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Working with the PowderyMildew dataset

Kaique S. Alves

2026-04-11

Source: vignettes/powdery-mildew-data.Rmd
powdery-mildew-data.Rmd
library(epifitter)
library(dplyr)
library(ggplot2)
library(cowplot)
theme_set(cowplot::theme_half_open(font_size = 12))
data("PowderyMildew")

Overview

PowderyMildew is an experimental dataset included in epifitter. It contains disease progress curves for powdery mildew in organic tomato under different irrigation systems and soil moisture levels.

The data are derived from the study by Lage, Marouelli, and Cafe-Filho (2019) on powdery mildew management under different irrigation configurations in organic tomato.

The dataset is especially useful for demonstrating workflows with:

  • a real epidemic dataset rather than simulated curves;
  • repeated observations over time within experimental blocks;
  • treatment comparisons using summary measures and fitted models.

Load the data

Use the usual data() interface for packaged datasets.

data("PowderyMildew")
knitr::kable(head(PowderyMildew, 12), digits = 4)
irrigation_type moisture block time sev
Drip High moisture 1 0 0.011
Drip High moisture 2 0 0.011
Drip High moisture 3 0 0.011
Drip High moisture 1 7 0.034
Drip High moisture 2 7 0.040
Drip High moisture 3 7 0.036
Drip High moisture 1 14 0.114
Drip High moisture 2 14 0.109
Drip High moisture 3 14 0.097
Drip High moisture 1 21 0.126
Drip High moisture 2 21 0.120
Drip High moisture 3 21 0.103

The dataset contains five variables:

  • irrigation_type for the irrigation system;
  • moisture for the soil moisture regime;
  • block for the experimental block;
  • time for the assessment date;
  • sev for disease severity on a proportional scale.

Inspect the experimental structure 

PowderyMildew %>%
  distinct(irrigation_type, moisture, block) %>%
  arrange(irrigation_type, moisture, block) %>%
  knitr::kable()
irrigation_type moisture block
1 Drip High moisture 1
2 Drip High moisture 2
3 Drip High moisture 3
91 Furrow Moderate moisture 1
92 Furrow Moderate moisture 2
93 Furrow Moderate moisture 3
31 MS High moisture 1
32 MS High moisture 2
33 MS High moisture 3
61 MS Moderate moisture 1
62 MS Moderate moisture 2
63 MS Moderate moisture 3
121 MS above canopy High moisture 1
122 MS above canopy High moisture 2
123 MS above canopy High moisture 3
151 MS above canopy Moderate moisture 1
152 MS above canopy Moderate moisture 2
153 MS above canopy Moderate moisture 3
181 Overhead High moisture 1
182 Overhead High moisture 2
183 Overhead High moisture 3
211 Overhead Moderate moisture 1
212 Overhead Moderate moisture 2
213 Overhead Moderate moisture 3

This is a repeated-measures dataset: each block was assessed across several time points within each irrigation-by-moisture combination.

Visualize treatment means over time

A useful first step is to summarize replicated blocks within each treatment and visualize the mean disease progress curve.

pm_summary <- PowderyMildew %>%
  group_by(irrigation_type, moisture, time) %>%
  summarise(
    mean_sev = mean(sev),
    .groups = "drop"
  )

knitr::kable(head(pm_summary, 12), digits = 4)
irrigation_type moisture time mean_sev
Drip High moisture 0 0.0110
Drip High moisture 7 0.0367
Drip High moisture 14 0.1067
Drip High moisture 21 0.1163
Drip High moisture 28 0.1527
Drip High moisture 35 0.1810
Drip High moisture 42 0.3237
Drip High moisture 49 0.3543
Drip High moisture 56 0.4190
Drip High moisture 63 0.4340
Furrow Moderate moisture 0 0.0100
Furrow Moderate moisture 7 0.0373 
ggplot(pm_summary, aes(time, mean_sev, color = irrigation_type)) +
  geom_point(size = 1.8) +
  geom_line(linewidth = 0.9) +
  facet_wrap(~ moisture) +
  labs(
    title = "Mean powdery mildew progress by treatment",
    x = "Time",
    y = "Mean severity",
    color = "Irrigation"
  )

Line plot of mean powdery mildew severity over time for each irrigation treatment, faceted by soil moisture level.

Calculate AUDPC and AUDPS per experimental unit

Because block identifies repeated experimental units, a common analysis is to calculate one summary value per block within each treatment.

pm_area <- PowderyMildew %>%
  group_by(irrigation_type, moisture, block) %>%
  summarise(
    audpc = AUDPC(time = time, y = sev, aggregate = "none"),
    audps = AUDPS(time = time, y = sev, aggregate = "none"),
    .groups = "drop"
  )

knitr::kable(pm_area, digits = 4)
irrigation_type moisture block audpc audps
Drip High moisture 1 13.1530 14.7105
Drip High moisture 2 13.8040 15.3615
Drip High moisture 3 13.3700 14.9275
Furrow Moderate moisture 1 13.7270 15.3615
Furrow Moderate moisture 2 14.1645 15.7990
Furrow Moderate moisture 3 13.8670 15.4210
MS High moisture 1 8.3020 9.6005
MS High moisture 2 9.3625 10.6260
MS High moisture 3 8.3755 9.5620
MS Moderate moisture 1 10.7205 12.1905
MS Moderate moisture 2 11.3330 12.7645
MS Moderate moisture 3 11.6970 13.1285
MS above canopy High moisture 1 3.8395 4.3225
MS above canopy High moisture 2 4.2245 4.7775
MS above canopy High moisture 3 4.1930 4.7740
MS above canopy Moderate moisture 1 4.6935 5.2535
MS above canopy Moderate moisture 2 5.2010 5.8940
MS above canopy Moderate moisture 3 5.0365 5.6455
Overhead High moisture 1 3.5770 3.9865
Overhead High moisture 2 3.5665 3.9795
Overhead High moisture 3 3.9725 4.4940
Overhead Moderate moisture 1 3.9935 4.4695
Overhead Moderate moisture 2 3.7065 4.1825
Overhead Moderate moisture 3 3.8360 4.2910

This differs from pooling all rows together. If all blocks are passed at once, AUDPC() and AUDPS() assume that you want one treatment-level summary curve and aggregate repeated observations at each time point before calculating the area.

To compare treatments visually, it is often useful to plot one point per block on top of a boxplot.

pm_area_long <- pm_area %>%
  tidyr::pivot_longer(
    cols = c(audpc, audps),
    names_to = "summary_measure",
    values_to = "value"
  )

facet_aud <- if (requireNamespace("lemon", quietly = TRUE)) {
  lemon::facet_rep_grid(summary_measure ~ moisture, scales = "free_y")
} else {
  ggplot2::facet_grid(summary_measure ~ moisture, scales = "free_y")
}

ggplot(
  pm_area_long,
  aes(irrigation_type, value, fill = irrigation_type)
) +
  geom_boxplot(
    width = 0.65,
    outlier.shape = NA,
    alpha = 0.28,
    linewidth = 0.6
  ) +
  geom_jitter(
    aes(color = irrigation_type),
    width = 0.12,
    height = 0,
    size = 2.4,
    alpha = 0.85
  ) +
  facet_aud +
  labs(
    title = "Area-under-the-curve summaries by treatment",
    x = "Irrigation treatment",
    y = "Summary value",
    color = "Irrigation"
  ) +
  cowplot::theme_half_open(font_size = 12) +
  background_grid(major = "y", minor = "none") +
  theme(
    legend.position = "none",
    axis.text.x = element_text(angle = 20, hjust = 1),
    strip.background = element_rect(fill = "#e7f1f3", color = NA),
    strip.text = element_text(face = "bold")
  )

Boxplots with jittered points showing the distribution of AUDPC and AUDPS values across irrigation treatments, faceted by moisture level and summary metric.

Fit a model to one observed curve

To work with a single disease progress curve, first filter one treatment-by-block combination.

single_curve <- PowderyMildew %>%
  filter(
    irrigation_type == "Drip",
    moisture == "High moisture",
    block == 1
  )

knitr::kable(single_curve, digits = 4)
irrigation_type moisture block time sev
1 Drip High moisture 1 0 0.011
4 Drip High moisture 1 7 0.034
7 Drip High moisture 1 14 0.114
10 Drip High moisture 1 21 0.126
13 Drip High moisture 1 28 0.160
16 Drip High moisture 1 35 0.183
19 Drip High moisture 1 42 0.297
22 Drip High moisture 1 49 0.331
25 Drip High moisture 1 56 0.389
28 Drip High moisture 1 63 0.434 
ggplot(single_curve, aes(time, sev)) +
  geom_point(size = 2, color = "#15616d") +
  geom_line(linewidth = 0.9, color = "#15616d") +
  labs(
    title = "Single observed disease progress curve",
    subtitle = "Drip irrigation, high moisture, block 1",
    x = "Time",
    y = "Severity"
  )

Scatter and line plot of a single observed powdery mildew disease progress curve for drip irrigation under high moisture in block 1.

Now fit the candidate models to that curve.

single_fit <- fit_lin(time = single_curve$time, y = single_curve$sev)
knitr::kable(single_fit$stats_all, digits = 4)
best_model model r r_se r_ci_lwr r_ci_upr v0 v0_se r_squared RSE CCC y0 y0_ci_lwr y0_ci_upr
1 Gompertz 0.0253 0.0018 0.0212 0.0293 -1.3374 0.0659 0.9625 0.1120 0.9809 0.0222 0.0119 0.0379
2 Monomolecular 0.0089 0.0006 0.0074 0.0104 -0.0319 0.0240 0.9603 0.0408 0.9797 -0.0324 -0.0912 0.0232
3 Logistic 0.0593 0.0076 0.0418 0.0768 -3.5948 0.2833 0.8844 0.4819 0.9386 0.0267 0.0141 0.0501
4 Exponential 0.0504 0.0078 0.0323 0.0685 -3.5629 0.2932 0.8374 0.4989 0.9115 0.0284 0.0144 0.0558 
plot_fit(single_fit, point_size = 2, line_size = 0.9)

Faceted plot comparing fitted disease progress curves for a single observed powdery mildew epidemic.

Fit models to many observed curves at once

fit_multi() is useful when each treatment-by-block combination should be fitted separately.

pm_multi_fit <- fit_multi(
  time_col = "time",
  intensity_col = "sev",
  data = PowderyMildew,
  strata_cols = c("irrigation_type", "moisture", "block")
)

knitr::kable(head(pm_multi_fit$Parameters, 12), digits = 4)
irrigation_type moisture block best_model model r r_se r_ci_lwr r_ci_upr v0 v0_se r_squared RSE CCC y0 y0_ci_lwr y0_ci_upr
Drip High moisture 1 1 Gompertz 0.0253 0.0018 0.0212 0.0293 -1.3374 0.0659 0.9625 0.1120 0.9809 0.0222 0.0119 0.0379
Drip High moisture 1 2 Monomolecular 0.0089 0.0006 0.0074 0.0104 -0.0319 0.0240 0.9603 0.0408 0.9797 -0.0324 -0.0912 0.0232
Drip High moisture 1 3 Logistic 0.0593 0.0076 0.0418 0.0768 -3.5948 0.2833 0.8844 0.4819 0.9386 0.0267 0.0141 0.0501
Drip High moisture 1 4 Exponential 0.0504 0.0078 0.0323 0.0685 -3.5629 0.2932 0.8374 0.4989 0.9115 0.0284 0.0144 0.0558
Drip High moisture 2 1 Gompertz 0.0269 0.0019 0.0225 0.0314 -1.3544 0.0718 0.9609 0.1221 0.9801 0.0208 0.0103 0.0375
Drip High moisture 2 2 Monomolecular 0.0100 0.0010 0.0078 0.0122 -0.0456 0.0360 0.9313 0.0612 0.9645 -0.0466 -0.1372 0.0367
Drip High moisture 2 3 Logistic 0.0615 0.0073 0.0447 0.0784 -3.6037 0.2729 0.8987 0.4643 0.9466 0.0265 0.0143 0.0486
Drip High moisture 2 4 Exponential 0.0515 0.0075 0.0341 0.0689 -3.5582 0.2819 0.8535 0.4795 0.9209 0.0285 0.0149 0.0546
Drip High moisture 3 1 Gompertz 0.0268 0.0019 0.0225 0.0311 -1.3806 0.0696 0.9628 0.1184 0.9811 0.0187 0.0094 0.0338
Drip High moisture 3 2 Monomolecular 0.0097 0.0009 0.0076 0.0118 -0.0473 0.0339 0.9347 0.0576 0.9663 -0.0484 -0.1336 0.0303
Drip High moisture 3 3 Logistic 0.0621 0.0069 0.0461 0.0781 -3.6884 0.2591 0.9093 0.4409 0.9525 0.0244 0.0136 0.0435
Drip High moisture 3 4 Exponential 0.0524 0.0072 0.0359 0.0689 -3.6411 0.2672 0.8703 0.4546 0.9307 0.0262 0.0142 0.0486

This output keeps the original stratification variables, which makes it easier to compare fitted parameters among irrigation systems, moisture regimes, and blocks.

Practical guidance

  • Use data("PowderyMildew") to load the bundled dataset.
  • Use grouped summaries by block when you want one AUDPC or AUDPS value per experimental unit.
  • Use grouped means over time when the goal is a treatment-level visualization.
  • Use fit_lin() for a quick model ranking on one observed curve.
  • Use fit_multi() when you want to fit many treatment-block curves in a single workflow.

Data source

The PowderyMildew dataset included in epifitter comes from:

Lage, D. A. C., Marouelli, W. A., and Cafe-Filho, A. C. (2019). Management of powdery mildew and behaviour of late blight under different irrigation configurations in organic tomato. Crop Protection, 125, 104886.