleg(nr,nc,nt,r,ncr,des2,eff2)!$omp SECTION call optimize_dogleg(nr,nc,nt,r,ncr,des3,eff3)!$omp SECTION call optimize_dogleg(nr,nc,nt,r,ncr,des4,eff4)!$omp END PARALLEL SECTIONS Select the optimal design from des1,des2,des3,des4
25 Higher order considerations Neighbour balance for spatial analysis & interplot inference Shading of neighbouring plots Spread of diseases & pests Count how often treatments neighbour each other Different definitions of neighbours
26 Neighbour balanced design Optimized design Neighbour Balance (co-occurrences) No self neighbours
27 The End GenStat Discovery
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