This vignette shows how to generate a rectangular lattice design using both the FielDHub Shiny App and the scripting function rectangular_lattice() from the FielDHub package.

## 1. Using the FielDHub Shiny App

To generate a rectangular lattice design using the FielDHub app:

First, go to Lattice Designs > Rectangular Lattice

Then, follow the following steps where we will show how to generate a rectangular lattice design with 56 treatments and 3 reps.

## Inputs

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 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 and NAME. The ENTRY column must have a unique entry integer number for each treatment. The column NAME must have a unique name that identifies each treatment. 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 12 treatments.

ENTRY NAME
1 GenotypeA
2 GenotypeB
3 GenotypeC
4 GenotypeD
5 GenotypeE
6 GenotypeF
7 GenotypeG
8 GenotypeH
9 GenotypeI
10 GenotypeJ
11 GenotypeK
12 GenotypeL
1. Input the number of treatments in the Input # of Treatments box. In a rectangular lattice design, the number of treatments must be a rectangular number, the product of two consecutive integers. For example, 7 x 8 = 56 is a valid entry, which we will use in this example.

2. Select the number of replications of these treatments with the Input # of Full Reps box, which is 3.

3. Set the number of plots in each incomplete block in the Input # of Plots per IBlock box, which is 7.

4. Enter the number of locations in Input # of Locations. We will run this experiment over a single location, so set it to 1.

5. Select serpentine or cartesian in the Plot Order Layout. For this example we will use the default cartesian layout.

6. 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. Set it to 101.

7. Enter a name for the location of the experiment in the Input Location box. If there are multiple locations, each name must be in a comma separated list. Set it to "FARGO".

8. To ensure that randomizations are consistent across sessions, we can set a seed number in the box labeled Seed Number. In this example, we will set it to 1235.

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

## Outputs

After you run a rectangular lattice design in FielDHub, there are several ways to display the information contained in the field book.

### Field Layout

When you first click the run button on a rectangular lattice design, FielDHub displays the Field Layout tab, which shows the entries and their arrangement in the field. In the box below the display, you can change the layout of the field or change the location displayed. You can also display a heatmap over the field by changing Type of Plot to Heatmap. To view a heatmap, you must first simulate an experiment over the described field with the Simulate! button. A pop-up window will appear where you can enter what variable you want to simulate along with minimum and maximum values.

### 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. If we have simulated data for a heatmap, an additional column for that variable appears in the field book.

## 2. Using the FielDHub function: rectangular_lattice()

You can run the same design with a function in the FielDHub package, rectangular_lattice().

First, you need to load the FielDHub package typing,

library(FielDHub)

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

rect <- rectangular_lattice(
t = 56,
r = 3,
k = 7,
l = 1,
plotNumber = 101,
locationNames = "FARGO",
seed = 1235
)

#### Details on the inputs entered in rectangular_lattice() above

• t = 56 is the number of treatments.
• r=3 is the number of replicates.
• k = 7 is the number of plots per incomplete block.
• l = 1 is the number of locations.
• plotNumber = 101 is the starting plot number.
• locationNames = "FARGO" is an optional name for each location
• seed = 1235 is the seed number to replicate identical randomizations.
print(rect)
Rectangular Lattice Design

Information on the design parameters:
List of 7
$Reps : num 3$ iBlocks         : num 8
$NumberTreatments: num 56$ NumberLocations : num 1
$Locations : chr "FARGO"$ seed            : num 1235
$lambda : num 0.327 10 First observations of the data frame with the rectangular_lattice field book: ID LOCATION PLOT REP IBLOCK UNIT ENTRY TREATMENT 1 1 FARGO 101 1 1 1 54 G-54 2 2 FARGO 102 1 1 2 9 G-9 3 3 FARGO 103 1 1 3 32 G-32 4 4 FARGO 104 1 1 4 21 G-21 5 5 FARGO 105 1 1 5 2 G-2 6 6 FARGO 106 1 1 6 47 G-47 7 7 FARGO 107 1 1 7 35 G-35 8 8 FARGO 108 1 2 1 3 G-3 9 9 FARGO 109 1 2 2 44 G-44 10 10 FARGO 110 1 2 3 13 G-13 ### Access to rect object The function rectangular_lattice() 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. rect$layoutRandom or rect$fieldBook.

rect$fieldBook is a list containing information about every plot in the field, with information about the location of the plot and the treatment in each plot. As seen in the output below, the field book has columns for ID, LOCATION, PLOT, REP, IBLOCK, UNIT, ENTRY, and TREATMENT. field_book <- rect$fieldBook
head(rect\$fieldBook, 10)
   ID LOCATION PLOT REP IBLOCK UNIT ENTRY TREATMENT
1   1    FARGO  101   1      1    1    54      G-54
2   2    FARGO  102   1      1    2     9       G-9
3   3    FARGO  103   1      1    3    32      G-32
4   4    FARGO  104   1      1    4    21      G-21
5   5    FARGO  105   1      1    5     2       G-2
6   6    FARGO  106   1      1    6    47      G-47
7   7    FARGO  107   1      1    7    35      G-35
8   8    FARGO  108   1      2    1     3       G-3
9   9    FARGO  109   1      2    2    44      G-44
10 10    FARGO  110   1      2    3    13      G-13

### Plot the field layout

For plotting the layout in function of the coordinates ROW and COLUMN, you can use the the generic function plot() as follows,

plot(rect)