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January 31, 2023

Logarithmic trial designs: A useful tool

Logarithmic trial designs: A useful tool for accurate PPP dose-responses from large data sets

Background: Image technology and drones can provide high-resolution pictures and assessments of all plots in a trial, a feature that is difficult when standing on the ground conducting visual assessments. Digital imaging is especially useful for assessing products that change crop color, cause desiccation, greening, crop stand changes etc.

Plant protection product development and registration requires detailed information on the products dose-response relation. The objective of this posting is to introduce the possibility of getting valuable data from a small trial with 3 replicates using drone images and logarithmic sprayers.

Methodology: The drone image and figure 1 below show the results from a cycloxydim application to a spring barley crop. We applied two formulations of cycloxydim. The application was made at BBCH 24 on the 23rd of June 2022. The trial was made with 3 replicates, and the drone images were taken 28 days after application. The methodology of the logarithmic sprayer is to start with an initial high dose of 400 g cycloxydim/ha and to decrease subsequent doses in a logarithmic manner, ending with a final application of close to zero g/ha.

Figure 1: Drone image of the trial.

We used the open-source program R to analyze the trial. To extract the data from the images, we used FieldImageR ( which is developed for analyzing drone images of field trials. For the statistical modeling of the dose-response curves, we have used the R package DRC ( (see the also (

Each plot in the trial was divided into 50 subplots which have a length of 40 cm, and the center dose of each plot was calculated. The first 80 cm and the last 80 cm were not included in the calculation to avoid the effect of border spraying. This gave 46 doses to model the dose-response curves. The number of doses you can retrieve of such an Image is shown in Figure 2.

Figure 2: Data for the 2 treatments plotted on a logarithmic scale.

With a normal RGB image you can calculate different vegetation indexes. We used the index Excess Green, which is 2 * Green band – red band – blue band. Numerous other indexes can be calculated from the RGB bands, and even more indexes are possible if you have infrared.

Given that the two treatments we compared are the same active, just different formulations, we will assume that the products have the same upper and lower limit. The data indicates there could be hormesis (a small amount of the active gives a positive plant growth) which is not uncommon for herbicides, and the DRC package allows you to model the dose-response curve both with and without hormesis (se figure 3).

Figure 3: Dose-response modeling of two formulations of cycloxydim. The left side shows the curve with the assumption of no hormesis, and the right graph shows the curves with an assumption of hormesis.

Results and Conclusion: With the program, it is possible to calculate different EDx (effective dose) values. We calculated the values and presented them with a 95% confidence interval. In table 1 you can see the ED50 values estimated for the dose-response curves with and without hormesis.

ED50 estimate without hormesis
ProductED50 estimateStd. errorLower 95% confidenceUpper 95% confidence
Formulation A99.83613.342293.2560106.4162
Formulation B119.32494.7821109.9100128.7398
ED50 estimate with hormesis
ProductED50 estimateStd. errorLower 95% confidenceUpper 95% confidence
Formulation A120.12610.33199.786140.466
Formulation B146.15813.511119.557172.759
Table 1: Results from the DRC model of the dose-response curves fitted with and without hormesis in g ai/ha.

The advantage of using logarithmic trials for analyzing dose-response relations is obvious. In a plot where we sprayed 60 m2, we get an unlimited number of doses. If this had been done with a normal randomized block design, we would have needed at least 6 well-chosen doses to model the curve, and this would require larger trials and would be more time consuming. With the logarithmic trial, you only need to choose a starting dose where you are confident that you get almost 100% efficacy. Following the analyses of the dose-response curves, you can determine which doses are interesting for future investigation.

If you would like to learn more about Agrolab’s digital imaging solutions, please contact Martin Gejl (Email:; or Mobile +45 20736575).

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