Un-replicated Optimized Arrangement Design

This vignette shows how to generate an un-replicated optimized arrangement design using both the FielDHub Shiny App and the scripting function optimized_arrangement() from the FielDHub R package.


One un-replicated design you can use in FielDHub is the optimized arrangement. Unlike the diagonal design, the optimized arrangement completely randomizes the positions for the checks instead of putting them in a systematic diagonal pattern(Clarke and Stefanova 2011). Randomization is subject to some restrictions. These restrictions seek to optimize the distribution of control plots in the field and ensure they are spread while keeping a minimum distance between them.

FielDHub includes a function to run such experimental designs, features include options to set the number of entries and the number of checks for the experiment. Users can also choose to run the same experiment over multiple locations.

Use case

An early generation plant breeding project needs to test 401 genotypes of winter wheat. It is planned to carry out this experiment on a field containing 29 rows and 15 columns of plots. In this project, these 401 genotypes are allocated into one experiment and tested over three locations. In addition, three checks are randomly included across field to fill 34 plots representing 7.8% of the total number of experimental plots.

Running the Shiny App

To launch the app you need to run either,




1. Using the FielDHub Shiny App

Once the app is running, go to un-replicated Designs > Optimized Arrangement

Then, follow the following steps where we will show how to generate an un-replicated optimized arrangement design.


  1. Import entries’ list? Choose whether to import a list with entry numbers and names for genotypes or treatments.
    • If the selection is No, that means the app is going to generate synthetic data for entries and names of the treatment/genotypes based on the user inputs.

    • If the selection is Yes, the entries list must fulfill a specific format and must be a .csv file. The file must have the columns ENTRY, NAME, and REPS. The ENTRY column must have a unique entry integer number for each treatment/genotype. The column NAME must have a unique name that identifies each treatment/genotype. The REPS column must have an integer entry for the replications of the checks and other entries. Both ENTRY and NAME must be unique, duplicates are not allowed. In the following table, we show an example of the entries list format. This example has an entry list with three checks and nine treatments/genotypes. It is crucial to allocate the checks in the top part of the file.

1 CHECK1 10
2 CHECK2 10
3 CHECK3 10
4 G-4 1
5 G-5 1
6 G-6 1
7 G-7 1
8 G-8 1
9 G-9 1
10 G-10 1
11 G-11 1
12 G-12 1
  1. Enter the number of checks in the Input # of Checks box, which is 3 in our case.

  2. Enter the number of replications of the checks in a comma separated list containing a number for each check in the Input # Check’s Reps box. For our example experiment, we will enter 12,11,11.

  3. Enter the number of entries/treatments in the Input # of Entries box, which is 401 in our case.

  4. Select serpentine or cartesian in the Plot Order Layout. For this example we will set the serpentine layout.

  5. Since we want to run this experiment over 3 locations, set Input # of Locations to 3.

  6. To ensure that randomizations are consistent across sessions, we can set a random seed in the box labeled random seed. For instance, we will set it to 130.

  7. Enter the name for the experiment in the Input Experiment Name box. For example, PYT_WHEAT_22.

  8. Enter the starting plot number in the Starting Plot Number box. If the experiment has multiple locations, you must enter a comma separated list of numbers the length of the number of locations for the input to be valid. Since we have 3 locations in this experiment, we will enter 1001,2001,3001.

  9. Enter the name of the site/location in the Input the Location box. In our case we will run the experiment in three locations, the name for each location must be enter separate by comma, for example: FARGO, CASSELTON, MINOT.

  10. Once we have entered the information for our experiment on the left side panel, click the Run! button to run the design.

  11. You will then be prompted to select the dimensions of the field from the list of options in the drop down in the middle of the screen with the box labeled Select dimensions of field. In our case, we will select 15 x 29.

  12. Click the Randomize! button to randomize the experiment with the set field dimensions and to see the output plots. If you change the dimensions again, you must re-randomize.

If you change any of the inputs on the left side panel after running an experiment initially, you have to click the Run and Randomize buttons again, to re-run with the new inputs.


After you run an un-replicated optimized arrangement design in FielDHub and set the dimensions of the field, there are several ways to display the information contained in the field book. The first tab, Get Random, shows the option to change the dimensions of the field and re-randomize, as well as a reference guide for experiment design.

Data Input

On the second tab, Data Input, you can see all the entries in the randomization in a list, as well as a table of the checks with the number of times they appear in the field. In the list of entries, the reps for each check is included as well.

Randomized Field

The Randomized Field tab displays a graphical representation of the randomization of the entries in a field of the specified dimensions. The checks are all colored uniquely, showing the number of times they are distributed throughout the field. The display includes numbered labels for the rows and columns. You can copy the field as a table or save it directly as an Excel file with the Copy and Excel buttons at the top.

Plot Number Field

On the Plot Number Field tab, there is a table display of the field with the plots numbered according to the Plot Order Layout specified, either serpentine or cartesian. You can see the corresponding entries for each plot number in the field book. Like the Randomized Field tab, you can copy the table or save it as an Excel file with the Copy and Excel buttons.

Field Book

The Field Book displays all the information on the experimental design in a table format. It contains the specific plot number and the row and column address of each entry, as well as the corresponding treatment on that plot. This table is searchable, and we can filter the data in relevant columns.

2. Using the FielDHub function: optimized_arrangement().

You can run the same design with the function optimized_arrangement() in the FielDHub package.

First, you need to load the FielDHub package typing,


Then, you can enter the information describing the above design like this:

optim_expt <- optimized_arrangement(
  nrows = 29,
  ncols = 15,
  lines = 401, 
  amountChecks = c(12,11,11),
  checks = 3, 
  l = 3,
  plotNumber = c(1001,2001,3001),
  exptName = "WINTER_WHEAT_22", 
  locationNames = c("FARGO", "CASSELTON", "MINOT"),
  seed = 130

Details on the inputs entered in optimized_arrangement() above

The description for the inputs that we used to generate the design,

Access to optim_expt object

The optimized_arrangement() function returns a list consisting of all the information displayed in the output tabs in the FielDHub app: design information, plot layout, plot numbering, entries list, and field book. These are Accessible by the $ operator, i.e. optim_expt$layoutRandom or optim_expt$fieldBook.

optim_expt$fieldBook is a data frame containing information about every plot in the field, with information about the location of the plot and the treatment in each plot. As seen in the output below, the field book has columns for ID, EXPT, LOCATION, YEAR, PLOT, ROW, COLUMN, CHECKS, ENTRY, and TREATMENT.

Let us see the first 10 rows of the field book for this experiment.

field_book <- optim_expt$fieldBook
head(field_book, 10)
1   1 WINTER_WHEAT_22    FARGO 2024 1001   1      1      0    70       G70
2   2 WINTER_WHEAT_22    FARGO 2024 1002   1      2      0   357      G357
3   3 WINTER_WHEAT_22    FARGO 2024 1003   1      3      0   217      G217
4   4 WINTER_WHEAT_22    FARGO 2024 1004   1      4      0   280      G280
5   5 WINTER_WHEAT_22    FARGO 2024 1005   1      5      0   259      G259
6   6 WINTER_WHEAT_22    FARGO 2024 1006   1      6      0    50       G50
7   7 WINTER_WHEAT_22    FARGO 2024 1007   1      7      0   223      G223
8   8 WINTER_WHEAT_22    FARGO 2024 1008   1      8      0   348      G348
9   9 WINTER_WHEAT_22    FARGO 2024 1009   1      9      0   180      G180
10 10 WINTER_WHEAT_22    FARGO 2024 1010   1     10      0   153      G153

Plot the field layout

For plotting the layout in function of the coordinates ROW and COLUMN in the field book object we can use the generic function plot() as follow,


The figure above shows a map of an experiment randomized as an un-replicated optimized arrangement design. Gray plots represent the un-replicated treatments, while distinctively colored check plots are randomly replicated throughout the field.

It is possible to pass more arguments to plot() such as the specific location. For example, you can plot specifically the layout for location 2.

plot(optim_expt, l = 2)


Clarke, G. Peter Y., and Katia T. Stefanova. 2011. “Optimal Design for Early-Generation Plant-Breeding Trials with Unreplicated or Partially Replicated Test Lines.” Australian & New Zealand Journal of Statistics 53 (4): 461–80. https://doi.org/10.1111/j.1467-842X.2011.00642.x.