Control efficacy

In our simulations, we used meta-analytic estimates of mean and confidence intervals of control efficacy of tebuconazole applied once (1྾) or twice (2྾) (Machado et al. 2007). We assumed that control efficacy follows a uniform distribution within the 95% confidence interval estimates.

# Fungicide applied once (1x)
set.seed(280)
efficacy1 <- runif(280, min = 46.9, max = 67.5) / 100 # max and min valeus extracted from Machado et al. (2017)

# Funficide applied twice (2x)
set.seed(280)
efficacy2 <- runif(280, min = 44.3, max = 60.7) / 100 # max and min valeus extracted from Machado et al. (2017)

Yield response to fungicide

The mean yield difference (D) for one spray was given by the difference in yield between fungicide-protected (Yieldf) and no fungicide (Yieldnf) plots. However, the D from using two sprays was calculated by adding a simulated (normally distributed) mean yield gain estimated in the meta-analytic study (Machado et al. 2017), from using a second spray of tebuconazole.

# Obtaining standard deviations from confidence intervals

CIL <- 87.28
CIU <- 115.9
N <- 36
conv_value <- 3.92

sd <- (sqrt(N) * ((CIU - CIL) / conv_value))

gain_2x <- rnorm(280, mean = 101.6, sd = sd) # The 101.6 is the mean of yield gain observed due to a second fungicide spray.

Let’s now assemble a new the dataset with the control efficacy and yield gain estimations values.

simul_loss1 <- simul_loss %>%
  mutate(efficacy1 = efficacy1) %>%
  mutate(efficacy2 = efficacy2) %>%
  mutate(gain_2x = gain_2x) %>%
  mutate(sev_control_1 = FHB_index * efficacy1) %>%
  mutate(yield_fungicide_1 = attainable_yield - (attainable_yield * (sev_control_1 * 1.05 / 100))) %>%
  mutate(gain_kg_1x = yield_fungicide_1 - actual_yield) %>%
  mutate(sev_control_2 = FHB_index * efficacy2) %>%
  mutate(yield_fungicide_2 = attainable_yield - (attainable_yield * (sev_control_2 * 1.05 / 100))) %>%
  mutate(gain_kg_2x = (yield_fungicide_2 - actual_yield) + gain_2x)


simul_loss2 <- simul_loss1 %>%
  group_by(year) %>%
  summarise(
    vi_gain_1x = var(gain_kg_1x),
    vi_gain_2x = var(gain_kg_2x)
  )

simul_loss3 <- full_join(simul_loss1, simul_loss2, by = "year")

simul_loss3_1x <- simul_loss3 %>%
  dplyr::select(sow_date, year, class_year, gain_kg_1x, vi_gain_1x) %>%
  rename(
    gain = gain_kg_1x,
    vi = vi_gain_1x
  ) %>%
  mutate(trat = "1x") %>%
  mutate(n_appl = 1)

simul_loss3_2x <- simul_loss3 %>%
  dplyr::select(sow_date, year, class_year, gain_kg_2x, vi_gain_2x) %>%
  rename(
    gain = gain_kg_2x,
    vi = vi_gain_2x
  ) %>%
  mutate(trat = "2x") %>%
  mutate(n_appl = 2)

library(knitr)

simul_all <- simul_loss3_1x %>%
  bind_rows(simul_loss3_2x)

simul_all

profit <- function(D, Fc, Wp, vi) {
  p <- 1 - pnorm(((D - (Fc / Wp)) / sqrt(vi)))
  return(p)
}

Fc <- seq(5, 35, by = 5)
Wp <- seq(100, 250, by = 25) / 1000
year <- simul_all$year
D <- simul_all$gain
vi <- simul_all$vi
trat <- simul_all$trat
n_appl <- simul_all$n_appl
dat_simul <- data.frame()
xxi <- matrix(0, length(D), 6)
ppi <- matrix(0, 0, 6)

for (i in 1:length(Fc)) {
  for (j in 1:length(Wp)) {
    for (k in 1:length(D)) {
      xxi[k, 1] <- year[k]
      xxi[k, 2] <- Fc[i]
      xxi[k, 3] <- Wp[j]
      xxi[k, 4] <- D[k]
      xxi[k, 6] <- trat[k]

      xxi[k, 5] <- profit(D = D[k], Fc = Fc[i] * n_appl[k], Wp = Wp[j], vi = vi[k])
    }
    ppi <- rbind(ppi, xxi)
  }
}
dat_simul <- data.frame(year = as.numeric(ppi[, 1]), trat = ppi[, 6], Cost = as.numeric(ppi[, 2]), Price = as.numeric(ppi[, 3]), gain = ppi[, 4], prob = as.numeric(ppi[, 5]))

dat_simul