3.2 Design the experiment

The experimental design is described by the number of plots per location, the number of locations, the number of replications of the different germplasms within and between locations.

Function design_experiment sets the experimental design based on :

  • the number of entries
  • the number of controls per block
  • the number of blocks
  • the number of columns in the design. The number of rows is computed automaticaly.

The function returns a list with

  • a data frame
  • an image of the experimental design

A description of the algorithm is describe in the help of the function: ?design_experiment.

The four experimental designs are

  • D1 - fully-repicated
  • D2 - incomplete block design
  • D3 - row-colum
  • D4 - satellite-farm and regional-farm

3.2.1 Fully-replicated (D1)

In fully replicated design, all entries are replicated with randomly choosen order into different blocks.

The decision tree where fully-replicated designs are used is displayed in Figure 3.3.

The decision tree where fully-replicated designs are used.

Figure 3.3: The decision tree where fully-replicated designs are used.

The R code to implement is the following :

p_fr = design_experiment(
  location = "Location-1",
  year = "2016",
  expe.type = "fully-replicated",
  germplasm = paste("germ", c(1:20), sep = ":"),
  nb.blocks = 3,
  nb.cols = 4)

By default, the data frame is under a standard format:

head(p_fr$"fully-replicated"$data.frame)
##     location year germplasm block X Y
## 1 Location-1 2016    germ:3     1 A 1
## 2 Location-1 2016   germ:10     1 A 2
## 3 Location-1 2016   germ:13     1 A 3
## 4 Location-1 2016    germ:2     1 A 4
## 5 Location-1 2016   germ:17     1 A 5
## 6 Location-1 2016   germ:19     1 B 1

You can set the format to a SHiNeMaS5 reproduction template file:

p_fr = design_experiment(
  location = "Location-2",
  year = "2016",
  expe.type = "fully-replicated",
  germplasm = paste("germ", c(1:20), sep = ":"),
  nb.blocks = 3,
  nb.cols = 4,
  return.format = "shinemas")
head(p_fr$"fully-replicated"$data.frame)
##   project sown_year harvested_year        id_seed_lot_sown
## 1              2016                germ:17_Location-2_2016
## 2              2016                 germ:9_Location-2_2016
## 3              2016                 germ:2_Location-2_2016
## 4              2016                 germ:1_Location-2_2016
## 5              2016                germ:10_Location-2_2016
## 6              2016                 germ:6_Location-2_2016
##   intra_selection_name etiquette split quantity_sown quantity_harvested
## 1                                                                      
## 2                                                                      
## 3                                                                      
## 4                                                                      
## 5                                                                      
## 6                                                                      
##   block X Y
## 1     1 A 1
## 2     1 A 2
## 3     1 A 3
## 4     1 A 4
## 5     1 A 5
## 6     1 B 1
p_fr$"fully-replicated"$design
Fully replicated design where all germplasms are replicated three time in bocks

Figure 3.4: Fully replicated design where all germplasms are replicated three time in bocks

3.2.2 Incomplete Block Design (D2)

The decision tree where incomplete block designs are used is displayed in Figure 3.5.

The decision tree where incomplete block designs are used.

Figure 3.5: The decision tree where incomplete block designs are used.

Entries are not replicated on a location. Some entries are common to some locations. Each block is an independent unit and can be allocated to any location. Each farmer has to choose one or several pre-designed blocks. Therefore, the experiment can be handled by several locations that can not receive a high number of plots.

p_ibd = design_experiment(
  year = "2016",
  expe.type = "IBD",
  germplasm = paste("germ", c(1:10), sep = ":"),
  nb.blocks = 8, # i.e. number of location if each location has one block
  nb.cols = 4)
head(p_ibd$`IBD`$data.frame)
##   germplasm block X Y year
## 1    germ:1     1 A 1 2016
## 2    germ:1     2 A 2 2016
## 3    germ:4     3 A 3 2016
## 4    germ:3     4 A 4 2016
## 5    germ:3     5 A 5 2016
## 6    germ:2     6 A 6 2016
p_ibd$`IBD`$design
Example of incomplete block design where different germplasms are replicated over some blocks.

Figure 3.6: Example of incomplete block design where different germplasms are replicated over some blocks.

3.2.3 Row-column (D3)

In Row-column design, a control is replicated in row and columns to catch as much as possible of the variation.

The decision tree where row-column design are used is displayed in Figure 3.7.

The decision tree where row-column designs are used.

Figure 3.7: The decision tree where row-column designs are used.

The R code to implement is the following :

p_case2 = design_experiment(
  location = "Location-3",
  year = "2016",
  expe.type = "row-column",
  germplasm = paste("germ", c(1:20), sep = ":"),
  controls = "toto",
  nb.controls.per.block = 7,
  nb.blocks = 1,
  nb.cols = 7)
head(p_case2$"row-column"$data.frame)
##     location year germplasm block X Y
## 1 Location-3 2016    germ:8     1 A 1
## 2 Location-3 2016      toto     1 A 2
## 3 Location-3 2016    germ:6     1 A 3
## 4 Location-3 2016   germ:20     1 A 4
## 5 Location-3 2016   germ:15     1 B 1
## 6 Location-3 2016   germ:12     1 B 2
p_case2$"row-column"$design
Row column design where a control (toto) is replicated in rows and columns.

Figure 3.8: Row column design where a control (toto) is replicated in rows and columns.

Note that if controls are missing in rows or columns, the function will return an error message. The controls must catch as much as possible of the trial variation.

3.2.4 Regional and satellite farms (D4)

Regional farms receive several entries (i.e. a germplasm in an environment) in two or more blocks with some entries (i.e. controls) replicated in each block. Satellite farms have a single block and only one entry (i.e. the control) is replicated twice. Farmers choose all entries that are not replicated. The number of entries may vary between farms. Note that at least 25 environments (location \(\times\) year) are need in order to get robust results.

The decision tree where regional and satellite farms designs are used is displayed in Figure 3.9.

The decision tree where regional and satellite farms designs are used.

Figure 3.9: The decision tree where regional and satellite farms designs are used.

The R code to implement is the following :

As an example here, six designs are generated: four for satellite farms and two for regional farms.

p_case3_sf1 = design_experiment(
  location = "Location-4",
  year = "2016",
  expe.type = "satellite-farm",
  germplasm = paste("germ", c(1:6), sep = ":"),
  controls = "toto",
  nb.controls.per.block = 2,
  nb.blocks = 1,
  nb.cols = 2)
p_case3_sf1 = p_case3_sf1$`satellite-farms`$design
p_case3_sf1
Example of a satellite farm design.

Figure 3.10: Example of a satellite farm design.

p_case3_sf2 = design_experiment(
  location = "Location-5",
  year = "2016",
  expe.type = "satellite-farm",
  germplasm = paste("germ", c(1:6), sep = ":"),
  controls = "toto",
  nb.controls.per.block = 2,
  nb.blocks = 1,
  nb.cols = 2)
p_case3_sf2 = p_case3_sf2$`satellite-farms`$design
p_case3_sf2
Example of a satellite farm design.

Figure 3.11: Example of a satellite farm design.

p_case3_sf3 = design_experiment(
  location = "Location-6",
  year = "2016",
  expe.type = "satellite-farm",
  germplasm = paste("germ", c(1:6), sep = ":"),
  controls = "toto",
  nb.controls.per.block = 2,
  nb.blocks = 1,
  nb.cols = 2)
p_case3_sf3 = p_case3_sf3$`satellite-farms`$design
p_case3_sf3
Example of a satellite farm design.

Figure 3.12: Example of a satellite farm design.

p_case3_rf1 = design_experiment(
  location = "Location-7",
  year = "2016",
  expe.type = "regional-farm",
  germplasm = paste("germ", c(1:16), sep = ":"),
  controls = c("c1", "c2", "c3", "c4"),
  nb.controls.per.block = 4,
  nb.blocks = 2,
  nb.cols = 4)
p_case3_rf1 = p_case3_rf1$`regional-farms`$design
p_case3_rf1
Example of a regional farm design.

Figure 3.13: Example of a regional farm design.

p_case3_rf2 = design_experiment(
  location = "Location-8",
  year = "2016",
  expe.type = "regional-farm",
  germplasm = paste("germ", c(1:16), sep = ":"),
  controls = c("c1", "c2", "c3"),
  nb.controls.per.block = 3,
  nb.blocks = 2,
  nb.cols = 3)
## Warning in place_controls(d, expe.type): Controls are missing in columns 1.
## You can rise nb.controls.per.block.
## Warning in place_controls(d, expe.type): Controls are missing in rows 4.
## You can rise nb.controls.per.block.
## Warning in place_controls(d, expe.type): Controls are missing in columns 3.
## You can rise nb.controls.per.block.
## Warning in place_controls(d, expe.type): Controls are missing in rows 1.
## You can rise nb.controls.per.block.
p_case3_rf2 = p_case3_rf2$`regional-farms`$design
p_case3_rf2
Example of a regional farm design.

Figure 3.14: Example of a regional farm design.

If you have enought space and lots of seeds, you can adapt the satellite farm design with only one column. Each row beeing a sower width. Then you must be careful to have several sample for a given row to be as representative as possible.

p_case3_sf4 = design_experiment(
  location = "Location-9",
  year = "2016",
  expe.type = "satellite-farm",
  germplasm = paste("germ", c(1:6), sep = ":"),
  controls = "C",
  nb.controls.per.block = 2,
  nb.blocks = 1,
  nb.cols = 1)
p_case3_sf4 = p_case3_sf4$`satellite-farms`$design
p_case3_sf4
Example of a satellite farm design.

Figure 3.15: Example of a satellite farm design.

There some constraints regarding expe.type = "satellite-farm":

  • if nb.entries > 10, a warning message recommands to have less than 10 germplasms or to choose expe.type = "regional-farm".
  • There are two controls per block
  • There is one block
  • There are maximum two columns

For expe.type = "regional-farm", there is a warning message if controls are missing in rows or columns. It is better to catch as much as possible of the trial variation. If there are less than 2 blocks, an error message is returned.